Bidirectional Power Flow Control of a Multi Input Converter for Energy Storage System

Abstract

The objective of this paper is to propose a multi-input DC-DC converter with bidirectional power flow control capability. Compared to the traditional power converter, the multi-input converter (MIC) can save on the number of components and the circuit cost. Under normal conditions, the MIC is able to transfer energy from different input sources to the load. However, if the battery module is adopted, both the charging or discharging features should be considered. Therefore, the bidirectional power flow control of the MIC is necessary. On the other hand, because of the inconsistency characteristics of batteries, unbalanced circuit operation might occur whereby the circuit and the battery might be damaged. Therefore, dynamic current regulation strategies are developed for the MIC. Consequently, the proposed MIC circuit is able to achieve the bidirectional power flow control capability as well as control the input currents independently. Detailed circuit analysis and comprehensive mathematical derivation and of the proposed MIC will be presented in this paper. Finally, both simulation and experimental results obtained from a 500 W prototype circuit verify the performance and feasibility of the proposed bidirectional multi-input converter.

1. Introduction

Nowadays, global environmental protection and green energy sources are being paid high attention to deal with the fossil fuel usage and carbon dioxide emission issues [1,2]. Novel energy technologies such as photovoltaic (PV) power generation systems, wind power systems, electric vehicles and advanced consumer electronics have been rapidly developed [3,4,5,6]. The battery module is an essential component for energy storage [7,8,9,10]. In addition, a battery charger consisting of DC-DC converters integrated with the pulse-width-modulation (PWM) technology is necessary to control the battery energy [11,12,13]. Moreover, the bidirectional power flow control of the battery charger is also an essential function to realize both charging and discharging ability for the battery [14,15,16,17].

If two different sources are considered and expected to connect to the same load, two DC-DC converters should be utilized, as seen in the conceptual diagram shown in Figure 1a, where if the two input sources, V_in1 and V_in2 are replaced by battery modules, the charging or discharging current can be controlled independently via the two DC-DC converters. However, the number of required DC-DC converters will increase if more input sources are adopted. Consequently, the size and cost of the system will be increased while the stability will be decreased. In order to reduce the size and cost of the system as well as to enhance the circuit stability, the multi-input converter (MIC) has been developed with the circuit diagram shown in Figure 1b. It can be confirmed that two or more input sources can be included with one shared DC-DC converter. Moreover, the DC sources can be connected either in series or in parallel to transfer energy to the load via the MIC.

Different kinds of MIC circuit topologies and applications have been proposed [18,19,20,21,22,23]. First, a multi-input DC-DC converter based on flux additivity was proposed in [18]. A multi-winding transformer was adopted in this MIC topology. Reference [19] proposed a MIC for the photovoltaic (PV) power system and AC mains applications with maximum power point tracking, power factor correction and ripple-free input current features. In [20], a novel double-input pulse-width-modulation DC-DC converter for high-/low-voltage sources is proposed. The two input sources can be connected either in series or in parallel to transfer the energy to the load. Besides, a multi-input inverter for the grid-connected hybrid photovoltaic/wind power system is proposed in [21]. The output power characteristics of the PV array and the wind turbine are also considered. Reference [22] proposed a general approach for developing multi-input converters (MICs). In this literature, it was confirmed that all of the MIC topologies can be summarized as two families, which are: (1) PVSCs and (2) PCSCs. In addition, a semi-isolated MIC for hybrid PV/wind power charger system was presented in [23], with a topology composed of isolated and/or non-isolated DC-DC converters. Although these proposed circuits and methods are effective, battery charging applications and the bidirectional power flow control are not considered and discussed.

Therefore, the aim of this paper is to propose a multi-input DC-DC converter with bidirectional power flow control ability for energy storage applications. The novelty and main features of this paper can be summarized as follows: (1) Four power switches with synchronous rectification feature are included in the MIC circuit to enhance the control flexibility as well as to improve the circuit efficiency; (2) the bidirectional power flow control with both charging and discharging capability are realized; (3) the dynamic current regulation are proposed and developed to control the input currents independently. The circuit modeling and comprehensive mathematical derivartions of the proposed bidirectional MIC circuit are also presented. Eventually, the performance and feasibility of the proposed bidirectional MIC topology and control strategies will be verified by both simulation and experimental results of a 500 W prototype circuit.

2. Circuit Configurations and Equivalent Models

2.1. Circuit Diagrams of the Proposed Bidirectional MIC

The circuit diagram of the proposed bidirectional multi-input DC-DC converter is shown in Figure 2. Four power switches integrated with one inductor and one capacitor are included in the circuit. The input ports of the converter are connected to two DC source whereas the output port will be connected to the DC load. It should be mentioned that different from the circuit topology presented in [19], two power switches, S₃ and S₄, are utilized to replace the rectifying diodes as well as to enhance control feasibilities. Therefore, the synchronous rectification function will be achieved for the four power switches. Moreover, if DC loads are adopted for the input ports while the DC source is utilized for the output port, the proposed MIC can transfer the power from the other direction. As a result, the bidirectional power flow control can be realized.

2.2. Analyzation of Different Equivalent Models

Compared to the MIC circuit in [20], in the proposed circuit the rectifying diodes are replaced by two power switches. Therefore, the synchronous rectification should be considered. With the synchronous rectification feature, the bidirectional power flow control can be realized whereas the circuit efficiency can be increased. Besides, in general control of complex systems, introduction of switching has been intensively studied in coordination [24,25]. In the following, different circuit operation modes should be analyzed according to different switching combinations. In order to simplify the control, the upper side switches, S₁ and S₃, are controlled with synchronous rectification whereas the lower side switches, S₂ and S₄, are controlled with synchronous rectification. According to different switching states, seven operation modes can be obtained and described as follows:

➢

Mode I: The equivalent circuit of Mode I is shown in Figure 3a. In this mode, S₁ and S₂ are turned on while S₃ and S₄ are off. In the meantime, V_in1 and V_in2 are in series to charge the inductor, L. The demanded load energy is supplied from the capacitor, C.

➢

Mode II: During this state, S₁ and S₄ conduct. S₂ and S₄ are off. V_in1 charges L and C by S₁ and S₄ as well as provide energy to the load, as shown in Figure 3b.

➢

Mode III: The equivalent circuit of this mode is shown in Figure 3c. In this mode, S₂ and S₃ are turned on while S₁ and S₄ are turned off. V_in1 charges L whereas the load energy is supplied by C.

➢

Mode IV: Figure 3d shows the equivalent circuit of Mode IV. Under this mode, V_in1 and V_in2 will not transfer energy due to the off state of S₁ and S₂. In the same time, S₃ and S₄ are turned on and the demanded load energy can be obtained from L and C.

➢

Mode V: In this mode, S₃ and S₄ are turned on while S₁ and S₂ are turned off. L and C are charged by V_DC, as shown in Figure 3e.

➢

Mode VI: Figure 3f shows the equivalent circuit of Mode VI. Under this condition, S₂ and S₃ are off. V_DC charges L, C and V_in1 in the same by S₁ and S₄.

➢

Mode VII: Under this mode, S₁ and S₄ are off. V_DC charges L, C and V_in2 in the same by S₂ and S₃. The equivalent circuit of Mode VII is shown in Figure 3g.

It is worth mentioning that with the combination of Mode I, Mode II, Mode III and Mode IV, the MIC can transfer energy from input sources to the output load. In this paper, these fours modes are defined as the discharging scenario.

On the other hand, if R is replaced by a DC source, V_DC, the energy can be transferred from V_DC to V_in1 and V_in2 via the combination of Mode V, Mode VI and Mode VII. Therefore, the operation of these three modes are defined as charging scenario. As a result, the bidirectional power flow control capability of the MIC can be realized by these seven operation modes.

3. Circuit Operation Principles and the Proposed Bidirectional Power Flow Control

Detailed circuit operation principles and the bidirectional power flow control will be presented in this section. First, all circuit elements are considered as ideal without parasitic components. The MIC will be operated in the continuous conduction mode (CCM). In addition, the resistive load is utilized for the output port in both charging and discharging scenarios.

3.1. The Discharging Scenario

In the discharging scenario, V_in1 and V_in2 are defined as input ports whereas V_in1 is set to be larger than V_in2. Therefore, the duty ration of S₁ should be greater than the duty ration of S₂. On the other hand, with the synchronous rectification, S₃ and S₄ will be the complementary PWM signals of S₁ and S₂, respectively. PWM signal waveforms of the four power switches under the discharging scenario are shown in Figure 4.

By adopting the PWM control concept shown in Figure 4 as well as combining Mode I, Mode II and Mode IV shown in Figure 3, theoretical waveforms of the discharging scenario can be obtained, as shown in Figure 5. In Figure 5, V_GS1 and V_GS2 represent the gate signals of S₁ and S₂, respectively. It should be mentioned that the gate signals of S₃ and S₄ will be the complementary waveforms of S₁ and S₂ and which are not revealed in Figure 5. V_L and i_L are the inductor voltage and current, respectively. i_in1 and i_in2 are the input currents of V_in1 and V_in2, respectively. i_O’ is the output current before the capacitor, C, whereas i_C is the current flow into the capacitor. In the following, three intervals of T₁, T₂ and T₃ will be distinguished from one switching cycle to analyze the MIC circuit.

In the T₁ period, the MIC circuit is operated in Mode I. The inductor, L, is charged by both of the two input sources. Therefore, the inductor voltage, V_L, will be equal to the summation of V_in1 and V_in2, as shown in Equation (1). Besides, T₁ will be equal to the conduction time of S₂, as Equation (2) shows:

$$V_L{=V}_{in1}{+V}_{in2}$$

(1)

$$T_1{=d}_2{T}_S,$$

(2)

where d₂ is the duty cycle of S₂ and T_S represents the switching period.

During the T₂ interval, the MIC circuit is operated in Mode II. V_L will be the difference of V_in1 and V_O, as Equation (3) shows. In addition, the conduction time of T₂ can be written as Equation (4):

$$V_L{=V}_{in1}{-V}_O$$

(3)

$$T_2{=(d}_1{-d}_2{)T}_S$$

(4)

where d₁ is the duty cycle of S₁.

For the T₃ interval, the MIC circuit is operated in Mode IV. In the meantime, V_L and T₃ can be calculated as:

$$V_L{=-V}_O$$

(5)

$$T_3{=(1-d}_1{)T}_S$$

(6)

According to the volt-second balance theory, the increasing amount of the inductor current, ∆I_ON, will be equal to the decreasing amount of the inductor current, ∆I_OFF, within one switching period, as:

$$∆I_{ON}=∆I_{OFF}$$

(7)

With the volt-second balance principle of the inductor, Equation (7) can be modified as:

$$∆V_{ON}{\times T}_{ON}=∆V_{OFF}{\times T}_{OFF}$$

(8)

where ∆V_ON and ∆V_OFF are the changing amount of inductor voltage during the conduction period, T_ON, and the cut off period, T_OFF, respectively.

In Equation (8), ∆V_ON can be obtained from the inductor derived in Equations (1) and (3). T_ON can be obtained from T₁ and T₂ shown Equations (2) and (4). ∆V_OFF will be equal to the voltage shown in Equation (5). T_OFF can be expressed as T₃ shown in Equation (6). Therefore, by the combination from Equations (1) to (6), Equation (8) can be expressed as:

$$d_2{T}_S\left(V_{in1}{+V}_{in2}\right){+(d}_1{-d}_2{)T}_S\left(V_{in1}{-V}_O\right){=(1-d}_1{)T}_S\left(V_O\right).$$

(9)

Eventually, by the rearrangement of Equation (9), the output voltage, V_O, can be derived as Equation (10). It can be confirmed that with proper control of d₁ and d₂, V_O can be regulated with a function of V_in1 and V_in2:

$$V_O=\frac{d_1}{{1-d}_2}{V}_{in1}+\frac{d_2}{{1-d}_2}{V}_{in2}.$$

(10)

In addition, if d₂ larger than d₁, Equation (9) should be modified as:

$$d_1{T}_S\left(V_{in1}{+V}_{in2}\right){+(d}_2{-d}_1{)T}_S{V}_{in2}{+(1-d}_2{)T}_S\left({-V}_O\right)=0.$$

(11)

However, if Equation (11) is rearranged, the output voltage will be the same as V_O shown in Equation (10). Therefore, the two input sources, V_in1 and V_in2 can be controlled independently.

On the other hand, the input currents, I_in1 and I_in2 will be equal to the inductor current, I_L, when S₁ or S₂ conducts. Therefore, I_in1 and I_in2 can be expressed as:

$$I_{in1}{=d}_1{\times I}_L$$

(12)

$$I_{in2}{=d}_2{\times I}_L.$$

(13)

Besides, the output current, I_O, can be written as:

$$I_O{=(1-d}_2{)I}_L.$$

(14)

As a result, by the rearrangement of Equations (12)–(14), relations between the input currents and the output current can be derived as:

$$I_{in1}=(\frac{d_1}{{1-d}_2}{)I}_O$$

(15)

$$I_{in2}=(\frac{d_2}{{1-d}_2}{)I}_O$$

(16)

3.2. The Charging Scenario

In the charging scenario, Mode V, Mode VI and Mode VII will be adopted. In Figure 3, it can be confirmed that a DC source, V_DC, is used to replace R and determined as the input port. On the contrary, V_O1 and V_O2 are defined as output ports. Besides, two charging scenarios can be defined, which are: (1) the charging scenario A and (2) the charging scenario mode B. In the following, the two different charging scenarios will be described individually.

3.2.1. The Charging Scenario A

For the charging scenario A, Mode V and Mode VI are utilized to transfer the energy from V_DC to V_O1. The equivalent circuit diagram of this scenario is shown in Figure 6a. The conceptual diagram of PWM control signals is shown in Figure 7a whereas theoretical waveforms of the charging scenario A are shown in Figure 8a. V_GS1 and V_GS2 are the gate signals of S₁ and S₂, respectively. i_O1 and i_O2 are the output currents. i_O1’ is the current before C_O1 whereas i_CO1 is the C_O1 capacitor current. In the following, interval T₁ and T₂ are distinguished from one switching cycle to analyze this scenario.

During the T₁ period, the MIC circuit is operated in Mode VI. In the meantime, V_L will be the difference of V_O1 and V_DC, as shown in Equation (17). Besides, T₁ will be equal to the conduction time of S₁, as Equation (18) shows:

$$V_L{=V}_{O1}{-V}_{DC}$$

(17)

$$T_1{=d}_1{T}_S.$$

(18)

In the T₂ interval, the MIC circuit is operated in Mode V. V_L is equal to V_DC, as Equation (19) shows. In addition, the conduction time of T₂ can be written as Equation (20).

$$V_L{=V}_{DC}$$

(19)

$$T_2{=(1-d}_1{)T}_S.$$

(20)

By the combination of Equations (17)–(20), Equation (21) can be obtained as:

$$d_1{T}_S\left(V_{O1}{-V}_{DC}\right){=(1-d}_1{)T}_S{V}_{DC}.$$

(21)

After the simplification, Equation (21) can be modified as:

$$V_{DC}{=d}_1{V}_{O1}.$$

(22)

From Equation (22), it can be confirmed that the MIC in this scenario will be operated as a conventional DC-DC boost converter.

3.2.2. The Charging Scenario B

If the charging scenario B is considered, Mode V and Mode VII should be adopted. The equivalent circuit diagram of this scenario is shown in Figure 6b. The conceptual diagram of PWM control signals is shown in Figure 7b. Theoretical waveforms of the charging scenario B are shown in Figure 8b. V_GS1 and V_GS2 are the gate signals of S₁ and S₂, respectively. i_O1 and i_O2 are the output currents. i_O2’ is the current before C_O2 whereas i_CO2 is the C_O2 capacitor current. In the following, interval T₁ and T₂ are distinguished from one switching cycle to analyze this scenario.

During the T₁ period, the MIC circuit is operated in Mode VII. V_L is equal to the output voltage, V_O2, as shown in Equation (23). Besides, T₁ will be equal to the conduction time of S₂, as Equation (24) shows:

$$V_L{=V}_{O2}$$

(23)

$$T_1{=d}_2{T}_S.$$

(24)

In the T₂ interval, the MIC circuit is operated in Mode V. V_L is equal to V_DC, as Equation (25) shows. In addition, the conduction time of T₂ can be written as Equation (26):

$$V_L{=V}_{DC}$$

(25)

$$T_2{=(1-d}_2{)T}_S.$$

(26)

By the combination of Equations (23)–(26), Equation (27) can be written as:

$$d_2{T}_S{V}_{O2}{=(1-d}_2{)T}_S{V}_{DC}.$$

(27)

Eventually, Equation (27) can be derived as:

$$V_{O2}=\frac{{1-d}_2}{d_2}{V}_{DC}.$$

(28)

From Equation (28), it can be confirmed that the MIC in this scenario will be operated as a conventional DC-DC buck-boost converter.

4. Simulation and Experimental Validations

In order to verify the performance and feasibility of the proposed bidirectional MIC, a 500 W prototype circuit is designed and implemented. The specifications of the circuit are shown in

Table 1. Circuit specifications of the proposed bidirectional MIC.

Parameters	Value or Type
Rated power	500 W
Inductance of L	100 μH
Capacitance of C	470 μF
Capacitance of Cin1	330 μF
Capacitance of Cin2	470 μF
Switches of S1, S2, S3 and S4	MOSFET IRF640N
Switching frequency	50 kHz
Gate driver IC for the switches	TLP250
System controller	TI DSP TMS320F28335

. The inductance, L is determined as 100 μH. The capacitance of C, C_in1 and C_in2 are calculated as 470 μF, 330 μF and 470 μF, respectively. The MOSFET, IRF640N, is chosen as main switches, whereas the switching frequency is determined as 50 kHz. The gate drive IC, TLP250 is used to drive the power switches. It is worth mentioning that the DSP TMS320F28335 made by Texas Instruments is utilized as the system controller. It is worth mentioning that all components of the circuit are assumed to be functional while he robustness consideration can be found in [26,27]. In the following, both simulation and experimental results are presented.

4.1. Simulation Results

The proposed bidirectional MIC are first verified via the Matlab/Simulink with the circuit diagrams shown in Figure 9. Simulation results of the discharging scenario are shown in Figure 10. Two cases are simulated to illustrate the discharging scenario. Figure 10a shows waveforms of the I_in1, I_in2, I_O and V_O of case I. In this case, I_in1 is set as 1 A and I_in2 is set as 6 A in the beginning. At t = 0.3 s, I_in1 is increased to 2 A. In order to remain the constant I_O and V_O, I_in2 will be decreased by the controller. Besides, Figure 10b shows waveforms of the I_in1, I_in2, I_O and V_O of case II. In this case, I_in1 is set as 6 A and I_in2 is set as 1 A in the beginning. During t = 0.3 s, I_in2 is increased to 2 A whereas I_in1 is decreased by the controller to remain the constant I_O and V_O. In other words, the dynamic input current regulation can be achieved. It should be mentioned that I_O and V_O are determined as 5 A and 50 V, respectively.

On the other hand, simulation results of the charging scenario are shown in Figure 11. Figure 11a shows the results of V_DC, I_DC, V_O1 and I_O1 under the charging scenario A. In this case, V_DC and I_DC are set as 50 V and −20 A, respectively. V_O1 and I_O1 are set as 100 V and −10 A, respectively. Under this case, the MIC is operated as a boost converter. Simulation results of V_DC, I_DC, V_O2 and I_O2 under the charging scenario B are shown in Figure 11b. In this case, both V_DC and V_O2 are set as 50 V while both I_DC and I_O2 are set as −10 A. It is worth mentioning that the MIC is acted as a buck-boost converter under this scenario.

4.2. Experimental Validations

In this section, experimental results of the bidirectional MIC will be presented. First, the prototype circuit figure of the MIC is shown in Figure 12a. It can be seen that the main circuit, the ASC712 and amplifier circuit and the DSP TMS320F28335 are included. In addition, the gate signal waveforms, V_GS1, V_GS2 and the inductor current waveform, I_L of the discharging scenario are shown in Figure 12b. The gate signal waveforms, V_GS1, V_GS3 and the inductor current waveform, I_L of the charging scenario A are shown in Figure 12c. The gate signal waveforms, V_GS2, V_GS4 and the inductor current waveform, I_L of the charging scenario B are shown in Figure 12d.

On the other hand, Figure 13 demonstrates the experimental results under the same conditions of shown in Figure 10 and Figure 11, respectively. First, Figure 13a shows experimental waveforms of case I. At t = t₁, I_in1 is increased. In order to remain the power flow balance, I_in2 should be decreased. Therefore, it can be seen that I_O and V_O are well regulated as constant values. On the contrary, Figure 13b demonstrate the opposite scenario of Figure 13a. In Figure 13b, I_in1 is decreased at t = t₁. In the meantime, I_in2 should be increased to maintain the power flow balance. As a result, I_O and V_O are well stabilized in a constant value.

Moreover, experimental waveforms of V_DC, I_DC, V_in1 and I_in1 with the charging scenario A are shown in Figure 13c whereas experimental waveforms of V_DC, I_DC, V_in2 and I_in2 with the charging scenario B are shown in Figure 13d.

According to the simulation and experimental waveforms, the steady-state operation, dynamic current regulation and the bidirectional power flow control capability of the proposed MIC circuit are verified.

Finally, Figure 14 shows the circuit efficiency of the proposed MIC under different load condition. It can be confirmed that the peak efficiency is about 87%. It should be mentioned that the efficiency from 10% to 70% load are measured by the experiments of the prototype MIC circuit. However, because of the limitation of the experimental equipment, the efficiency of 80%, 90% and 100% load operation are calculated and estimated. In the future work, the soft-switching function can be included for the MIC to further improve the circuit efficiency.

5. Conclusions

A multi-input DC-DC converter with bidirectional power flow control feature is proposed in this paper. The main features of the MIC circuit can be summarized as follows: (1) Two power switches are utilized to replace diodes as well as to achieve the synchronous rectification; (2) The bidirectional power flow control with both charging and discharging capability are realized; (3) The dynamic current regulation are developed to control the input currents independently as well as to stabilize the output voltage and current. Moreover, detailed circuit analysis, the circuit modeling and comprehensive mathematical derivartions of the proposed bidirectional MIC circuit are also presented. Finally, both simulation results and hardware experiments obtained from a 500 W circuit demonstrate the performance and feasibility of the proposed bidirectional MIC. In the future, the soft-switching technology can be adopted for the proposed MIC further increase the circuit efficiency.