A Nested Control Strategy for Single Phase Power Inverter Integrating Renewable Energy Systems in a Microgrid A.Chatterjee Department of Electrical Engineering National Institute of Technology Rourkela, India contactaditi247@gmail.com K.B. Mohanty Department of Electrical Engineering National Institute of Technology Rourkela, India kbmohanty@nitrkl.ac.in Abstract In this paper a nested power-current-voltage control scheme is introduced for control of single phase power inverter, integrating small-scale renewable energy based power generator in a microgrid for both stand-alone and grid-connected modes. The interfacing power electronics converter raises various power quality issues such as current harmonics in injected grid current, fluctuations in voltage across the local loads, voltage harmonics in case of non-linear loads and low output power factor. The proposed nested proportional resonant current and model predictive voltage controller aims to improve the quality of grid current and local load voltage waveforms in grid-tied mode simultaneously by achieving output power factor near to unity. In stand-alone mode, it strives to enhance the quality of local load voltage waveform. The nested control strategy successfully accomplishes smooth transition from grid-tied to stand-alone mode and vice-versa without any change in the original control structure. The performance of the controller is validated through simulation results. Keywords Microgrid, stand-alone mode, grid-connected mode, voltage harmonics, current harmonics, proportional resonant control, model predictive control. I. INTRODUCTION Nearly 6% of the power generation sector is contingent on fossil fuels. The fossil fuel reserves are depleting at an alarming rate and it is expected that the price of fuels will be sky-scraping in near future. Moreover, excessive burning of fossil fuels has raised serious environmental issues such as air pollution and global warming. Hence, the focus is shifting towards the use of renewable energy sources (RES) such as wind, solar, fuel-cells, geo-thermal etc. for electricity generation. With the increasing population, the electricity demand is escalating. To meet the growing demands two options are available one is to expand the existing transmission corridors and the other is to embed the generation plant in the distribution system. The earlier option has certain constraints but the later solution seems to be more convincing. So, the power generation plants based on RES are embedded in the 978--4799-4-3/4/$3. 26 IEEE distribution system, and are called as distributed generation (DG) plants or embedded generators (EG). But the RES are highly intermittent in nature and add complexity to normal grid operation. An emerging concept, known as the smart grid enables the RES based power plants to transmit power to the public grid as well as meet the local load demands. It facilitates two way communication between the grid and the customers. The smart grid exists in synergy with the existing utility grid, making it more secure, efficient, reliable and environment friendly. The smart grid evolves through integration of certain basic structures called as microgrid []. Microgrid is an integrated network of DG, loads and energy storage devices. Small scale RES based plant embedded in microgrid are called microsources. The microsources are interfaced with the grid through power electronics converters (PEC) to convert the generated power into the required form which is compatible with the grid [2, 3]. A microgrid can operate in both grid-connected and standalone mode i.e. separated from the main grid. In grid-tied mode the objective of the control strategy is to monitor the active and reactive power exchange between the grid and the microsource, achieve a high output power factor near to unity and reduce harmonic pollution of the current injected by the inverter into the grid and local load voltage at the same time. In off-grid mode, the objective of the controller is to maintain constant voltage across the load and reduce the output voltage total harmonic distortion (THD) [4]. In [] a seamless transfer strategy for single phase grid tied inverter between grid-connected and stand alone modes is proposed. Where a proportional integral (PI) voltage controller regulates the load voltage in off grid mode and a hysteresis current controller controls the grid current in grid tied mode. But the lacuna of the scheme is that, when the grid current controller and load voltage controller is switched between two operation modes, it causes voltage or current spikes which is not desirable. In [6] the authors implemented a model predictive control strategy for three phase inverters in renewable power generation applications for both islanded and
grid-connected operations. But here a separate resynchronisation scheme is introduced to achieve smooth grid connection. The prerequisite is to introduce a control scheme for RES based generators in microgrid, which can reduce the harmonic pollution in local load voltage and improve the injected grid current waveform quality at the same time and can also achieve flawless transfer of operation modes from grid connected to off grid and vice-versa. II. PROPOSED CONTROL SYSTEM STRUCTURE In the system shown in Fig., the RES based plant is replaced by a fixed dc source and the dc link voltage is assumed to be constant. The dc-link voltage control is not demonstrated in this paper. The H-bridge voltage source inverter (VSI) interfaces the RES with the grid through a LCL filter. The filter design method for grid-tied converter is detailed in [4]. A nested control structure is proposed for the system. The outermost is the average power controller cascaded by the current controller. The inner voltage controller generates switching pulses for the inverter. Two control variables are required to control the active and reactive power of the system independently. Hence, grid voltage is delayed by one-fourth period to generate a fictitious signal orthogonal to the original signal. The phase locked loop unit detects the phase angle of the grid voltage. The grid voltage signals in α-β frame are transformed to d-q frame by coordinate transformation using () and (2). As the dc-link voltage is assumed to be constant, the active and reactive power references are given as input commands. Otherwise, an outer voltage control loop used to regulate the dc link voltage generates active power reference. The average power controller calculates the active and reactive current references by (3). vgd = vgα sinωt vgβ cosωt () vgq = vgα cosωt vgβ sinωt (2) ref i d 2 vgd vgq Pref = ref i v q vgd v gq gq v gd Q ref ( ) Where and are the active and reactive current references which controls the active and reactive power of the system respectively. The current references are used to generate a reference current synchronized with the grid voltage (4). ref ref iref = id sinθ iq cosθ (4) The grid current is sensed and compared with the synchronized reference current and the error is processed by the proportional resonant current controller (PRCC). The current controller generates reference voltage signal for the voltage controller. The output voltage across the filter capacitor is sensed and compared with the reference voltage. The model predictive voltage controller (MPVC) minimizes the voltage error and generates switching pulses for the inverter without a pulse width modulator (PWM). (3) H-Bridge DC Source VSI - Vu MPC Voltage Controller S-S4 Vcref Vi PR Current Controller Fig.. Proposed control system structure ev - Vc Vg α αβ Li if V g Delay dq III. CONTROLLER DESIGN As explained in the previous section the average power controller generates reference signal for the current controller. While designing the current controller only the L part of the LCL filter is considered as the plant and LC part is taken for designing the voltage controller. Since, the inner voltage control loop is faster than the outer current control loop, the outer current loop can be designed under the assumption that the inner loop has attained steady state. A. Design of Model Predictive Voltage Controller The development of model predictive control (MPC) scheme dates back to late seventies when it was first applied in chemical process industries. The term MPC does not describe a specific control technique but it includes a wide range of control methods and implementation. The application of MPC strategy in the area of electrical drives and PEC is more recent [7-]. The MPC application for control of power converter takes into account the discrete nature of PEC. The discretized system model is used to predict the future values of states of the system until a time horizon. A cost function is used to optimize the error between the reference and predicted values of states in order to obtain desired output. Basically, implementation of MPC scheme involves a huge amount of computational time when the optimization problem is solved online for systems with large time constants like in process industries. But application of MPC strategy for control of PEC does not engross much computational burden, because the power converters have finite number of switching states. The schematic diagram of MPVC scheme is shown in Fig.2. A single phase H-bridge inverter model consists of four switches S -S 4, hence four switching states which are possible are tabulated in Table I. The inverter output voltage v o can be associated with the switching state S as in (). Where v dc is the dc-link voltage of the VSI. The consequent four voltage levels obtained are tabulated in Table II. vo = vdcs () il ic θ Vg β V gd V gq Local load ei Breaker i o - i ref ( ) Lg Grid ref i d io V g Synchronized reference current generation ref i q Φ PLL ref i d 2 Vgd VgqPref = ref i V q Vgd V gq gq V gd Q ref Q ref P ref θ
Fig. 2. Block diagram of MPVC scheme TABLE I. SWITCHING STATES OF THE INVERTER S a = {, if S ON and S 2 OFF S a = {, if S OFF and S 2 ON S b = {, if S 3 ON and S 4 OFF S b = {, if S 3 OFF and S 4 ON TABLE II. VOLTAGE LEVELS GENERATED BY THE INVERTER S a S b Voltage level V V = V = V dc V 2 = -V dc V 3 = In off-grid mode, the aim of the voltage controller is to establish a stable voltage across the load. The dynamics of the system can be represented by the following equations (6)-(8). di f vo = vc Li dt (6) dvc if = il (7) dt Where v o and v c are the voltage across the inverter output and capacitor respectively. i f and i l are the filter inductor and load current respectively. The system equations can be representated in state space as: dx Ax Bvo Bqil dt = (8) Where i f x =, v c L i A =, C f B = L i, B q = C f To implement the MPVC scheme for this system, the system model has to be discretized. The continuous time state space system (8) can be discretized for a sampling time Ts by (9). x( k ) = A x( k) B v ( k) B i ( k) (9) Where, Ad H-Bridge DC VSI Source - AT s = e, Switching(S-S4) d d o qd l T s Li Vc(K) Predictive Minimization Model of Cost function Vc ref(k) (From Current Controller) Local load Aτ Bd = e Bdτ, T s Aτ Bqd = e Bqd By using Taylor series expansion () is obtained: if MPC Voltage Controller il ic Vc(K) if(k) Breaker Lg Grid io τ 2 ( ) ( ) AT AT s s ATs ATs e =... ()! 2! n! As the sampling time Ts is very small, () can be approximated as (). AT e s AT s () The predicted value of voltage across capacitor at (k) instant is given by (2). Ts/ T / ( ) s C C f f e Ts c = c f o l L v ( k ) v ( k) e i ( k) v ( k) i ( k) (2) For voltage prediction the load current is not measured, rather it is calculated from filter inductor current using (3). C f il( k ) = if ( k ) ( vc( k) vc( k ) ) (3) Ts As the sampling time is very small i.e. µs, the load current at (k-) instant can be considered approximately equal to k-th instant current as in (4). il( k) il( k ) (4) A cost function is defined as square of difference between the reference and predicted capacitor voltages and is expressed in orthogonal coordinates as in (). The central goal of the cost function is to control a particular system variable by minimizing the error between the reference and predicted value. ref p ( ) 2 ref p ( ) 2 α α β β gv = vc vc vc v () c Where and are the real and imaginary parts of the reference capacitor voltage vector, are the real n and and imaginary part of the predicted capacitor voltage vector v c (k). Since the sampling frequency is quite high, the reference voltage at (k) instant is considered equal to k-th interval voltage vector. The future value of capacitor voltage vector is predicted for each of the four switching states. The cost function evaluates error between the reference and predicted value of voltage. The switching state for which the cost function is minimized is selected for converter switching. B. Design of proportional resonant current controller The Proportional resonant (PR) controller is a new breed of controllers which has gained ample recognition in recent years for single phase grid tied RES based plants. The major benefit of PR controller is that the controller is designed in stationary reference frame, hence the requirement of coordinate transformation is eliminated unlike the conventional PI controllers. Moreover, this control strategy is successful in achieving perfect sinusoidal reference signal tracking [-3]. During design of the current controller, it is assumed that the voltage controller is in steady state, hence only the grid side inductance is considered as the control plant. From Fig. it can be observed that as the voltage loop attains steady state (6) is obtained.
vcref = (6) vc vc = vg vi (7) From (7) it is proved that v i, is the voltage drop across grid inductor L g and v g is the base local load voltage for inverter. Same value of v g appears across both side of grid inductor. So the grid voltage feed forward can be discarded during the design process. From Fig. it can be observed that the reference current synchronized with the grid voltage (4) is compared with the measured grid current and the PR current controller minimizes the current error and generates reference signal for the voltage control loop. The transfer function of an ideal PR compensator is given by (8). 2ks i Gipr () s = kp (8) s ω Where k p and k i are the proportional and integral gains of the controller respectively and is the grid frequency. From the frequency response of ideal PR compensator, it is observed that the gain becomes interminably high at the resonant frequency and much lower at other frequencies [3]. Hence, a damping factor is introduced to diminish the gain and enhance the bandwidth of the controller. The transfer function of nonideal PR controller with the damping term is mentioned by (9). 2kiωcs Gnpr () s = kp (9) s 2ωc s ω The performance of the controller depends on three parameters k p, k i and ω c which is the damping frequency. To achieve desired response the controller parameters are tuned by performing frequency response analysis. The corresponding value of k p, k i and ω c used for simulation are 2, and respectively. The resonant term acts as integrator for sinusoidal signal. To obtain zero steady state error and track the reference current signal effectively the PR controller introduces very high gain at the resonant frequency (grid frequency). IV. SIMULATION RESULTS AND ANALYSIS To assess the performance of the proposed nested control strategy a single phase VA grid tied VSI with a local load is simulated using Matlab/Simulink software. The simulation parameters are tabulated in Table III. The performance of the proposed nested controller is assessed under different operating scenarios. TABLE III. SIMULATION PARAMETERS Parameters Values Grid voltage (v g ) 22 V (rms) Grid frequency Hz DC link voltage (v dc ) 36 V Grid side filter inductance (L g ).8 mh Inverter side filter inductance(l i ).8 mh Filter capacitance (C f ) 3.3 µf Resistive load 93.6 Ohm Diode bridge rectifier load C = 47 µf, R=38 Ohm Switching frequency (f sw ) khz A. Steady State Operation in Grid-Tied Mode In steady state during grid tied mode the inverter powers a 2 W local load and injects 7 W of power to the grid. The proposed control strategy aims to achieve a high output power factor near to unity and reduce the THD value of grid current and local load voltage. The active power reference P ref is set equal to 7 W and the reactive power reference Q ref is zero. Correspondingly the active and reactive current references are 4.82 A and zero respectively. From Fig. 3(a), it is observed that with a resistive load the grid current is aligned with the grid voltage and load voltage is also stable. The output power factor is calculated to be.98. The THD value of load voltage is 2.% and.99% for grid current as observed from Fig. 4(a) and (b). Similar simulation study is carried out with a diode bridge rectifier load which introduces voltage harmonics. It is shown in Fig. 3(b),that the voltage across the non-linear load is stable and aligned with the grid voltage. It is observed from Fig. 4(c) and 4(d) that the controller is able to obtain a THD of 2.32% in case of load voltage and 3.38% in case of grid current which is less that %. 2-2.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 Fig. 3(a). Steady state grid voltage, load voltage and grid current waveforms with resistive load 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 2 -.2.4.6.8..2.4.6.8.2 Fig. 3(b). Steady state grid voltage, load voltage and grid current waveforms with non-linear load.3.2. Fundamental (Hz) = 3., THD= 2.% 2 4 6 8 2 4 6 8 2 (a) Load voltage with resistive load.8.6.4.2 Fundamental (Hz) = 3., THD= 2.32% 2 4 6 8 2 4 6 8 2 2 4 6 8 2 4 6 8 2 (b)grid current with resistive load (c)load voltage with non linear load (d)grid current with non linear load Fig. 4. THD values of voltage and current waveforms in grid connected mode Mag (% of Fundamental) grid current Mag (% of Fundamental) grid current.8.6.4.2.8.6.4.2 Fundamental (Hz) = 4.83, THD=.99% Fundamental (Hz) = 4.89, THD= 3.38% 2 4 6 8 2 4 6 8 2
B. Steady State Operation in Stand Alone Mode During grid failure, the breaker opens and the grid is detached from the RES plant. In that case, the plant only powers the local loads and there is no power exchange with the grid. Hence, current controller is not active during stand-alone mode only the voltage controller is active. The active and reactive power references are set to zero. The voltage controller reference is set equal to the grid voltage, to achieve grid synchronization during transfer of operation modes. The voltage error is processed by the MPVC controller and it generates pulses for the inverter to minimize the error. From Fig. (a) and (b), it can be observed that local load voltage is stable without any dynamics and tracks the reference voltage i.e. the grid voltage waveform effectively in case of resistive and non-linear loads respectively.. The THD value of load voltage with resistive and non-linear loads are 2.3% and 2.8% as demonstrated in Fig. 6(a) and 6(b) respectively. Filter Current (A) 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 2-2.2.4.6.8..2.4.6.8.2 Time (sec) Fig. (a). Steady state grid voltage, load voltage and filter current waveforms with resistive load Vg(V) 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 Fig. (b). Steady state grid voltage and load voltage waveforms with non-linear load.4.3.2. Vc(V) Fundamental (Hz) = 3, THD= 2.2% 2 4 6 8 2 4 6 8 2 (a)load voltage with resistive load (b)load voltage with non linear load Fig. 6. THD values of load voltage waveform in stand-alone mode C. Transient State Operation (a)response to change in active power demand: The active power reference is changed from 37 W to 7 W at. s and reactive power reference is set to zero. Correspondingly the active current reference changes from 2.4 A to 4.82 A. It is depicted in Fig. 7(a) that the grid current tracks the reference current without much transients and the voltage across the local load also remains constant. (b)response to change in reactive power demand: The reactive power demand of the grid might change with change in type of load. When the grid has to supply an inductive load, the inverter needs to inject reactive power into the grid. On the.8.6.4.2 Fundamental (Hz) = 3, THD= 2.8% 2 4 6 8 2 4 6 8 2 other hand, when a capacitive load is connected, reactive power demand falls and the inverter draws reactive power from the grid. The operating power factor also changes. The reactive power reference is changed from 37 W to -37 W at. s. Correspondingly, the reactive current reference changes from 2.4 A to -2.4 A. The active power reference is fixed at 7 W. It is shown in Fig. 7(b) that the grid current was lagging the grid voltage before. s and after that it starts leading. Hence, it is proved that the control strategy successfully meets the requirement of reactive power compensation, while maintaining a constant active power flow to grid. (c)response during voltage sag: A voltage sag of 3% is created at. s during simulation. In Fig. 7(c) it is shown that the grid current remains constant and phase alignment with grid voltage is maintained during voltage sag. This implies that the proposed controller is robust during grid voltage distortions. 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 Fig. 7(a). Transient state grid voltage, load voltage and grid current waveforms with change in active power reference Current (A) 4 2-2 Ref. current Grid Current -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 Fig. 7(b). Transient state grid voltage, load voltage and grid current waveforms with change in reactive power reference 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 Fig. 7(c). Grid voltage, load voltage and grid current waveforms during voltage sag D. Smooth Transfer of Operation Modes (a)stand-alone to grid-tied mode: In this scenario the breaker is closed at t=.s and the inverter is connected to grid. The proposed control strategy strives to achieve a smooth grid connection without deteriorating the quality of grid current and load voltage. The active power reference is changed from to 7 W at t=.s. Correspondingly the active current reference changes from to 4.82 A. Fig. 8(a) reveals that smooth grid connection is achieved without much dynamics in the grid current and local load voltage
waveforms. The grid current is synchronized with grid voltage after. s without changing the control scheme or synchronization algorithm. The grid current tracking error is also low as shown in Fig. 9(a). (b)grid-tied to stand-alone mode: In this case the breaker is opened at t=.s and the inverter is disconnected from grid. After disconnection the inverter does not injects power to grid but only powers the resistive load. It is shown in Fig. 8(b) that a smooth transition from grid tied to off grid mode is achieved without any distortions in current and voltage waveforms. The grid current tracking error is also minimized as depicted in Fig. 9(b). Filter current (A) 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 (a) Transfer from stand-alone to grid-tied mode Filter current (A) 4 2-2 -4.2.4.6.8..2.4.6.8.2 4 2-2 -4.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 (b) Transfer from grid-tied to stand-alone mode Fig.8. Grid voltage, load voltage, filter inductor current, grid current waveforms (a) Transfer from stand-alone to grid-tied mode Error (A) Error (A). -.. -. -.2.4.6.8..2.4.6.8.2 -.2.4.6.8..2.4.6.8.2 (b) Transfer from grid-tied to stand-alone mode Fig.9. Grid current tracking error waveforms V. CONCLUSION In this paper, a nested proportional resonant current and model predictive voltage controller is introduced for control of single phase VSI integrating a RES based plant in a microgrid. This strategy improves the quality of local load voltage and grid current waveforms with both linear and non linear loads. A non-linear load such as the diode bridge rectifier introduces voltage harmonics, but this scheme is successful in achieving low THD values for inverter local load voltage and grid current simultaneously. Simulation results validates the outstanding performance of the proposed controller in both steady state and transient state operations. 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