Power Management of a Stand-AloneWind/Photovoltaic/Fuel Cell Energy SystemCaisheng Wang, Senior Member, IEEE, and M. Hashem Nehrir, Senior Member, IEEEAbstractThis paper proposes an ac-linked hybrid wind/ photovoltaic (PV)/fuel cell (FC) alternative energy system for stand-alone applications. Wind and PV are the primary power sources of the system, and an FCelectrolyzer combination is used as a backup and a long-term storage system. An overall power management strategy is designed for the proposed system to man- age power flows among the different energy sources and the storage unit in the system. A simulation model for the hybrid energy system has been developed using MATLAB/Simulink. The system perfor- mance under different scenarios has been verified by carrying out simulation studies using a practical load demand profile and real weather data.Index TermsAlternative energy, electrolyzer, fuel cell (FC), hybrid, photovoltaic (PV), power management, stand-alone, wind.I. INTRODUCTIONHE EVER increasing energy consumption, the soaring cost and the exhaustible nature of fossil fuel, and the worsening global environment have created increased interest in green [renewable and/or fuel celll (FC)-based energy sources] power generation systems. Wind and solar power generation are two of the most promising renewable power generation tech- nologies. The growth of wind and photovoltaic (PV) power generation systems has exceeded the most optimistic estima- tion [1][3]. FCs also show great potential to be green power sources of the future because of many merits they have (such as high efficiency, zero or low emission of pollutant gases, and flexible modular structure) and the rapid progress in FC tech- nologies. However, each of the aforementioned technologies has its own drawbacks. For instance, wind and solar power are highly dependent on climate while FCs need hydrogen-rich fuel. Nevertheless, because different alternative energy sources can complement each other to some extent, multisource hybrid alter- native energy systems (with proper control) have great potential to provide higher quality and more reliable power to customers than a system based on a single resource. Because of this fea- ture, hybrid energy systems have caught worldwide researchattention [4][28].

Manuscript received August 14, 2006; revised December 27, 2006. This work was supported in part by the National Science Foundation (NSF) Grant ECS-

0135229 and in part by the HiTEC fuel cell project at Montana State University,

funded by the United States Department of Energy, as a subcontract from Bat- telle Memorial Institute and Pacific Northwest National Laboratory (PNNL) under Award DE-AC06-76RL01830. Paper No. TEC-00399-2006.

C. Wang is with the Division of Engineering Technology, Wayne State Uni-versity, Detroit, MI 48202 USA (e-mail: caisheng.wang@gmail.com).M. H. Nehrir is with the Electrical and Computer Engineering Department, Montana State University, Bozeman, MT 59717 USA (e-mail: hnehrir@ ece.montana.edu).

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/TEC.2007.914200

Many alternative energy sources including wind, PV, FC, diesel system, gas turbine, and microturbine can be used to build a hybrid energy system [4][28]. Nevertheless, the major renewable energy sources used and reported are wind and PV power [4][28]. Due to the intermittent nature of wind and solar energy, stand-alone wind and PV energy systems normally require energy storage devices or some other generation sources to form a hybrid system. The storage device can be a battery bank, supercapacitor bank, superconducting magnetic energy storage (SMES), or an FCelectrolyzer system.

In this paper, a stand-alone hybrid alternative energy system consisting of wind, PV, FC, electrolyzer, and battery is proposed. Wind and PV are the primary power sources of the system to take full advantage of renewable energy, and the FCelectrolyzer combination is used as a backup and a long-term storage system. A battery bank is also used in the system for short-time backup to supply transient power. The different energy/storage sources in the proposed system are integrated through an ac link bus. The details of the system configuration, system unit-sizing, and the characteristics of the major system components are also discussed in the paper. An overall power management strategy is designed for the system to coordinate the power flows among the different energy sources. Simulation studies have been carried out to verify the system performance under different scenarios using practical load profile and real weather data.

The paper is organized as follows. The system configuration and system unit-sizing are discussed in Section II. The system component characteristics are given in Section III. Section IV discusses the overall power management strategy for the system. Section V gives the simulation results. Section VI concludes the paper.

II. SYSTEM CONFIGURATION AND UNIT-SIZING

A. System ConfigurationFig. 1 shows the system configuration for the proposed hy- brid alternative energy system. In the system, the renewable wind and PV power are taken as the primary source while the FCelectrolyzer combination is used as a backup and storage system. This system can be considered as a complete green power generation system because the main energy sources and storage system are all environmentally friendly. When there is excess wind and/or solar generation available, the electrolyzer turns on to begin producing hydrogen, which is delivered to the hydrogen storage tanks. If the H2 storage tanks become full, the excess power will be diverted to the dump load shown in Fig. 1. When there is a deficit in power generation, the FC stack will begin to produce energy using hydrogen from the reservoir

0885-8969/$25.00 2008 IEEE

Fig. 2. Hourly average demand of five typical homes in the Pacific Northwest area.

The hybrid system is designed to supply power to five homes. A typical hourly average residential load demand for a home in the Pacific Northwest regions, reported in [29], is used in this simulation study. The total hourly average load demand of the five homes is shown in Fig. 2. A 50 kW wind turbine is assumed to be available for the hybrid system. The following unit-sizing procedure is used to determine the size of the PV array, FC stack, electrolyzer, and the battery.

Before the discussion of unit-sizing, the following concept is applied for indicating the overall efficiency and the availability of a renewable energy source.

Capacity factor (kcf ) of a renewable energy source is definedasFig. 1. System configuration of the proposed multisource alternative hybrid energy system (coupling inductors are not shown).

kcf =

PPra te d

(1)

tanks, or in case they are empty, from the backup H2 tanks. A battery bank is also used in the system to supply transient power to load transients, ripples, and spikes. There are several ways to integrate different alternative energy sources to form a hybrid system. Each method has its own advantages and disadvantages. In this paper, a 60 Hz ac link is used due to its high reliability, modular and scalable structure, and readiness for grid connec- tion [25], [27]. Different energy sources are connected to the ac bus through appropriate power electronic interfacing circuits. The system can be easily expended, i.e., other energy sources can be integrated into the system when they are available, as shown in Fig. 1. The main system unit-sizing is discussed in the following section.

B. System Unit-SizingThe unit-sizing procedure discussed in this section is assumed for a stand-alone hybrid system with the proposed structure

where P is the actual average output power over a period of time and Pra te d is the nominal power rating of the renewable energy source.

For the wind and solar data reported in [5] and [20], the capac- ity factor of the wind turbine (kcf wtg ) and the PV array (kcf PV ) used in the proposed hybrid system for the southwestern part of Montana are taken as 13% and 10%, respectively.

The purpose of unit-sizing is to minimize the difference be- tween the generated power (Pge n ) from the renewable energy source and the demand (Pde m ) over a period of time T . T is taken as one year in this study:

P = Pge n Pde m= kcf wtg Pwtg ,ra te d + kcf PV PPV ,ra te d Pde m(2)where Pwtg ,ra te d is the power rating of the wind turbine gener- ator and PPV ,ra te d is the power rating of the PV array.

To balance the generation and demand, the rated power for the PV array is

(Fig. 1) for residential electricity supply in the southwestern

part of Montana. The purpose of the study is to properly size the system components to assure reliable electricity supply. Hence,

PPV ,ra te d =

Pde m

kcf wtg kcf PV

Pwtg ,ra te d

. (3)

the systems economic aspect is not considered in the paper. Some details on the economics of similar wind/PV/FC systems are given in another paper by the authors [5].

From Fig. 2, the average load demand is 9.76 kW. Then, according to (3), the size of the PV array is calculated to be

32.6 kW.

TABLE ISYSTEM COMPONENT PARAMETERS

Fig. 3. Cp characteristics of the WECS at different pitch angles ().

Battery capacity can be determined based on the transient power at the load site. In this study, a 10 kWh battery bank is used. In single-phase systems, a larger size battery may be needed for reactive power compensation purposes. In three- phase systems, as discussed in this paper, reactive power com- pensation can be achieved by proper control of power electronic switching devices [39], and only a small size battery is needed for this purpose [40].

The details of the system component parameters are listed in

Table I.III. SYSTEM COMPONENT CHARACTERISTICS

To develop an overall power management strategy for the sys- tem and to investigate the system performance, dynamic models for the main components in the proposed hybrid system have been developed using MATLAB/Simulink [27]. The models are for the following: wind energy conversion system (WECS), PV, FC, and electrolyzer.

In this section, the characteristics of the aforementioned main system components are discussed. For the details of model de- velopment, the reader is referred to [27].

A. Wind Energy Conversion SystemThe power Pwin d (in watts) extracted from wind isThe FCelectrolyzer combination provides backup for the

system. The FC needs to supply the peak load demand (Fig. 2) when there is no wind and solar power. Therefore, the size of the FC stack is 14.6 kW. To leave some safe margin (20% used in this paper), an 18 kW FC array is used.

The electrolyzer should be able to handle the excess power from the wind and solar power source. The maximum possible excess power is

Pge n , ma x Pde m ,min = 50 + 32.6 5.85 = 76.75 kW. (4) However, the possibility that both wind and solar power reach

their maximum points while the load demand is at its lowest value is very small. According to the data reported in [26], the excess available power normally is less than half of the maxi- mum possible value. And the electrolyzer is also very expensive. Therefore, a 50 kW electrolyzer [over 60% of the maximum available given in (4)] is used in this paper.

P = 1 Av3 C (, ) (5)win d 2pwhere is the air density in kilogram per cubic meter, A is the area swept by the rotor blades in square meter, and v is the wind velocity in meters per second. Cp is called the power coefficient or the rotor efficiency and is a function of tip speed ratio (TSR or ) and pitch angle () [30], [31].

A variable-speed pitch-regulated wind turbine is considered in this paper, where the pitch angle controller plays an important role. Fig. 3 shows the groups of Cp curves of the wind turbine used in this study at different pitch angles [31]. It is noted from the figure that the value of Cp can be changed by changing the pitch angle (). In other words, the output power of the wind turbine can be regulated by pitch angle control.

A self-excited induction generator (SEIG) model [27], [37], [38] was developed and used as a part of the WECS model. The ratings of the SEIG are given in Table I.

Fig. 4. Wind turbine output power characteristic.

Fig. 4 shows the output power of the WECS vs. wind speed. It can be observed that the output power is kept constant when wind speed is higher than the rated wind velocity even though the wind turbine has the potential to produce more power. This is done through the pitch angle control to protect the electrical system and to prevent over speeding of the rotor. When wind speed is higher than the cutout speed (25 m/s), the system is taken out of operation for protection of its components.

B. PhotovoltaicPV effect is a basic physical process through which solar energy is converted directly into electrical energy. The physics of a PV cell, or a solar cell, is similar to the classical p-n junction diode [32]. The relationship between the output voltage V and the load current I of a PV cell or a module can be expressed as [15], [32]

Fig. 5. IV characteristic curves of the PV model at different irradiances.

I = IL I0

exp

V + IRs 1

(6)

Fig. 6. PV characteristic curves of the PV model at different operating tem- peratures.

where IL is the light current of the PV cell (in amperes), I0 isthe saturation current, I is the load current, V is the PV output

voltage (in volts), Rs is the series resistance of the PV cell (in ohms), and is the thermal voltage timing completion factor of the cell (in volts).

The IV characteristic curves of the PV model used in this study under different irradiances (at 25 C) are given in Fig. 5 [27]. It is noted from the figure that the higher the irradiance, the larger are the short-circuit current (Isc ) and the open-circuit voltage (Voc ). As a result, the larger will be the output PV power. Temperature plays an important role in the PV performance because the four parameters (IL , I0 , Rs , and ) in (6) are all functions of temperature. The effect of the temperature on the PV model performance is illustrated in Fig. 6. It is noted from the figure that the lower the temperature, the higher is the maximumpower and the larger the open circuit voltage.

C. Fuel CellTwo types of FCs have been modeled for this study. They are low-temperature proton-exchange membrane FC (PEMFC) [33] and high-temperature solid oxide FC (SOFC) [34]. Both of

them show great potential in hybrid energy system applications. For the purpose of simplicity, only the PEMFC application is discussed in this paper.

The PEMFC model is based on the validated dynamic model for a PEMFC stack reported in [33]. It is an autonomous model operated under constant channel pressure with no control on the input fuel flow into the FC. The model was validated by experimental data measured from an Avista Labs (ReliOn now) SR-12 500 W PEMFC stack. The FC will adjust the input fuel flow according to its load current to keep the channel pressure constant. Fig. 7 shows the output voltage vs. load current (VI) characteristic curve of the 500 W PEMFC model compared with the experimental data [33]. This characteristic curve can be divided into three regions. The voltage drop across the FC associated with low currents is due to the activation loss inside the FC; the voltage drop in the middle of the curve (which is approximately linear) is due to the ohmic loss in the FC stack; and as a result of the concentration loss, the output voltage at the end of the curve will drop sharply as the load current increases.

Fig. 7. PEMFC VI characteristic: comparison of model response with exper- imental data.

D. ElectrolyzerAn electrolyzer is a device that produces hydrogen and oxy- gen from water. Water electrolysis can be considered a reverse process of a hydrogen-fueled FC. In contrast to the electro- chemical reaction occurring in an FC to produce dc electricity, an electrolyzer converts dc electrical energy into chemical en- ergy stored in hydrogen. From electrical circuit point of view, an electrolyzer can be considered as a voltage-sensitive nonlinear dc load [15]. For a given electrolyzer, within its rating range, the higher the dc voltage applied, the larger is the load current. That is, by applying a higher dc voltage, more H2 can be generated. Of course, more electrical power is consumed at the same time. The model of an electrolyzer stack developed for this study is based on the empirical IV equation reported in [15] and [26], described as

r1 + r2 T

Fig. 8. VI characteristics of the electrolyzer model under different tempera- tures.

IV. OVERALL POWER MANAGEMENT STRATEGY

An overall control strategy for power management among dif- ferent energy sources in a multisource energy system is needed. Fig. 9 shows the block diagram of the overall control strategy for the proposed hybrid alternative energy system. The WECS, controlled by a pitch angle controller, and a PV electricity gen- eration unit, controlled by a maximum power point tracking (MPPT) controller (not discussed in this paper) [27], are the main energy sources of the system. The power difference be- tween the generation sources and the load demand is calculated as

Pne t = Pwin d + PPV Pload Psc (8)where Pwin d is the power generated by the WECS, PPV is the power generated by the PV energy conversion system, Pload is the load demand, and Psc is the self-consumed power for operating the system. The system self-consumed power is the power consumed by the auxiliary system components to keep it running, for example, the power needed for running the cool- ing systems, the control units, and the gas compressor. For the

Velec ,cell = Vre v ++ kelec ln

IA kT 1 + kT 2 /T + kT 3 /T 2A

I +1

(7)

purpose of simplification, only the power consumed by the com- pressor (Pco m p ) is considered in this study.

The governing control strategy is that, at any given time, anyexcess wind and PV-generated power (Pne t > 0) is supplied to the electrolyzer to generate hydrogen that is delivered to the

where Velec ,cell is the cell terminal voltage (in volts), Vre v is the reversible cell voltage, r1 (in ohms square-meter) and r2 (in ohms square-meter per degree Celsius) are the parameters for the ohmic resistance inside the electrolyzer, kelec (in volts), kT 1 (in square meters per ampere), kT 2 (square-meter degrees Celsius per ampere), and kT 3 (square-meter degree Celsius square per ampere) are the parameters for the overvoltage, A is the area of the cell electrode (in square-meters), I is the electrolyzer current (in amperes), and T is the cell temperature (in degrees Celsius). The VI characteristics of the electrolyzer model used in this study at different cell temperatures are given in Fig. 8. At a given current, the higher the operating temperature, the lower isthe terminal voltage needed.

hydrogen storage tanks through a gas compressor. Therefore, the power balance equation given in (8) can be written as

Pwin d + PPV = Pload + Pelec + Pco m p , Pne t > 0(9)where Pelec is the power consumed by the electrolyzer to gener- ate H2 and Pco m p is the power consumed by the gas compressor. When there is a deficit in power generation (Pne t < 0), the FC stack begins to produce energy for the load using hydrogen from the storage tanks. Therefore, the power balance equationfor this situation can be written as

Pwin d + PPV + PFC = Pload , Pne t < 0(10)where PFC is the power generated by the FC stack.

Fig. 9. Block diagram of the overall control scheme for the proposed hybrid alternative energy system.

Dynamic models have been used for all the components of the system shown in Fig. 9. The details of these models can be found in [27].

V. SIMULATION RESULTSUsing the component models discussed in Section IV, a

A. Winter Scenario1) Weather Data: The weather data for the winter scenario simulation were collected on February 1, 2006. The wind speed data were collected at the height of 2 m, corrected to the turbine hub height (assumed to be 40 m) using the following expression [20], [36]:

H1 simulation system test bed for the proposed wind/PV/FC

electrolyzer energy system has been developed using

Ws 1 = Ws 00

(11)

MATLAB/Simulink. In order to verify the system performance under different situations, simulation studies have been carried out using practical load demand data and real weather data (wind speed, solar irradiance, and air temperature). As dis- cussed in Section II, the system is designed to supply electric power demand of five houses in the southwestern part of Montana. A typical hourly average load demand for a house in the Pacific Northwest regions, reported in [29], is used in this simulation study. The total hourly average load demand profile of five houses over 24 h is shown in Fig. 2. The weather data are obtained from the online records of the weather station at Deer Lodge, Montana, affiliated with the Pacific Northwest Coopera- tive Agricultural Weather Network (AgriMet) [35]. Simulation studies are carried out for power management during a typical winter day and a summer day. The load demand is kept the same for the two cases. Simulation results for the winter and summer scenarios are given and discussed in the following section.

where Ws 1 (in meters per second) is the wind speed at the hub height H1 (in meters), Ws 0 (in meters per second) is the wind speed at the height H0 (in meters), and is the wind speed correction exponent. The exponent is taken as 0.13 in this study, as suggested and used in [20] and [36].

Fig. 10 shows the corrected hourly wind speed profile over

24 h on the day (February 1, 2006) the data were collected. The hourly solar irradiance data and air temperature collected on the same day are shown in Figs. 11 and 12, respectively.

2) Simulation Results: The system performance under the load profile given in Fig. 2 and the weather data shown in Figs. 1012 is evaluated and discussed later.

The output power from the wind energy conversion unit in the hybrid energy system over the 24 h simulation period is shown in Fig. 13. When the wind speed is over 14 m/s, the output power is limited to 50 kW by the pitch angle controller (discussed in Section III). When the wind speed is less than the wind turbine cutin speed (3 m/s), there is no wind power generated.

Fig. 10. Wind speed data for the winter scenario simulation study.

Fig. 11. Solar irradiance data for the winter scenario simulation study.

Fig. 12. Air temperature data for the winter scenario simulation study.

The output power from the PV array in the system over the

24 h simulation period is shown in Fig. 14. As shown in Fig. 9, the PV array output power is controlled by an MPPT controller to give maximum power output under different solar irradiances. It is noted that the PV output power curve, shown in Fig. 14,

Fig. 13. Wind power for the winter scenario study.

Fig. 14. PV power for the winter scenario.

has a wave shape similar to that of the solar irradiance profile shown in Fig. 11.

As discussed in Section III (Fig. 6), temperature plays an im- portant role in the PV modules performance. Fig. 15 shows the PV temperature response over the simulation period. Two main factors for determining the temperature of the PV module are the solar irradiance (Fig. 11) and the surrounding air temperature (Fig. 12). It is noted from Fig. 6 that the higher the temperature, the lower is the maximum power value. Figs. 14 and 15 also show the effect of temperature upon the PV performance.

When Pne t > 0 [see (8) and (9)], there is excess power avail- able for H2 generation. Fig. 16 shows the available power profile over the 24 h simulation period. The available power is used by the electrolyzer to generate H2 . Fig. 17 shows the H2 gener- ation rate over the simulation period. The corresponding dc voltage applied to the electrolyzer and the electrolyzer current are shown in Fig. 18. It is noted from Figs. 1618 that the more power available for storage, the higher is the dc input voltage to the electrolyzer, and as a result, the more is the generated H2 .

When Pne t < 0, the sum of wind and PV-generated power isnot sufficient to supply the load demand. Under this condition,

Fig. 15. PV temperature response over the simulation period for the winter scenario.

Fig. 16. Power available for H2 generation of the winter scenario.

Fig. 17. H2 generation rate for the winter scenario study.

the FC turns on to supply the power shortage. Fig. 19 shows the actual power delivered by the FC stack.

B. Summer Scenario1) Weather Data: The weather data collected in Dear Lodge, MT, on June 21, 2005, are used for the summer scenario study [35]. The wind speed data, corrected to the height of 40 m, is shown in Fig. 20. The solar irradiance and air temperature data at the same site on the same day are shown in Figs. 21 and 22, respectively.

Fig. 18. Electrolyzer voltage and current for the winter scenario study.

Fig. 19. Power supplied by the FC stack of the winter scenario study.

Fig. 20. Corrected wind speed data for the summer scenario simulation study.

By comparing the winter solar irradiance data shown in Fig. 11 and the summer solar irradiance data given in Fig. 21, it is obvious that the daily time frame when solar energy is available is wider in the summer than in the winter.

2) Simulation Results: In this section, the system perfor- mance under the same load demand profile given in Fig. 2 and the weather data shown in Figs. 2022 is evaluated. The output power from the WECS and the PV array in the hybrid energy system over the 24 h simulation period are shown in Figs. 23 and

24, respectively. The spikes in Fig. 24 are due to the MPPT con- trol, which tries to keep the PV array operating at its maximum

Fig. 21. Irradiance data for the summer scenario simulation study.

Fig. 22. Air temperature data for the summer scenario simulation study.

Fig. 24. PV power generated for the summer scenario study.

Fig. 23. Wind power generated for the summer scenario study.

power points under different temperatures and solar irradiances. The time range of the spike is small (about 1 s).

When Pne t > 0, there is excess power available for H2 gen- eration. Fig. 25 shows the H2 generation rate over the simu- lation period. When Pne t < 0, the sum of the wind and the PV-generated power is not sufficient to supply the load demand. Under this scenario, the FC stack turns on to supply the power shortage by using the H2 stored in the storage tank. Fig. 26 shows the corresponding H2 consumption rate.

Fig. 25. H2 generation rate for the summer scenario study.

Fig. 26. H2 consumption rate for the summer scenario study.

The H2 storage tank pressure varies as H2 flows in and out. It is apparent that the storage tank pressure will go up when there is excess power available for H2 generation and will decrease when the FC stack turns on (consuming H2 ) to supply power to the load. Fig. 27 shows the tank pressure variations over the

24 h simulation period for the summer scenario study.

Fig. 27. Tank pressure over the 24 h for the summer scenario study.

VI. CONCLUSIONIn this paper, an ac-linked stand-alone wind/PV/FC alterna- tive energy system is proposed. The system configuration and unit-sizing are discussed; the characteristics of the main compo- nents in the system, namely, the WECS, PV, FC, and electrolyzer are given; and the overall control and power management strat- egy for the proposed hybrid energy system is presented. The wind and PV generation systems are the main power genera- tion devices, and the electrolyzer acts as a dump load using any excess power available to produce H2 . The FC system is the backup generation and supplies power to the system when there is power deficit. The simulation model of the hybrid system has been developed using MATLAB/Simulink. Simulation studies have been carried out to verify the system performance under different scenarios using the practical load profile in the Pacific Northwest regions and the real weather data collected at Deer Lodge, MT. The simulation results, given for a winter and a summer scenario, show the effectiveness of the overall power management strategy and the feasibility of the proposed hybrid alternative energy system.

ACKNOWLEDGMENTThe authors thank Dr. D. Pierre at Montana State University for his comments and suggestions.

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1984.

M. Hashem Nehrir (S68M71SM89) received the B.S., M.S., and Ph.D. degrees from Oregon State University, Corvallis, in 1969, 1971, and 1978, respectively, all in electrical engineering.

Since 1987, he has been with the Electrical and

Computer Engineering Department, Montana State University, Bozeman, where he is currently a Pro- fessor. His current research interests include control and modeling of power systems, alternative energy power generation systems, and application of intelli- gent controls to power systems. He is the author of

two textbooks and an author or coauthor of numerous technical papers.

Caisheng Wang (M02SM08) received the B.S. and M.S. degrees from Chongqing University, Chongqing, China, in 1994 and 1997, respec- tively, and the Ph.D. degree from Montana State University, Bozeman, in 2006, all in electrical engineering.

From August 1997 to May 2002, he was an Elec- trical Engineer at Zhejiang Electric Power Test and Research Institute, Hangzhou, China. Since August

2006, he has been a faulty member in the Division of Engineering Technology, Wayne State University,

Detroit, MI. His current research interests include modeling and control of power systems and electrical machinery, alternative/hybrid energy power generation

systems, and fault diagnosis and online monitoring of electric machines.

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