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Abstract-- A detailed electrical model of a wind turbine system equipped with a permanent magnet alternator (PMA), diode rectifier, boost dc to dc converter and inverter is presented. The power conversion system topology is explained and the electrical model of each component is presented. Based on this electrical model, a Simulink model of the system is constructed. The simulation was implemented in the power system simulation tools in MatLab SIMULINK. The output curves of the Simulink model (currents, power and voltages) and the actual measurement at the same wind speed taken from the actual operation of the 2.4 kW wind turbine installed at UMass-Lowell are in good agreement. The analysis of the results demonstrates the effectiveness of the constructed Simulink model which can be used to predict the performance of the wind turbine generator system. The steady state performance of the said wind turbine is also presented.

Index Terms-- Modeling, Renewable Energy, Wind Turbine

I. INTRODUCTION N recent years, the electrical power generation from renewable energy sources, such as wind, is increasingly

attracting interest because of environmental problem and shortage of traditional energy source in the near future [1]. There are two configurations used for wind energy conversion system; the stand-alone or autonomous systems and utility or grid-connected systems. Stand-alone systems directly supply electrical load especially in remote areas which will eliminate the need for extensive transmission lines from a utility. However, as wind is an ever-changing energy source, power generation is not always possible in stand-alone systems without some sort of energy storage. Hence, interaction with a utility is required in most cases to ensure continuous power supply. Another advantage is that, excess electricity can be sold to the grid. Utility-connected systems thus guarantee a backup energy source in situations where wind availability is insufficient [1]. The wind power mainly depends on geographic and weather conditions and varies from time-to-time. Therefore, it is necessary to construct a system that can generate maximum power for all operating conditions.

A. B. Cultura II is with the Department of Electrical Engineering,

Mindanao University of Science and Technology, Lapasan, Cagayan de Oro, Philippines (e-mail: acultura2003@yahoo.com).

Z. M. Salameh is with the Department of Electrical and Computer Engineering, University of Massachusetts Lowell, MA, 01854 USA (e-mail: ziyad_salameh@uml.edu).

Recently, permanent magnet alternator (PMA) is used for wind power generating system because of its advantages such as better reliability, lower maintenance and more efficient [1], [2].

In order to achieve variable speed operation, a power electronics converter interface is used to connect the generator to the grid as illustrated in Fig 2. The converter consists of an uncontrolled 3-phase diode rectifier, a DC/DC boost converter, a single-phase PWM voltage source inverter and possibly a step-up transformer. In this paper, the modeling of the generator and power electronics interface is presented in the steady state condition [2]. Power electronics have an important role for controlling electrical characteristics of wind turbines. For the simulation of wind turbine generator in a grid connected applications, DC-DC boost converters have been used for modifying the electrical load in order to maximize energy generation. Input of the DC-DC converter is connected to bridge rectifier and the output is connected to the input of the inverter. This scheme with a proper control algorithm to modify duty-cycle of DC-DC converter and the modulation index of inverter is used to control the voltage generated by the system. Thus, the aim of this paper is to investigate the performance of a grid connected permanent magnet wind generator and to predict the output based on the given wind speed data. The authors derived and presented the following models: wind turbine, permanent magnet generator, rectifier, dc-dc converter and inverter. Then simulink model was constructed and implemented using the power system simulation tools in MatLab SIMULINK. This model is used to predict the performance of the wind turbine generator system. It predicts the power output, the current and the output voltage at a certain average wind speed. A 2.4 kW nominal wind turbine is installed on the roof of Ball Hall building of UMass –Lowell, Fig. 1.

Fig. 1. A 2.4kW Wind Turbine at UMass Lowell

Modeling and Simulation of a Wind Turbine-Generator System

A. B. Cultura II, Student Member, IEEE, and Z. M. Salameh, Senior Member, IEEE

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978-1-4577-1002-5/11/$26.00 ©2011 IEEE

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II. SYSTEM DESIGN AND MODELING

A. Wind Tturbine-Generator Power System Design The system used a high efficiency low speed permanent

magnet wind generator (PMWG) where gear box has been eliminated. In low-speed permanent magnet alternator, the rotor rotates at the same speed as the rotor of the turbine. The PMA is connected directly to the wind turbine, which results in a simple mechanical system [3].

The system is composed of a permanent magnet alternator, rectifier, dc-dc converter and inverter as shown in block diagram in Fig. 2. The voltage generated by the permanent magnet machine is rectified using a three-phase passive rectifier, which converts the AC voltage generated by the PMA to a DC voltage. The DC output voltage is boosted to a higher dc voltage. This dc voltage is then converted to ac voltage using a pulse width modulated (PWM) inverter which is connected to the grid.

Fig. 2. Wind Power System Block Diagram

B. System Modeling

1. Modeling of the Wind Turbine

A wind turbine extracts energy from moving air by slowing the wind down, and transferring this harvested energy into a spinning shaft, which usually turns an alternator or generator to produce electricity. The power available at the shaft depends on both the wind speed and the area that’s swept by the turbine blades which is given as [3], [6];

3),(5.0 vACP PS ρβλ= (1) Where: ρ = air density (kg/m3)

A = swept area (m2) V = wind speed (m/s) Cp = power coefficient or aerodynamic efficiency λ = tip speed ration of the rotor blade tip speed

to wind speed ß = blade pitch angle (degree)

The equation below is used to model the performance

coefficient of the turbine based on the modeling turbine characteristics of [1], is;

λβλ

λ643

21

5

ceccccC i

c

ip +⎟⎟

⎠

⎞⎜⎜⎝

⎛−−=

−

(2)

where:

1035.0

08.011

2 +−

+=

ββλλi

c1 = 0.5176; c2 = 116; c3 = 0.4; c4 = 5; c5 = 21; c6 = 0.0068

2. Modeling of the PM Alternator Permanent magnet (PM) machines are a well-known class

of rotating and linear electric machines used in both the motoring and generating modes. PM machines have been used for many years in applications where simplicity of structure and a low initial cost were of primary importance. More recently, PM machines have been applied to wind energy applications, primarily as the result of the availability of low-cost power electronic control devices and the improvement of permanent magnet characteristics [3]. Permanent magnet alternator is used for wind power generating system because of its advantages such as better reliability, lower maintenance, and more efficient [4]. The equivalent circuit for one phase is represented in Fig. 3.

Fig. 3. Equivalent Circuit of PMA for one phase system

The magnitude of the generated rms electromotive force (emf) E is given by ϖφ1kE = (3) Where: φ = constant for permanent magnet generator ϖkE = The terminal power per phase can be solve as,

LL

RXRR

EP 22

2

)( ++=

3

LL

L RkR

XRRkP

22

22

22

)(ϖϖ =

++= (4)

Where: k is the machine constant and ω the

rotational speed in rad/s.

3. Three-phase Diode Bridge Rectifier

The diode rectifier is most commonly used topology in

converting AC to DC voltage output. The circuit is shown in Fig. 4. The AC power generated from the generator is converted into DC power through diode bridge rectifier circuits [4].

Fig. 4. Equivalent circuit of a diode bridge rectifier

The dc output voltage (Vdc) is calculated as the average of the output voltage waveform over a sub-period from /6 to /2 [6],

gdcdc VdvVπ

θπ

π

π

233/

1 2/

6/1 == ∫ (5)

π

231 =g

dc

VV

And the dc output current can be solved as,

13/

2

321

dcdcg IdII == ∫π

π

θπ

(6)

32

1

=dc

g

II

(7)

Neglecting the power losses in three-phase rectifier, the AC power input is equal to dc power output,

113 dcdcgg VIVI =

Hence, the dc output current can be expressed as,

2

3

11

g

dc

ggdc

IV

VII

π== or

21g

dc

ii

π= (8)

4. Modeling of a dc-dc Boost Converter

The voltage and current equations of a dc-dc converter

under steady-state conditions can be found by using the two basic principles namely; the principle of inductor volt-second balance and the principle of capacitor amp-second or charge balance. The principle of inductor volt-second balance states that the average value, or dc component of voltage applied across an ideal inductor winding must be zero and the principle of capacitor amp-second or charge balance, states that the average current that flows through an ideal capacitor must be zero. Thus, to determine the voltages and currents of dc-dc converters operating in periodic steady state, one averages the inductor current and capacitor voltage waveforms over one switching period, and equates the results to zero [1]. Based on this power circuit on Fig. 5, the output voltage, inductor current and output current are being derived.

Fig. 5. Power circuit of a dc-dc converter

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−=

load

L

dcdc

RDRD

VV

2

12

)1(11

(9)

Assuming a lossless circuit, 2211 dcdcdcdc IVIV =

( ) 122 )1(11 dc

load

Ldc I

RDRDI ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+−= (10)

5. Single-Phase Inverter with Sinusoidal PWM

The sinusoidal PWM Inverter is commonly used in many

industrial applications. There are various techniques to vary the inverter gain. The most efficient method of controlling the

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output voltage is to incorporate PWM control within the inverters. In this modeling, a sinusoidal PWM control is being considered. The width of each pulse is varied in proportion to the amplitude of a sine wave evaluated at the center of the same pulse. In single and multiple PWM, the output voltage is varied by the pulse-width control and harmonics are profiled by modulation of pulse width or switching frequency [7]. All the PWM schemes may be evaluated under a certain switching frequency and the reference signal frequency ratio, and the input and output voltage ratio, which is also named as the modulation index (a) or the PWM constant. The definition of the modulation index (a) is given in [7];

2dc

L

VV

a =

Where: a = the modulation index

VL = the peak value of the line-to-line voltage Vdc2 = the boost converter output voltage

The on time of switch pair in each of the legs of the single-phase inverter of Fig. 6, is designed to vary sinusoidally. The rms value of the output voltage waveform can be approximated for the large number of pulses per half period as [8]:

22 dcL VaV π= (11)

Fig. 6 Single-phase inverter

Assuming that the power output of the inverter is equal to the power input, LLdcdc IVIV =22

and L

dcdcL V

IVI 22= (12)

Substituting (11) to (12) to solve for IL;

πa

II dcL

22= (13)

The total power output of the system is, Poutave = VLIL (14)

III. THE SIMULINK MODEL The Simulink model is presented in Fig. 7 below. The wind

turbine block implements a variable pitch but in the sample simulation the value of pitch angle was set to zero since performance coefficient (Cp) reaches its maximum value at zero beta. The Cp of the turbine is the mechanical output power of the turbine divided by wind power and a function of wind speed, rotational speed, and pitch angle (beta). The three input parameters of the wind turbine are generator speed in per unit, blade pitch angle in degrees and wind speed in m/s. The output is the torque applied to the permanent magnet alternator shaft. The permanent magnet alternator implements a 3-phase permanent magnet synchronous machine with sinusoidal back EMF. The preset model of the PMSG used was the 24 Nm, 300 Vdc, 41.5 Nm.

Fig 7. Simulink Model of a Wind Turbine Directly Coupled with PMA

The rectifier block implements a bridge of selected power

electronics devices. Series RC snubber circuits are connected in parallel with each switch device. The output of the PMA is rectified to have a dc voltage output. The dc voltage is boosted using the designed Simulink dc-dc boost converter. The duty cycle of the gate driver in a dc-dc converter is adjusted in order to step up the voltage to a certain level. The DC output power is converted to AC for electric utility connection. The PWM inverter uses IGBT power electronic devices. This inverter is used to convert this dc voltage to a comparable ac utility voltage. The controller is used to achieve the optimal operating by keeping the output voltage more or less constant by controlling PWM modulation index of PWM inverter and duty ratio of the boost converter to utilize completely the available wind energy. The LC filter is connected between inverter and load to have a smooth ac

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output voltage. Scopes are added to monitor and plot the output waveform at different points in the wind turbine power system.

IV. SIMULATION RESULTS The detailed modeling of the wind turbine, PM alternator,

the rectifier, the DC-DC converter and the inverter is very important in obtaining the accurate picture of all the system waveforms (voltages, currents, power,). Simulation results for steady state operating conditions are shown in Fig. 8 which are composed of load voltage & current. In the simulation, the three input parameters used were; 1.0 pu generator speed, zero (0) pitch angle and 12 m/s for the wind speed.

Figure 8 represents the steady state ac load current and voltage output waveforms of a wind system after passing through the power electronics control. We noted that after start-up, the output current and voltage reached the stabilize values of 228Vrms and 11.48 A rms respectively at 3.8 seconds.

Fig. 8. Steady state output current and voltage waveform of the load

V. SIMULATION AND EXPERIMENTAL RESULTS The 2.4kW wind turbine installed at UMass-Lowell is one

of the examples of a wind turbine with direct-driven permanent magnet alternator whose power conversion topology is presented in section 2. This wind turbine was installed at the roof top of Ball Engineering building and it is already in operation for more than a year. The actual operation of this turbine was being monitored and data was recorded by a data acquisition system. This wind turbine is one of the wind turbine products manufactured by Southwest. This turbine is a brand new product from one of the world’s leading small wind turbine manufacturers. It has a nominal rating of 2.4 kW, 240 V rating and is the first fully integrated small wind generator specifically designed for the utility-connected market. The wind turbine is a down-wind (wind hits the blades on the downwind side of the tower), direct drive (gearless or no transmission) permanent magnet alternator. It uses an innovative 12 foot (3.7 m) rotor. This wind turbine uses a permanent magnet alternator that is directly connected

to the grid via power electronics. It is the first all-inclusive wind generator with built-in controls and inverter. It was designed to produce energy in very low winds, reaching rated power at just over 23 mph (10 m/s). Its full 2,400 watts is achieved at 29 mph (13 m/s) with a maximum rotor speed of 325 RPM. Because of the exceptionally low RPM, the machine operates nearly sound free.

TABLE I TECHNICAL SPECIFICATIONS OF THE 2.4 KW WIND TURBINE

Generator rating 1.8 kW at 10 m/s; 2.4kW at 13 m/s Rotor speed 325 rpm nominal (variable) Cut-in wind speed 3.5 m/s Survival wind speed 63 m/s (140 mph) Rotor diameter 3.7 m Rotor orientation Downwind Number of blades 3 Blade material Carbon reinforced fibreglass. Control system Electronic stall control. Gearbox None Brakes Electro-dynamic Generator Permanent magnet alternator Yaw control Passive downwind yawing Tower height 10m or 14m Free Standing Tower Free standing.

The Wind turbine will begin producing power at a wind speed of approximately 3.5 m/s. At that speed the blades will start rotating at approximately 120 rpm. Once it has started producing power, it will continue to produce power at lower speeds down to 80 rpm and less than 3 m/s. As the wind speed increases, the blade speed will also increase. At about 9 m/s the blades achieve a rotational speed of 330 rpm. This is the wind’s rated speed. Should the wind speed increase above 9 m/s, the blades speed will remain essentially fixed at 330 rpm. If a condition occurs that causes the rotational speed to exceed 360 rpm, the turbine will shut down for approximately 10 minutes after which it will resume normal operation unless a fault is detected causing it to remain shut down.

The load current and load voltage generated at same wind speed used in the Simulink model are being measured using the Data Acquisition System. Figure 9 and 10 are the steady state sinusoidal curves of load voltage and load current.

Fig. 9. Output Load Voltage of the Skystream Wind Turbine system

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The rms current is 8.5A and rms voltage is 244V when the wind speed was 12 m/sec, same speed at which Simulink model output were measured. It was observed that the output voltage and current waveform characteristics in the simulation and experiment are approximately the same as shown in Fig. 8, Fig 9 and Fig. 10.

Fig. 10. Output Load Current of the Skystream Wind Turbine system

Figure 11 shows the comparison between the simulation and actual operation of the wind turbine measured in rms values. These values were recorded at a wind speed of 12 m/s. It shows that the average values of power generated is approximately equal to the values of power recorded in the simulation results

Fig. 11. Simulation and Actual Measured load current, voltage and power

Results of monthly energy generated of the wind turbine from October 2009 to October 2010 are shown in Fig. 12. It has been observed that the system generates more energy in winter than in summer.

Fig. 12. Monthly Energy Generated of the Skystream Wind Turbine

VI. CONCLUSIONS A detailed electrical model of a wind turbine system

equipped with a permanent magnet synchronous generator, diode rectifier, boost dc to dc converter and inverter is presented and used to predict the performance of the wind turbine system. The computer simulations proved to be a valuable tool in predicting the system behavior, selecting certain components, designing a controller, and determining the output generation of the wind turbine. The simulation results obtained by using the Matlab Simulik tool clearly show the effectiveness of the studied model. This model is reasonably accurate when used to predict the steady state response of the wind power system. The Simulink model load output current as well as the load output voltage waveforms concur with the values taken under the same wind speed from an actual operation of the installed Skystream wind turbine.

A skystream 3.7 is an example of a wind turbine with a direct-driven permanent magnet generator whose performance characteristics are presented. The energy generated by the wind energy conversion system is recorded by a Data Acquisition System. The monthly energy production in one year operation is reported. Due to the grid connection, the output voltage does not change dramatically even the wind speed changes. It has been observed that the system generates more energy in winter than in summer.

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VII. REFERENCES Periodicals:

[1] Hadiza Mohammed and Chika O. Nwankpa, Stochastic Analysis and Simulation of Grid-Connected Wind Energy Conversion System, IEEE Transactions on Energy Conversion, VOL. 15, No. 1, pp. 85-90, March 2000

[2] D.C. Aliprantis, S.A. Papathanassiou, M.P. Papadopoulos, A.G. Kladas, Modeling and Control of a Variable-Speed Wind Turbine Equipped with Permanent Magnet Synchronous Geneator, ICEM 2000; International Conference on Electrical Machines, pp. 558-562, August 2000, [Online]. Avialable: http://users.ntua.gr/ stpapath/ paper_2.32.pdf

[3] A. Kilk, Low-Speed Permanent Magnet Synchronous Generator for Small-Scale Wind Power, Oil Shale, 2007, Vol. 24, No. 2 Special ISSN 0208-189X pp. 318–331 © 2007 Estonian Academy Publishers, [Online]. Available: http://www.kirj.ee/ public/oilshale/oil-2007-2s-12.pdf

[4] M.L. Elhafyani, S. Zouggar, M. Benkaddour, Y. Zidani, Permanent and Dynamic Behaviour of Self-excited Induction Generator in Balance Mode, M.J. Condensed Mater, Vol. 7 No.1, pp. 49-53, January 2006 [Online]. Available: http://users. ncs.concordia.ca/~m_sikder/Pillay/dastagir/equvalent%20ckt%20SEIG.pdf

[5] S. Belakehal, H. Benalla and A. Bentounsi, Power Maximization Control of Small Wind System Using Permanent Magnet Synchronoua Generator, Revue des Energies Renouvelables Vol. 12 No. 2 pp. 307-319, 2009

Books:

[6] Mukund R. Patel, Wind and Solar Power Systems, Copyright @ 1999, CRC Press LLC, New York, pp. 35-57

[7] Muhammad H. Rashid, Power Electronics, Circuits Devices, and Applications, third edition , Copyright @ 2001, Prentice-Hall, Inc. New Jersey, pp. 167-290

[8] Jai P. Agrawal, Power Electronic Systems Theory and Design, Copyright @ 2001, Prentice-Hall, Inc. New Jersey, pp. 242-253

VIII. BIOGRAPHIES Ambrosio Cultura was born in Misamis Oriental, Philippines on February 5, 1968. He received his B.S. Electrical Engineering degree from the Mindanao Polytechnic State College (MPSC), Cagayan de Oro City, Philippines in March 1990. He joined the faculty of the Department of Electrical Engineering of this College on June 1992 as full-time Instructor after passing the Electrical Engineering Licensure Examination. From 1998 to 2002, he served the College as the Department Head of School of Engineering and Architecture. He

became Assistant Professor from March 2002 to present. He obtained his MS Energy Engineering in 2005 and currently enrolled Doctoral Program in Electrical Power and Energy Engineering at the University of Massachusetts Lowell, Electrical and Computer Engineering Department. His interests are in Renewable Energy Hybrid Systems, Energy Storage and Distributed Generation.

Ziyad Salameh (S-78, M82, SM-88) received his Diploma in Electrical engineering from Moscow Power Engineering Institute, Russia, in 1974 (with honors) and his M.S. and Ph.D. from the University of Michigan, Ann Arbor, in 1980 and 1982 respectively. Ziyad Salameh taught at Yarmouk University in Irbid Jordan from 1982 to 1985. In 1985 he joined the faculty at the University of Massachusetts Lowell, where he is currently a professor and director of Center for Electric Cars

and Renewable Energy. He Chaired the Department of Electrical and Computer engineering 2001-2004. He is a member of the IEEE Power Engineering, Industrial applications and power Electronics Societies. He has authored and co-authored more than 120 research papers. He is the author of a book entitled “Renewable Energy Systems Design and Analyis”.