High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters

Transcription

1 J Electr Eng Technol.2015; 10(?): ISSN(Print) ISSN(Online) High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters Byeng-Joo Byen*, Jung-Muk Choe** and Gyu-Ha Choe Abstract This study proposes high-performance voltage controller design that employs a capacitor current control model for single-phase stand-alone inverters. The single-phase stand-alone inverter is analyzed via modeling, which is then used to design the controller. A design methodology is proposed to maximize the bandwidth of the feedback controller. Subsequently, to compensate for the problems caused by the bandwidth limitations of the controller, an error transfer function that includes the feedback controller is derived, and the stability of the repetitive control scheme is evaluated using the error transfer function. The digital repetitive controller is then implemented. The simulation and experimental results show that the performance of the proposed controller is high in a 1.5 kw singlephase stand-alone inverter prototype. Keywords: AC-DC converter, Digital control, Repetitive control, Capacitor current control model 1. Introduction Stand-alone type inverters are widely used to supply electrical power at places with no grid connections. Moreover, they can be used for emergency power supply under grid power fault conditions. Therefore, the output waveforms of these inverters must be sinusoidal, similar to those of the ac supply of commercial utility lines. Recently the nonlinear loads of residential electrical loads are increasing dramatically because of the introduction of electronic loads, thus leading to problems such as voltage variations and waveform distortion. These problems can result in steady-state errors and distortions in supply voltage waveform in stand-alone type inverters. Therefore, control strategies for stand-alone type inverters have been proposed to overcome these problems [1-31]. Typically, the structure of an inverter output voltage controller comprises multiple feedback loops rather than a single feedback loop. Although the response of an inverter is faster with a single feedback loop, a multiple feedback loop is more advantageous in shutting off overcurrent and improving the transient response of inductor [1-8]. The multiple feedback loop control method is widely used by researchers because of the ease of implementation and good performance [9, 10]. A multiple feedback loop controller is typically composed of voltage control in the outer loop and current control in the inner loop. Numerous control strategies such as PI [9, 10], predictive control [11, 12], deadbeat control [13, 14], and repetitive control [15- Corresponding Author: Dept. of Electrical Engineering, Konkuk University, Korea. (ghchoe@konkuk.ac.kr) * Dept. of Electrical Engineering, konkuk University, Korea. (cooks321@konkuk.ac.kr) ** Dept. of Electrical Computer Engineering, Virginia Polytechnic Institute and State University, USA. (jmchoe@vt.edu) Received: December 1, 2014; Accepted: March 29, ] are used for controlling the outer and inner loops. However, these controllers have a problem to make a design of controller optimally, which should be considered on both outer loop and inner loop. Generally, a repetitive control scheme is used to compensate the periodic components at multiples of the electrical fundamental frequency. Studies on the repetitive control scheme can be classified into two categories: those focusing on compensating periodic components using the repetitive control scheme [15-26] and those focusing on improving the repetitive control scheme [27-33]. This study belongs to the first category. Numerous studies exist on controlling the output voltage of stand-alone inverters. In order to reduce steady-state errors, this controller can be used directly with an open-loop SPWM inverter [15]. A zero-phase odd-harmonic repetitive controller has been proposed to reduce data memory usage and ensure faster convergence of the tracking error [16, 17]. Moreover, this controller can be employed in uninterruptible power supply (UPS) inverters to supply sinusoidal voltage under nonlinear loads [18-23]. Further, by connecting the repetitive controller in parallel, steady state and rapid response can be achieved and harmonic components can be reduced. In [24], both repetitive control and resonance control schemes were used to achieve rapid response. Also, control structure of combining with PI controller and repetitive controller is researched by [25, 26] for reducing the output voltage distortion. However, those studies are just focused on repetitive controller s performance with feedforward controller for diminishing nonlinear characteristics without considering on feedback controller s performance. In this study, analytical design method is proposed for performance improvement of output voltage controller in the stationary reference frame. The controller consists of both multiple feedback controller and feedforward controller. Copyright c The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. 709

2 High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters The feedforward controller is chosen as repetitive controller, and the multiple feedback controller is selected as PI controller at the outer loop and Type-III compensator at the inner loop. Prior to designing the controller, the inverter is modeled for comparing capacitor and inductor current control models, and a Type III compensator-based feedback controller is designed. Thereafter, a plug-in repetitive controller is designed to compensate the frequency component, which cannot be handled with a feedback controller alone. In order to verify the effectiveness of the designed controllers, simulations were performed using the PSIM simulation software package. Experiments are conducted with a 1.5 kw single-phase stand-alone inverter prototype to verify the proposed control strategy. 2. Single Phase Inverter Modeling and Controller Design 2.1 Modeling of single-phase inverter Single-phase inverters with two types of controllers are shown in Fig. 1. Input voltage is usually supplied by lithium-ion or lead batteries. They are composed of four switches (S 1, S 2, S 3, S 4 ), an output filter inductor (L), an output filter capacitor (C), an inductor parasitic resistance (R L ), and a capacitor parasitic resistance (R c ). The output filter plays a role in rejecting switching noise. The singlephase inverter uses the multiloop control method in which Controller design of inductor current sensing model Controller design of capacitor current sensing model Fig. 1. Schematic of single-phase stand-alone inverter. the outer loop is the capacitor voltage control loop and the inner loop is either capacitor current or inductor current control loop, as shown in Fig. 1. In this study, the implemented controller is a digital controller. Therefore, the voltage and current controllers can be adjusted. Because digital controllers are different from analog controllers, they must consider digital delay effects. These effects are generated owing to sampling of the control variables, computation of the control algorithm, updating of the pulse-width modulation (PWM) signal in single PWM switching mode [25]. The inverter must be first modeled for designing the controller. The two types of inverters can be modeled from Fig. 1. The inductor current control model can be given by (1), and the capacitor current control model can be obtained as (2). 1 Rc 1 RR L c + Rc Rc L ' C L () () LR v c o s Rc R v c o s L + = u ' R c il R R il 1 1 RL L L L v o () s vo = [1 0] (1) il 1 0 C ' v o() s R vo() s c R L L = ' 1 R R R ic( s + ) c c + L + + R C ic LR c LR L L C + + R R V + dc u c LR L + c R v o v o () s = [1 0] ic where, V dc is inverter dc-link voltage, and u c represents the inverter output voltage before the LC filter is scaled by dclink voltage. In order to analyze the characteristics of these models, the bode plots of both duty ratio to voltage and duty ratio to current of each model are needed. There is no difference of the bode plot of duty ratio to voltage between these models. But the bode plot of duty ratio to current has a different characteristics of frequency response as like Fig. 2. The Fig. 2 shows the bode plot of duty ratio to current. The magnitude and phase vary between 10 Hz and 1000 Hz in the inductor current control model whereas they are nearly the same in the capacitor current control model (2) 710 J Electr Eng Technol.2015; 10(3):

3 Byeng-Joo Byen, Jung-Muk Choe and Gyu-Ha Choe Fig. 2. Frequency response of duty ration to current: Capacitor current control model; Inductor current control model according to load power. Therefore, the capacitor current control model is more independent of load than the inductor current control model and thus is more suitable for controller design. 2.2 Design of controller for single-phase inverter As mentioned above, the capacitor current control model is more appropriate for the controller of this study; thus, the inverter control block diagram shown in Fig. 1 is selected. The purpose of a single-phase inverter is to supply a stable sinusoidal voltage. The multiple feedback loop control strategy is selected for controlling the singlephase inverter. The outer loop G dcv (z) is controlled through a PI controller that is easy to implement and exhibits good performance. The inner loop G dci (z) is implemented with a Type III compensator. The Type III compensator can boost the phase and gain of the controller and enables analytic controller design. The conventional PI controller, namely, s-domain expression, is given by Eq. (3). The voltage controller G dcv (z) used in this study is given by Eq. (4) by converting the s-domain to the z-domain. * ki iref = ( vref vo ) kp + s kt i s z+ iref = ( vref vo ) kp + 2 z 1 * 1 where, v * ref is the reference output voltage, i * ref is the reference inductor current. Further, k i and k p are the PI controller gains, and T s is the control period. The switching frequency is denoted as fs, and the maximum bandwidth of the outer loop controller is limited to approximately fs/50 [34-36]. However, the bandwidth of the outer loop voltage controller is dependent on the bandwidth of the inner loop current controller. Therefore, the design of the inner loop controller must be optimized, and that affects control performance. The inner loop controller G ci (z) must be optimized for tracking the voltage controller output. Moreover, the maximum bandwidth of (3) (4) Fig. 3. Compensated frequency response of current controller the inner loop controller is limited to approximately fs/10 in the digital controller [34-36]. Therefore, the inner loop controller must be analytic control design to ensure optimal performance. In this case, the Type III compensator is more suitable than other types of compensators because the phase boost can range from 0º to 180º in the highfrequency region. Therefore, the phase near the crossover frequency can primarily be determined by the phase of G ci (z). In this study, the current controller is designed such that the targeted phase margin is 80º at the crossover frequency. The results of the design are shown in Fig. 3. As shown in Fig. 3, the crossover frequency and the phase margin, which are the bandwidth and the phase margin of the system, satisfy the design specifications. 3. Repetitive Controller Design As mentioned above, the capacitor current control model is more independent of loads than the inductor current control model. Accordingly, the capacitor current controller achieves high quality sinusoidal voltage regulation. However, both residential and industrial applications primarily have nonlinear loads. The nonlinear characteristics distort the output voltage thus resulting in quality degradation because a conventional controller cannot completely compensate the distortion. In order to compensate the harmonics, a plug-in type repetitive controller is used in this study for supplying high-quality voltage. Conventional repetitive controllers are compared in terms of frequency response, and the most suitable repetitive controller is selected. 3.1 Repetitive controller components selection The repetitive control method, which is based on the internal model principle, is widely used to obtain very accurate reference tracking for closed-loop control systems 711

4 High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters Fig. 4. Types of repetitive controllers: Plug-in repetitive structure; Cascade repetitive structure. in which the tracking error is repeated periodically [25]. A repetitive controller can be divided into three parts, as shown in Fig. 4. First, the data saving section is used for storing data during the sampling period of fundamental frequency for eliminating repetitive errors to obtain the internal model. Second, the data filtering part rejects harmonics on the basis of the stability factor q(z). Third, the output scaling part is obtained by evaluating the system model gain of the repetitive controller G f (z). Moreover, according to previous research, there are two types of repetitive controllers, as shown in Fig. 4 and Fig. 4. The two types of repetitive controllers are represented as follows: G ( z) N+ L L z Gf z z Gf z = = 1 z q z z q z rp N N N+ L L f rp = = N N z G z z Gf z G z q z q z 1 z q z z q z where L is the constant that compensates the time delay effect. The time-delay effects are caused by the digital PWM update and the computation delay. Further, L leads the actual error [25]. In addition, as can be seen from (5) and (6) and Fig. 8, it differs with the type of repetitive controller used. Stability factor q(z) such as a low pass filter (LPF) typically rejects harmonic components. When q(z) is an LPF, Fig. 5 shows the frequency response of G rp (z). For (6), we can see a deviation from the original source in the magnitude and phase in the high frequency region. The harmonic rejection performance of (5) is better than that of (6). Therefore, in this study, the repetitive controller given by (5) is chosen. There are many types of stability factors q(z) in a repetitive controller. The stability factors are given by (5) (6) q = k (0 < k < 1) (7) cons 2 ωn 2 z 1 lpf = 2 2 = s + 2ζω T ns+ωn s z+ 1 q z s (8) Fig. 5. Comparison of frequency responses of repetitive controllers. q nt ( z) 1 z + 2+ z = (9) 4 Fig. 6 compares the frequency responses of (7), (8), and (9) up to the Nyquist frequency. Further, q cons (z) is the magnitude of the repetitive controller output amplified at all-frequency range, and the repetitive controller has zero phase delay whereas q lpf (z) is the magnitude of the repetitive controller output in the low-frequency range and reduces from the cutoff frequency range, and the phase of the repetitive controller is delayed in the high-frequency range. Further, q nt (z) is the magnitude of the repetitive controller output equaling that of an LPF, and the repetitive controller has zero phase delay. In this study, the stability factor is chosen to be q nt (z). 3.2 Design of repetitive controller The proposed repetitive control algorithm is shown in Fig.. The control algorithm includes a plug-in repetitive control scheme such as a feedforward structure. In Fig. 7, T v (z) is defined as follows: = kp ( z ) T z G z G z v cv dv ( ) kt i s z+ 1 Ts z+ 1 = + + Rc 2 1 C z 1 (10) In order to design a stable controller, the relationship between the reference input voltage (v*) and the voltage error (v err ) can be obtained from Fig. 7, which is similar to the form derived in [25], as follows: * / arp ( z) 1/ { 1 Tv ( z) } G z = v z v z = a z b z (11) e err rp rp = + (12) 712 J Electr Eng Technol.2015; 10(3):

5 Byeng-Joo Byen, Jung-Muk Choe and Gyu-Ha Choe Fig. 8. Trajectories for the root of H(z). Fig. 9. Frequency response of G e (z). Fig. 6. Comparison of frequency responses of repetitive controllers: Constant type stability factor; Low pass filter type stability factor; (c) Zero phase delay low pass filter type stability factor. b ( z) Fig. 7. Plug-in repetitive control scheme. N z q( z) /1 ( ) = z q z G z G + T z { f ( dv v )} rp N L (13) If all the magnitudes of the roots for G e (z) are less than unity, all the poles of G e (z) are located in the unit circle in the z-domain so that G e (z) remains stable. In that situation, the stability of G e (z) depends on a rp (z) and b rp (z). The roots of the denominator of a rp (z) are identical to the roots of T v (z). Hence, the roots of the denominator of a rp (z) are located within the unit circle as long as T v (z) is stable. Accordingly, the stability of G e (z) is determined by the roots of b rp (z). Let the function of the roots of H(z) be defined as follows: L f { dv / v} H z = q z G z G 1+ T z 1 (14) In order to design a stable repetitive controller, the design parameters L, q(z), and G f (z) must be selected to satisfy (14). Fig. 8 shows a comparison of the trajectories of the roots up to the Nyquist frequency (10 khz) at different values of G f (z). In Fig. 8, if G f (z) is less than 0.2, the trajectories of the roots converge into the unit circle. Accordingly, the repetitive control system is considered to be stable because condition (14) is satisfied. Fig. 8 shows the relationship between v * and the output voltage v o of the repetitive controller. Fig. 9 shows the depths of each notch at multiples of 60 Hz. This indicates that the repetitive controller can effectively block the repetitive error. 4. Simulation Results In order to investigate the effectiveness of the designed 713

6 High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters Table 1. Single-phase stand-alone inverter parameter Inductor(L) Capacitor(C) Output Voltage(V o ) Frequency(f o ) Input Voltage(V dc ) Switching Frequency(f sw ) 2 mh 50 uf 220 V rms 60 Hz 380 V dc 20 khz Fig. 12. Simulation results under nonlinear loads: without and with repetitive controller. Fig. 10. Simulation results with inductor current control model under 1.5 kw loads. Fig. 13. Simulation results under step nonlinear loads: without and with repetitive controller. Fig. 11. Simulation results with capacitor current control model under 1.5 kw loads. controllers, simulations were performed using the PSIM simulation software package. All the parameters used in the simulation are identical to the values given in Table 1. Fig. 10 shows the simulation results of the repetitive controller with the inductor current control model. It shows the results for a load of 1500 W, and RMS of the output voltage and peak-to-peak magnitude of the voltage error are 220 V and approximately 110 V, respectively. Fig. 11. shows the simulation results with the capacitor current control model as load. It shows the results for a load of 1.5 kw, and the RMS of the output voltage is 220 V. Further, the peak-to-peak magnitude of the voltage error is approximately 30 V. Figs. 12 and 13 show the simulation results under different nonlinear load conditions. Without the repetitive controller, the peak-to-peak magnitude of the current error is approximately 38 V, as can be seen in Fig. 12. However, with the designed repetitive controller, the peak-to-peak magnitude of the voltage error is limited to 1.5 V, as can be seen in Fig 12. Further, the total harmonic distortion (THD) varies from 0.08% to 0.04%. Before using the repetitive controller, the peak-to-peak magnitude of the voltage error is approximately 38 V, as shown in Fig. 13. However, with the designed repetitive controller, the peak-to-peak current errors are limited to 4 V. Moreover, the THD varies from 3.8% to 1.3%, and the RMS value varies from 216 V to 219 V. 5. Experimental Results The proposed control scheme has been tested with a 1.5-kW single-phase inverter whose parameters are the same as the values in Table 1. The SKM75GM128D IGBT module manufactured by SEMIKRON was chosen as the switch, and the switching frequency is 20 khz. The TMS320F bit floating-point digital signal processor (DSP) manufactured by Texas Instruments was used as the digital controller. Numerous experiments were conducted to analyze the closed-loop performance of the proposed controller. The closed-loop performance of the controller investigated under the following conditions: 714 J Electr Eng Technol.2015; 10(3):

7 Byeng-Joo Byen, Jung-Muk Choe and Gyu-Ha Choe Fig. 14. Experimental results with the inductor current control model: no load; 1.5 kw load 1) Controllers Based on Inductor and Capacitor current control Models: The closed-loop performances of the controllers based on the capacitor and inductor current control models are compared. Each test was conducted using linear loads from no-load to full-load conditions for analyzing characteristics of the output voltage. Fig. 14 shows the output waveforms of the controller based on the inductor current control model under different loads. The controller is optimized to full-load condition, and Figs show the output waveforms corresponding to 0 W and 1500 W loads. As the load power increases, the output voltage approaches 311 V; however, the error of the output voltage also increases. Fig. 15 shows the output waveforms of the controller based on the capacitor current control model under different loads. This controller is also optimized to fullload condition, and Figs show the output waveforms at 0 W, 500 W, 1000 W, and 1500 W loads. As opposed to the inductor current control model, the output voltage is controlled and nearly constant at 311V and the magnitude of voltage error also varies minimally regardless of load. Figs. 16, 17, and 18 compare the peak output voltage values, output voltage errors, and THDs of the output voltage waveforms, respectively, of the controllers based on the inductor and capacitor current control models. As can be seen in Fig. 16, the peak output voltage value of the inductor current control model varies from 0% to 8% whereas that of the capacitor current control model varies slightly from 0.3% to 0.7% regardless of load. The output Fig. 16. Comparison of output voltage peak values. Fig. 15. Experimental results with the capacitor current control model: no load; 1.5 kw load. Controller based on both inductor and capacitor current control models (linear load) Nonlinear load Fig. 17. Comparison of output voltage errors between reference and output voltage

8 High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters voltage error of the inductor current control model is approximately twice as that of the capacitor current control model, as shown in Fig. 17. Additionally, the THD of the inductor current control model is evaluated to be approximately 2.5% on average, and that the capacitor current control model is evaluated to be approximately 1.5%, as shown in Fig. 18. Therefore, the experimental results show that the capacitor current control model is superior to the inductor current control model in all the cases. 2) Nonlinear Loads: The Fig. 19 shows two types of nonlinear loads and nonlinear thyristor loads. These load configuration is followed by IEC Former consists of a diode rectifier, R serise, R L and C, where (R serise = 9 Ω, R L = 48 Ω /C= 3300 μf) and latter consists of a thyristor rectifier and R L where (R L = 23.8 Ω). Figs. 20 and 21 show the output voltage, output current and voltage error without and with the proposed repetitive controller under the nonlinear loads. The analysis of the experimental results is given in Table 2. From Fig. 20, the output voltage, voltage error, and THD are determined to be V, 42 V, and 2% Fig. 18. Comparison of THDs. Fig. 20. Experimental results of a diode rectifier load: without repetitive controller; with repetitive controller. Fig. 19. Nonlinear load structure: nonlinear load; nonlinear thyristor load. Table 2. Comparison controller performance Fig. 20 Fig. 21 Without With Without With repetitive repetitive repetitive repetitive v out v err THD Fig. 21. Experimental results of a thyristor rectifier load: without repetitive controller; with repetitive controller. 716 J Electr Eng Technol.2015; 10(3):

9 Byeng-Joo Byen, Jung-Muk Choe and Gyu-Ha Choe without the repetitive controller and 311 V, 0 V, and 1.37% with the repetitive controller, respectively. In Fig. 21, the output voltage, voltage error, and THD are V, 28.2 V, and 4.07% and V, 0.42 V, and 4.76% without and with the repetitive controller, respectively. In the case of Fig. 21, the output voltage THD is degraded; however, its level is within a permissible range of grid code. This problem can be overcome by increasing the capacitance in the output filter. The results clearly show that the proposed repetitive controller improves the quality of the output voltage under nonlinear loads. 6. Conclusion A high-performance voltage controller based on capacitor current control model is proposed for singlephase stand-alone inverters in this study. The proposed controller was designed using the repetitive control scheme to handle voltage distortions under nonlinear loads in 1.5kW single phase stand-alone inverter prototype. The simulation and experimental results verify the effectiveness of the proposed control scheme under nonlinear loads. The output voltage error is decreased by 39.8% in rate power, and the THD is increased by 36.8% under stable linear load condition. The output voltage error is decreased by over 98% in step response. This high-performance voltage controller can be employed in ESS and UPS applications. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MOE) (NRF-2013R1A1A ). References [1] P. C. Loh, D. G. Holmes, Analysis of multiloop control strategies for LC/CL/LCL-filtered voltagesource and current-source inverters, IEEE Trans. Ind. Appl., vol. 41, pp , Mar-Apr [2] M. Monfared, S. Golestan, J. M. Guerrero, Analysis, Design, and Experimental Verification of a Synchronous Reference Frame Voltage Control for Single-Phase Inverters, IEEE Trans. Ind. Electron., vol. 61, pp , Jan [3] J.W. He, Y.W. Li, Generalized Closed-Loop Control Schemes with Embedded Virtual Impedances for Voltage Source Converters with LC or LCL Filters, IEEE Trans Power Electron., vol. 27, pp , Apr [4] Y. A. R. I. Mohamed, Mitigation of Dynamic, Unbalanced, and Harmonic Voltage Disturbances Using Grid-Connected Inverters With LCL Filter, IEEE Trans. Ind. Electron., vol. 58, pp , Sep [5] Q. Lei, F. Z. Peng, S. T. Yang, Multiloop Control Method for High-Performance Microgrid Inverter Through Load Voltage and Current Decoupling With Only Output Voltage Feedback, IEEE Trans Power Electron., vol. 26, pp , Mar [6] D. Dong, T. Thacker, R. Burgos, F. Wang, D. Boroyevich, On Zero Steady-State Error Voltage Control of Single-Phase PWM Inverters With Different Load Types, IEEE Trans Power Electron., vol. 26, pp , Nov [7] S. Buso, S. Fasolo, P. Mattavelli, Uninterruptible power supply multiloop control employing digital predictive voltage and current regulators, IEEE Trans. Ind. Appl., vol. 37, pp , Dec [8] G. Willmann, D. F. Coutinho, L. F. A. Pereira, F. B. Libano, Multiple-loop H-infinity control - Design for uninterruptible power supplies, IEEE Trans. Ind. Elctron., vol. 54, pp , Jun [9] N. M. Abdel-Rahim, E. Q. John, Analysis and Design of a Multiple Feedback Loop Control Strategy for Single-phase Voltage-Source UPS Inverters, IEEE Trans Power Electron., vol. 11, pp , Jul [10] P. C. Loh, M. J. Newman, D. N. Zmood, D. G. Holmes, A comparative analysis of multiloop voltage regulation strategies for single and threephase UPS systems, IEEE Trans Power Electron., vol. 18, pp , Sep [11] J. Rodriguez, J. Pontt, C.A. Silva, P. Correa, P. Lezana, P. Cortes, U. Ammann, Predictive Current Control of a Voltage Source Inverter, IEEE Trans Power Electron., vol. 54, pp , Feb [12] J.M. Espi Huerta, J. Castello-Moreno, J.R. Fischer, R. Garcia-Gil, A Synchronous Reference Frame Robust Predictive Current Control for Three-Phase Grid- Connected Inverters, IEEE Trans. Ind. Elctron., vol. 57 pp , Aug [13] J.S. Cho, S.Y. Lee, H.S. Mok, G.H. Choe, Modified deadbeat digital controller for UPS with 3-phase PWM inverter, IEEE Ind Appl Conf. 34th IAS Annul. Meeting, vol. 4, pp , Oct [14] O. Kukrer, H. d. Komurcugil, Deadbeat control method for single-phase UPS inverters with compensation of computation delay, IEE Proc. Electric Power Appl., vol. 146, pp , Jan [15] K. Zhang, Y. Kang, J. Xiong, J. Chen, Direct repetitive control of SPWM inverter for UPS purpose, IEEE Trans Power Electron., vol. 18, pp , May [16] K. L. Zhou, K. S. Low, D. W. Wang, F. L. Luo, B. Zhang, Y. G. Wang, Zero-phase odd-harmonic re

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11 Byeng-Joo Byen, Jung-Muk Choe and Gyu-Ha Choe Gyu-Ha Choe was born in Pusan, Korea. He received the B.S, M.S and ph.d. degrees from Seoul National University, Seoul, Korea, in 1978, 1980, and 1986, respectively. Since 1980, he has been with the Department of Electrical Engineering, Konkuk University, Seoul, where he is currently a Professor and the Director of the Energy Electronics Research Center. Dr. Choe was the President ( ) of the Korean Institute of Power Electronics. From 2012 to 2013, he was the Vice President of Konkuk University. His research interests are in the fields of harmonic cancellation and active power filtering, pulse width-modulation control for ac voltage regulators and inverter welding machines, PCS design of Brown s gas generation, photovoltaic generation, and fuel-cell generation, Various technology related to DC distribution and EV charging with smart grids