Self Excitation and Harmonics 

in Wind Power Generation 

Preprint 

November 2004 • NREL/CP-500-33138 

E. Muljadi and C.P. Butterfield 

National Renewable Energy Laboratory 

H. Romanowitz 

Oak Creek Energy Systems, Inc. 

R. Yinger 

Southern California Edison

To be presented at the 43rd AIAA Aerospace Sciences 

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January 10–13, 2005 

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1

Self Excitation and Harmonics in Wind Power Generation

 E. Muljadi and C.P. Butterfield*

National Renewable Energy Laboratory, Golden,, Colorado, U.S.A. 

H. Romanowitz 

Oak Creek Energy Systems Inc., Mojave, California, 93501, U.S.A. 

and 

R. Yinger 

Southern California Edison, Rosemead, California, 91770 U.S.A. 

Abstract—Traditional wind turbines are equipped with induction generators. Induction 

generators are preferred because they are inexpensive, rugged, and require very little 

maintenance. Unfortunately, induction generators require reactive power from the grid to 

operate and some capacitor compensations are often used. Because reactive power varies 

with the output power, the capacitor compensation is adjusted as the output power varies. 

The interactions among the wind turbine, the power network, and the capacitor 

compensation, are important aspects of wind generation. In this paper, we will show the 

interactions among the induction generator, capacitor compensation, power system network, 

and magnetic saturations and examine the cause of harmonic currents and self-excitation. 

I. Introduction 

ANY of today’s operating wind turbines have fixed speed induction generators that are very reliable, 

rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid 

at all times. Thus, the general practice is to compensate reactive power locally at the wind turbine and at the 

point of common coupling where the wind farm interfaces with the outside world. The most commonly used 

reactive power compensation is capacitor compensation. It is static, low cost, and readily available in different 

sizes. Different sizes of capacitors are generally needed for different levels of generation. A bank of parallel 

capacitors is switched in and out to adjust the level of compensation. With proper compensation, the power factor of 

the wind turbine can be improved significantly, thus improving overall efficiency and voltage regulation. On the 

other hand, insufficient reactive power compensation can lead to voltage collapse and instability of the power 

system, especially in a weak grid environment. 

Although reactive power compensation can be beneficial to the overall operation of wind turbines, we should be 

sure the compensation is the proper size and provides proper control. Two important aspects of capacitor 

compensation, self-excitation1, 2 and harmonics3, 5, are the subjects of this paper. 

In section II, we describe the power system network, in section III, we discuss the self-excitation in a fixedspeed wind turbine, and in section IV, we discuss harmonics. Finally, our conclusions are presented in section V. 

II. Power System Network Description 

We investigated a very simple power system network consisting of one 1.5 MW, fixed-speed wind turbine 

with an induction generator connected to a line feeder via a transformer (2 MVA, 3 phase, 60Hz, 690V/12kV). The 

low-speed shaft operates at 22.5 rpm and the generator rotor speed is 1200 rpm at its synchronous speed. 

A diagram representing the system we investigated is shown in Figure 1. The power system components 

analyzed include the following: 

 

*

 This material is declared as a work of the U.S. Government and is not subject to copyright protection in the United 

States 

M 
2

- An infinite bus and a long line connecting the wind turbine to the substation. 

- A transformer at the pad mount 

- Capacitors connected in the low voltage side of the transformer 

- An induction generator 

For the self-excitation, we focused on the turbine and the capacitor compensation only (the right half of Figure 

1). For harmonic analysis, we considered the entire network shown in Figure 1. 

III. Self-Excitation 

A. The Nature of Self-Excitation in an Induction Generator 

Self-excitation can occur in a fixed-speed wind turbine equipped with an induction generator. Fixed capacitors 

are the most commonly used method of reactive power compensation in a fixed-speed wind turbine. Induction 

generators alone cannot self excite. It requires reactive power from the grid to operate normally. The grid dictates 

the voltage and frequency of the induction generator. 

Although self-excitation does not occur during normal grid-connected operation, it can occur during off-grid 

operation. For example, if a wind turbine operating in normal mode becomes disconnected from the power line due 

to a sudden fault or disturbance in the line feeder, the capacitors connected to the induction generator will provide 

reactive power compensation. However, the voltage and the frequency are determined by the balancing of the 

systems. 

One disadvantage to self-excitation is the safety aspect. Because the generator is still generating voltage, it may 

compromise the safety of the personnel inspecting or repairing the line or generator. Another disadvantage is that 

the generator’s operating voltage and frequency are determined by the balance between the system’s real power and 

the reactive power. Thus, if sensitive equipment is connected to the generator during self-excitation, the equipment 

may be subjected to over/under voltage and over/under frequency operation. In spite of the disadvantages of 

operating the induction generator in self-excitation, some people use self-excitation for dynamic braking to help 

control the rotor speed during an emergency such as a grid loss condition. Thus, with the proper choice of 

capacitance and resistor load (to dump the energy from the wind turbine), the wind turbine can be brought to a safe 

operating speed during grid loss and mechanical brake malfunctions. 

In an isolated operation, the conservation of real and reactive power must be preserved. The equation governing 

the system can be simplified by looking at the impedance or admittance of the induction machine. To operate in an 

isolated fashion, the total admittance of the induction machine and the rest of the connected load must be zero. The 

voltage of the system is determined by the flux and frequency of the system. Thus, it is easier to start the analysis 

from a node at one end of the magnetizing branch. Note that the term “impedance” in this paper is the conventional 

impedance divided by the frequency. The term “admittance” in this paper corresponds to the actual admittance 

multiplied by the frequency. 

B. Steady-State Representation 

Figure 2 shows an equivalent circuit of a capacitor-compensated induction generator. The principle of excitation 

for the parallel-compensated system is the same as in the series compensation. That is, the balance of real and 

reactive power must be maintained. Equation 1 gives the total admittance of the system: 

Fig. 1. The physical diagram of the system under investigation.

Infinite 

Bus

Line Feeder Transformer

Wind 

Turbine

Caps 

Fig. 2. Per phase equivalent circuit under self-excitation. 
3

 ' ' 0 YY Y smr ++= (1) 

Equation 1 can be expanded into the equations for imaginary and real parts as shown in Equations 2 and 3. 

 

 (2) 

 

 (3) 

where: 

One important characteristic needed to solve the self-excitation is the magnetizing characteristic of the induction 

generator. Figure 3 shows the relationship between the flux linkage and the magnetizing inductance, where an 

increase in the flux linkage increases the saturation level thus reducing the effective magnetizing inductance Lm. 

This graph can be derived from the no-load characteristic of the induction generator obtainable from the experiment. 

To solve the above equations, we can set the capacitor (C) and the resistive load (RL) values and then find the 

operating points for different frequencies. From Equation 2, we can find the operating slip at a particular frequency. 

Then, from Equation 3, we can find the corresponding magnetizing inductance Lm’, and from here, we can find the 

operating flux linkage at this frequency (by using the Lm’ vs flux linkage λm shown in Figure 3). The process is 

repeated for different frequencies. 

1

2 2

1 2 2

1

1

2 2

1 2 2

1

r

r

lr

lr

m r

lr

R R ’

S 0

R R ’ + + L L ’ S

1 ’ L L 0

L ’ R R ’ + + L L ’ S

ω ω

ω ω

ω ω

+ =

        

++ =

        

L

1 s 2

L

2

L

1 ls 2

L

R R R = + 

( C +1 R )

CR

 = - L L ( C +1 R )

ω

ω

Fig. 3. The magnetization characteristic presented as L’m versus λm. 

Lm vs Flux Linkage

0 .5 1 1.5 2

0

.005

.010

.015

.020

Flux Linkage (Wb-turns) 

Fig. 4. The slip as a function of rotor speed for different RL and C. 
4

As a base line, we consider a capacitor with a capacitance of 3.8 mF (milli-farad) connected to the generator to 

produce approximately rated VAR compensation for full load generation (high wind). The load resistance RL = 1.0 

ohm is used as the base line load. The slip versus rotor speed is presented in Figure 4. It shows that the slip is 

roughly constant throughout the speed range for a constant load resistance. The capacitance does not affect the 

operating slip for a constant load resistance. A higher resistance (RL high = lower generated power) corresponds to 

a lower slip. 

The voltage at the terminals of the induction generator (refer to Figure 5) can be computed to show the impact 

of the capacitance and load resistance. As shown above, the load resistance does not affect the terminal voltage, 

especially in the higher rpm (higher frequency). However, the capacitance has a significant impact on the voltage 

profile at the generator terminals. As shown, a larger capacitance gives a more constant voltage while a smaller 

capacitance makes the voltage increase as the rotor speed increases. This concept of self-excitation can be exploited 

to provide dynamic braking for a wind turbine to prevent the turbine from running away when it loses its connection 

to the grid. By choosing the correct values for capacitance and load resistance (or variable resistance), as shown in 

Figure 5, one can tailor the torque speed characteristic of the generator to provide dynamic braking during 

emergency shutdown when the turbine loses its connection to the grid. 

Figure 6 shows that for the same capacitance, changing the effective value of the load resistance can modulate 

the torque-speed characteristic. 

C. Dynamic Behavior 

 If an induction generator connected to a local grid, is a suddenly disconnected from that grid, the local load, the 

capacitor compensation, and the induction generator will operate in self-excitation mode. A short while later, the 

grid is reconnected to the wind turbine generator. 

A value of 3.8 mF capacitance and a load resistance of 1.0 ohm was chosen for this simulation. The constant 

driving torque was set to be 4500 N.m. Note that the wind turbine characteristic is not included in this simulation, 

because we are more interested in the self-excitation process itself. Thus, we focused on the electrical side of the 

equations. 

Figure 7 shows the rotor speed and the electrical output power. In this case, the induction generator is at zero 

speed when it is started. The speed increases until it reaches its rated speed. It is initially connected to the grid until 

t=3.1 seconds at which time the grid is disconnected and the induction generator operates in self-excitation mode. 

At t=6.375 seconds, the generator is reconnected to the grid, which terminates the self-excitation. The rotor speed 

increases slightly during self-excitation, but eventually, the generator torque matches the driving torque (4500 Nm), 

and the rotor speed is stabilized. When the generator is reconnected to the grid, there is a sudden brief change in the 

torque transient. This change occurs when the system is reconnected to the grid without any synchronization. When 

the induction generator is resynchronized with the grid, the rotor speed settles at the same speed as the rotor speed at 

t < 3 sec. 

Fig. 5. Terminal voltage versus rotor speed for different RL and C. Fig. 6. The generator torque vs. rotor speed for different RL and C.
5

 Figure 8 shows the trace of per phase stator voltage. It shows that the stator voltage is originally the same as the 

grid voltage to which it is connected. During the self-excitation mode (3.1s < t < 6.375s), the voltage increases and 

the frequency is a bit higher than 60 Hz. The frequency then returns to its rated voltage when the induction 

generator is reconnected to the grid. 

 To observe the change in voltage during transient, the above graph is zoomed between t=3.0s to t=3.5 s. Note, 

that the frequency and voltage increase during self-excitation. 

Fig. 8. The terminal voltage versus the time 

a) the voltage and frequency are shown to vary 

b) before, during self-excitation, and after reconnection.

Fig. 7. The generator output power and rotor speed vs. time. 

P e r P hase S tator V oltage

Time (se c )

0 2 4 6 8 10

-600

-400

-200

0

200

400

600

800

P e r Pha se S ta tor V olta ge

Tim e (se c )

3 3.1 3.2 3.3 3.4 3.5

-600

-400

-200

0

200

400

600

800

a) 

b) 
6

s r

h

s

h

S

h

ω ω

ω

− =

IV. Harmonic Analysis 

A. Simplified Per Phase Higher Harmonics Representation 

We replaced the power network shown in Figure 1, with a per phase equivalent circuit. In this circuit 

representation, the harmonics is denoted with h to indicate the higher harmonics multiples of 60 Hz. Thus h=5 

indicates the fifth harmonics (300 Hz). In wind turbine applications, the induction generator, transformer, and 

capacitors are three phases and either Wye or Delta is connected. Thus, the flow of even harmonics, the third, and its 

multiples do not exist (only h = 5, 7, 11, 13, 17 . . . etc.). 

1. Infinite Bus and Line Feeder 

The infinite bus and the line feeder connecting the wind turbine to the substation are represented by a simple 

Thevenin representation of the larger power system network. Thus, we consider a simple RL line rep. 

2. Transformer 

We considered a three-phase transformer with standard impedance of 6%. Because the magnetizing inductance 

of a large transformer is usually very large compared to the leakage inductance, only the leakage inductance will be 

considered. Assuming the efficiency of the transformer is about 98% at full load, and the copper loss is equal to the 

core loss (general assumption for an efficient, large transformer), we can approximate the winding resistance, which 

is generally very small for an efficient, large transformer. 

3. Capacitor Compensation 

 The capacitors representing the compensation of the wind turbine are switched capacitors. Although the 

manufacturer equipped the wind turbine with only 400 kVAR of reactive power compensation, the wind turbine we 

considered is equipped with an additional 1.5 MVAR reactive power compensation. The wind turbine is 

compensated at different levels of compensation depending on the level of generation. The capacitor is represented 

by the capacitance C. In series with the capacitance, is the parasitic resistance (Rc), representing the losses in the 

capacitor. This resistor is usually very small for a good quality capacitor. 

4. Induction Generator 

The induction generator (1.5 MW, 480V, 60 Hz) used for this wind turbine can be represented as the per phase 

equivalent circuit shown. Figure 8, shows the equivalent circuit of the induction generator. The operating slip of 

the generator at fundamental frequency (60Hz) is around 1%. The slip of induction generator at harmonic frequency 

can be computed as: 

where 

Sh = slip for hth harmonics 

h = harmonics order 

ωs = synchronous speed of the generator 

ωr = rotor speed of the generator 

Thus for higher harmonics (5th and higher) the slip is close to one (Sh = 1) and for practical purposes is assumed to 

be one. 

B. Steady State Analysis 

 Figure 9 shows the simplified equivalent circuit of the interconnected system representing higher harmonics. 

Note that the magnetizing inductance of the transformers and the induction generator are assumed to be much larger 

than the leakages and are not included for high harmonic calculation. From the superposition theorem, we can 

analyze a circuit with only one source at a time while the other sources are turned off. For harmonics analysis, the 

fundamental frequency voltage source can be turned off. In this case, the fundamental frequency voltage source 

(infinite bus), Vs, is short-circuited. Based on the parameters given, we can use a steady-state analysis based on the 

simplified equivalent circuit shown in Figure 9. 

(4)
7

 Wind farm operator experience shows us that harmonics occur when the transformer operates in the saturation 

region. Thus, the transformer operates at a higher flux causing the non-linearity of the magnetizing inductance L`m

of the transformer. During the operation in this saturation region, the resulting current can be distorted so that we 

can see a sharply peaked sinusoidal current due to larger magnetizing current imbedded in the primary current. This 

non-sinusoidal current can excite the harmonics when the power network and the capacitor compensations hit its 

resonance frequency. 

From the circuit diagram we can compute the impedance seen by the harmonic source as: 

 Z C,h = Z + 0.5 Z // 0.5 Z + Z //Z ( )( ) line xfmr xfmr C gen ( ) (5) 

The admittance can be found from the impedance. 

 ( ) ( )

1 Z C,h = Z C,h (6) 

 The admittance corresponds to the corresponding harmonic current for a given harmonic voltage excitation. In 

this section, we analyze the system admittance from the most dominant harmonic frequency (up to 23rd harmonics, 

excluding even and multiples third harmonics) and vary the size of the capacitor compensation. Because the data in 

the field only consists of the total harmonic distortion, and does not provide information about individual harmonics, 

we can only compare the trends shown by the admittance from the admittance calculation shown in Equations 5 and 

6 to the measured data. Figure 10a shows the total admittance computed from equation 6 for all higher harmonics 

of interest up to 23rd harmonics (odd and non-triplen harmonics) are plotted as a function of the total reactive power 

Fig. 10a. The total admittance for higher harmonics (odd and 

non-triplen) as a function of reactive compensation. 

Ytot vs Reactive Power

0

50

100

150

200

250

300

0.00 0.20 0.40 0.60 0.80 1.00

Reactive Power (p.u.)

Ytot (mhos)

 Rxf/2 j hXxf/2 Rxf/2 j hXxf/2 

 VS 

 Vh 

 Rc Rgen 

 jhXgen

(j hω C )-1

 (a) Complete Representation 

Rline 

j hXline

 j hXline

 Rline 

(b) Harmonic Representation 

 Vh Rc Rgen 

(j hωC )-1 j hXgen

Rxf /2 

 j hXxf/2 

 Rxf/2 j hXxf/2 

Fig. 9. The per phase equivalent circuit of the simplified model for harmonic analysis.

PU VAR Support on a MW Class WT Near 

Full Ge ne ration Magnitude of VAR 

Support, 0.95 PF Leading at Rate d KW

-0.3

-0.1

0.1

0.3

0.5

0.7

0.9

1.1

0.0 0.2 0.4 0.6 0.8 1.0

PU Supplem ental VARs

PU Volts

0

1

2

3

4

5

6

7

8

% THD

PU V 

% THD Cap A 

% THD U

Figure 10b. Total harmonic distortion of the current as a 

function of the reactive compensation in per unit. 
8

| | M

M

B

E λ

ω ≈

[in per unit] as the size of switched capacitors varied. For a comparison, the measured data of the total harmonic 

distortion as a function of the total reactive power (in per unit) is presented in Figure 10b. It is shown in both Figure 

10a and Figure 10b that when the size of the capacitor compensation is increased, the circuit admittance (in Figure 

10a) or the total harmonic distortion (in Figure 10b) shows resonance at different higher harmonics. The two graphs 

show the same trend. There are two values of capacitances that amplify the total harmonic distortions revealed from 

the calculation and from the field measurement. Although the magnitudes do not match completely, the size of 

reactive power at which the two resonance frequencies occur shows a good correlation between the field 

measurement and the calculated values. 

 From Figure 10, we can say that the circuit will resonate at different higher harmonics when that particular 

harmonics presents or excites the circuit. 

C. Dynamic Simulation 

 In this section, we want to show how the harmonic sources are generated in the transformer. When a certain 

harmonic source is present, and the circuit presents a resonance circuit to the harmonic source, there will be a 

harmonic current flowing in the network. From the previous section, we learned that the wind turbine is 

compensated by increasing the reactive power as the generated power increases. Different sizes of capacitors that 

are connected to the power system network can lead to different resonance frequencies. 

 Most utility-size wind turbines are equipped with a pad-mount step-up transformer that connects them to the 

utility. In this section, we will show the nature of a transformer that can lead to producing current harmonics in the 

circuit. The non-linear characteristic of the magnetic circuit in the transformer shows that a non-sinusoidal current 

is generated when the transformer saturated. This non-sinusoidal current can excite the power system circuit. 

 Figure 11 shows the per-phase equivalent circuit of a transformer. The iron core loss of a transformer is usually 

represented as a parallel resistance, R’C, commonly found in a per-phase equivalent circuit. In this study, the core 

loss is neglected, and the equivalent resistance, R’C, is eliminated from the equivalent circuit. The magnetizing flux 

linkage is proportional to the ratio of the voltage and the frequency. 

 (7) 

where 

E’M = the magnetizing voltage 

λM = flux linkage 

ωB = the base angular frequency 

Figure 12 shows the relationship between the voltage and current when the transformer is operated under 

saturation. The flux linkage of the transformer can be found from equation 6. The relationship between the flux 

linkage and the exciting current I’M magnetizing inductance L’M is non-linear. When the exciting current is low, the 

flux (and flux linkage) varies linearly, but eventually the saturation is reached, and the non-linear characteristic 

starts. A further increase in exciting current I’M, will produce a smaller increase in the flux linkage. In the 

saturation region, the exciting current I’M will be non-sinusoidal due to the non-linearity of the magnetizing 

inductance. Figure 12 shows the resulting current to be non-sinusoidal. This non-sinusoidal current can be 

displayed on the oscilloscope, and it can be measured by using a power quality meter to measure harmonic contents 

of the current. 

There are two types of operation that can affect the nonlinear current (I`M). The first one occurs when the 

transformer operates in a higher voltage level thus driving the operation in to the saturation region. This can happen 

when the voltage across E’M is high. One example of this operation is when the transformer is lightly loaded, thus 

the voltage drop across the line feeder and the primary-winding impedance is small. Thus the magnetizing branch is 

Fig.11. Per-phase equivalent circuit of a transformer. 
9

exposed to a high voltage E`M producing a large magnetizing current I’M in the magnetizing branch. Another 

example of operation that can result in the high saturation is when the transformer is operated with a leading power 

factor. The voltage across the magnetizing branch can be expressed as: 

 

 ( ) ' E = V - I Z + Z M S 1 LINE 1 (8) 

 When the current I1 is small and/or leading, the corresponding E’M will be closer or higher than VS, and, if the 

voltage VS is high to begin with, the transformer will operate in a saturation region. Under normal operation, the 

current I1 is at rated current, thus there is a sufficient voltage drop across Z1 and ZLINE, and the voltage E’M will be at 

its rated voltage (linear region). 

 The resulting current for operation under saturation is a distorted current waveform as shown in Figure 12. The 

distorted portion of the current shows that the operating point moves into a non-linear saturation region. The 

harmonic contents of the current can be observed from the frequency spectrum shown in Figure 13. As can be 

expected, for a three phase balanced system, the even and third multiples harmonics do not exist. As a comparison, 

the current of the transformer under a loaded condition is shown in Figure 14. It is obvious that the voltage drops 

across the leakage reactance and the winding resistance keep the voltage across the magnetizing branch from 

becoming excessively high, thus the operation of the transformer is in the linear region. 

Another factor that can affect the transformer saturation is the tap changer. A tap changer is a device fitted into a 

transformer programmed to change the turn-ratio or the number of turns of the transformer on-line. The purpose of 

the tap changer is to control the voltage on the customer side to be as constant as possible. With an increase in the 

effective number of turns of the transformer, the magnetizing inductance L’M will increase accordingly (proportional 

to the square of the number of turns). It means that for the same voltage E`M, we get the less exciting current I’M. 

With the less exciting current, we operate the transformer in a less saturate condition (closer to linear region). In 

Fig.12. The voltage and current of a transformer under 

light load condition. 

Plot

Time (sec)

4.95 4.96 4.97 4.98 4.99 5

-800

-600

-400

-200

0

200

400

600

800

Voltage Current 

Figure 13. Harmonic content of the distorted light 

load current. 

Frequency (Hz) 

Plot

Time (sec)

4.95 4.96 4.97 4.98 4.99 5

-2000

-1000

0

1000

2000

3000

Figure 14. Sinusoidal Current of a Transformer under 

Loaded Condition. 
10

essence, we can avoid the non-linear region completely if we have enough room to change the tap on the 

transformer. 

 For a comparison between unsaturated and saturated conditions, we can compare the current shown in Figure 12 

(saturated, light load condition) to the current shown in Figure 14 (unsaturated, loaded condition). The current 

distortions due to saturation as shown in Figure 12 do not show up when the transformer is loaded (unsaturated) as 

shown in Figure 14. 

V. Conclusion 

This paper presents the nature of self-excitation and harmonics generated by a fixed-speed induction generator 

commonly used in wind turbine generation. Although neither self-excitation nor harmonics are desired outcomes of 

electricity generated by wind turbines, without proper design and control, either may occur. 

In self-excitation, the operator is concerned about the safety of personnel repairing the line. However, selfexcitation can be used for dynamic braking to keep the wind turbine from running away as well as for other 

applications. The size of dynamic resistor and capacitor installed must be pre-calculated to ensure the desired result. 

The saturation of the magnetic circuit in the transformer and the resonance circuit between the capacitor 

compensation and the rest of the circuit can make the power system susceptible to harmonic flows. Although the 

power network stays the same, the resonance occurs at several different frequencies because the capacitors change 

sizes as the wind speed increases. The source of harmonics is generated in the magnetizing branch due to magnetic 

saturation of the iron core. The tap changer, the power factor, and the level of generation of the wind turbine affect 

the level of saturation, and thus, the nature of the harmonic source. 

Acknowledgments 

We acknowledge the support of the U.S. Department of Energy and we also thank Jorge Chacon from Southern 

California Edison for his help and discussions. 

References 

1. Sallan, J., Muljadi, E., Sanz, M., Butterfield, C.P.; “Control of Self-Excited Induction Generators Driven by Wind 

Turbines.” 8th European Conference on Power Electronics and Applications Conference (EPE99) in Lausanne 

(Switzerland), 7-9 September 1999. 

2. Tang, L. Zavadil, R.M., Smith, J.C., Childs, S.; “Parametric Study of the Performance of a Passive Dynamic Brake.” 

Windpower ’91 Conference Proceedings, Palm Spring, CA, Sept. 24-27, 1991, pp. 273-280. 

3. Krause, P.C.; Analysis of Electric Machinery, McGraw Hill Book Company, 1986. 

4. Fitzgerald, A.E., Kingsley, C. Jr., Uman, S.D; Electric Machinery, Sixth Edition, McGraw Hill Book Company, 2003. 

5. Neves, W., Dommel, H., “Saturation Curve of Delta-Connected Transformer from Measurements,” IEEE Transactions on 

Power Delivery, Vol. 10, Issue: 3, July 1995, pp. 1432-1437. 

6. VisSim/Simulink Translator User’s Guide-Version 5, Visual Solutions, Inc., 2002. 

7. MathCad User’s Guide with Reference Manual, MathSoft Inc., 2001. 
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January, 12-13 2005 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE

Self Excitation and Harmonics in Wind Power Generation: Preprint 

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

NREL/CP-500-33138 

5e. TASK NUMBER

WER5-3108 

6. AUTHOR(S)

E. Muljadi, C.P. Butterfield, H. Romanowitz, and R. Yinger 

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

H. Romanowitz: Oak Creek Energy Systems, Inc. 

R. Yinger: Southern California Edison 

8. PERFORMING ORGANIZATION 

REPORT NUMBER

 

10. SPONSOR/MONITOR'S ACRONYM(S)

NREL 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden, CO 80401-3393 11. SPONSORING/MONITORING 

AGENCY REPORT NUMBER

NREL/CP-500-33138 

12. DISTRIBUTION AVAILABILITY STATEMENT

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

13. SUPPLEMENTARY NOTES

NREL Technical Monitor: 

14. ABSTRACT (Maximum 200 Words)

Traditional wind turbines are equipped with induction generators. Induction generators are preferred because they 

are inexpensive, rugged, and require very little maintenance. Unfortunately, induction generators require reactive 

power from the grid to operate. Because reactive power varies with the output power, the terminal voltage at the 

generator may become too low to compensate the induction generator. The interactions among the wind turbine, the 

power network, and the capacitor compensation, are important aspects of wind generation. In this paper, we will 

show the interactions among the induction generator, capacitor compensation, power system network, and magnetic 

saturations and examine the cause of resonance conditions and self-excitation. 

15. SUBJECT TERMS

Wind turbine; induction generator; capacitor compensation; wind energy 

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a. REPORT 

Unclassified 

b. ABSTRACT 

Unclassified

c. THIS PAGE 

Unclassified

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OF ABSTRACT

UL 

18. NUMBER 

OF PAGES 

19b. TELEPONE NUMBER (Include area code)

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