# I. INTRODUCTION

Energy storage systems (ESSs) are widely used in many applications such as UPS, electrical vehicles and distributed power generation systems [1]-[3]. The voltage rating for each cell in an energy storage device (ESD) such as supercapacitors or batteries is relatively low. To allow for use in high voltage applications, many cells are series connected, which decreases the system reliability by adding a voltage equalizer to each cell [4], [5]. Therefore, it is desirable to keep the number of cells as low as possible to avoid complicated voltage equalizing circuits. This leads to the amplitude of the DC side voltage being lower than that of the AC side grid voltage.

The well-known voltage-source inverter (VSI) is a buck type inverter when power flows from DC to AC and a boost type PWM rectifier when it is the other way around [6], [7]. This means the amplitude of the DC side voltage must be greater than that of the AC side. In addition, the DC current cannot be regulated tightly due to the lack of a DC side inductor. This makes it unsuitable for ESSs with low voltage ESDs.

In order to overcome the shortcomings of the conventional VSI, a double-stage power conversion system typically involving a bidirectional DC/DC converter cascaded with the VSI, as shown in Fig. 1, can be used [8], [9]. The DC/DC converter stage is to boost the low DC voltage to a higher voltage DC bus, while the VSI connects to the AC grid. However, this topology requires two separate control strategies and bulky electrolytic capacitors at the DC bus, resulting in lower reliability and efficiency, as well as a more complicated control scheme.

**Fig. 1.**Bidirectional DC/DC converter cascaded with VSI.

In literature [10], [11], a high frequency AC link (HFACL) is used for isolation and to raise the low DC voltage. However, the front end switches may suffer from high voltage stress resulting from hard switching during current commutation. In addition, the high frequency transformer will decrease the conversion efficiency.

To achieve direct power conversion between a high voltage AC grid and a low voltage ESD and to eliminate the drawbacks of the previous solutions, a single-stage bidirectional current-source converter, as shown in Fig. 2, can be used. In the conventional current-source inverter (CSI) [12]-[16], each switch is composed of a MOSEFT in series with a diode. Then the power flow can only move from DC to AC, which makes it non-applicable for ESSs. By replacing the diode with another MOSFET, the power flow can be bidirectional. It can also operate as a step-down rectifier from AC to DC with tight control of the DC current. Owing to the DC inductor, the DC current ripple can be dramatically reduced, which is desirable for ESDs.

**Fig. 2.**Bidirectional Single-Stage DC/AC Converter.

The power circuit and mode analysis are given and analyzed in section II. The control strategy implementation is provided in section III. The simulation results are illustrated in section IV. A 1kW experimental prototype is fabricated and tested in section V. Section VI presents some conclusions.

# II. CIRCUIT TOPOLOGY AND MODE ANALYSIS

Fig. 2 shows the power circuit for the single-stage bidirectional three-phase DC/AC converter, where vdc is the voltage of the ESD. va, vb and vc are three-phase line-to-neutral voltages. The converter connects to the DC side through a DC inductor Lf and to the AC side through a filter formed by Lfa, Lfb, Lfc and Ca, Cb, Cc. The converter is composed of six bidirectional switches, in which two MOSFETs are in anti-series connection with a common source. Therefore, an isolated power supply for the gate drivers of the two MOSFETs is not necessary. An RC snubber circuit can be connected to each bidirectional switch in parallel to avoid voltage spikes.

When it works during the discharging mode, all six of the bottom switches of each bidirectional switch (Sxb) are off, while the top switches (Sxa) conduct alternately. The current flows through the body diode of the bottom switches when the corresponding top switches are turned on. This is completely opposite to the charging mode. Therefore, only the discharging mode operation will be discussed in detail.

Like the conventional CSI, the current in the DC side cannot be interrupted due to the existence of the DC inductor. Therefore, at least one bidirectional switch in the three upper bridges and another switch in the three lower bridges should conduct at the same time. However, if any two switches in the upper or lower bridges are turned on simultaneously, the voltage of one of the filtering capacitors may be clamped to that of another. Thus, only two bidirectional switches can conduct at the same time, one in the upper bridges, and the other in the lower bridges. This leads to nine combinations of switching patterns.

It can be readily determined that the DC current idc is the same as the current flowing through each switch. This indicates that the current iat, ibt and ict is either 0 or idc. Through a Clark transformation, the nine current vectors can be projected onto a phase plane.

As shown in Fig. 3(a), I1 to I6 are non-zero vectors, and I7, I8, I9 are zero vectors. Therefore, the current vector space can be divided into six sectors separated by six non-zero vectors whose magnitudes are

**Fig. 3.**(a) Current vector space. (b) Six sectors boundaries under three-phase current

Fig. 3(b) shows the boundaries of the six sectors with respect to the three-phase reference current. In fact, the zero-crossing point of each phase current is right at the position where the sector changes. For a given reference vector in Fig. 3(a), two adjacent vectors can be chosen to compose it. Therefore, in one switching period, three switching modes are used. Two of them are adjacent vectors, and the third one is one of the three zero vectors that is used to occupy the remaining time. It should be noted that in a specific sector, two adjacent vectors have a common conducting switch. In order to reduce the switching times, the zero vector should be selected to have the same conducting switch. Hence, the selection of the vectors is fixed in each sector and can be shown in Table I.

**TABLE I**SELECTION OF CURRENT VECTORS IN EACH SECTOR

According to the gate sequence for the converter, the operation can be classified into three modes in each sector. To simplify the analysis, only sector I is analyzed. The respective working modes are sketched in Fig. 4.

**Fig. 4.**Operating modes in sector I.

Mode 1: Zero vector I7 is applied. S1a and S4a are turned on. The voltage of the DC inductor is equal to vdc. In the discharging mode, the magnetic energy stored in the inductor increases with idc. During this period, no energy is transferred to the AC side. While in the charging mode, the other one of the same bidirectional switch (Sxb) is turned on. The DC current idc decreases in the opposite direction.

Mode 2: Non-zero current vector I6 is used. S4b is turned off, and S6b is turned on. Regardless of the voltage of the filtering inductors, the voltage of the DC inductor is vdc-vab. Since the DC voltage is lower than the AC voltage in the discharging mode, vdc-vab is negative. Therefore, the DC current idc decreases and is injected to the AC gird.

Mode 3: Non-zero vector I1 is used. S6b is turned off, and S2b is turned on. Similar to Mode 2, the voltage of the DC inductor is vdc-vac. The DC current idc continues to decrease during this period.

The time duration calculation of each mode can be expressed as follows. Supposing the reference vector lies in sector I, the two adjacent vectors are I6 and I1. The time durations of the two non-zero vectors are T1 and T2, and T0 is the time duration of the zero vector.

Where iα and iβ are the projection of the reference vector into α, β axis. Ts is the switching period. Then the following can be obtained:

The time duration in other sectors can be calculated in the same way.

As mentioned previously, only one of the switches in the upper bridge and the other switch in the lower bridges should be on at any time. However, to avoid high-voltage spikes across the switches of the converter during the current commutation between two adjacent switching modes, the gate signals for the two consecutive switches should be overlapped. This implies that the consecutive mode switch has to be turned on before the current mode switch is turned off. For example, in sector I, when mode 1 switches to mode 2, the switch S6a is turned on before S4a is turned off by Δt. Although both of the switches are gated on during the overlapping time duration, the three-phase AC side line-to-line voltage vab cannot be short-circuited for the reverse blocking capability of the body diodes of the switches S6b and S4b. The current does not shift to S4a until S6a is completely turned off.

It should be noted that the voltage of the ESD cannot be too low or too high. In the discharging process, the simplified equivalent circuits in sector I are shown in Fig. 5, where Req is the sum of the inductor ESR, the MOSFET Rds(on) and the inner resistor of the ESD. The maximum voltage gain can be obtained when the sector changes. At the beginning of sector I, the time duration of Mode 3 is quite short compared with Mode 1 and Mode 2. Therefore, Mode 3 is neglected. The voltage of the inductor is given by

**Fig. 5.**Equivalent circuit of three operating modes in sector I.

Where vD is the diode voltage drop when it conducts, and vC is the voltage of the filtering capacitor. The current of the capacitor is given by

Where ic is the current flowing into the filtering capacitor and io is the current flowing into the grid.

Assume that the time duration of Mode 1 is DTs and that Mode 2 is (1-D)Ts. According to the volt-second balance and charge balance, vc=(vdc-idcReq-2vd)/(1-D) and io=(1-D)idc. Therefore

For example, the peak line to line voltage is 200V. The power flowing into the grid is 1kW. Therefore, the output current io is 5A. Assume that Req is equal to 1Ω, and that vD is 1V. As a result, vdc=200 (1-D)+5/(1-D)+2. The DC voltage vdc and the current idc versus duty cycle D are shown in Fig. 6. As can be seen, the minimum DC voltage is 65V when D is 0.84. Therefore, the maximum gain is about 3. However, the gain increases if the output current and ESR of the circuit decrease.

**Fig. 6.**DC voltage vdc and current idc vs duty cycle D.

On the other hand, the DC voltage must be lower than vc at all times. Fig. 7 shows that in each sector the minimum voltage of the capacitor is half of the peak line to line voltage. Therefore, the ESD voltage must be satisfied as follows

**Fig. 7.**Line to line voltage and phase voltage in sector I.

While in the charging process, this system works as a buck type rectifier. The DC voltage can be as low as 0V, and the maximum DC voltage can approach the peak line to line voltage when it acts as an uncontrolled rectifier. However, in this situation, the three-phase AC current cannot be sinusoidal. If a unity power factor is required, the DC voltage cannot exceed the minimum voltage of the capacitors in each sector. This is similar to the discharging process. Therefore, during the charging process, the DC voltage can range from 0V to Vline,peak/2.

# III. CONTROL STRATEGY

## A. General Control Strategy

Fig. 8 shows the general control strategy for an ESS. The three-phase AC side voltage and current are sampled and transformed by the Clark and Park transformations. This leads to two phases being decoupled and time invariant outputs id in the d-axis and iq in the q-axis. Both of them along with the charging/discharging function signal, idc and vdc work as the inputs for the regulator whose specific design will be discussed later in Fig. 9 and Fig. 10.

**Fig. 8.**General control strategy.

**Fig. 9.**Regulator design in the charging mode. (a) d-axis design. (b) q-axis design.

**Fig. 10.**Regulator design in the discharging mode. (a) d-axis design. (b) q-axis design.

Through the regulator, two independent outputs ird and irq can be obtained. These two values along with the value of θ achieved from phase lock loop (PLL) of the AC grid work as the inputs for the inverse Park transformation. Then the outputs irα and irβ can be obtained. These are the two components in the α/β stationary orthogonal reference frame. They are also the inputs of the current space vector modulation unit whose outputs are the gate signals S1, S2 … S6 for the converter.

The detailed regulator design can be explained as follows. Fig. 9 shows the design of the d-axis and q-axis in the charging mode. In this mode, the charging process needs to be switched from constant current (CC) to constant voltage (CV) to prevent overcharging. In the conventional charger design, the transfer moment is usually determined by the instantaneous value of the DC voltage vdc. However, it is difficult to define a suitable set point for the voltage over the ESD since it varies with the charging currents due to the existence of a parasitical resistance. To achieve a smooth transfer from CC to CV, a transfer-logic is proposed and illustrated in Fig. 9(a). For the d-axis design, idcref is the current reference for the current compensator. Meanwhile, vdcref works as the voltage reference for the voltage compensator. This is determined by the maximum charging voltage for the ESD. idcout and vdcout are the outputs of the current compensator and the voltage compensator, respectively. At any instant, the actual outer loop regulator output for the d-axis is the minimum value between idcout and vdcout. This can be explained as follows. At the initial state of the charging mode, the voltage vdc is lower than the voltage reference vdcref. Therefore, the voltage compensator becomes saturated and the charging process works in CC state. When the voltage of the ESD becomes larger than vdcref, the voltage compensator comes out of saturation and vdcout becomes lower. When vdcout is lower than idcout, the charging current becomes lower than the current reference idcref and the current compensator become saturated. Then, the charging process works in the CV state and the transfer is very smooth.

The minimum value can be regard as the reference for the d-axis. Fig. 9(b) shows the regulator of the q-axis in the charging mode. Since a unity power factor from the AC side is required, the reference for the q-axis iqref is set to zero.

In the discharging mode, the control strategy to achieve a fixed DC current is provided in Fig. 10. As shown in Fig. 10(a), the d-axis compensator is also composed of two loops. The outer loop is the DC side current tracking loop whose output works as the current reference for the d-axis component. To achieve a unit power factor, the current reference for the q-axis is also set to zero, as shown in Fig. 10(b). It should be noted that in the discharging mode, the regulator output is actually the magnitude of the reference vector projected to the d/q axis. The larger the magnitude becomes, the shorter the time duration of the zero vector becomes, which results in less energy being transferred to the AC side. Therefore, the output of the regulator should be inverted before the continued inverse Park transformation.

## B. Regulator Design

In the synchronous reference frame (SRF), the sinusoidal variables are transformed into DC variables. Theoretically, PI controllers have a good dynamic response and can track DC signals with zero steady-state error. However, the steady state error does not become zero by using PI controller due to an unbalanced grid voltage and some nonlinear factors. Using a repetitive controller (RC) can deal with the issue of a periodic disturbances. It has a good steady-state performance but poor dynamic response. Therefore, both controllers are used together.

Fig. 11 shows the structure of the control system, where P(z) is the model of the converter, and d represents a periodic disturbance. ref denotes idref or iqref. ur represents the controller output, and the currents in the d/q axis are the output y. In fact, the RC is only a complement to the PI controller. Therefore, the PI controller should be designed and verified before the RC is applied to the system. Due to the fact that many publications have discussed PI controller design methods for current source inverter and rectifier [13], [14], only the design of the RC is discussed here in detail.

**Fig. 11.**Discrete block diagram of the control system.

Since the switching frequency is 10kHz and the line frequency is 50Hz, the value of N is chosen as 200. The loop in the RC can be written as u(z)/e(z)=1/(1-Q(z)z-200) or u(k)=Q(z)u(k-200)+ e(k). In practice, Q(z) is generally a constant that is slightly less than 1, typically 0.95, otherwise the system tends to become unstable. Although there is a small steady state tracking error, it is acceptable.

C(z) is a compensator and it can be equal to P-1(z) if the modeling of the converter is acquired accurately. However, this is so difficult that C(z) is usually given by C(z)=Kr zk S(z), where Kr is a constant, in order to adjust the gain. zk is a phase-lead compensator and S(z) is a low pass filter. In the experiment, the gain of the RC is set to be 10% of the PI controller. Since three-phase current mainly contains low order harmonics, S(z) is chosen as a first order low pass filter whose cutoff frequency is 500Hz and phase-lag is 5.8 degree at 50Hz. Allow for one step delay of the digital controller and some other tiny factors, k=1+5.8/360*200=5. A Bode diagram of the repetitive controller is shown in Fig. 12. It can be determined that the errors at the integral times of the fundamental frequency of 50Hz can be mitigated dramatically.

**Fig. 12.**Bode diagram of repetitive controller.

# IV. SIMULATION VERIFICATION

Simulations of the converter and the control strategy are carried out in PSIM. The specific parameters of the system are shown in Table II.

**TABLE II**SIMULATION PARAMETERS

Fig. 13 shows simulation results of the three working states: charging from CC to CV and discharging consecutively. The initial voltage is set to 95V. At first, the system works in the charging mode with the constant charging current set as 20A. As can be sees, the three-phase current is in phase with the corresponding phase voltage indicating that a unity power factor is achieved. When the voltage of the supercapacitor increases to 100V, the voltage compensator of the outer loop comes out of saturation and becomes lower than the DC current compensator. Then it changes to the CV state when the DC current becomes lower and lower, and finally becomes zero. The DC voltage becomes stable and a little more than 100V. When a discharging signal occurs, it changes to the discharging mode, which is opposite to the charging mode in the CC state. The three-phase AC current is out of phase with each phase voltage.

**Fig. 13.**Simulation results of three working states.

The first six waveforms in Fig. 14 illustrates the gate signals for all of the working switches in a line cycle, in which six sectors can be readily figured out. The seventh waveform shows the time duration of the three current vectors, which are almost the same in each sector, although the current vectors are not.

**Fig. 14.**Simulation results of gate signals and time duration.

# V. EXPERIMENTAL VERIFICATION

A prototype rated at 1kW was built in the laboratory. The main parameters of the system are chosen as follows: Lf=2mH, Lfa=Lfb=Lfc=1mH, Ca=Cb=Cc=30μF. The twelve power MOSFETs of the converter are IXFH44N50P (500V/44A) whose on-resistance RDS(on) is 0.14Ω. A supercapacitor bank consisting of three modules connected in series is chosen as the ESD. Each module is composed of twelve supercapacitor cells connected in series and each cell is 120F/2.7V. With this setup, the total capacitance of the bank is 3.3F and its maximum voltage rating is 97.2V. The rated RMS value of the line-to-line AC voltage is 150V with 50Hz. The digital control strategy was implemented on a DSP (TMS320F28335), with which 12 channel PWM signals are generated. To guarantee the sensing accuracy, an external 14-bit A/D AD7657 is used to measure the DC and three-phase AC current and voltage.

Fig. 15 shows a photo of the experimental prototype. The three circuit boards on the left from top to bottom are the driving circuit, the DSP control board and the auxiliary power supply. The elements on the right are the main circuit, three filtering capacitors and inductors. The supercapacitor and DC inductor are not shown in the photo.

**Fig. 15.**Photo of the experimental prototype.

Fig. 16 shows the actual gate signals for the switches in the upper bridge S1, S3 and S5. These are the same as the simulation results. Taking S1 as an example, due to the requirement of a unity power factor, the phase current ia should be in phase with the phase voltage va or 30 degrees ahead of vab. Therefore, sector I starts 30 degrees after vab reaches its maximum. S1 remains on, and S3 and S5 remain off during the whole sector.

**Fig. 16.**Gate signals for a complete line cycle.

On the other hand, the lower switches S2, S4 and S6 are turned on and off alternately. This is shown in Fig. 17. The zero vector time duration T0 is actually the modulation ratio of S4, while the non-zero vector time durations T1 and T2 are the modulation ratios of S6 and S2, respectively. As can be sees, T1 decreases gradually from being constantly on in sector III to being constantly off in sector V, and T2 is on the opposite of this, which also correspond simulation results.

**Fig. 17.**Gate signals of S2, S4 and S6 in sector I.

Fig. 18 and 19 show the charging and discharging process respectively with a constant DC current set as 13A. The phase current ia is almost sinusoidal and has little distortion.

**Fig. 18.**Charging process.

**Fig. 19.**Discharging process.

Fig. 20 shows the transition from the charging mode to the discharging mode with an almost constant DC side current. Before the transition, the phase current ia is almost sinusoidal and in phase with its phase voltage va, indicating a high power factor for the AC side. After the transition, ia is out of phase with va, which also leads to a high power factor. The transition is smooth and fast. Fig. 21 shows the transition from the discharging mode to the charging mode. The sharp increase and decrease of the DC voltage vdc at the transition moment result from the inner resistance of the supercapacitor, which is determined to be nearly 1Ω.

**Fig. 20.**Transition from discharging mode to charging mode.

**Fig. 21.**Transition from charging mode to discharging mode.

Fig. 22 and 23 show the drain-to-source voltage of the two MOSFETs in a bidirectional switch when the converter operates in the charging mode. In Fig. 22, the MOSFET works as a switch which turns on and off according to the gate signal. In Fig. 23, the MOSFET only works as a diode. All of the other bidirectional switches share the same waveforms except for a phase delay. During the discharging mode, the situations of the two kinds of switches only interchange with each other. The maximum voltage is the peak value of the line-to-line voltage regardless of the voltage spike. As can be seen, the voltage spike can be suppressed significantly by adding an 1μs overlapping time for the switches when they commutate.

**Fig. 22.**Drain-to-source voltage of MOSFET working as switch.

**Fig. 23.**Drain-to-source voltage of MOSFET working as diode.

Due to the desire to achieve a constant DC current, the power of the DC side and the AC side is always changing. Therefore, it is difficult to obtain the instantaneous power of both sides simultaneously. In order to get the efficiency, an oscilloscope is used to measure the power. The efficiency at the maximum charging power, rated at 1kW, is 95.7%. In addition, a unity power factor is achieved according to the power quality analyzer.

# VI. CONCLUSIONS

In this paper, a unified control strategy using the CSVM technique for a single stage bidirectional three-phase grid connected DC/AC converter is proposed. In the charging mode, the converter works as a buck type AC/DC rectifier. While in the discharging mode, it operates as a boost type DC/AC inverter. The operating principle, mode analysis, gate signals generation, control strategy and transfer logic from CC to CV in the charging mode are also given.

When compared with the conventional two-stage topology typically composed of a Buck/Boost DC-DC converter cascaded with a VSI, the proposed topology requires twelve power switches rather than eight and has more power loss due to the conduction of the diodes. However, it still has many advantages over the conventional topology. First, the conventional two-stage units need two separate control systems, making them a bit more complicated. Second, the voltage rating of all of the eight switches in the conventional topology are equal to the high voltage DC bus regardless of the voltage spike. Meanwhile, in the proposed topology, it is only the peak line to line voltage of the AC grid, which is much lower. Third, bulky electrolytic capacitors are necessary to stabilize the high voltage DC bus when the transient power between the two stages is not matched. This results in lower reliability and efficiency. In addition, the boost ratio of the first stage must be higher so that the high voltage DC bus can be inverted by the VSI. Furthermore, the AC side filtering inductance of the proposed topology can be smaller because of the existence of the DC inductor. Therefore, this topology is a good alternative to the conventional two-stage topology.

In addition to these advantages over the conventional topology, it also has many benefits including high conversion efficiency, a high power factor and tight control of the DC current. Furthermore, a fast transition can be achieved from the charging mode to the discharging mode and vice versa. A 1kW ESS prototype using supercapacitors is fabricated and evaluated. The simulation and experimental results validate the advantages and effectiveness of the proposed control strategy.