MODELING AND CONTROL OF DISTRIBUTED ENERGY SYSTEMS DURING TRANSITION BETWEEN GRID CONNECTED AND STANDALONE MODES. A Dissertation.

Transcription

1 MODELING AND CONTROL OF DISTRIBUTED ENERGY SYSTEMS DURING TRANSITION BETWEEN GRID CONNECTED AND STANDALONE MODES A Dissertation Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Md Nayeem Arafat August, 214

2 MODELING AND CONTROL OF DISTRIBUTED ENERGY SYSTEMS DURING TRANSITION BETWEEN GRID CONNECTED AND STANDALONE MODES Md Nayeem Arafat Dissertation Approved: Accepted: Advisor Dr. Yilmaz Sozer Department Chair Dr. Abbas Omar Committee Member Dr. Tom Hartley Dean of the College Dr. George K. Haritos Committee Member Dr. Malik Elbuluk Dean of Graduate School Dr. George R. Newkome Committee Member Dr. Ping Yi Date Committee Member Dr. Alper Buldum ii

3 ABSTRACT Distributed generation systems (DGs) have been penetrating into our energy networks with the advancement in the renewable energy sources and energy storage elements. These systems can operate in synchronism with the utility grid referred to as the grid connected (GC) mode of operation, or work independently, referred to as the standalone (SA) mode of operation. There is a need to ensure continuous power flow during transition between GC and SA modes, referred to as the transition mode, in operating DGs. In this dissertation, efficient and effective transition control algorithms are developed for DGs operating either independently or collectively with other units. Three techniques are proposed in this dissertation to manage the proper transition operations. In the first technique, a new control algorithm is proposed for an independent DG which can operate in SA and GC modes. The proposed transition control algorithm ensures low total harmonic distortion (THD) and less voltage fluctuation during mode transitions compared to the other techniques. In the second technique, a transition control is suggested for a collective of DGs operating in a microgrid system architecture to improve the reliability of the system, reduce the cost, and provide better performance. In this technique, one of the DGs in a microgrid system, referred to as a dispatch unit, takes the additional responsibility of mode transitioning to ensure smooth transition and supply/demand balance in the microgrid. iii

4 In the third technique, an alternative transition technique is proposed through hybridizing the current and droop controllers. The proposed hybrid transition control technique has higher reliability compared to the dispatch unit concept. During the GC mode, the proposed hybrid controller uses current control. During the SA mode, the hybrid controller uses droop control. During the transition mode, both of the controllers participate in formulating the inverter output voltage but with different weights or coefficients. Voltage source inverters interfacing the DGs as well as the proposed transition control algorithms have been modeled to analyze the stability of the algorithms in different configurations. The performances of the proposed algorithms are verified through simulation and experimental studies. It has been found that the proposed control techniques can provide smooth power flow to the local loads during the GC, SA and transition modes. iv

5 ACKNOWLEDGEMENTS My sincere gratitude to Dr. Yilmaz Sozer without whose ardent initiatives, constant compassionate advice and astute guidance this research work would not have materialized. Also I would like to thank Dr. Iqbal Husain for his valuable suggestions and guidelines for my research. Many thanks to all of the committee members, Dr. Tom Hartley, Dr. Malik Elbuluk, Dr. Ping Yi and Dr. Alper Buldum, for their excellent suggestions in making this research a success. The financial support of The University of Akron during my research period is also highly appreciated. I would also like to thank my parents, Md. Shafiqul Alam and Khadiza Begum, my wife, Rulia Farzana, my first son, Affan, my lab mates specially Ali Elrayyah and my sister, Jannatul Ferdous, for their invaluable love and encouragement over the years. v

6 TABLE OF CONTENTS LIST OF TABLES... Page xii LIST OF FIGURES xiii CHAPTER I. INTRODUCTION Overview of the Renewable Energy Sources Overview of the Distributed Generation System Overview of the Microgrid System Literature Review of Mode Transfers between GC and SA Modes Literature Review of the Control Strategies for an Independent Utility Interactive Inverter during Transition Operations Control Strategies of for Parallel Inverters Working in a Microgrid during Transition Modes Modeling of the Microgrid System for Stability Analysis Thesis Outline. 17 II. MODE TRANSITIONS FOR INDEPENDENT VOLTAGE SOURCE INVERTERS Introduction Bidirectional Inverter Architecture Components of the VSI for all Modes of Operations Phase Lock Loop Algorithm Current Controller Algorithm Design of a Current Controller Gains 29 vi

7 2.3.4 Voltage Control Algorithm Modeling and Stability Analysis of a VSI operating in SA Mode Modulation Index PWM Generation Transition from SA Mode to GC Mode for VSI Trapezoidal Frequency Variation Technique Closed Loop Frequency Variation Technique Smooth Frequency Variation Technique Simulation Results Inverter Operation in GC Mode Performance of the Current Controller Operating GC Inverter with Full Load Performance of the Current Controller with the Effect of Hardware Delay Performance of the Current Controller with Abrupt Change in Current Command Performance of the Current Controller with Gradual Commanded Change Performance of the Inverter in the Face of DC Voltage Fluctuations The Performance of the Inverter during Battery Charging RMS Voltage Control in SA Mode Operation of the VSI in Transition Mode GC Mode to SA Mode Transition SA Mode to GC Mode Transition Conclusion.. 54 vii

8 III. SMOOTH TRANSITION TECHNIQUE BETWEEN SA AND GC MODES FOR VSIS OPERATING IN MICROGRID USING DISPATCH UNIT Introduction Microgrid System Architecture Control Strategy for VSIs using Dispatch Unit in Transition Mode Droop Control Technique Modeling and Stability Analysis of the Microgrid System using Dispatch Unit Modeling for VSIs Operating in SA Mode The Effect of Droop Coefficients in a Microgrid System The Effect of the Load Changes in a Microgrid System Inductor Sizing for VSIs in a Microgrid VSIs Operating in Transition Mode using Dispatch Unit Impact of the Current Controller Gains on the Stability Effect of the Droop Coefficients on the Performance of a Droop Based VSIs GC Mode of Operation of the VSIs with Dispatch Unit Simulation Results VSIs Operating during SA Mode VSIs Operating during GC Mode Transition Mode of Operation for the VSIs using Dispatch Unit Technique GC to SA during Grid Delivering the Power to the System GC to SA during Grid Taking the Power from a Microgrid System viii

9 SA to GC during the Grid Delivering Power to the System SA to GC during Grid Taking Power from the System Effect of the Load Change during Mode Transition Conclusion IV. SMOOTH TRANSITION TECHNIQUE BETWEEN SA AND GC MODE FOR VSIS IN MICROGRID USING HYBRID CONTROL Introduction Microgrid System Architecture Control Algorithm of the Hybrid Controller Current Control Droop Control Modeling and Stability Analysis of the Hybrid Mode Transition Control Simulation Results VSIs Operate in SA Mode using Hybrid Control Technique VSIs Operate in GC Mode Transition Mode of Operation for VSIs GC to SA Mode SA to GC Mode Effect of the Load Change during Transition Mode Comparisons between Two Proposed Transition Techniques in a Microgrid System Study of the Electrical Characteristic of the Proposed Two Methods Conclusion. 167 V. EXPERIMENTAL RESULTS 169 ix

10 5.1 Introduction Hardware setup of the VSI Expermental Test Bench of the Microgrid System Experimental Tests of the Control Algorithm Developed for Independent VSI VSI operates in GC Mode Real Power Processing into the Grid Reactive Power Processing Abrupt Change in the Commanded Inverter Output Current Charging Operation through the Inverter VSI Operates in SA Mode Implementation of the Proposed Transition Control during Transition Mode GC to SA Mode SA to GC Mode Experimental Results of the VSIs in Microgrid using Dispatch Unit VSIs Operating in SA Mode VSIs Operating during GC Mode VSIs Operating during Transition Mode GC to SA Mode SA to GC Mode Experimental Results of VSIs in Microgrid using Hybrid Control Technique VSIs Operating in SA Mode using Hybrid Control Technique GC Mode of Operation using Hybrid Control Technique. 22 x

11 5.6.3 Hybrid Controller Performance during Transition Mode GC to SA Mode SA to GC Mode Conclusion.. 21 VI. CONCLUSION AND FUTURE WORKS Summary Outline of the Future Research REFERENCES APPENDICES APPENDIX A. SIMULINK CONTROL BLOCK. 226 APPENDIX B. PCB LAYOUT 232 APPENDIX C. SCHEMETIC DIAGRAM APPENDIX D. MATLAB CODE 245 APPENDIX E. DSP CODE. 25 xi

12 LIST OF TABLES Table Page 2.1 The THD of the grid current at different output power The steady state values of a microgrid system parameters The steady state values of a microgrid system in SA mode The steady state values of a microgrid system in GC mode The microgrid system parameters in SA mode Comparisons between the proposed transition techniques Comparisons of the electrical characteristic between the dispatch unit and hybrid methods Parameters for the single phase utility interactive inverter Performance comparison of the recent methods and the two proposed methods 214 xii

13 LIST OF FIGURES Figure Page 1.1 World net electricity generation by fuel (trillion kilowatt-hours) The chart of the renewable energy distribution in The grid tied inverter using solar system The image of the data center for TV broadcasting The microgrid system The output current of the individually operated inverter from SA to GC mode Variation of Δf with time Frequency change of a conventional UPS control The architectural diagram of a typical microgrid system Load voltage and inverter output current waveform from SA to GC mode Distributed generation system architecture and control The currents of the inverters and the load voltage in microgrid system Single line diagram for the independent utility interactive inverter Single line diagram of the microgrid system using dispatch unit concept Single line diagram of the microgrid system using Hybrid control Block diagram of utility interfaced bidirectional inverter State diagram of the operating mode transitions of the individually operated utility interactive grid tied inverter The block diagram of the single phase PLL Current control algorithm of the VSIs. 29 xiii

14 2.5 Control diagram of the grid connected inverter system Control diagram the GC inverter system incorporating the delay effect The effect of various hardware delay time in the current controller Effect of k p variation of the current controller of the grid tied inverter (a) the eigen value propagation of the system matrix and (b) SIMULINK Simulation Effect of k i variation of the current controller of the grid tied inverter (a) Small signal model and (b) Simulation by MATLAB/SIMULINK RMS voltage control in SA mode The impulse response of the circuit shows stable condition PWM generation technique Frequency variation techniques for transition from SA to GC modes Block diagram of the PI based phase adjustment method to synchronize the inverter voltage with the grid THD and the frequency deviation in the inverter output voltage during the transition from SA to GC mode Voltage at PCC, inverter current, load current and grid current in the GC mode, when = 45 A and = A and local load = 5.6 Ω The DC bus voltage, inverter input and output power in GC mode The effect of hardware delay on the current control of the grid tied inverter Voltage at PCC, inverter, load and grid current when changes from 1 to 3 A considering the load of 5.6 Ω Inverter output power, dq-axes command current of the inverter, when changes abruptly from 1 to 3 A considering the load of 5.6 Ω The voltage at PCC, inverter current, load current and grid current, when changes from 1A to 3 A within.9 sec The DC bus voltage, grid voltage, inverter current when = 3 A and = A xiv

15 2.23 Local load current, grid current in GC mode during the DC voltage change from 2 V to 18 V Battery charging current,, DC bus voltage, various output power flow by the inverter depending on the loads demand in SA mode Inverter output voltage, grid current, inverter current and load current during transition from GC to SA considering 2V, L = 1.5 mh, R = 5Ω The inverter output voltage synchronization with grid voltage after the grid returns with leading phase with PI phase adjustment technique The Inverter voltage synchronization with grid voltage after the grid returns with lagging phase using the smooth frequency variation technique Conventional microgrid system using dispatch unit Block diagram of the dispatch unit current controller from SA to GC State diagram of the operating mode transitions in a microgrid system The block diagram of the droop control Linear droop based control for SA and GC mode Microgrid AC side equivalent circuit in dq frame d axis model for a DG system where two inverters run in SA mode providing the power to the local load Complete eigen values of microgrid study system Stability analysis of the microgrid in face of varying droop coefficients The effect of the variation of droop coefficient of the microgrid system The variation of the local load in a microgrid system System frequency of the microgrid system The model predicts the critical value of the inductor (a) Inverter or unit 1 current, voltage at PCC in DG system when L = 2 mh. (b) unit 1 power, voltage at PCC in microgrid system when L =.5 xv

16 mh SA to GC mode transition modeling for a microgrid system The eigen values of microgrid system in transition mode Eigen values in the microgrid system in low and medium frequency range Simulation results of a microgrid system where two DGs run in droop control and dispatch unit operates in current control mode The variation of the droop coefficient during transition Inverters currents, dispatch unit and the load current during transition Microgrid system architecture of the d-axis equivalent circuit Eigen values of a microgrid system Propagation of the eigen values of the microgrid system when the droop coefficients of DGs changes from 1ˣ1-4 rad/w to 4ˣ1-3 rad/w The inverters current, voltage at PCC and load current in SA mode Frequency of a microgrid system Power flow for the VSIs and the local load in a microgrid system The effect of load variations of inverters currents, voltage at PCC and load current The frequency of the microgrid system Power flow for the inverters and the local load in a microgrid system Inverters current, grid current and load current in GC mode The effect of load variations of the inverters currents, grid current, load current in GC mode Inverters, dispatch unit and grid currents during GC to SA mode transition Load current and voltage at PCC from GC to SA mode DGs, load and dispatch unit currents during GC to SA transition mode Inverters current from SA to GC in microgrid xvi

17 3.36 Dispatch unit and the grid current during SA to GC mode transition Microgrid frequency and phase difference between the microgrid and the grid voltage from SA to GC Voltage at PCC and load current during transition Power flow of the inverters, dispatch unit, grid and load during transition mode Inverters, dispatch unit and grid current from SA to GC mode transition Voltage at PCC and load current during transition Power flow of the inverters, dispatch unit and load during transition The effect of the load changing on the inverters current, grid current and a dispatch unit during SA to GC mode The effect of the load changing on the voltage at PCC and the load current during SA to GC mode Microgrid system where the VSIs use hybrid controller The variation of the weight factors of the current and droop control in all modes of operations Overall block diagram of the hybrid controller Current control algorithm of the VSIs The block diagram of the droop control d-axis equivalent circuit diagram of a microgrid system Phase Lock Loop of a inverter Poles of system matrix in a microgrid system Inverters currents, voltage at PCC, load current in SA mode System Frequency of the microgrid system in SA mode Power flow of the local load, unit 1 and unit 2 in SA mode Inverters current, voltage at PCC and the load current during the effect of load changes in SA mode xvii

18 4.13 System frequency, load and inverters power flow during SA mode Inverters current in GC mode, where and, The grid current and load current in GC mode DGs, grid, load power flow and overall system frequency in GC mode The effect of the commanded current variation by the inverters, when load current remains constant in GC mode Power flow of the VSIs, grid and load in GC mode Microgrid frequency and the output coefficients behavior from GC to SA The output currents of DGs, load and grid during GC to SA mode transition Microgrid frequency and the output coefficients behavior from GC to SA DGs currents, load and voltage from SA to GC mode Power flow of unit 1, unit 2, grid and the local load during transition The effect of the load changes on the inverters currents, grid current, load current and voltage at PCC from SA to GC mode Experimental setup of the VSI Grid interactive inverter setup: (a) Power module, (b) Interface board, (c) DSP development board Relay driving circuit Voltage isolation amplifier AD22 to measure voltage Conditioning circuit for analog measurements PWM level shifter and buffer circuit Fault protection circuit Simplified diagram of one line microgrid test bench Overall test bench setup for microgrid system Experimental setup for the microgrid system xviii

19 5.11 Experimental setup of an independent VSI Output of the Phase Locked Loop (a) grid voltage (b) d-axis voltage, (c) q-axis voltage, (d) Output of Phase angle of the PLL The grid voltage, inverter current, grid voltage and grid current, d-axis and q-axis current of the inverter Reactive power injection into utility grid ( = A, = 2 A), (a) Utility grid voltage, (b) Inverter output current, (c) Grid voltage/ Inverter current, (d) d-axis and q- axis current The effect of abrupt change on the reference current of VSI Battery charging operation ( = -4A) Steady state load voltage and load current with 2 A peak magnitude Transition from GC mode to SA mode. (a) Switch status; (b) Inverter voltage and (c) Load current (a) Transition from SA to GC mode. (b) Detailed view of transition from SA to GC mode Inverter phase adjustment to grid during SA to GC transition mode Grid voltage, load voltage and inverter output current during SA to GC transition mode Inverter output voltage frequency during SA to GC transition mode THD analysis of inverter output voltage during SA to GC transition: (a) using smooth frequency variation method and (b) using abrupt frequency variation method Inverters current, dispatch unit current, voltage at PCC and the load current in SA mode Inverters currents at PCC in GC mode Dispatch unit current, grid current, voltage at PCC and load current in GC mode Inverters current, grid current, dispatch unit current from GC to SA Microgrid voltage at the PCC point and the local load from GC to SA Inverters current, grid current and dispatch unit current from GC to SA xix

20 mode Local load takes 35 A current during the entire modes of operation Currents of the inverters, dispatch unit and grid during SA to GC mode transition Synchronization of the microgrid with the grid during SA to GC transition Operating frequency of the microgrid during SA to GC operation The DC bus voltage of unit 1 and unit 2, where has 1% voltage fluctuation Inverters current during SA to GC mode transition Dispatch unit current, grid current, voltage at PCC and load current from SA to GC mode Comparisons between the simulation and experimental results of Inverters currents, and load current during transition mode Inverters current, voltage at PCC and load current in SA mode Inverters currents, grid current and voltage at PCC in GC mode Inverters currents and grid current during GC to SA Microgrid frequency, the output coefficients behavior, the load voltage and current from GC to SA mode Inverters currents, grid current, voltage at PCC from GC to SA mode Inverters currents, grid current and the load current during SA to GC The wave shape of the DC bus voltage of unit 1 and unit Inverters current, grid current and load current during SA to GC mode Comparison between the simulation and experimental results of VSIs in a microgrid using hybrid control technique Considered microgrid system xx

21 CHAPTER I INTRODUCTION Overview of the Renewable Energy Sources Conventional energy sources based on oil, coal, and natural gas have proven to be highly effective drivers for the economic progress of the world. With the growing demand for electricity and limited fossil based energy resources, the focus has been moved to alternative energy sources [1]. In addition to economical reasons, environmental impacts of the conventional energy sources motivate us to search for alternative energy systems. In particular, emissions from vehicles lead to global warming and push governments to make efforts towards the development of clean renewable energy resources, such as wind, bio-gas, and solar. It is expected that renewable energy sources in world net electricity generation will increase continuously in the near future as presented in Fig. 1.1 [2]. Figure 1.1. World net electricity generation by fuel (trillion kilowatt-hours). 1

22 In the past few decades, distributed generation systems (DGs) [3]-[6] have gained significant attention due to the environmentally-friendly feature of alternative energy, the development of new generation units, and their ability to offer more options of pricequality combination to meet the changing electricity market. Photovoltaic modules (PV) [7], wind turbines [8], fuel cells [9], and micro-turbines [1] are commonly used as the sources for the DGs. Since the first two energy sources do not require purchasing fuel and their installation cost falls in the order of $1/W, the installation of PV and wind turbines increased at a rate of 2-4% per year in the last few years [11]-[12]. Figure 1.2 shows the distribution of renewable energy by type around the world in 211. Figure 1.2. The chart of the renewable energy distribution in 211. Renewable energy sources provide benefits over the natural fossil based sources due to Their low initial costs compared to conventional energy sources [13]. Environmental friendly [4, 6] operations. Their small sizes enabling the utilization of DG concept especially in remote areas where the grid is not accessible [12]. 2

23 1. 2. Overview of the Distributed Generation Systems Most of the renewable energy sources are distributed in nature. DGs help in achieving low cost power system expansion and improve power quality in addition to other environmental and economical benefits. DG reduces the amount of energy lost in transmitting electricity because the electricity is generated very near where it is used, perhaps even in the same building. This reduces the size and number of power lines that must be constructed. Figure 1.3 shows the DG powered for the house which can also be connected to grid [12]. Figure 1.3. The grid tied inverter using solar system. The DGs produce direct current which needs to be converted to alternating current by a DC/AC inverter, as all the electric appliances run through the AC supply. The voltage sources inverter (VSI) either runs in the grid connected (GC) mode or the standalone (SA) mode. In GC mode, inverters run in parallel with the grid and deliver the required active or reactive power to the utility grid. In the SA mode the inverter delivers the power to local loads in AC from provided the grid is not there. Between these modes there is another mode called transition mode which requires the most concern. During the transition mode, the main objective is to deliver continuous power to local loads. An 3

24 unexpected power disruption could cause injuries, fatalities, serious business disruption or data loss. DGs are also commonly used in medical centers, TV broad casting stations, instrumentation plants, satellite, industrial controllers, and telecommunication centers which [14-16] require clean input voltage with low total harmonic distortion (THD). For example, there is a specific power supply requirement from the International Broadcast Centre (IBC) to maintain a continuous and stable power supply with low THD which would allow uninterrupted sportscasts all around the world [17] [18]. Figure 1.4 shows the data center which it requires uninterrupted power supply [13]. Figure 1.4. The image of the data center for TV broadcasting. In summary, the technical challenges for the bidirectional DC/AC inverters are: Continuous power flow during the transition period [17, 18]. The deviations of the system frequency should be kept within very narrow margins in GC, SA or the transition mode, as the well functioning of many industrial and household applications depends on that [16]. When the grid returns, the DG unit must be re-synchronized with the grid voltage, and connect to the grid with minimum voltage fluctuation [18]. Proper voltage waveform across the load voltage should be maintained during the transition period [14, 15]. 4

25 1. 3. Overview of the Microgrid System A typical microgrid system consists of parallel DGs, storage systems, and a cluster of loads within a local area [19]-[22]. Renewable Energy Sources (RES), conventional energy sources like diesel generators or non renewable alternative energy sources could function as a member of the micro grid. Most of the alternative energy sources in the microgrid produce electricity in DC form. Solar PV cells and fuel cells provide DC voltage, where as small and mid size wind generators output AC which is then rectified into DC voltage. The DC electric energy is usually converted into AC electric energy by use of an inverter. The resulting AC electric energy has to be compatible with the energy within the AC utility system at the point where the inverters are connected to the utility system. The inverters can be controlled to operate with either leading or lagging power factor depending on the reactive power requirements of the system. A microgrid not only has the inherited advantages of DG but also can offer several substantial benefits including: increased reliability from the redundant configuration of paralleled DG units; flexible, cost effective, and energy efficient features by power management and control. The microgrid can operate in both the SA and the GC mode, but is mostly connected to the grid as it would balance the energy requirement and provide a filter in the absence of adequate energy storage capability [23, 24]. In the absence or the loss of a utility grid, the microgrid sustains the loads through its network. As shown in Fig. 1.5, a typical microgrid system consists of several RESs and local loads. 5

26 Figure 1.5. The microgrid system. A smart storage device is sometimes included in a microgrid to regulate the power flow during transitions. When the grid is down or the quality of the power deteriorates, the microgrid can disengage from the grid and work in SA mode. The transitioning from GC mode to SA mode or SA mode to GC mode is referred to as transition mode as mentioned before. The ability to switch between grid-tie and SA modes is one of the main targets to guarantee uninterrupted power to critical loads within the microgrid. Most DGs used in a microgrid are inverter-based and require constant control and monitoring in order to function properly. Sometimes a master controller unit is used to communicate among the voltage source inverters (VSIs). VSIs are also much more 6

27 sensitive to overloading and other abnormal operating conditions than synchronous generators. Microgrid operation has the following technical challenges: Continuous power flow is challenging during the transition period [24]. A complex communication network is needed for strong interaction between active and reactive power and transition control among the VSIs [21]. From all of the above discussion, we can conclude that both DG system and the microgrid system suffer during the transition mode and a better control technique is required for maintaining the quality the power across the system. In our research we focus on the transition problem of the inverter and try to develop simple and robust algorithms to give a better solution to the problem Literature Review of Mode Transfers Between GC and SA Modes As we know, the demands for energy from renewable sources have increased to address the energy crisis and environmental pollution problems. This has resulted in the proliferation of renewable based DGs for power generation into the grid and the penetration rate is expected to increase in the coming years. As discussed before, DG systems are connected to the utility grid (UG) through VSIs. The utility interactive inverters play an important role in the power distribution system [25-29]. For mode transfer between two basic modes, the first step is to determine if the microgrid should operate in GC or SA mode by islanding detection techniques [3]-[36]. Different active methods including current injection [31], PLL based detection [32], and the frequency-drift method [33] are proposed to identify the grid availability. When the grid is in an abnormal condition, the microgrid needs to switch from GC to SA mode 7

28 [37]. Once the grid recovers, the microgrid or individual inverter should re-connect back to the utility without harming the system. In order to minimize the transients, the phaselock loop (PLL) design and the mode transfer procedure were proposed in [38]-[4]. In [41], a PLL is designed with an orthogonal filter to increase the robustness when grid voltage is distorted or unbalanced. In [42], admittance compensation is proposed to reduce the transients during the startup of grid connection. By controlling the peak value of the output current with an inner voltage loop, the indirect current control can achieve smooth mode transfers between the two modes [43]. Past studies on microgrid operation typically focused on a single inverter with a single power conditioning system for islanding operation or mode transfers between SA and GC modes [44] Literature Review of the Control Strategies for an Independent Utility Interactive Inverter during Transition Operations The utility interactive inverter should be able to operate both in GC and SA modes in order to provide power to the emergency load during outages. The SA and GC modes of the inverter operation require different control methods. Moreover, the transition between the two modes should be seamless to minimize any sudden voltage change across the emergency load or any sudden current change provided into the grid. The transitions between the two modes should be fast and precise to minimize the interruption in the power supply. The utility interactive inverters for DGs reported in the literatures [45, 46, 47, and 48] have the capability to operate in both GC and SA modes, but do not address the issues of stresses on the converter and total harmonic distortion (THD) on the voltage and current waveforms during transition. The harmonic currents cause the transformer to overheat resulting in reduced life and rating, and stress on the power factor correction 8

29 capacitors. The harmonics in the voltage cause losses in the motors resulting in increased heating, reduced power output and shorter life expectancy [49]. Figure 1.6. The output current of the individually operated inverter from SA to GC mode. In [5], the connection is done at positive zero crossing where often load voltages match with the grid voltage. The current controller starts increasing the reference current slowly from zero to the desired value in the six electrical cycles. The synchronization of a small wind turbine with a local grid is done using a switch but without a prescribed transition algorithm in the literature [46]. In [46], high current passes through the inverter phase after the grid recovers, and the inverter ceases the operation until the synchronization is achieved between the inverter and the utility grid. After connecting the grid, the inverter then starts to regulate the power within 1 sec [46], as shown in Fig. 1.6 (Fig. 17.(b). in [46]). In [47], a control algorithm for utility interactive PWM inverters to maintain a continuous, uninterrupted voltage across critical and sensitive loads has been proposed. For the transfer from SA to GC mode, the inverter voltage should match the grid voltage both in magnitude and phase, before the static transfer switch can be turned on and the 9

30 grid current should be slowly ramped up to a reference value. According to their proposed algorithm form, the SA to GC mode to make the synchronization with the grid voltage, the frequency of the system changes from 6 Hz to 59 Hz and then gradually increases to 6 Hz. Figure 1.7 (Fig. 9 as in [49]) shows the deviation of the system frequency during the transition period. In [5], the grid interactive inverter with LC filter and the isolating transformer has been used to describe the transition mode operation of a single inverter. The hysteresis control technique is used which requires high performance of the DSP. In [5] the phase angle error between the grid and the inverter is sent to a PI controller, thus obtaining the Figure 1.7. Variation of Δf with time required frequency variation. Figure 1.8 shows the frequency variation of the inverter and the grid respectively. In all cases, the inverter generates the abrupt frequency change in the beginning of the transition time which increases the THD of the load voltage [5]. Adding an extra capacitor bank at the output of the inverter and the transformer will add extra cost in their proposed system. 1

31 Figure 1.8. Frequency change of a conventional UPS control Control Strategies of for Parallel Inverters Working in a Microgrid during Transition Modes A microgrid has been an alternative energy network providing flexible solutions to interface DG units [51-53], as shown in Fig DGs may be located in a distribution network or on the local load side [54-56]. The generation technology can be gas turbines, fuel cells, photovoltaic systems or wind turbines. In addition to energy sources, energy storage devices can also be used in microgrid. A typical microgrid has two operating modes: GC mode and SA mode, both modes require effective regulations and control of the DG. A power electronic system is used to interface the DG and microgrid, the control of the power electronic converter is the key point. The third mode can also be considered as the transition mode between these two modes of operations. If care has not been taken, power disruption or power oscillation between sources can happen during transition mode. In [57], a transition between SA and GC is proposed. From the GC to SA mode, the inverter is operated in the ride through mode, which will be triggered when the inverter current reaches to zero to avoid asynchronous grid connection. Then the virtual inductance concept [58] is used for soft start up. The authors in [58] consider three 11

32 different kinds of variable virtual inductance L as exponential decay, ramp decay and constant. The initial value of the virtual inductor is defined to limit the large inrush current. A small initial value of inductance may cause the inverter switching to ride through mode more than one time. After presetting time delay, the control algorithm is changed back to the droop controlled mode. The system needs to shut down for a small period of time. Figure 1.1 shows the inverter output currents from SA to GC mode (as in Fig. 17, ref. [57]). GRID Dispatch Unit ENERGY STORAGE MICROGRID Line Load Line Line Line Line Line Load Load Load Load Load Synchronous Generator RENEWABLE ENERGY SOURCE 1 RENEWABLE ENERGY SOURCE N NON RENEWABLE MEP ENERGY SOURCE 1 NON RENEWABLE MEP ENERGY SOURCE K DER- R1 DER- RN DER- MEP 1 DER- MEP K Figure 1.9. The architectural diagram of a typical microgrid system. Frequency and phase synchronization techniques have been described in [58]. In [58], a synchronization controller which adjusts the phase and the frequency at the same time has been described for the seamless transfer from SA to GC modes. 12

33 Figure 1.1. Load voltage and inverter output current waveform from SA to GC mode. In [59-6], CAN based communication using a master-slave technique is used to make the transient between GC mode and SA mode with promising results. In masterslave control, the master unit collects the information and delivers control data to distributed slave units, which require communication infrastructure. If the grid is not available, the switch remains disconnected and the system supplies its own power to critical loads. One of the inverter, assigned as a master unit, has to operate in voltage control mode and serve as a voltage source, while the rest of the inverters operate in single current-loop control to share the current as required. When the grid recovers, the switch is reconnected and all the VSIs in the system run in a current mode to supply energy to the critical load and to exchange energy with the grid. Figure 1.11 (as Fig. 1 in [61]) shows the microgrid structure using the master slave technique where the main controller selects one of the inverters as the master and runs in voltage control mode and the rest of the inverters run in the current control mode and send the command through the communication network. The main controller always needs to monitor the grid voltage availability by sensors and send the necessary signal to the VSIs. A robust communication network is necessary for the technique which is sometimes unrealistic in rural areas. 13

34 Figure Distributed generation system architecture and control. Figure 1.12 shows the inverter current and the load voltage during transition with the technique proposed in [61]. Here, the master unit tries to achieve voltage control in SA modes of operation and many times transition can overload the master unit. Moreover, the master unit must always be the one which needs to turn on fast to maintain the system voltage sinusoidal. The system is unreliable, as the whole system would fail if the master DG fails. From SA to GC mode, when the phase of the system voltage and the grid voltage is matched, the main controller connects the grid and all the inverters start to run in the current control mode. The master function could be dynamically allocated to the unit that first comes into operation, and then to the unit that has the maximum power rating as more units are connected. This, however, will result in a much more 14

35 complicated control system as each unit will have to be designed for both master and slave operation which also requires system communication. Figure The currents of the inverters and the load voltage in microgrid system. From the above literature review, the state of the art can be summarized as follows: (i) The utility-interactive inverters for DGs reported in the literatures [45, 46, 47, and 48] have the capability to operate in both GC and SA modes, but do not address the issues of stresses on the converter and total harmonic distortion (THD) on the voltage and current waveforms during transition period. In the single phase system as we have more control and flexibility over the system we can get better performance from the system during the transition period. (ii) During the transition between SA to GC mode for parallel VSIs, different techniques have been proposed such as virtual inductance based droop control [62] inverters, frequency and phase synchronization [63], adaptive droop coefficients control [64], resistive virtual output-impedance loop [65] and master-slave [59-6] to get the 15

36 continuous power flow to the local loads. Master-slave [59-6] with CAN-based communication network shows better performance during the transition period, but the complexity and the stability becomes a major issue. There is a need to develop better control algorithms to provide seamless transition without needing additional hardware or communicational infrastructure Modeling of the Microgrid System for Stability Analysis Due to the larger system uncertainties and the interface design, the inverter-based microgrid suffers more challenges which call for the need of stability analysis [66], [67]- [69], [7]-[71]. As there connected several VSIs at the AC bus of point of common connection (PCC), the system faces some challenges to meet the stability of the system. The DC bus fluctuation, the inductor size of the inverter, the gains of the controller of the VSIs, and the load changes play important roles in the stability issues. Due to the presence of these challenges, there is a strong need for stability analysis to guarantee proper and stable system operations. The stability of a single inverter can be determined by Bode plots using the phase margin and gain margin as the stability criteria. In single LCL grid-tie inverter systems, Bode plots were used to study the effects of changing feedback scheme [72], controller gain [73], [74], and plant parameters [66], [75], [76]-[78]. This method, however, cannot determine the stability of parallel-inverter system due to the possible interactions among different control loops and the current-sharing controller. The stability of cascaded systems reasonable input filter design of a converter [79]-[8]. The system stability can also be determined by analyzing the system pole and zero locations using the eigen value analysis. With the state-space analysis, the single inverter systems studied the stability of 16

37 changing the controller gain [73], [72]-[74], the plant parameters [66], [81]-[82], and different feedback signals [76], [83]. Also, the state-space analysis is usually adopted to investigate the LCL filter resonance issue of grid-tie inverter systems with passive damping methods [82], [83] and active damping techniques [66], [72], [76]. The stability of large-scale DGs with droop control is also usually being analyzed by the state-space model. The system stability was studied by changing the load type [84], the droop controller gain [69], [85], and the output power [69]. This model is relatively easy to expand by combining single inverter state-space equations to build state-space equations for parallel VSIs. In [86], the state-space model is adopted to investigate the stability of the paralleled inverter system with a low-bandwidth communication currentsharing scheme. Even though the state-space tool is already widely used in other applications, it is worth investigating stability of a newly built system using an existing tool. The control variables described in previous stability analysis papers such as controller gain, output power, and load type, can be used as system variations to investigate the stability of a newly built microgrid system. Once the state-space model is constructed, many modern controller design techniques, such as pole assignment [74], [87]-[89], and eigen value sensitivity [85]-[86], [9] can be utilized to optimize the system operations Thesis Outline Previous studies have given solutions to VSIs in either GC mode or SA mode, but rarely mentioned the inverter design in both operation modes. However, it is necessary for a microgrid application that basic operation modes and transition mode need to be considered. For a microgrid system consisting of several small parallel DGs and loads, 17

38 the proper controller should be built which can do the smooth transition between SA and GC modes and also able to flow power in the both modes. With the above research motivations, the research objectives can be summarized as: 1. To design and build a single bidirectional inverter that can operate in GC, SA and transition mode. 2. To develop transition technique between the operating modes of the power electronic inverters this reduces the fluctuations on the load voltage. 3. To develop a mode transition system for microgrids using a dispatch unit without requiring external communication links. 4. To develop a transition control method which does not require external communications and a dispatch unit for proper mode transition. This dissertation aims to develop a robust, reliable and stable microgrid system. The study will cover from a single unit in different modes of operation, to multiple unit operation with the ability to perform mode transfers. Finally, the stability of the whole system will be studied to help the controller design and ensure system reliability. Here we use the dq based control architecture because of its simplicity and reduction of the input variables. In Chapter II, the inductor (L) filter design considerations and the controller designs of a single inverter in both GC and SA modes are discussed. For GC mode, a PI current controller in a rotating reference frame and the PLL has been developed. For SA mode, a droop control and RMS voltage control is used for voltage regulation. In transition mode a smooth frequency variation transition control technique for VSI has been developed and its performance is compared with the other existing techniques. 18

39 Switch Signal Inv. Load SW G Figure Single line diagram for the independent utility interactive inverter. In Chapter III, a smooth transition control strategy is proposed for voltage source inverters between SA and GC modes of operation. In both GC and SA modes of operation, the inverters use the droop control method to regulate the real power flow without the need of any external communication between them. One of the DGs working in the microgrid system is designated as a dispatch unit to facilitate interconnection with utility grid and achieve smooth transition between the modes of operation. In the transition mode, the dispatch unit takes extra responsibility and ensures the continuous power delivery to the load. For smooth transition from GC to SA, the dispatch unit compensates for the grid current instantly after the transition and then gradually makes the other sources to share that current. The dispatch unit also adjusts its output power to make the transition from SA to GC mode as that power affects the frequency through the droop control. The performance of the proposed control technique has been verified with simulation results. The state-space model and implementation results of a power conditioning system are presented. Eigen values with different controller gains and load conditions for GC, SA and transition modes are found to analyze the system stability of the system. 19

40 μg PCC Inv. Inv. SW G Inv. Load Figure Single line diagram of the microgrid system using dispatch unit concept. In Chapter IV, an alternative transition technique between SA and GC modes has been proposed without needing a dispatch unit. During transition, both current control and droop control participate in formulating the inverter output voltage, but with different weights or coefficients. The controller, referred to as a hybrid controller, varies the output coefficients of the current and droop control depending on the system frequency variation to regulate the real power flow. The state-space model of a microgrid system is derived. μg PCC Inv. SW G Inv. Load Figure Single line diagram of the microgrid system using Hybrid control. Eigen values with different controller gains and load conditions for GC, SA and transition modes are derived to analyze the system stability. The experimental results of 2

41 the proposed algorithm of Chapters II, III and IV have been presented in Chapter V. The experimental setup of the system and power up procedure also has been discussed in this chapter. Chapter VI provides the conclusions of this dissertation and some suggestions for future works with some simulation results. 21

42 CHAPTER II MODE TRANSITIONS FOR INDEPENDENT VOLTAGE SOURCE INVERTERS 2. 1 Introduction Due to the need of continuous power flow for critical loads [24], the utility interactive inverter needs to operate consistently in the GC, SA and transition modes. In GC mode, the amount of power exchanged with the utility grid (UG) is controlled by regulating the phase currents. In SA mode, the load voltage is regulated by the inverter with its phase dictated by the inverter control. The main challenge that the inverter will face is to maintain the proper flow of the power to the load during transitions between SA and GC modes. The transition between SA and GC operations that will ensure continuous power delivery to the load requires continuation in the phase of the system voltage. If the transition mode of operation is not smooth then the critical loads will face sudden shut down which may cause injuries, fatalities, serious business disruption, or data loss. There has been little research on seamless transition control. In practical life, the inverter faces two types of transitions. From GC to SA mode the inverter needs to maintain consistent phase of the load voltage. From SA to GC the phase of the system voltage needs to be adjusted with the grid voltage. This phase adjustment is done through the variation of the system frequency by the controller of the inverter. The PI, trapezoidal, sinusoidal and staircase frequency variation techniques have been analyzed to make the proper phase adjustment. The purpose of this chapter is to develop a smooth transition control strategy 22

43 for VSI between SA and GC modes of operation, which provides lower THD on the voltage waveforms compared to the other techniques. This chapter has been divided into five subsections. In first subsection, the control algorithm of the bidirectional inverter in GC, SA and transition modes has been described. Second, the performance comparison has been studied of all the recent transition controller techniques with our proposed smooth transition control. Third, the stability analysis and proper controller design of the bidirectional inverter has been derived to test the system for different operating conditions. The simulation results have been provided to show the effectiveness of the controller. In Chapter V, the new algorithm has been implemented on an experimental 5 kw single phase utility interactive inverter having the SA operation capability Bidirectional Inverter Architecture The operation capability of the utility interactive inverter, (shown in Fig. 2.1) with the SA mode, GC mode and the transition mode operation capability has been analyzed in this research, as shown in Fig A renewable source like a solar cell, wind energy, storage units, or conventional energy sources is connected in parallel with the bidirectional DC/AC inverter. The local loads are connected in parallel with the inverter and the grid through the smart switch (SW). The inverter output voltage is filtered through the inductor L which is having an internal resistance of to make total impedance. The grid also has an internal resistance of. The inverter controller is typically implemented digitally. 23

44 Local Load i L V DC C DC SW Z L Zg i INV Vg INVERTER PWM Generation Modulation Index, m a Voltage Controller Vg State Transition Control Block AND V d f Phase Lock Loop ( PLL ) Vg i q_act Current Controller i d_ref i q_act i d_act abc à dq i INV DSP CONTROLLER Figure 2.1. Block diagram of utility interfaced bidirectional inverter Components of the VSI for all Modes of Operations As there are there modes of operation, the controller has to find out the proper mode and apply the required control algorithm. Figure 2.2 shows the control strategy of the VSI in SA mode, GC mode and transition mode. From GC to SA mode transition occurs instantly and does not require separate operating conditions. Initially when the system is turned on, the controller gets the grid voltage through sensors, completes PLL, and 24

45 checks the grid availability by checking, if V d, V q, f are in the range or not. If the grid is available, then the system runs in GC modes where the inverter is controlled by the current control technique. If the grid is not available, then the inverter runs in SA mode taking grid phase as an initial phase and generates the phase as The controller continues to check whether the grid is available or not. V d,v q & f out of range (2.1) GC ϴ GC-SA SA PLL Current control ϴ S =ϴ GC-SA + ʃ f S dt Voltage control phase match & relay contact SA to GC If (ϴ g ǂ ϴ inv ) Phase adjustment PLL, voltage control else PLL, current control Δϴ diff V d,v q & f in range Figure 2.2. State diagram of the operating mode transitions of the individually operated utility interactive grid tied inverter. If the grid is available, the inverter goes into the SA to GC transition mode. During the transition mode, the phase needs to be adjusted and connection is established at the zero crossing of the voltage. The inverter runs in the voltage control mode during this transition time until the zero crossing is detected. After the zero crossing occurs, the inverter starts operating in the current control mode. There is a typical delay time for the operation of the switch. 25

46 Phase Lock Loop Algorithm In the GC mode, estimating the phase of the grid is essential in processing the right amount of power. The purpose of the PLL system is to estimate the phase of the utility [91]. The PLL grid synchronization technique has been the preferred from the literature [91-93], and is also used in this study. The PLL system consists of an abc-to-αβ transform, a αβ-to-dq transform, a loop filter, and a voltage-controlled oscillator (VCO). The single phase PLL algorithm is shown in Fig. 2.2 where the grid voltage is shifted by 9 and converted into dq axes voltages based on the estimated phase. The loop filter brings the q axis voltage to zero by adjusting the phase. The estimated phase is assumed to be locked to the grid when the q-axis voltage is zero. Based on the estimated phase, the utility current can be converted into the dq reference frame the same way as the utility voltage is converted; the regulation in dq reference frame is easier and has better dynamic response characteristics. The dq axes currents dictate the real and reactive power flow through the transmission line [94-97]. + Σ - Kf (s) Loop Filter 1/s θg V q V d Vαβ to Vdq Vα Delay Vβ Grid voltage Figure 2.3. The block diagram of the single phase PLL. 26

47 The grid voltage and its phase shifted versions can be represented as (2.2) (2.3) The to dq transformation is called Park Transformation and can be represented as (2.4) where the maximum peak voltage, θ is the phase and is the estimated phase of the grid voltage. After the transformations, the two utility voltages in dq reference frame can be represented as (2.5) (2.6) As approaches θ, goes to zero. We can linearize it for control purposes as (2.7) The PLL phase can track the utility phase angle θ respectively by the proper design of the loop filter [63]. A proportional-integral (PI) type filter for the second order loop can be given as (2.8) The transfer functions of the closed loop system are rewritten in the general form of second order system as (2.9) where and. 27

48 where is the loop filter gain, is a time constant, is the damping coefficient and is the system natural frequency Current Controller Algorithm The amount of desired output power delivered to the utility is controlled through the current regulation algorithm. The accuracy of the current regulation algorithm is important for effective power processing. The quality of the current regulation algorithm is also important to meet the total harmonic distortion restrictions imposed by the applicable standards. Many control algorithms have been proposed to control inverter output current for utility interactive operations. Hysteretic type controllers with different closed loop compensators have been used running at varying or constant switching frequencies [98]-[1]. We present here an easily implementable and effective current regulation algorithm that works harmoniously with grid synchronization methods. Figure 2.3 shows the block diagram of the utility interactive voltage source inverter controller based on current regulation in the dq reference frame. The dq axes currents are controlled in their reference frame through PI controllers and converted into the reference phase voltage. The electrical dynamics of the inverter after transformation to the dq reference frame are given as (2.1) (2.11) where and are the dq component of the grid voltage and and are the required voltages to be applied from the inverters for current regulations. The cross coupling and feed forward terms help in simplifying the controller design. The reference dq axes voltages are converted to inverter switch gate signals through a PWM generation. 28

49 Id_ref + Σ - PI controller Vgd + Σ + - Vd_ref Id_act Iq_act L*ω dq v C Iq_ref + Σ - PI controller Vgq + Σ + + Vq_ref θg PLL Iq_act Id_act L*ω vg Figure 2.4. Current control algorithm of the VSIs Design of a Current Controller Gains The dq control structure is using the ab dq transform module to transfer the control variables from their abc frame to a frame that synchronously rotates with the grid voltage. As a consequence, the control variables are becoming DC signals which help simplify the control design. The controller transfer function can be represented as [25]: (2.12) where and are the proportional and integral gains of the current controller. Figure 2.5 shows the closed loop control of the current controller in dq axes, where L is the value of the inverter output filter and r is the internal resistance of the inductor i dq, ref + - Σ GPI () s PI controller 1 sl r Plant i dq, act Figure 2.5. Control diagram of the grid connected inverter system. The closed loop transfer function of the system is (2.13) where D(s) is the plant transfer function, is the closed loop transfer function. 29

50 A practical system has some delay because of the filter and the hardware circuit. The addition of a delay introduces poor performance to the current controller. So the proper values of the controller gains need to be found. Figure 2.6 presents a delay having a transfer function,, infront of the PI controller added to the system. The closed loop transfer function of the feedback system becomes (2.14) where T is the total delay time of the hardware components. i dq, ref +- Σ Ts e GPI () s 1 sl r Delay PI controller Plant i dq, act Figure 2.6. Control diagram the GC inverter system incorporating the delay effect. The controller gains can be determined based on the Eqn using Routh Locus technique. Figure 2. 7 shows the effect of the various hardware delay times on the current controller. Beyond a certain delay, the system poles get into right half plane and the system becomes unstable for specific gain selections. 1 Delay Effect Delay (degree) Delay increases kp=5; ki=16: Real axis Figure 2.7. The effect of various hardware delay time in the current controller. 3

51 Figure 2.8 shows the eigen values and simulation response of the VSI during GC mode of operation. In the GC mode, the inverter performance depends on the selection of the gains of the current controller. Figure 2.8 shows that increasing the values of k p makes the system stable for k i = 16. As the value of k p becomes lower, the response of system enters into the unstable region, which also agrees with the simulation results, shown in Fig 2.9.b. 5 Kp Variation of the current controller Imeginary Axis kp increases kp=5 kp=-8; ki= Real axis 3 (a) Variation of kp 2 kp 1 units (V/A) i inv Inverter current and grid voltage Vg Time (s) (b) Figure 2.8. Effect of k p variation of the current controller of the grid tied inverter (a) the eigen value propagation of the system matrix and (b) SIMULINK Simulation. 31

52 3 Ki variation of the current controller Imeginary axis ki increases ki=-1, kp=26 ki=1,kp= Real axis 15 (a) Variation of ki Ki 1 5 Units (V/I) Inverter Current and Grid Voltage 2 i v g inv Time (s) (b) Figure 2.9. Effect of k i variation of the current controller of the grid tied inverter (a) Small signal model and (b) Simulation by MATLAB/SIMULINK. Figure 2.9 shows the effect of the variation of the k i on the performance of current controller. In this case we consider k p = 26 and k i varies from -1 to 15. The current controller performance deteriorates when the value of k i becomes lower than 1. 32

53 Voltage Control Algorithm In the absence of the utility grid, renewable energy systems could be used to provide energy to the local loads [22, 23, 24, 25] assuming an adequate supply of energy for the inverter to draw upon. The control structure on the DC and AC sides are changed to accommodate the needs of the local loads. Unless there is battery backup in the system, the system cannot work on the principle of maximum power extraction from the source since this would lead to a sustained power imbalance. If there is enough energy available at the source, the local loads are fully supported by the inverter. If the demand from the loads is higher than the available energy at the source then lower priority loads are needed to be shed to make energy available for supporting the higher priority loads. The voltage and frequency of the AC side is set by the inverter. Similar voltage regulation algorithms can be used as in uninterruptable power supplies. Depending on the steady state and transient requirements different voltage control techniques can be used [45, 46, 47, and 48]. One of the attractive methods used in UPS systems is the RMS voltage control. The RMS voltage is controlled by a PI compensator. The output of the compensator adjusts modulation index of the sine PWM operating at the utility frequency. This type of control provides stable output in the steady state [26]. When the Vrms,ref + Σ - PI controller V DC PWM Generation PWM Signals Vrms,act Sin ϴref Figure 2.1. RMS voltage control in SA mode. 33

54 utility grid is not available or it is out of the specified range, the inverter controller immediately switches to the SA mode of operation to provide sustainable power to the critical loads. The phase starts with its value at the start of the transition ( GC SA ) and continues with the rated utility frequency. Figure 2.1 shows the RMS voltage control method of the SA inverter. The PI controller produces the right amount of inverter RMS voltage and the result is multiplied with sinusoidal variation based on the estimated utility phase. The PWM signals are generated from the reference sine wave voltage for the inverter to produce the desired output voltage Modeling and Stability Analysis of a VSI operating in SA Mode In the SA mode the VSI runs in RMS voltage control mode. The inverter acts as an AC voltage source [11], as shown in Fig. 2.11, providing sinusoidal output voltage. In our analysis we consider the load as resistive. The transfers function of the system. (2.15) where R is the Local load, and r is the internal resistance of the inductor, is the load voltage and is the inverter output voltage. 34

55 25 Impulse Response 2 15 Amplitude Time (seconds) x 1-3 Figure The impulse response of the circuit shows stable condition. Figure 2.11 shows the impulse response of the system transfer function in SA mode. The transfer function shows the system is first order and has one pole, which is in the left half s-plane. So the system will remain stable Modulation Index The reference signal that goes to the PWM generation block needs to be normalized by the DC bus voltage. So that it can compensate the DC voltage fluctuations. The resultant duty ratio produced by the controller would be (2.16) where is the reference signal of the controller output, is the measured DC voltage signal, bus terminal, and is the actual reference signal that should available across the DC are nominal values of the DC bus and the grid voltage respectively. The duty ratio, d a, would vary between +1 to -1, therefore a saturation block needs to be placed before the power generation. 35

56 PWM Generation Depending on the d a, the PWM generation block makes the appropriate switching frequency for the gate of the IGBT module. The d a is compared with the triangular wave shape of the switching frequency, is shown in Fig The output of the comparator would determine switching commands. PWM Signals Vα,ref Carrier Frequency time (sec) Figure PWM generation technique. time (sec) The ON time of the switches is determined based on the PWM frequency and Duty cycle, (2.17) where, is the ON time upto which the PWM block will give the high signal, is the period of PWM Transition from SA Mode to GC Mode for VSI During SA mode of operation, the inverter controller continuously monitors the presence of the grid and makes grid connection decisions based on that. When the UG becomes available; the inverter controller would detect its presence and connect UG within the prescribed time. Depending on the phase difference between the inverter 36

57 output voltage and the UG voltage at the instant of the UG s availability, the inverter frequency could be adjusted to synchronize the inverter and UG phases within a given connection wait time (T G ). This operation should be done with the minimum impact on the critical loads and the UG. The available transition techniques have been explored and analyzed to evaluate their impact on the critical loads. The PI and trapezoidal frequency variation technique are first evaluated for the transition, and then two special cases are studied: 1) abrupt frequency variation, and 2) triangular frequency variation. The THD of the voltage wave shape was observed for each case to find out the optimum condition for which the THD is the minimum. In all the cases, the average frequency deviation has been kept the same for a given wait time (T G ) Trapezoidal Frequency Variation Technique The phase deviation between the UG and the inverter output voltage is measured when the grid is available. Using the prescribed waiting time, the amount of the diff frequency deviation ( f ) is obtained from f. The phase is adjusted by 2 T varying the inverter operating frequency with the trapezoidal shape as shown in Fig When the phases of the inverter and the UG match, the inverter is connected to the UG at the zero crossing of the voltage. The frequency of the inverter can be varied and adjusted for the duration of connection time (T G ) to synchronize with the phase of the UG. The rate or slope for the transition can be obtained from (2.18) where x is the time duration for the frequency transition and f is the maximum frequency deviation in the phase adjustment algorithm. 37 G

58 T G Frequency (Hz) Δf x Trapezoidal frequency variation technique y Abrupt frequency variation Smooth frequency variation t1 t2 t3 Time (s) Figure Frequency variation techniques for transition from SA to GC modes. The frequencies during the transition can be represented as when (2.19) when (2.2) when (2.21) where T G is the time to make the synchronization, and f s is the system frequency. The two special cases for frequency adjustment are described as: (1) Abrupt frequency variation: If the initial duration is instantaneous (i.e. x = in Fig. 2.14), then there is a sharp frequency transition effect in the system. (2) Triangular frequency variation: The other extreme case of the frequency variation algorithm is the condition where. In this algorithm, would be the maximum frequency variation. The applied frequency to the inverter control is when (2.22) when (2.23) The objective is to minimize the frequency deviation without disturbing the conditions of the critical loads. One of the measures for the quality of the inverter output 38

59 is the voltage THD. Different frequency transition slopes or rates have been tested to compare the THD s of the inverter output voltage during the phase adjustment period. The shapes of the frequency transition functions change with different slopes; each frequency transition function would have different harmonic contents Closed Loop Frequency Variation Technique In typical UPS systems, the practical method used for phase adjustment is the closed loop PI controller [46, 49]. Figure 2.14 shows the block diagram of the PI controller based synchronization technique of the inverter output voltage phase with the grid. The angle error between the grid and the inverter is passed to the PI controller to obtain the required frequency variation. The bandwidth of the controller is then tied to the required phase adjustment time. The closed loop transfer function of the PI angle tracker is (2.26) where denotes the gain of the PI angle tracker. The transfer functions of the closed loop system can be rewritten in the general second order form as (2.27) where n k pf 1 and k pf 1 2 n Equating Eqn and 2.27 we can find the value of and τ. If we want make only the P controller then the value of τ should be zero. But there will be huge deviation in frequency at the initial time and as the time passes the frequency deviation becomes lower. For the proper value of and τ, considering ξ =.7 would be appropriate. 39

60 g PI Controller f 1 s s Figure Block diagram of the PI based phase adjustment method to synchronize the inverter voltage with the grid Smooth Frequency Variation Technique The analysis of the trapezoidal frequency variation with different parameters provided the insight to develop the smooth frequency variation technique. When the grid is available the phase of the inverter output voltage is gradually adjusted according to the phase relationship between the inverter output and the grid voltages until they match. If the phase of the grid is greater than the inverter output, the system frequency is increased and brought back to the rated utility frequency within the designated wait time (T G ). Otherwise, the frequency of the system is decreased and brought back to the rated utility grid frequency within the designated wait time. The amount of frequency deviation ( ) that needs to be applied can be obtained from diff f (2.24) 2 T G where diff is the phase difference between the inverter output voltage and the UG voltage at the instant of grid availability. The system frequency is determined from the following equation for smooth transition f 6 f sin t (2.25) s m where is the system frequency, is the maximum frequency deviation and. 4

61 The comparison of the different frequency variation techniques has been presented in Fig The objective of the algorithm is to adjust the inverter phase to the utility THD & frequency deviation Inverter output voltagethd & freq deviation with x THD Maximum frequency deviation THD for smooth frequency variation Variation of x (s) Figure THD and frequency deviation in the inverter output voltage during the transition from SA to GC mode. within the prescribed time with minimum frequency variation and minimum THD at the inverter output voltage. The initial duration x is varied from to T G /2 which sweeps the frequency variation from the abrupt variation method to the triangular variation method. In the simulation, the grid is considered to be turned off at.3 sec. and returned at 3.3 sec. The inverter voltage is leading the grid voltage by 127 (2.4 rad) at the time of interruption, and the total adjustment time is prescribed as 4 sec to synchronize the phase after the grid returns. As seen in Fig , the optimum value of x is in between 1 sec to 1.2 sec where the lowest THD and the frequency deviation are obtained. The smooth frequency variation technique gives a THD of.88% for a frequency deviation of 1.99 Hz, which is better than all other values of x with the trapezoidal frequency variation technique. 41

62 2. 5. Simulation Results The operation of the 5 kw, 2 VDC, 12 V AC, 4 A, bi-directional single phase inverter is simulated in the SIMULINK/MATLAB environment. The inverter is able to run in GC mode, SA mode and transition modes Inverter Operation in GC Mode Performance of the Current Controller Operating GC Inverter with Full Load The 5 kw inverter, 12 V AC grid and the local load are connected together at the point of common coupling (PCC). The inverter outputs 45 A peak current, 3 A of it is supplied to the local load and rest of it is taken by the grid, as shown in Fig The commanded and are 3 A and A respectively to ensure that the inverter flows real power to the system in GC mode. 2 Voltage at PCC 5 Local Load Voltage (V) Current (A) Inverter Grid Current (A) Current (A) Time (s) Time (s) Figure Voltage at PCC, inverter current, load current and grid current in the GC mode, when 45 A and = A and local load = 5.6 Ω. 42

63 35 DC Bus Voltage (V) Inverter Input Power Power (kw) Power (kw) Inverter output Power Time (s) Figure The DC bus voltage, inverter input and output power in GC mode. Figure 2.17 shows the DC bus voltage, inverter input and output power of the previous case. The DC bus has 3.3 mf capacitance at its terminal which allows maintaining 3 V. The inverter provides 3.9 kw, 2.6 kw is taken by the local load and 1.3 kw is provided to the grid. The current controller gains are selected as 26 and 16 respectively. The inverter can also provide the reactive power depending on the d-axis or q-axis command current. The d-axis command current regulates the real power and the q- axis command current regulates the reactive power which is provided by the inverter. 43

64 Performance of the Current Controller with the Effect of Hardware Delay Figure 2.18 shows the delay effect of the inverter output current. The inverter output filter and the sensor system causes around 3.4 of delay. After considering Fig a shows the inverter output current with 4 sample delay. The inverter currents become worst considering 6 delay with same gains, as shown in Fig b. These suggested that a new set of gains need to be selected using Eqn for getting the same output current response from the inverter. 2 Inverter Output Current C`urrent (A) (a) Inverter Output Current 2 Voltage (V) Time (s) (b) Figure The effect of hardware delay on the current control of the grid tied inverter. 44

65 Performance of the Current Controller with Abrupt Change in Current Command Figure 2.19 shows that the grid voltage at PCC, inverter current, load current, and grid current. Initially the inverter delivers 1 A, and the grid delivers 25 A to the load. At.5 sec, the commanded d axis current is changed from 1 A to 3 A. 2 Voltage at PCC Voltage (V) Inverter current Current (A) Time (s) 4 Local load Current (A) Current (A) Grid Time (s) Figure Voltage at PCC, inverter, load and grid current when changes from 1 to 3 A considering the load of 5.6 Ω. 45

66 3 Inverter Power (kw) Time (s) D-axis Inverter Current 4 Current (A) q-axis Inverter Current Current (A) Time (s) Figure 2.2. Inverter output power, dq-axes command current of the inverter, when changes abruptly from 1 to 3 A considering the load of 5.6 Ω. Figure 2.2 shows the inverter output power, d-axis and q-axis current. The inverter initially delivers.9 kw power to the system. After.5 sec it starts to push around 2.5 kw, as the i d,ref current is changed from 1 A to 3 A. The load power remains constant during the abrupt current change by the inverter. The grid will reduce its power flow to the load as seen by the grid current in Fig There is a sudden change in the q axis current but it gets to zero within.2 sec. It is suggested that gradual change of the commanded current is better for the system. If the inverter d-axis commanded current gets reduced from 1 A to 5 A then the grid current would be increased to sustain the load requirements. 46

67 Performance of the Current Controller with Gradual Commanded Change Gradual increase in the commanded current of the inverter from 1 A to 3 A at.2 sec to 1.2 sec and the effect of the voltage at PCC, inverter current, load current and grid current, are presented in Fig As the inverter increases its output power the grid power gets reduced to sustain the load requirements. 2 Voltage at PCC Voltage (V) Inverter 4 Current (A) 2-2 Current (A) Local Time Load (s) Grid Current (A) Time (s) Figure The voltage at PCC, inverter current, load current and grid current, when changes from 1A to 3 within.9 sec. 47

68 Performance of the Inverter in the Face of DC Voltage Fluctuations Voltage (V) DC bus voltage change Voltage at PCC Voltage (V) Inverter Current (A) Current (A) Inverter current (zoom) Time (s) Figure The DC bus voltage, grid voltage, inverter current when = A. 48 = 3 A and The variation in the DC bus voltage would be company the change in the duty ratio. Figure 2.22 shows the performance of the current control when the DC voltage is changed from 2 V to 18 V. It seems down to 19 V or 5% reduction of the DC bus

69 voltage of its actual value, the inverter power flow will not hamper. At 1.13 sec the DC bus voltage becomes 18 V, then the inverter current peaks gets flatter, which introduces a higher rate of harmonics in the inverter current, because of the insufficient DC voltage. 4 Local load Current (A) Grid Current (A) Time (s) Figure Local load current, grid current in GC mode during the DC voltage change from 2 V to 18 V The Performance of the Inverter during Battery Charging Figure shows the steady-state waveforms of the inverter output voltage and the inverter current in the GC mode with = -4 A and = A using a PI current controller. The inverter current is 18 out of phase of the grid voltage which means the inverter takes the power from the grid and charges the storage device. 49

70 V/I (units) 2 1 Battery charging i inv vg Time (s) Figure Battery charging current,, RMS Voltage Control in SA Mode In the SA mode, the inverter runs in RMS voltage control mode [63]. Figure 2.25 shows the variation in the output power of the inverter according the load demands in SA mode. The DC bus voltage is kept at 2V, the PWM switching frequency is 2 khz, the output inductor value is 1.5 mh, the output AC voltage is 12 V RMS and the fundamental frequency is 6 Hz. During the time between sec to.5 sec the resistive load is kept at 5 Ω, then from.5 sec to.7 sec the load is changed to 2.5 Ω and from.7 sec to 1 sec it is again changed to 1.66 Ω. 21 DC BUS voltage Voltage (V) Inverter output power Power (kw) Time (s) Figure DC bus voltage, various output power flow by the inverter depending on the loads demand in SA mode. 5

71 Operation of the VSI in Transition Mode GC Mode to SA Mode Transition The mode transition algorithm has been simulated based on a 5 kw, 2 V DC, and 12V AC single phase bidirectional inverter. Figure 2.26 shows the operation of the inverter during the transition from the GC to the SA mode. The simulation starts with the GC mode when the inverter regulates the output current and its phase is synchronized with the grid thorough the PLL algorithm. The inverter delivers 5 kw power, 3 kw of which is delivered to the grid and 2 kw is delivered to the local load. At.3 sec the grid gets off, the inverter changes its mode from current control to voltage control and only provides 2 kw to the local loads. Voltage (V) Current (A) Time (s) 5 Inverter output voltage Grid current Time (s) Current (A) Current (A) 1 Inverter output current Time (s) 5 Load current Time (s) Figure Inverter output voltage, grid current, inverter current and load current during transition from GC to SA considering 2 V, L = 1.5 mh, R = 5 Ω. 51

72 SA Mode to GC Mode Transition When the grid becomes available during the SA mode of operation, the inverter gets into the SA to GC transition mode. During this mode of operation, the inverter phase is gradually adjusted to the grid phase within the prescribed time ( ). The inverter regulates the local load voltage during the transition mode and connects at the voltage zero crossing after the phase adjustment is completed. The PI based phase adjustment technique has been presented in Fig The utility grid is recovered at 3.3 sec, with a phase of 26.7 (.466 radians) less than the inverter output voltage. In order to match the phase of the inverter output voltage with the grid within.365 sec, the bandwidth of the controller is adjusted with k pf and τ values of and 12.35, respectively. 62 Frequency change to match the phase Frequency (Hz) Voltage (V) Time (s) Inverter and grid voltage -2 Inverter Time (s) Figure The inverter output voltage synchronization with grid voltage after the grid returns with leading phase with PI phase adjustment technique. 52

73 In Fig. 2.28, the grid becomes available at 3.3 sec with a phase of 26.7 (.466 radians) less than the inverter output voltage. The smooth frequency variation technique gradually decreases the inverter operating frequency from 6 Hz to 58 Hz and then back to 6 Hz. The phases of the UG and the inverter output voltage matches at sec. The inverter is connected to the grid at the zero crossing level of the inverter output voltage to minimize the inrush current from the inverter to the utility grid. Frequency (Hz) Inverter frequency change to match the phase Voltage (V) Time (s) Inverter voltage and grid voltage 2 Vgrid(return) Vinv Time (s) Figure The Inverter voltage synchronization with grid voltage after the grid returns with lagging phase using the smooth frequency variation technique. Table 2.1 shows the comparison of the performance of the PI and the proposed smooth frequency variation technique considering different power demands by the load. As seen in these results, the smooth frequency variation phase adjustment technique significantly reduces the THD of the inverter output voltage during the SA to GC transition period [59]. 53

74 Table. 2.1: The THD of the grid current at different output power [59]. Pout (kw) PI based Frequency Variation Method THD of THD of Vout Iout Smooth Frequency Variation Method THD of THD of Vout Iout % 2.43%.88%.99% % 2.63%.94% 1.5% % 2.93% 1.17% 1.39% Conclusion In this chapter, the control techniques are presented for VSI to run in GC, SA and transition modes. A smooth transition technique between SA and GC modes for VSI has been developed and compared with the various techniques. The developed algorithm varies the frequency smoothly to match the system phase voltage with the grid voltage at the instant of reconnecting to the grid. The algorithm ensures that the transition is accomplished at zero voltage, and it could achieve very low THD during the transition period compared to the other transition techniques. First in GC mode the proper values of the gains of the control algorithm has been derived and simulated considering the hardware delay, DC voltage fluctuation up to 1% and load variation. Second, in SA mode the controller has been tested considering the previous factors. Third, in transition mode the various control techniques and the proposed smooth frequency variation technique have been implemented in the simulations and the THD levels of the output voltage during the transition period are compared. The proposed algorithm shows low THD of the voltage at the PCC considering different loading condition. The load power level varies from 1 kw to 5 kw. 54

75 CHAPTER III SMOOTH TRANSITION TECHNIQUE BETWEEN SA AND GC MODES FOR VSIS OPERATING IN MICROGRID USING DISPATCH UNIT Introduction This chapter proposes a smooth transition control strategy for parallel VSIs during transition between SA and GC modes. Little research has been done on this topic. Among those, a master-slave [59-61] with CAN based communication shows better performance during transition period. As discussed in Chapter I, there is a need to develop a technique that controls the transition the operation modes of VSIs to ensure the stable and seamless transition without the need of additional hardware or communication infrastructure. In this proposed method during both GC and SA modes of operations, the VSIs use the droop control to regulate the power flow without the need of any external communication between them. In the proposed method, one of the DGs working in the microgrid system can be designated as a dispatch unit to facilitate interconnection with utility grid and achieve smooth transition between the modes of operations. During transition modes this selected unit takes the responsibility to ensure the continuous power delivery to the load. During GC to SA mode, the dispatch unit compensates for the current that is supplied to/for the grid before the grid disconnection and then gradually, decreases its power flow such that other units regulate their power flow gradually through their individual droop controllers. The dispatch unit adjusts its output power flow to the 55

76 system to synchronize the voltage of the PCC, as shown in Fig. 3.1, with the grid voltage during the transition from SA to GC mode. The method is expected to have very low or no disturbance in voltage and current during transition. The other VSIs in the microgrid do not require any communication between them or with the dispatch unit. There should have a smart switch that connects or disconnects the grid from the PCC, as shown in Fig The inverter closer to the switch can be selected as a dispatch unit as it has easy access to the switch. The dispatch unit can also provide the commanded current during the normal operating condition. This chapter is divided into five sections. First, the architectural diagram of the microgrid system is explained. Second, the proposed transition control strategy has been discussed for parallel VSIs. Third, the small signal modeling is derived to verify the stability of the overall microgrid system. Forth, the simulation results are given considering the various operating conditions. Then the conclusion of the analysis of the chapter is provided Microgrid System Architecture A typical power system consists of parallel DG units, storage systems, and a cluster of loads within a local area [14]-[17]. Figure 3.1 shows a typical microgrid system where two DGs always run with the droop control method [12] and an additional DG referred to as the dispatch unit has been placed near the PCC to observe the grid voltage and assure necessary power flow to the system during mode transitions. If the grid is not available, then the smart switch disconnects the grid from the system through the dispatch unit command. After the transition, DGs in the microgrid operate in droop control mode and the dispatch unit operates in the current control mode to share the 56

77 required power for the local loads. When the grid returns, the dispatch unit, starts regulating the power to the microgrid system in such a way that the system voltage synchronizes with the grid voltage. The dispatch unit could be also selected from one of VSIs in the microgrid system but selecting one of the storage units would provide more reliability in the microgrid system. Normally the dispatch unit slowly regulates the power during the transition period, so that the other DGs get enough time to share the required power and the system would remain stable. The proposed algorithm does not require any communication between the individual units in the microgrid system. The only communication network is between dispatch unit and the interconnection switch. Current Control Grid Synchronization v g V dc Z 3 PCC i dispatch P 1, Q 1 V s1, δ 1 P l, Q l P 2, Q 2 V s2, δ 2 SW grid connection Zg 2 V dc Z 1 Droop Control Local Loads V dc Z 2 Droop Control v g Figure 3.1. Conventional microgrid system using dispatch unit. 57

78 3. 3. Control Strategy for VSIs using Dispatch Unit in Transition Mode The microgrid system includes DGs and distributed loads, which are connected to the grid through a bypass switch. During SA operation, the DG inverters in the microgrid system regulate their output power using droop control depending on the loading conditions, where the frequency in the microgrid system is set by the droop equations. To make the transition from SA to GC, the dispatch unit adjusts its output power in such a way that the frequency and phase of the voltage of the microgrid system matches with the grid frequency and phase before making the connection to the grid. To make the transition from GC to SA, the dispatch unit always monitors the grid current fed to the microgrid system. When the grid gets is unavailable, the dispatch unit sends a command to open the switch to disconnect the grid and provides the necessary current to prevent any disturbance in the power flow of the microgrid system. The dispatch unit then changes its output power gradually to allow other DGs to adjust to a new condition. In droop control mode the inverter frequency is dictated as (3.1) At the steady state,, for two inverters, where f s is the microgrid system frequency. The power delivered by the two inverters is equal to the load power, P 1 +P 2 =P Load (3.2) When the grid returns, the system frequency,, need to be equal to the grid frequency,. To make the frequency synchronization, the output powers of the two inverters are changed to control the system frequency. In order to provide constant power to the loads, the dispatch unit would act to compensate for the balance of the power requirement as: P 1 +P 2 + P dispatch =P Load (3.3) 58

79 During GC to SA mode transition, amount of current needed to be provided or taken by the dispatch unit can be determined through the closed loop controller as: (3.4) where and are the phases of the grid and the microgrid system respectively. Here, the dispatch unit runs in the current control mode the other inverters run in the voltage control mode with the droop control method. After the phase and the frequency match the inverters in the microgrid system, continue to run in this configuration. and are determined through PLL algorithms operating based on the measured grid voltage and microgrid voltage, as shown in Fig v g v g PLL PLL g g + - PI i disp Figure 3.2. Block diagram of the dispatch unit current controller from SA to GC. As the dispatch unit starts pushing power in the current control mode, the output powers of the other two inverters decrease gradually as the local load remains same. During the phase and the frequency synchronization, the inverters of the microgrid system should be run in droop control. At zero crossing, the switch is closed to make grid connection then the dispatch unit gradually reduces its output power. Figure 3.3 shows the state diagram of the control strategy of the parallel inverters operating in SA, GC and SA-GC transition modes. 59

80 Vd,Vq & f out of range GC All inverters run in Droop control phase match & Switch contact SA to GC Dispatch unit run in current control and Push required current Other inverters run in Droop control SA Dispatch unit provide the required power. All inverters run in Voltage control using droop method V d,v q & f in range Figure 3.3. State diagram of the operating mode transitions in a microgrid system. In our proposed microgrid system inverters in the microgrid always run in droop control in all modes of operation and the dispatch unit always runs in current control mode to provide the necessary power to the system. To get better understanding of the system the control methods of the VSIs are presented in detail in the following sections Droop Control Technique In [13], the control strategy for a flexible microgrid is presented using the droop control method. With the aim of connecting several parallel inverters without control intercommunications, the droop method is often proposed [14]. Thus by their control technique a flexible microgrid can be obtained where the VSIs can operate in either GC or SA mode using droop control. The conventional droop method is based on the principle that the phase and the amplitude of the inverter can be used to control active and 6

81 reactive-power flows [74]. Hence, the conventional droop method for the n th source in a microgrid are given by: (3.4) (3.5) where and are the output and reference voltages, respectively. and are the real and reactive powers of the individual sources in the microgrid respectively,, are the actual and reference frequency, respectively, and, are the droop parameters. Droop coefficients are given below: (3.6) (3.7) where is the maximum output, is the active power output when DG network working under the nominal frequency, is the nominal angular frequency of the grid, is the allowable minimum frequency when the DGs output maximum power, is the maximun reactive power output when the voltage at the DG drop to allowable minimum value. The real power and reactive power of the n th inverter are calculated by (3.8) (3.9) where, are the dq axes output voltage of the n th inverter,, are the dq axes output current of the inverter. Figure 3.4 shows the block diagram of the droop control where the voltage at PCC and the inverter output current have been measured by the sensors. The values in the abc reference frame has been converted into the dq reference frame. Using Eqn. 3.8 and

82 the active and reactive power are calculated and processed through a low pass filter. The reference applied voltage,, can be calculated by Eqn. 3.4 and 3.5, to pass it into the PWM generation block. This droop method increases the system performance due to the autonomous operation among the modules. This way, the amplitude and frequency output voltage can be influenced by the current sharing through a self-regulation mechanism that uses both the active and reactive local power from each unit [59], [8]. In order to obtain good power sharing, the frequency and amplitude output voltage must be fine-tuned in the control loop [64], [54]. v pcc PLL v d v q v d i d +v q i q p c s c p flt ω ref -k pn p flt ω cmd 1 s i inv θ abc-dq Transform i d i q v d i q -v q i d q c s c q flt V ref -k dn q flt v cmd X θ cmd v α-cmd Figure 3.4. The block diagram of the droop control. f (Hz) f op K p1 K p2 Total Demand = P 1 +P 2 Frequency changing Load changing f (Hz) Total Demand = P 1 +P 2 +P g fg K p2 K p1 Load Change P g will change P 2 P 1 P (kw) Standalone Grid Connected Figure 3.5. Linear droop based control for SA and GC mode. P 2 P 1 P (kw) Figure 3. 5 shows the droop setting in active power and frequency characteristic in SA and GC modes. In SA mode, a desired droop operating point with a particular 62

83 generator power sharing (P 1, P 2 ) and system operating frequency,, can be achieved with a range of combinations of droop characteristics. The settings also determine how the droop operating point moves in response to external influences such as load changes, as shown in Fig In GC mode, two inverters should follow the grid frequency as their reference frequency and to inject desired active and reactive power to the grid. If the load changes, then the rest of the power should be balanced with the grid. There have been several droop control techniques like nonlinear droop control, dynamic frequency droop [14], adaptive droop control [15] etc. which can also be implemented to regulate the power flow of the VSIs in GC mode. In this chapter, the main discussion is related to the smooth transition between SA and GC modes for parallel VSIs in microgrid system. So in both GC and SA modes we use the droop control technique for the VSIs. The current controller of the dispatch unit has been explained in Section Modeling and Stability Analysis of the Microgrid System using Dispatch Unit The microgrid system has to be modeled in the SA mode, GC mode and the transition modes to determine the stability of the system. Each VSI will have an outer power loop based on droop control to share the fundamental real and reactive powers with other DGs. Inverter internal controls include droop based voltage controllers which are designed to reject high frequency disturbances and damp the output filter to avoid any resonance with the external network. The small-signal state space model of an individual inverter is constructed by including the controller, output filter and coupling inductor in a synchronous reference frame whose rotation frequency is set by the power controller of that inverter. An arbitrary choice is made to select one inverter frame as the common reference frame and all other inverters are translated to this common reference frame 63

84 using Park transformations. For the dispatch unit the current controller, output L filter and coupling inductor have been used to derive the model. Once the small-signal model has been formed, eigen values (or modes) can be identified and analysis of the system stability yeilds proper values of the system parameters. The analytical nature of this examination then allows further investigation so that the relation between system stability and system parameters, such as the gains of controllers, sizing of the inductor, and load effect, are established. The overall model needs to be verified in all modes. For simplification they are divided into three cases. Case I: VSIs run in SA mode in a microgrid system. Case II: VSIs run in GC mode in a microgrid system. Case III: VSIs run in transition mode in a microgrid system Modeling for VSIs Operating in SA Mode Most of the renewable energy sources are interfaced with the power system (whether grid, DG system or SA) through DC/AC inverter whose input is in DC form. In most of the existing research work, the DC bus at the input of the inverters is assumed to be stiff and therefore its dynamics are usually ignored [13]. This simplifies the analysis of the microgrid system since only AC circuits are needed to be modeled. With the realization of high switching frequencies (4 1 khz), the switching process of the inverter may also be neglected [13]. An external power control of the inverter, which sets the magnitude and frequency (and hence phase) for the fundamental component of the inverter output voltage according to the droop characteristics, set the real and reactive powers [14]. In this section, a state-space model is presented for all the subsystems: control loops, output 64

85 filter and coupling inductor. The model is constructed in a rotational reference frame set by the external power controller of the particular individual inverter. The output voltage of the k th inverter in the microgrid system can be represented as: (3.1) where, and are the DC bus voltage, modulation index and the phase respectively for the k th inverter. A convenient way to analyze AC circuits is to transform all the voltages and currents into the dq rotating reference frame. In this way, the AC circuit can be modeled as two coupled equivalent DC circuits one for the d axis state variables and the other contains the dynamics of the q axis variables. To perform the transformation, a common reference signal is needed. Let the global reference of the DG system be which can be the phase of one of the sources or it can be a hypothetical one [12]. The reference is considered to coincide with the d axis so it has no q axis component. All currents and voltages in the microgrid can be transformed to dq reference frame using as a reference. ωl k i qk ωl k i dk L k L k V dk i dk DG system D model V qk i qk DG system Q model Figure 3.6. Microgrid AC side equivalent circuit in dq frame. Then, the d and q axis components of the inverter voltages can be represented as: (3.11) (3.12) 65

86 i ds1 ωl 1 I qs1 ωl 2 I qs2 + + i ds2 L1 L2 V ds1 RL ir V ds2 Figure 3.7. d axis model for a DG system where two inverters run in SA mode providing the power to the local load. Figure 3.7 shows a system consisting of two parallel inverters islanded from the grid operating with the droop control providing power to the load. The power processing section consists of an inverter, an output filter and coupling inductor. In Park s dq frame that rotates synchronously with the inverter output voltage angular speed ω, the current and voltage dynamics can be reasonably represented by the following equations: For droop control inverters: (3.13) (3.14) (3.15) (3.16) where, are the output inductor of the inverters, and are dq axes output voltage of the inverters, and are dq axes inductor current of the k th inverter, R is the local load. 66

87 For the first inverter, the dq axis output voltage equations are (3.17) (3.18) where, is the DC bus voltage, is the phase difference between the inverter voltage and the reference voltage, is the reference DC voltage, and is the droop coefficient of inverter 1. The injected instantaneous active and reactive power components of the inverter 1, and, are given by (3.19) (3.2) where is the filter cut off frequency. The phase difference between inverter 1 with reference frame is (3.21) Similarly for inverter 2 (which operates in droop based control) (3.22) (3.23) (3.24) (3.25) (3.26) 67

88 where is the DC bus voltage, is the phase difference between the voltage of the inverter 2 with inverter 1, is the reference DC voltage, is the droop coefficient of inverter 2, and and are the active and reactive power components of the inverter 2. Eqn shows that is a function of and of inverter 1. By linearizing and perturbing this equation we get. (3.28) Similarly perturbing Eqns (3.24)-(3.2), we get (3.29) Perturbing the Eqn we get (3.3) Considering Eqn and 3.29 in Eqn. 3.31, we get (3.31) Similarly perturbing the Eqn. 3.27, we get (3.32) (3.33) 68

89 Considering the Eqn. 3.28, 3.29 and Eqn. 3.33, we get (3.34) From Eqn ,,,, and are the steady state value. Perturbing the Eqn and 3.14, we get 1 1 1, 1 (3.35) (3.36) Droop control of inverter 2: Similarly, for inverter 2 of Eqn to Eqn. 3.27, we get, (3.37) (3.38) (3.39) (3.4) (3.41) (3.42) 69

90 (3.43) Perturbing Eqn and 3.16, we get 2 2 2, 2 (3.44) (3.45) A complete state-space small-signal model of the inverter can be obtained by combining the state-space models of the power controller; output L filter, loop equations in SA mode. There are a total of 1 states. The overall linearized model of a microgrid system can be written in the standard form as: (3.46) where X=. is the system matrix. By analyzing the eigen values of the system matrix we can easily identify the stability of the system. A=[a1 a2 a3 a4 a5 a6 a7 a8 a9 a1; b1 b2 b3 b4 b5 b6 b7 b8 b9 b1; c1 c2 c3 c4 c5 c6 c7 c8 c9 c1; d1 d2 d3 d4 d5 d6 d7 d8 d9 d1; e1 e2 e3 e4 e5 e6 e7 e8 e9 e1; f1 f2 f3 f4 f5 f6 f7 f8 f9 f1; 7

91 g1 g2 g3 g4 g5 g6 g7 g8 g9 g1; h1 h2 h3 h4 h5 h6 h7 h8 h9 h1; i1 i2 i3 i4 i5 i6 i7 i8 i9 i1; j1 j2 j3 j4 j5 j6 j7 j8 j9 j1;] where a1= -R/L 1 ; a2= -ω; a3= -R/L 1 ; a4= a5= ; a6= -(1/L 1 )k p1 cos(δ s1 ); a7= -(1/L 1 )sin(δ s1 )(V ref -k p1 q s1 ); a8= a9= a1= ; b1= ω; b2= -R/L 1 ; b3= ; b4= -R/L 1 ; b5= ; b6= -(1/L 1 )k p1 sin(δ s1 ); b7= -(1/L 1 )cos(δ s1 )(Vref-k p1 q s1 ); b8= ; b9= ; b1= ; c1= -R/L 2 ; c2= ; 71

92 c3= -R/L 2 ; c4= -ω; c5= c6= c7= c8= ; c9= -(1/L 2 )k p2 cos(δ s2 ); c1= -(1/L 2 )sin(δ s2 )(Vref-k p2 q s2 ); d1= ; d2= -R/L 2 ; d3= ω; d4= -R/L 2 ; d5= ; d6= ; d7= ; d8= ; d9= -(1/L 2 )k p2 sin(δ s2 ); d1= -(1/L 2 )cos(δ s2 )(Vref-k p2 q s2 ); e1= V ds1 ; e2= V qs1 ; e3= ; e4= ; e5= - ; e6= (-k p2 sin(δ s1 )I qs1 +I ds1 (-k p2 )cos(δ s1 )); e7= (cos(δ s1 )I qs1 (V ref -k p2 q s1 )-I ds1 sin(δ s1 )(V ref -k p2 q s1 )); e8= ; 72

93 e9= ; e1= ; f1= V qs1 ; f2= - V ds1 ; f3= f4= f5= ; f6= (-k p2 cos(δ s1 )I qs1 -I ds1 (-k p2 )sin(δ s1 )-1); f7= (-sin(δ s1 )I qs1 (V ref -k p2 q s1 )+I ds1 cos(δ s1 )(V ref -k p2 q s1 )); f8= ; f9= ; f1= ; g1= ; g2= g3= ; g4= ; g5= -k q1 ; g6= g7= g8= g9= ; g1= ; h1= ; h2= ; h3= V ds2 ; h4= V qs2 ; h5= h6= ; h7= ; h8= - ; 73

94 h9= (-k p2 sin(δ s2 )I qs2 +I ds2 (-k p2 )cos(δ s2 )); h1= (cos(δ s2 )I qs2 (V ref -k p1 q s2 )-I ds2 sin(δ s2 )(V ref -k p2 q s2 )); i1= ; i2= ; i3= V qs2 ; i4= - V ds1 ; i5= ; i6= ; i7= ; i8= ; i9= (-k p2 cos(δ s2 )I qs2 -I ds2 (-k p2 )sin(δ s2 )-1); i1= (-sin(δ s2 )I qs2 (V ref -k p2 q s2 )-I ds2 cos(δ s2 )(V ref -k p2 q s2 )); j1= j2= j3= j4= j5= j6= j7= ; j8= -k q2 ; j9= ; j1= ; The parameters of the system are taken as R = 5 Ω; L 1 = 2 mh; L 2 = 2 mh; k p1 = k p2 = 5ˣ1-4 rad/w; k q1 = k q2 = 2ˣ1-4 rad/var; = 37.7 rad. The same microgrid system with two VSIs and a local load has been simulated for SA mode in MATLAB/SIMULINK environment. Through the simulation we have obtained: δ s1 = rad; δ s2 = 1.9ˣ1-3 rad ; V ds1 = 17 V; V ds2 = 17 V; V qs1 = V; V qs2 = V; 74

95 V ref = 17.5 V; Q s1 =1 VAR; Q s2 = 1 VAR; I ds1 = I ds2 =17 A; I qs1 = -.5 A; I qs2 = -.4 A; = 377 rad; k p = 26; k i = 16; The Eigen values of the microgrid system are = 1 3 [ i; i; i; i; i; ; ; ; i; i] Figure 3.8 indicates that the eigen values of the microgrid system have a wide range of dynamics. Frequency-scale separation is expected due to the time-scale separation between different control loops. The low-frequency modes are dictated mainly by the power sharing of droop coefficients of the controllers and the power filters, which are designed with low bandwidth (around 2 1 Hz). The medium-frequency modes are mainly dictated by the gain of the current control, which are designed with medium bandwidths (4 6 Hz). The high frequency modes are dictated by the L filters and the inverter output currents, which should be designed with high resonance frequencies (in the range of 1.5 khz). By varying the value of the droop coefficients and inductors in the system matrix and observing the propagation of the eigen values, we can properly identify the system stability [15]. 75

96 Two droop based inverter 1 eigen valuse in the Left hand side plane Figure 3.8. Complete eigen values of microgrid study system The Effect of Droop Coefficients in a Microgrid System By analyzing the eigen values of the system matrix it is possible to determine the system stability [15]. If the droop coefficients of one of the DGs are varied from 1ˣ1-4 rad/w to 1ˣ1-3 rad/w, then one of the eigen values related to the droop coefficient will be propagating from the left half s-plane to the right half s-plane which makes the system unstable. Figure 3.9 shows the effect of the droop coefficient variation in the microgrid system. In the system matrix model the droop coefficient of one of the inverter is varied keeping the other parameters same. 2 x 1-5 Power droop coefficient variation 1 Kp2=2e-3 (one droop bases inverter gets unstable) 1e-4<kp2<1.2e-3 (system stable) -1-2 kp2 increases Samples (N) Figure 3.9. Stability analysis of the microgrid in face of varying droop coefficients. 76

97 .15 Variation of droop coefficient K p1 Power (kw) Inverter Time Inverter (s) 1 Current (A) Inverter 2 Current (A) Voltage (V) Voltage at PCC Time (s) Figure 3.1. The effect of the variation of droop coefficient of the microgrid system. It seems that at 1.5ˣ1-3 rad/w of the droop coefficient, the system goes unstable. Figure 3.1 shows the effect of the variation of the droop coefficients of the microgrid system where two DGs operate in SA mode. At.5 sec one of the inverter droop coefficients change from 5ˣ1-4 rad/w to 2ˣ1-3 rad/w. As soon as the droop coefficients are changed the system goes unstable, this is consistent with the prediction of the small 77

98 signal model. When one of the inverters gets unstable then the total microgrid system will be disrupted, as shown in Fig The Effect of the Load Changes in a Microgrid System The value of the load has been changed from 5 Ω to 2.5 Ω in the system matrix model and the propagation of the eigen values in the complex plane is observed. It is observed that load changes do not have significant impact on the Eigen values to make the system unstable. Figure 3.11 shows the variation of the load change while other parameters remain same. The load resistor is changed from 5 Ω to 2.5 Ω at.5 sec in the microgrid system. The system stays stable in the face of load changes as predicted from stability analysis. 12 Variation of the Load Power (kw) Unit 1 Current (A) Unit 2 Current (A) Voltage (V) Voltage at PCC Time (s) Figure The variation of the local load in a microgrid system. 78

99 65 System Frequency Frequency (Hz) Time (s) Figure System frequency of a microgrid system. Figure 3.12 shows the system frequency of the microgrid system. According to Eqn. 3.1, the system frequency is 59.4 Hz before.5 sec. At.5 sec there is a load change causing the system frequency to drop down to 49 Hz but it settles stable at 57.8 Hz within.17 sec. Through the simulation we can conclude that abrupt load change doesn t make the overall microgrid system unstable as long as the DGs can provide the power Inductor Sizing for VSIs in a Microgrid The DGs are connected through the L filter in the microgrid system [16]. For DG interfaced sources, L type filters are very useful for decoupling real and reactive power controls [15]. In the system matrix, the value of the inductor is varied and the eigen value starts propagating from left half s-plane to right half s-plane. If the inductor value is more than.5 mh then the system remains stable, as shown in Fig Otherwise, reactive power flow increases in the system significantly, which makes the system unbalanced. Figure 3.14 shows the effect of the output inductor value on the inverter output voltage. In this simulation we consider the values as: R (Load) = 2.5 Ω; L 1 = 2 mh; L 2 = 2 mh; droop coefficients, k q1 = 2ˣ1-4 rad/var; k p1 = 6.28ˣ1-4 rad/w; k p2 = 6.28ˣ1-4 rad/w; k q1 = 2ˣ1-4 rad/var; = 37.7 rad. If the inductor value of inverter 1 is 79

100 less than.5 mh then the voltage at the PCC gets distorted and the controller fails to operate properly. The model perfectly agrees with the simulation results..5 Inductor sizing for Inverters axis Inductor (mh) Figure The model predicts the critical value of the inductor. 5 Unit 1 Current (A) Voltage (V) Voltage (V) Voltage at PCC (a) Voltage at PCC Unit 1 1 Power (kw) Time (s) (b) Figure (a) Inverter or unit 1 current, voltage at PCC in microgrid system when L = 2 mh. (b) unit 1 power, voltage at PCC in microgrid system when L =.5 mh. 8

101 VSIs Operating in Transition Mode using Dispatch Unit Figure 3.15 shows the microgrid system in transition mode where two inverters run in droop control mode and one inverter, the dispatch unit, operates in current control mode. With the help of the small signal model a system matrix has been developed to evaluate the stability of the system by observing the eigen values of the system [15]. + ωl 3I qdisp i cc L 3 ids1 L1 ωl 1 I qs1 ωl 2 I qs2 ids2 VDs2 + + L2 VDs1 RL VDs2 ir Figure SA to GC mode transition modeling for a microgrid system. The dynamics of the system can be represented as: (3.47) (3.48) (3.49) (3.5) For the dispatch unit, (3.51) (3.52) 81

102 The output voltage of the k-th inverter in the microgrid system can be represented as: (3.53) For the first inverter, the dq axis output voltage equations are (3.54) (3.55) where, is the DC bus voltage, is the phase difference between the inverter voltage and the grid voltage. The injected instantaneous active and reactive power components of the first inverter, and, are given by (3.56) (3.57) where is the filter cut off frequency and is the angular speed of the inverter 1. Consider the dispatch unit as the reference frame (3.58) (3.59) Similarly for inverter 2 (which run in droop based control) (3.6) (3.61) (3.62) (3.63) 82

103 (3.64) A current controller is needed to shape the voltage across the filter inductor, so that minimum current error is yielded. A standard PI current regulator with decoupling and feed forward control loops is adopted for current regulation. The dynamics of the current controller can be given by (3.65) (3.66) (3.67) (3.68) (3.69) where and are the gains of the PI controller, and are the reference inputs of the d-axis and the q-axis currents. In the above equations the following parameters have the constant value. For the DGs run in the droop control mode are:,,,, R are constant. For the dispatch unit:,,,, are constant. Some of the above equations are nonlinear expressions. To make an average model, we need to make the nonlinear expression in the linear from. Perturbations on the output voltage of the current controller are considered. From Eqn we get, (3.7) (3.71) (3.72) 83

104 (3.73) (3.74) where is the phase difference between inverter 1 and dispatch unit. Through the perturbation of Eqn , we get, (3.75) (3.76) (3.77) (3.78) (3.79) (3.8) Take the perturbation of Eqn and , 1 (3.81) (3.83) 84

105 Similarly from Eqn , we get, (3.84) (3.85) (3.86) (3.87) (3.88) (3.89) (3.9) Through perturbation of Eqn and , 2 (3.91) (3.92) From Eqn and 3.52, we get (3.93) (3.94) 85

106 A complete state-space small-signal model of the inverter can be obtained by combining the state-space models of the power controller; voltage controller and output L filter in SA mode. The overall linearized model of a microgrid system can be given in the standard form of (3.95) where X=. is the system matrix. The parameters are taken as R = 2.5 Ω; L 1 = 2 mh; L 2 = 2 mh; k p1 = k p2 = 5ˣ1-4 rad/w; k q1 = k q2 = 2ˣ1-4 rad/var; = 37.7 rad; From the simulation, the steady state values are: δ s1 = rad; δ s2 = 1.9e-3 rad ; V ds1 = V ds2 = 17 V; V qs1 =V qs2 =.1 V; V ref = 17.5 V; Q s1 =1 VAR ; Q s2 =1 VAR; I ds1 = 17 A; I ds2 = 17 A; I qs1 = -.5 A; I qs2 = -.4 A; ω=377 rad; k p = 26; k i = 16; The eigen values of the overall linearized microgrid system are: 1 4 *[ i; i; i; i; i; i; i; i; ; ; 86

107 ; ; ; ; ] Observing the eigen values of the system state matrix, the overall system stability can be investigated in transition modes. As the eigen values are in the left half s-plane, we can conclude that the overall system is stable during the transition mode. 4 System Eigen values 3 Imaginary Axis All 14 eigen values are in the Left hand side. System is stable Real axis Figure The eigen values of microgrid system in transition mode. Imaginary Axis System Eigen values All 14 eigen values are in the Left hand side. System is stable Real axis Figure Eigen values in the microgrid system in low and medium frequency range Impact of the Current Controller Gains on the Stability Effects of the gains of the current controller of the dispatch unit in the microgrid are not significant. It seems that the poles of the current controller of the dispatch unit are in the high frequency range. So the gain variation has small effect in the stability of the 87

108 5 Unit 1 Current (A) Current (A) Unit Current controller gain kp (unit) Dispatch Unit 2 Current (A) Local Load Current (A) Time (s) Figure Simulation results of a microgrid system where two DGs run in droop control and dispatch unit operates in current control mode. 88

109 microgrid. In the transition mode, two DGs operate with droop control and the dispatch unit operates in the current control mode. Both in the model and the simulation we vary the gains of the current controller. The value of k p is changed from 26 to 2 and k i is changed from 16 to 9, where the other parameters remain same Effect of the Droop Coefficients on the Performance of a Droop Based VSIs If we vary the droop coefficients of the inverter during transition and observe the propagation of the eigen values of the microgrid system, we can easily identify the system stability. Figure 3.19 shows the effect of the droop coefficient variation in the microgrid system during transition. The system remains stable when the value of droop coefficient is 2.5ˣ1-4 rad/w, as the eigen values are in the left hand plane. The droop coefficient of one of the inverter is varied from 1ˣ1-4 rad/w to 4ˣ1-3 rad/w considering other parameters, like local load, the gain of the current controller remains same. Changing the droop coefficient values from 1ˣ1-4 rad/w to 4ˣ1-3 rad/w the system becomes unstable as shown in Fig The model properly agrees with the simulation results..3 Droop coefficient variation.2.1 Unstable Region Real axis Stable region droop coefficient x 1-3 Figure The variation of the droop coefficient during transition. 89

110 .15 Variation of droop coefficient kp1 Current (A) Current (A).1.5 Current (A) Current (A) Unit Unit Local Load Dispatch Unit Time (s) Figure 3.2. Inverter currents, dispatch unit and the load current during transition. In the simulation, two DGs run in droop control and one dispatch unit runs in current control mode during transition mode. The droop coefficient of unit1 has been changed at.5 sec, which brings the unit 1 in unstable condition. As other VSIs also connected in parallel to it, the whole microgrid becomes unstable, as shown in Fig

111 GC Mode of Operation of the VSIs with Dispatch Unit Figure 3.21 shows a block diagram of a microgrid system where V s1 and V s2 are the voltages of two VSIs, V cc is the output voltage of the dispatch unit, V g is the grid and R is the load. Inductors are worked as L output filter. The model is used to derive the small signal model of the overall microgrid. Figure Microgrid system architecture of the d-axis equivalent circuit. In Park s dq frame that rotates synchronously with the inverter output voltage angular speed ω, the current and voltage dynamics can be reasonably represented by the following equations. In the dq axis, a =, when V cc is disabled and a = 1, when V cc is enabled. For inverters operating with droop controllers (3.96) (3.97) (3.98) (3.99) 91

112 For the grid (3.1) (3.11) For the current control inverter (3.12) (3.13) where,,,,,, are the dq axes current of the inverter 1 and 2, grid and dispatch unit respectively. For the first inverter, the dq axis output voltage equations are (3.14) where (3.15) and is the DC bus voltage, is the phase difference between the inverter voltage and the grid voltage. The injected instantaneous active and reactive power components of the first inverter, and, are given by (3.16) (3.17) where is the filter cut off frequency, 92

113 and where. And the angular frequency of the grid,, is considered as a reference. (3.18) Similarly for inverter 2 (which operates in droop based control) (3.19) (3.11) (3.111) (3.112) (3.113) For Grid (3.114) (3.115) where is the peak amplitude of the grid voltage. From the dq current controller of the dispatch unit. The controller equations can be written as (3.116) (3.117) (3.118) (3.119) (3.12) where and are the gains of the PI controller, and are the reference values of the d-axis and the q-axis currents, is the phase difference between the dispatch unit and the grid. 93

114 For the inverters operating with the droop control mode:,,,, R, ω are kept constant and,,,,ω for the dispatch unit.to make the average model we need to linearize these equations like we did for the other modes of operations. Taking the perturbations of the output voltage of the current controller of Eqn to 3.12, we get, (3.121) (3.122) (3.123) (3.124) (3.125) From Eqn , we get, (3.126) (3.127) (3.128) (3.129) 94 (3.13)

115 Similarly from Eqn , we get, (3.131) (3.132) (3.133) (3.134) (3.135) A complete state-space small-signal model of the inverter can be obtained by combining the state-space models of the power controller; voltage controller and output L filter in SA mode. The system is (3.136) where X=. is the system matrix. 95

116 The microgrid system where two DGs, one dispatch unit, and a grid, feed the power to the local load is simulated in the MATLAB/SIMULINK environment. Using the parameters R = 2.5 Ω; L 1 = L 2 = 2 mh; =37.7*1 rad; V ds1 = V ds2 = 17 V; V qs1 = V; V qs2 = V; V ref = 17.5 V; ω =377 rad; k p = 26; k i = 16. Steady state values from the simulations are represented in Table. 3.1: Table. 3.1: The steady state values of a microgrid system parameters. =.1 rad/w = 1995 W sin =.443 rad sin =.443 rad =.5 rad/var = 1995 W =.46 rad = rad =.1 rad/w = 192 VAR =.46 rad cos = rad =.5 rad/var =192 VAR cos =.896 rad sin = rad = 2.15 A =15 A = 15 A = 2.15 A Eigen values of the overall microgrid in GC mode are = 1 4 *[ i; i; i ; i; ; ; ; ; i; i; i; i; ; -.484; i; i] Eigen values of the system for these conditions are presented in Fig The eigen values are in the left half s-plane assuming the stability of the system. 96

117 4 x 14 Poles of the system Figure Eigen values of a microgrid system. Figure 3.23 shows the eigen values of the system. As k p1 and k p2 are increased, the system poles move towards unstable region making the system more oscillatory and eventually leading to instability. 4 x 14 poles of the overall system Kp increases Figure Propagation of the eigen values of the microgrid system when the droop coefficients of DGs change from 1ˣ1-4 rad/w to 4ˣ1-3 rad/w. 97

118 3. 5. Simulation Results The model and control algorithm of the laboratory scale microgrid system is developed in the MATLAB/SIMULINK environment to verify the effectiveness of the proposed seamless transition control strategy. In the simulations, two DG units, which are controlled by the droop control method, local loads and the dispatch unit, are connected in parallel at the point of common coupling (PCC). The grid is also connected to the PCC through the switch. Simulation results have been presented for all modes of operations VSIs Operate during SA Mode Regular Operating Condition Two VSIs run in SA mode using droop based control, shown in Fig The inverters share the amount of power according to their droop coefficients for the local load. Depending on the local load demand unit 1 and unit 2 provide 35 A peak AC output current at 12 V (RMS) individually, based on their droop coefficients. Figure 3.24 also shows the voltage at PCC and load current of a microgrid system. The system parameters that we consider for simulating the SA mode are given in Table 3.2. Table. 3.2: The steady state values of a microgrid system in SA mode. Symbol Value Symbol Value 3 V 1ˣ1-4 rad/var 1.5 mh 1ˣ1-4 rad/var.15 Ω 6 Hz 17 V 6.1 Hz 6.28ˣ1-4 rad/w 6.28ˣ1-4 rad/w 98

119 4 Unit 1 Current (A) Unit 2 Current (A) 2-2 Voltgae (V) Current (A) Time (s) 2 Voltage at PCC Local Loads Time (s) Figure The inverters current, voltage at PCC and load current in SA mode. Figure 3.25 shows the microgrid system frequency in SA mode. The system frequency is varied by the droop frequency provided in Eqn If the value of droop coefficients decreases the rate of the change of the system frequency will be lower with load changes. 99

120 65 System frequency Frequency (Hz) Time (s) 1 Figure Frequency of a microgrid system. Local Loads Power (kw) Unit 1 4 Power (kw) Unit 2 4 Power (kw) Time (s) Figure Power flow for the VSIs and the local load in a microgrid system Effect of the Load Changes Figure 3.27 shows the effect of load variation for the DGs operating in SA mode of operation. At.25 sec the local load changes from 1 Ω to 5 Ω, then at.5 sec it changes to 2.5 Ω. Depending on the load demands the units start giving more power according to 1

121 4 Unit 1 Current (A) Current (A) Voltage (V) Unit Time (s) Voltage at PCC Local Loads Current (A) Time (s) Figure The effect of load variations of inverters currents, voltage at PCC and load current. their droop coefficients. Fig shows the system frequency variation. Before.25 sec the system frequency is Hz, after that it reaches to 58 Hz with the increase in the load, and after.5 sec it reduces to 56.1 Hz. One observation we can make is 11

122 that if the loads gradually change, then the system frequency also gradually changes enabling less overshoot. 65 System Frequency Frequency (Hz) Time (s) 1 Figure The frequency of the microgrid system. Local Loads Power (kw) Unit 1 Power (kw) Power (kw) Unit Time (s) Figure Power flow for the inverters and the local load in a microgrid system. Figure 3.29 shows the variation of the power flow of the VSIs depending on the load demands. Before.25 sec the load takes 2.2 kw power, then the load changes to 3.3 kw, 12

123 after.5 sec the load demand goes to 6.1 kw. The unit 1 and unit 2 deliver the required power according to their droop coefficients VSIs Operating in GC Mode Normal Operating Condition In the GC mode, unit 1 and unit 2 also run in the droop control [112] as before. All the inverters in the system should follow the grid frequency. According to the droop Eqn. 3.1, unit 1 and unit 2 should deliver the power to the system. If we want to change the power flow of the two units we need to change the slope of the droop equation [112]. Figure 3.3 shows the currents of two DGs, grid and the load of a microgrid system. Unit 1 and unit 2 deliver 17.5 A (peak) current at 12V (RMS) individually. But the load requires 45 A current. So the rest of the power comes from the grid. The parameters of the system in GC mode are given in Table 3.3. Table 3.3: The steady state values of a microgrid system in GC mode. Symbol Value Symbol Value 3 V 1ˣ1-4 V/VAR 1.5 mh 1ˣ1-4 V/VAR.15 Ω 6 Hz 17 V 6.1 Hz 6.28ˣ1-4 rad/w ˣ1-4 rad/w 16 Figure 3.31 shows the effect of the variation of the demands of the local load. From 2.4 sec to 2.8 sec the local load demands gradually increases from 45 A (peak) to 78 A 13

124 (peak) at 12 V (RMS). Unit 1 and unit 2 deliver the same amount of power as the system. frequency remains same. The grid then supplies the rest of the required power to the loads. 2 Unit 1 Current (A) Unit 2 Current (A) Current (A) Time (s) 1 Grid Local Load Current (A) Time (s) Figure 3.3. Inverters currents, grid current and load current in GC mode. 14

125 2 Unit 1 Current (A) Unit 2 Current (A) Current (A) Time (s) Grid Local Load Current (A) Time (s) Figure The effect of load variations of the inverters currents, grid current, load current in GC mode. 15

126 Transition Mode of Operation for the VSIs using Dispatch Unit Technique GC to SA during Grid Delivering the Power to the System The simulation starts with a microgrid system where two VSIs run in droop control in parallel with grid and processing the power to the load in GC mode considering the dispatch unit remains in an idle condition. At.395 sec the grid become unavailable, the and of the PLL of the dispatch unit goes out of range and the dispatch unit identifies that there is a fault in the grid and sends the command signal to the switch to disconnect the grid. At that instant the dispatch unit pushes the required power, as it always monitors the grid current, so that the load power remains constant. Then the dispatch unit gradually decreases its output power and at 1 sec the other two inverters share the total load power depending on their droop coefficients. Figures 3.32 and 3.33 show the inverters currents, dispatch unit current, the grid current, the grid voltage, and local load current during transition from GC to SA. It seems that the local loads feel very low disturbance at the PCC voltage. The faster the response of the dispatch unit, the less fluctuation would be observed at the PCC voltage. The following system parameters have been used for the GC to SA transition mode simulations. Output inductors of the VSIs, L 1 = L 2 = L 3 = 2 mh, Gain of the current controller, k p = 26, k i = 16, Droop coefficients, k p1 = k p2 = 1ˣ1-4 rad/w, k q1 = k q2 = 6.28ˣ1-4 rad/var, DC bus voltage V DC = 3V. 16

127 5 Unit1 Current (A) Current (A) Current (A) Current (A) Unit Dispatch unit Grid Time (s) Figure Inverters, dispatch unit and grid currents during GC to SA mode transition. 17

128 1 Load Current (A) Load Voltage and Current V/I (units) 1-1 Vgu iload Grid OFF Time (s) Figure Load current and voltage at PCC from GC to SA mode GC to SA during Grid Taking the Power from a Microgrid System Figure shows the output currents of the DGs, dispatch unit and load considering the grid takes the power from the microgrid system. When the grid goes off, the dispatch unit takes the extra power and charges the storage devices. Then it gradually decreases its power and reaches to zero when the energy storage elements are fully charged. As the local load remains constant, both of the inverters gradually decrease their power flow and supply the necessary power to the load. 18

129 1 Unit 1 Current (A) Unit 2 Current (A) 5-5 Current (A) Time (s) Local Load V/I (units) Voltage at PCC and dispatch current i dispatch v PCC Time (s) Figure DGs, load and dispatch unit currents during GC to SA transition mode. 19

130 SA to GC during the Grid Delivering Power to the System The simulation starts with microgrid working in SA mode where the dispatch unit works in idle condition. When the grid becomes available at 2.25 sec the dispatch unit monitors the grid availability through PLL and starts preparing the microgrid for the grid connection. Before the switch gets connected, the phase of the grid voltage and the system voltage needs to be synchronized. Up to 2.25 sec, the output current of the two inverters is 38 A (peak) at 12 V (RMS), as shown in Fig Then the dispatch unit gradually increases its power flow. As the load current remains constant the other two inverters gradually decrease their output power which also changes the system frequency. At 2.88 sec the grid gets connected to the microgrid system and 22 A (peak) current, where as the other two inverters flow 25 A (peak) current individually, as shown in Fig Unit 1 Current (A) Current (A) Unit Time (s) Figure Inverters current from SA to GC in microgrid. 11

131 4 Dispatch Unit Current (A) 2-2 Current (A) Grid Time (s) Figure Dispatch unit and the grid current during SA to GC mode transition. Frequency (Hz) Standalone mode Microgrid Frequency Transition mode Grid connected mode Phase Difference Theta (rad) Time (s) Figure Microgrid frequency and phase difference between the microgrid and the grid voltage from SA to GC. 111

132 2 Voltage at PCC Voltage (V) Local Loads Current (A) 5-5 Figure Voltage at PCC and load current during transition. Figure 3.37 shows the microgrid frequency and the phase difference between the microgrid voltage and the grid voltage. In the SA mode the system frequency is 59.4 Hz, in transition mode the system frequency continues to vary and reaches to 6 Hz before the grid connection. The grid phase returns with 3 lagging and matches to the microgrid phase at 2.87 sec Time (s) Figure 3.39 shows the power flow for the inverters, the dispatch unit, the grid and the load during transition mode. Two units push 5.2 kw power individually, according to the droop equations. At 2.25 sec the grid becomes available. To match the frequency and the phase of system voltage with the grid voltage, the dispatch unit needs to deliver the required power slowly. As the dispatch unit pushes some power the other two units need to reduce the power flow. Because of the load power remains constant. As the two units gradually decrease their power sharing, the system frequency gets changed. 112

133 6 Unit 1 Power (kw) Unit 2 6 Power (kw) 4 2 Power (kw) Power (kw) Power (kw) Dispatch Time (s) Unit Local Time Load (s) Grid Time (s) Figure Power flow of the inverters, dispatch unit, grid and load during transition mode. The dispatch unit gradually pushes more power from kw to 3.6 kw within.6 sec to synchronize the system with the grid. When the system synchronizes with the grid, the dispatch unit sends the command to the switch to connect the grid. After that if the system needs the dispatch unit can provide some power to the system or remain idle. The 113

134 dispatch unit also can gradually decreases it power so that the grid gets enough time to take care of the system, by slowly pushing the required power to the system. From sec, the grid pushes 3.6 kw power to the system. During all modes of operations the load takes 1.5 kw power from the system SA to GC during grid Taking Power from the System Two VSIs deliver 2 A peak current at 12 V (RMS) individually to the load in SA mode, as shown in Fig The system frequency is 6.4 Hz. When the grid becomes available, the dispatch unit monitors that and starts taking the power from the system. The other two inverters individually increase their output current from 18 A to 3 A between 2.2 sec to 2.8 sec. The system frequency and phase matches to the grid and at zero crossing the dispatch unit commands the switch to enable grid connection. The load takes 36 A (peak) current and the rest of the current will flow to the grid, as shown in Fig Unit 1 4 Dispatch Unit Current (A) 2-2 Current (A) 2-2 Current (A) Unit Time (s) Current (A) Grid Time (s) Figure 3.4. Inverters, dispatch unit and grid currents from SA to GC mode transition. 114

135 2 Voltage at PCC Voltage (V) Current (A) Time (s) Figure Voltage at PCC and load current during transition. Figure 3.42 shows the power flow of unit 1, unit 2, dispatch unit, grid and load during SA to GC mode transition. Initially two units deliver 2.3 kw power individually. At 2.25 sec the grid becomes available and the dispatch unit monitors that. As the system frequency is higher than the grid frequency, according to the droop equations, the dispatch unit starts to take more power from the system. The dispatch unit gradually increases the power it gets from kw to 4 kw. When the system gets synchronized with the grid, the switch connects the grid. During all modes of operations the load always gets the continuous power flow of 4.5 kw. Local Loads 115

136 6 Unit 1 Power (kw) Unit 2 6 Power (kw) 4 2 Power (kw) Power (kw) Power (kw) Time (s) Dispatch unit Grid Time (s) Local Load Time (s) Figure Power flow of the inverters, dispatch unit and load during transition. 116

137 Effect of the Load Change during Transition During transition from SA to GC mode the load changing effect has been introduced in the simulation. Up to.25 sec two units share the load power of 33 A individually, as shown in Fig and at.25 sec the grid becomes available. The dispatch unit then increases its power flow which makes the other inverters lower their power flow, this 5 Unit 1 Current (A) Current (A) Current (A) Unit Grid Dispatch Unit Current (A) Time (s) Figure The effect of the load changing on the inverters current, grid current and a dispatch unit during SA to GC mode. 117

138 2 Voltage at PCC Voltage (V) Local Load Current (A) 6-6 Figure The effect of the load changing on the voltage at PCC and the load current during SA to GC mode. makes the system frequency increase and get synchronized with the grid frequency. But at.5 sec, the demand of local loads is changed from 6 A to 1 A at 12 V (RMS). The two units and the dispatch unit compensate the power in the early stage which makes the system frequency lower and the dispatch unit again starts to increase its power flow in such a way that the other units lower their power flow and the synchronization is achieved with the grid at 1.29 sec, as shown in Fig The voltage at the PCC faces small fluctuation during load change but it is in the tolerable range, as shown in Fig Conclusion Time (s) In this chapter, a control technique is developed for DGs in microgrid system to run in GC, SA and transition modes. Effective and efficient smooth transition techniques between SA and GC modes for DGs have been developed for a microgrid system. The proposed technique is based on using a unit called the dispatch unit to manage the 118

139 transition operation. The dispatch unit varies the phase and the frequency smoothly to make SA to GC transition by controlling its output power to match the microgrid phase voltage with the grid voltage at the instant of reconnecting to the grid. The dispatch unit also compensates for the grid current immediately after GC to SA transition before it makes other sources in the microgrid participate in that but gradually. The proposed algorithm does not require any communication between the DGs and provides smooth stable mode transition operation. The selected dispatch unit could be any DG unit, preferably the energy storage system working in the microgrid. First the microgrid system architecture with the dispatch unit has been presented and the control algorithm of the inverters in GC mode, SA mode and transition mode has been developed. Secondly, the overall microgrid system matrix has been derived using small signal modeling [15] and from that the stability of the system has been analyzed by observing the eigen values of the system matrix. Thirdly the simulation results have been presented using the proposed control algorithm in all modes of operations. 119

140 CHAPTER IV SMOOTH TRANSITION TECHNIQUE BETWEEN SA AND GC MODE FOR VSIS IN MICROGRID USING HYBRID CONTROL Introduction An alternative transition technique is proposed in this chapter without needing communication infrastructure or the dispatch unit proposed in Chapter III. In our proposed method DGs can be controlled through the combination of the current controller and voltage droop controllers. The outputs of the two controllers are hybridized using weight factors which are determined through the system frequency. In the proposed method, during GC mode, the inverters are controlled by current controllers. When the grid gets disconnected, the system frequency will decay. This frequency signal can be used as a notification of the change in the mode of operation and to update the weight factors. As each of the inverters can estimate the frequency through PLL, there is no need for communication between the different sources. In SA mode, the inverters run in droop control. From SA to GC mode, the smart switch measures the phase difference between the system voltage and the grid voltage. When the phases are matched, the smart switch gets closed. All inverters switch from their droop control to current control in GC mode as the frequency gets back to the nominal values. During transition both current control and droop control participate in formulating the inverter output voltage, but with different weights or coefficients. 12

141 This chapter has been divided into five subsections. First, the architectural diagram of the microgrid system has been shown. Second, the proposed smooth transition control strategy has been discussed for parallel VSIs. Third, the small signal modeling has been derived to verify the stability of the system. Forth, the simulation results are provided considering the various conditions of the system. Then the conclusion of the analysis of the chapter has been given Microgrid System Architecture A typical microgrid architecture is shown in Fig. 4.1, where inverters and local loads are connected in parallel at PCC. The grid is connected to the microgrid through the smart switch, which can determine the conditions of both the microgrid and the grid. Through the proposed hybrid controller inverters can identify the modes of operation and regulate their power flow in the microgrid system. The frequency is used in the proposed method to determine the mode of operation. As each of the inverters can estimate the Smart Switch v g PCC P 1, Q 1 V s1, δ 1 P l, Q l P 2, Q 2 V s2, δ 2 SW Zg 2 V dc Z 1 Hybrid Control Local Loads V dc Z 2 Hybrid Control v g Figure 4.1. Microgrid system where the VSIs use hybrid controller. 121

142 frequency, there is no need for communication between the different sources in the microgrid. The frequency variation detection allows all inverters to participate in the transition process which eliminates the need for a master unit or dispatch unit. To ensure smooth transition, both voltage droop control and current control could be active and they collectively formulate the inverter output voltage Control Algorithm of the Hybrid Controller In the proposed control, during GC mode, the inverters are controlled by current controllers. When the grid gets disconnected, the system frequency will decay. This frequency signal can be used as a notification of the change in the mode of operation. As each of the inverters can estimate the frequency, there is no need for communication between the different sources in the microgrid. Each of the two controllers participates in making the output voltage based on factors and, which depend on the frequency deviation from the nominal value (i.e. 6 Hz). For example, when frequency is 6 Hz, = 1 and =, indicating full current control. When frequency is less than a certain threshold value, = 1 and =, which represents full droop control. During transition, <, < 1, which makes both controller active to ensure the smooth transition as what will be shown later. Figure 4.2 shows the concept of our proposed control method for smooth transition between GC and SA mode. In GC mode, the current control factor = 1 and in SA mode, the droop control factor = 1, as there is small frequency deviation between SA and GC. From SA to GC mode, starts increasing and starts decreasing gradually, as shown in Fig From GC to SA mode, the reverse occurs. 122

143 The equations of the output coefficients are = (4.1) where = -, is the grid frequency, is the maximum value of Δf, is replaced by the lowest allowable frequency and sat means saturation and =1- (4.2) where is the weight factor of the current controller. GC-SA SA-GC GC SA f 1 k 1 k 2 t Figure 4.2. The variation of the weight factors of the current and droop control in all modes of operations. Figure 4.3 shows the overall structure of the proposed controller, which can work both in the GC mode and SA mode, and the transition mode. Each inverter can easily detect the system frequency and use Eqn. 4.1 and 4.2 it calculate the value of and. The weight factor is multiplied by the droop controller output and is multiplied with the current controller output. Then the combined output is sent to the PWM generation block. 123

144 v g PLL f f Droop Controller sat( f (.)) Current Controller v D k 1 k 2 v C + + PWM Figure 4.3. Overall block diagram of the hybrid controller Current Control A brief description of the current controller provided in Section is presented here again to recall the working principle of the current controller. In the GC mode, estimating the phase of the grid is essential in processing the right amount of power. The phase-locked-loop (PLL) grid synchronization technique has been the preferred method in the literature [2-21], and is also used in this study. The single phase PLL algorithm is implemented by [22]. The grid voltage is shifted by 9 and converted into dq axes voltages based on the estimated phase. The loop filter brings the q axis voltage to zero by adjusting the phase. Based on the estimated phase, the utility current can be converted into the dq domain the same way as the utility voltage is converted. The regulation in dq domain is easier and has better dynamic response characteristics [23-25]. Figure 4.4 shows the block diagram of the utility interactive voltage source inverter controller based on current regulation for the dq axes components of the utility current. The dq axes currents are controlled in their domain through PI controllers and converted into the reference phase voltage. The cross coupling and feed forward terms help to linearize the system and simplify the controller design. 124

145 Id_ref + Σ - PI controller Vd + Σ + - Vd_ref Id_act Iq_act L*ω dq v C Iq_ref + Σ - PI controller + Vq Σ + + Vq_ref θ PLL Iq_act Id_act L*ω vg Figure 4.4. Current control algorithm of the VSIs Droop Control Parallel-connected inverters are controlled to act as VSIs in SA mode. To ensure proper current and power sharing, droop characteristics can be incorporated into the control of the active and reactive power for each unit. A droop based complex impedance method [23], [26] is used in SA mode to achieve the proper power balance and minimize the circulating current. The voltage and the frequency in the microgrid are regulated through the droop control at every source. v pcc PLL v d v q v d i d +v q i q p c s c p flt ω ref -k pn p flt ω n 1 s i g θ abc-dq Transform i d i q v d i q -v q i d q c s c q flt V ref -k dn q flt v n X θ cmd v αd Figure 4.5. The block diagram of the droop control. 125

146 The droop control relations for the n th source in a microgrid are given by: (4.3) (4.4) where and are the output and reference voltages, respectively. and are the real and reactive powers of the individual sources in the microgrid respectively,, are the actual and reference frequency, which will be equal to the grid frequency, respectively, and, are the droop parameters Modeling and Stability Analysis of the Hybrid Mode Transition Control A microgrid system made of a cluster of inverter based DG units empowered by micro sources, such as fuel cells, micro turbines, DC storage, etc is shown in Fig A DC/AC VSI is commonly used as an interfacing module. Figure. 4.6 shows a block diagram of a microgrid system where V s1 and V s2 are the two equivalent VSIs, and V g is the grid. Inductors are used as L filters. The model is used to derive the small signal model of the overall microgrid. In the dq axis, a =, when the grid is off and a = 1, when the grid is available. Figure 4.6. d-axis equivalent circuit diagram of a microgrid system. 126

147 For inverters 1 and 2 (4.5) (4.6) (4.7) (4.8) where,,,,, are the d-axis and q-axis currents of the inverter 1, inverter 2 and grid respectively.,,, are the dq axes voltage of the inverter 1, inverter 2. For the grid (4.9) (4.1) The output voltage of the k-th inverter in a microgrid can be represented as: (4.11) where, and are the DC bus voltage, modulation index and the phase respectively of the k th inverter. A convenient way to analyze AC circuits is to transform all the voltages and currents into the dq rotating reference frame. In this way, the AC circuit can be modeled as two coupled equivalent DC circuits one for the d state variables and the other contains the dynamics of the q variables. To perform the transformation, a common reference signal is needed. Let the global reference of the microgrid be which can be the phase of one of the sources or it can be a hypothetical one. The reference is considered to coincide with the d axis so it has no q component. All currents and voltages in the microgrid can be transformed to dq reference frame using 127

148 as a reference. In GC mode the grid voltage is considered as reference voltage. In SA mode one for the inverters output voltage in the microgrid system is considered as reference. For inverter 1 will be represented as and will be. The dq voltage of source 1 will be given by (4.12) (4.13) where, is the phase difference between the 1 st inverter and the grid, and are the weight factors of the hybrid controller. The d-axis voltage of the current controller is (4.14) (4.15) where and are gains of the current controller. The phase difference of the inverter 1 with respect to the reference frame = (4.16) The q-axis voltage of the inverter 1 is (4.17) (4.18) where and is the reactive droop coefficient of the 1 st inverter. The q-axis voltage of the current controller is (4.19) (4.2) 128

149 where is the q axis of the reference current, is the actual q axis current, and are gains of the current control. Similarly the d-axis voltage of inverter 2 would be (4.21) (4.22) where and is the phase difference between the second inverter and the reference (in GC mode grid is the reference and in SA mode one of the inverter will be the reference.), (4.23) (4.24) The q-axis voltage of the inverter 2 is (4.25) (4.26) where, is the reactive droop coefficient of the 1 st inverter. The q-axis voltage of the current controller is (4.27) (4.28) (4.29) where is the angular frequency of inverter 2 with respect to reference frame. From equation we get (4.3) The instantaneous power of inverter 1 is 129

150 (4.31) The instantaneous reactive power of inverter 1 is (4.32) Similarly for inverter 2 (4.33) (4.34) where is the cut off frequency of the filter. For the grid (4.35) (4.36) where is the maximum peak of the grid voltage. For the and variables are functions of the frequency as = (4.37) (4.38) For the Phase Lock Loop of the VSI. We know, = cos ; (4.39) = sin ; (4.4) From the PLL figure, (4.41) (4.42) where is the phase of the grid voltage and is the estimated phase of the PLL of inverter 1. 13

151 cos V g Delay V X X - + V q LPF V xf PI 1 1 s n sin Figure 4.7. Phase Lock Loop of a inverter. as the difference between the angle is less than 4. From Fig (4.43) (4.44) (4.45) (4.46) (4.47) (4.48) where and are the gain of the PI controller of the PLL of inverter 1. is phase difference of the phase of the PCC and the estimated phase (4.49) Taking the perturbation of Eqn (4.5) where and 131

152 (4.51) Similarly for the PLL of the inverter 2 (4.52) (4.53) Eqn described that the is a function of and of inverter 1. The linearlized from of Eqn is obtained by taking the derivatives of Eqn with respect to and. (4.54) Similarly Eqn becomes (4.55) (4.56) Taking the perturbation q-axis voltage of the droop and current controller of inverter 1, Eqn. 4.18, 4.19 & 4.2 becomes (4.57) (4.58) (4.59) From Eqn we can write (4.6) From the PLL (4.61) (4.62) Taking the perturbation of Eqn and 4.38, we get 132

153 (4.63) (4.64) Perturbing the Eqn we get (4.65) From Eqn we get (4.66) Taking the perturbation of Eqn Replacing the value of, we would get 133

154 (4.67) , 1 1 s ,2 (4.68) Taking the perturbation of Eqn and ,1 1+ 1, 1 1 s ,2 1+ 1,2 1 2, 1 1 s (4.69) (4.7) 134

155 Similarly for inverter 2, taking the perturbation d-axis voltage of the droop and current controller of inverter 2, Eqn & 4.16 becomes (4.71) (4.72) (4.73) Taking the perturbation q-axis voltage of the droop and current controller of inverter 2. Eqn & 4.19 & 4.2 becomes (4.74) (4.75) (4.76) From Eqn we write (4.77) From the PLL of inverter 2 (4.78) (4.79) (4.8) (4.81) Taking the perturbation of Eqn

156 (4.82) From Eqn (4.83) Taking the perturbation of Eqn ,1 2 2+, 2 2( 2.( s2 2)+ 2 ) ,2 2+ 2,2 2 3, 2 2( 2( s2 2)+ 2 )2 +, 2 2+ (4.84) 136

157 (4.85) Taking the perturbation of Eqn. 4.7 and ,1 2+, 2 2 s ,2 2+ 2,2 3, 2 2 s , 2 (4.86) (4.87) Form Eqn. 4.9 and 4.1 we obtain (4.88) (4.89) A complete state-space small-signal model of the inverter is obtained by combining the state-space models of the power controller; voltage controller, current controller, PLL of the individual inverter and output L filter. The overall linearized model of a microgrid system can be given in the standard form of (4.9) 137

158 where X =. is the system matrix of microgrid system in transition mode. A HY _ TM a1 a2 a3 a4 a5 a6 a7 a8 a9 a1 a11 a12 a13 a14 a15 a16 a17 a18 a19 a2 b1 b2 b3 b4 b5 b6 b7 b8 b9 b1 b11 b12 b13 b14 b15 b16 b17 b18 b19 b2 c1 c c2 d1 d d2 e1 e e2 f1 f f2 g1 g g2 h1 h h2 i1 i i 2 j1 j j k k k l1 l l2 m1 m m2 n1 n n2 O1 O O 2 p1 p p2 q1 q q2 r1 r r2 s1 s s2 t1 t t2. where, a 1 1 K s 1,2k p R ; L L 1 a2 ; a 3 R ; a4 ; L 1 138

159 a a 5 ar ; a6 ; L K 1 s1,2 i 7 ; L k a8 a9 a1 a11 ; a a k p 1K s 1,1 cos s 1 ; L 1 sin s 1 V ref k p 1Q s 1 K s 1,1 ; L a14 a15 a16 ; 1 a 17 (V V ) k 2 fl d1, s1 d 2, s1 if 1 1 ; a 18 (V V ) k 2 fl d1, s1 d 2, s1 pf 1 1 ; a 19 (V V ) k 2 fl d1, s1 d 2, s1 pf 1 1 ; a2 ; b1 ; b 2 1 K s 1,2k p R ; L L 1 b3 ; b 4 R ; L 1 b5 ; 139

160 b 6 ar ; L 1 b7 ; b K s1,2 i 8 ; L k b9 b1 b11 ; b k K sin p1 s1, 1 s1 12 ; b 13 L cos s 1 V ref k p 1Q s 1 K s 1,1 ; L 1 b14 b15 b16 ; b 17 (V V ) k 2 fl d1, s1 d 2, s1 if 1 1 ; b 18 (V V ) k 2 fl d1, s1 d 2, s1 pf 1 1 ; b 19 (V V ) k 2 fl d1, s1 d 2, s1 pf 1 1 ; b2 b21 b22 ; c 1 R ; L 2 c2 ; c 3 R L K s 2,2k p L 2 2 c4 ; 14

161 c 5 ar ; L 2 c6 c7 c8 ; c K k s2,2 i 9 ; L2 c1 c11 c12 c13 c14 ; c c k p 2K s 2,1 cos s 2 ; L 2 sin s 2 V ref k p 2Q s 2 K s 2,1 ; L c17 ; 2 c 18 (V V ) k 2 fl d1, s2 d 2, s2 if 2 2 ; c 19 (V V ) k 2 fl d1, s2 d 2, s2 pf 2 2 ; c 2 (V V ) k 2 fl d1, s2 d 2, s2 pf 2 2 ; d1 ; d 2 R ; L 2 d3 ; d 4 R L K s 2,2k p L 2 2 d5 ; 141

162 d 6 ar ; L 2 d7 d8 d9 ; d K k s2, 2 i 1 ; L d11 d12 d13 d14 ; d d k p 2K s 2,1 sin s 2 ; L 2 cos s 2 V ref k p 2Q s 2 K s 2,1 ; L d17 ; 2 d 18 (V V ) k 2 fl d1, s2 d 2, s2 if 2 2 ; d 19 (V V ) k 2 fl d1, s2 d 2, s2 pf 2 2 ; d 2 (V V ) k 2 fl d1, s2 d 2, s2 pf 2 2 ; e ar e e ; L g e 2 e4 ; e6 ; e7 e8 e9 e1 e11 e12 e13 e14 e15 e16 e17 e18 e19 e2 f ar f f ; L g 142

163 f 1 f3 ; f5 ; f7 f8 f9 f1 f11 f12 f13 f14 f15 f16 f17 f18 f19 f2 ; g1 1; g2 g3 g4 g5 g6 g7 g8 g9 g1 ; g11 g12 g13 g14 g15 g16 g17 g18 g19 g2 ; h2 1; h1 h3 h4 h5 h6 h7 h8 h9 h1 ; h11 h12 h13 h14 h15 h16 h17 h18 h19 h2 ; i3 1; i1 i2 i4 i5 i6 i7 i8 i9 i1 ; i11 i12 i13 i14 i15 i16 i17 i18 i19 i2 ; j4 1; j1 j2 j3 j5 j6 j7 j8 j9 j1 ; j11 j12 j13 j14 j15 j16 j17 j18 j19 j2 ; k I k ; 1 ( Vd, s1 ds1k s 1,2 p) c k I k ; 2 ( Vq, s1 qs1k s 1,2 p) c k3 k4 k5 k6 ; k K k I ; 7 c s1,2 i ds1 k 9 k1 ; 143

164 k ; 11 c k12 ci qs1k p1ks1,1 sin s 1 ck p1ks1,1id s1 cos s 1 ; k ( I cos K K I sin ) V k Q ; 13 qs1 s1 s1,1 s1,1 ds1 s1 ref p1 s1 k14 k15 k16 ; ( k k I V V I V I V I 2 f ) if 1 17 qs1 q1, s1 q2, s1 qs1 d1, s1 ds1 d2, s1 ds1 c ; pf 1 k18 ( Vd 1, s1iqs1 Vd 2, s1iqs1 Ids 1V q1, s1 Ids 1V q2, s1) c 2 f k ( k k I V I V 2 f ) pf 1 19 Vd 1, s1iqs1 Vd 2, s1iqs1 ds1 q1, s1 ds1 q2, s1 ; c k2 ; l K k ; 1 ( Vq, s1 Iqs 1 s1,2 p) c l K k ; 2 ( Vd, s1 Ids 1 s1,2 p) c l3 l4 l5 l6 ; l I K k ; 7 qs1 s1,2 i c l I K s k i c ; 8 ds1 1, 2 l9 l1 l11 ; l ( k K I cos I ds k p K s sin 1) ; 12 p1 s1,1 qs1 s ,1 s1 c l13 ( sin K I I cos K ) V k Q ; l14 l15 l16 ; s1 s1,1 qs1 ds1 s1 s1,1 ref p2 s1 c ( k l V I V I I V I V 2 f ) if 1 17 d1, s1 qs1 d 2, s1 qs1 ds1 q1, s1 ds1 q2, s1 ; c 144

165 l 2 f pf 1 18 ( Vd 1, s1iqs1 Vd 2, s1iqs1 Ids 1V q1, s1 Ids 1V q2, s1) c ; k ( k l I V I V 2 f ) pf 1 19 Vd1, s1iqs1 Vd 2, s1iqs1 ds1 q1, s1 ds1 q2, s1 ; c l2 l21 l22 ; m1 m2 m3 m4 m5 m6 m7 m8 m9 m1 ; m11 k q 1; m12 m13 m14 m15 m16 m17 m18 m19 m2 ; n 1 n2 ; n3 ( V ds 2 I ds 2K s 2, 2 k p ) c ; n I k ; n5 n6 n7 n8 ; 4 ( V qs 2 qs 1K s 2, 2 p ) c n9 cks2,2kii ds2 ; n1 ciqs2ks2,2ki; n11 n12 n13 ; n ; 14 c n15 ci qs1k p2ks2,1 sin s2 ck p2ks2,1ids 2 cos s 2 ; n ( I cos K K I sin ) V k Q ; 16 qs2 s2 s2,1 s2,1 ds2 s2 ref p2 s2 c n17 n18 n19 ; ( k n I V V I V I V I 2 f ) if 2 2 qs2 q1, s2 q2, s2 qs2 d1, s2 ds2 d2, s2 ds2 c ; O 1 O2 ; O k ; 3 ( V qs2 Iqs2K s 2,2 p ) c O k ; 4 ( Vds 2 Ids2K s 2,2 p ) c 145

166 O5 O6 O7 O8 ; O I K k ; 9 qs2 s2,2 i c O I K s k i c ; 1 ds2 2, 2 O O O O ; O15 ( k p1ks2,1i qs2 cos s 2 I ds 2k p 2K s 2,1 sin s2 1) c ; O16 ( sin s2ks2,1i qs2 Ids2 cos s2ks2,1) Vref kp2qs 2 c ; O17 ; ( k O V I V I I V I V 2 f ) if 2 18 d1, s2 qs2 d 2, s2 qs2 ds2 q1, s2 ds2 q2, s2 ; c O 2 f pf 2 19 ( Vd 1, s2iqs2 Vd 2, s2iqs2 Ids2Vq 1, s2 Ids2Vq 2, s2) c ; k ( k O I V I V 2 f ) pf 2 2 Vd1, s2iqs2 Vd 2, s2iqs2 ds2 q1, s2 ds2 q2, s2 ; c p1 p2 p3 p4 p5 p6 p7 p8 p9 p1 ; p14 k q 2 ; p11 p12 p13 p15 p16 p17 p18 p19 p2 ; q1 q2 q3 q4 q5 q6 q7 q8 q9 q1 q11 q12 q13 q14 q15 q16 ; q 17 q18 1 ; q 19 q2 ; r1 r2 r3 r4 r5 r6 r7 r8 r9 r1 r11 r12 r13 r14 r15 r16 ; r17 k if 1 ; 146

167 r18 r19 k pf 1 ; r2 ; s1 s2 s3 s4 s5 s6 s7 s8 s9 s1 s11 s12 s13 s14 s15 s16 ; s17 k if 1; s18 s19 k pf 1 ; s2 ; t1 t2 t3 t4 t5 t6 t7 t8 t9 t1 ; t11 t12 t13 t14 t15 t16 t17 t18 ; t 19 t2 1 ; Following parameters are used for the analysis R = 5 Ω; L 1 = L 2 = 2 mh; k p1 = k p2 = 5ˣ1-4 rad/w; k q1 = k q2 = 2ˣ1-4 rad/var; = 37.7 rad; The same microgrid system with two VSIs and a local load has been simulated for SA mode in MATLAB/SIMULINK environment to determine the steady state values. From the simulation: =1.8ˣ1-3 rad; =1.9ˣ1-3 rad ; V ds1 = 17 V; V ds2 = 17 V; V qs1 = V; V qs2 = V; V ref = 17.5 V; Q s1 =1 VAR; Q s2 = 1 VAR; I ds1 = I ds2 = 17 A; I qs1 = -.5 A; I qs2 = -.4 A; = 377 rad; k p = 26; k i = 16,, ; Eigen values of the overall microgrid system: 1 4 [ i; i; i; i; 147

168 ; ; i; ; ; i; i; i; i; ; ; i; i; ; i; i] The eigen values are presented in Fig The proposed transition algorithm is stable as eigen values stay in left half s-plane. 1 x 15 Overall System model Imazinary axiss Figure 4.8. Poles of system matrix in a microgrid system. 148

169 4. 5. Simulation Results The model and control of a small microgrid system is developed in thw MATLAB/SIMULINK environment to verify the proposed seamless transition control strategy. In this simulation, two DGs and a local load are connected at the PCC. The grid is also connected to the PCC through the switch VSIs Operate in SA Mode using Hybrid Control Technique In SA mode, the proposed hybrid controllers of the inverters run the droop control and share the power. The inverters share the amount of power according to their droop coefficients for the local load. The currents of the DGs, voltage at PCC, local load current at SA mode are shown in Fig. 4.9, where unit 1 and unit 2 cumulatively provide 7A (peak) at 12 V (RMS), to the local load. The system parameters that we consider for simulating the SA system are given in Table 4.1. Table. 4.1: The microgrid system parameters in SA mode. Symbol Value Symbol Value 3 V 1ˣ1-4 V/VAR 1.5mH 1ˣ1-4 V/VAR.15 Ω 6 Hz 17 V 6.1 Hz 6.28ˣ1-4 rad/w ˣ1-4 rad/w

170 Figure 4.9 shows the operation of two units in SA mode to sustain the load in a microgrid. 4 Unit 1 Current (A) Unit 2 Current (A) 2-2 Voltgae (V) Current (A) Voltage at PCC Local Loads Time (s) Figure 4.9. Inverters currents, voltage at PCC, load current in SA mode. 15

171 65 System frequency Frequency (Hz) Time (s) Figure 4.1. System Frequency of the microgrid system in SA mode. 1 Local Loads Power (kw) Unit 1 4 Power (kw) Unit 2 4 Power (kw) Time (s) Figure Power flow of the local load, unit 1 and unit 2 in SA mode. Figure 4.11 shows the power flow to the local load from unit 1 and unit 2 operating in SA mode. In SA mode, two units provide 3.1 kw power individually and the local load takes 6.2 kw power. If the load demands changes then the two inverters adjust their power flow according to their droop coefficients. 151

172 4 Unit 1 Current (A) Current (A) Voltage (V) Unit Voltage at PCC Local Loads Current (A) Time (s) Figure Inverters current, voltage at PCC and the load current during the effect of load changes in SA mode. 152

173 65 System Frequency Frequency (Hz) Time (s) 1 Local Loads Power (kw) Unit 1 Power (kw) Power (kw) Unit Time (s) Figure System frequency, load and inverters power flow during SA mode. Figure 4.12 shows the load changing effect in SA mode. Between sec to.25 sec the load is kept at 1 Ω, from.25 sec to.5 sec it is 5 Ω and after.5 sec it is kept 2.5 Ω. Depending on the load demands the inverters increase their power flow. Figure 4.13 shows the variation of the system frequency, power flow of the inverters and load in SA mode. From sec to.25 sec system frequency is 59.5 Hz. As the load increases the system frequency drop down according to the droop equations. Between.25 sec to.5 153

174 sec, the load demands 3.5 kw power, the inverters share the power and the system frequency becomes 58 Hz. After.5 sec the load demand is changed to 5.8 kw which is supplied by the expense of change in the system frequency. It seems large variation of the load demand takes time to settle the units at the power flow of the inverter and the system frequency VSIs Operate in GC Mode Normal Operating Condition In GC mode, the proposed hybrid controller of the inverter runs in current control as the weighted factor of the current controller becomes 1. Depending on the current command, the inverters deliver power to the PCC. Unit 1 and unit 2 push 14 A (peak) and 2 A (peak) at 12 V (RMS) respectively, as shown in Fig 4.14 and Since the load takes 45 A, the rest of the power is delivered by the grid. As the grid frequency is 6 Hz, the system frequency also remains the same. 2 Unit 1 Current (A) Current (A) Unit Time (s) Figure Inverters current in GC mode, where,, and. 154

175 1 Grid Current (A) Local Load 5 Current (A) Time (s) Figure The grid current and load current in GC mode. Figure 4.16 shows the power flow of the inverters when the local load remains constant in GC mode. In the GC mode, the weight factor of of the hybrid controller is equal to 1 and the VSIs run in current control mode. Unit 1 and unit 2 deliver 2.4 kw and 1.5 kw power respectively, according to their current command while the rest of the power is provided by the grid. As the grid acts like an ideal source or sink, it can take or provide any amount of power to the microgrid system. The system frequency remains 6 Hz, as the grid frequency. If the current command of the individual inverters change then depending on the load demands the grid provides the rest of the power. 155

176 4 Unit 1 Power (kw) Unit 2 3 Power (kw) 2 1 Power (kw) Time Grid(s) Local Load 8 Power (kw) Time (s) Frequency of the RES 65 Frequency (Hz) Time (s) Figure DGs, grid, load power flow and overall system frequency in GC mode. 156

177 Gradually Changing of the Power Flow during Transition Figure 4.17 shows the DGs current, grid current and load current when one of the inverter starts varying its power output, provided that it has the sufficient energy in its 4 Unit 1 Current (A) Unit 2 Current (A) 2-2 Current (A) Grid Local Load Current (A) Time (s) Figure The effect of the commanded current variation by the inverters, when load current remains constant in GC mode. 157

178 6 Unit 1 Power (kw) Unit 2 Power (kw) Grid 2 Power (kw) Local Load Power (kw) Time (s) Figure Power flow of the VSIs, grid and load in GC mode. energy storage devices. Unit 1 delivers 15 A (peak) current up to 2.3 sec. Unit 2 and grid also delivers 2 A and 12 A to the local load. From 2.3 sec to 2.7 sec unit 1 gradually 158

179 increases its output current from 15 A to 32 A. As the load always requires 47 A current, the rest of the power will obviously flow to the grid. Prior to the grid delivers 12 A current and then it gradually reduces to A. After 2.55 sec the grid starts taking the power from the system. Figure 4.18 also shows the power flow of the inverters, grid and local load to get better understanding of the system. The local load always requires 5.2 kw. Unit 2 always pushes 3.4 kw as its commanded current always remains the same. Unit 1 initially pushes 2 kw up to 2.3 sec and then gradually starts increasing its output power up to 5 kw within.3 sec. Before 2.3 sec, the grid pushes 2 kw, then its output power decreases and at 2.57 sec it starts taking power from the microgrid system as Unit 1 starts to deliver more power Transition Mode of Operation for VSIs GC to SA mode - The simulation starts with the microgrid is operating in GC mode. At.45 sec, the grid becomes unavailable, after that instant the system frequency starts decreasing which causes the coefficients to start decreasing and the coefficient to start increasing. Denoting as and as. This makes both the current and droop controllers work together and compensates the system power requirement. In GC mode, the VSIs run in current control mode and the microgrid frequency is at 6 Hz. In SA mode, VSIs run in droop control and the microgrid frequency is 59.7 Hz. Figure 4.19 shows the microgrid frequency deviation at PCC point and the output coefficients of the current and voltage controller from GC to SA. After.65 sec the inverters run in droop control mode, as the value of becomes 1 and the value of becomes. 159

180 6.5 Microgrid Frequency Frequency (Hz) Weighted factors Unit.5 k 2 k Time (s) Figure Microgrid frequency and the output coefficients behavior from GC to SA. Figure 4.19 shows the currents of the DGs, load and the grid in the microgrid system respectively during transition. Prior to the grid disconnection, both of the inverters run in current control mode and individually deliver 1.2 kw power to the PCC point, as the local load needs 3 kw and the rest of the power comes from the grid. After the grid disconnection, the hybrid controller then starts regulating the voltage through the droop control and pushes the required 3 kw to the local load. During the transition period, the local load s power has small fluctuation because of the slower response to the droop controller and the system does not get the extra power from any additional inverter such as the dispatch unit. It is seen from Fig that the value of gradually increases from GC to SA mode. There is a slight oscillation on the local load voltage during transition as shown in Fig

181 3 Unit1 Current (A) Unit 2 Current (A) Local Time Load (s) 5 Current (A) Current (A) Grid Time (s) Figure 4.2. The output currents of DGs, load and grid during GC to SA mode transition SA to GC mode - The simulation starts with the microgrid working in SA mode. When the grid becomes available at.2 sec, the switch waits to connect the grid to the PCC when the phase error between the microgrid and the grid voltage is zero. Figure 4.21 shows the variation of the microgrid frequency, the output coefficients of the current and 161

182 droop control during SA to GC mode transition. When the grid is connected the system, the frequency starts increasing to reach at 6 Hz. During this transition, coefficients adjust automatically as shown in Fig Microgrid Frequency Frequency (Hz) Weighted Factors 1 Units.5 k 1 k Time (s) Figure Microgrid frequency and the output coefficients behavior from GC to SA. Figure 4.22 shows the current of DGs from SA to GC mode transition. The inverters run in droop control mode and at.782 sec the grid is connected to PCC and the controller then starts regulating the power and individually pushes 1.7 kw to the PCC. As the controller smoothly changes from the droop control to current control mode, the inverters output current is smoothly regulated. Figure 4.23 shows the power flow of the inverters, grid and local load from SA to GC mode. Two of the inverters cumulatively push 5.5 kw to the load with 59.8 Hz system frequency. At.78 sec the phases of the grid voltage and the voltage at PCC match and the switch gets connected. As the hybrid controller needs time to switch the controller 162

183 from droop control to current control, the grid provides the extra power for the short period of time. 2 Inverter 1 Current (A) Current (A) Current (A) Voltage (V) Inverter Local Time Load (s) Voltage at PCC Time (s) Figure DGs currents, load and voltage from SA to GC mode. 163

184 3 Unit 1 Power (kw) Unit 2 Power (kw) Time Grid(s) Power (kw) Local Load Power (kw) Time (s) Figure Power flow of unit 1, unit 2, grid and the local load during transition Effect of the Load Change during Transition Mode The simulation starts from the SA mode where two units individually provide 18 A current to the load. As the units run in droop control mode, the system frequency has slight deviation from the grid frequency according to the droop equation. Because the deviation the phase synchronization will be achieved in time and in our case at.6 sec the 164

185 3 Unit 1 Current (A) Current (A) Current (A) Current (A) Voltage (V) Unit Grid Local Load Voltage at PCC Time (s) Figure The effect of the load changes on the inverters currents, grid current, load current and voltage at PCC from SA to GC mode. 165

186 phase error between the system voltage and the grid voltage becomes zero and the switch gets connected. The grid then pushes some of the power and hybrid controller starts switching the controller from droop control to current control depending weight factors. But at.65 sec the load demands change from 36 A to 54 A, as shown in Fig The grid provides the extra power to the load so that the other units can smoothly change controllers to current control mode. At.9 sec both of the units push 15 A individually by their current controller Comparisons between Two Proposed Transition Techniques in a Microgrid System Depending on the simulation and the experimental results, the performance of the proposed dispatch unit concept and the hybrid concept can be summarized in Table 4.2. Table 4.2: Comparisons between the proposed transition techniques. Dispatch Unit Concept for Transition Mode Hybrid Controller Concept for Transition Mode i. Constant power supply to the local load can be possible during transition period. i. Slight power disturbance during transition. Upto 2 or 3 electrical cycles the fluctuation has been observed. ii. Low THD on the voltage at PCC. For 1 kw system the THD is 2.45% during transition. ii. THD on the voltage at PCC is high. For 1 kw system the THD is 4.495% during transition. iii. Requires an additional unit which will increase the cost. But this unit can provides power during normal operating condition. iv. VSIs used droop control in all modes of operations which gives slower dynamic response of power flow. iii. No extra unit is necessary. It is appropriate in the rural area where slight power disturbance can be allowable. iv. VSIs run by current control in GC and droop control in SA mode. By this during GC mode faster dynamic response can be achieved. 166

187 4. 7. Study of the Electrical Characteristic of the Proposed Two Methods The microgrid system has been tested with the dispatch unit and hybrid control techniques with various loading conditions. Table 4.3: Comparisons of the electrical characteristic between the dispatch unit and hybrid methods. Proposed Methods Load (kw) Voltage Fluctuation at PCC during Transition THD of the Voltage at PCC (%) Settling Time for Normal Operation (ms) Dispatch Unit Technique V (Fig ) ms (Fig ) V ms Hybrid Control V (Fig ) ms (Fig ) V ms Conclusion In this chapter an alternative transition control algorithm between SA and GC modes of operation has been developed for parallel VSIs in microgrid system. The developed algorithm varies the output coefficients of the current and droop controller depending on the frequency variation during the transition period. The proposed algorithm does not require any communication between the DGs and neither the central controller nor the 167

188 dispatch unit is required. First the architectural overview of the microgrid system and the microscopic overview of the control algorithms of the inverter are presented. Second, theoretical analysis of the hybrid controller and the stability of a microgrid system, with two inverters having hybrid controllers and a grid, has been derived using a small signal modeling technique. The stability of the system has been verified through the position of the eigen values of the system matrix. Third, simulation results have been presented using our new proposed control technique considering the various conditions in all modes of operations. 168

189 CHAPTER V EXPERIMENTAL RESULTS Introduction In order to verify the effectiveness of the proposed control algorithms, an experimental test setup has been developed at the Alternative Energy Laboratories of the University of Akron. Four DC/AC inverters along with associated controllers have been built to form a microgrid system. Single phase portion of the inverters have been used but they can be extended to form three phase system Hardware setup of the VSI A bi-directional 5 kw utility interactive inverter has been developed to test the developed algorithms. The experimental setup is shown in Fig. 5.1, which has an inverter, Table. 5.1: Parameters for the single phase utility interactive inverter. Grid voltage and frequency Battery Voltage Battery Current Inverter Inductor Switching Frequency 12 V (rms), 6 Hz. 2 V -25 A IAP1T mh 2 khz 169

190 Figure 5.1. Experimental setup of the VSI. a filter (inductor),a local load, a utility grid, a battery, an interfacing board, and a DSP and computer for programming and communications. The developed system parameters are provided in Table Voltage Source Inverter IAP1T12 inverter hardware from Applied Power Systems is used as a base for the bi-directional inverter. The unit has built in DC-link capacitors of 33 µf, protective circuits for over current, short circuit, over voltage, under voltage and over temperature and gate drive circuits to drive IGBTs. The power module contains three independent IGBT legs which are capable of handling 8 V DC, 2 khz switching frequency, and a peak 2 A. Figure 5.2.a shows the inverter module used for the experiments Interface Board An interface board between the DSP and the inverter module is developed to measure utility grid voltage, inverter voltage, inverter current, DC bus voltage, and DC current. 17

191 An additional interface board is equipped with PWM buffer circuits, protection circuits for over/under voltage/current and relay driving circuit. The picture of the inverter module, interface board and DSP board for experiments presented in Fig Figure 5.2. Grid interactive inverter setup: (a) Power module, (b) Interface board, (c) DSP development board Relay Driving Circuit Physical connection between utility grid and grid tie inverter is achieved using a soft switching relay. A driver circuit to drive the relay is developed on interface board and it is shown in Fig The DSP generates a turn ON/OFF which drives a Metal Oxide 171

192 Semiconductor Field Effect Transistor (MOSFET) after passing through a Schmitt trigger. A MOSFET is connected to drive coil of the relay. C14 DGND R2mos 1 Input pulses for Relay U6 oe1 a a1 a2 a3 a4 a5 a6 a7 Vcc oe2 y y1 y2 y3 y4 y5 y u R_mos 1 G D S MOSFET DGND +5V DGND 2 1 U7 S D TB1 Relay terminal 1 gnd y7 11 DGND Schimtt trigger Figure 5.3. Relay driving circuit Voltage Sensor (measurement) Circuit A voltage amplifier, AD22, is used to measure DC or AC voltages of the system. The voltage divider circuit is used to reduce the AC voltage from 17 V to 4.25 V and DC voltage from 2V to 5V. C 11, C 12, C 13 and R 13 values are used as recommended for the amplifier, the output of voltage sensor can be +Ve or Ve depending on the input voltage. Figure 5.3 shows the conditional circuitry for the analog measurements. Figure 5.4 shows the voltage isolation amplifier AD22 and its conditioning circuitry. 172

193 Voltage (+Ve) Voltage divider Voltage (-Ve) R11 195k R12 5k C11.1u Voltage isolater/sensor R13 2k C12 1pf Input+ Input- ISO_Voltage_Sensor Input Feedback Input common AD22 Power Output VISO- Power common Output HI Output LO Output VISO DGND C13.1u +15V Figure 5.4. Voltage isolation amplifier AD22 to measure voltage Processing Sensor Data The output of the voltage sensor is between V and V for a single phase AC utility grid and 5 V for DC bus voltage of 2V. Since ADC channels of the DSP are unidirectional, measured signals are level shifted accordingly. Vbatt1_F_pos R1Fneg3 Input signal 47k Cb3.1u +15V R1in1 +5V 5k Cb1 R1f 1 5k R1Fpos 1k Buffer OUT1 OUT In1- IN IN1+ IN VDD -VDD 12 6 IN2+ IN IN2- IN3-1 8 OUT2 OUT3 9 NC NC R2in1 AD713 1k 1k R1Fneg2 1k R1Fneg1 R2f 2 2.5k -15V Cb2.1u R_Vbatt1F R_v ia Vbatt1_F_neg Cb4 1u p n NC To DSP Filter Z1 zener.1u R1in2 5k 5k TP1 Port Figure 5.5. Coditioning circuit for analog measurements. 173

194 PWM Buffer Circuit The input signal for the IAP1T12 s gate driver circuit is between and 15 V, but the DSP can generate the PWM signals of 3.3 V magnitude. Hence this signal is level shifted to 15 V to run the IGBT modules. Three MCP144 chips are used for level shifting; one MCP144 with supply voltage is shown in Fig The developed PWM signals are processed through a PWM buffer, which is enabled by the signal provided from the DSP. PWM1L_DSP_1 PWM level shifter PWM1 1 NC NC 2 INA OutA 3 GND VDD DGND 4 INB OUTB CPW1.1u +15V DGND PWM1L_module PWM1H_module PWM1H_DSP_1 MCP V C2.1u DGND PWM1L_DSP PWM1H_DSP PWM2L_DSP PWM2H_DSP PWM3L_DSP PWM3H_DSP Driv eenable U V Sof tsw DGND RF2 3k R59.1u 1 C17 R52 1k DGND.1u C24 RF1 3k DGND +3.3V C18.1u RF3 3k DGND DGND DGND DGND U A VCC 3 1B 4 GND 1Y OR Gate 74LVC Shut_DSP VCC 19 3 A1 Fault_DSP 18 4 A2 Y A3 Y A4 PWM Buffer Y A5 Y A6 Y A7 Y A8 Y7 11 GND Y8 74LVC541 Green LED RF4 +3.3V C19 DGND.1u C3 DGND.1u +3.3V Fault_shut P2 1 DGND DGND DGND DGND DGND DGND DGND RZ6 RZ5 RZ4 RZ3 RZ2 1k 1k 1k 1k 1k RZ1 1k PWM3H_DSP_1 PWM3L_DSP_1 PWM2H_DSP_1 PWM2L_DSP_1 PWM1H_DSP_1 PWM1L_DSP_1 Figure 5.6. PWM level shifter and buffer circuit. 174

195 Fault Protection Circuit Fault protection based on the utility grid voltage, DC voltage and inverter output current is developed as shown in Fig If any of these faults occur, then it generates a fault signal which turns off the PWM signal to the IGBT module. LED signals are provided for easy debugging of the interface board for fault conditions. If there is any fault then the corresponding LED will glow. Once the fault is cleared, the DSP generates a fault reset signal which resets the LED and fault holding latches. +3.3V C5.1u DGND +3.3V C5.1u DGND +3.3V C9.1u DGND +3.3V Grid Voltage Over Current DC voltage Gate driver Latch1 EN S R S1 R1 S2 R2 S3 R3 Latch Q Q1 Q2 Q3 VDD Nc Vss DGND HexBuf f er E VCC A 2E Y 1Y A1 2A Y1 1Y A2 2A Y2 1Y A3 2A Y3 1Y3 11 GND 2A3 DGND MC1444 Hex_Buf f er2pin DGND +3.3V DGND C15 DGND DGND.1u DGND RED LED RF7 1 RF5 DGND 1 1 RF6 DGND R58 3k DF114 D1N42 DF113 F1 F2 RED LED RF8 F3 1 RED LED F4 Fault_shut D1N42 DF112 RED LED D1N42 DF111 D1N42 Figure 5.7. Fault protection circuitry. 175

196 Digital Signal Processor An Analog Devices DSP BF56F is used for software implementation of algorithms and software programs are developed in the Visual DSP++ integrated development and debugging environment. The BF56F is a high performance and low power processor. The evaluation board (EZ-KIT Lite) is used to interface the BF56F to VisualDSP++. The VisualDSP++ development environment can create, compile, assemble, and link programs written in C/C++ to BF56F assembly. We can read or write data/program memory and core/peripheral registers. The ADSP BF3F is a 4 MHz processor. Internal memory and clock speeds are high enough to implement the developed control algorithm. The interfacing board between the power module and the EZKIT-LITE is developed and measurement data is processed Expermental Test Bench of the Microgrid System The test platfrom consists of power eletronics inverters, interface hardware boards for the inverters, local AC and resistive loads, inverter output filter and the DSP to implement the proposed algorithm. Figure 5.8 shows the complete block diagram of the test platfrom. Two inverters are used to for the microgrid system with local loads, one inverter works as a dispatch unit which can provide power in normal operating condition or do the synchronization, and the forth inverter works as a grid. The dispatch unit monitors the grid voltage and if the grid gets a fault, it sends a command to turn of the switch. The DSP can send the high or low signals to the switch to connect the VSIs to the PCC where as the local loads are kept connected in to the PCC. The grid is also connected through the relay or switch to the PCC. The picture of the microgrid system is shown in Fig

197 DC Supply Inverter #3 V,I Relay L Signal Relay Grid V,I DC Supply Inverter #2 L Signal Local Load V,I DC Supply Inverter #1 L Relay Signal PCC Figure 5.8. Simplified diagram of one line microgrid test bench. In the microgrid test bed the following instrumentaton units have been used; (i) 2 Tektronix DPO224 Digital Oscilloscopes; (ii) 2 Tektronix THDP2 High voltage differential voltage probes; (iii) 5 Tektronix A66 AC/DC current probes. The connection of the instrumentation system is shown in Fig

198 Computer #1 Computer #2 Computer #3 Signals Signals Signals Inverter #1 Inverter #2 Inverter #3 Grid Local Load Current Signals V/I Signals Oscilloscope #1 Oscilloscope #2 Figure 5.9. Overall test bench setup for microgrid system. 178

199 Figure 5.1. Experimental setup for the microgrid system. 179

200 5. 4. Experimental Tests of the Control Algorithm Developed for Independent VSI A 5 kw, 2V DC, 12 V AC, utility interactive single phase inverter has been developed for experimental verification as shown in Figure The control algorithms have been implemented using a BF56F digital signal processor from Analog Devices and in all modes of operation. The ADC sampling, and PWM switching rates are kept at 2 khz. Figure Experimental setup of an independent VSI VSI Operates in GC Mode A bi-directional inverter is interfaced to the grid through the switch. The PLL is applied to measure the grid voltage to obtain the dq-axis voltage and the phase angle. Once the VSI s phase is locked to grid, then the inverter runs with the same phase angle. The utility grid voltage for the experiment is shown in Fig a. Hence the same will 18

201 be reflected in dq-axis voltages and phase angle, which can be seen in Fig b, 5.12.c and 5.12.d respectively. As soon as reaches zero, and settles into steady state, the inverter synchronizes with the grid. Once the inverter gets synchronized to the grid, power flow control is done through current controllers. 2 Grid Voltage Voltage (V) Time (S) D-axis voltage 2 Voltage (V) Time (S) Q-axis voltage 2 Voltage (V) Phase angle (radian) Time (S) Theta (Grid phase angle) Time (S) Figure Output of the Phase Locked Loop (a) grid voltage (b) d-axis voltage, (c) q-axis voltage, (d) Output of Phase angle of the PLL. 181

202 Real Power Processing into the Grid Active power of the inverter is controlled through d-axis command current and the reactive power is controlled by. Figure 5.13 shows grid interface results when the command current = 22 A, and = A. If the inverter only provides real power, then the inverter current is in phase with the grid voltage. Actual and currents are shown in Fig d. 2 Grid Voltage Voltage (V) Time (S) Inverter output current 2 Current (A) Voltage (V)/Current (A) Current (A) Time (S) Grid Voltage/Inverter output Current 2 Grid voltage Inverter current Time (S) d-axis and q-axis values of inverter output current 4 2 Id Iq Time (S) Figure The grid voltage, inverter current, grid voltage and grid current, d-axis and q-axis current of the inverter. 182

203 Reactive Power Processing Reactive power injection to the grid is tested at no load conditions and presented in Fig As we are injecting only reactive power to grid, the phase difference between inverter output current and utility grid voltage is 9. Figure 5.14.c shows the utility grid voltage and inverter output current. 2 Grid Voltage Voltage (V) Time (S) Inverter output current 5 Current (A) Voltage (V)/Current (A) Current (A) Time (S) Grid Voltage/Inverter output Current 2 Grid voltage Inverter current Time (S) d-axis and q-axis values of inverter output current 4 2 Id Iq Time (S) Figure Reactive power injection into utility grid ( = A, = 2 A): (a) Utility grid voltage, (b) Inverter output current, (c) Grid voltage/ Inverter current, (d) d-axis and q- axis current. 183

204 Abrupt Change in the Commanded Inverter Output Current Figure 5.15.a and 5.15.b show the experimental results of the current controller where is changed from 15 A to 3 A at 5.41 sec. The current controller has good transient response in following the change in the reference current. 4 Inverter output current Current (A) Current (A) Time (s) Transient effect of dq current change Time (s) Figure The effect of abrupt change on the reference current of VSI. id iq Charging Operation through the Inverter A bi-directional inverter can charge the battery by taking the power from the grid. Battery charging is tested for - 4 A. A negative sign of the d-axis command current indicates the charging action. Figure 5.16 shows the grid voltage and inverter current for - 4 A, which represents 3.6 kw of power operation. 184

205 Inverter voltage and current V/I (units) Vinv Iinv Time (s) Figure Battery charging operation ( VSI Operates in SA Mode -4A). If the utility grid is not available, the inverter runs in SA mode, where the power control is done through voltage control. When the utility grid voltage or frequency is out of the specified range of values, then the system automatically moves to SA operation. The system provides power to the local connected loads by controlling the voltage at PCC through RMS voltage control, described in Chapter II. A resistive load of 13 is connected across the inverter to test the SA operation, for which the current from the inverter is 13.7 A (peak) is as shown in Fig The system frequency is 6 Hz and RMS reference voltage of 12 V are the assumed input parameters for the SA mode. Inverter output power for this operation is 1.19 kw. As soon as the grid voltage is available, then the inverter gets connected to the utility grid Steady State voltage & current in SA ILoad (2 A p) Vload V/I (units) Time (s) Figure Steady state load voltage and load current with 2 A peak magnitude. 185

206 Implementation of the Proposed Transition Control during Transition Mode GC to SA mode Both the voltage and current regulators perform well and produce sinusoidal voltage and current waveforms in GC and SA modes. The transition operation from GC to SA is presented in Fig Initially, the inverter runs in the current control mode during GC mode, the inverter controller immediately transitions into the voltage control mode when the grid gets off. The condition of the grid is determined by checking if is in range or not. A DSP controls the connection switch to disconnect the inverter from the grid to enable SA mode of operation. The output voltage of the inverter is 12V (RMS) where the load current is 1 A (peak). The transition is seamless except for a minor increase in the load voltage. Switch status OFF NO Grid is connected through the switch Grid is disconected through the switch Voltgae (V) Time (s) (a) Inverter output voltage GC SA Time (s) (b) Load Current Current (A) Time (s) (c) Figure Transition from GC mode to SA mode. (a) Switch status; (b) Inverter voltage and (c) Load current. 186

207 SA to GC Mode - The most challenging event is the transition from SA to GC mode of operation. Initially, the inverter runs in the voltage control mode. The time that is required to wait before connecting into the grid is prescribed by the standards. During this wait time, the inverter adjusts its phase to the utility. Current (A) 5 Load current Grid current Time (s) 2 Current (A) SA GC (a) Voltage (V) Voltage (V) Phase adjustment Relay ON Time (s) Grid voltage 4 Grid available 2-2 Current is injected to the grid Time (s) Time (s) (b) 5 Inverter output voltage SA GC Figure 5.19.(a) Transition from SA to GC mode. (b) Detailed view of transition from SA to GC mode. The inverter waits for the zero crossing of the utility voltage to command the switch to be turned on. In practical cases, the switch has 4 electrical cycles of delay. So the inverter 187

208 runs in SA mode during the switch connection time. In order to have better transition during the switch connection time, the inverter runs in the current control mode with the command current set at the same value that was in producing the correct magnitude of inverter output voltage. As shown in Fig. 5.2, the inverter output and the utility voltages are in phase when the relay is turned on. When the switch is connected, the inverter continues to operate in the current regulation mode. V/I (units) Load voltage & inverter voltage when relay is turn ON Phase match between Vg Vg & Vload Grid is connected Vload Iinv -2-3 Relay turn ON time turn ON comamand for relay and current regulation starts Time (s) Figure 5.2. Inverter phase adjustment to grid during SA to GC transition mode. Voltage (V) Inverter voltage and the grid voltage Frequency change to match the phase Phase match Time (s) Vg Vinv Figure Grid voltage, load voltage and inverter output current during SA to GC transition mode. 188

209 System frequency (Hz) Frequency change during the phase adjustment Time (s) Figure Inverter output voltage frequency during SA to GC transition mode. Figure THD analysis of inverter output voltage during SA to GC transition: (a) using smooth frequency variation method and (b) using abrupt frequency variation method. The phase adjustment of the inverter during the transition period is shown in Fig The transition is seamless and there is not any disturbance in the inverter output current. The inverter frequency is smoothly varying from 6 Hz to 59.2 Hz and then again going back to 6 Hz, as shown in Fig. 5.22, during the transition period. Fig shows the THD analysis of inverter voltage for both the transition methods. The THD of the output voltage is 1.9% for smooth frequency variation algorithm and it is 2.98% for the abrupt frequency variation algorithm which also agree with the simulation results. 189

210 5. 5. Experimental Results of VSIs in Microgrid using Dispatch Unit The proposed topology and control method are tested on a laboratory setup having four of 5 kw VSIs, local loads are connected at the PCC. Two of the inverters work as DG unit 1 and DG unit 2, one of the inverter is used as the grid and the forth one is used as a dispatch unit. The control algorithms have been implemented using BF56F and TMS32F28335 digital signal processors. The transition control operations are tested and presented as following VSIs Operating in SA Mode Two inverters and a dispatch unit deliver 18 A, 2 A and 18 A of current respectively to the PCC where the local load takes 36A at 12 V (RMS), as shown in Fig In respect of power the local load takes 3.6 kw where unit 1 and unit 2 deliver 1.15 kw, 1.3 kw respectively and the dispatch unit provides the rest of the power. Here unit 1 and unit 2 Unit 1 2 Dispatch Unit Current (A) 1-1 Current (A) 1-1 Current (A) Unit Time (s) V/I (units) Voltage at PCC and Load Current V PCC 1-1 I Load Time (s) Figure Inverters current, dispatch unit current, voltage at PCC and the load current in SA mode. 19

211 2 run in droop control and dispatch unit runs in current control. The inductor values of unit 1, unit 2 and the dispatch unit are 2.95 mh, 2.8 mh, 2.66 mh respectively. The DC bus voltage of unit1, unit 2 and the dispatch unit are around 23 V, 222V, 22V respectively and 33 Ω is manually set by the resistive bank. The gains of the droop controller and the current controller are same as the simulated results VSIs Operating during GC Mode A grid interfaced microgrid system with two inverters, a dispatch unit and local loads are connected at PCC, as shown in Fig in GC mode. As the local load requires 42 A at 12V (RMS), unit 1, unit 2, dispatch unit and grid provide 12 A, 12 A, 1A and 8A respectively to the system. 2 Unit 1 Current (A) Current (A) Unit Figure Inverters currents at PCC in GC mode. 191

212 2 Dispatch Unit Current (A) Grid 1 Current (A) 5-5 V/I (units) VSIs during Transition Mode GC to SA mode Voltage at PCC and Load Current V PCC ILoad Time (s) Figure Dispatch unit current, grid current, voltage at PCC and load current in GC mode. This experimental test starts with GC operation, where grid, DG units provide 2.2 kw to the loads. After the grid becomes unavailable at 1.14 sec, the dispatch unit takes the grid s responsibility to provide power as shown in Fig At 1.14 sec the grid goes off, the dispatch unit then provides 5 A current at 12 V. The current taken by the loads and PCC voltage are not disturbed throughout this operation as shown Fig

213 5 Unit 1 1 Grid Current (A) Current (A) Unit Dispatch Unit Current (A) Current (A) Time (sec) Figure Inverters current, grid current, dispatch unit current from GC to SA. 2 Microgrid Voltage and load current Grid off Time (sec) V/I (units) 1-1 i Load Time (sec) Figure Microgrid voltage at the PCC point and the local load from GC to SA. The Dispatch unit also can push the power to the system in the normal operating condition and provides the necessary power to the system during transition, as shown in Fig Experimentally in GC mode unit 1, unit 2, grid and dispatch unit provide 8 A, 7 A, 11 A and 8 A respectively. When the grid goes off, the dispatch unit increases its output current to 18 A and remains stable for some electrical cycles and then gradually decreases its current flow to 1 A within 15 sec, as shown in Fig The dispatch unit 193

214 output current can be set to any value by the current controller. During the transition, the load does not feel any disturbance, as shown in Fig The load takes 35 A current in all modes of operation which is the main concern of our research work. 2 Unit 1 Current (A) Current (A) Current (A) Current (A) Unit Grid Dispatch Unit Time (s) Figure Inverters current, grid current and dispatch unit current from GC to SA mode. 194

215 4 Local Load Current (A) Figure 5.3. Local load takes 35 A current during the entire modes of operation SA to GC Mode Local Time Load (s) 4 Current (A) Time (s) The two of DG units work in SA mode with the dispatch unit operating in idle condition. After the grid becomes available at 1.2 sec, the dispatch unit starts increasing its output power, as the other two DG units gradually decrease their power flow through their droop controllers. Figure 5.31 show the individual currents of the inverters, grid and load throughout the operation. When the phase of the microgrid voltage and the grid voltage match, the dispatch unit sends a high signal to the switch to connect the grid to the PCC. Grid and PCC voltage and the microgrid operating frequency are shown in Fig Throughout this process, the frequency of the microgrid is brought to 6 Hz from 59 Hz and synchronized to the grid, as shown in Fig At zero crossing, the dispatch unit commands to the switch to connect the grid. 195

216 2 Unit 1 Current (A) Unit 2 2 Current (A) Dispatch Unit 1 Current (A) Grid 2 Current (A) Time (sec) Local load 4 Current (A) Time (sec) Figure Currents of the inverters, dispatch unit and grid during SA to GC mode transition. 196

217 2 Grid and Microgrid Voltage V/I (units) Grid Microgrid Time (ms) Figure Synchronization of the microgrid with the grid during SA to GC transition. Frequency (Hz) Phase Matching Microgrid Frequency Synchronize with grid No. of Samples (N) Figure Operating frequency of the microgrid during SA to GC operation. In the next experiment, we try to verify that the dispatch unit can provide power to the system in normal operation and the slight fluctuation (around 1%) of the DC bus voltage of the inverters does not affect the system performance during transition. Figure 5.33 shows the DC bus voltages of unit 1 and unit 2 where = 235 V and varies from 22 V to 23 V during transition. The experiment starts in SA mode where two inverters and dispatch unit push 15 A, 18 A and 5 A respectively to the local load. After a while, the grid becomes available and the dispatch unit increases its output current from 5 A to 15 A, as shown in Fig As the load remains constant the other inverters reduces their power flow, according to the droop equation which can be observed in Fig

218 Voltage (V) Voltage (V) DC voltage of Unit DC voltage of Unit Figure The DC bus voltage of unit 1 and unit 2, where fluctuation. has 1% voltage 2 Unit 1 Current (A) Current (A) Unit Time (s) Figure Inverters current during SA to GC mode transition. When the phases are matched, the dispatch unit sends a high signal to the switch and the switch gets connected. As soon as the grid gets connected the value of the commanded current of the current controller is changed to a new value of 5 A. As the 198

219 loads demand is constant, the grid starts to push the same amount of current to the system. In GC mode two units run in droop control and the dispatch unit runs in current control. 2 Dispatch Unit Current (A) Current (A) Voltage (V) Grid Voltage at PCC Local Load 4 Current (A) Time (s) Figure Dispatch unit current, grid current, voltage at PCC and load current from SA to GC mode. 199

220 2 Unit 1 Power (kw) Experimental results Simulation results Unit Power (kw) 1.5 Experimental result Simulation result Local Time Load (s) 3.5 Power (kw) Simulated Results Experimental Results Time (s) Figure Comparisons between the simulation and experimental results of inverters currents, and load current during transition mode. Figure 5.37 shows the comparison between the inverters currents and the load current during transition mode. The local load demands 3.45 kw, which is supplied by the two inverters, the grid and the dispatch unit. 2

221 5. 6. Experimental Results of VSIs in Microgrid using Hybrid Control Technique Two of 5 kw inverters, 4V DC supply unit, 12 V AC and one inverter working as a simulated grid have been used for experimental verification of the proposed hybrid control algorithm. The control algorithms have been implemented using TIDSP28335 DSP from Texas Instruments. The ADC sampling, and PWM switching rates are kept at 2 khz. The values of the inductors are 2.85 mh, 2.8 mh, 2.7 mh. The gains of the inverters have been kept same as the simulated once. The system has been tested for both the GC to SA and SA to GC and also SA and GC mode transition modes VSIs Operating in SA Mode using Hybrid Control Technique 4 Unit 1 Current (A) Unit 2 4 Current (A) 2-2 V/I (units) Voltage at PCC and Load Current Time (s) Figure Inverters current, voltage at PCC and load current in SA mode. 21

222 Figure 5.38 shows that the two inverters push individually 25 A and 2 A individually at 12 V (RMS) in SA mode. The value of the resistive load is set to 3.77 Ω. The system frequency is 59 Hz, according to the droop equation GC Mode of Operation using Hybrid Control Technique In GC mode, unit 1 delivers 15 A and unit 2 deliver 8 A according to the current command as the weighted factor of the current controller of the hybrid controller becomes 1. As the load requires 33 A, the rest of the power is provided by the grid, as shown in Fig Unit 1 Current (A) Unit 2 1 Current (A) Time Grid(s) Current (A) 5-5 Voltage (V) Voltage at the PCC Time (s) Figure Inverters currents, grid current and voltage at PCC in GC mode. 22

223 Hybrid Controller Performance during Transition Mode GC to SA Mode - Figure 5.4 shows the output currents of unit 1, unit 2 and the grid current during GC to SA transition mode. Initially, Inverter 1, Inverter 2 and the grid deliver 12 A, 1 A and 16.5 A respectively to the local load. At 2.77 sec the grid goes off and the controllers of the inverters gradually decrease the weights on the current control and increase weights on the droop control and share the required load current. During the transition, the load suffers with small fluctuation which is within the tolerable range. But 2 Inverter 1 Current (A) Current (A) Current (A) Inverter Grid Time (s) Figure 5.4. Inverters currents and grid current during GC to SA. 23

224 Frequency (Hz) 61 GC Microgrid frequency SA Weights 1 k 2 k 1 Units (V/A) Time (s) Figure Microgrid frequency, the output coefficients behavior, the load voltage and current from GC to SA mode. the main contribution is that during transition the inverter can change its controller from current control to droop control by using the hybrid control technique without having any communication network Samples (N) Microgrid & Load V I L Grid OFF Figure 5.4 shows the microgrid frequency and weights during GC to SA. The data has been taken from the microcontroller. Initially, in the grid connected mode, the system frequency is 6 Hz. When the grid is OFF, the system frequency decreases and the value of k 2 of the inverter increases which bring the droop controller in action. In the SA mode 24

225 the system frequency is 59.7 Hz. The microgrid voltage and the load current during transition from GC to SA mode, is shown in Fig There is a small voltage fluctuation at the PCC point during transition. 4 Unit 1 Current (A) Current (A) Unit Grid Current (A) 1-1 Voltage (V) Voltage at PCC Time (s) Figure Inverters currents, grid current, voltage at PCC from GC to SA mode. Figure 5.42 shows the inverters current, the grid current and voltage at PCC from GC to SA mode considering long duration of the time scale where unit 1 and unit 2 provide 25

226 1 A and 16 A current in GC mode. As the load requires 4 A current the grid provides the rest of the power SA to GC Mode - The two VSIs in the microgrid system run in islanded condition 2 Inverter 1 Current (A) Inverter Current (A) Grid 1 Current (A) Local load 4 Current (A) Time (s) Figure Inverters currents, grid current and the load current during SA to GC. 26

227 using the droop based control by the hybrid controller. The grid becomes available at 2.9 sec. The grid becomes available with a different phase from the system voltage. As the system runs with different frequency, the phase of the grid voltage and the system voltage will match. The switch will connect the grid at the PCC. The grid then also starts pushing some power to the load and the inverters gradually decrease their power. The overall system frequency will be 6 Hz. Figure 5.43 shows the inverters current, grid current and load current from SA to GC transition. Inverter 1 and inverter 2 push 1 A and 12 A current simultaneously. At 1.6 sec the grid becomes available, then the switch waits for some time to match the phase of the grid voltage and the microgrid voltage, and connects the grid at 2.5 sec. The grid then starts pushing some power to the local load. The other two inverters gradually decrease their power. The power taken by the local load remains constant during the transition. The same experiment has been repeated again with the variation of the DC bus voltage. 25 DC Bus Voltage of Unit 1 Voltage (V) DC Bus Voltage of Unit 2 Voltage (V) Time (s) Figure The wave shape of the DC bus voltage of unit 1 and unit 2. 27

228 2 Unit 1 Current (A) 1-1 Current (A) Unit Grid Current (A) Local Load Current (A) Time (s) Figure Inverters current, grid current and load current during SA to GC mode. Unit 1 and unit 2 push 19 A and 18 A current at 12 V (RMS) respectively to the local load. The DC bus voltage of unit 1 is changes from 238 V to 246 V and the other unit s voltage is 234 V, as shown in Fig When the phase voltage of the grid and the system is matched, then at zero crossing the grid is connected to the PCC by the switch. The two units smoothly switch their controller from droop control to current controller by 28

229 the hybrid controller as discussed before and push the commanded current of 1 A and 18 A current separately, as shown in Figure Power (kw) Unit 1 Simulation result Experimental result Unit 2 Power (kw) Simulation result Experimental result Grid 1 Power (kw) Simulation result Experimental result Power (kw) Local Load Simulation Result Expimental Result Time (s) Figure Comparison between the simulation and experimental results of VSIs in microgrid using hybrid control technique. 29

230 5. 7. Conclusion In this chapter, experimental results have been presented to verify the simulation results of Chapter II, III and IV simultaneously. First the hardware setup of the single line diagram of the prototype microgrid system has been developed. Secondly, four of 5 kw bidirectional inverters have been built in the Alternative Energy Lab of the University of Akron and the proposed control algorithm for transition of the individual inverter has been tested and presented for SA, GC and transition modes of operations. Third, the proposed smooth transition technique of the parallel inverters in the microgrid system using a dispatch unit but without having any communication network has been experimentally tested. Fourth, an alternative transition technique with poor wave shapes during transition mode have been tested, as described in Chapter IV. In all the cases the experimental results shows good agreement with the simulation results. 21

231 CHAPTER VI CONCLUSION AND FUTURE WORK Summary This dissertation presents an analysis of a single phase grid-tie inverter as well as the microgrid with paralleled power conditioning VSIs operating in the GC mode, SA mode, and transition mode, and tries to solve the complexity of the system during the transition time with better performance. In Chapter II, the controller design of a single inverter in both GC and SA modes are discussed. For GC mode, a dq axis current controller with PI controller and a phase lock loop (PLL) has been developed. For SA mode, a droop control and RMS voltage control is developed. In transition mode, a smooth frequency variation control technique for VSI has been developed and its performance is compared with the other existing techniques. In Chapter III, a smooth transition control strategy has been proposed for VSIs operating in microgrids. In both GC and SA modes of operations, the VSIs use the droop control method to regulate the real power flow without the need of any external communication between them. One of the DGs working in the microgrid system is designated as a dispatch unit to facilitate interconnection with utility grid and achieve smooth transition between the modes of operations. During the transitions, the dispatch unit takes extra responsibility and ensures the continuous power delivery to the load. For smooth transition from GC to SA, the dispatch unit compensates for the grid current 211

232 immediately after the transition and makes the other sources share that current gradually. The dispatch unit also adjusts its output power to make the transition from SA to GC mode as that power affect the frequency through the droop control. In Chapter IV, an alternative transition technique between SA and GC modes has been proposed without having a dispatch unit. During transition, both current control and droop control participate in formulating the inverter output voltage, but with different weights or coefficients. The controller, referred as to a hybrid controller, varies the output coefficients of the current and droop control depending on the system frequency variation to regulate the real power flow. Major contributions of the research can be summarized as follows: - 5 kw bidirectional inverter development A bidirectional inverter is designed and implemented with the L type filter which successfully operates in GC, SA and transition modes without any hardware modification. Design and implementation of PLL, current controllers, and voltage controllers on experimental hardware. Implementation of bidirectional power control operation. Development and implementation of a smooth frequency variation technique providing better performance during the transition mode for an independent inverter connected to a grid at a single point of connection. 212

233 - Development of an autonomous 2 kw microgrid system with a dispatch unit technique for proper transition between GC and SA modes Experimental development of a microgrid system with two inverters, dispatch unit and a grid simulator. Implementation of droop controllers for VSIs operating in SA and GC modes. Theoretical modeling of the microgrid system to determine the stability analysis of the proposed technique. Experimental implementation of a dispatch unit concept to verify the effectiveness of the proposed transition control technique. - Development of a 2 kw microgrid system which does not need a dispatch unit or communication network but can perform well in transition mode Development of a new controller, referred to a hybrid controller, which can identify the modes of operation and regulate the power flow. Theoretical modeling of a microgrid system with the hybrid controller for VSIs to determine the stability of the system. Experimental implementation of the control technique in a microgrid system with two inverters, and a simulated grid. The comparison of the proposed an existing control technique is provided in Table 6.1. Overview of the proposed and existing control techniques for 2 kw microgrid system. 213

234 Table 6.1: Performance comparison of the recent methods and the two proposed methods. Decentralized Microgrid ([58]) Master-slave based Microgrid ([6]) Dispatch Unit based Microgrid (Chapter III) Hybrid Control based Microgrid (Chapter IV) Communication Network Not Applicable High Low Not Applicable Power Quality during transition mode 7 electrical cycles needed to provide stable power supply. 1 electrical cycle needed to provide stable power supply. 1 electrical cycle needed to provide stable power supply. 3 electrical cycles needed to provide stable power supply. Installation Cost For 2 kw system the four inverters require $12 (assumption has been consider depending on the installation of our microgrid system). For 2 kw system the CAN Bus network and the four inverters require $15. For 2 kw system the four inverters and another extra inverter will require $14. For 2 kw system the four inverters require $ Outline of the Future Research We can implement the hybrid controller for the VSIs and a dispatch unit operating with droop control method in the microgrid system for proper transition control. This combined method has some advantages. First, the VSIs do not require any communication network as before. Second, the droop control of the dispatch unit compensates the grid current automatically. Therefore, no grid current sensor is needed for the dispatch unit. Third, in GC mode, as VSIs run in current control mode by the 214

235 hybrid control method, better power control can be achieved. Fourth, the dispatch unit can operate as a source in a microgrid which cannot be achievable with the method proposed in Chapter III. This functionality adds an extra level of reliability. The proposed system architecture is shown in Fig Droop Control Grid Synchronization v g V dc Z 3 PCC i dispatch P 1, Q 1 V s1, δ 1 P l, Q l P 2, Q 2 V s2, δ 2 SW grid connection Zg 2 V dc Z 1 Hybrid Control Local Loads V dc Z 2 Hybrid Control v g Figure 6.1. Considered microgrid system. 215

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245 APPENDICES 225

246 APPENDIX A SIMULINK CONTROL BLOCK A. 1. Utility Interactive Single Phase Inverter Figure A.1. Simulated block diagram of the single phase utility interactive inverter which can operate in GC, SA and transition modes. 226

247 Figure A.2. Simulink blocks of the dq axes current controller. Figure A.3. Simulink blocks of a Phase lock loop control. 227

248 A. 2. Microgrid System using Dispatch Unit Concept Figure A.4. Simulink control blocks of an overall microgrid system using dispatch unit technique. 228

249 Figure A.5. Simulink blocks of the droop controller. Figure A.6. Simulink blocks of a current controller for a dispatch unit. 229

250 A. 3. A Microgrid System Where VSIs Use Hybrid Control Technique Figure A.7. Simulation blocks of an microgrid system where VSIs operate with hybrid controller. 23

251 Figure A.8. Simulink blocks of the droop controller. Figure A.9. Simulink diagram of the dq axes current controller Figure A.1. Simulink block for the PWM generator of the hybrid controller. 231

252 APPENDIX B PCB LAYOUT Figure B.1. Components position for the interfacing board of a VSI. 232

253 Figure B.2. Routing on the top layer of the interfacing board of a VSI. 233

254 Figure B.3. Routing on the inner 2 layer of the interfacing board of a VSI. 234

255 Figure B.4. Bottom layer of the interface board of a VSI. 235

256 Schematic Diagram of the Interface Board APPENDIX C SCHEMATIC DIAGRAM Figure C.1. Voltage sensor circuit. 236

257 Figure C.3. Current sensors of a VSI. 237

258 Figure C.4. External current sensors of a VSI. 238

259 Figure C.5. Schematic diagram of a DC voltage and temperature sensor. 239

260 Figure C.6. Schematic diagram of a fault circuit diagram of a VSI. 24

261 Figure C.7. Schematic diagram of a buffer circuit diagram. Figure C.8. CAN circuit diagram of a VSI. 241

262 Figure C.9. DSP Terminal block. Figure C.1. Connector for the Interface board and the power module. 242