Parameter Design of a Two-Current-Loop Controller Used in a Grid ...

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 11, NOVEMBER 2009

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Parameter Design of a Two-Current-Loop Controller Used in a Grid-Connected Inverter System With LCL Filter Fei Liu, Yan Zhou, Shanxu Duan, Jinjun Yin, Bangyin Liu, and Fangrui Liu

Abstract—LCL filters offer a better choice of attenuating switching frequency harmonics. However, in a grid-connected system, an LCL filter may cause resonance which is a disaster for the system’s stability. In order to solve the problem, a two-currentloop control strategy, which includes grid-current outer loop and filter-capacitor-current inner loop, is adopted here. The implementation of this strategy is easy, but the tuning procedure is complex since the outer and inner controllers cannot cooperate well if the parameters of the controllers are not suitable. There is no literature which mentions a method to help give out accurate parameters of the controller. The difficulty of designing the controller is that only two feedbacks cannot provide complete information of a three-order LCL filter. A specific method is proposed in this paper to design the controller. The advantage of this method is to provide a way to maximize the utilization of the two feedbacks to get good system performance through parameter determination. The practicability of the method is tested by using bode diagram, and the antidistortion ability of the system is analyzed. Finally, experimental results verify the availability and correctness of the proposed method. Index Terms—Grid connected, LCL filter, renewable energy generation, two-current-loop controller.

I. I NTRODUCTION

D

UE TO the features of better attenuation for switching frequency harmonics and lower cost, LCL filters exhibit much popularity for grid-connected power electronic systems. The inductance required to achieve the same performance of damping the switching harmonics is smaller compared with L or LC filters. The merits of LCL filter would be more eminent for high-power converters. In spite of such advantages, LCL filter has its own drawbacks. More attention has been paid to the possible instability of the system caused by the zero impedance at the LCL filter resonance frequency. There are two main methods to damp the resonance: passive damping and active damping. Manuscript received July 8, 2008; revised April 10, 2009. First published May 5, 2009; current version published October 9, 2009. This work was supported in part by the National Basic Research Program of China under Grant 2009CB219701. F. Liu was with Huazhong University of Science and Technology, Wuhan 430074, China. He is now with the Department of Electrical Engineering, Wuhan University, Wuhan 430074, China (e-mail: [email protected]). Y. Zhou, S. Duan, J. Yin, B. Liu, and F. Liu are with the Department of Applied Power Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; fangruihust@ 163.com). 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.2009.2021175

The passive damping is to add a passive resistor in the LCL filter [1], [2]. Due to the simple implementation, it is usually employed for industry application. However, the added resistor will produce extra loss. Active damping methods are proposed to ensure the stability of the system without power loss. One kind of control strategy is to control the inverter-side-inductor current. In [3] and [4], only the inverter-side-inductor current is used to damp the resonance by using two-order or four-order digital filters. The number of sensors is the least. However, the final control is complicated. In [5] and [6], additional signals are used while they are all estimated, so the number of sensors is also the least. The drawbacks of this method are that the estimated signals are calculated with assumptions and the robustness of the system is weak because it highly depends on the filter parameters. For example, in [5], the filter-capacitor voltage is calculated with the assumption that the filter-capacitor current is zero. Moreover, filter-capacitor current or voltage can be measured to damp the resonance [7], [8]. It is all known that to control the inverter-side-inductor current cannot reject the grid distortion well unless the grid voltage feedforward control is adopted. Another strategy of active damping is to control the grid current directly. Single-loop control is used in [10]; although the system is stable, the grid-current distortion is visible from the experimental results. In references [11]–[13], one more feedback is used to ensure the stability of the system. Moreover, there are methods that use three feedbacks of the LCL filter [14]–[16]. The control methods using three variables show the optimal performance, and the robustness of the system is good. However, the cost of such a system is obviously increased due to the numerous sensors. An interesting method is proposed in [9]: The LCL filter is simplified from a three-order to a one-order system by splitting the filter-capacitor current into two parts. The filter-capacitor current or inverter-side-inductor current is also needed in the method. For a three-order filter, in order to get the desired performance, the three poles of the filter should be assigned to a suitable position. Methods in [14]–[16] get all the information of the filter, so the three poles of the filter can be assigned as wished. Methods with two feedback variables can also assign the poles to some extent and obtain good performance with fewer sensors. In [11], the filter-capacitor current is measured to form the inner control loop, and the grid current is chosen as the outer loop variable. The difficulty of this method is produced during the tuning procedure. In [11], the choice of

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Fig. 1. Topology of the three-phase system with LCL filter. TABLE I DETAILS OF THE HARDWARE SETUP

Fig. 2.

Block of the single-phase circuit.

B. Control Strategy

the controller parameters is discussed, but no specific method is given to calculate the precise parameters. In this paper, a specific design method for the two-currentloop controller is firstly proposed to determine the controller parameters which can make the tuning procedure easier. Pole placement and pole–zero cancellation methods, which are rather conventional, are used in this method. However, the proposed method provides a way to get the parameters of the twocurrent-loop controller which can maximize the use of the two feedbacks and get good control performance. Practicality of this design method is discussed, and experimental results are also provided to verify the feasibility and correctness of the design method. II. M ATHEMATICAL M ODEL AND C ONTROL S TRATEGY A. Mathematical Model of the System Fig. 1 shows the main circuit topology, where R1 and R2 are the resistors associated with inverter-side and grid-side inductors, respectively. The system parameters are provided in Table I. The three-phase circuit can be transformed into two single decoupled circuits by abc to αβ transformation. The two single circuits can be represented as 1 1 u1k − (i1k R1 + uck ) L1 L1 ˙ = 1 uck − 1 usk − 1 i2k R2 i2k L2 L2 L2 1 1 u˙ck = i1k − i2k C C ˙ = i1k

(1)

Adopting the control strategy in [11], the filter-capacitor current is used as the inner loop variable, and grid current is measured as the outer loop variable. The inner regulator is a proportional controller, and the outer regulator is a proportional resonant (PR) controller. In order to simplify the analysis, the PR controller is firstly substituted by a PI controller. Fig. 3 shows the control block of the system which can be changed into the form as shown in Fig. 4. It is shown that the feedbacks are the grid current, capacitor current, and integral of the grid current multiplied by Kc Kp , Kc , and Ki Kc , respectively. Formerly, the system is a three-order one as the LCL filter is three-order, but the adoption of the integral of the grid current increases the system one more order. Consequently, the three feedbacks cannot assign the four poles of the system completely. Therefore, it is difficult to get any control performance as wished as illustrated in [14]–[16]. This situation can be called partial state feedback. However, it is also possible to get a suitable performance with partial state feedback. How to get this suitable performance depends on the choice of the value of Kc Kp , Kc , and Ki Kc . III. C ONTROLLER D ESIGN A. One Criterion for the Controller The Routh’s stability criterion is used for giving out the scope of the three parameters of the controller. The principle of the Routh’s criterion is presented in the Appendix. From Figs. 3 or 4, the open-loop transfer function and closed-loop transfer function of the system are obtained as Gd1 (s) =

i2 A0 s + A1 = i∗2 − i2 B0 s4 + B1 s3 + B2 s2 + B3 s

Gd2 (s) =

i2 A0 s + A1 = ∗ 4 3 i2 B0 s + B1 s + B2 s2 + (B3 + A0 )s + A1

(2)

(3) where i1k is the inverter-side current, i2k is the grid-connected current, u1k is the inverter output voltage, uck is the filtercapacitor voltage, usk is the grid voltage, and k = α, β. The block of one single circuit can be seen in Fig. 2.

where A0 = Kp Kc , A1 = Ki Kc , B0 = L1 L2 C2 , B1 = R1 L2 C2 + R2 L1 C2 + L2 C2 Kc , B2 = L1 + L2 + R1 R2 C2 + R2 C2 Kc , and B3 = R1 + R2 .

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Fig. 3.

Control block of the system.

Fig. 4.

Partial state feedback.

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We can easily obtain the characteristic equation as Dd2 (s) = s4 +

B1 3 B2 2 (B3 + A0 ) A1 s + s + s+ . B0 B0 B0 B0

(4)

According to the Routh’s stability criterion, for a four-order system, the following equation must be satisfied to ensure the stability of the system: ⎧ B0 > 0 ⎪ ⎪ ⎪ B1 > 0 ⎪ ⎪ ⎪ ⎪ ⎨ B2 > 0 B3 + A0 > 0 (5) ⎪ ⎪ > 0 A ⎪ 1 ⎪ ⎪ ⎪ ⎪ ⎩ B1 B2 − B0 (B3 + A0 ) > 0 2 B1 B2 − B0 (B3 + A0 ) > B1 A1 /(B3 + A0 ). Since B0 , B1 , B2 , B3 + A0 , A1 , and B12 A1 /(B3 + A0 ) are all greater than zero, (5) is equivalent to B1 B2 − B0 (B3 + A0 ) > B12 A1 /(B3 + A0 ).

(6)

Only by choosing the controller parameters that fulfill (6) can the system be stable. Since (6) cannot provide accurate value of the parameters, it is used to verify the stability of the system after the controller parameters are chosen. B. Controller-Parameter Design As the poles of the system cannot be assigned as wished, the location of the poles should be firstly observed. Here, root locus is used to help us find out the track of the poles. Fig. 5 shows the root locus with variation of Kp . When describing the root locus, Kc and Ki are fixed. Fig. 5 shows the general location of the system poles. It can be seen that pole 1 and pole 2 are conjugated poles and pole 3 and pole 4 are both near imaginary axis. When Kp grows bigger, pole 4 escapes from the imaginary axis, while pole 3 remains near the imaginary axis. Moreover, it can be noticed that the system contains one zero. In such a situation, an ideal method is to assign pole 3 and the zero to the same location to weaken their influence, to put pole 4 far away from the imaginary axis to ensure pole 1 and pole 2 as the dominated poles.

Fig. 5. Root locus of the system with variation of Kp .

First, pole–zero cancellation is used for pole 3 and the zero; consequently, the following equation should be established: Y3 − X1 (Y2 − X1 (Y1 − X1 )) = 0

(7)

where X0 =

A0 A1 B1 B2 B3 , X1 = , Y1 = , Y2 = , Y3 = . B0 A0 B0 B0 B0

After the pole–zero cancellation, the open-loop transfer function and closed-loop transfer function are obtained as Gd3 (s) =

X0 s3 + (Y1 − X1 )s2 + (Y2 − X1 (Y1 − X1 )) s

Gd4 (s) =

X0 . s3 + (Y1 − X1 )s2 + (Y2 − X1 (Y1 − X1 )) s + X0

(8)

(9) Assume that the desired damping ratio and natural frequency are ζr and ωr , respectively, and −mζr ωr represents the position of a nondominant pole. The characteristic equation with desired parameters is derived as   (10) Dr (s) = s2 + 2ζr ωr s + ωr2 (s + mζr ωr ).

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Comparing with (9), three equations can be obtained ⎧ ⎨ Y1 − X1 = (m + 2)ζr ω r  Y2 − X1 (Y1 − X1 ) = 2mζr2 + 1 ωr2 ⎩ Y3 − X1 (Y2 − X1 (Y1 − X1 )) + X0 = mζr ωr3 .

(11)

Combining (7) and (11), there are four equations. Here, three variables Kp , Ki , and Kc cannot fulfill four independent equations at the same time. One solution is to set one of ζr , ωr , and m as a free parameter to help fulfill the four equations. If ωr is set as a free parameter, it may fall in the vicinity of the filter resonant frequency when ζr and m are chosen unsuitably. However, from (7) and (11), the following equation can be derived to show the relationship among ζr , ωr , and m:    2 (m + 2)ζr B3 − 2mζr2 + 1 wr B2 + 2mζr2 + 1 ωr3 B0 = 0 (12) where B0 and B3 are constant and B2 can be approximated to be L1 + L2 , since L1 + L2 is three orders of magnitude higher than R2 C2 . Therefore, B2 is also treated as a constant here. m is firstly set to be 5 to make pole 4 a nondominated pole and poles 1 and 2 dominated ones. When choosing m = 5, the relationship between ζr and ωr can be plotted as in Fig. 6. It is seen that when ζr = 0.5, ωr = 4754 is a suitable one. Other groups of ζr and ωr can also be chosen according to one’s own requirement. As a result, ζr and m are treated as inputs of equations composed by (7) and (11), and Kp , Ki , Kc , and m are outputs of the equations. However, the selection of ζr and m is not arbitrary and should be referred to (12). Solving the equations, one can get one group of parameters as Kp = 0.2635

Ki = 27.12

Kc = 79.89

ωr = 4256

where ωr = 4256 rad/s is close to the value of 4754 obtained from Fig. 6. The difference is caused by the approximation of B2 in (12). Fig. 7 shows the position of the poles and zero in z-domain. The location of four poles and one zero in z-domain is that s1,2 = 0.767 ± j0.28, s4 = 0.363, and z0 , s3 = 0.99. The poles and zero are just in the desired position. Finally, the calculated parameters are substituted in (6). It is seen that B1 B2 − B0 (B3 + A0 ) = 1.767 × 10−7 and B12 A1 /(B3 + A0 ) = 2.511 × 10−8 , so the calculated parameters can satisfy (6).

Fig. 6. Relationship of damping ratio and natural frequency when m = 5. (a) Complete view. (b) Enlarged view.

IV. P RACTICABILITY OF THE D ESIGN M ETHOD After the parameters of the two-current-loop controller are chosen, the bode diagram of the open-loop system can be plotted as in Fig. 8 from which one can see that the phase margin is 53.8◦ and the gain margin is 13.9 dB. The phase margin and gain margin illustrate the stability of the system. Furthermore, since, in experiments, the parameters of the controller cannot be exactly Kp = 0.2635, Ki = 27.12, and Kc = 79.89 and the parameters of the LCL filter may not be precise, it is necessary to consider the change of system performance relating to the change of the parameters of the controller and LCL filter.

Fig. 7.

Pole–zero placement of the closed-loop system with PI regulator.

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V. H ARMONIC I MPEDANCE In this section, the influence of grid harmonic distortion is considered. Whether the controller can mitigate the current distortion under distorted supply can be investigated by harmonic impedance which is defined as the ratio of the grid voltage and the grid current. The harmonic impedance of this system is shown as zin =

Fig. 8.

Bode diagram of the open-loop system with the chosen parameters.

Us B0 s4 + B1 s3 + B2 s2 + (B3 + A0 )s + A1 . = I2 L1 Cs3 + (R1 C + Kc )s2 + s (13)

From the definition of harmonic impedance, when the harmonic impedance increases, the antidistortion ability grows. The bode diagram of the harmonic impedance is plotted as in Fig. 10. Apparently, the system is capable of rejecting lowfrequency harmonic distortion which is existed in grid voltage. The harmonic impedance around the resonant frequency is relatively low, but the resonant frequency is far beyond the grid voltage distortion range.

A. Variation of the Controller Parameters When Kp is increased by 50% or decreased by 50%, Fig. 9(a) shows the bode diagram of the open-loop system. As the phase margin is the only reliable test for stability through the bode diagram, the phase margin, instead of the gain margin, is considered in the following. From Fig. 9(a), the phase margin changes from 42.3◦ to 66.6◦ . The system is far from instability, and the change of bode diagram of the system is slight. Likewise, when Ki is increased by 50% or decreased by 50%, the phase margin changes from 52.6◦ to 54.8◦ as shown in Fig. 9(b). When Kc is increased by 50% or decreased by 50%, the phase margin changes from 41.3◦ to 78.8◦ as shown in Fig. 9(c). Therefore, the system can remain good performance, although the parameters of the controller change greatly. The reason is that, although pole 3 and the zero in Fig. 5 cannot be cancelled completely, their position is also near and they form one pair of dipole which will decrease their influence. B. Variation of the Filter Parameters In this section, we can study the influence on the system when the LCL filter parameters change. Fig. 9(d)–(f) shows the change of the bode diagram of the open-loop system when L1 , L2 , and C change ±50%, respectively. The phase margin changes from 34.7◦ to 66.6◦ when L1 changes, from 46.2◦ to 67.7◦ when L2 changes, and from 48.5◦ to 66◦ when C changes. Therefore, the same conclusion can be derived as in Section IV-A. Such a result manifests that the design method is practical.

I2∗

VI. A DOPTION OF PR C ONTROLLER Since the PI regulator under αβ coordinate cannot track the reference command without error, a PR regulator is adopted here [18]–[20]. The transfer function of the PR regulator is shown as GPR (s) = Kp +

Kr s s2 + ω02

(14)

where ω0 stands for the fundamental frequency. In order to investigate the characteristic of the PR controller, the bode diagram of the PI and PR regulators is shown in Fig. 11 in which Kp ’s of the two regulators are the same and Ki = Kr . From Fig. 11, it can be seen that comparing with the PI regulator, the PR regulator has big magnitude at the fundamental frequency, which ensures to track without static error and is nearly the same with the PI regulator after the fundamental frequency. Because of the similarity of PI and PR regulators, it is reasonable to use the same method to design the parameters of Kp , Kr , and Kc . The open-loop and closed-loop transfer functions of system with PR regulator are shown as (15) and (16) at the bottom of the page. The root locus of the system with PR regulator is plotted as in Fig. 12 when Kp is the variable and Kr and Kc are constant. Fig. 12(b) shows partial enlarged view of the root locus. From Fig. 12, we can know that the adoption of PR regulator gives the system two more poles and one more zero. Due to the similarity of PI and PR, the two regulators with the same parameters

I2 A0 s2 + Kr Kc s + A0 ω02 = 5 4 − I2 B0 s + B1 s + (B2 + B0 ω02 ) s3 + (B3 + B1 ω02 ) s2 + B2 ω02 s + B3 ω02 I2 A0 s2 + Kr Kc s + A0 ω02 = ∗ 2 5 4 3 I2 B0 s + B1 s + (B2 + B0 ω0 ) s + (A0 + B3 + B1 ω02 ) s2 + (Kr Kc + B2 ω02 ) s + (A0 + B3 )ω02

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(15) (16)

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Fig. 9. Bode diagram of the open-loop system when controller parameters and filter parameters change. (a) Kp changes ±50%. (b) Ki changes ±50%. (c) Kc changes ±50%. (d) L1 changes ±50%. (e) C changes ±50%. (f) L2 changes ±50%.

Fig. 10. Harmonic impedance of the system.

should get similar performance. If Kp , Kr , and Kc are set as 0.2356, 27.12, and 79.89, respectively, the result is just as expected. The location of the poles and zeros in z-domain is s1,2 s3 s4,5 z1,2

= 0.767 ± j0.28 = 0.363 = 0.995 ± j0.0299 = 0.995 ± j0.0294.

Fig. 11.

Bode diagram of PI and PR regulators.

It is evident that pole 4 and pole 5 are near zero 1 and zero 2. They can be treated as two pairs of dipoles. The pole–zero placement of the system in z-domain with PR regulator is shown in Fig. 13. VII. E XPERIMENTAL R ESULTS To verify the proposed design method, a three-phase experimental platform based on DSP TMS320LF2407 is established.

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Fig. 12. Root locus of the system with PR regulator. (a) Complete view. (b) Enlarged view.

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Fig. 14. Experimental waveforms for grid-connected current of the system (a) with PI regulator (1 A/div, 5 ms/div) and (b) with PR regulator (1 A/div, 5 ms/div).

Under the two-current-loop control, the system is connected to the grid safely. The waveforms of the grid current are shown in Fig. 14. Fig. 14(a) and (b) shows the three-phase grid currents of the system with PI controller (system 1) and PR controller (system 2), respectively. THD of the grid voltage is 5.067%, while the THDs of the grid current of systems 1 and 2 are respectively 3.686% and 2.930%. The magnitude of the current of system 2 is slightly bigger than the current of system 1, while the current reference commands are all 2 A (peak value) for them. To test the dynamic performance of the system, current reference command is changed from 2 to 3 A when operating. Fig. 15 shows the dynamic performance of systems 1 and 2. The change occurs at the place where the arrows point at. The current of phase A arrives at the peak value at that time. It is seen that the process is smooth with little overshoot for all three-phase currents. The results agree with the analysis. Since the damping ratio ζr is 0.5, the overshoot related to it is low. The setting time Ts is short because ζr ωr is big. VIII. C ONCLUSION Fig. 13. Pole–zero placement of the closed-loop system with PR regulator.

In this paper, a parameter-design method has been proposed for the two-current-loop controller used in a LCL-based

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tem unstable. The requirement for all coefficients to be positive is necessary, but it is not sufficient. That is to say, all positive coefficients cannot guarantee that the system is stable. Step 2) If there are no negative coefficients, the Routh array must be formed in the following manner: s4 s3 s2 s s0

a0 a1 b1 c1 d1

a2 a3 b2 0

a4 0

where a1 a2 − a0 a3 a1 a1 a4 − a0 × 0 b2 = a1

b1 =

c1 =

b1 a3 − a1 b2 b1

d1 =

c1 b2 − b1 × 0 . c1

The stability of the system may be determined by the Routh array. The number of closed-loop poles in the right-hand half complex plane is equal to the number of sign changes of the elements of the first column of Routh array. R EFERENCES

Fig. 15. Dynamic performance of the system (a) with PI regulator (2 A/div, 20 ms/div) and (b) with PR regulator (2 A/div, 20 ms/div).

grid-connected inverter system. The practicality of this method was tested using a Bode diagram. Experimental results proved the feasibility of the proposed design method. The adoption of filter-capacitor-current inner loop can damp the resonance of the LCL filter as analyzed. The design method made the tuning procedure easier and the system performance good. A PPENDIX The Routh’s method is used to determine the number of roots located in the right-hand half of the complex plane using only the coefficients of the characteristic equation without actually solving the characteristic equation for the roots themselves. The method may be used by following these steps. Step 1) Take a fourth-order system as an example. The characteristic equation in the polynomial form is written as a0 s4 + a1 s3 + a2 s2 + a3 s + a4 = 0.

(A.1)

If any of the coefficients are negative or zero, there is at least one positive root which will make the sys-

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LIU et al.: PARAMETER DESIGN OF A TWO-CURRENT-LOOP CONTROLLER USED IN AN INVERTER SYSTEM

[12] L. Mihalache, “A high performance DSP controller for three-phase PWM rectifiers with ultra low input current THD under unbalanced and distorted input voltage,” in Conf. Rec. IEEE IAS Annu. Meeting, 2005, pp. 138–144. [13] A. Papavasiliou, S. A. Papathanassiou, S. N. Manias, and G. Demetriadis, “Current control of a voltage source inverter connected to the grid via LCL filter,” in Proc. IEEE PESC, 2007, pp. 2379–2384. [14] F. A. Magueed and J. Svensson, “Control of VSC connected to the grid through LCL-filter to achieve balanced currents,” in Conf. Rec. IEEE IAS Annu. Meeting, 2005, pp. 572–578. [15] E. Wu and P. W. Lehn, “Digital current control of a voltage source converter with active damping of LCL resonance,” IEEE Trans. Power Electron., vol. 21, no. 5, pp. 1364–1373, Sep. 2006. [16] F. Liu, S. Duan, P. Xu, G. Chen, and F. Liu, “Design and control of three-phase PV grid connected converter with LCL filter,” in Proc. IEEE IECON, 2007, pp. 1656–1661. [17] V. Blasko and V. Kaura, “A novel control to actively damp resonance in input LC filter of a three-phase voltage source converter,” IEEE Trans. Ind. Appl., vol. 33, no. 2, pp. 542–550, Mar./Apr. 1997. [18] 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. [19] D. N. Zmood and D. G. Holmes, “Frequency-domain analysis of threephase linear current regulators,” IEEE Trans. Ind. Appl., vol. 37, no. 2, pp. 601–610, Mar./Apr. 2001. [20] M. J. Newman and D. G. Holmes, “Delta operator digital filters for high performance inverter applications,” IEEE Trans. Power Electron., vol. 18, no. 1, pp. 447–454, Jan. 2003. [21] S. Mariethoz and M. Morari, “Explicit model-predictive control of a PWM inverter with an LCL filter,” IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 389–399, Feb. 2009. [22] J. T. Bialasiewicz, “Renewable energy systems with photovoltaic power generators: Operation and modeling,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2752–2758, Jul. 2008.

Fei Liu received the M.Eng. and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2004 and 2008, respectively. He is currently a Postdoctoral Research Fellow in the Department of Electrical Engineering, Wuhan University, Wuhan, China. His major fields of interest include renewable energy generation, distributed generation systems, microgrid, and unified power quality conditioners.

Yan Zhou received the B.Eng. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2007, where he is currently working toward the M.Eng. degree in the area of power electronics in the Department of Applied Power Electronic Engineering. His major fields of interest include three-phase photovoltaic grid-connected inverters, distributed generation systems, and microgrid.

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Shanxu Duan received the B.Eng., M.Eng., and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 1991, 1994, and 1999, respectively. Since 1991, he has been a Faculty Member in the Department of Applied Power Electronic 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. Prof. 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.

Jinjun Yin received the B.S. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2000, where he is currently working toward the Ph.D. degree in the area of power electronics in the Department of Applied Power Electronic Engineering. His major research interests include control technology of converters and renewable energy applications.

Bangyin Liu received the B.S., M.S., and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2001, 2004, and 2008, respectively. He is currently a Postdoctoral Research Fellow in the Department of Applied Power Electronic Engineering, Huazhong University of Science and Technology. His major research interests include renewable energy applications and soft-switching converters.

Fangrui Liu received the B.Eng. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2002, and the Ph.D. degree from Nanyang Technological University, Singapore, in 2006. He is currently a Lecturer in the Department of Applied Power Electronic Engineering, Huazhong University of Science and Technology. His current research interests include renewable energy resources and distributed power systems.

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