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并联三相PWM变换器连接系统环流控制的带宽扩展方法的详细资料说明

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采用无隔离变压器的公共直流并联三相EPWM变换器会引起零序环流问题。以往的工作已经证明，循环电流主要受各次PWM周期所采用的零矢量的影响。提出了一种抑制环流的新方法。基于推导出的平均模型，详细分析了零序环流产生的原因。提出了零矢量前馈控制策略与传统PI控制相结合的方法来抑制零轴电流系统中的扰动。此外，还采用了双电流采样和双电流比例更新方案来扩展零轴电流环的带宽。结果表明，在不同的滤波电感和变换器输出电流条件下，可以获得较好的循环电流抑制性能。

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 12, DECEMBER 2014

6847

Bandwidth Expansion Method for Circulating

Current Control in Parallel Three-phase PWM

Converter Connection System

Zhang Xueguang, Member, IEEE, Chen Jiaming, Ma Yan, Wang Yijie, and Xu Dianguo, Senior Member, IEEE

Abstract—The use of common dc-link parallel three-phase PWM parallel module and degrade the overall performance of the par-

converters without isolating transformers will cause zero-sequence

circulating current problem. Previous works have proven that the

circulating current is mainly affected by zero vectors employed in

each PWM cycle. This paper proposes a novel method to suppress

allel system. Consequently, circulating current suppression has

become a focus in this ﬁeld [4].

The zero-sequence circulating path can be cut open by using

an isolating transformer at ac side [5], but the parallel system will

the circulating current. Detailed analysis is presented on the causes

of zero-sequence circulating current based on a derived average become costly and bulky. Using separate dc power supply will

model. A zero vectors feed-forward control strategy in combina-

tion with traditional PI control method is proposed to reject dis-

turbances in zero-axis current system. In addition, a dual current

sampling and dual PWM duty ratio update (DSDU) scheme is used

encounter similar problems [6]. For parallel systems with both

common dc-link and ac bus to reduce costs and size, interphase

reactors may be used to provide high zero-sequence impedance

[7], [8]. Nevertheless, the reactors cannot prevent low-frequency

to expand the bandwidth of zero-axis current loop. As a result, bet-

ter circulating current suppression performance can be achieved in components in the circulating current.

different ﬁlter inductance and converter output currents condition.

The mechanism of circulating current has been analyzed

Compared with the PI control method, the converters operated in

parallel can be switched on and switched off separately with small

current impact. Experimental results conﬁrm the performance and

effectiveness of the proposed method.

in pervious works [9], [10]. The paralleled converters can be

centrally controlled as one converter [11], for example, a two-

converter parallel system can be controlled as a six-phase con-

verter, however, whereas design of this control system will

be complicated. Special PWM techniques are proposed to in-

hibit the circulating current [12]–[14]. The discontinuous space

modulation-based interleaved PWM method would effectively

reduce the circulating current, but it would result in high cur-

rent ripple in converter output currents, and this drawback may

be alleviated by the phase-shifted scheme proposed in [13]. The

proposed HEPWM method of Chen [14] would effectively elim-

inate both the high-frequency and low-frequency components

of circulating current, but it suffers from high switching losses.

Due to the fact that the zero-sequence circulating current is

mainly affected by zero vectors employed in each PWM cycle,

control method for decreasing common mode voltage distur-

bance with multicarrier technique is proposed by Hou [15]. The

multicarrier can effectively mitigate the circulating current by

means of nullifying the use of zero vectors. On the other hand,

the circulating current control method for SVPWM technique

was discussed in [16]. A control variable was introduced to ad-

just the distribution of zero vectors in each PWM cycle with

a proportional integral (PI) controller. However, the limitations

to the bandwidth of zero-axis circulating current loop is rarely

discussed. Nonlinear control methods were also presented to

resist the circulating current [17], [18], yet the algorithms are

too complicated to implement. An open-loop control method

is proposed in [19] and the control methods on zero-sequence

circulating current caused by dead time effect [20] has been

developed.

Index Terms—Bandwidth expansion, circuiting currents control,

DSDU, module parallel connection, three-phase PWM converter,

zero vectors feed-forward.

I. INTRODUCTION

HREE-PHASEPWM converter hasbeenwidelyemployed

in low-voltage high-current applications [1]–[3] owing to

its advanced features. As the capacity of converter is increased,

the use of parallel three-phase converters has become more pop-

ular due to its simplicity, low cost, and high ﬂexibility. However,

when the common dc-link converters are connected in parallel

without using of isolating transformers, the zero-sequence cir-

culating current problem will occur. Circulating current can be

produced by the differences in inductors and converter currents,

other aspects such as dead time, measuring errors, analog to digi-

tal conversion, discretization, loose of synchronism between the

carriers cause the circulating current problem. The circulating

current will result in current distortion and harmonic loss in

Manuscript received December 15, 2013; revised February 17, 2014; accepted

February 23, 2014. Date of publication March 11, 2014; date of current version

August 13, 2014. This work was supported in part by the National Natural

Science Foundation of China under Grant 51107020 and Grant 51237002.

Recommended for publication by Associate Editor D. Vinnikov.

The authors are with the Department of Electrical Engineering, Harbin

Institute of Technology, Harbin 150001, China (e-mail: ;

; ; ; xudiang

@hit.edu.cn).

In this paper, an average model of the parallel system is de-

rived to analyze the mechanism of zero-sequence circulating

current with SVPWM modulation technique. It is found that the

circulating current suppression performance can be enhanced by

Color versions of one or more of the ﬁgures in this paper are available online

Digital Object Identiﬁer 10.1109/TPEL.2014.2311046

6848

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 12, DECEMBER 2014

expanding the bandwidth of zero-axis current loop. However,

both the difference in ﬁlter inductance and output currents would

cause disturbances to the zero-axis current system. More im-

portantly, in low-voltage high-current applications, low switch-

ing frequency is usually required as to reduce the switching

losses [21], [22]. Unfortunately, the time delayed by the digital

control system and disturbances will all make it difﬁcult to ex-

pand the bandwidth of zero-axis current loop and even degrade

the suppression effect. Hence, it is very meaningful to improve

the suppression performance by simultaneously decreasing the

time delayed by the digital control system and eliminating the

impacts of disturbances without increasing switching frequency.

Based on the analysis, a feed-forward control method in com-

bination with a dual current sampling and dual PWM duty ratio

update (DSDU) scheme on the basis of traditional PI control

method is proposed. As a result, the bandwidth of zero-axis

circulating current loop can be effectively improved with dis-

turbances rejected by the feed-forward strategy. Better circu-

lating current suppression performance can be obtained both

in transient state and steady state. Compared to the PI method

combined with DSDU scheme, online converter module switch-

ing on when another converter is running and switching off (by

inhibiting pulse of the switched converter) with small current

impact can be realized. As a result, the reliability of the parallel

system is greatly enhanced.

Fig. 1. Topology structure of parallel connection system of three-phase PWM

converter.

effects would also contribute to the generation of circulating

current. The circulating current of the parallel system can be

deﬁned as

i_zx= i_ax+ i_bx+ i_cx

(1)

where x = 1, 2 represents the number of converters 1 and 2,

respectively. For the sake of convenience, choose the dc negative

side as reference point, and assume the duty ratio of the top

switch in phase k (k = a,b,c) of converter x(x = 1,2) to be

d_kx,then the average model of the parallel system in three-phase

stationary frame can be obtained as

The remainder of the paper is organized as follows.

Section II reviews the theoretical background of the parallel con-

verter system with SVPWM modulation technique. The analysis

of zero-axis current loop bandwidth with PI method is detailed

in Section III and the feed-forward strategy for eliminating the

restrictions in combination with DSDU scheme for expanding

zero-axis current loop bandwidth is proposed in Section IV.

Section V presents the experimental results and Section VI con-

cludes the paper.

⎡

⎤

⎡

⎤

⎡

⎤

⎡

⎤

⎡

⎤

i_ax

e_a

e_b

e_c

u_N

d_ax

d_bxu_dc

d_cx

⎣

⎦

⎣

⎦

⎣

⎦

⎣

⎦

⎣

⎦

L_x

i_bx=−R_sxi_bx

−

i_cx

(2)

where L_xand R_sxare the inductance and equivalent series

resistances of converters 1 and 2, respectively.

II. THEORY OF CIRCULATING CURRENT SUPPRESSION

This model canbe transformedintothe synchronous reference

frame by (3) with a 3-D nonsingular matrix deﬁned as

A. Model of Three-Phase Parallel-Converter System

⎡

⎤

In this paper, parallel converters are assumed to be con-

nected to the ac gird through ﬁlter inductance as illustrated

in Fig. 1. As Fig. 1 shows, the switches of parallel modules

in the same phase are connected in series. Consequently, cir-

culating current path is formed. Ideally, if the parallel con-

verters with equal output currents are completely identical in

parameters, uniformly modulated, no circulating current would

be generated as the output voltages in the ac side have the

same frequency, phase, and amplitude [23]. However, in prac-

tical applications, while parallel modules are usually designed

to have the same parameters, tolerance in parameter disper-

sion is very common, which in return would result in differ-

ent ﬁlter inductance [24] and unequal measured values of out-

put currents. Moreover, the synchronism between the carriers

of different converters may be interfered. As a consequence,

differences will occur in the output voltages of the parallel

modules during the short switching process, both in amplitude

and phase. Consequently, circulating current would be gener-

ated as asynchronous action emerges. Besides, the dead time

cos ωt

cos(ωt − 2π/3)

cos(ωt + 2π/3)

⎢

⎣

⎥

⎦

− sin ωt − sin(ωt − 2π/3) − sin(ωt + 2π/3)

T_s−r

(3)

(4)

x_dqz= T_s−r.x_abc

where ω is the grid fundamental angular frequency, and x_dqz

is the transformed variable in synchronous frame of x_abc. With

this understanding, the average model of the parallel system in

synchronous frame d–q–z can be obtained as

ꢀ

ꢁ

ꢀ

ꢁ

−ω

ꢀ

ꢁ

i_dx

i_qx

i_dx

i_qx

i_dx

i_qx

e_d

e_q

L_x·

= −R_sx

− L_x·

ꢀ

ꢁ ꢀ

ꢁ

ꢀ

ꢁ

u_dx

u_qx

−

(5)

(6)

di_z2

(L₁+ L₂) ·

= −(R_s1+ R_s2) · i_z2+ Δd_z· u_dc

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并联三相PWM变换器连接系统环流控制的带宽扩展方法的详细资料说明

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