# The Study of Operation Modes and Control Strategies of a Multidirectional MC for Battery Based System

Authors: Saman Toosi; Norhisam Misron; Tsuyoshi Hanamoto; Ishak Aris; Mohd Amran Mohd Radzi; Hiroaki Yamada
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

To enhance the performance of stand-alone battery based system and to achieve the continuous power transmission, the behavior of multidirectional matrix converter (MDMC) has been analyzed in different operation modes. A systematic method interfacing a renewable source, a storage battery, and a load is proposed for a stand-alone battery based power system (SABBPS) to utilize the MDMC as PWM converter, inverter, or PWM converter and inverter in different operation modes. In this study, the Extended Direct Duty Pulse Width Modulation (EDDPWM) technique has been applied to control the power flow path between the renewable source, load, and the battery. Corresponding to generator voltage, input frequency, and loads demands, several operating states and control strategies are possible. Therefore, the boundaries and distribution of operation modes are discussed and illustrated to improve the system performance. The mathematical equation of the EDDPWM under different operation modes has been derived to achieve the maximum voltage ratio in each mode. The theoretical and modulation concepts presented have been verified in simulation using MATLAB and experimental testing. Moreover, the THD, ripple, and power flow direction have been analyzed for output current to investigate the behavior of system in each operation mode.


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## Body

## 1. Introduction

Renewable sources, such as hydro, solar, and wind, have the potential to play an important role in providing energy with sustainability to the vast populations of the world who do not have access to clean energy. Currently the stand-alone power system supplies the local villages or individual users in remote area where the grid extension is difficult or not economical. In stand-alone renewable power system storage elements such as battery or supercapacitor are used to supply power to the loads continuously [1]. The complexity of the control system remarkably rises by increasing the number of input sources as several separate converters are employed to control the power flow direction between the input ports and output ports of system. The type and number of power electronic converters change based on the type and number of energy sources and loads.Multi-input DC-DC converter has been proposed to combine several types of energy sources and to obtain a desired DC output voltage [2]. This type of converter is commonly employed in the hybrid electric vehicles [3] and renewable power system to stabilize the voltage and frequency of system [4].Several schemes of converter with two source inputs and single output have been proposed for the stand-alone hybrid renewable energy system in order to increase the power quality and reliability of system [5, 6]. A double-input sources’ single-output source power converter was developed to combine the energy sources of wind and solar in one power system [5]. However, it will be difficult to acquire the regulated voltage output if one of the DC sources is diminished, since the input voltage variation is significant. Therefore, Chen et al. (2001) proposed the high frequency transformer for double source system with isolated electrical circuit to reduce the voltage variation effect. These circuits have no charging path for the backup battery storage and could not control the power flow direction in system [6].A multidirectional power converter (MDC) has been presented by Mei et al. (2006) for a battery based stand-alone hybrid renewable energy system to supply the battery and to control the power flow direction in a system. The MDC provided a battery storage path to supply the power demand in the days of deficit in solar and wind powers. However, the proposed MDC control was very complicated due to the number of modes and effect of power flow direction in high frequency isolated converter [7]. Later, the directional power converter is changed with bidirectional high-power-density DC-DC converter to interface with multiple energy storage components such as batteries and ultracapacitors. The proposed system needs multiwinding transformer for soft-switching conditions which cannot justify the unique features of low component count and compact structure for the integrated multiport converter [8].Four-port DC/DC converter with bidirectional capability and isolated output feature has been proposed to reduce the size. Zero-voltage switching is introduced for all four main switches. Three of the four ports were tightly regulated by adjusting their independent duty-cycle values, while the fourth port was left unregulated to maintain the power balance for the system. In addition, a decoupling network is introduced to allow the separate controller design for each power port. This four-port converter is suitable for low-power applications, where the energy storage is required while allowing tight load regulation [9]. However, the major problem is that the input and output port are DC and isolated transformer is essential for this structure.In order to achieve maximum power tracking (MPT) through rotor speed control under varying wind speeds and control of the magnitude and the frequency of the load voltage, the new multiport system has been introduced based on two back-to-back voltage source converters (VSCs) with a battery energy storage system at their DC link. The proposed hybrid system was able to control the power flow, by which it controls the magnitude and the frequency of the load voltage [10]. The number of converters and passive components is still high and it is not suitable for the integrated multiport converter. Moreover, the size and cost increase and efficiency decreases due to multiple-stage conversion through the converters and transformers.Most desired feature of multidirectional converter can be fulfilled by using matrix converter (MC) structure. In the MC, several bidirectional switches are used to couple the power sources to load side. With proper switching method, the bidirectional switches in MC can be utilized as inverter or rectifier. The first principle of MC control has been proposed by Venturini and Alesina in 1980, which is known as a “direct transfer function” approach [11]. They also extended the voltage ratio to 0.866 by using the third harmonic injection technique [12]. In 1983, Rodriguez introduced the novel control method based on “fictitious DC link” to reduce the complexity of direct method [13]. Ziogas et al. expanded Rodriguez’s “fictitious DC link” idea to provide a rigorous mathematical explanation [14, 15]. Later, Kastner and Rodriguez (1985) used space vectors modulation in the switching control of matrix converters to increase the voltage ratio and reduce the number of switching states [16, 17]. Several techniques have been reported which may have simplified the modulation [18–21] and solved the commutation problems in MC [22, 23]. Although the SVPWM technique is the proper method for the three-phase matrix converters, the complexity of the implementation remarkably rises by increasing the number of inputs or outputs of MC and there is no attention to the input current.To synthesize the sinusoidal input current with unity power factor and desired output voltage a new carrier based modulation method has been proposed based on the conventional space vector pulse modulation (SVPWM), with complex calculation [24]. In order to simplify the modulation method, the preliminary concepts of a new carrier based PWM strategy, named direct duty ratio PWM (DDPWM), are presented in [25]. They extended the DDPWM to various topologies of matrix converter and derived the control schemes for alternative structures converters in [26]. This modulation scheme is highly flexible and intuitive and it can be applied to any configuration of the matrix converter.Toosi et al. in 2014 combined the characteristics of several separate converters in multidirectional matrix converter (MDMC) and proposed a novel modulation method that can control the power flow direction between each of input power supplies and output loads. The proposed modulation method is able to inject power from DC and AC supply to the load simultaneously by using the proper switching pattern. They validated that the MDMC with EDDPWM can work as modular converter, where the frequency and voltage of each output phase are independent of other output phases [27]. However, the system has been tested in simulation and operated in one mode.Due to the high number of system parameters (i.e., number of inputs/outputs, load parameters and input filter, output frequency, switching frequency, modulation methods, and number of passive components) and the inherent differences between the converter topologies such as the maximum voltage transfer ratio, it is difficult to compare the proposed MDMC with the other multisource converters such as multidirectional power converter [7], ZVS bidirectional DC-DC converter [8], AC-DC-AC converter [28], multiport with several voltage sources converter [10], integrated four-port DC/DC converter [9], multi-input DC/DC converter [2], and double-input single-output power converter [5]. The main advantage of the MDMC for multi-input/output power system compared to other converters is its potential to decrease size of system by combining all characteristics of different rectifiers and inverters in one compact silicon converter and eliminating the passive component such as bulky capacitor and multiwinding transformer. In addition, the EDDPWM technique can provide bidirectional power flow, control input power factor, and synthesize the sinusoidal input current and output voltage waveforms.The voltage ratio of MDMC varied when the system switched from one operation mode to another mode. In order to keep the output voltage constant, the output voltage command should be calculated based on the type and number of input sources and output loads which are connected to the system. Accordingly, the behaviour of MDMC has been investigated in different operation modes to achieve the continuous power transmission and increase the efficiency by reducing the number of switches and calculating the maximum voltage ratio in each operation mode. By adjusting the time subinterval in EDDPWM method and analysing the power flow direction among the input and output ports of system, MDMC can work as inverter, PWM converter, or both PWM converter and inverter. In addition, this study is dedicated to analysis of the output current quality and derives the necessary equation of EDDPWM method in each operation mode.


## 2. Principle of Extended Direct Duty PWM

The operating principle of the EDDPWM has been described in [27], for MDMC with 15 bidirectional switches. Figure 1 indicates the circuit configuration of the MDMC in stand-alone battery based system (SABBS) when three-phase generator and two batteries are connected to the source side of the MDMC. The RL-dc and LL-dc and RL-ac and LL-ac indicate the DC and AC load, respectively.Figure 1
Multidirectional matrix converter circuit.According to Figures2 and 3, a switching period Ts is divided into two time periods, Tc and T3. During Tc, the input phases of AC generator are connected to a corresponding output terminal, and during T3 the input phases of DC battery are connected to a corresponding output terminal. In addition, the time interval Tc is divided into two periods, T1 and T2. Also, the MX, MD, and MN denote the instantaneous values of maximum, medium, and minimum input voltages of AC generator.Figure 2
Switching pattern I, outputR phase switching state.Figure 3
Switching pattern II, outputR phase switching state.Furthermore, POS and NEG denoted the instantaneous values of positive and negative input voltages of DC battery, respectively. DuringT1, the line-to-line voltage between MX and MN is used, which is the maximum line-to-line voltage among three line-to-line input voltages of generator at the sampling instant. During T2, the second maximum line-to-line voltage is used which is MX to MD for switching pattern I and MD to MN for switching pattern II. Finally, during T3 the line-to-line voltage between POS and NEG is employed.


### 2.1. Switching Pattern I

Figure2 indicates the switching pattern I, where the R phase duty ratio value (dR1) is compared with triangular carrier waveform to generate the R phase output voltage. The output phase is changed during the switching pattern I from MN→MX→MX→MD→NEG→POS, consequently. As illustrated in Figure 2, the output phase “R” is connected to the input phase “MN” during TR1 and when Ts is the sequence switching period. And it is connected to phases “MX,” “MX,” “MD,” “NEG,” and “POS” during time periods TR2, TR3, TR4, TR5, and TR6, respectively. These six time subintervals can be represented as (1), where dR1 is the R phase duty ratio value and carrier slops are defined as m=T1/Tc and n=Tc/Ts. Consider (1)TR1=dR1·m·n·Ts,TR2=1-dR1·m·n·Ts,TR3=1-dR1·1-m·n·Ts,TR4=dR1·1-m·n·Ts,TR5=dR1·1-n·Ts,TR6=1-dR1·1-n·Ts.The fluctuation of the input voltage is negligible during the switching periods. Thus, the integration of the output voltage voR over Ts can be expressed in(2)∫0TsvoRdt≅TR1·MN+TR2+TR3·MX+TR4MD+TR5·NEG+TR6·POS.Based on (1) and (2), the average output voltage can be expressed in terms of m and n as presented in(3)v-OR=1Ts∫0TsvoRdt≅dR1-1-n·POS-n·MX+1-m·n·MD+m·n·MN+1-n·NEG+n·MX-1-n·POS.Therefore, for present switching cycle, the duty ratio value, dR1, can be written as(4)dR1=voR∗-n·MX-1-n·POS-1-nPOS-n·MX+1-m·n·MD+m·n·MN+1-n·NEG,where voR∗ is the R phase output voltage command which is equal to v-OR.


### 2.2. Switching Pattern II

The procedure to drive the equation for switching pattern II is the same as the previous switching pattern. Figure3 illustrates the case of switching pattern II where the R phase duty ratio value (dR2) is compared with triangular carrier waveform to generate the R phase output voltage. The output phase is changed during switching pattern II from MN→MX→MD→MN→NEG→POS, consequently.Similarly, the integration of the output voltagevoR and the average output voltage v-OR is presented in(5)∫0TsvoRdt≅TR1+TR4·MN+TR2·MX+TR3·MD+TR5·NEG+TR6·POS,v-OR=1Ts∫0TsvoRdt≅dR2-1-n·POS-m·n·MX-1-m·n·MD+n·MN+1-n·NEG+1-n·POS-m·n·MX+1-m·n·MD.By letting v-OR be equal to voR∗ the duty ratio value dR2 can be written as (6)dR2=voR∗-n·MX-1-n·POS-1-n·POS-n·MX+1-m·n·MD+m·n·MN+1-n·NEG-1.When the switching state for output phase “R” is POS, NEG, MX, MD, or MN, the output phase “R” is connected to the input phase voltage POS, NEG, MX, MD, or MN, respectively. In fact, by using logic devices such as FPGA, the circuit for generating the PWM signal can easily be implemented.It is possible to synthesize the input current and control the power factor in EDDPWM by adjusting the amount ofm and n, when m and n are related to the maximum and minimum current as represented:(7)m≡T1Tc=-isMXisMN,n≡TcTs=isMNisMN-isPOS.


## 2.1. Switching Pattern I

Figure2 indicates the switching pattern I, where the R phase duty ratio value (dR1) is compared with triangular carrier waveform to generate the R phase output voltage. The output phase is changed during the switching pattern I from MN→MX→MX→MD→NEG→POS, consequently. As illustrated in Figure 2, the output phase “R” is connected to the input phase “MN” during TR1 and when Ts is the sequence switching period. And it is connected to phases “MX,” “MX,” “MD,” “NEG,” and “POS” during time periods TR2, TR3, TR4, TR5, and TR6, respectively. These six time subintervals can be represented as (1), where dR1 is the R phase duty ratio value and carrier slops are defined as m=T1/Tc and n=Tc/Ts. Consider (1)TR1=dR1·m·n·Ts,TR2=1-dR1·m·n·Ts,TR3=1-dR1·1-m·n·Ts,TR4=dR1·1-m·n·Ts,TR5=dR1·1-n·Ts,TR6=1-dR1·1-n·Ts.The fluctuation of the input voltage is negligible during the switching periods. Thus, the integration of the output voltage voR over Ts can be expressed in(2)∫0TsvoRdt≅TR1·MN+TR2+TR3·MX+TR4MD+TR5·NEG+TR6·POS.Based on (1) and (2), the average output voltage can be expressed in terms of m and n as presented in(3)v-OR=1Ts∫0TsvoRdt≅dR1-1-n·POS-n·MX+1-m·n·MD+m·n·MN+1-n·NEG+n·MX-1-n·POS.Therefore, for present switching cycle, the duty ratio value, dR1, can be written as(4)dR1=voR∗-n·MX-1-n·POS-1-nPOS-n·MX+1-m·n·MD+m·n·MN+1-n·NEG,where voR∗ is the R phase output voltage command which is equal to v-OR.


## 2.2. Switching Pattern II

The procedure to drive the equation for switching pattern II is the same as the previous switching pattern. Figure3 illustrates the case of switching pattern II where the R phase duty ratio value (dR2) is compared with triangular carrier waveform to generate the R phase output voltage. The output phase is changed during switching pattern II from MN→MX→MD→MN→NEG→POS, consequently.Similarly, the integration of the output voltagevoR and the average output voltage v-OR is presented in(5)∫0TsvoRdt≅TR1+TR4·MN+TR2·MX+TR3·MD+TR5·NEG+TR6·POS,v-OR=1Ts∫0TsvoRdt≅dR2-1-n·POS-m·n·MX-1-m·n·MD+n·MN+1-n·NEG+1-n·POS-m·n·MX+1-m·n·MD.By letting v-OR be equal to voR∗ the duty ratio value dR2 can be written as (6)dR2=voR∗-n·MX-1-n·POS-1-n·POS-n·MX+1-m·n·MD+m·n·MN+1-n·NEG-1.When the switching state for output phase “R” is POS, NEG, MX, MD, or MN, the output phase “R” is connected to the input phase voltage POS, NEG, MX, MD, or MN, respectively. In fact, by using logic devices such as FPGA, the circuit for generating the PWM signal can easily be implemented.It is possible to synthesize the input current and control the power factor in EDDPWM by adjusting the amount ofm and n, when m and n are related to the maximum and minimum current as represented:(7)m≡T1Tc=-isMXisMN,n≡TcTs=isMNisMN-isPOS.


## 3. System Operation Modes

According to the type and number of outputs and inputs connected to the system, the operation states of SABBPS system can be classified into five possible modes which are listed in Table1. Whether energy sources provide power for the load or battery, when the converter is connected to the AC load and when the battery bank absorbs or supplies power. In Table 1 the renewable source, supplying power to the battery, or the AC load is defined by “O” or “X.” For the battery bank, “▼” illustrates a discharge, whereas “▲” illustrates a charge. In addition, the AC load connecting to the MDMC is indicated by “O” or by “X.”Table 1
The operation states of SABBPS.
Parameters
SABBS operation mode
1
2
3
4
5
Three-phase generator
O
O
O
X
O
AC load
O
O
X
O
O
Battery bank
X
▲
▲
▼
▼
O = connected, X = disconnected, ▲ = charging, and ▼ = discharging.Power sources of the MDMC change for different operation modes. In operation mode 1, power is transferred from the AC generator to the AC output load. Thus, the battery bank is disconnected from the system and the MDMC acts as three-to-single-phase AC/AC converter. In operation mode 2, power is transferred from the AC generator to the battery bank and the AC output load; thus, the MDMC supplies power for the AC load and charges up the battery bank via the charging controller circuit; MDMC acts as inverter and PWM converter. In operation mode 3, the AC load is disconnected from system; the variable speed turbine only exports energy to the battery bank through the bidirectional switches of the MDMC (just charges up the battery bank). Thus, MDMC works as PWM converter. By following the above analytic approach, other operation modes also can be educated.Figure4 indicates the simplified sketch of the stand-alone battery based system under five different operation modes, where “G,” “BB,” and “L” represent the three-phase generator, the battery bank, and the AC load, respectively.Figure 4
Simplified sketch of the SABBS under different operation modes.


### 3.1. Battery Charging

Several methods, such as SOC estimation based on the terminal voltage and internal resistance [29], cell-impedance and impedance variation of cells/batteries [30, 31], error-correction mechanism based on Kalman filter for both state observation and prediction problems [32, 33], SOC estimation based on artificial neural networks [34], and fuzzy logic principles [35], have been reported by researchers to predict SOC. According to [36] the open circuit voltage method is online and cheap and makes it easily to determine SOC in battery based system. Open circuit voltage technique for SOC estimation monitors the terminal voltage and current under discharging state to determine the voltage of a battery under load.The MDMC with EDDPWM method introduced by [27] is able to read the voltage at the DC side continually and monitor the amount of current injection to DC load to determine the SOC and charging the battery. Therefore, the output phases S and T indicated in Figure 1 can be used for battery charging or supplying the DC load. However, the extra charge control circuit should be added to the system to increase the safety and reduce the charging time of system.


## 3.1. Battery Charging

Several methods, such as SOC estimation based on the terminal voltage and internal resistance [29], cell-impedance and impedance variation of cells/batteries [30, 31], error-correction mechanism based on Kalman filter for both state observation and prediction problems [32, 33], SOC estimation based on artificial neural networks [34], and fuzzy logic principles [35], have been reported by researchers to predict SOC. According to [36] the open circuit voltage method is online and cheap and makes it easily to determine SOC in battery based system. Open circuit voltage technique for SOC estimation monitors the terminal voltage and current under discharging state to determine the voltage of a battery under load.The MDMC with EDDPWM method introduced by [27] is able to read the voltage at the DC side continually and monitor the amount of current injection to DC load to determine the SOC and charging the battery. Therefore, the output phases S and T indicated in Figure 1 can be used for battery charging or supplying the DC load. However, the extra charge control circuit should be added to the system to increase the safety and reduce the charging time of system.


## 4. Equivalent Circuit of the Converter

The EDDPWM control method can be applied to the MDMC as a modular structure for each phase where each output phase has the independent reference control signal. This reference control signal can be different in terms of frequency, waveform shape, and amplitude [27]. The MDMC works in operation modes 1, 2, and 3 when the line-to-neutral voltage of AC generator vs-rms is bigger than battery voltage vs-dc and works in operation modes 4 and 5 when vs-dc is bigger than the line-to-neutral vs-rms.Regarding the semiconductor finite switching times and propagation delays in practical, switches cannot be switched on and off instantaneously in MDMC. In addition, due to the lack of a natural free-wheeling in this structure, reliable current commutation between switches in MDMC is too difficult. Therefore, in this study, current commutation or four-step commutation method introduced by [37, 38] has been improved based on MDMC structure for safe commutation between an outgoing and an incoming switch. Furthermore, in MDMC, any problem in supplying the current to load can be generated over voltages at output phase. Also, overvoltages can appear from the input side caused by line disturbance. Hence, a clamp circuit introduced by [39] has been modified based on MDMC structure to avoid overvoltages coming from the grid and from the load to the system.


### 4.1. Operation Mode 1

In this mode, the MDMC acts as three-phase to single-phase matrix converter. The power is transferred through the three bidirectional switches which are connected to input phasesa, b, and c to output phase R. According to switching patterns I and II when n=1, the input of MDMC is connected to the AC generator and battery is disconnected from the system. Figure 5 indicates the circuit configuration of MDMC in operation mode 1 with neutral connection.Figure 5
Circuit configuration of MDMC in operation mode 1.According to EDDPWM switching method, output terminals can separately be controlled to follow their reference signals. Therefore, the EDDPWM can be used as modular configuration at each output phase. The duty ratio for phaseR in operation mode 1 can be represented as (8). Due to the existence of neutral connection in this mode the maximum voltage ratio is limited to qmax⁡=0.5. q is the voltage ratio of the input terminal voltage to the output terminal voltage (vo-rms/vs-rms). The duty cycle in operation mode 1 for switching pattern I and switching pattern II can be calculated in the same manner of (4) and (6) while n=1 in this operation mode. The duty ratio can be represented as follows for switching patterns I and II, respectively: (8)dR1=voR∗-MX-MX+1-m·MD+m·MN,(9)dR2=voR∗-n·MX+1-m·MD-m·MX+-1+m·MD+MN.The output voltage command voR∗ of the converter can be represented as below:(10)voR∗=23·q·vs-rms·sin⁡2πfot,where vs-rms is the line-to-line RMS value and fo is the desired output frequency for the corresponding phase.


### 4.2. Operation Mode 2

In this mode, the MDMC acts as three-phase to single-phase matrix converter [40] (through the switches SaR, SbR, and ScR) and two three-phase to single-phase PWM converter (through the switches SaS, SbS, and ScS for output phase S and SaT, SbT, and ScT for phase T). The power is transferred through the nine bidirectional switches which are connected to input phases a, b, and c to output phases R, S, and T. As described in operation mode 1 when n=1, the input of MDMC is connected to the AC generator and battery is disconnected from the system. Figure 6 shows the circuit configuration of MDMC in operation mode 2 with three output terminals.Figure 6
Circuit configuration of MDMC in operation mode 2.Three bidirectional switches are used for each output phase to apply the switching patterns I and II. The POS and NEG input phases are always disconnected while MX, MD, and MN are selected by instantaneous comparison of the AC input phases. When the switching state for output phase “R” is MX, MD, or MN, the output phase “R” is connected to the input phase where the voltage is MX, MD, or MN, respectively. The duty ratio formula is the same as direct duty PWM presented in [25].The duty ratio of phasesS and T is indicated as dS and dT and can be derived in the same way of phase R by letting v-OS and v-OT be equal to the S and T phase voltage commands voS∗ and voT∗, respectively. The duty ratio for phases S and T can be presented as(11)dS=dS1=voS∗-MX-MX+1-m·MD+m·MNdS2=voS∗-n·MX+1-m·MD-m·MX+-1+m·MD+MNdT=dT1=voT∗-MX-MX+1-m·MD+m·MNdT2=voT∗-n·MX+1-m·MD-m·MX+-1+m·MD+MN.The voltage command for phase R is the same as (10), and the voltage command for phases S and T can be expressed as follows:(12)voS∗=-voT∗=23·q·vs-rms.


### 4.3. Operation Mode 3

In this mode, the MDMC acts as double three-phase to single-phase PWM converter. The power is transferred through the six bidirectional switches which are connected to input phasesa, b, and c to output phases S and T. The time subinterval for AC switch is equal to switching period (Tc=Ts), the input of MDMC is connected to the AC generator, and battery is disconnected from the system. Figure 7 illustrates the circuit configuration of MDMC in operation mode 3 when the bidirectional switches connected to phase R are turned off.Figure 7
Circuit configuration of MDMC in operation mode 3.The duty ratio for phasesS and T can be calculated in the same way as (11). The voltage command is also the same as (12) for phases S and T. The DC voltage can be used for DC load or charging the battery through the proper charging circuit.


### 4.4. Operation Mode 4

In this mode, the MDMC acts as single PWM converter. The power is transferred through the two bidirectional switches which are connected to DC input phasesP and N to output phase R. The time subinterval for AC switch becomes zero (n=Tc=0), the input of MDMC is connected to the battery, and AC generator is disconnected from the system. Figure 8 demonstrates the circuit configuration of MDMC in operation mode 4 when the bidirectional switches SPR and SNR are connected to phase R.Figure 8
Circuit configuration of MDMC in operation mode 4.By puttingn=0 in (4) and (6), the duty ratio for operation mode 4 in switching patterns I and II can be expressed as below:(13)dR=vR∗-POS-POS+NEGwhen the vR∗ is (14)voR∗=122·q·vs-PN·sin⁡2πfot.For this operation mode, the voltage ratio can be increased to 1/2≈0.7 as the input is connected to DC sources.


### 4.5. Operation Mode 5

In conventional battery based system when the generator power is less than load demands, the generator is disconnected from system and battery will supply the system. According to the EDDPWM method, the generator and battery can supply the load, simultaneously. Therefore, in this operation mode, the MDMC acts as five-phase to single-phase converter. The power is transferred through the five bidirectional switches which are connected to AC and DC input phasesa, b, c, P, and N to output phase R. The duty ratio of phase R is indicated in (4) and (6) for switching patterns I and II, respectively. The voltage command for phase R can be expressed as follows: (15)voR∗=122·q·vs-PN·sin⁡2πfot.Figure 9 demonstrates the circuit configuration of MDMC in operation mode 5 when the bidirectional switches SaR, SbR, ScR, SPR, and SNR are connected to phase R. For this operation mode, the voltage ratio can be increased to 0.6 as the input is connected to AC and DC sources.Figure 9
Circuit configuration of MDMC in operation mode 5.In this mode, the maximum voltage ratio can change within0.6<q<0.7 as expressed in (14): (16)q=0.7-k-0.252.5fork>0.25,0.7-0.25-k2.5fork<0.25,where k=vs-rms/(vs-rms+vsP) indicates the magnitude variation between line-to-neutral RMS value of input AC and DC power supplies and vs-rms and vsP indicate the RMS value of generator input voltage and DC power supply, respectively.


## 4.1. Operation Mode 1

In this mode, the MDMC acts as three-phase to single-phase matrix converter. The power is transferred through the three bidirectional switches which are connected to input phasesa, b, and c to output phase R. According to switching patterns I and II when n=1, the input of MDMC is connected to the AC generator and battery is disconnected from the system. Figure 5 indicates the circuit configuration of MDMC in operation mode 1 with neutral connection.Figure 5
Circuit configuration of MDMC in operation mode 1.According to EDDPWM switching method, output terminals can separately be controlled to follow their reference signals. Therefore, the EDDPWM can be used as modular configuration at each output phase. The duty ratio for phaseR in operation mode 1 can be represented as (8). Due to the existence of neutral connection in this mode the maximum voltage ratio is limited to qmax⁡=0.5. q is the voltage ratio of the input terminal voltage to the output terminal voltage (vo-rms/vs-rms). The duty cycle in operation mode 1 for switching pattern I and switching pattern II can be calculated in the same manner of (4) and (6) while n=1 in this operation mode. The duty ratio can be represented as follows for switching patterns I and II, respectively: (8)dR1=voR∗-MX-MX+1-m·MD+m·MN,(9)dR2=voR∗-n·MX+1-m·MD-m·MX+-1+m·MD+MN.The output voltage command voR∗ of the converter can be represented as below:(10)voR∗=23·q·vs-rms·sin⁡2πfot,where vs-rms is the line-to-line RMS value and fo is the desired output frequency for the corresponding phase.


## 4.2. Operation Mode 2

In this mode, the MDMC acts as three-phase to single-phase matrix converter [40] (through the switches SaR, SbR, and ScR) and two three-phase to single-phase PWM converter (through the switches SaS, SbS, and ScS for output phase S and SaT, SbT, and ScT for phase T). The power is transferred through the nine bidirectional switches which are connected to input phases a, b, and c to output phases R, S, and T. As described in operation mode 1 when n=1, the input of MDMC is connected to the AC generator and battery is disconnected from the system. Figure 6 shows the circuit configuration of MDMC in operation mode 2 with three output terminals.Figure 6
Circuit configuration of MDMC in operation mode 2.Three bidirectional switches are used for each output phase to apply the switching patterns I and II. The POS and NEG input phases are always disconnected while MX, MD, and MN are selected by instantaneous comparison of the AC input phases. When the switching state for output phase “R” is MX, MD, or MN, the output phase “R” is connected to the input phase where the voltage is MX, MD, or MN, respectively. The duty ratio formula is the same as direct duty PWM presented in [25].The duty ratio of phasesS and T is indicated as dS and dT and can be derived in the same way of phase R by letting v-OS and v-OT be equal to the S and T phase voltage commands voS∗ and voT∗, respectively. The duty ratio for phases S and T can be presented as(11)dS=dS1=voS∗-MX-MX+1-m·MD+m·MNdS2=voS∗-n·MX+1-m·MD-m·MX+-1+m·MD+MNdT=dT1=voT∗-MX-MX+1-m·MD+m·MNdT2=voT∗-n·MX+1-m·MD-m·MX+-1+m·MD+MN.The voltage command for phase R is the same as (10), and the voltage command for phases S and T can be expressed as follows:(12)voS∗=-voT∗=23·q·vs-rms.


## 4.3. Operation Mode 3

In this mode, the MDMC acts as double three-phase to single-phase PWM converter. The power is transferred through the six bidirectional switches which are connected to input phasesa, b, and c to output phases S and T. The time subinterval for AC switch is equal to switching period (Tc=Ts), the input of MDMC is connected to the AC generator, and battery is disconnected from the system. Figure 7 illustrates the circuit configuration of MDMC in operation mode 3 when the bidirectional switches connected to phase R are turned off.Figure 7
Circuit configuration of MDMC in operation mode 3.The duty ratio for phasesS and T can be calculated in the same way as (11). The voltage command is also the same as (12) for phases S and T. The DC voltage can be used for DC load or charging the battery through the proper charging circuit.


## 4.4. Operation Mode 4

In this mode, the MDMC acts as single PWM converter. The power is transferred through the two bidirectional switches which are connected to DC input phasesP and N to output phase R. The time subinterval for AC switch becomes zero (n=Tc=0), the input of MDMC is connected to the battery, and AC generator is disconnected from the system. Figure 8 demonstrates the circuit configuration of MDMC in operation mode 4 when the bidirectional switches SPR and SNR are connected to phase R.Figure 8
Circuit configuration of MDMC in operation mode 4.By puttingn=0 in (4) and (6), the duty ratio for operation mode 4 in switching patterns I and II can be expressed as below:(13)dR=vR∗-POS-POS+NEGwhen the vR∗ is (14)voR∗=122·q·vs-PN·sin⁡2πfot.For this operation mode, the voltage ratio can be increased to 1/2≈0.7 as the input is connected to DC sources.


## 4.5. Operation Mode 5

In conventional battery based system when the generator power is less than load demands, the generator is disconnected from system and battery will supply the system. According to the EDDPWM method, the generator and battery can supply the load, simultaneously. Therefore, in this operation mode, the MDMC acts as five-phase to single-phase converter. The power is transferred through the five bidirectional switches which are connected to AC and DC input phasesa, b, c, P, and N to output phase R. The duty ratio of phase R is indicated in (4) and (6) for switching patterns I and II, respectively. The voltage command for phase R can be expressed as follows: (15)voR∗=122·q·vs-PN·sin⁡2πfot.Figure 9 demonstrates the circuit configuration of MDMC in operation mode 5 when the bidirectional switches SaR, SbR, ScR, SPR, and SNR are connected to phase R. For this operation mode, the voltage ratio can be increased to 0.6 as the input is connected to AC and DC sources.Figure 9
Circuit configuration of MDMC in operation mode 5.In this mode, the maximum voltage ratio can change within0.6<q<0.7 as expressed in (14): (16)q=0.7-k-0.252.5fork>0.25,0.7-0.25-k2.5fork<0.25,where k=vs-rms/(vs-rms+vsP) indicates the magnitude variation between line-to-neutral RMS value of input AC and DC power supplies and vs-rms and vsP indicate the RMS value of generator input voltage and DC power supply, respectively.


## 5. Results and Discussion

### 5.1. Simulation Result

Simulation of the EDDPWM method for MDMC is performed by using MATLAB software. The voltage ratio has been changed in each operation mode to investigate the stability of system. The switching periodTs is assumed to be 200 μs in all operation modes. The simulation parameters shown in Table 2 are the same for all operation modes.Table 2
Simulation parameter.
Parameter
Value
R
-
L load
R
=
5 Ω, L=10 mH
Input filter inductorLf
100μH
Input filter capacitorCf
60μF
Input voltage(line-to-neutral) Vs-rms
56 V
Battery voltage(line-to-neutral) Vs-dc
±48 V
Input frequencyfs
60 Hz
Output frequencyfo
50 HzThe input line-to-neutral input voltage (Vs-rms) in operation modes 1, 2, and 3 is bigger than the battery voltage (Vs-dc) as shown in Table 2. The AC voltage Vs-rms is less than Vs-dc in operation modes 4 and 5 and it is equal to 35 V.Figure10 indicates the AC output voltage and current waveforms of proposed MDMC in operation mode 1, respectively. In this mode the voltage ratio (q) has been increased from 0.3 to 0.5 at time t=0.07 (s). The simulation result indicates that the MDMC is able to reach the maximum voltage ratio (q=0.5) in operation mode 1 without any distortion in output voltage or output current waveforms.Figure 10
Simulation waveforms of operation mode 1.
(a)
AC output voltage
(b)
AC output currentFigures11(a) and 11(b) illustrate the line-to-line DC output voltage of voST and line-to-neutral and AC output voltage of voR. Figure 11(c) shows the simulated responses of MDMC in operation mode 2 when the voltage ratio is changed in AC and DC side at t=0.07 and t=0.09 s, respectively. According to Figure 11(c), the current in ioS and ioT is constant at t=0.07 regardless of the changing in ioR which is increased by 0.4 pu. In addition, when the voltage ratio for DC phase is reduced from 0.5 to 0.3, the current in AC side remains constant at t=0.09 s. The simulation result validates that the proposed EDDPWM is able to track the variation in reference control signal for each phase without disturbing the signal in other output terminals.Figure 11
Simulation waveforms of operation mode 2.
(a)
DC output voltage
(b)
AC output voltage
(c)
Output current waveformsFigure12 indicates the DC output voltage and current waveforms of proposed MDMC in operation mode 3, respectively. In this mode the voltage ratio (q) has been reduced from 0.5 to 0.3 at time t=0.09 (s). The simulation result reveals that the MDMC is able to track the control signal in terms of waveforms, frequency, and amplitude regardless of the type and the number of outputs connected to the system.Figure 12
Simulation waveforms of operation mode 3.
(a)
DC output voltage
(b)
DC output currentFigure13 illustrates the line-to-neutral AC load voltage and current waveforms in operation mode 3, respectively. According to Figure 13 the voltage ratio can reach 0.7 in operation mode 4, when the AC power supply is disconnected from the system. The simulation result reveals that the output voltage has been synthesized well with maximum voltage ratio of 0.7.Figure 13
Simulation waveforms of operation mode 4.
(a)
AC output voltage
(b)
AC output currentMeanwhile, the maximum voltage ratio is equal to 0.5 for operation modes 1, 2, and 3 when the line-to-neutral voltage of AC generatorvs-rms is bigger than battery voltage vs-dc.In conventional battery based system when the voltage of generator is less than battery voltage, AC power supply will be disconnected from system and demand power will be supplied by battery bank. By using the EDDPWM for MDMC, it is possible to inject the power from AC and DC power supply and reach the maximum voltage ratio that is expressed in (12).Figure14 indicates the AC output voltage and current waveforms of proposed MDMC in operation mode 5, respectively. In this mode the voltage ratio (q) has been increased from 0.4 to 0.63 at time t=0.07 (s).Figure 14
Simulation waveforms of operation mode 5.
(a)
AC output voltage
(b)
AC output currentIt can be clearly seen from Figure14 that the system is able to track the variation of reference voltage output of terminal R. Moreover, the simulation results exhibited that the undershoot/overshoot and steady-state error for output currents are acceptable in all operation modes.


### 5.2. Experimental Result

To verify the feasibility of the novel EDDPWM method for the proposed MDMC, an experimental setup was built and the EDDPWM controller was implemented using Xilinx Virtex-6 FPGA DSP development kit. Figure15 shows the experimental setup built in laboratory.Figure 15
Experimental setup of multidirectional matrix converter.In order to test the stability of the system, reference voltage is changed in AC and DC sides while the loads are constant. Table3 indicates the experimental parameters of the proposed system when reference voltage is changed. The output voltage variation is not visible in voltage waveform as the switching frequency is high in this modulation method. At constant load the current waveform increases or decreases in accordance with sudden change of reference voltage variation. Figure 16 shows the responses of MDMC when the reference voltage is changed in AC and DC side at t=4.01 s and t=5.27 s, respectively, in operation mode 2. According to Figure 16(a), the output current ioS remains constant at t=4.01 s regardless of the changing in ioR which results in voltage reduction of 0.4 pu, where the step change of Flag signal indicates the instant change of the reference voltage. Furthermore, when the DC reference voltage is reduced by 0.4 pu, as shown in Figure 16(b), the current in AC side remains constant at t=5.27 s.Table 3
Dynamic state experimental parameter and reference voltage variation.
Parameter
Value
R
-
L load
R
=
3.1 Ω, L=6.4 mH
AC input voltage(line-to-neutral RMS) Vs-RMS
30 V
DC input voltageVs-dc
±24 V
Input frequencyfs
60 Hz
Output frequencyfo
50 Hz
Switching frequencyfsw
5 KHz
Switching periodTs
200μsFigure 16
The dynamic state of experimental waveform: current reference variation.
(a)
When reference current is reduced by 0.4 pu in phaseR
(b)
When reference current is reduced by 0.4 pu in phaseSIt can clearly be seen from Figure16 that the system is able to track the variation of reference voltage in each phase separately. The experimental result validates that the reference control signal of each output terminal is independent of other output terminals in terms of frequency, waveform shape, and amplitude. Moreover, the experimental results exhibited that the undershoot/overshoot and dynamic-state error for current waveforms are acceptable for SABBS.


### 5.3. Total Harmonic Distortion

While there is no national standard dictating total harmonic distortion limits on systems, there are suggested values for acceptable harmonic distortion. IEEE-519 provides recommended harmonic values for power electronic systems. The allowable THD in the input current of the power converter generally is restricted between 10 and 30% depending on the grid impedance limits [41, 42].According to IEEE-519 standards, the maximum THD in the grid current cannot exceed 5% for THD and 3% for any single harmonic. It is important to note that the recommendations and values given in this standard are purely voluntary. However, keeping low THD values on a system will further ensure proper operation of equipment and a longer equipment life span.Table4 compares the DC output current ripple and AC output current THD of simulation and experimental results for MDMC in different operation modes. The results indicated that the THD is different in each operation mode as the number of switches, type of input/output, and input voltage and frequency have been varied in each operation mode. Furthermore, the nonideal characteristic of component, total propagation delay of system, inherent noise and distortion of input power supply, and finite switching times in practical could be the reason for THD gap between the experimental and simulation results. In addition, both generator and DC power supply in experimental setup have some noise and distortion which have direct effect on system performance and output waveform quality.Table 4
Experimental and simulation distortions comparison.
Parameter
Operation mode 1
Operation mode 2
Operation mode 3
Operation mode 4
Operation mode 5
Simulation THD
7.22%
7.29%
—
5.7%
3.59%
Simulation DC current ripple
—
4.1%
3.9%
—
—
Experimental THD
14.32%
14.54%
—
13.95%
13.77%
Experimental DC current ripple
—
11.2%
8.7%
—
—According to Table4 and waveform result, the highest THD and ripple appear in operation mode 2 as the AC and DC appear in output phase together. The THD in operation mode 5 is less than other operation modes since 5 bidirectional switches are used to supply the load. In addition, in operation mode 5 the AC voltage is less than the DC voltage and input current has been synthesized by adjusting two variables, n and m. Therefore, the input current distortion is compensated by proper switching between the two input power supplies.


## 5.1. Simulation Result

Simulation of the EDDPWM method for MDMC is performed by using MATLAB software. The voltage ratio has been changed in each operation mode to investigate the stability of system. The switching periodTs is assumed to be 200 μs in all operation modes. The simulation parameters shown in Table 2 are the same for all operation modes.Table 2
Simulation parameter.
Parameter
Value
R
-
L load
R
=
5 Ω, L=10 mH
Input filter inductorLf
100μH
Input filter capacitorCf
60μF
Input voltage(line-to-neutral) Vs-rms
56 V
Battery voltage(line-to-neutral) Vs-dc
±48 V
Input frequencyfs
60 Hz
Output frequencyfo
50 HzThe input line-to-neutral input voltage (Vs-rms) in operation modes 1, 2, and 3 is bigger than the battery voltage (Vs-dc) as shown in Table 2. The AC voltage Vs-rms is less than Vs-dc in operation modes 4 and 5 and it is equal to 35 V.Figure10 indicates the AC output voltage and current waveforms of proposed MDMC in operation mode 1, respectively. In this mode the voltage ratio (q) has been increased from 0.3 to 0.5 at time t=0.07 (s). The simulation result indicates that the MDMC is able to reach the maximum voltage ratio (q=0.5) in operation mode 1 without any distortion in output voltage or output current waveforms.Figure 10
Simulation waveforms of operation mode 1.
(a)
AC output voltage
(b)
AC output currentFigures11(a) and 11(b) illustrate the line-to-line DC output voltage of voST and line-to-neutral and AC output voltage of voR. Figure 11(c) shows the simulated responses of MDMC in operation mode 2 when the voltage ratio is changed in AC and DC side at t=0.07 and t=0.09 s, respectively. According to Figure 11(c), the current in ioS and ioT is constant at t=0.07 regardless of the changing in ioR which is increased by 0.4 pu. In addition, when the voltage ratio for DC phase is reduced from 0.5 to 0.3, the current in AC side remains constant at t=0.09 s. The simulation result validates that the proposed EDDPWM is able to track the variation in reference control signal for each phase without disturbing the signal in other output terminals.Figure 11
Simulation waveforms of operation mode 2.
(a)
DC output voltage
(b)
AC output voltage
(c)
Output current waveformsFigure12 indicates the DC output voltage and current waveforms of proposed MDMC in operation mode 3, respectively. In this mode the voltage ratio (q) has been reduced from 0.5 to 0.3 at time t=0.09 (s). The simulation result reveals that the MDMC is able to track the control signal in terms of waveforms, frequency, and amplitude regardless of the type and the number of outputs connected to the system.Figure 12
Simulation waveforms of operation mode 3.
(a)
DC output voltage
(b)
DC output currentFigure13 illustrates the line-to-neutral AC load voltage and current waveforms in operation mode 3, respectively. According to Figure 13 the voltage ratio can reach 0.7 in operation mode 4, when the AC power supply is disconnected from the system. The simulation result reveals that the output voltage has been synthesized well with maximum voltage ratio of 0.7.Figure 13
Simulation waveforms of operation mode 4.
(a)
AC output voltage
(b)
AC output currentMeanwhile, the maximum voltage ratio is equal to 0.5 for operation modes 1, 2, and 3 when the line-to-neutral voltage of AC generatorvs-rms is bigger than battery voltage vs-dc.In conventional battery based system when the voltage of generator is less than battery voltage, AC power supply will be disconnected from system and demand power will be supplied by battery bank. By using the EDDPWM for MDMC, it is possible to inject the power from AC and DC power supply and reach the maximum voltage ratio that is expressed in (12).Figure14 indicates the AC output voltage and current waveforms of proposed MDMC in operation mode 5, respectively. In this mode the voltage ratio (q) has been increased from 0.4 to 0.63 at time t=0.07 (s).Figure 14
Simulation waveforms of operation mode 5.
(a)
AC output voltage
(b)
AC output currentIt can be clearly seen from Figure14 that the system is able to track the variation of reference voltage output of terminal R. Moreover, the simulation results exhibited that the undershoot/overshoot and steady-state error for output currents are acceptable in all operation modes.


## 5.2. Experimental Result

To verify the feasibility of the novel EDDPWM method for the proposed MDMC, an experimental setup was built and the EDDPWM controller was implemented using Xilinx Virtex-6 FPGA DSP development kit. Figure15 shows the experimental setup built in laboratory.Figure 15
Experimental setup of multidirectional matrix converter.In order to test the stability of the system, reference voltage is changed in AC and DC sides while the loads are constant. Table3 indicates the experimental parameters of the proposed system when reference voltage is changed. The output voltage variation is not visible in voltage waveform as the switching frequency is high in this modulation method. At constant load the current waveform increases or decreases in accordance with sudden change of reference voltage variation. Figure 16 shows the responses of MDMC when the reference voltage is changed in AC and DC side at t=4.01 s and t=5.27 s, respectively, in operation mode 2. According to Figure 16(a), the output current ioS remains constant at t=4.01 s regardless of the changing in ioR which results in voltage reduction of 0.4 pu, where the step change of Flag signal indicates the instant change of the reference voltage. Furthermore, when the DC reference voltage is reduced by 0.4 pu, as shown in Figure 16(b), the current in AC side remains constant at t=5.27 s.Table 3
Dynamic state experimental parameter and reference voltage variation.
Parameter
Value
R
-
L load
R
=
3.1 Ω, L=6.4 mH
AC input voltage(line-to-neutral RMS) Vs-RMS
30 V
DC input voltageVs-dc
±24 V
Input frequencyfs
60 Hz
Output frequencyfo
50 Hz
Switching frequencyfsw
5 KHz
Switching periodTs
200μsFigure 16
The dynamic state of experimental waveform: current reference variation.
(a)
When reference current is reduced by 0.4 pu in phaseR
(b)
When reference current is reduced by 0.4 pu in phaseSIt can clearly be seen from Figure16 that the system is able to track the variation of reference voltage in each phase separately. The experimental result validates that the reference control signal of each output terminal is independent of other output terminals in terms of frequency, waveform shape, and amplitude. Moreover, the experimental results exhibited that the undershoot/overshoot and dynamic-state error for current waveforms are acceptable for SABBS.


## 5.3. Total Harmonic Distortion

While there is no national standard dictating total harmonic distortion limits on systems, there are suggested values for acceptable harmonic distortion. IEEE-519 provides recommended harmonic values for power electronic systems. The allowable THD in the input current of the power converter generally is restricted between 10 and 30% depending on the grid impedance limits [41, 42].According to IEEE-519 standards, the maximum THD in the grid current cannot exceed 5% for THD and 3% for any single harmonic. It is important to note that the recommendations and values given in this standard are purely voluntary. However, keeping low THD values on a system will further ensure proper operation of equipment and a longer equipment life span.Table4 compares the DC output current ripple and AC output current THD of simulation and experimental results for MDMC in different operation modes. The results indicated that the THD is different in each operation mode as the number of switches, type of input/output, and input voltage and frequency have been varied in each operation mode. Furthermore, the nonideal characteristic of component, total propagation delay of system, inherent noise and distortion of input power supply, and finite switching times in practical could be the reason for THD gap between the experimental and simulation results. In addition, both generator and DC power supply in experimental setup have some noise and distortion which have direct effect on system performance and output waveform quality.Table 4
Experimental and simulation distortions comparison.
Parameter
Operation mode 1
Operation mode 2
Operation mode 3
Operation mode 4
Operation mode 5
Simulation THD
7.22%
7.29%
—
5.7%
3.59%
Simulation DC current ripple
—
4.1%
3.9%
—
—
Experimental THD
14.32%
14.54%
—
13.95%
13.77%
Experimental DC current ripple
—
11.2%
8.7%
—
—According to Table4 and waveform result, the highest THD and ripple appear in operation mode 2 as the AC and DC appear in output phase together. The THD in operation mode 5 is less than other operation modes since 5 bidirectional switches are used to supply the load. In addition, in operation mode 5 the AC voltage is less than the DC voltage and input current has been synthesized by adjusting two variables, n and m. Therefore, the input current distortion is compensated by proper switching between the two input power supplies.


## 6. Conclusion

This paper presents a systematic approach for MDMC based on the power flow direction among the input and output ports to enhance the performance of stand-alone battery based system and to achieve the continuous power transmission. According to the proposed power flow strategy, the connected input and output terminals with corresponding bidirectional switches have been determined to supply the power demand with minimum number of switches. The maximum possible voltage ratio has been calculated in each operation mode. The result validates that the MDMC can work as inverter, PWM converter, or PWM converter and inverter by adjusting the time subinterval in EDDPWM method. In addition, the proposed EDDPWM was able to change the function of the MDMC from inverter to rectifier, rectifier to inverter, rectifier and inverter to inverter, or rectifier based on the operation modes of system.Particularly, this study exhibited that the maximum voltage ratio is achievable for each operation mode when the undershoot/overshoot and steady-state error for output currents are acceptable in all operation modes. In addition, the quality of output currents has been analysed in terms of THD and ripples.Based on the literature and result of the present study, as the proposed converter switched from inverter to rectifier in different operation mode, an active power filter can improve the output waveform quality and reduce the noise in input current.In addition, the modulation control method can be applied to the MDMC as a modular structure for each phase where each output phase has the independent reference control signal. Therefore, the proposed MDMC structure can be used for programmable power supply and extended to the hybrid system with higher number of input and output phases.



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*Source: 452740-2015-10-19.xml*