Simplified PWM With Switching Constraint Method to Prevent

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 62, NO. 7, JULY 2015

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Simplified PWM With Switching Constraint Method to Prevent Circulating Currents for Paralleled Bidirectional AC/DC Converters in Grid-Tied System Using Graphic Analysis Yi-Hung Liao, Member, IEEE, and Hung Chi Chen, Member, IEEE Abstract—In this paper, a simplified pulsewidth modulation with switching constraint control scheme is proposed to eliminate the circulating currents for bidirectional paralleled ac/dc converters in grid-tied system. The proposed control scheme can reduce the circulating currents and does not need additional current sensors and communication device among paralleled converters compared with conventional methods. Therefore, the paralleled system cost can be reduced. In addition, the current shaping and sharing between the paralleled converters can be well accomplished so that the overall performance of the paralleled converter system can be raised. Furthermore, the dc, ac, and self-generated circulating currents are clearly analyzed by graphics, and the synchronous circulating currents are first explored. Finally, a prototype system is constructed, and the proposed control scheme is implemented using a Spartan-3E XC3S250E FPGA. Both simulation and experimental results verify the validity of the proposed theory and control scheme. Index Terms—Bidirectional ac/dc converter, circulating currents, current shaping/sharing, simplified pulsewidth modulation (PWM), switching constraint control scheme.

I. I NTRODUCTION ITH the rapid development of renewable energy [15]– [19], many distribution energy resources (DERs) are constructed and expanded, as shown in Fig. 1. In order to fit power converter capacity for the DERs expansion, adopting a modularized power converter is a good choice to increase the power capacity for increasing DERs [20]–[25]. On the other hand, it is also well known that converters can be paralleled to increase the system reliability, efficiency, and redundancy [1]–[3], [7]. Thus, the parallel structure is suitable for modularized system design and provides more flexibility in the power-capacity-augmented system in the alternative energy applications.

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Manuscript received January 18, 2014; revised June 18, 2014; accepted July 21, 2014. Date of publication August 27, 2014; date of current version May 15, 2015. This work was supported by the Ministry of Science and Technology of China under Grant MOST 103-2221-E346-004-MY2. Y.-H. Liao is with the Department of Electrical Engineering, National Penghu University of Science and Technology, Penghu 880, Taiwan (e-mail: [email protected]). H. C. Chen is with the Department of Electrical and Computer Engineering, National Chiao Tung University, Hsinchu 330, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2014.2352597

Fig. 1.

Power-capacity-augmented distribution energy system.

However, when the converters are connected in parallel directly, the circulating currents are automatically generated due to the unsynchronized operation of the paralleled converter system. Hence, the operation of paralleled converters usually requires isolation [4]. The weight, size, and cost associated with isolation transformers and/or additional power sources may cause system complexity and bulk. Thus, the high-frequency power distribution architecture is proposed [11] to decrease hardware size. However, it still needs common signals for circulating current control. Therefore, the reduction of circulating currents between paralleled converters becomes a key issue for power-capacity-augmented distribution energy system. Up to the present, several methods for reducing circulating currents have been proposed [4], [6]–[12], [26]. When converters are paralleled directly without adding passive components to reduce size and cost, interphase reactors may be used to provide high zero-sequence impedance [5] to reduce circulating currents. Nevertheless, the reactors can provide reasonably high impedance only at medium and high frequencies. They cannot prevent low-frequency circulating currents. Recently, ideal operation status of parallel inverters has been studied [13] for reducing circulating currents using synchronization operation. In practice, the synchronized operation to make uniform modulation is difficult while one of the paralleled converters malfunctions and needs to be replaced with a new one. Moreover, the synchronized operation requires additional communication among each converter and increases system cost [6]–[9], [13], [26]. Therefore, in this paper, a simplified pulsewidth modulation (PWM) with switching constraint method is proposed to prevent circulating currents without any communication between

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TABLE I R ECTIFIER M ODE S WITCHING C OMBINATION IN THE S IMPLIFIED PWM [14]

Fig. 2. Bidirectional single-phase ac/dc converter system utilized in the renewable energy system.

the paralleled converters. In order to understand this control method, the ac and dc circulating current loops in the paralleled converter system are analyzed and defined. In addition, the selfgenerated circulating currents and synchronous circulating currents are clearly explained. For reducing ac and dc circulating current loops, the simplified PWM strategy is utilized in the paralleled converter system. Then, none of the dc circulating current loops exists, and there only exist ac circulating current loops. In order to eliminate the ac circulating current loops among the paralleled converters, a switching constraint method is proposed to control the self-generated circulating currents. Finally, both dc and ac circulating current loops are eliminated in the proposed circulating current control scheme. The proposed control strategy provides more flexibility in modularized system and reduces weight, size, and cost in the powercapacity-augmented grid-tied paralleled converter system.

TABLE II I NVERTER M ODE S WITCHING C OMBINATION IN THE S IMPLIFIED PWM [14]

TABLE III S TATE -S PACE AVERAGED E QUATIONS AND I NDUCTOR S TATUSES (R ECTIFIER M ODE )

II. O PERATION OF S IMPLIFIED PWM A bidirectional single-phase ac/dc converter is usually utilized as the interface between the DERs and the ac grid system, as shown in Fig. 2. In order to increase the utilization of renewable energy, high-performance converters that involve good current shaping and good voltage regulation are always concerned. However, when system power rating is augmented, the current sharing and/or shaping among the paralleled converters are often neglected. That may lead to line currents distortion and unbalanced power sharing, and the overall performance will be degraded. Up to now, the conventional unipolar PWM (UPWM) and bipolar PWM (BPWM) are often used for the bidirectional single-phase ac/dc power-augmented converters in the grid-tied renewable energy system [13]. In [5]–[12], there exists a circulating current problem, and it results in ac line current distortion and unbalanced power sharing among the paralleled converters. Therefore, the literature [6]–[9] proposed a control method to eliminate the zero-sequence circulating currents. Nevertheless, an additional current sensor is required for each converter, and only dc circulating currents are eliminated. In this paper, a novel control strategy of circulating currents based on simplified PWM [14] in the paralleled converter system is proposed. The switching statuses of simplified PWM are listed in Tables I and II for bidirectional power flow in both rectifier mode and inverter mode operations. From Tables I and II, one can find that the simplified PWM only changes one active switch status in the switching period to achieve both current shaping at the

TABLE IV S TATE -S PACE AVERAGE E QUATIONS AND I NDUCTOR S TATUSES (I NVERTER M ODE )

ac side and voltage regulation at the dc side. Hence, it reduces the switching losses and provides high conversion efficiency. Therefore, simplified PWM is a good candidate and is suitably adopted for the paralleled converter system in this paper. The state-space averaged equations corresponding to switching statuses in simplified PWM operated in rectifier mode and inverter mode are arranged in Tables III and IV, respectively. The gridside current iL —voltage vs characteristic of simplified PWM is presented in Fig. 3. As shown in Fig. 3, the simplified PWM is capable of operating at all four quadrants of the iL −vs plane. During intervals I and III, the instantaneous power flow is from grid to dc bus as rectifier mode operation, and during intervals II and IV, the instantaneous power flow is from dc bus to grid as inverter mode operation. Therefore, the bidirectional power flow can indeed be achieved in the simplified PWM.

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Fig. 3. Simplified PWM switching statuses in four-quadrant operation for bidirectional single-phase ac/dc converter systems.

Fig. 5.

Fig. 4.

Two paralleled single-phase boost converters (do work).

Two paralleled single-phase boost converters (do not work).

III. C IRCULATING C URRENTS For a convenient explanation of how circulating current is generated, the two-paralleled bidirectional single-phase converter system is considered and shown in Fig. 4. The grid side and the dc bus of two boost converters are connected in parallel directly without any isolation. During unsynchronized operation of paralleled converters, there exist several undesired current paths, i.e., circulating current loops, which result in additional currents, namely, circulating currents, and cause current distortion and unbalanced current sharing. For instance, when active switches TB1+ and TB2− are turned on, one can find that there exists a current loop as follows: + − Loop : Vdc → TB1 + → B1 → vs− → B2 → TB2− → Vdc .

The output voltage Vdc is shorted directly by the current loop, which produces huge short-circuit current and causes severe damages to the paralleled converters. In order to avoid short-path circuit loop caused by the output voltage during unsynchronized operation, symmetrical inductors are required

Fig. 6. DC circulating current loop in the paralleled converter system under UPWM operation.

to be placed between the grid voltage tips and the middle point of each switch leg, as shown in Fig. 5. A. Analysis of Circulating Currents 1) DC and AC Circulating Currents: Consider two paralleled single-phase boost converters, shown in Fig. 5, with inductors at each leg in each converter. When UPWM is used and switches TA1+ , TB1+ , TA2+ , and TB2− are turned on, one can find that there exist two different kinds of circulating current loops, i.e., dc and ac circulating current loops. In this condition, the dc and ac circulating current loops shown in Figs. 6 and 7, respectively, are formed as follows: + − DC Loop: Vdc → TB1+ → B1 → vs− → B2 → TB2− → Vdc ; + + − AC Loop: vs → A2 → TA2+ → Vdc → TB1+ → B1 → vs

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Fig. 7. AC circulating current loop in the paralleled converter system under UPWM operation.

Fig. 9. AC circulating current loop in the paralleled converter system under BPWM operation. TABLE V C OMPARISON OF BPWM, UPWM, AND THE P ROPOSED S IMPLIFIED PWM W ITH S WITCHING C ONSTRAINT M ETHOD O PERATED IN THE PARALLELED S YSTEM

Fig. 8. DC circulating current loop in the paralleled converter system under BPWM operation.

where dc circulating current loop is defined as the current loop caused by the output voltage Vdc without passing through Vs , and ac circulating current loop is defined as the current loop caused by the grid voltage Vs without passing through Vdc . Both dc and ac circulating current loops are the undesired loops in the paralleled converter system. Similarly, when bipolar PWM is used and switches TA1+ , TB1− , TA2− , and TB2+ are turned on, there exist dc and ac circulating current loops, as shown in Figs. 8 and 9, respectively. In this paper, utilizing simplified PWM strategy combined with the proposed switching constraint method can eliminate the dc circulating current loops and control the ac circulating current loops without any communication among the paralleled converters. For further revealing the potential merits of the proposed simplified PWM with switching constraint method, Table V is provided to summarize comparison of the dc and ac circulating currents, whether additional current sensors are required, switching number, and switching power losses for the conventional BPWM, UPWM, and the proposed simplified PWM with switching constraint method.

Fig. 10. Two-paralleled converter system. (a) Self-generated circulating current of converter 1. (b) Self-generated circulating current of converter 2.

Fig. 11.

Three-paralleled converter system.

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Fig. 12. Self-generated circulating current loops are uncontrollable in the parallel system under the rectifier mode while changing the system configuration from (a) status (A, A) to (b) status (A, E) while Vs > 0.

Fig. 13. Self-generated circulating current loops are controllable in the parallel system under the rectifier mode while changing the system configuration from (a) status (B, B) to (b) status (B, E) while Vs > 0.

In addition, if the same passive components are employed for the conventional BPWM, UPWM, and the proposed simplified PWM with switching constraint method, the line current distortion still depends on circulating currents. However, the similar techniques with regard to switching constraint for UPWM and/or BPWM are more complex than those for the simplified PWM because the number of switchings in one carrier cycle is four times that of simplified PWM. 2) Self-Generated and Synchronous Circulating Currents: Consider a two-paralleled converter system as shown in Fig. 8. If circulating current C1 flows from converter 1 to converter 2, as shown in Fig. 10(a), then C1 is defined as the self-generated circulating current of converter 1. Similarly, if circulating current C2 flows from converter 2 to converter 1, as shown in Fig. 10(b), then C2 is defined as the self-generated circulating current of converter 2. Furthermore, consider a threeparalleled converter system as shown in Fig. 11. If circulating currents C12 and C13 flow from converter 1 to converter 2, C12 and C13 are all called the self-generated circulating currents of converter 1. In contrast, C12 and C13 can be called the non-selfgenerated circulating currents of converters 2 and 3. In the existing literature [13], while the paralleled converters are operated in synchronized mode, namely, uniform modulation, there will be no circulating current among paralleled

converters. However, in simplified PWM, when two converters are paralleled together directly in the synchronized mode, for instance, in Fig. 5, the two paralleled converters are operated in system configurations (A, A) and (B, B) shown in Figs. 12 and 13, respectively, under the rectifier mode operation or (C, C) and (D, D) shown in Figs. 14 and 15, respectively, under the rectifier mode operation, one can find that there exist circulating currents, namely, synchronous circulating currents, which is not explored before. In this paper, a novel circulating current control strategy is proposed to eliminate the dc circulating current and control the ac circulating currents. In addition, both the self-generated circulating currents and the synchronous circulating currents are all suppressed without any extra circuit sensor. Therefore, the cost of power-augmented renewable energy system can be reduced, and the modularparalleled system can be easily achieved. B. Proposed Switching Constraint Control Scheme To achieve better current shaping and reduce the circulating currents in the parallel system, the conventional methods [11] control the single-phase paralleled converter system to prevent circulating currents. However, those methods use two current sensors in each converter and only prevent dc circulating

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Fig. 14. Self-generated circulating current loops are uncontrollable in the parallel system under the rectifier mode while changing the system configuration from (a) status (C, C) to (b) status (C, E) while Vs < 0.

Fig. 15. Self-generated circulating current loops are controllable in the parallel system under the rectifier mode while changing the system configuration from (a) status (D, D) to (b) status (D, E) while Vs < 0. TABLE VI C OMBINATION OF S WITCHING S TATUSES IN THE T WO -PARALLELED S INGLE -P HASE C ONVERTER S YSTEM U SING S IMPLIFIED PWM U NDER THE R ECTIFIER M ODE

currents without considering ac circulating currents. In this paper, a novel circulating control method is proposed. The proposed method combines simplified PWM with switching constraint control scheme to prevent both dc and ac circulating

TABLE VII C HOSEN S TATUSES FOR THE PARALLEL S YSTEM IN THE S WITCHING C ONSTRAINT M ETHOD U NDER THE R ECTIFIER M ODE O PERATION

currents with only using one current sensor in each converter in the paralleled system. Both current shaping and sharing are achieved, and the dc link voltage is also well kept. For a convenient explanation of how the switching constraint control scheme functions, one can consider that the paralleled converter system is operated under the rectifier mode when Vs > 0, as shown in Fig. 12. The operation status of the two paralleled converters is indicated as paralleled configuration (x, y), where x and y represent the switching statuses of the two paralleled converters, i.e., converters 1 and 2, respectively. The paralleled configurations (A, A) and (A, E) are shown in Fig. 12(a) and (b), respectively. As can be observed from Fig. 12(a), although the paralleled converters are operated in

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Fig. 16. Self-generated circulating current loops are uncontrollable in the paralleled system under the inverter mode while changing the system configuration from (a) status (G, G) to (b) status (G, H) while Vs > 0.

synchronized mode, there exist circulating currents, namely, synchronous circulating currents. It follows from Fig. 12(b) that, while converter 2 changes status from A to E, the circulating current loop that flows from converter 2 to converter 1 still remains, as shown in the black color, and the circulating current loop that flows from converter 1 to converter 2 vanishes, as shown in the gray color. According to the previous explanation, the black- and gray-colored circulating currents are the synchronous circulating currents while the paralleled configuration is (A, A). They also can be considered as the self-generated circulating currents of converters 2 and 1, respectively. However, in this situation, when converter 2 changes status from A to E, the self-generated circulating current loop of converter 2 in the black color still exists and cannot be eliminated. One can claim that the self-generated circulating current loop of converter 2 in the black color is uncontrollable by itself. This implies that converter 2 cannot control the self-generated circulating current while the switching status of converter 2 is changed from A to E. In this condition, the self-generated circulating current loops are uncontrollable and result in input current distortion and current unbalance in the parallel system. Thus, in order to control the self-generated circulating current loop, one can replace status A by B in each converter in the parallel system, as shown in Fig. 13. Fig. 13(a) and (b) shows the parallel system in statuses (B, B) and (B, E), respectively. In Fig. 13(a), when the paralleled converters are operated in synchronized mode, there exist synchronous circulating currents. However, in Fig. 13(b), it can be observed that, when converter 2 changes status from B to E, converter 2 can eliminate the self-generated circulating current loop, as shown in the black color in Fig. 13(a). Another self-generated circulating current loop can be also easily eliminated by converter 1 while converter 1 changes status from B to E. In such a situation, the inductor currents in each converter can be properly charged and discharged, and the self-generated circulating current loops in the parallel system can be also controlled. Similarly, one can consider that the paralleled converter system is operated under the rectifier mode when Vs < 0, as shown in Figs. 14 and 15. The self-generated circulating currents are uncontrollable in Fig. 14 and controllable in Fig. 15.

The combinations of switching statuses of two paralleled converters under the rectifier mode are listed in Table VI. One can find that, when two paralleled converters are operated in synchronous mode, it cannot guarantee zero circulating current. In addition, only ac circulating current loops exist while adopting simplified PWM in the paralleled single-phase converter system. Therefore, in order to eliminate circulating currents, the chosen switching statuses, i.e., switching constraint, under the rectifier mode operation are achieved and listed in Table VII. Next, consider that the paralleled system is operated under the inverter mode when Vs > 0, as shown in Figs. 16 and 17. From Fig. 16(a) and (b), one can find that the self-generated circulating current loops are uncontrollable. However, from Fig. 17(a) and (b), one can find that the self-generated circulating current loops are controllable. Similarly, one can consider that the paralleled converter system is operated under the inverter mode when Vs < 0, as shown in Figs. 18 and 19. The self-generated circulating current loops are uncontrollable in Fig. 18 and controllable in Fig. 19. The combinations of switching statuses in the two-paralleled single-phase converter system under the inverter mode are listed in Table VIII. One can find that, when two paralleled converters are operated in synchronous mode, it also cannot guarantee zero circulating current under the inverter mode. In addition, only ac circulating current loops exist while adopting simplified PWM in the paralleled single-phase converter system. Therefore, in order to eliminate circulating currents, the chosen switching statuses, i.e., switching constraint, in the simplified PWM for the paralleled system under the inverter mode operation are achieved and listed in Table IX. IV. S IMULATION AND E XPERIMENTAL R ESULTS To verify the validity of the proposed simplified PWM with switching constraint method, the well-known software Power SIM is adopted to carry out the simulation process. The simulation parameters of two paralleled single-phase bidirectional ac/dc converters shown in Fig. 5 are listed in Table X. The input voltage is a distorted sinusoidal waveform with total harmonic distortion THDv ≈ 5% measured from an actual ac grid source.

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Fig. 17. Self-generated circulating current loops are controllable in the paralleled system under the inverter mode while changing the system configuration from (a) status (F, F) to (b) status (F, H) while Vs > 0.

Fig. 18. Self-generated circulating current loops are uncontrollable in the paralleled system under the inverter mode while changing the system configuration from (a) status (I, I) to (b) status (I, K) while Vs < 0.

Fig. 19. Self-generated circulating current loops are controllable in the paralleled system under the inverter mode while changing the system configuration from (a) status (J, J) to (b) status (J, K) while Vs < 0.

The control block of the proposed switching constraint control scheme in the simplified PWM [14] for each bidirectional ac/dc converter to eliminate circulating currents in the parallel system is shown in Fig. 20. The switching signal generator requires signals Son , the grid voltage sign(vs ), and power flow direction PFD combined with Tables VII and IX to generate switching signals TA+ , TA− , TB+ , and TB− . The detailed

switching signal generator block is also shown in Fig. 21, which is composed of both rectifier mode and inverter mode with the proposed switching constraint control scheme whose four-quadrant operation of grid-tied voltage vs and line current iL is shown in Fig. 22. Compared with Fig. 3, the switching constraint method only reduces one switching status in each quadrant.

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TABLE VIII C OMBINATION OF S WITCHING S TATUSES IN THE T WO -PARALLELED S INGLE -P HASE C ONVERTER S YSTEM U SING S IMPLIFIED PWM U NDER THE I NVERTER M ODE

Fig. 21. Construction of switching constraint control scheme for each converter in the parallel system.

TABLE IX C HOSEN S TATUSES FOR THE PARALLELED S YSTEM IN THE S WITCHING C ONSTRAINT M ETHOD U NDER THE I NVERTER M ODE O PERATION

TABLE X S IMULATION PARAMETERS OF T WO PARALLELED S INGLE -P HASE C ONVERTERS

Fig. 20. Control block of the proposed switching constraint control scheme in the simplified PWM for each bidirectional ac/dc converter in the parallel system [14].

It is worth mentioning that the simplified PWM has a current commutation interval through the antiparalleling diode during both rectifier mode and inverter mode. Then, the closed-loop feedback control force must overcome the diode forward voltage. Therefore, the duty ratio feedforward control and the PDF are added into the traditional dual-loop control to enhance the

Fig. 22. Switching constraint statuses of simplified PWM in fourquadrant operation for bidirectional single-phase ac/dc converter systems.

control force to achieve current shaping and voltage regulation in the steady state and fast response during the transient. Next, consider that the paralleled converter system is operated in the rectifier mode. Fig. 23 shows the simulation results without switching constraint control in the rectifier mode operation. The input voltage Vs , line currents iL1a and iL1b of converter 1, and line currents iL2a and iL2b of converter 2 are shown in Fig. 23(a)–(c), respectively. The phase-current deviation iL1a − iL1b of converter 1 and the phase-current deviation (iL1a − iL2a )/2 of the two paralleled converters are shown in Fig. 23(d) and (e), respectively. From Fig. 23, one can find that the line currents iL1a , iL1b , iL2a , and iL2b are significantly distorted because of the circulating currents. This will result in current distortion and unbalanced load sharing, and the overall performance will be degraded. Fig. 24 shows the simulation results with switching constraint control in the rectifier mode, which corresponds to the control blocks shown in Figs. 20 and 21. The input voltage Vs , line currents iL1a and iL1b of converter 1, and line currents iL2a and iL2b of converter 2 are shown in Fig. 24(a)–(c), respectively. The phase-current deviation iL1a − iL1b of converter 1 and the phase-current deviation (iL1a − iL2a )/2 of the two paralleled converters are shown in Fig. 24(d) and (e), respectively. Comparing Fig. 23(b) and (c) with Fig. 24(b) and (c), one can see that the shapes of the line currents have been improved and approach those of sinusoidal waveforms. This implies that both current shaping and current sharing for each converter are achieved in the paralleled converter system operated in the rectifier mode.

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Fig. 23. Simulation results without switching constraint control in the simplified PWM operated in the rectifier mode condition. (a) Vs . (b) iL1a (black) and iL1b (gray). (c) iL2a (black) and iL2b (gray). (d) iL1a − iL1b . (e) (iL1a − iL2a )/2.

Fig. 24. Simulation results with switching constraint control in the simplified PWM operated in the rectifier mode condition. (a) Vs . (b) iL1a (black) and iL1b (gray). (c) iL2a (black) and iL2b (gray). (d) iL1a − iL1b . (e) (iL1a − iL2a )/2.

Furthermore, consider that the paralleled converter system is operated in the inverter mode. Fig. 25 shows the simulation results without switching constraint control in the inverter mode operation. The input voltage Vs , line currents iL1a and iL1b

Fig. 25. Simulation results without switching constraint control in the simplified PWM operated in the inverter mode condition. (a) Vs . (b) iL1a (black) and iL1b (gray). (c) iL2a (black) and iL2b (gray). (d) iL1a − iL1b . (e) (iL1a − iL2a )/2.

of converter 1, and line currents iL2a and iL2b of converter 2 are shown in Fig. 25(a)–(c), respectively. The phase-current deviation iL1a − iL1b of converter 1 and the phase-current deviation (iL1a − iL2a )/2 of the two paralleled converters are shown in Fig. 25(d) and (e), respectively. From Fig. 25, one can find that the line currents iL1a , iL1b , iL2a , and iL2b are significantly distorted due to the circulating currents. This will result in current distortion and unbalanced load sharing, and the overall performance will be degraded. Fig. 26 shows the simulation results with switching constraint control in the inverter mode that corresponds to the control blocks shown in Figs. 20 and 21. The input voltage Vs , line currents iL1a and iL1b of converter 1, and line currents iL2a and iL2b of converter 2 are shown in Fig. 26(a)–(c), respectively. The phase-current deviation iL1a − iL1b of converter 1 and the phase-current deviation (iL1a − iL2a )/2 of the two paralleled converters are shown in Fig. 26(d) and (e), respectively. Comparing Fig. 25(b) and (c) with Fig. 26(b) and (c), one can see that the shapes of the line currents have been improved and approach those of sinusoidal waveforms. This implies that both current shaping and current sharing for each converter are achieved in the paralleled converter system operated in the inverter mode. From the simulation results, in summary, regardless of whether the parallel system is operated in rectifier mode or inverter mode, the proposed simplified PWM with switching constraint control scheme can indeed reduce the circulating currents, improve the line current shaping, and achieve current balancing in the paralleled converter system. To facilitate understanding of the proposed theoretical results and as verification, a prototype system, as shown in

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TABLE XI E XPERIMENTAL PARAMETERS OF T WO PARALLELED S INGLE -P HASE C ONVERTERS

Fig. 26. Simulation results with switching constraint control in the simplified PWM operated in the inverter mode condition. (a) Vs . (b) iL1a (black) and iL1b (gray). (c) iL2a (black) and iL2b (gray). (d) iL1a − iL1b . (e) (iL1a − iL2a )/2.

Fig. 27. Realized prototype of two paralleled single-phase boost converters.

Fig. 27, with two paralleled single-phase bidirectional converters is constructed with the corresponding parameters listed in Table XI. However, the implemented actual ac grid voltage source was a distorted-sinusoidal-waveform voltage source with total harmonic distortion THDv ≈ 5%. The system controller is implemented with a Spartan-3E XC3S250E FPGA. First, consider that the paralleled converter system is operated in the rectifier mode. Figs. 28–30 show the experimental results without switching constraint control. The measured waveforms Vs , line currents iL1a and iL1b , and current deviation iL1a − iL1b for converter 1 are shown in Fig. 28, and the measured waveforms Vs , line currents iL2a and iL2b , and current deviation iL2a − iL2b for converter 2 are shown in Fig. 29

Fig. 28. Measured waveforms of converter 1 without switching constraint control in the simplified PWM operated in the rectifier mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL1b (black). (Bottom) Current deviation iL1a − iL1b for converter 1.

Fig. 29. Measured waveforms of converter 2 without switching constraint control in the simplified PWM operated in the rectifier mode. (Top) Input voltage Vs and input line currents iL2a (gray) and iL2b (black). (Bottom) Current deviation iL2a − iL2b for converter 2.

for comparison. Fig. 30 shows the measured waveform Vs , line currents iL1a and iL2a , and current deviation (iL1a − iL2a )/2 in the two-paralleled converter system. From Figs. 28–30, one can find that currents iL1a , iL1b , iL2a , and iL2b are significantly distorted and current sharing is unbalanced because of the circulating currents in the parallel system. Figs. 31–33 show the experimental results with switching constraint control in the paralleled system operated in the rectifier mode. The measured waveforms Vs , line currents iL1a and iL1b , and current deviation iL1a − iL1b for converter 1 are shown in Fig. 31, and the measured waveforms Vs , line currents iL2a and iL2b , and current deviation iL2a − iL2b for converter 2 are shown in Fig. 32 for comparison. Fig. 33 shows the measured waveforms Vs ,

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Fig. 30. Measured waveforms without switching constraint control in the simplified PWM operated in the rectifier mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL2a (black). (Bottom) Current deviation (iL1a − iL2a )/2 between the two converters.

Fig. 31. Measured waveforms of converter 1 with switching constraint control in the simplified PWM operated in the rectifier mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL1b (black). (Bottom) Current deviation iL1a − iL1b for converter 1.

Fig. 32. Measured waveforms of converter 2 with switching constraint control in the simplified PWM operated in the rectifier mode. (Top) Input voltage Vs and input line currents iL2a (gray) and iL2b (black). (Bottom) Current deviation iL2a − iL2b for converter 2.

line currents iL1a and iL2a , and current deviation (iL1a − iL2a )/2 in the two-paralleled converter system. Comparing Figs. 31–33 with Figs. 28–30, one can see that the shapes of the line currents have been improved and approach those of sinusoidal waveforms. This implies that circulating currents in the paralleled converter system are nearly zero. Thus, both current shaping and current sharing for each converter are achieved in the paralleled converter system operated in the rectifier mode.

Fig. 33. Measured waveforms with switching constraint control in the simplified PWM operated in the rectifier mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL2a (black). (Bottom) Current deviation (iL1a − iL2a )/2 between the two converters.

Fig. 34. Measured waveforms of converter 1 without switching constraint control in the simplified PWM operated in the inverter mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL1b (black). (Bottom) Current deviation iL1a − iL1b for converter 1.

Fig. 35. Measured waveforms of converter 2 without switching constraint control in the simplified PWM operated in the inverter mode. (Top) Input voltage Vs and input line currents iL2a (gray) and iL2b (black). (Bottom) Current deviation iL2a − iL2b for converter 2.

Next, consider that the paralleled converter system is operated in the inverter mode. Figs. 34–36 show the experimental results without switching constraint control. The measured waveforms Vs , line currents iL1a and iL1b , and current deviation iL1a − iL1b for converter 1 are shown in Fig. 34, and the measured waveforms Vs , line currents iL2a and iL2b , and current deviation iL2a − iL2b for converter 2 are shown in Fig. 35 for comparison. Fig. 36 shows the measured waveform Vs , line currents iL1a and iL2a , and current deviation (iL1a − iL2a )/2 in the two-paralleled converter system. From Figs. 34–36, one

LIAO AND CHEN: PWM WITH SWITCHING CONSTRAINT METHOD TO PREVENT CIRCULATING CURRENTS

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Fig. 36. Measured waveforms without switching constraint control in the simplified PWM operated in the inverter mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL2a (black). (Bottom) current deviation (iL1a − iL2a )/2 between the two converters.

Fig. 39. Measured waveforms with switching constraint control in the simplified PWM operated in the inverter mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL2a (black). (Bottom) Current deviation (iL1a − iL2a )/2 between the two converters.

Fig. 37. Measured waveforms of converter 1 with switching constraint control in the simplified PWM operated in the inverter mode. (Top) Input voltage Vs and input line currents iL1a (gray) and iL1b (black). (Bottom) Current deviation iL1a − iL1b for converter 1.

Fig. 40. Measured efficiency of the paralleled converter system under BPWM with current sharing control and the simplified PWM with and without switching constraint method.

Fig. 38. Measured waveforms of converter 2 with switching constraint control in the simplified PWM operated in the inverter mode. (Top) Input voltage Vs and input line currents iL2a (gray) and iL2b (black). (Bottom) Current deviation iL2a − iL2b for converter 2.

can find that the currents iL1a , iL1b , iL2a , and iL2b are significantly distorted and current sharing is unbalanced because of the circulating currents in the parallel system. Figs. 37–39 show the experimental results with switching constraint control in the paralleled system operated in the inverter mode. The measured waveforms Vs , line currents iL1a and iL1b , and current deviation iL1a − iL1b for converter 1 are shown in Fig. 37, and the measured waveforms Vs , line currents iL2a and iL2b , and current deviation iL2a − iL2b for converter 2 are shown in Fig. 38 for comparison. Fig. 39

shows the measured waveform Vs , line currents iL1a and iL2a , and current deviation (iL1a − iL2a )/2 in the two-paralleled converter system. Comparing Figs. 37–39 with Figs. 34–36, one can see that the shapes of the line currents have been improved and approach those of sinusoidal waveforms. This implies that circulating currents in the paralleled converter system are nearly zero. Thus, both current shaping and current sharing for each converter are achieved in the paralleled converter system operated in the inverter mode. On the basis of the experimental results, regardless of whether the parallel system is operated in the rectifier or the inverter mode, it is shown that the proposed switching constraint control scheme in simplified PWM can efficiently reduce the circulating currents and improve the line current waveforms in the paralleled converter system. To understand the merits of the proposed simplified PWM with switching constraint method, the efficiency of the two paralleled single-phase boost converters is measured under BPWM with current sharing control and simplified PWM with and without switching constraint method, which are shown in Fig. 40. From Fig. 40, one can see that the proposed simplified PWM with switching constraint method has higher efficiency than the other two cases because the proposed simplified PWM with switching constraint method can both reduce switching losses and prevent circulating currents for paralleled powercapacity-augmented converter system.

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V. C ONCLUSION In this paper, a simplified PWM with switching constraint control scheme has been proposed to eliminate the circulating currents for bidirectional paralleled ac/dc converters in gridtied system. The proposed control scheme eliminates the dc circulating currents and controls the ac and self-generated circulating currents. Both current shaping and current sharing in the paralleled system operated under rectifier and inverter modes are accomplished. Compared with conventional method, there is no need requiring additional current sensors or communication device in the paralleled system to reduce circulating currents. The cost of paralleled converter system can be reduced, and the overall system performance can be increased. Furthermore, a prototype system consisting of two bidirectional paralleled ac/dc converters is constructed and tested. Both simulation and experimental results are also given to verify the validity of the proposed control scheme. Finally, it is worth mentioning that the proposed control scheme can be modularized and extended to N-paralleled ac/dc converters for higher power grid-tied system. R EFERENCES [1] J. S. S. Prasad and G. Narayanan, “Minimization of grid current distortion in parallel-connected converters through carrier interleaving,” IEEE Trans. Ind. Electron., vol. 61, no. 1, pp. 76–91, Jan. 2014. [2] C. B. Jacobina, E. Cipriano dos Santos, N. Rocha, B. de Sá Gouveia, and E. R. C. da Silva, “Reversible ac drive systems based on parallel ac–ac dclink converters,” IEEE Trans. Ind. Appl., vol. 46, no. 4, pp. 1456–1467, Jul./Aug. 2010. [3] M. Cichowlas et al., “Active filtering function of three-phase PWM boost rectifier under different line voltage conditions,” IEEE Trans. Ind. Electron., vol. 52, no. 2, pp. 410–419, Apr. 2005. [4] S. Kim, M. H. Todorovic, and P. N. Enjeti, “Three-phase active harmonic rectifier (AHR) to improve utility input current THD in telecommunication power distribution system,” IEEE Trans. Ind. Appl., vol. 39, no. 5, pp. 1414–1421, Sep./Oct. 2003. [5] Y. Sato and T. Kataoka, “Simplified control strategy to improve ac-inputcurrent waveform of parallel-connected current-type PWM rectifiers,” Proc. Inst. Elect. Eng.—Elect. Power Appl., vol. 142, no. 4, pp. 246–254, Jul. 1995. [6] Z. Ye, D. Boroyevich, J. Y. Choi, and F. C. Lee, “Control of circulating current in two parallel three-phase boost rectifiers,” IEEE Trans. Power Electron., vol. 17, no. 5, pp. 609–615, Sep. 2002. [7] C. T. Pan and Y. H. Liao, “Modeling and coordinate control of circulating currents in parallel three-phase boost rectifiers,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 825–838, Apr. 2007. [8] Y. Zhang, Y. Kang, and J. Chen, “The zero-sequence circulating currents between parallel three-phase inverters with three-pole transformers and reactors,” in Proc. IEEE APEC Expo., Sep. 2006, pp. 1709–1715. [9] T. P. Chen, “Zero-sequence circulating current reduction method for parallel HEPWM inverters between ac bus and dc bus,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 290–300, Jan. 2012. [10] J. W. Moon, C. S. Kim, J. W. Park, D. W. Kang, and J. M. Kim, “Circulating current control in MMC under the unbalanced voltage,” IEEE Trans. Power Del., vol. 28, no. 3, pp. 1952–1959, Jul. 2013. [11] Y. Zhongming, P. K. Jain, and P. C. Sen, “Circulating current minimization in high-frequency ac power distribution architecture with multiple inverter modules operated in parallel,” IEEE Trans. Ind. Electron., vol. 54, no. 5, pp. 2673–2687, Oct. 2007. [12] C.-T. Pan and Y.-H. Liao, “Modeling and control of circulating currents for parallel three-phase boost rectifiers with different load sharing,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2776–2785, Jul. 2008. [13] H. Cai, R. Zhao, and H. Yang, “Study on ideal operation status of parallel inverters,” IEEE Trans. Power Electron., vol. 23, no. 6, pp. 2964–2969, Nov. 2008. [14] Y. H. Liao, “A novel reduced switching loss bidirectional ac/dc converter PWM strategy with feed-forward control for grid-tied micro grid systems,” IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1500–1513, Mar. 2014.

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