RAPIDLY increasing energy demand from industrial and

Transcription

1 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 4, APRIL Parallel PI Voltage H Crrent Controller for the Netral Point of a Three-Phase Inverter Tomas Hornik, Member, IEEE, and Qing-Chang Zhong, Senior Member, IEEE Abstract For applications in renewable energy and distribted generation, there is often a need to have a netral line to provide a crrent path for nbalanced loads. This can be achieved by sing a netral-point circit that consists of a conventional netral leg and a split dc link. In this paper, an H crrent controller is proposed to force the crrent flowing throgh the split dc link to be nearly zero so that the netral-point voltage is stable, and then, a voltage control loop is added to eliminate the imbalance of the voltage so that the netral-point voltage is balanced with respect to the dc terminals. The combination of these two controllers, connected in parallel, is able to maintain the netral point at the midpoint of the dc bs even when the netral crrent is large. Hence, the inverter can be connected to nbalanced loads and/or the tility grid. Experimental reslts are presented to demonstrate the excellent performance of the proposed control scheme. The proposed strategy can also be applied to netral-point-clamped three-level converters. Index Terms DC AC power converter, dc-link balancing, H control, mltilevel plsewidth modlation (PWM) converter, netral line, parallel control strctre, three-phase for-wire power system. I. INTRODUCTION RAPIDLY increasing energy demand from indstrial and commercial sectors, particlarly in the crrent climate of increased concerns abot environmental changes, has led to the fast development of distribted power generation systems (DPGSs) based on renewable energy sorces [1. A recent concept is to grop DPGSs and the associated loads to a common local area to form a small power system called a microgrid. The introdction of microgrids improves power qality, redces transmission line congestion, decreases emission and energy losses, and effectively facilitates the tilization of renewable energy resorces [2 [7. In some circmstances, the inverters sed in microgrids and/or DPGS mst spply a mixtre of single- and threephase loads via a for-wire three-phase distribtion network. A netral line is often needed to provide a crrent path for nbalanced loads, and the traditional six-switch inverter mst Manscript received April 29, 2011; revised Agst 27, 2011, October 14, 2011, December 1, 2011, and Jne 9, 2012; accepted Jly 11, Date of pblication Jly 25, 2012; date of crrent version November 22, The work of Q.-C. Zhong was spported by the Engineering and Physical Sciences Research Concil, U.K., nder Grant EP/J001333/1 and Grant EP/J01558X/1. T. Hornik is with Trbo Power Systems, NE11 0NX Gateshead, U.K. ( t.hornik@liv.ac.k). Q.-C. Zhong is with the Department of Atomatic Control and Systems Engineering, The University of Sheffield, S1 3JD Sheffield, U.K. ( Q.Zhong@Sheffield.ac.k). Color versions of one or more of the figres in this paper are available online at Digital Object Identifier /TIE be spplemented with a netral connection [8 [10. If the netral point of the inverter that provides the netral line is not well balanced, then the netral-point voltage may deviate severely from the midpoint of the dc sorce of the inverter. This may reslt in an nbalanced or variable otpt voltage, dc voltage/crrent components, large netral crrent, or even more serios problems. Ths, the generation of a balanced netral point in a simple and effective manner has become an important isse [8 [10. Three different circit topologies are sed to generate a netral point [11, [10. The most poplar topology is a split dc link, as shown in Fig. 1(a), with the netral point clamped at half of the dc-link voltage. Since the netral crrent flows throgh the capacitors, high capacitance is necessary. Moreover, the netral point sally shifts becase of the mismatch of capacitors and/or switches. In order to improve the performance of the split-dc-link topology, different netral-point-balancing strategies are reported, sally sing redndant states of the space vector plsewidth modlation (PWM) [12 [14 or varied voltage-balancing modlation techniqes as proposed in [15 [20. The main drawback is that the netral-point balancing is not flly decopled from the three-phase converter control and, as a reslt, the power qality of the otpt voltages can be significantly affected. Fig. 1(b) shows another way to handle the netral-point control. An additional forth leg, called the netral leg, is added to a conventional three-leg converter. Varios control strategies are available for this topology [21, [22. However, the additional netral leg cannot be flly independently controlled to maintain a stable netral point. The third topology is an actively balanced split dc link shown in Fig. 1(c), which is the combination of the aforementioned two. The control of the netral point in this case can be decopled from the control of the three-phase converter [10, [11, [23 [25. Becase of this, the design of the control strategy for a three-phase inverter is not limited by the control of the netral point, which makes it very easy to eqip inverters controlled by advanced control strategies, e.g., the synchronverters [26, with a netral line. Both classical [11 and advanced [10 control strategies are available for this topology. In this paper, a parallel voltage crrent control strategy is proposed to improve the performance of the actively balanced split dc link. The crrent controller is designed by sing the H control methods to minimize the crrent i C flowing throgh the split dc capacitors. Since the netral point can slightly shift de to the mismatch of capacitors and/or the nonlinearity of switches, an extra voltage control loop is added to bring the shift back to normal. Since the voltage controller mainly concerns the dc signals and the crrent controller mainly concerns /$ IEEE

2 1336 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 4, APRIL 2013 Fig. 2. Block diagram of the actively balanced split dc link. to be zero. Moreover, a two-inpt one-otpt controller was adopted in [10, bt a single-inpt single-otpt controller is adopted in this paper for the crrent controller, with the add-on of the voltage controller. It is worth noting that the proposed control strategy can also be applied to maintain the midpoint of mltilevel inverters [27, [28. The rest of this paper is organized as follows. The overall strctre of the system is presented in Section II, followed by the H crrent controller designed in Section III and the voltage control loop designed in Section IV. The experimental setp is briefly described in Section V, followed with experimental reslts. Finally, conclsions are made in Section VI. II. DESCRIPTION OF THE ACTIVELY BALANCED SPLIT DC LINK As mentioned earlier, the circit topology shown in Fig. 1(c) is the combination of the split dc link and the netral leg [10, [11. The control of the netral point is decopled from the control of the three-phase inverter. The total dc-link voltage is the difference between the two capacitor voltages measred with respect to the netral point, i.e., Fig. 1. Circit topologies to generate a netral point [10, [11. (a) Split dc link. (b) Additional netral leg. (c) Actively balanced split dc link. the harmonic crrent components, these two controllers are decopled in the freqency domain and can be arranged in a parallel control strctre instead of a cascaded control strctre. This improves the stability of the system. The proposed strategy leads to very small deviations of the netral point from the midpoint of the dc sorce, in spite of the possibly very large netral crrent. Experimental reslts are presented to demonstrate the excellent performance of the proposed control strategy. Moreover, the experimental reslts of the classical and H voltage crrent controllers proposed in [11 and [10, respectively, are also provided for comparison. The performance has been considerably improved with the proposed controller. Althogh the H control methods are sed in both this paper and in [10, the design principles are completely different. The controlled variables in [10 are the netral-point voltage shift and the netral line indctor voltage, bt the controlled variables in this paper are chosen as the crrent flowing throgh the split dc capacitors and the dty cycle for the switches, in the hope to directly control the netral-point voltage shift. In this paper, the netral-point voltage shift is indirectly maintained by forcing the crrent flowing throgh the split dc capacitors V dc = V CN+ V CN. Since the control objective is to maintain the point N as a netral point, then the average voltage V ave = V CN+ + V CN (1) 2 is expected to be as close to zero as possible all the time. As a reslt, i L is expected to be almost eqal to i N. This means the majority of the netral crrent shold flow throgh the indctor L N bt not throgh the capacitors. A small crrent i C wold lead to a small variation of the netral point N. The capacitors do not have to be chosen very large, as those needed in the conventional split dc link. The block diagram of the actively balanced split dc link is shown in Fig. 2, where p is the average of the control signal over one switching period normalized with respect to half of the dc bs voltage. The dty cycle for the pper switch is d = p The resistance of the indctor is inclded, and the capacitors C N+ and C N cold be different. The control objective is to

3 HORNIK AND ZHONG: PARALLEL PI VOLTAGE H CURRENT CONTROLLER FOR NEUTRAL POINT OF INVERTER 1337 z =[z 1 z 2 T, denoted by T zw = F l ( P,C). The closed-loop system can be represented as [ [ z = y P w = Cy Fig. 3. Block diagram of the H crrent control scheme. where P is the generalized plant that incldes the original control plant and weighting fnctions, C is the controller to be designed, and y is the measred crrent i C that contains the effect of the measrement noise n. It is worth noting that the measrement noise n is an imaginary variable introdced to facilitate the design of the controller so that the impact of the measrement noise n in the crrent i C is reflected and minimized. When the controller is implemented, as shown in Fig. 3, the feedback signal to the controller C is the measred crrent i C, which contains the effect of the measrement noise, so there is no need to determine or calclate the vale of the measrement noise n. Fig. 4. Formlation of the H control problem for netral-point control. maintain a stable and balanced netral point, i.e., to make i C as small as possible while maintaining the stability of the system. In this paper, an advanced control strategy will be developed to make i C as small as possible (ideally, i C =0). III. DESIGN OF AN H CURRENT CONTROLLER A. Controller Description The sketch of the H crrent control scheme is shown in Fig. 3, where P is the transfer fnction of the plant (the actively balanced split dc link) and C is the transfer fnction of the controller. The controller C is designed by solving a weighted sensitivity H problem [29, as formlated later, to assre the stability of the entire system. The netral crrent i N is regarded as an external distrbance, and the control signal is = p. B. Formlation as a Standard H Problem Since the crrent i C contains significant ripples at the switching freqency, it is measred throgh a low-pass filter. The remaining ripple after this filter can be regarded as part of the measrement noise n. The distrbance is expected to be within a certain freqency range, so a weighting fnction W is introdced to reflect this. A weighting factor μ is introdced to avoid a large control action, and a weighting factor ξ is introdced so that the impact of the measrement noise n can be tned dring the process of controller design. The weighting factors ξ and μ can be sed to adjst the relative importance of the distrbances i N and n in the H norm. The H control problem, as shown in Fig. 4, is then formlated to minimize the H norm of the transfer fnction from w =[ni N T to C. Realization of the Plant P The indctor crrent i L and the voltage V c are chosen as state variables x =[i L V c T. The otpt signal from the plant P is the capacitor crrent i C = i N i L, i.e., the difference between the netral crrent and the crrent throgh the indctor. The plant P can then be described by the state eqation and the otpt eqation with ẋ = Ax + B 1 i N + B 2 (2) y = e = C 1 x + D 1 i N + D 2 (3) [ A = [ B 1 = B 2 = R N L N 1 L N C N+ +C N C N+ +C N [ Vdc 2L N 0 C 1 =[ 1 0 D 1 =[1 D 2 =[0. The corresponding plant transfer fnction is then or, in short P =[D 1 D 2 +C 1 (si A) 1 [B 1 B 2 [ A B1 B 2 P = C 1 D 1 D 2. (4) In the seqel, this notation will be sed for transfer fnctions.

4 1338 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 4, APRIL 2013 D. Realization of the Generalized Plant P Since there are harmonics in the netral crrent, the weighting fnction W can be realized as a resonant filter W = [ Aw B w C w 0 with a high gain at the vicinity of the line freqency while providing small gains at all the other freqencies. It can be designed to cover the fndamental freqency only or to cover the fndamental freqency and some harmonic freqencies, e.g., the third and fifth harmonics, as well. From Fig. 4, the following eqations can be obtained: y = i C + ξn [ A B1 B 2 = ξn + C 1 D 1 D 2 [ A 0 B1 B 2 = C 1 ξ D 1 D 2 z 1 = W (i C + ξn) = [ in n i N (5) [ [ Aw B w A 0 B1 B 2 n i N C w 0 C 1 ξ D 1 D 2 A 0 0 B 1 B 2 = B w C 1 A w B w ξ B w D 1 B w D 2 0 C w n i N (6) z 2 = μ. (7) Combining (5) (7), the realization of the generalized plant is then obtained as A 0 0 B 1 B 2 B w C 1 A w B w ξ B w D 1 B w D 2 P = 0 C w μ C 1 0 ξ D 1 D 2. (8) The controller can then be obtained by sing the standard H control algorithms to garantee the stability of the system. TABLE I PARAMETERS OF THE NEUTRAL LEG E. Design Example The parameters of the netral leg circit to be tested are given in Table I. The switching freqency is f s =5kHz. The weighting parameters are chosen to be ξ =0.5 and μ =0.5. This is to reflect the case that the netral crrent i N weights more than the noise n, and the otpt z 1 weights more than the control signal. Controllers with different nmbers of harmonics compensators (i.e., with different weighting fnctions W ) are designed in this section. Controller C 1 is designed according to the weighting fnction W (s) =(K 1 2ζωs)/(s 2 +2ζωs + ω 2 ) that has a high gain at the fndamental grid freqency ω only. Controller C 3 is designed according to W (s) =[(K 1 2ζωs)/(s 2 + 2ζωs + ω 2 ) + [(K 3 6ζωs)/(s 2 +6ζωs +9ω 2 ), which has an extra high gain at the third harmonic freqency to frther improve the performance of the controller. Similarly, controllers C 5 and C 7 are designed with weighting fnctions having an added high gain at the fifth and seventh harmonic freqencies, respectively. The gains in the weighting fnctions are chosen as K 1 =10, K 3 =1.666, K 5 =0.5, and K 7 =0.5, and the damping factor is chosen as ζ =0.005, according to the gidelines reported in [30. Using the MATLAB hinfsyn algorithm, the H controllers C 1 (s), C 3 (s), C 5 (s), and C 7 (s) are obtained as (9) (12), shown at the bottom of the page. The Bode plots of these controllers are shown in Fig. 5. It can be seen that high gains appear at the harmonic freqencies inclded in the corresponding weighting fnction W, which helps redce the harmonic components in i C. These controllers can be discretized for digital implementation. With a sampling freqency of 5 khz, the discretized controllers can be obtained, e.g., by sing the MATLAB c2d (ZOH) algorithm, as (13) (16), shown at the bottom of the next page. IV. ADDITION OF A VOLTAGE CONTROL LOOP As mentioned earlier, the netral point sally shifts becase of capacitor mismatches and/or nonlinearity of switches, even if C 1 (s)= (s 55.09)(s2 +296s ) (s+1147)(s+82.99)(s s ) C 3 (s)= (s 87.02)(s s )(s s ) (s+1323)(s+71.9)(s s )(s s ) C 5 (s)= (s 97.26)(s s )(s s )(s s ) (s+1374)(s+69.27)(s s )(s s )(s s ) C 7 (s)= (s 104)(s s )(s s )(s s )(s 2 133s ) (s+1405)(s+67.71)(s s )(s s )(s s )(s s ) (12) (9) (10) (11)

5 HORNIK AND ZHONG: PARALLEL PI VOLTAGE H CURRENT CONTROLLER FOR NEUTRAL POINT OF INVERTER 1339 Fig. 6. Proposed parallel PI voltage H crrent control scheme for the actively balanced split dc link. Fig. 5. Bode plots of the controllers designed. Hence, adding the voltage controller does not affect the stability of the crrent loop. As long as the voltage control loop is stable, which can be easily achieved by tning the PI controller, the whole system is stable. It is worth noting that the derivation of the analytic stability condition cold be difficlt bt the stability of the system can be easily achieved according to the earlier analysis. This control strategy does not only lead to a stable netral point (by the crrent controller) bt also leads to a balanced netral point with respect to the dc-link terminals (by the voltage controller). the crrent i C is maintained zero. In order to make sre that this does not happen, there are generally two options. One option is to simply add an offset to the control signal according to the netral-point shift. By doing this, there is no need to measre the voltages across the capacitors, and only one sensor is needed to measre the crrent i C for the H crrent controller. Since this is an open-loop control method, the netral point may shift frther when the circmstances change. The other option is to add a voltage control loop. In this case, the capacitor voltages are measred with respect to the netral point N, asshownin Fig. 1(c). Since the balance between the two capacitor voltages is desired, which can be achieved by making V ave very small, the average voltage V ave is sed to form a voltage control loop. The crrent controller is designed to maintain i C to be nearly zero, i.e., to remove any components having a freqency higher than zero; the voltage controller is jst to bring the constant voltage deviation of the netral-point voltage back to zero, i.e., to work on the dc component. Hence, the fnctions of the two controllers are decopled in the freqency domain. As a reslt, the voltage controller and the crrent controller can be pt together to form a parallel voltage crrent control strctre, as shown in Fig. 6. The voltage controller can be chosen as a proportional integral (PI) controller, which has a high dc gain. The otpt of the voltage controller enters the crrent control loop, taking the role of the measrement noise n in Fig. 4. V. E XPERIMENTAL VALIDATION The experimental setp consists of an inverter board, a three-phase LC filter, a board consisting of voltage and crrent sensors, a dspace DS1104 R&D controller board with ControlDesk software, and MATLAB Simlink/SimPower software package. The inverter board consists of two independent three-phase inverters and has the capability to generate PWM voltages from a constant 42-V dc voltage sorce. The first inverter is sed to generate a three-phase otpt voltage, and one leg of the second inverter is sed to control the netral point. By changing the load of the first inverter, different netral crrents can be generated. The parameters of the system are the same as those given in Table I. The netral crrent i N and the indctor crrent i L were measred, and the crrent i C was calclated; the dc-bs voltage and the voltage across the capacitor C N were measred, and the average voltage V ave was calclated. The control strategies designed earlier were implemented to evalate their steady-state and transient performance. The steady-state performance was tested when balanced resistive, nbalanced resistive, and nonlinear loads were connected to the three-phase inverter, and the transient performance was tested when the resistive load connected to the three-phase inverter was changed. C 1 (z)= (z 1.011)(z z ) (z )(z )(z z ) C 3 (z)= (z 1.018)(z z )(z z+1.03) (z )(z )(z z )(z z ) (z 1.02)(z z )(z z+1.034)(z z+1.021) C 5 (z)= (z )(z )(z z )(z z )(z z ) C 7 (z)= (z 1.021)(z z )(z z+1.036)(z z+1.025)(z z+1.027) (z 0.755)(z )(z z )(z z )(z z )(z z ) (13) (14) (15) (16)

6 1340 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 4, APRIL 2013 Fig. 7. Steady-state responses when a balanced resistive load was connected to the three-phase inverter (I N =0A). (a) Three-phase crrents i R, i S,andi T of the inverter to generate the netral crrent. (b) Netral crrent i N, capacitor crrent i C, and indctor crrent i L. (c) Netral-point shift. Fig. 8. Steady-state responses when an nbalanced resistive load was connected to the three-phase inverter (I N =1.0 A). (a) Three-phase crrents i R, i S, and i T of the inverter to generate the netral crrent. (b) Netral crrent i N, capacitor crrent i C, and indctor crrent i L. (c) Netral-point shift. A. Steady-State Performance: With a Resistive Load Connected to the Three-Phase Inverter In this experiment, the proposed PI voltage H crrent control scheme (with C 1 and C 3 ) is compared with the classical controller (voltage and crrent proportional controllers) proposed in [11 and the H voltage crrent controller proposed in [10. The control strategies were evalated nder three different sitations when the rms vales of the netral crrent i N were I N =0A, I N =1A, and I N =2A. The three-phase inverter was connected to a resistive local load in the open-loop mode to generate the netral crrent needed for the tests. When I N =0A(R A = R B = R C =6Ω), Fig. 7(a) shows the crrents (i S, i R, and i T ) of the inverter to generate the netral crrent, and Fig. 7(b) shows the netral crrent i N, the indctor crrent i L, and the capacitor crrent i C. The netral-point shift, i.e., the average voltage V ave, is shown in Fig. 7(c). The relevant crves are shown in Fig. 8 when I N =1A(R A = R C =6Ωand R B =12Ω) and Fig. 9 when I N =2 A(R A = R C =6 Ω and R B = ). The proposed controllers maintained a small voltage shift nder all three cases. As expected, the majority of the netral crrent was forced to flow throgh the indctor, and the crrent i C remained nearly zero. There are no visible fndamental components in V ave when C 1 and C 3 were sed. There were visible thirdharmonic components in V ave when C 1 was sed. There were no visible third-harmonic components in V ave when C 3 was sed, and the variation of V ave is very small. The netralpoint shift remained almost nchanged when the netral crrent was increased. The proposed strategy clearly otperformed the classical and H voltage crrent controllers, with which the netral-point variation and the capacitor crrent were proportionally increased with the increased netral crrent. As a conseqence, the netral point was not well balanced. Moreover, in the case of the classical controller, there is a visible netralpoint shift, i.e., an increased dc component in the average voltage V ave.

7 HORNIK AND ZHONG: PARALLEL PI VOLTAGE H CURRENT CONTROLLER FOR NEUTRAL POINT OF INVERTER 1341 Fig. 9. Steady-state responses when an nbalanced resistive load was connected to the three-phase inverter (I N =2.0A). (a) Three-phase crrents i R, i S,and i T of the inverter to generate the netral crrent. (b) Netral crrent i N, capacitor crrent i C, and indctor crrent i L. (c) Netral-point shift. Fig. 10. Steady-state responses when an nbalanced nonlinear load was connected to the three-phase inverter. (a) Three-phase crrents i R, i S,andi T of the inverter to generate the netral crrent. (b) Netral crrent i N, capacitor crrent i C, and indctor crrent i L. (c) Netral-point shift. B. Steady-State Performance: With a Nonlinear Load Connected to the Three-Phase Inverter In this experiment, a single-phase nonlinear load (an ncontrolled rectifier loaded with an LC filter L = 150 μh, C = 1000 μf, and a resistor R =20Ω) was connected to Phase S of the three-phase inverter. Experiments were carried ot with the controllers C 1, C 3, C 5, and C 7 designed earlier. The steady-state crrents (i S, i R, and i T ) are shown in Fig. 10(a), and the netral crrent i N, the indctor crrent i L, and the capacitor crrent i C are shown in Fig. 10(b). The netral-point shift, i.e., the average voltage V ave, is shown in Fig. 10(c). When controller C 1 was adopted, there was a visible third harmonic in V ave. This was improved when controller C 3 was adopted. However, after the third harmonic was removed, there was a visible fifth harmonic in V ave. When controller C 5 was adopted, the fifth harmonic was removed from V ave ; when controller C 7 was adopted, the performance was frther improved. This clearly shows that, when the nmber of harmonics compensated is increased, the tracking performance of the proposed controller is significantly improved. C. Transient Response: Change of the Resistive Load Connected to the Three-Phase Inverter In this experiment, the transient response of the proposed controller C 7 was tested when the resistive load connected to the three-phase inverter was changed from R B =6 Ω to R B = (R A = R C =6Ω) at time t =0s. Fig. 11(a) shows the crrents (i S, i R, and i T ) of the inverter; Fig. 11(b) shows the responses of the netral crrent i N, the indctor crrent i L, and the crrent i C. Fig. 11(c) shows the netral-point shift V ave. It only took one cycle to settle down. VI. CONCLUSION A control strategy has been proposed to force the netral crrent, e.g., in microgrids, to flow throgh the indctor of

8 1342 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 4, APRIL 2013 Fig. 11. Transient response when the resistive load was changed from R B = 6Ωto R B = (R A = R C =6Ω). (a) Three-phase crrents i R, i S,andi T of the inverter to generate the netral crrent. (b) Netral crrent i N, capacitor crrent i C, and indctor crrent i L. (c) Netral-point shift. the netral leg so that the netral point is maintained stable and balanced for an inverter, even when the netral crrent is large. The strategy takes the form of a voltage controller and a crrent controller connected in parallel becase their fnctions are decopled in the freqency domain. Intensive experimental reslts have shown that, for an increased netral crrent i N, the proposed parallel voltage H crrent controller is effective and is able to maintain a stable netral point even when the netral crrent contains significant harmonic components. 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9 HORNIK AND ZHONG: PARALLEL PI VOLTAGE H CURRENT CONTROLLER FOR NEUTRAL POINT OF INVERTER 1343 [27 H. Ab-Rb, J. Holtz, J. Rodrigez, and G. Baoming, Medim-voltage mltilevel converters, state of the art, challenges, reqirements in indstrial applications, IEEE Trans. Ind. Electron., vol. 57, no. 8, pp , Ag [28 J. Rodrigez, S. Bernet, P. Steimer, and I. Lizama, A srvey on netralpoint-clamped inverters, IEEE Trans. Ind. Electron., vol. 57, no. 7, pp , Jl [29 K. Zho and J. Doyle, Essentials of Robst Control. Englewood Cliffs, NJ: Prentice-Hall, [30 M. Castilla, J. Miret, J. Matas, L. Garcia de Vicna, and J. Gerrero, Control design gidelines for single-phase grid-connected photovoltaic inverters with damped resonant harmonic compensators, IEEE Trans. Ind. Electron., vol. 56, no. 11, pp , Nov Tomas Hornik (M 11) received the Diploma in electrical engineering from Technical College V Uzlabine, Prage, Czech Repblic, in 1991 and the B.Eng. and Ph.D. degrees in electrical engineering and electronics from the University of Liverpool, Liverpool, U.K., in 2007 and 2010, respectively. From 2010 to 2011, he was a Postdoctoral Researcher with the University of Liverpool. Since 2011, he has been a Control Engineer with Trbo Power Systems, Gateshead, U.K. His research interests cover power electronics, advanced control theory, and DSP-based control applications. He had more than ten years working experience in indstry as a system engineer responsible for commissioning and software design in power generation and distribtion, control systems for central heating systems, and bilding management systems. Dr. Hornik is a member of the Instittion of Engineering and Technology (IET). Qing-Chang Zhong (M 04 SM 04) received the B.S. degree in electrical engineering from Hnan Institte of Engineering, Xiangtan, China, in 1990, the M.Sc. degree in electrical engineering from Hnan University, Changsha, China, in 1997, the Ph.D. degree in control theory and engineering from Shanghai Jiao Tong University, Shanghai, China, in 1999, and the Ph.D. degree in control and power engineering from Imperial College London, London, U.K., in He was with Technion Israel Institte of Technology, Haifa, Israel; Imperial College London; the University of Glamorgan, Cardiff, U.K.; the University of Liverpool, Liverpool, U.K; and Loghborogh University, Loghborogh, U.K. He is crrently the Chair in control and systems engineering with the Department of Atomatic Control and Systems Engineering, The University of Sheffield, Sheffield, U.K. He is the athor or coathor of Robst Control of Time-Delay Systems (Springer-Verlag, 2006), Control of Integral Processes with Dead Time (Springer-Verlag, 2010), and Control of Power Inverters in Renewable Energy and Smart Grid Integration (Wiley-IEEE Press, 2012). His crrent research focses on power electronics, electric drives and electric vehicles, distribted generation and renewable energy, smart grid integration, robst and H-infinity control, time-delay systems, and process control. Dr. Zhong is a Fellow of IET and was a Senior Research Fellow of the Royal Academy of Engineering/Leverhlme Trst, U.K. ( ). He serves as an Associate Editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS and the Conference Editorial Board of the IEEE Control Systems Society.