Energy storage system has been widely applied in power distribution sectors as well as in renewable energy sources to ensure uninterruptible power supply. This paper presents a model predictive algorithm to control a bidirectional ACDC converter, which is used in an energy storage system for power transferring between the threephase AC voltage supply and energy storage devices. This model predictive control (MPC) algorithm utilizes the discrete behavior of the converter and predicts the future variables of the system by defining cost functions for all possible switching states. Subsequently, the switching state that corresponds to the minimum cost function is selected for the next sampling period for firing the switches of the ACDC converter. The proposed model predictive control scheme of the ACDC converter allows bidirectional power flow with instantaneous mode change capability and fast dynamic response. The performance of the MPC controlled bidirectional ACDC converter is simulated with MATLAB/Simulink® and further verified with 3.0kW experimental prototypes. Both the simulation and experimental results show that, the ACDC converter is operated with unity power factor, acceptable THD (3.3% during rectifier mode and 3.5% during inverter mode) level of AC current and very low DC voltage ripple. Moreover, an efficiency comparison is performed between the proposed MPC and conventional VOCbased PWM controller of the bidirectional ACDC converter which ensures the effectiveness of MPC controller.
1. Introduction
Renewable energy sources are playing an indispensable role to satisfying the future energy demand. The power provided by renewable energy sources is interruptible and unpredictable because these energy sources depend on the weather conditions
[1]
. Hence, an energy storage system is necessary to use in renewable energy sources to provide a reliable power supply and make it dispatchable on demand
[2

4]
.
Fig. 1
shows an energy storage system which composes of a Liion battery bank, a bidirectional isolated DCDC converter and a threephase bidirectional ACDC converter
[5]
. The threephase bidirectional ACDC converter is an essential part of the energy storage system due to its bidirectionalpowerflow and synchronization capabilities
[6]
. This bidirectional ACDC converter should to be highly efficient as it needs to prevent the problems of poor power quality such as high total harmonic distortion (THD), low power factor, ac voltage distortion, ripple in DC current and DC voltage pulsations
[7

9]
. Therefore, several topologies and control methods have been investigated to improve the efficiency and performance of this bidirectional ACDC converter. The classical control of ACDC converter is generally based on voltageoriented control (VOC) scheme, which decomposes the active and reactive power in stationary αβ coordinate and synchronize the powers with rotating dq reference frames by characterizing the current control loops using PI controllers
[10]
. Moreover, a virtualfluxoriented control has been proposed in
[11]
, which also uses the PI controllers. The major limitation of these control schemes is tuning the PI controllers which further affect the coordinate transform accuracy. Furthermore, direct power control (DPC) scheme
[12
,
13]
has been applied for gridtied ACDC converter based on direct torque control (DTC)
[14
,
15]
principle, which also uses the PI controllers.
An energy storage system [5]
In order to improve the performance of the converter, lookup table (LUT) based direct power control (DPC) scheme has been proposed in
[16]
and
[17]
, in which the switching action of the converter is done with predefined switching state table on the basis of active and reactive power characteristics. This lookup table based DPC method has variable switching problem, which produces undesirable harmonic spectrums. To overcome this variable switching, a fuzzylogic based switching state selection criteria has been presented in
[18]
by avoiding predefined switching table. Although the active and reactive power are smoothed in fuzzylogic based DPC algorithm compared with classical DPC, but its sampling frequency is little bit high. Therefore, a sliding mode nonlinear control approach has been investigated in
[19]
for active and reactive power regulation of grid connected DCAC converter, which is very much dependent on variables.
The principle feature of the model predictive control (MPC) scheme is to predict the future behavior of the control variables. This MPC algorithm has become an attractive mode of control technique for bidirectional ACDC converter comparing with all the classical solutions due to its simple and intuitive concept with fast dynamic responses
[20

22]
. Moreover, MPC algorithm is very easy to configure with constraints and nonlinearity and also for practical implementation. The fast and powerful microprocessors are available today to implement the predictive control algorithm very easily as it requires higher number of calculations compared with all the classical controls
[6
,
20]
. Till to date, this algorithm is proposed for an active frontend rectifier
[23

25]
, indirect matrix converter
[26

28]
and voltage source inverter
[22]
. Although model predictive algorithm is an attractive alternative for controlling the power converters, it has been used very limitedly to control power flow of a bidirectional ACDC converter.
This paper proposes a model predictive control (MPC) algorithm that is applied in a bidirectional ACDC converter for energy storage system. The system configuration and working principle of the bidirectional ACDC converter are elaborately described in section 2. The formulation of MPC method with discrete time model, the cost function used for selection of switching states and a detailed explanation of control scheme and algorithm are in section 3. The performance of the proposed MPC method for bidirectional ACDC converter is tested with MATLAB/Simulink and the simulation results are presented in section 4. The simulation results are further verified with a 3.0 kW experimental configuration, which are discussed in section 5. Section 6 describes the efficiency comparison between the proposed MPC and conventional VOCbased PWM controller of the bidirectional ACDC converter. Finally section 7 draws the conclusion of the proposed MPC controlled bidirectional ACDC converter for energy storage system.
2. Bidirectional ACDC Converter Topology
 2.1 System configuration
Fig. 2
shows the threephase bidirectional ACDC converter topology which transfers power between the threephase AC voltage supply and the DC voltage bus. The bidirectional ACDC converter consists of six IGBTDiode switches (
S
_{1}

S
_{6}
), which is connected with threephase AC voltage supply through series filter inductance (
L
_{s}
) and resistance (
R
_{s}
). A DC capacitor (
C
_{dc}
) is connected across DC voltage bus to keep the voltage (
V
_{dc}
) constant. The bidirectional ACDC converter operates in two modes. The first mode is rectifier mode, in which the bidirectional ACDC converter operates as a front end rectifier and allows power transfer from the threephase AC voltage end to the DC voltage bus. The second mode is inverter mode, where the power flows from DC voltage bus to threephase AC voltage end and the converter acts as a voltage source inverter.
Threephase bidirectional ACDC converter topology
 2.2 Working principle
Model predictive control (MPC) algorithm is applied to control the power flow of the threephase bidirectional ACDC converter. The working principle of MPC scheme is based on a finite number of possible switching states, which utilizes the discrete behavior of a static power converter. In the case of threephase bidirectional ACDC converter, MPC algorithm utilizes the discrete nature of filter inductances (
L
_{s}
) to control the power flow by appropriate switching action. In order to select the appropriate switching state to be applied for firing the converter switch, a selection criterion must be defined with a cost function which measures the error between references and predicted values. Then, the state that minimizes the cost function is selected for the next sampling interval.
In order to avoid short circuit, the two switches in each leg of the bidirectional ACDC converter should be operated in a complementary mode. Hence, the gating signals
S
_{a}
,
S
_{b}
and
S
_{c}
determine the switching states of the threephase bidirectional ACDC converter as follows:
Therefore, the switching function vector (
) of the bidirectional ACDC converter can be expressed as,
where,
=
e
^{ j2π /3}
, is the unity vector.
The output voltage space vector (
) of the ACDC converter for both the rectifier and inverter mode can be presented with phase to neutral voltages (
ν
_{ao}
,
ν
_{bo}
and
ν
_{co}
) as,
The output voltage space vector (
) can also be related to the DC bus voltage (
V
_{dc}
) and the switching function vector (
) as,
There are eight possible voltage vectors can be obtained from the eight consequence switching states of the switching signals
S
_{a}
,
S
_{b}
and
S
_{c}
. These eight voltage space vectors are listed in
Table 1
.
Voltage space vectors of the bidirectional ACDC converter
Voltage space vectors of the bidirectional ACDC converter
The energy storage system allows bidirectional power transfer between threephase AC voltage side and energy storage device through the bidirectional ACDC converter. Hence, the bidirectional ACDC converter needs to be operated in two modes, which are specified as rectifier mode and inverter mode. The operating principle of the bidirectional ACDC converter for both the rectifier and inverter modes are elaborately described in the following subsection.
 2.2.1 Rectifier and inverter modes of operation
During the rectifier mode of operation, the bidirectional ACDC converter acts as a front end rectifier that is connected to the threephase AC voltage source through the input filter inductance
L
_{s}
and resistance
R
_{s}
as shown in
Fig. 2
. By applying Kirchhoff’s voltage law at the ac side of the rectifier, the relationship between the threephase AC voltage and rectifier input voltage vectors are,
The spacevector model of threephase AC voltage
and current
can be derived from phase voltage and current as,
and
where
ν
_{sa}
,
ν
_{sb}
, and
ν
_{sc}
are phase voltages;
i
_{sa}
,
i
_{sb}
, and
i
_{sc}
are phase currents of threephase AC voltage source during the rectifier mode.
The input current dynamics of the bidirectional ACDC converter during rectifier mode operation can be evaluated from (5) and (7) as,
The bidirectional ACDC converter works as a voltage source inverter during the inverter mode, which allows the power transfer from the DC voltage bus to the threephase AC voltage end. Therefore, the load current dynamics of the converter remains same as in (10). However, it is 180° outofphase with respect to the load voltage.
3. MPC Formulation
The formulation of model predictive control (MPC) algorithm for threephase bidirectional ACDC converter is described in the following section. The MPC controller is formulated in discrete time domain. Therefore, it is necessary to transform the dynamic system of bidirectional ACDC converter for both rectifier and inverter mode of operation represented in (10) into discrete time model at a specific sampling time
T
_{s}
.
 3.1 Discrete time model for prediction horizon
A discrete time model is used to predict the future values of currents and voltages in the next sampling interval (
k
+1), from the measured currents and voltages at the
k^{th}
sampling instant. The system model derivative
d_{x} / d_{t}
from Euler approximation can be expressed as:
Using the above approximation, the discrete time model of predictive currents and voltages for the next (k+1) sampling instant of the bidirectional ACDC converter in rectifier and inverter mode can be derived.
The discrete time model of predictive input currents at the next sampling instant (
k
+1) for the rectifier and inverter mode of the bidirectional ACDC converter can be evaluated from (10) with the help of Euler approximation as,
 3.2 Cost function
The main objective of model predictive control algorithm is to minimize the error with fast dynamic response between the predicted and reference values of the discrete variables. To achieve this objective, an appropriate cost function (
e
) is defined with a measurement of predicted input error. Hence, the cost function for the rectifier and inverter can be expressed with the absolute error between the predictive and reference values of input and load current for both the rectifier and inverter mode of operation as,
where,
e
is the cost function. The reference input and predicted current are
(
k
+1) and
(
k
+1) and
(
k
+1) and
(
k
+1) for the rectifier and inverter modes, respectively.
 3.3 Control scheme
Fig. 3
shows the proposed control strategy of model predictive control (MPC) algorithm. At first, the operating mode of the bidirectional ACDC converter is selected depending on charging state of the energy storage device, which is determined by the DC bus voltage
V
_{dc}
. If the charging state (determined by DC voltage) is less than threshold level, then it is operated in rectifier mode, otherwise it is operated in inverter mode.
Proposed MPC control scheme
During the rectifier mode of operation, threephase input AC current
(
k
) is measured and the future value of this current
(
k
+1) is predicted by using the discrete time Eq. (12) for each one of eight possible switching vector (
) of the converter. This future value of threephase input AC current
(
k
+1) is compared with the reference current
(
k
+1) of the rectifier mode by utilizing the cost function (
e
) of Eq. 13). The reference current
(
k
+1) of the converter in rectifier mode is calculated from the threephase input AC voltage vector (
) and DC bus voltage (
V
_{dc}
) by using PI controller. Finally, the switching states of the bidirectional ACDC converter which minimizes cost function, is selected for next sampling time.
Similarly, in inverter mode of operation, the future value of the threephase AC load current (−
(
k
+1)) is predicted by using the discrete time Eq. (12). Hence, the optimizing switching states are selected for firing the switches by using cost function (13).
 3.4 Control algorithm
Fig. 4
presents the control algorithm of MPC method for the threephase bidirectional ACDC converter. The whole predictive control process completes the following steps for selecting the optimized switching state of the converter in the next sampling interval (
k
+1).

The control algorithm starts with measuring and sampling the threephase AC current(k) for thekthsampling period.

After sampling this threephase AC current, the future value of this current(k+1) is predicted by using the discrete time equation of the converter in next (k+1)thsampling period.

Then the reference currents for the rectifier mode () and inverter mode () are calculated and set to correspond with the amount of desired power flow.

Therefore, the cost function (e) of the threephase bidirectional ACDC converter is calculated with the predicted and reference values of grid current.

Finally, the switching state associated with the minimum cost function is finally selected for firing the converter in the next sampling time period (k+1).
Proposed MPC control algorithm
4. Simulation Results
The proposed MPC algorithm is carried out by using MATLAB/Simulink to validate the feasibility of the control method. To verify the proposed control method of bidirectional ACDC converter for energy storage system, both the rectifier and inverter mode of operations have been investigated for power transfer between threephase AC voltage side and DC voltage bus. The parameters shown in
Table 2
are used in the simulation of the rectifier and inverter modes with the sampling time of 50 μs.
Simulation and experimental parameters
Simulation and experimental parameters
Fig. 5
shows the threephase AC (phaseneutral) voltage and current of the bidirectional ACDC converter in both the rectifier and inverter modes with instant mode changing capability. During the rectifier mode, the converter is operated as a front end rectifier. Therefore, the reference current is fixed with PI controller to transfer power from threephase AC voltage source to DC bus by controlling the input current, in which the output DC voltage is fixed at 270 V. Results in
Fig. 5(a)
show that, the AC phase voltage and current are exactly in phase, which ensure the unity power factor. Again in inverter mode, the bidirectional ACDC converter allows power transfer from DC voltage bus to AC voltage end by keeping the phase voltage and current in 180° phase shift. Therefore, the unity power factor is also maintained very accurately during this operating mode.
Fig. 5(b)
shows the phasetophase AC voltage generated by the converter. On the other hand, the threephase AC current drawn by the converter in rectifier mode and injected by the converter in inverter mode, is presented in
Fig. 5(c)
. During the rectifier mode, the current drawn by the converter is controlled using PI controller at a value of 6 A (peak) for each phase current.
Fig. 5(c)
shows that, each phase AC current is accurately tracking the reference value, which verifies the feasibility of the model predictive control method. In inverter mode, the reference current is also fixed at a value of 6 A (peak) per phase. Therefore, the output current corroborates the accuracy of the proposed control method by accurately tracking the reference current. Furthermore, the MPC algorithm effectively reduces the THD of AC current by accurately tracking the sinusoidal reference current, which is presented in
Fig. 5(e)
.
The DC bus voltage and current are depicted in
Fig. 5(d)
. The DC voltage pulsations are very low in both the operating modes. The instantaneous operatingmode changing capability is one of the most attractive advantages of the converter with model predictive control method. The positive value (5.10 A) of DC current means that, the bidirectional ACDC converter is working in rectifier mode and the power is transferring from threephase AC source to energy storage device. On the other hand, the DC current goes to negative value (–5.05 A) during the inverter mode of operation.
Simulation results of the bidirectional ACDC converter for both rectifier and inverter mode: (a) AC phase voltage and current; (b) phase to phase AC voltage generated by the converter; (c) threephase AC current; (d) DC bus voltage and current and (e) AC current tracking with reference.
5. Experimental Verifications
A 3.0 kW scaled down laboratory prototype of the bidirectional ACDC converter that has been developed for the energy storage system. The experimental setup is presented in
Fig. 6
. The same parameters as in
Table 2
are employed. During the experimentation, a threephase portable power supply [KOSIJAYA, MODEL: KA19530] was used for voltage supply and STMICROELECTRONICS  STGW20NC60VD – IGBT, 600V, 20A was used as power devices. Moreover, inductor [SMP, MODEL: 9936.1, S:0004] was used as filter inductor and resistor [TERCO, MODEL: MV1100] was used as a resistive load.
Experimental system of the bidirectional ACDC converter with model predictive control
The experimental verification of the proposed model predictive controlled bidirectional ACDC converter is carried out by using the rapid prototyping and realtime interface system dSPACE with DS1104 control card which consist of Texas Instruments TMS320F240 subprocessor and the Power PC 603e/250 MHz main processor. This dSPACE control desk works together with Mathwork MATLAB/Simulink R2011b realtime workshop and realtime interface (RTI) control cards to implement the proposed MPC algorithm.
The voltage is measured with differential probe [PINTEK DP25] and the current with current transducer [LEM LA 25NP].
Fig. 7(a)
shows that the threephase AC phase voltage and current are exactly in phase during the rectifier operation mode, which ensures the unity power factor. Again in the inverter mode, the converter allows power transfer with unity power factor from the DC voltage bus to AC voltage end by keeping the phase voltage and current with an 180o phase shift, as presented in
Fig. 7(b)
.
The DC bus voltage and current for both operating modes are depicted in
Figs. 7(c)
and
7(d)
. The results illustrate that the DC voltage ripple and the pulsation in DC current are very low during both operating modes.
During rectifier mode, the DClink reference voltage (
V
_{dc}
) is varied from 270 V to 320 V to check the stability and transient responsiveness of the MPC control algorithm.
Figs. 7(a)
and
7(c)
show the experimental results of AC phase current, DC bus voltage and current that have been changed and reached its steady state level within very short time (less than 20 ms). This rapid step change confirms the fast response of the PMC method.
Fig. 7(c)
also shows that the steady state output of DClink voltage and current remain linear in wide range of time with very low voltage and current ripple, which ensure the stability and good performance of the proposed MPC algorithm. Similarly, the stability and responsiveness of the proposed MPC method for ACDC converter have been tested with
Figs. 7(b)
and
7(d)
by varying the AC reference current (
), during the inverter mode of operation.
Finally, the harmonic analysis of threephase AC current for both rectifier and inverter mode is illustrated in
Figs. 7(e)
and
7(f)
, which show that the total harmonic distortion (THD) is 3.3% and 3.5% in the rectifier and inverter modes, respectively. The THD of grid current is measured with FLUKE 1735 Power Logger. The accuracy of this power logger is ±0.2% of its full scale.
Experimental results: (a) AC phase voltage and current at rectifier mode; (b) AC phase voltage and current at inverter mode; (c) DC bus voltage and current at rectifier mode; (d) DC bus voltage and current at inverter mode; (e) THD of AC current at rectifier mode, and (f) THD of AC current at inverter mode.
6. Efficiency Comparison
The efficiency of MPC controlled bidirectional ACDC converter is measured with FLUKE 1735 Power Logger. The accuracy of this power logger is ±0.2% of its full scale. The efficiencies of ACDC converter are measured in MPC method against the power transfer ranges from 0.5 kW to 3.0 kW. In order to confirm the effectiveness of MPC algorithm, the efficiencies of MPC controlled bidirectional ACDC converter are compared with conventional VOCbased PWM controlled bidirectional ACDC converter for both the rectifier and inverter mode of operation, presented in
Fig. 8
and
Fig. 9
. The VOCbased PWM method is applied in the 3.0 kW bidirectional ACDC converter topology with employing the same parameters and measurement techniques as in MPC algorithm. Although, MPC algorithm has variable switching frequency problem, the efficiencies associated with the MPC control are higher compared to the VOCbased PWM control method due to the elimination of reactive power, minimized DC voltage ripple and low THD level.
Fig. 8
shows the efficiency comparison of the converter in rectifier mode. The maximum efficiency is 96.8% using the MPC method and it is 95.6% using the VOCbased PWM method, at the power transfer of 2 kW. On the other hand,
Fig. 9
describes the efficiency comparison of proposed MPC controlled ACDC converter with the conventional VOCbased PWM controlled converter during the inverter mode. The maximum efficiency associated with the MPC control algorithm is 96%, while the highest efficiency associated with VOCbased PWM controller is 95% during the inverter mode of operation at 2.0 kW. It can be seen that the efficiencies of the bidirectional ACDC converter decrease with the increase of the power transfer. The flow of current increases with the power transfer which results the increase of conduction and switching loss. But, still the MPC algorithm shows the better efficiency than the VOCbased PWM control method for the whole ranges of power transfer.
Efficiency comparison between MPC and VOCbased PWM control method during rectifier mode of operation.
Efficiency comparison between MPC and VOCbased PWM control method during inverter mode of operation.
7. Conclusion
In this paper, a model predictive controlled bidirectional ACDC converter is presented for energy storage system to transfer power between threephase AC voltage source and DC voltage bus. MPC is a powerful control algorithm in the field of bidirectional ACDC power converters which provides bidirectional power flow with instantaneous mode changing capability and fast dynamic response. The most important outcomes of this investigation are as follows:

The threephase bidirectional ACDC converter is operated with unity power factor in both the rectifier and inverter modes of operation.

The total harmonic distortions (THD) are 3.3% and 3.5% during the rectifier and inverter operating modes, respectively, which are within the accepted limit.

The DC voltage and current ripples are very low during both operating mode.

Higher efficiency achieved compared to the VOC PWM method.
The results associated in this investigation are very much encouraging and will continue to play a strategic role in the improvement of modern high performance bidirectional ACDC converter in energy storage system and will open a new prospect in the power electronics research.
Acknowledgements
The authors would like to thank the Ministry of Higher Education and University of Malaya for providing financial support through HIRMOHE project UM.C/HIR/MOHE/ ENG/24 and UMRG project No. RP006E13ICT.
BIO
Md. Parvez Akter was born in Pabna, Bangladesh. He received the B.Sc. degree from Chittagong University of Engineering and Technology (CUET), Chittagong, Bangladesh, in 2011. In 2011, He joined the Research and Development (R&D) department of the HAMKO Corporation Ltd, Bangladesh as an Executive Engineer. Currently he is continuing the M.Sc. degree and working as a research assistant with the Power Electronics and Renewable Energy Research Laboratory (PEARL), Department of Electrical Engineering, University of Malaya, Kuala Lumpur, Malaysia. His research interest is on power converters and electrical drives, bidirectional power conversion techniques, predictive and digital control, renewable energy, and wireless power transfer.
Saad Mekhilef received the B.Eng. degree in Electrical Engineering from the University of Setif, Setif, Algeria, in 1995, and the Master of Engineering Science and Ph.D. degrees from the University of Malaya, Kuala Lumpur, Malaysia, in 1998 and 2003, respectively. He is currently a Professor at the Department of Electrical Engineering, University of Malaya, Kuala Lumpur. He is the author or coauthor of more than 250 publications in international journals and proceedings. He is a Senior Member of the IEEE. He is actively involved in industrial consultancy, for major corporations in the power electronics projects. His research interests include power conversion techniques, control of power converters, renewable energy, and energy efficiency.
Nadia Mei Lin Tan was born in Kuala Lumpur, Malaysia. She received the B.Eng. (Hons.) degree from the University of Sheffield, Sheffield, U.K., in 2002, the M. Eng. degree from Universiti Tenaga Nasional, Kajang, Malaysia, in 2007, and the Ph.D. degree from Tokyo Institute of Technology, Tokyo, Japan, in 2010, all in electrical engineering. Since October 2010, she has been a Senior Lecturer in the Department of Electrical Power Engineering, Universiti Tenaga Nasional. Her current research interests include power conversion systems and bidirectional isolated dc–dc converters. Dr. Tan is a Graduate Member of the Institution of Engineers Malaysia (IEM) and a Member of the Institution of Engineering and Technology (IET).
Hirofumi Akagi was born in Okayama, Japan, in 1951. He received the B.S. degree from the Nagoya Institute of Technology, Nagoya, Japan, in 1974, and the M. S. and Ph. D. degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1976 and 1979, respectively, all in electrical engineering. In 1979, he was with the Nagaoka University of Technology, Nagaoka, Japan, as an Assistant and then Associate Professor in the Department of Electrical Engineering. In 1987, he was a Visiting Scientist at the Massachusetts Institute of Technology, Cambridge, MA, for ten months. From 1991 to 1999, he was a Professor in the Department of Electrical Engineering, Okayama University, Okayama, Japan. From March to August of 1996, he was a Visiting Professor at the University of Wisconsin, Madison, and then the Massachusetts Institute of Technology. Since January 2000, he has been a Professor in the Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Tokyo, Japan. His research interests include power conversion systems, ac motor drives, active and passive EMI filters, highfrequency resonant inverters for induction heating and corona discharge treatment processes, and utility applications of power electronics such as active filters for power conditioning, selfcommutated BTB systems, and FACTS devices. He has authored or coauthored more than 80 IEEE Transactions papers, and two invited papers in Proceedings of the IEEE. According to Google Scholar, the total citation index for all his papers is more than 6,000. He has made presentations many times as a keynote or has been an invited speaker internationally. Since January 2007, he has been the President of the IEEE Power Electronics Society (PELS). He was elected as a Distinguished Lecturer of the IEEE Industry Applications Society (IAS) and PELS for 1998–1999. He received two IEEE IAS Transactions Prize Paper Awards in 1991 and 2004, and two IEEE PELS Transactions Prize Paper Awards in 1999, and in 2003, nine IEEE IAS Committee Prize Paper Awards, the 2001 IEEE William E. Newell Power Electronics Award, the 2004 IEEE IAS Outstanding Achievement Award, and the 2008 IEEE Richard H. Kaufmann Technical Field Award.
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