Eliminating DC Current Injection in Current-Transformer ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 8, AUGUST 2013

Eliminating DC Current Injection in Current-Transformer-Sensed STATCOMs Yanjun Shi, Student Member, IEEE, Bangyin Liu, Member, IEEE, and Shanxu Duan

Abstract—Grid-connected power electronics converters/ inverters usually have certain amount of dc component at their ac terminal. They are likely to inject unwanted direct current into the power grid, unless a line-frequency transformer is employed. This study investigates this dc injection problem for static synchronous compensator (STATCOM) and connects the dc injection with current transformer (CT), a current sensing element widely used in high-voltage converters. By introducing CT’s model into the STATCOM’s model, this study found that using CT for current feedback control can cause large dc injection, if no extra means is taken. Expressions of the dc injection for different controllers were derived. Then, a dc injection elimination method was proposed. This method eliminates the dc component of the output current by building an indirect dc feedback loop; therefore, it can prevent injecting the direct current even when it cannot be sensed. Experimental results taken on a 25-level cascaded multilevel STATCOM prototype verifies the analysis and the proposed method. Index Terms—Cascaded multilevel converter (CMC), current transformers (CTs), dc injection, static synchronous compensator (STATCOM).

I. INTRODUCTION RID-CONNECTED power converters usually involve dc–ac conversion to exchange ac power with the grid. Typical examples include power inverter, static synchronous compensator (STATCOM), and active power filter (APF). Because ac power of these converters comes from a dc source, it is crucial to guarantee that there is no direct current injected into the grid. Excessive amount of dc injection can lead to problems like corrosion in underground equipment, transformer saturation, transformer magnetizing current distortion, and malfunction of protective equipment [1]–[4]. Therefore, utility companies always require equipment provider to eliminate direct current injection under a certain level [5] or a line-frequency transformer, which is designed to be able to withstand certain level of direct current, has to be installed between the converter and the grid [6]. This line-frequency transformer is bulky, expensive, and will bring extra power loss to system. Moreover,

G

Manuscript received June 4, 2012; revised September 19, 2012; accepted November 11, 2012. Date of current version January 18, 2013. Recommended for publication by Associate Editor J. H. R. Enslin. The authors are with the State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: [email protected]; [email protected]; [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/TPEL.2012.2228883

as the line-frequency transformer separates the direct current at the cost of letting dc flow into its own magnetizing circuit, large audio noise often occurs. Therefore, many researchers aim to enable grid-connected converters run without transformers [7]–[14], especially in the field of cascaded STATCOMs where high output voltage is easier to achieve [9]–[12]. However, little attention has been paid to the elimination of the dc injection for transformerless STATCOMs. There are many reasons that can be linked to dc injection, such as imbalance in modulation, truncation error during signal digitalizing, offset drifting in current sensing, and dc voltage unbalance for multilevel converters. The major cause of dc injection can be summarized as nonideal current sensing. This is because the controller in the output current feedback loop of grid-connected converters usually has large gain at very low frequency. Therefore, any direct current that exists in the output will be compensated, as long as it can be correctly sensed. The worst situation is when current transformers (CTs) are used as the current sensing element. Because of better insulation, better electromagnetic compatibility, ability to withstand inrush currents, and lower cost, CT is widely used in the field of high-voltage (typically at 10 or 35 kV level) converter like STATCOMs, on which this paper is focused. Because no direct current can pass a CT, any dc component introduced into current loop (by drifting in sensing circuit for example) will be open-looped magnified by dc gain of feedforward pass. Therefore, the system using CT will have a significantly larger dc injection than those using Hall-effect current transducers. Sometimes, even specially designed grid interface transformers will not withstand this large direct current unless the controller gain of the converter is small enough. The most straightforward way to eliminate dc injection is to put a large capacitor between the dc bus and the grid [13], [14]. This capacitor can block the direct current at the expense of consuming certain amount of voltage. However, this kind of method will lead to using large expensive capacitors or bring extra voltage stress on switching devices; therefore, it is economically unsuitable for high-voltage applications. Also, there are methods that use control technique to eliminate dc injection [15]–[17]. These methods usually need an extra circuit or element to get the dc component from the converter output. Sharma [15] uses a transformer connected at the ac terminal of the inverter bridge charging a capacitor through an RL branch to get the dc offset from the inverter output voltage and uses it to compensate direct current. Bowtell and Ahfock [16] use a similar principle but the dc offset sensing circuit is connected at the output filter rather than the ac terminal. Armstrong et al. [17] use an extra dc-link sensor to autocalibrate the drifting of the

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SHI et al.: ELIMINATING DC CURRENT INJECTION IN CURRENT-TRANSFORMER-SENSED STATCOMS

Fig. 1.

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Fig. 2.

Control scheme of each cluster.

Fig. 3.

Equivalent circuit of a CT.

Circuit configuration of a CT-sensed cascaded STATCOM.

output current sensor; all sensors are Hall-effect. Since these methods are designed for low-voltage applications, they are not easy to use for high-voltage converters, for the dc sensing circuit will be much more expensive. Guo et al. [18] proposed a method called virtual capacitor. This method uses the integration of output current building another feedback loop to compensate dc injection; therefore, this method is only valid when the current sensing circuit is perfect. If the sensors drift or they cannot sense dc, this virtual capacitor method is likely to fail. This paper proposes a software method to eliminate the dc injection for CT-sensed STATCOMs. In Section II, the mechanism of dc injection for CT-sensed systems is analyzed. And the value of the dc injection is calculated for four typical current controllers, namely P (proportional) controller, PI (proportional + integral), PR (proportional + resonant) controller, and quasi-PR controller. In Section III, a method called indirect dc feedback (IDCF) is proposed. This method uses the amplitude of line-frequency voltage ripple on the dc capacitor to build an IDCF loop that was used to compensate the dc component of the output current. Because dc capacitor voltage has already been sensed in the system, no extra hardware is needed. After that, the algorithms used to measure the amplitude of dc-side line-frequency voltage ripple are presented, along with discussions on controller design; In Section IV, experimental results on a 100-kvar 25-level cascaded multilevel STATCOM prototype are presented to verify the proposed method. Results show that the proposed method can eliminate dc injection for CT-sensed STATCOM without needing extra hardware.

II. DC INJECTION ANALYSIS A. System Modeling This study deals with a typical kind of high-voltage gridconnected converter, namely, the cascaded multilevel converter (CMC) [19]–[24]. The CMC can achieve high-voltage output by connecting a number of H-bridge converter cells in serial. Each H-bridge uses relatively low-voltage, commercially available semiconductor devices (e.g., 1700-V insulated-gate bipolar transistor). The most popular application for CMC is STATCOM, for separate dc sources are no longer needed. Fig. 1 shows the circuit configuration of a cascaded STATCOM in delta connection. It is often connected to a 6–35 kV grid, where CTs are widely used. Each cluster in Fig. 1 is connected line to line; therefore, it can be controlled separately. The system is treated as three independent single-phase converters, and its control scheme is shown in Fig. 2. The phase-locked loop (PLL) detects the phase angles of three-phase grid voltage. Gvdc controls dc voltages of each cluster individually, generating the active parts of the current references. Then, the active current references are summarized with the reactive current references forming the instantaneous current references that are controlled by Gi . To analyze the CT-sensed system, it is important to get an appropriate model of CT. Based on previous studies [25], [26], a CT can be modeled, as shown in Fig. 3. It consists of a current source as input current, an ideal transformer, a magnetizing

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Fig. 4.

Simplified equivalent circuit of a CT.

Fig. 5.

Current feedback model for the CT-sensed system.

Fig. 6.

Root locus of the current loop.

Fig. 7.

Bode diagram of the current loop.

circuit (Lm , Rm ), a parasitic inductance Lf , and a parasitic capacitance Cp . The model of a CT in Fig. 3 can be seen as a high-pass filter cascading a low-pass filter. Its transfer function can be written as in (1). Equation (1), shown at the bottom of the page, is a thirdorder system that is unnecessarily complex for control system analysis. Consider following facts: 1) the focus of this study is at very low frequency; and 2) high-pass effect caused by Lf and Cp usually exists at frequencies higher than control bandwidth. Therefore, it is reasonable to simplify the model of CT into a high-pass filter shown in Fig. 4. And a simplified transfer function is RL Rm VCT s = · · . (2) HCT (s) = I n Rm + RL s + ωCT Therefore, the system output current control loop can be modeled as in Fig. 5, where Gi (z) is the current controller. z −1 indicates one cycle delay introduced by a digital controller. Note that the current feedback pass containing CT is normalized.

analyzing system dc response, which can be written as Idc (z) =

B. DC Injection Analysis The only difference between Fig. 5 and a conventional gridconnected converter is that it has a high-pass filter in the feedback loop. The root locus of the current loop in Fig. 6 shows that this CT-sensed system still has its stable range. However, as the Bode diagram Fig. 7 shows, this closed-loop system has a very large steady-state error. This large closed-loop gain at low frequencies (shown in Fig. 7) is the reason for the dc injection. Because no dc can pass through the feedback, any small amount of dc error, either introduced by drifting in sensing circuit or by truncation error during digitizing, will be open-loop amplified by the gain of forward pass. The value of the dc injection can be found by

HCT (s) =

VCT = I

Lf Cp Rm

·

s3

 + Cp +

Lf Cp Lm

+

Gi (z) · z −1 · G(z) · IBias (z) 1 + Gi (z) · z −1 · GH(z)

(3)

where IBias (z) = IBias /(1−z −1 ); and IBias stands for any dc component introduced into input. G(z) is the Z-domain transfer function of plant 1/(L·s+R), while H(z) is the transfer function of CT. At the steady state, for the P controller Gi (z) = kp , the dc injection is calculated as Idc = lim (1 − z −1 ) · z →1

·

Gi (z) · z −1 · G(z) 1 + Gi (z) · z −1 · GH(z)

kp IBias · IBias . = 1 − z −1 R

(4)

The same calculation can be done for PI, PR controller, and quasi-PR controller; the results are listed in Table I.

Lf Rm RL

s/n   · s2 + R1L +

Lf Lm RL

+

1 Lm



·s+

1 Lm

(1)

SHI et al.: ELIMINATING DC CURRENT INJECTION IN CURRENT-TRANSFORMER-SENSED STATCOMS

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TABLE I DC INJECTION ANALYSIS FOR DIFFERENT CONTROLLERS

Fig. 9.

Control diagram of the proposed dc injection elimination method.

Assuming US (t) = VS cos(ω0 t), iS (t) = Iac cos(ω0 t + ϕi ) + Idc . (6) And because this investigation is about line frequency and dc, only the fundamental component of switching function is considered Fig. 8.

Simplified model of one cluster of the cascaded STATCOM.

S(t) = M cos(ω0 t + ϕM ).

The dc injection of four most commonly used controllers for grid-connected converters is listed. The dc injection is calculated under the stationary frame. For the synchronous frame, same results can be achieved by changing PI to PR and PR to quasi-PR [27]. From Table I, it can be concluded that for the CT-sensed system, the PI controller should never be used in the stationary frame, for the direct current will be continuously added up by the integration item. For the other three controllers, the dc component of the output current is proportional to controller gain. Designers have to compromise between dc injection and system performance. III. DC INJECTION ELIMINATION The analysis in Section II can be summarized as follows: high-pass effect of CT prevents the dc component of the output current from being sensed; and any dc input will be open-loop amplified by controller gain. Therefore, if the direct current can be reintroduced into a feedback loop, the dc component will be eliminated. Key to this idea is finding another physical quantity in connection with the direct current. In this research, the linefrequency voltage ripple at dc side is used for measuring the dc injection indirectly. The following investigations will show that this is a reasonable choice because the amplitude of the linefrequency ripple is the linear amplification of the dc injection. A. Relationship Between DC Injection and Line-Frequency Voltage Ripple A simplified one-cluster model of a cascaded STATCOM is shown in Fig. 8, where Ceq is the equivalent dc-side capacitor, iS (t) is the grid-side current, iC (t) is the dc-side current that flows into Ceq , and S(t) is the switching function. From a previous study [28], it is known that iC (t) = iS (t) · S(t).

(5)

(7)

In (7), M is the modulation ratio, ω0 is the angular frequency of the grid, and ϕi and ϕM are the phase angles of output current and fundamental component of switching function referring to the grid voltage phase. Therefore iC (t) = iS (t) · S(t) = [Iac cos(ω0 t + ϕi ) + Idc ] · [M cos(ω0 t + ϕM )] =

Iac M [cos(ϕi − ϕM ) + cos(2ω0 t + ϕi + ϕM )] 2 (8) + Idc M cos(ω0 t + ϕM ).

Line-frequency dc voltage ripple is caused by the linefrequency component of iC Idc Idc cos(ω0 t + ϕM ) = sin(ω0 t + ϕM ). jω0 Ceq ω0 Ceq (9) Because ω0 Ceq is usually smaller than one, (9) indicates that the amplitude of line-frequency ripple is the linear amplification of the dc injection. v1 (t) =

B. Proposed DC Injection Elimination Method The proposed dc injection elimination method called IDCF is shown in Fig. 9. An indirect feedback loop from dc voltage Udc to current reference is added on the control loop. Ginj is the controller that is used to eliminate dc component of output current by controlling the amplitude of line-frequency dc voltage ripple to zero. Blocks in the dashed lines are used to extract the amplitude of line-frequency ripple that reflects the dc component of the output current indirectly. First, Udc is spanned into a set of “virtual three-phase” signals, as shown in Fig. 10. Park’s transformation is then performed for these “virtual threephase” signals using the rotation angle ω0 t from PLL. The q-axis value of Park’s transformation is used after passing through a frequency-adaptive mean average filter (MAF) as the input of Ginj .

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 8, AUGUST 2013

Fig. 10.

Fig. 11.

Bode diagram of the MAF filter.

Fig. 12.

Equivalent control diagram for IDCF.

Scheme of virtual three phases.

The job of the line-frequency ripple extraction algorithm is to extract the line-frequency ripple from dc-side voltage (equivalently, because there are n separate dc buses in a cascaded STATCOM. The equivalent dc-side voltage is the sum of Hbridge dc voltages from one cluster). When there is dc component at the output terminal, the dc-side voltage is a combination of dc component, double line-frequency component, and other frequency components including line-frequency component, see (10). Therefore, a bandwidth pass filter that passes only linefrequency component is needed for the algorithm Udc = Vdc + V2 cos(2ω0 t + ϕ2 ) + v1 (t) +

∞ 

Vn cos(nω0 t + ϕn ).

(10) GM AF =

n =3

In (10), Vdc and V2 usually are much larger than the amplitude of v1 (t). It is not easy to design a bandwidth filter to extract only the line-frequency component without significant attenuation. This is the reason why Park’s transformation is used here. Because Park’s transformation serves as a frequency band shifter that moves the frequency band of original signal toward dc by one line frequency ω0 , expressed as     X(ω − ω0 ) Xd (ω) (11) = π Xq (ω) −X(ω − ω0 ) · e−j 2 where the original signal is X(ω). Therefore, the q-axis value of Udc after Park’s transformation is Idc Uq = −Vdc sin(ω0 t) − V2 sin(2ω0 t + ϕ2 ) + cos(ϕM ) ω0 Ceq −

∞ 

Vn sin((n − 1)ω0 t + ϕn ).

teger multiples of the line frequency ω0 . They are separate in the frequency domain and change with ω0 . Therefore, the target filter should be frequency-adaptive, and should have very large attenuation at nω 0 (n ∈ {1, ∞}}, where n is an integer). In this study, a frequency-adaptive MAF is used. The window width of the MAF is adjusting to the line period in real time. The z-domain transfer function for the MAF is

(12)

(13)

where N is the window width that is equal to the number of samples in one line period. From (13), it can be seen that GM AF has N equally distributed zeros at Z-domain unit cycle, and one pole at z = 1. This will cause GM AF to have very large attenuation at these zeros except at dc, also shown by Bode diagram in Fig. 11, where fw is the window frequency equal to the line frequency. This feature lets MAF serve as an ideal lowpass filter if fw changes with the line frequency synchronously. Therefore, the value used for eliminating dc injection is shown as Uq 1 = K · Idc , K = 1/ω0 Ceq .

(14)

The equivalent control loop for dc injection control is shown in Fig. 12, where Ginner is the closed-loop transfer function for current loop (see Figs. 6 and 7), given by

n =3

For STATCOM applications, the converter phase angle is almost the same with the phase angle of the grid voltage. Therefore, cos(ϕM ) ≈ 1, the dc component of Uq is the amplitude of line-frequency voltage ripple and also the linear amplification of the output direct current. A low-pass filter is needed to filter out the dc component of Uq . The ideal filter for this application should have little attenuation at dc while removing any other frequency components. From (12), it can be seen that all unwanted frequencies are in-

1 1 − z −N N 1 − z −1

Ginner =

Gi z −1 G 1 + Gi z −1 GH

(15)

For the P controller (16), as shown at the bottom of the next page. It is a second-order system with complicated parameters. Because the focus of this analysis is at very low frequency range , Ginner can be approximated as a large gain, given by (17) Ginner ≈ kp /R.

(17)

SHI et al.: ELIMINATING DC CURRENT INJECTION IN CURRENT-TRANSFORMER-SENSED STATCOMS

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TABLE II PARAMETERS OF THE CASCADED MULTILEVEL PROTOTYPE

Fig. 13. Disturbance to dc injection Bode diagram with indirect direct current feedback.

Equation (17) is right for the P controller, PR controller, and quasi-resonant controller. And the PI controller should not be used for CT-sensed system. Based on previous discussion on MAF, it can be approximated that GM AF ≈ 1.

(18)

Because the ability of rejecting IBias is the main concern, consider IBias = IDC 1+ ≈

Ginner (z)GM AF (z) Ginner (z)Ginj (z)GM AF (z)

1 ω0 Ceq

1+

kp /R kp 1 ω 0 C e q R Ginj (z)

≈

ω0 Ceq . Ginj (z)

(19)

Equation (19) is the transfer function that indicates the relationship between dc error and dc injection. It should be small enough. A way to design Ginj is using the PI controller to achieve large dc gain and letting the closed-loop system in Fig. 12 cover the stopband of CT, like in Fig. 13. However, in practice, R is the equivalent resistance stands from converter loss adding the serial resistance in the output filter, which is difficult to be accurate. Therefore, it is better to make the gain of Ginj smaller. IV. EXPERIMENTAL VERIFICATION A 25-level cascaded multilevel STATCOM prototype is used in this research to verify the proposed method. This is a downscaled laboratory prototype designed to verify algorithms for Mvar-level STATCOM. The circuit configuration is as in Fig. 1, and the parameters are listed in Table II. Fig. 14 shows a photograph of the prototype. This prototype consists of one control box and 36 full digital controlled H-bridge cells. Each H-bridge cell is controlled by a DSP and complex programmable logic device. 72 phase-

R

Ginner = 1+

L

kp L e −ω C T T

e −R T / L

−ω C T ω C T L −R

+

kp L

Fig. 14.

Experimental prototype of the cascaded STATCOM.

shift carrier PWM signals are generated by field-programmable gate array of the control box and transmitted to each H-bridge cell through optical fibers. The 36 dc voltages of each cell are transmitted through a two-layer communication network to the DSPs of control box. This prototype has the same architecture as real Mvar-level STATCOM product. After verifying the algorithm, the control box can be directly used on real Mvar-level STATCOMs. Figs. 15 and 16 are experimental results without using the proposed IDCF. In Fig. 15, the output current of CMC is controlled under a PI controller. It can be seen that the dc component of output current kept ramping with time. Note that the linefrequency component in dc-side voltage was also increasing with the ramping of the direct current. This phenomenon can be

z −1 −

k p e −ω C T T L

z −2

 − e−ω C T T − e−R T /L · z −1 + e−ω C T T −R T /L · z −2

(16)

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Fig. 15. Experimental result of the output current without the proposed IDCF, under PI control (current ramping).

Fig. 16. Experimental result of the output current without the IDCF, under P control (707 mA/14% direct current).

seen as a proof of the previous analysis that line-frequency ripple is in connection with the dc injection. In Fig. 16, the output current of CMC is controlled under a P controller. Though the current had not been ramping, there was still 707 mA direct current shown in the oscilloscope. Also, there were line-frequency ripples in dc-side voltage too. Figs. 17 and 18 are experimental results showing the effect of the proposed IDCF. To test the effect of this dc elimination method, this experiment is performed using PI controller, for it is the worst case for the CT-sensed system. In Fig. 17, at time zero, IDCF was not used, and the output current kept ramping (ramping to 3.34 A after 2 s), until time 2 s, when IDCF was switched ON, and the dc component of the output current was gradually eliminated. Fig. 18 is the steady-state current under the PI control with IDCF. It can be seen that with IDCF, the dc component of the output current is 4.86 mA even under PI control. Because the direct current scope (Tektronix A622) used in this experiment has a manual bias adjustment error about 5 mA, it can be concluded that the dc injection

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 8, AUGUST 2013

Fig. 17. Experimental result of the output current under PI control; IDCF was started after 2 s.

Fig. 18. Experimental result of the output current with IDCF, under PI control (4.86 mA/0.1% direct current).

has been eliminated. Meanwhile, it can also be seen in Fig. 18 that the line-frequency ripple was also eliminated. Therefore, the proposed IDCF method can eliminate the dc injection for STATCOMs. V. CONCLUSION This study focuses on the dc injection problem for CT-sensed STATCOM. By introducing the CT model into a cascaded STATCOM model, and analyzing the magnification of the direct current component, this study found using CTs as the current feedback device will deteriorate the dc injection problem. Expressions of dc injection for different controllers were derived. Then, a dc injection elimination method called IDCF is proposed to build an extra feedback loop for the dc component of the output current. This method can eliminate the dc component of the output current even when the direct current cannot be sensed. Experiments were performed on a 25-level cascaded multilevel STATCOM prototype. The results are consistent with the analysis that CT sensing can cause large dc injection. Also, the results

SHI et al.: ELIMINATING DC CURRENT INJECTION IN CURRENT-TRANSFORMER-SENSED STATCOMS

show that the proposed method can eliminate dc injection for STATCOM. Since this method is not based on any feature that is particular to cascaded STATCOM, the proposed method can be applied to other types of STATCOMs and APFs as well. This idea of using dc-side ripple to measure or control ac-side bias is possible to be transferred to other types of grid-connected converters too.

REFERENCES [1] K. Masoud and G. Ledwich, “Grid connection without mains frequency transformers,” J. Electr. Electron. Eng., vol. 19, no. 1–2, pp. 31–36, Jun. 1999. [2] A. Ahfock and A. J. Hewitt, “DC magnetisation of transformers,” IEE Proc. Electr. Power Appl., vol. 153, no. 4, pp. 601–607, Jul. 2006. [3] S. Bradley and J. Crabtree, “Effects of DC from embedded generation on residual current devices and single-phase metering,” Eng. Australia Technol. Rep., Rep. no. WS4-P11, 2005. [4] L. Gertmar, P. Karlsson, and O. Samuelsson, “On DC injection to AC grids from distributed generation,” in Proc. Eur. Conf. Power Electron. Appl., 2005, pp. 1–10. [5] IEEE Standard for Interconnecting Distributed Resources With Electric Power Systems, IEEE Standard 1547–2003 2003. [6] IEEE Guide for the Functional Specification of Transmission Static Var Compensators, IEEE Standard 1031–2011 2011. [7] B. Yang, W. Li, Y. Gu, W. Cui, and X. He, “Improved transformerless inverter with common-mode leakage current elimination for a photovoltaic grid-connected power system,” IEEE Trans. Power Electron., vol. 27, no. 2, pp. 752–762, Feb. 2012. [8] H. Xiao and S. Xie, “Transformerless split-inductor neutral point clamped three-level PV grid-connected inverter,” IEEE Trans. Power Electron., vol. 27, no. 4, pp. 1799–1808, Apr. 2012. [9] K. Sano and M. Takasaki, “A transformerless D-STATCOM based on a multivoltage cascade converter requiring no DC sources,” IEEE Trans. Power Electron., vol. 27, no. 6, pp. 2783–2795, Jun. 2012. [10] H. P. Mohammadi and M. T. Bina, “A transformerless medium-voltage STATCOM topology based on extended modular multilevel converters,” IEEE Trans. Power Electron., vol. 26, no. 5, pp. 1534–1545, May 2011. [11] M. K. Sahu and G. Poddar, “Transformerless hybrid topology for mediumvoltage reactive-power compensation,” IEEE Trans. Power Electron., vol. 26, no. 5, pp. 1469–1479, May 2011. [12] H. Akagi, H. Fujita, S. Yonetani, and Y. Kondo, “A 6.6-kV transformerless STATCOM based on a five-level diode-clamped PWM converter: System design and experimentation of a 200-V 10-kVA laboratory model,” IEEE Trans. Ind. Appl., vol. 44, no. 2, pp. 672–680, Mar.–Apr. 2008. [13] R. Gonzalez, E. Gubia, J. Lopez, and L. Marroyo, “Transformerless singlephase multilevel-based photovoltaic inverter,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2694–2702, Jul. 2008. [14] W. M. Blewitt, D. J. Atkinson, J. Kelly, and R. A. Lakin, “Approach to low-cost prevention of DC injection in transformerless grid connected inverters,” IET Power Electron., vol. 3, no. 1, pp. 111–119, Jan. 2010. [15] R. Sharma, “Removal of DC offset current from transformerless PV inverters connected to utility,” in Proc. 40th Int. Universities Power Eng. Conf., 2005, pp. 1230–1234. [16] L. Bowtell and A. Ahfock, “Direct current offset controller for transformerless single-phase photovoltaic grid-connected inverters,” IET Renew. Power Gener., vol. 4, no. 5, pp. 428–437, Sep. 2010. [17] M. Armstrong, D. J. Atkinson, C. M. Johnson, and T. D. Abeyasekera, “Auto-calibrating DC link current sensing technique for transformerless, grid connected, H-bridge inverter systems,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1385–1393, Sep. 2006. [18] X. Guo, W. Wu, H. Gu, and G. San, “DC injection control for gridconnected inverters based on virtual capacitor concept,” in Proc. Int. Conf. Electr. Mach. Syst., 2008, pp. 2327–2330. [19] H. Akagi, S. Inoue, and T. Yoshii, “Control and performance of a transformerless cascade PWM STATCOM with star configuration,” IEEE Trans. Ind. Appl., vol. 43, no. 4, pp. 1041–1049, Jul.–Aug. 2007. [20] F. Z. Peng, J. S. Lai, J. W. McKeever, and J. Vancoevering, “A multilevel voltage-source inverter with separate DC sources for static VAr generation,” IEEE Trans. Ind. Appl., vol. 32, no. 5, pp. 1130–1138, Sep.–Oct. 1996.

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[21] Z. Liu, B. Liu, S. Duan, and Y. Kang, “A novel DC capacitor voltage balance control method for cascade multilevel STATCOM,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 14–27, Jan. 2012. [22] S. Qiang and L. Wenhua, “Control of a cascade STATCOM with star configuration under unbalanced conditions,” IEEE Trans. Power Electron., vol. 24, no. 1, pp. 45–58, Jan. 2009. [23] X. She, A. Q. Huang, T. Zhao, and G. Wang, “Coupling effect reduction of a voltage-balancing controller in single-phase cascaded multilevel converters,” IEEE Trans. Power Electron., vol. 27, no. 8, pp. 3530–3543, Aug. 2012. [24] L. Maharjan, T. Yamagishi, and H. Akagi, “Active-power control of individual converter cells for a battery energy storage system based on a multilevel cascade PWM converter,” IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1099–1107, Mar. 2012. [25] N. Kondrath and M. K. Kazimierczuk, “Bandwidth of current transformers,” IEEE Trans. Instrum. Meas., vol. 58, no. 6, pp. 2008–2016, Jun. 2009. [26] A. Cataliotti, D. Di Cara, P. A. Di Franco, A. E. Emanuel, and S. Nuccio, “Frequency response of measurement current transformers,” in Proc. IEEE Instrum. Meas. Technol. Conf., May 12–15, 2008, pp. 1254–1258. [27] D. N. Zmood and D. G. Holmes, “Stationary frame current regulation of PWM inverters with zero steady-state error,” IEEE Trans. Power Electron., vol. 18, no. 3, pp. 814–822, May 2003. [28] S. Sirisukprasert, A. Q. Huang, and J. S. Lai, “Modeling, analysis and control of cascaded-multilevel converter-based STATCOM,” in Proc. Power Eng. Soc. Gen. Meet., 2003, vol. 4, pp. 2561–2568.

Yanjun Shi (S’11) was born in Luoyang, China, in 1985. He received the B.E. degree in electrical and electronic engineering and the Ph.D. degree in power electronics from the Huazhong University of Science and Technology, Wuhan, China, in 2007 and 2012, respectively. His research interests include the application of power electronics in power system, LED driver, and renewable energy power conversion.

Bangyin Liu (M’10) received the B.S., M.S., and Ph.D. degrees in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 2001, 2004, and 2008, respectively. He is currently a faculty member in the College of Electrical and Electronics Engineering, Huazhong University of Science and Technology. His current research interests include renewable energy applications, soft-switching converters, and power electronics applied to power system.

Shanxu Duan received the B.Eng., M.Eng., and Ph.D. degrees in electrical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 1991, 1994, and 1999, respectively. Since 1991, he has been a faculty member in the College of Electrical and Electronics Engineering, Huazhong University of Science and Technology, where he is currently a Professor. His main research interests include stabilization, nonlinear control with application to power electronic circuits and systems, fully digitalized control techniques for power electronics apparatus and systems, and optimal control theory and corresponding application techniques for high-frequency pulsewidth-modulation power converters. Dr. Duan is a Senior Member of the Chinese Society of Electrical Engineering and a Council Member of the Chinese Power Electronics Society. He was chosen as one of the New Century Excellent Talents by the Ministry of Education of China, in 2007, and received the honor of “Delta Scholar” in 2009.