Modeling and Control of Bidirectional DC-DC Converters for DC Power Systems with Renewable Energy

Transcription

1 九州大学学術情報リポジトリ Kyushu University Institutional Repository Modeling and Control of Bidirectional DC-DC Converters for DC Power Systems with Renewable Energy フサーム, アーメドラマダンアーメド 出版情報 : 九州大学, 2014, 博士 ( 学術 ), 課程博士バージョン :published 権利関係 : 全文ファイル公表済

2 Modeling and Control of Bidirectional DC- DC Converters for DC Power Systems with Renewable Energy BY Husam Ahmed Ramadan Ahmed A thesis submitted to Department of Electrical and Electronic Engineering In partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering Graduate School of Information Science and Electrical Engineering Kyushu University JAPAN December, 2014

3 ACKNOWLEDGMENT In the name of Allah, most Gracious, most Merciful All deepest thanks are due to Almighty God, the merciful, and the compassionate for uncountable gifts given to me. I would like to express my deepest gratitude and sincere appreciation to my academic advisor Prof. Masahito Shoyama for his help, precious continuous guidance, and kind encouragement during carrying out this research. I am very grateful for the cooperative spirit and the excellent working atmosphere in the green electronics circuits laboratory. I would like to express my deep appreciation to my country (Egypt) for supporting my stay during my graduate studies at Kyushu University. Importantly, I would like to express my gratitude to my parents, brothers and sisters for their continuous encouragement and prayers. Finally, with my deepest love, I would like to thank my lovely wife for her support and encouragement from my life to my study. Her company made my life in Fukuoka fruitful and meaningful. I also should thank my son, Ayias, for the special happiness he brought to us. Husam Ahmed Ramadan Fukuoka, Nov i

4 Abstract ABSTRACT Bidirectional dc-dc converters (BDC) have recently received a lot of attention due to the increasing need to systems with the capability of bidirectional energy transfer between two dc buses. Apart from traditional application in dc motor drives, new applications of BDC include energy storage in renewable energy systems, fuel cell energy systems, hybrid electric vehicles (HEV) and uninterruptible power supplies (UPS). The fluctuation nature of most renewable energy resources, like wind and solar, makes them unsuitable for standalone operation as the sole source of power. A common solution to overcome this problem is to use an energy storage device besides the renewable energy resource to compensate for these fluctuations and maintain a smooth and continuous power flow to the load. As the most common and economical energy storage devices in medium-power range are batteries and super-capacitors, a DC-DC converter is always required to allow energy exchange between storage device and the rest of system. Such a converter must have a bidirectional power flow capability with flexible control in all operating modes. The modeling and the control of bi-directional DC-DC converters is an important issue. By using conventional modeling method, two different models are needed. One model for each power direction (each operation mode). Furthermore, the control loop also should be changed according to the direction of the power flow. ii

5 Abstract Therefore, analyzing and controlling of a bi-directional DC-DC converter became very complex. For the sake of solving this problem, unified dynamic models of bidirectional DC-DC converters are proposed in this thesis. Furthermore, the stability issue for the bi-directional DC-DC converters is investigated in this thesis. The thesis consists of five chapters, which can be organized as follows: Firstly, Chapter 1 conveys the detailed introduction of the research background, a literature review of bidirectional DC-DC converters, their types (isolates and nonisolated), modeling and control. Moreover, it presents the thesis objective and outlines. Then, in Chapter 2, a unified model for bi-directional DC-DC converters for both directions of power flow is presented. The bi-directional DC-DC converter is analyzed using a seamless dynamic model with an independent voltage source and an independent current source, which polarity depends on the direction of the power flow. A small signal model is derived using a state space averaging method. Furthermore, the transient response and the frequency characteristics are discussed. Example circuits for bi-directional DC-DC converter are investigated analytically, using simulation, and experimentally. Afterwards, Chapter 3 introduces a new control strategy for bidirectional DC-DC converter, as well. This strategy aims at controlling a bidirectional DC-DC converter to behave like a multi-level virtual conductor. As a matter of fact, the iii

6 Abstract voltage difference between the terminals of any conductor is zero volts. Conversely, the main target of this proposed control strategy is to keep the voltage difference between the converter terminals constant at a certain value. In other words, this strategy permits the DC-DC converter to transfer the power between two nodes at different voltage levels. In this way, the converter performs like a conductor, but unlike the normal conductor, has a voltage difference between its terminals. Thus, the authors call it a virtual conductor. This virtual conductor is considered a base for power routing in dc networks; as it can transfer the electric power between nodes at different voltage levels. Furthermore, it allows an easy plug-and-play feature. The proposed bidirectional DC-DC system configuration is investigated analytically, using PSIM simulator, and experimentally. Further, in Chapter 4, a new criterion for the stability assessment in a dc power system is presented. This criterion is the node impedance criterion. The concept, mathematical, simulation, and experimental analysis of node impedance criterion, are investigated, as well. The results of the node impedance criterion are compared with those of the conventional criterion. The comparison shows the validity of the node impedance as a stability criterion. Moreover, the node impedance criterion is applied to a dc power system using a MLVC to assess it stability. Finally, Chapter 5 summarizes the conclusions of this thesis and the future work. iv

7 Table Of Contents TABLE OF CONTENTS AKNOWLEDGMENT ABSTRACT TABLE OF CONTENTS. Page i ii v CHAPTER CHAPTER CHAPTER INTRODUCTION Background... State-of-the-art Bidirectional DC-DC Converters Introduction to Bidirectional DC-DC Converters.. Non-isolated Bidirectional DC-DC Converters. Isolated Bidirectional DC-DC Converters. Soft-switching Techniques in Bidirectional DC-DC Converters.. State-of-the-art Bidirectional DC-DC Converter Modeling and Control Traditional Method without Mode Transition Consideration. Bidirectional DC-DC Power Stage Modeling and Control Thesis objectives and out lines SEAMLESS DYNAMIC MODEL FOR BI- DIRECTIONAL DC-DC CONVERTER Introduction.. Circuit Topology.. Seamless Averaged Model... Frequency Characteristics... Transient Response. Summary.. DC POWER SYSTEMS USING MULTI- LEVEL VIRTUAL CONDUCTOR BASED A CONTROLLED BIDIRECTIONAL DC-DC CONVERTER Introduction.. v

8 Table Of Contents CHAPTER CHAPTER References Using a bi-directional DC-DC converter for charging and discharging of a battery Dc power system using the proposed bidirectional DC-DC converter (The virtual conductor). Implementation of the virtual conductor using a bi-directional DC-DC converter. Configuration examples and features of the virtual conductor in dc power system The proposed bi-directional DC-DC circuit configuration. Transient response Summary. A New Stability Assessment Criterion for DC Power Systems with Multi-level Virtual Conductors Introduction.. Analysis of Bidirectional DC-DC Converter. Small Signal model Small Signal Model considering AC Impedance of Load/Source Modules Node impedance and system stability. Numerical analysis and application example. Numerical analysis. Application example.. Summary... CONCLUSIONS AND FUTURE WORK Conclusions Future work vi

9 Chapter 1: Introduction CHAPTER 1 INTRODUCTION 1.1 Background Nowadays, a system uses various types of energy sources has been sought after, and a hybrid system based on fuel cells and super-capacitors as an environmentally renewable energy system has been applied in many fields, such as hybrid electric vehicle (HEV), uninterruptible power supply (UPS) and so on [1]-[6]. The bidirectional DC-DC converter along with energy storage has become a promising option for many power related systems, including hybrid vehicle [1], fuel cell vehicle renewable energy system and so forth. It not only reduces the cost and improves efficiency, but also improves the performance of the system. Figure (1-1): Configuration of power system in electric vehicle. 1

10 Chapter 1: Introduction In the electric vehicle applications, an auxiliary energy storage battery absorbs the regenerated energy fed back by the electric machine. In addition, a bidirectional DC-DC converter, shown in Fig. (1-1), is also required to draw power from the auxiliary battery to boost the high-voltage bus during vehicle starting, accelerate and hill climbing [1]. With its ability to reverse the direction of the current flow, and thereby power, the bidirectional DC-DC converters are being increasingly used to achieve power transfer between two dc power sources in either direction. In renewable energy applications, the multiple-input bidirectional dc-dc converter can be Figure (1-2): Configuration of EMS 2

11 Chapter 1: Introduction used to combine different types of energy sources [2-8]. A configuration of EMS (Energy Management System) is shown in Fig. (1-2). In this configuration, a battery is connected between load modules and source modules through bi-directional DC-DC converter. The fluctuation nature of most renewable-energy sources, like wind and solar, makes them unsuitable for standalone operation. Thus, bi-directional DC-DC converter and battery are needed to manage this system. The multi-input bidirectional dc-dc converter is the core that interconnects power sources and storage elements and manages the power flow [5]. This bidirectional dc-dc converter features galvanic isolation between the load and the fuel cell, bidirectional power flow, capability to match different voltage levels [9], fast response to the transient load demand, etc. Recently, clean energy resources such as photovoltaic arrays and wind turbines have been exploited for developing renewable electric power generation systems. The bidirectional dc-dc converter is often used to transfer the solar energy to the capacitive energy source during the sunny time, while to deliver energy to the load when the dc bus voltage is low [9]. In this thesis, a background description and review of the state-of-the-art bidirectional dc-dc converters are presented firstly to define this work and its novelty. 1.2 State-of-the-art Bidirectional DC-DC Converters Introduction to Bidirectional DC-DC Converters Most of the existing bidirectional dc-dc converters fall into the generic circuit structure illustrated in Fig. (1-3), which is characterized by a current fed or voltage fed on one side - 3

12 Chapter 1: Introduction [10]-[14]. Based on the placement of the auxiliary energy storage, the bidirectional dc-dc converter can be categorized into buck and boost type. The buck type is to have energy storage placed on the high voltage side, and the boost type is to have it placed on the low voltage side. Figure (1-3): Illustration of bidirectional power flow. To realize the double sided power flow in bidirectional dc-dc converters, the switch cell should carry the current on both directions. It is usually implemented with a unidirectional semiconductor power switch such as power MOSFET (Metal-Oxide-Semiconductor-Field- Effect-Transistor) or IGBT (Insulated Gate Bipolar Transistor) in parallel with a diode, because the double sided current flow power switch is not available. For the buck and boost dc-dc type converters, the bidirectional power flow is realized by replacing the switch and diode with the double sided current switch cell shown in Fig. (1-4) [12]. Numerous topologies for possible implementation as bidirectional dc-dc converters have 4

13 Chapter 1: Introduction been reported so far [15-37]. Basically they are isolated converters, meeting different application requirements. divided into two types, non-isolated and Figure (1-4): switch celll in bidirectional DC-DC converter Non-isolated Bidirectional DC-DC Converters In the transformer-less non-isolated power conversion systems, the boost type and buck type dc-dcc converterr are chosen usually. The high frequency transformer based system is an attractive one to obtain isolation between the source and load sides. But from the viewpoint of improving the efficiency, size, weight and cost, the transformer-less type is much more attractive. Thus, in the high power or spacecraft power system applications [7, 17, 20, ], where weight or size is

14 Chapter 1: Introduction the main concern, the transformer-less type is more attractive in high power applications. The basic non-isolated bidirectional dc-dc converter topology shown in Fig. (1-5) is the combination of a step-up stage together with a step-down stage connected in antiparallel [45]. For the motor drive operations the converter step-up stage is used to step up the battery voltage and control the inverter input. The vehicle regenerativee braking is accomplished by using the converter step-down stage, which gives a path for the braking current and allows the recovery of the vehicle energy in the battery. Figure (1-5): Basic bidirectional DC-DC converter with buck and boost structure For the present highh power density bidirectional dc-dc converter, to increase its power density, multiphase current nterleaving technology with minimized inductance has been found in high power applications [38, 42]. It is reported that multiphase converter circuits have shown the advantage of less device current stress and better efficiency. A three phase bidirectional dc-dc converter is shown in Fig. (1-6), wheree the phase switch is controlled with 120-degree phase shift from each other. The ripple on the total current will become 6

15 Chapter 1: Introduction relatively small, so a small capacitance is enough in both low and high sides for acceptable voltage ripple. Figure (1-6): A high power density non-isolated interleaved bidirectional DC-DC converter Isolated Bidirectional DC-DC Converters In the bidirectional dc-dc converters, isolation is normally provided by a transformer. The added transformer implies additional cost and losses [1]. However, since transformer can isolate the two voltage sources and provide the impedance matching between them, it is an alternativee in those kinds of applications. As a current source, inductance is normally needed in between. 7

16 Chapter 1: Introduction For the isolated bidirectional dc-dc converters, sub-topology can be a full-bridge, a halfbridge, a push-pull circuit, or their variations [25, 27-30]. One kind of isolated bidirectional dc-dc converter is based on the half-bridge in the primary side and on the current fed push-pull in the secondary of a high frequency isolation transformer [48]. The converter operation is described for both modes; in the presence of dc bus the battery is being charged, and in the absence of the dc bus the battery supplies power. This converter is well suited for battery charging and discharging circuits in dc uninterruptible power supply (UPS). Advantages of this proposed converter topology include galvanic isolation between the two dc sources using a single transformer, low parts count with the use of same power components for power flow in either direction. The dual active bridge dc-dc converter with a voltage-fed bridge on each side of the isolation transformer operates utilization of the leakage inductance of the transformer as the main energy storing and transferring element to deliver bidirectional flow power [23],[49-50]. In summary, for the isolated bidirectional dc-dc converter, the operation of the circuit involves the utilization of the leakage inductance of the transformer as the main energy storing and transferring element. The half-bridge based topologies have been developed so far to reduce the device count and increase efficiency [3, 28, 31, 49]. However a voltage imbalance exists between the two split capacitors, thus an additional control circuit to eliminate the voltage imbalance problem is required. The full-bridge bidirectional dc-dc 8

17 Chapter 1: Introduction converter shown in Fig. (1-7) is considered one of the best choices. However, this system has a complicated configuration, high cost and large size. Figure (1-7): A bidirectional full-bridge DC-DCC converter with a unified soft switching scheme Soft-switching Techniques in Bidirectional DC-DCC Converters The efficiency is one of the needed performances for many bidirectional dc-dc converter applications. To improve the efficiency many advanced power conversion techniques such as resonant and soft-switching can be implemented in the power stage [6, 12-13, 38-39, 42, 44, 52-73] ]. A bidirectional dual full-bridge dc-dc converter has been developed with a unified soft switching scheme and soft start capability shown in Figure 1..8 [71]. The bridge on one side, preferably the lower voltage side, is current-fed, while that on the other side is voltage fed. A simple voltage clamp branch, which is composed of an active switch 9

18 Chapter 1: Introduction with its anti-paralleled diode and a capacitive energy storage element in series, is placed across the current-fed bridge to limit transient voltage across the current-fed bridge and realize zero-voltage-switching in boost mode operation, while achieving hybrid zerovoltage zero-current switching (ZVZCS) for the voltage-fed bridge in buck mode operation. In buck mode operation, the voltage-fed bridge is controlled by the well-known phase shift pulse width modulation (PWM). The clamping branch is activated only briefly each time after an on duty cycle is executed and the on-time of the clamp switch is just long enough to reset the transformer leakage current to zero and achieve ZVZCS operation even under maximum load current. 1.3 State-of-the-art Bidirectional DC-DC Converter Modeling and Control Traditional Method without Mode Transition Consideration Many controller schemes have been discussed for bidirectional dc-dc converter applications. Most designs follow the unidirectional dc-dc controller methodology [41, 43, 45, 74] because there are different circuits topological changes and associated operating principles involved in the two power flow directions. Normally, two independent controllers are needed for battery charging and discharging respectively [45, 92]. No mode transition discussion has been addressed since the power management is normally not included in the design. More efforts are needed for smooth mode transition. Otherwise the transition will cause large current or voltage stress on device. 10

19 Chapter 1: Introduction One example of dealing with smooth mode transition is shown in Fig. (1-8)[43]. This is a regulated bus system for the spacecraft power system application. The major effort in this system is according to study the trajectories of the system operating point, which are determined to the stability nature of the equilibrium points for the optimum performance and stability of the system. This type of study tends to complicate the design and reduce the system reliability. Figure (1-8): Block diagram of regulated bus system For example, the starting operation point is from point A in Fig. (1-9) for sunlight to eclipse transition. As illumination level decreases, the solar array current decreases. The shunt regulator current then decreases to regulate the bus voltage. As soon as the shunt current reaches zero, bus voltage drops rapidly. This is the dead band mode. According to the pre-set value, the bus voltage will be regulated by the battery discharger. Between the equilibrium points C and D, there is a dead band, which is to avoid undesired overlapping 11

20 operation. Chapter 1: Introduction Transient behavior during the dead band mode depends on the circuit parameters including bus capacitor, and cable inductance. The preset bus voltage value is needed to trigger the battery discharger for bus voltage regulation. Plus the transient behavior is sensitivee to circuit parameters. It is not easy to predict. Figure (1-9): Graphical analysis of sunlight to eclipse transition Bidirectional DC-DC Power Stage Modeling and Control Some researchers [31, 51, 72] developed a switch frequency-dependable average method to estimatee the system performance at different switching frequencies. This is an extended 12

21 Chapter 1: Introduction state-space averaging model and is developed to predict large- and small-signal characteristics of the converter in either direction power flow. The model is especially designed for isolated one. A digital controller was built after non-linear dynamic model of the converter was derived using a state space averaging method in [8, 75]. Although it utilized the simplified power stage model with the traditional modeling approach, it did claim to handle seamless bidirectional operation. In fact, to design a seamless bidirectional power flow control, more generalized power stage model is needed. Based on ref [43], an analog current-injection-control in multiphase was implemented in [44, 65, 76, 93]. One error amplifier was used for the spacecraft bus voltage regulation with internal peak current mode control. After careful analysis of the feature of the two modes (bus voltage regulation mode with charging and discharging mode), a sub-optimal controller was proposed for the regulation of the two mode operations. It was expected to reduce the overall system weight. Since the application was focused on the spacecraft power system, no more average current control for both directions was addressed. 1.4 Thesis objectives and out lines Thesis objectives can be listed as follows: Design and implement a unified dynamic model (seamless model) for the bidirectional DC-DC converter. 13

22 Chapter 1: Introduction Design and implement a new control strategy for the for the bidirectional DC-DC converter that begot the multi-level virtual conductor(mlvc), which can be considered as a paramount component in dc power routing. Investigate and test the stability issue for the seamless model and for a dc power system with multi-level virtual conductors, as well. The thesis consists of five chapters, which can be organized as follows: Firstly, Chapter 1 conveys the detailed introduction of the research background, a literature review of bidirectional DC-DC converters, their types (isolates and non-isolated), modeling and control. Moreover, it presents the thesis objective and outlines. Then, in Chapter 2, a seamless dynamic model for bidirectional DC-DC converters is presented, investigated and implemented; both analytically and experimentally. The frequency and the transient respond are studied, as well. Afterwards, Chapter 3 presents a new control strategy for bidirectional DC-DC converters that can be very useful for dc power routing. This control strategy allows the converter to behave as a multi-level virtual conductor. For the sake of the validation of this control strategy, a representative case study is addressed by simulation and experiment. Further, Chapter 4 introduces a new stability assessment criterion for dc power systems with interconnected multi-level virtual conductors. This criterion is the node impedance 14

23 Chapter 1: Introduction criterion. The concept, mathematical, simulation, and experimental analysis of node impedance criterion, are investigated, as well. Finally, Chapter 5 summarizes the conclusions of this thesis and the future work. 15

24 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter CHAPTER 2 SEAMLESS DYNAMIC MODEL FOR BI- DIRECTIONAL DC-DC CONVERTER 2.1 Introduction Bi-directional DC-DC converter has two operating modes as shown in Fig. (2-1), and they are frequently exchanged. These two modes are: 1- Discharging mode: The power is sent from the battery to load/source modules when load/source modules need the power. 2- Charging mode: The power is sent from the load/source modules to battery when load/source modules have enough amount of the power. Power Flow Battery DC/DC Load/Source Modules (a) Discharging mode Power Flow Battery DC/DC Load/Source Modules (b) Charging mode. Figure (2-1): Operating mode of a bi-directional DC-DC Converter. 16

25 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter By using conventional modeling method [94], two different models are needed. One model for each power direction (each operation mode), as shown in Fig. (2-2). Furthermore, the control loop also should be changed according to the direction of the power flow. Therefore, analyzing and controlling of a bi-directional DC-DC converter became very complex. 1 2 DC/DC Battery 1' D PWM 2' Load Modules V REF (a) Discharging mode. 1 2 DC/DC Battery 1' PWM D 2' Source Modules V REF (b) Charging mode. Figure (2-2): Conventional circuit model of bi-directional DC-DC converter. For the sake of solving this problem, a seamless dynamic model of a bi-directional DC-DC converter is proposed in this chapter. This model is derived using a state space averaging method [95]-[97]. As shown in Fig. (2-3), an independent voltage source represents the 17

26 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter battery, and an independent bi-polar current source represents the load/source modules. The polarity of the bi-polar current source decides the direction of the power flow. Herein, only the voltage of the bi-polar current source is sensed and controlled. Hence, the control loop does not need to be switched according to the direction of the power flow. In other words, a simple analyzing and controlling of bi-directional DC-DC converter can be fulfilled via this seamless model. 1 Battery 1' DC/DC D PWM Z 2 2 2' Bi-polar Current I 2 Source Load/Source Modules I 2 > 0 : Load { I2 < 0 : Source V REF Figure (2-3): Proposed seamless circuit model of bi-directional DC-DC converter. 2.2 Circuit Topology Seamless dynamic models based on two circuit topologies are analyzed and compared, herein. These two circuit topologies are shown in Fig. (2-4) and Fig. (2-5). Figure (2-4) presents a buck-based circuit topology, however Fig. (2-5) introduces a boost-based circuit topology. In Fig. (2-4) and Fig. (2-5), the current source side voltage v 2 is considered a control variable, and duty ratio d of the mean switch S M is considered an input variable. The current source side voltage v 2 is observed and duty ratio d is controlled by the control 18

27 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter circuit. Also, the synchronous switch S S, with a duty ratio d (=1- d), has a complementary state with the main switch S M. d controller S M i L (r S ) (r L ) L V 1 (r S ) S S (r c ) C v c I 2 v 2 Figure (2-4): Circuit topology of buck-based type. d controller V 1 i L (r L ) L S S (r S ) (r S) v c v 2 (r c ) C S I 2 M Figure (2-5): Circuit topology of boost-based type. 2.3 Seamless Averaged Model Considering the state-space vector [ ] and the input vector [ ], the state space equations at state 1 and state 2 become: 19

28 State 1 (S M : ON, S S : OFF) Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter (2-1) State 2 (S M : OFF, S S : ON) (2-2) Appling the state-space averaging method for Eq. (2-1) and Eq. (2-2), state equations become: (2-3) where: Next, on the steady state, circuit parameters are: U X : DC input vector : DC state vector 20

29 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter V 2 D : DC voltage at current source : DC duty ratio at S M Next, the converter waveforms are perturbed at this quiescent operating point as follows: U U+Δu X X+Δx V 2 V 2 +Δv 2 D D+ΔD where; ΔD is small ac variations in duty ratio and Δu is small ac variations in input values. The vectors Δx and Δv 2 are the resulting small ac variations in the state x and voltage v 2. The state equations of the small-signal ac model are: (2-4) where; The matrices of ( ) are illustrated in Table (2-1). 21

30 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter From Eq. (2-4), the transfer function G dv (s) between ΔD(s) and Δv 2 (s) can be developed, as in Eq. (2-5). Table (2-1) Elements of the matrices of ( ) Topology A B c e e p r r s r 1 r Buck [ L L ] [ 1 L L ] [r 1] [0 r ] [ 1 L0 ] C C r r s r 1 r 1 r r s Boost L L [ L L ] [ r 1] [0 r ] [ L L ] 1 1 [ 0 0 C ] C C r s s (2-5) By the same way, the transfer function G vv (s) between ΔV 1 (s) and Δv 2 (s), and G iv (s) between ΔI 2 (s) and Δv 2 (s) can be developed as: s s { } [ 1 0 ] (2-6) s s { } [ 0 1 ] (2-7) 2.4 Frequency Characteristics The frequency characteristics of the transfer function G dv (s) are analyzed according to Eq. (2-5), and to the circuit parameters that are listed in Table (2-1). The equations of the transfer function G dv (s) for both buck-based and boost-based type are presented in Eq. (2-8), Eq. (2-9) as follows: 22

31 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter s s s (2-8) s s {( ) (Cr ) } (2-9) Table (2-2) Circuit Parameters Symbol Parameters Buck Value Boost V 1 I 2 V 2 Voltage at Voltage Source [V] Current at Current Source [A] Voltage at Current Source [V] ~4-2~ L Inductance [μh] 120 C Capacitance [μf] 100 r L ESR of L [mω] 30 r C ESR of C [mω] 150 r S On-resistance of switches [mω] 150 f Switching Frequency [khz] 100 From Eq. (2-8) and Eq. (2-9), it is noticed that the frequency characteristics of buck-based type don t depend on I 2. Nevertheless, the frequency characteristics of boost-based 23

32 Phase (deg) Gain (db) Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter depend on I 2. The frequency characteristics of both buck-based type and boost-based type are analytically and experimentally investigated based on circuit parameters in Table (2-2). For buck-based type, analytical results are shown in Fig. (2-6), and experimental results are shown in Fig.7. According to Fig. 6 and Fig. (2-7), the frequency characteristics of G dv_buck for both current directions are the same, and they match with Eq. (2-8). These results mean that frequency characteristics of G dv_buck don t depend on the direction of current I Frequency (Hz) Figure (2-6) Frequency characteristics of G dv (analytical results, buck-based type, for any I 2 ). 24

33 Gain [db] Phase [deg] Gain [db] Phase [deg] Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter ,000 10, , Frequency [Hz] -240 (a) I 2 = +4 A ,000 10, , Frequency [Hz] (b) I 2 = - 4 A Figure (2-7) Frequency characteristics of G dv (experimental results, buck-based type) For boost-based type, analytical results are shown in Fig. (2-8), and experimental results are shown in Fig. (2-9). Considering Fig. (2-8) (a) and (b), it is obvious that the frequency characteristics of G dv_boost don t depend on the direction of the current I 2 at low frequency. However, at high frequency, phase plots depend on the direction of the current I The

34 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter stability of the circuit is better when direction of the current I 2 is negative. Based on Fig. (2-8) and Fig. (2-9), the frequency characteristics of G dv_boost for both current directions match with Eq. (2-9). In other words, the frequency characteristics of G dv_boost depend on the direction of current I 2. Gain (db) Phase (deg) Frequency (Hz) (a) I 2 = +2 A Gain (db) Phase (deg) Frequency (Hz) (a) I 2 = - 2 A Figure (2-8) Frequency characteristics of G dv (analytical results, boost-based type) 26

35 Gain [db] Phase [deg] Gain [db] Phase [deg] Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter Comparing the results of the buck-based type with those of the boost-based type; it is found that the buck-based type has an advantage over the boost-based type on designing the controller; since its frequency characteristics don t depend on current I ,000 10, , Frequency [Hz] -240 (a) I 2 = +2 A ,000 10, , Frequency [Hz] (b) I 2 = - 2 A -240 Figure (2-9) Frequency characteristics of G dv (experimental results, boost-based type) 27

36 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter 2.5 Transient Response To investigate the transient characteristics response of the converter; two prototype 100 watts converters are designed based on the proposed seamless model. One of these converters is buck-based type, while the other is boost-based type. Each converter is connected, at one side, to a battery, and at the other side, to a bipolar current source. The current waveform of the bipolar current source, I 2, is intentionally designated to have a stiff change from positive I 2 into negative I 2. Accordingly, the voltage at the bipolar current source side V 2 is measured. The voltage of the current source is fed back to control the duty ratio of the switch S M. The open loop transfer function T(s) becomes: where; K p G c (s) : Feedback proportional gain : Transfer function of compensator For the buck-based type: A compensator is not needed in buck-based type because its phase doesn t inverse. Compensator s transfer function in buck-based type becomes: 1 Proportional gain is designed as K p_buck = 0.72 [V -1 ]. 28

37 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter The simulated results are shown in Fig. (2-10), while the experimental results are shown in Fig. (2-11). It is noticed that the experimental results and the simulated results are conformed. Also, it is clear that the transient change in V 2 (when the I 2 change from positive to negative) is the same transient change in V 2 (when the I 2 change from negative to positive). This, in turn, confirms that the buck-based type does not depend on the direction of I 2. Figure (2-10) Transient response characteristics of buck-based type (simulated result). 29

38 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter i 2 5 A/div 0 v 2_AC 1 V/div 0 Figure (2-11) Transient response characteristics of buck-based type (experimental result, time: 1ms/div). For the boost-based type: A compensator is needed in boost-based type because its phase inverses when the direction of I 2 is positive. In this circuit, phase lag compensator is used. Compensator s transfer function in boost-based type becomes: where; 1 1 ω p = 4.4 krad/s ω z = 30 rad/s Proportional gain is designed as K p_boost = 0.36 [V -1 ]. 30

39 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter The simulated results are shown in Fig. (2-12), while the experimental results are shown in Fig. (2-13). It is noticed that the experimental results and the simulated results are the same. Furthermore, it is clear that the transient change in V 2 (when the I 2 change from positive to negative) is higher than the transient change in V 2 (when the I 2 change from negative to positive). This, in turn, confirms that the boost-based type depends on the direction of I 2. Figure (2-12) Transient response characteristics of boost-based type (simulated result) i 2 2 A/div 0 v 2_AC 1 V/div 0 Figure (2-13) Transient response characteristics of boost-based type (experimental result, time: 1ms/div) 31

40 Chapter 2: Seamless Dynamic Model For Bi-Directional DC-DC Converter 2.6 Summary A unified model for bi-directional DC-DC converters for both directions of power flow is introduced in this chapter. This unified model is a seamless dynamic model in which the bidirectional DC-DC converter is connected, at one side, to an independent voltage source and, at the other side, to independent current source. The direction of the power flow is designated by the polarity of the independent current source. This seamless dynamic model is applied to two DC-DC converter circuits (buck-based type and boost-based type). In case of boost-based type, its frequency characteristics depend on the direction of the current I 2. However, in case of buck-based type, its frequency characteristics don t depend on the direction of the current I 2. A simulated and experimental prototype for both circuits (buck-based type and boost-based type) are build up based on this seamless dynamic model, and their results are compered. Both of the simulated and experimental results support the seamless dynamic model idea and prove its superiority. 32

41 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter CHAPTER 3 DC POWER SYSTEMS USING MULTI-LEVEL VIRTUAL CONDUCTOR BASED A CONTROLLED BIDIRECTIONAL DC-DC CONVERTER 3.1 Introduction Nowadays, bidirectional DC-DC converters (BDCs) have various applications that include energy storage in renewable-energy systems, fuel cell systems, hybrid-electric vehicles (HEVs) and uninterruptible power supplies (UPSs) [20][42][46-47][65][84-85]. The fluctuation nature of most renewable-energy sources, like wind and solar, makes them unsuitable for standalone operation. A common solution to overcome this problem is to use an energy storage device besides the renewable-energy resource to compensate these fluctuations and maintain a smooth and continuous power flow. As the most common and economical energy storage devices in a medium-power range are batteries and super-capacitors, a DC-DC converter is usually required to allow energy exchange between storage device and the rest of the system. Such converters must have bidirectional power flow capability with flexible control in all operating modes. Moreover, 33

42 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter when integrating various renewable-energy sources with numerous voltage levels into a dc grid, the main challenge is to have an easy plug and play system with a flexible dc power routing. This system should be capable of integrating such sources at different voltage levels. To face this challenge, a proposed strategy based on a bidirectional DC-DC converter is introduced in this chapter. In this chapter, a bidirectional DC-DC converter is investigated and controlled. It is considered that both input and output are independent current sources. The current source may represent a load, electric double layer capacitors (EDLCs), a battery, or even another bi-directional converter. Therefore, for such converter, it is required to control both and to keep the voltage difference between them at a certain value regardless of any variation that may be occurred to the currents and. 3.2 Using a bi-directional DC-DC converter for charging and discharging of a battery Figure (3-1) illustrates an example of a smart house integrates a renewable-energy source (PV) and a storage battery. The PV is connected to the load via a maximum point power tracker (MPPT) and a unidirectional DC-DC converter. While, the battery is connected to the load via bidirectional DC-DC converter; since the power flow between the battery and the load is required to be bidirectional (charge/discharge). The coupling point Voltage, V N, is controlled based on V Ref-N. 34

43 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter VPV IPV Source PV Unidirectional DC-DC Converter I S-PV D MPPT Battery V N Load V B Bi-dirictional DC-DC Converter C I L D sa =1-D sb V Ref-N Figure (3-1) Using a bi-directional DC-DC converter for charging and discharging of a battery. 3.3 Dc power system using the proposed bi-directional DC-DC converter (The virtual conductor) Regarding the aforementioned example in Fig. (3-1), for the sake of having a flexible dc power system; it should be easy to integrate different multi-level voltage sources and loads together. In other words, the coupling point is required to be a multi-level voltages point. The bidirectional DC-DC converter, with the proposed control strategy, can play the role of a multi-level voltage coupling point as shown in Fig. (3-2). In this case, the bidirectional DC-DC converter is called a multi-level virtual conductor. 35

44 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter V P V I P V S o u r c e P V U n i - d i r e c t i o n a l D C - D C c o n v e r t e r D M P P T I S - P V W T MPPT included I S - W T L o a d V 1 V 2 S o u r c e I L 1 C 1 B i - d i r e c t i o n a l D C - D C c o n v e r t e r C 2 I L 2 D s a = 1 - D s b V 1 V R e f - 1 V 2 V R e f - 2 V R e f - 1 V R e f - 2 B a t t e r y V B B i - d i r e c t i o n a l D C - D C c o n v e r t e r C D s a = 1 - D s b V R e f - N Figure (3-2) The proposed bidirectional DC-DC converter as a multi-level voltage coupling point. 3.4 Implementation of the virtual conductor using a bi-directional DC- DC converter The proposed control strategy for a bidirectional DC-DC is shown in Fig. (3-3).The main target of this control strategy is to keep the voltage difference between the converter terminals constant at a certain value. V 1 and V 2 are adjusted according to V Ref-1 and V Ref-2 36

45 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter respectively. Therefore, the duty ratios and of the converter are adjusted to the desired value when (V 1 -V 2 ) = (V Ref-1 -V Ref-2 ). Since V Ref-1 and V Ref-2 are constant values; then the difference between V 1 and V 2 is kept constant at the steady state. For the former example in Fig. (3-1), there was only one coupling point (V N ), but with this proposed strategy; there are two coupling points V 1 and V 2. Source/load V 1 V 2 Source/load I 1 C 1 Bidirectional DC-DC converter C 2 I 2 Dsa =1-Dsb V1 VRef-1 V2 VRef-2 V Ref-1 V Ref-2 Figure (3-3) Implementation of multi-level virtual conductor using a bidirectional DC-DC converter. 3.5 Configuration examples and features of the virtual conductor in dc power system The virtual conductor allows a flexible power transfer through an energy system having multiple energy sources with different voltage levels, energy storage equipment, and loads. Factually, it is impossible to use a conductor to connect such an energy system; however, a virtual conductor, having the voltage conversion function of a bidirectional DC-DC converter, can be used. 37

46 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter The configuration examples of the virtual conductor in dc power system are shown in Fig. (3-4). The series connection is presented in Fig. (3-4) (a), while the branch connection at a central node is revealed in Fig. (3-4) (b), and Fig. (3-4) (c) shows a loop connection. A further complex connection, grid connection, is shown in Fig (3-4) (d). One practical application of these aforementioned connections can be used in a smart house that integrates different loads and voltages sources together; as shown in Fig. (3-5). Another practical application can be used in an electrical vehicles (EV) charger substation; as shown in Fig. (3-6).The features of a dc power system using virtual conductors can be V N1 PV System DC/DC V N2 Load WT System DC/DC Battery Bank PV System V N3 Load (a) Series connection. DC/DC V N4 PV System V N2 Battery Bank WT System V N3 Load DC/DC DC/DC PV System V N1 DC/DC DC/DC V N4 Battery Bank WT System Load V N5 Load (b) Regdial conection at central node. 38

47 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter WT System PV System Load/ source V 1 Bidirection al DC-DC converter V 2 Load/ source V N1 Battery Bank DC/DC DC/DC DC/DC V N2 Load I 1 Bidirection al DC-DC converter Bidirection al DC-DC converter Bidirection al DC-DC converter V 3 I 3 Bidirection al DC-DC converter Load/ source Bidirection al DC-DC converter I 2 Bidirection al DC-DC converter V N3 Load Battery Bank Load/ source Bidirection al DC-DC V converter 4 V 5 I 4 Load/ source I 5 summarized as following: 1- It is possible to have different voltage levels (V N1, V N2 etc. in Fig. (3-4)). 2- By using the isolated bidirectional DC-DC converter topologies; a galvanic isolation among nodes can be achieved. 3- The virtual conductor allows an easy plug and play of the equipment that is connected to the dc power system; hence the dc power system becomes flexible and reconfigurable. 4- If there is a fault or an accident occurs in one branch or at any node, it is easy to clear this fault by stopping the operation of the related bidirectional DC-DC converter. (c) Loop connection. (d) Grid connection Figure (3-4) The configuration examples of the multi-level virtual conductor in dc power system. 39

48 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter 5- Regarding Fig. (3-4) (c), even if there is a fault in one branch, the power will be transferred via the other branch, and this increases the reliability of the dc power system. Figure (3-5) Smart house integrates different voltage sources and loads Figure (3-6) Electrical vehicles charger substation 3.6 The proposed bi-directional DC-DC circuit configuration The proposed bi-directional DC-DC circuit configuration is shown in Fig. (3-7). It employs a DC-DC converter to connect two different Load/supply units. The voltage difference between the converter sides is controlled by the duty ratio of the main switch ( 40

49 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter ) and of the synchronously switch ( ). The two bidirectional dc current sources, and, have internal resistances, and, consequently. There are three storage components:, and. Inductor parasitic resistance and MOSFET turn-on resistance are included in the model. The transfer function for this converter has been driven based on the state space averaging method [95-99]. Considering the state space vector ( ) ( ) ( ) ( ), and the input vector ; the state space averaged dc model is shown in (1): V S a v L r 1 L V2 L 0 I 1 ri r s i i c2 c1 i L C v c1 1 C S 2 b r s r o v c2 I 2 0 Figure (3-7) Circuit configuration of the proposed bi-directional DC-DC converter. [ ] [ ] (3-1) where;, [ ] [ ] By solving (3-1), the following expressions are resulted: 41

50 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter (3-2) ( ) (3-3) ( ) ( ) (3-4) The state-space averaged ac model is shown in (3-5). (3-5) where,, [ ] [ ] By solving (3-5), the following equations (3-6)-(3-8) are obtained: (3-6) (3-7) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (3-8) Using (3-6)-(3-8), the control-to-voltage difference transfer function ( ) can be 42

51 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter obtained as in (3-9), where. ( ) [ ( ) ( ) ] ( ) (3-9) For the sake of the model verification, the frequency characteristics for the control-tovoltage difference transfer function ( ) are analytical and experimentally Figure (3-8) The frequency characteristics for ( ) (analytical results) investigated. Figure (3-8) shows the analytical results, however Fig. (3-9) presents the 43

52 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter experimental results. To obtain the frequency characteristics for ( ), the following parameters are considered:,,,,, Figure (3-9)The frequency characteristics for ( ) (experimental results) 3.7 Transient response To investigate the transient characteristics response of the virtual conductor; two 100 watt converters are designed. The transient response investigation for complex systems, such as the configuration examples in Fig. (3-4), can be extended in the future work. A prototype dc power system using the virtual conductor is shown in Fig. (3-10). The virtual conductor 44

53 Chapter 3: Dc Power Systems Using Multi-Level Virtual Conductor Based A Controlled Bidirectional Dc-Dc Converter is connected at its one end to a bi-polar current source (load/ source), and at the other end to another bi-polar current source and a battery via bidirectional converter. The circuit parameters are shown in Table (3-1). These parameters have been used for both simulation and experimental results. Three cases have been studied: 1- Case (a): when currents of the bipolar current sources I 1 =+2 A, I 2 =+4 A. 2- Case (b): when currents of the bipolar current sources I 1 =-2 A, I 2 =-4 A. 3- Case (c): when current waveforms of the bipolar current sources (I 1, I 2 ) are intentionally designated to have a stiff change from positive values of (I 1, I 2 ) into negative values of (I 1, I 2 ) to investigate the bidirectional power flow through the virtual conductor. Accordingly, voltages at the bipolar current sources sides (V 1, V 2 ) are measured. The simulation results for case (a), case (b) and case (c) are shown in Fig. (3-11), Fig. (3-12) and Fig. (3-13), respectively. However, the experimental results case (a), case (b) and case (c) are shown in Fig. (3-14), Fig. (3-15) and Fig. (3-16), respectively. From these results, it is obvious that the voltage deference between V 1 and V 2 is kept constant (12 V) regardless of the change in polarities of currents and powers. In other words the virtual conductor has successfully allowed the power to be transferred in both directions between two nodes with a voltage difference in between them. 45