A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Characteristics of Wind Turbines 

Under Normal and Fault 

Conditions 

Preprint 

E. Muljadi, C.P. Butterfield, and B. Parsons 

National Renewable Energy Laboratory 

A. Ellis 

Public Service Company of New Mexico

To be presented at the IEEE Power Engineering Society 2007 

General Meeting 

Tampa, Florida 

June 24-28, 2007 

Conference Paper 

NREL/CP-500-41051 

February 2007 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
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1

CHARACTERISTICS OF VARIABLE SPEED WIND TURBINES 

UNDER NORMAL AND FAULT CONDITIONS 

Abstract— Variable-speed wind turbines with full 

power processing capability are the new technology trend 

for large wind power plants. In this type of turbine, there 

is an interface between the generator and the utility grid. 

In this paper, we investigate the characteristics of a 

variable-speed wind turbine connected to a stiff grid or a 

weak grid, the role of reactive power compensation in 

optimizing the operation of the wind turbines, and the 

operation of a wind turbine under normal and fault 

conditions. Both steady state and dynamic analysis are 

presented. 

Index Terms—wind turbine, wind farm, wind power plant, 

stability, wind energy, power system, variable-speed 

generation, renewable energy, low-voltage ride-through, weak 

grid, fault conditions. 

I. INTRODUCTION 

o

r

 successfully deploy wind energy, we need to have the 

esources and the transmission to carry the electrical 

energy product to the load centers. Abundant resources can be 

profitable only if we can generate low-cost wind energy. The 

transmission line, the strength of the grid, and the proximity of 

the wind resource to the load center are all important factors in 

successful wind deployment. 

In an interconnected grid, the power system network and 

the wind power plant are interrelated. Knowing the 

characteristics of the wind power plant and the transmission 

and distribution systems is very important for identifying the 

problems and finding the resources to resolve the issues. 

When we discuss transmission lines, we are concerned 

about, among other things, the stability, power transfer 

capability, and the losses. The stability and power transfer 

capability are determined partly by the impedance between the 

sending and the receiving ends. In the transmission lines, the 

resistive part of the impedance is generally much smaller than 

its reactance. In the sections that follow, the resistive part of 

the impedance is often ignored to simplify the discussion. The 

reactance between the two points consists of the reactance 

presented by the lines, the transformer, and the electric 

machine impedances when the line reactance is the major 

component of the total impedance. The line reactance is 

mostly determined by the line length—the geometrical 

distance between the wires and the ground. 

Raising the voltage will significantly increase the transfer 

capability of the systems and reduce the losses, the voltage 

drop, and the per unit (p.u.) value of the reactance; however, 

higher voltage transmission requires significant investment. 

A large wind power plant (> 100 MW) is commonly 

connected to a transmission line. At the main substation, the 

voltage is stepped down from the transmission level to the 

subtransmission level through the main transformer. From the 

main substation, a collector system collects the power 

generated by the wind turbines through line feeders. The 

collector system impedance of many turbines can be 

represented by its equivalence and as a single impedance. One 

method to equivalence the collector system of a large wind 

power plant can be found in reference [1]. 

In Figure 1, the single-line diagram represents a wind power 

plant. Each wind turbine has a pad-mounted transformer to 

step down the voltage from the subtransmission level to the 

low voltage generated by the wind turbine. In the future, as 

wind turbines become larger, the voltage at the point of 

generation may be increased to medium. The transmission line 

connects the wind power plant to the grid or to a very large 

network, which can be treated as an infinite bus. The short 

circuit current at the point of interconnection plays an 

important role in the behavior of the wind power plant. 

The dynamic analysis is this paper is simulated by using 

Power System Simulator for Engineers [2], a commonly used 

program in utility planning. References [3] and [4] provide a 

good background on dynamic analysis for wind turbines. 

For a more detailed discussion of the dynamic model used 

in this section, see reference [5]. Figure 2 shows a single line 

diagram that describes the nature of the fault and the network 

topology in pre-fault, fault, and post-fault conditions. The 

transmission lines consist of two parallel paths. The fault 

occurs at the middle of line A, and the circuit breakers 

disconnect line A. The remaining line B continues to deliver 

the output of the wind power plant. The short circuit current 

(SCC) of the transmission line was originally at 10 p.u.; in the 

post-fault condition after line A was removed, the SCC 

dropped to 5 p.u. 

T 

Infinite Transmission Collector WTG 

Bus Line System 

Main Pad-Mount 

Substation Transformer 

Figure 1. A typical network topology of a wind power plant. 

A. Ellis 

Public Service Company of New Mexico 

Alvarado Square, MS 0604 

Albuquerque NM 87158 

 E. Muljadi C.P. Butterfield B. Parsons 

National Renewable Energy Laboratory 

1617 Cole Blvd 

Golden, CO 80401

1
2

Because we are interested only in the worst-case scenario, 

we simulate only the weak grid condition. Let us define a prefault condition with line A and line B, which are both on line. 

The SCC of both lines is 10 p.u. The wind power plant 

consists of wind turbines with a total capacity of 100 MW. The 

wind turbine is generating at its full rated capacity and the 

wind speed is at 125% of the rated wind speed. Because of the 

wind speed, the blade pitch is already deployed. Initially the 

wind turbine operates normally, then suddenly, a three-phase 

fault occurs near the main substation on line A at t = 1 s. The 

fault lasts for nine cycles, and line A is removed at the end of 

the fault, which creates a weaker system with an SCC of 5.0 

p.u. In this simulation, the relay protections are not set up, 

because we want to see the nature of the wind turbine and the 

system while exposed to this type of fault. 

In Section I, we described the nature of the fault tested in 

this paper. In Section II we discuss the variable-speed wind 

turbine generator (VSWTG). Finally, we summarize our 

conclusions in Section III. 

II. VARIABLE-SPEED WIND TURBINE GENERATOR 

In this section, we present a generic VSWTG. Although 

doubly fed induction generators [5-6] are commonly used by 

the wind industry today, in this paper we use a permanentmagnet, synchronous, variable-speed generator [7] because it 

represents the future of WTG capability. We assume that the 

WTG consists of a wind turbine connected to a generator via a 

gearbox or direct-drive generator. The output of the generator 

is connected to the utility via a power converter. The power 

converter provides a buffer between the utility and the 

generator. 

A. Normal Operation 

Under normal operation, the VSWTG operates at variable 

speed. At low to medium wind speeds it operates at optimum 

pitch angle (e.g., β = 0o

). At high wind speeds, the wind 

turbine operates at constant speed, and the pitch angle controls 

the rotor speed to be constant. 

The output power of the wind turbine operating in this 

mode is a cube function of the rotor speed until it reaches rated 

speed. Once the rated speed is reached, the wind turbine is 

operated at constant power by controlling the pitch angle. 

Normally, the pitch angle controller operates very smoothly, 

controlling the rotor speed so it does not exceed the rated 

speed. This pitch control mechanism, in effect, sheds 

aerodynamic power to keep the rotor speed from reaching a 

runaway condition. The wind turbine brakes will be deployed 

if the blade pitch control fails. 

Figure 3 shows the power curve of the VSWTG. Because 

the aerodynamic efficiency of a wind turbine is maximized at a 

specified tip-speed ratio, it is controlled so that it operates at 

that specific tip-speed ratio. This condition can be achieved 

when the ratio of rotor speed to wind speed is constant. Two 

curves are shown in Figure 3. Below rated speed, the curves 

coincide. Above rated speed, however, the curves deviate. The 

thick line represents a controller that maintains constant power 

above rated speed; thus, above the rated speed, the torque is 

inversely proportional to the rotor speed. The thin line 

represents a controller that maintains a constant torque above 

rated speed, so the power increases in proportion with the 

speed. The constant torque capability above rated speed can 

better prevent the wind turbine from reaching runaway 

condition. However, this capability requires a good oversized 

power converter with an extended speed range. In practice, 

the pitch controller will keep the rotor speed from over-speed 

conditions. In most cases, the blade pitch controller of a 

modern wind turbine accurately limits the rotor speed at or 

below the rated rotor speed, thus avoiding the need for a larger 

power converter. 

From the power converter perspective, the output of a wind 

turbine is limited by the generator capability and, more 

importantly, by the power converter capability. The generator 

limit is normally the thermal limit (generated mostly by losses 

in the windings). The power converter limit is more stringent, 

because power electronics are used as the building blocks of 

the power converter. The instantaneous value of the maximum 

current limit and the voltage blocking capability limit should 

never be violated. Thus, the power converter can be operated 

within the circle of current limit value. For a VSWTG, the 

power converter KVA limit is represented by a circle boundary 

(see Figure 4), which shows that the operating point can be 

anywhere in all quadrants as long as the tip of the complex 

power So is inside the boundary. Thus, we can generate or 

Infinite Transmission Substation 

 Bus Line Bus 

Figure 2. The location a fault on a weak grid. 

Wind 

Power 

Plant

Fault causes line A to 

disconnect 

 Line A 

 Line B 

constant 

Wind Speed 

Figure 3. Power curve of a typical VSWTG. 

constant 

power

torque

Optimum 

Pitch 

Angle

Pitch 

control is 

deployed

2
3

absorb real or reactive power within the circle. Real and 

reactive power can be controlled independently. A modern 

wind turbine can usually generate rated real power with a 

power factor (PF) range of 0.95 leading or lagging. The 

shaded triangle in Figure 4 shows the capability of the turbine. 

Because the terms leading and lagging power factor can be 

confusing in a generator or in a motor mode, the term 

overexcited is used to indicate that reactive power is generated 

by the equipment, and underexcited is used to indicate that the 

reactive power is absorbed by the equipment. 

The VSWTG is generally operated in either PF mode or 

voltage control mode. With a PF controller, the wind turbine is 

operated at a preset PF (usually unity PF) from low to high 

wind speeds. The voltage is controlled by other means 

(capacitor, SVC, Statcom, synchronous condenser, etc.). In 

voltage control mode, a reference voltage is used to control the 

reactive power output of the generator to keep the voltage 

constant. In a large wind farm, two control modes may be 

used. Some turbines may be set at voltage control mode, while 

other turbines may have preset power factors. 

Figure 5 shows (a) the control diagram, (b) the phasor 

diagram for constant PF control, and (c) the constant voltage 

control. The wind turbine is assumed to be connected to an 

infinite bus Vs. Between the wind turbine and the infinite bus 

is a reactance Xs. The control block diagram (5a) describes 

the constant voltage or constant PF control. Only the major 

loops and components are shown for simplicity. The VSWTG 

has three major components: the generator, the power 

converter, and the controller. Both electrical power 

(represented by the thick wire in Fig. 5a) and the electrical 

signal (represented by the thin wire in Fig. 5a) are 

interchanged among the generator, the power converter, and 

the utility. The input is the wind power feeding the wind 

turbine blades, and the output is the electrical power entering 

the utility grid. There are two choices of control objectives: PF 

or V. The controller has an input signal PF* or V* as the 

commanded power factor or the commanded reference 

voltage. This value is compared to the actual value PF or V. It 

uses the error signal to control the power converter, so that the 

actual PF or V moves closer to the commanded PF* or V*. 

The output of the controller is the reactive power command Q* 

that must be followed by the power converter to achieve the 

objective function (PF = PF* or V = V*). The output of the 

power converter is connected to the generator. Another loop to 

control the aerodynamic power is not included in this block 

diagram. Arrows show that the power can flow through the 

power converter and the generator to include the doubly fed 

induction generator (DFIG), where the output power can be 

accessed directly from the stator winding and from the rotor 

winding via a power converter. 

 b) constant power factor control 

Figure 5. Phasor and control block diagram for a VSWTG 

Vs

j I Xs

 I ” 

Vt

Vt

’’ Vt

’

Vs

Vs

I

 I’ 

φ 

Vs

 I ” j I Xs

Vt

Vs

Vs

I

 I ’ 

c) constant voltage control 

φ φ” ' φ

a) control block diagram 

Power 

Converter 

Generator 

UTILITY 

P, Q 

PF or V 

Controller 

PF* or V*

Q* P 

Q P > 0 

Q > 0 

S < Srate

P > 0 

Q < 0 

S <

d

 Srat

P < 0 

Q < 0 

S < Srated ed

P < 0 

Q > 0 

S < Srated So 

Figure 4. The operating boundary of a VSWTG with power converter. 

+ φ

- φ

3
4

1. Constant power factor 

Figure 5b shows that at constant power factor (cos φ = 

constant), the following can be observed: 

• Current magnitude and the power angle (δ) between 

the wind turbine voltage Vt and the infinite bus 

voltage Vs increases, as the power level increases 

• Terminal voltage at the wind turbine changes with the 

increase of power level 

o Underexcited condition (the generator absorbs 

reactive power), the terminal voltage decreases 

as the power level or wind speed increases. 

o Overexcited condition (the generator supplies 

reactive power), the terminal voltage increases as 

the power level or wind speed increases. 

As an illustration, let us consider a wind turbine connected 

to an infinite bus through a line feeder. As the worst-case 

scenario, we want to consider an underexcited condition with 

PF = 0.95 with no additional reactive power compensation. Let 

us change the line feeder to reflect different SCCs of the lines. 

Figure 6 presents a set of curves showing the terminal voltage 

versus output power of the wind power plant. Each curve has a 

different SCC. A very stiff grid (SCC = 50) performs best 

when the voltage varies minimally with the increase of output 

power. At SCC = 10, the terminal voltage drops to 0.96 p.u. at 

rated output power. 

At SCC = 5, the terminal voltage drops to 0.9 p.u. at rated 

power, and at SCC = 2.5, the voltage collapses at 86% rated 

power. Then, short circuit capabilities will be investigated 

(SCC = 10, 5, and 2.5). 

Figure 7 shows the terminal voltage for a wind power plant 

connected to a weak grid. As the output power increases, the 

voltage drops differently for the three PFs. At unity PF and 

0.95 PF (under an excited condition), the voltage drops 

accordingly. When the wind turbine is overcompensated to 

0.95 (overexcited), the terminal voltage rises as the output 

power increases. At unity PF, the terminal voltage drops by < 

2% at rated output power. In an overexcited condition, the 

terminal voltage rises by < 5%. The same phenomenon is also 

applicable to a stiff grid condition. The only difference is that 

the spread of voltage variation (from underexcited to 

overexcited) is much narrower (ΔV < + 1%) than in a weak 

grid. 

Figure 8 shows the terminal voltage variation as the wind 

turbine is connected to a stiff grid. The spread between overexcited and underexcited conditions is much narrower for a 

very stiff grid. 

2. Constant voltage operation 

The phasor diagram that describes the constant voltage 

control of a VSWTG is also shown in Figure 5c. The 

expanded description of the voltage control concept can be 

found in Section II (see Figure 1, Case I). The following can 

be said about constant voltage control: 

• Assume that Vs = Vt = 1.0 p.u. 

• The wind turbine must be operated in an overexcited 

condition. 

• The current magnitude and phase angle between the 

wind turbine voltage Vt and the infinite bus voltage 

Figure 6. Terminal voltage as a function of real power for a VSWTG 

operated at PF = 0.95 under-excited 

SCC = 2.5 

SCC = 5 

SCC = 10 

SCC =50 

Figure 7. Terminal voltage versus real power for three PFs for 

a weak grid condition 

PF = 0.95 

under exited 

PF = 0.95 

over exited 

PF = 1 

PF = 0.95 

under exited 

PF = 0.95 

over exited 

PF = 1 

0 0.2 0.4 0.6 0.8 1

0.99

0.995

1

1.005

1.01

Voltage versus Real Power (stiff grid)

Real Power

Vt

Figure 8. Terminal voltage versus real power for three PFs for 

a stiff grid condition 

PF = 0.95 

under exited 

PF = 0.95 

over exited 

PF = 1 

4
5

Vs increases as the power level increases. 

• The phase angle (φ) between the voltage Vs and the 

current I, increases as the power level increases. 

• The power angle (δ) between the voltage Vs and the 

voltage Vt, increases as the power level increases. 

• φ = δ/2.

Let us first consider different levels of grid stiffness to 

illustrate the concept of constant voltage control. As shown in 

Figure 9, the wind turbine must generate the reactive power to 

keep constant voltage at its terminal. The positive value of 

reactive power shown in Figures 9 and 10 is chosen to 

represent the reactive power generated by the wind turbine. 

The reactive power generated to maintain constant voltage 

varies with the level of grid stiffness. For example, for an SCC 

= 2.5, at rated output power, a wind turbine must generate 

reactive power as much as 21% of rated power. At SCC = 5, 

the reactive power needed is 10% of its rated value, and at 

SCC = 50, the reactive power needed is only 1% of its rated 

output. Thus, it is easy to see that the stiffer the grid, the less 

reactive power needed to keep the voltage constant. 

The control strategy can also be illustrated by plotting the 

PF of the operation. Figure 10 shows the PF at each operating 

point for constant voltage operation. For the weakest grid 

(SCC = 2.5), the wind turbine must be operated at PF = 0.98 

(overexcited) to keep the voltage at the terminal constant. For 

a grid with an SCC = 5, the PF at rated power must be kept at 

0.99 (overexcited). For a very stiff grid (SCC = 50), the wind 

turbine barely produces reactive power. Thus, we can conclude 

that the variable-speed wind turbine we studied can easily 

fulfill this requirement (power factor =+0.95, leading and 

lagging). 

B. Operation Under Fault 

VSWTGs tend to be more forgiving in operation under a 

fault condition because they can vary the speed and adjust the 

excitation (control reactive power via power converter). 

The significance of variability in speed is that the rotor of 

the wind turbine is a type of energy storage (kinetic energy). 

The kinetic energy stored is proportional to the rotational 

inertia and the square of rotor speed. Thus, increasing the 

speed to twice the original value means that the kinetic energy 

increment is four times higher. 

The significance of adjustable excitation is that the terminal 

voltage can be adjusted at will (within the allowable range). 

Obviously, the operating point of the WTG and the severity of 

the fault affect the survivability of the operation. Figure 11 

shows the power curve under various fault conditions. This is 

illustrated in the next two subsections. 

1. Most favorable condition 

The most favorable condition is a far fault when the wind 

turbine operates in a low wind speed condition. For a far fault, 

the terminal voltage is relatively high (non-zero), so it is easily 

corrected by the power converter. In addition, the WTG can 

still generate sufficient real power (there is enough generator 

torque to oppose aerodynamic torque), so a runaway condition 

is less likely. In a low wind condition, the rotational speed of 

the turbine is relatively low, so there is enough headroom to 

store kinetic energy from low rotor speed to rated rotor speed. 

Let us take a closer look at a far fault. Referring to Figure 11, 

assume that the fault occurs when the operating point of the 

WTG is at point A. The voltage at the terminal drops, 

assuming the VSWTG operates under constant voltage control, 

and the reactive power increases to increase the voltage to 

normal. If the power converter manages to control the voltage 

SCC = 2.5 

SCC = 50 

SCC = 5 

Figure 10. Operating PF to keep the terminal voltage constant for 

three levels of grid stiffness 

SCC = 2.5 

SCC = 5 

SCC = 50

Figure 9. Terminal voltage versus real power for three different 

levels of grid stiffness 

Figure 11. Power curve during fault conditions

pitch 

action

0 0.2 0.4 0.6 0.8 1 1.2

0

0.2

0.4

0.6

0.8

1

Real Power vs Rotor Speed

Rotor Speed or Wind Speed

Real Power

A 

B C 

D 

 E H 

F G 

F’ G’ 

 E’ H’ 

Rotor Speed 

far fault 

near fault 

5
6

generated to, say, 50% of pre-fault value during the fault, the C. Dynamic Simulation 

electrical power or the torque will be reduced to 50% of its 

normal value (line BC). The power converter switches have an 

absolute current limit that cannot be exceeded without 

damaging the power semiconductor. The pitch controller is 

normally not operated below rated speed. The aerodynamic 

torque remains the same as in a pre-fault condition. The 

aerodynamic power (line AD) accelerates the wind turbine 

about 30% in a pre-fault condition. The acceleration is 

illustrated by the polygon ABCD. As the wind turbine 

accelerates, the aerodynamic power has to oppose two things: 

(1) the electrical torque remains during the fault; and (2) the 

change in kinetic energy = 0.5 J (ω

To illustrate the dynamics of a VSWTG in a fault condition, 

let us use a VSWTG with a permanent-magnet generator that 

uses a power converter to process the electrical power and 

return it to the utility line. This system is commonly called 

full-power conversion as opposed to partial power conversion, 

as in a DFIG. 

For this particular run, the generator is set to generate rated 

output power at unity PF (reactive power is set to zero). 

Initially, the wind turbine is operated normally when the fault 

occurs at t = 1 s. The simulation is continued up to 10 s. The 

duration of the fault is nine cycles. The fault occurs in the 

middle of two parallel high-voltage transmission lines. The 

fault is cleared by disconnecting one of the two parallel lines. 

Before the fault, the SCC of the line is 10 (SCC = 10); after 

the fault is cleared the SCC is 5 (SCC = 5). The wind speed 

during the event is set at 125% of rated wind speed, so the 

pitch angle has been deployed at 13

B

2

 – ωA

2

). As the speed 

increases, the fault will probably clear in four to nine cycles. 

But even if the circuit breaker fails to clear the fault, the time 

and torque are sufficient to reduce acceleration. Let us assume 

that the fault condition remains uncorrected until the rotor 

speed reaches rated speed. At rated speed, the pitch controller 

starts to control the pitch angle to limit the rotor speed. 

o

. The upper limit of the 

blade pitch angle is 30o o and the optimal blade pitch angle is 0 . 

Figure 12 shows the terminal voltage of a VSWTG 

operated under constant PF at PF = 1. The terminal voltage has 

some residual voltage during the fault at about 0.18 p.u.; at the 

fault site, the voltage drops to zero. Small drops occur on the 

voltage traces before and after the fault occurs because the 

operation is at constant PF, so there is no attempt to correct the 

voltage. The voltage drop is caused by the difference between 

SCC = 10 and SCC = 5 (a weaker grid) when one of the 

parallel lines is disconnected. 

2. Least favorable condition 

The least favorable condition is a near fault, and it happens 

during high wind speed conditions. A near fault condition 

indicates that the remaining voltage at the terminal is very low, 

so the output power will decrease significantly to 

accommodate the current limit of the power converter. The 

generator power (represented by line FG in Figure 10) 

opposing the aerodynamic power (represented by line EH) will 

be much lower than in a normal condition. The acceleration is 

represented by the rectangle EFGH. At high wind speeds, the 

wind turbine operates at rated speed, and the pitch angle has 

been deployed to reduce the aerodynamic power. It is adjusted 

to keep the rotor speed from exceeding rated speed. Thus, the 

rotor speed does not have enough headroom to increase and to 

change the energy acquired aerodynamically into kinetic 

energy. In addition, the blade pitch angle is no longer zero but 

at a high position close to the upper limit pitch angle. The 

blade pitch angle also does not have enough headroom to shed 

aerodynamic power. The worst case is if the pitch controller 

fails to shed aerodynamic power. The fault is not cleared, and 

the rotor runaway problem can only be remedied by 

mechanical brakes (usually two alternative brakes must be 

provided to avoid this condition). 

Figure 13 shows the real and reactive power output of the 

VSWTG. The real power drops to a very small value during 

the fault because the current limit of the power converter has 

been reached. With a low voltage during the fault, the 

maximum power that can be generated during the fault is 

limited by the current limit of the power converter. In the postfault condition, there is a small reduction in output power 

because the voltage is reduced (see Figure 12). Because the 

control is set to provide a unity PF, the reactive power from 

the generator is set to zero. 

Let us back up a few steps and say that the fault is not a 

near fault, but is farther away from the WTG, so the voltage 

does not drop to zero. The generator power is illustrated by 

line F’G’. Now let’s say that the wind speed just reaches rated 

wind speed, so the blade pitch is barely deployed. If the pitch 

controller is fast enough to reduce the aerodynamic power, the 

aerodynamic power can be reduced quickly, say from line EF 

to line E’F’. In this condition, the acceleration is illustrated by 

E’F’G’H’, which is much smaller than the area EFGH. Thus, 

even at high wind speed the possibility of a runaway condition 

is remote. 

Figure 12. Terminal voltage for a VSWTG at PF = 1 

The lowest voltage at the WTG

Post fault voltage drop due 

to the difference in SCC

The lowest voltage at the fault

Voltage (p.u.)

0.4

0.8

1.2

1.6

2.0

Time (seconds)

0

0 2 4 6 8 10

The lowest voltage at the WTG

Post fault voltage drop due 

to the difference in SCC

The lowest voltage at the fault

Voltage (p.u.)

0.4

0.8

1.2

1.6

2.0

Time (seconds)

0

0 2 4 6 8 10

6
7

Figure 14 shows the variation of the high-speed and lowspeed shaft rotational speeds. The spread of the speed 

variation is < +4%. The pitch angle varies between 12.5o

 and 

13.5o

. For this fault event, the wind turbine stabilized to 

normal (no runaway condition). In this example, the grid 

condition is considered weak (SCC = 5), and the duration of 

the nine-cycle fault is considered long (four cycles clearing 

time is normally used for general studies). 

III. CONCLUSIONS 

This paper investigates a variable-speed wind turbine. From 

the steady state analysis, the operation under power factor 0.95 

underexcited indicates that the system will be driven to a 

voltage collapse at SCC=2.5. However, by having the 

capability to adjust the power factor to 0.98 overexcited, the 

grid condition of SCC=2.5 can be operated at rated voltage. 

This is important considering that the VSWTG we studied is 

capable of operating at 0.95 (under- or overexcited 

conditions). 

Dynamic simulation performed on this VSWTG indicates 

that the wind turbine can survive a nine cycle fault event with 

SCC=5. Note, the interaction between mechanical rotor 

oscillation and the electrical oscillation is practically nonexistent. The rotor oscillation caused by a sudden change in 

electrical generator output power is properly damped within a 

short time. The pitch angle controller performs very well 

under fault condition. 

-200

-120

- 40

40

120

200

Real Power (MW)

Real Power P

Reactive Power Q = 0

IV. ACKNOWLEDGMENT

We acknowledge the support of the U.S. Department of 

Energy and Public Service Company of New Mexico. 

V. REFERENCES 

[1] Muljadi, E.; Butterfield, C.P.; Ellis, A.; Mechenbier, J.; 

Hochheimer, J.; Young, R.; Miller, N.; Delmerico, R.; 

Zavadil, R.; Smith, J.C. Equivalencing the Collector 

System of a Large Wind Power Plant, presented at the 

IEEE Power Engineering Society Annual Meeting, 

Montreal, Canada, June 18 – June 22, 2006. 

[2] Shaw Power Technologies, Inc., 2004, August. PSS/E 

Version 3.0 Program Documentation, General Electric 

International, Inc. 2004, December. PSLF Version 14.2 

User’s Manual. 

[3] Slootweg, H. Wind Power: Modeling and Impact on 

Power System Dynamics, Ph.D. Thesis, Technical 

University Delft, Delft, the Netherlands, 2003. 

[4] Tande, J.O.G.; Muljadi, E.; Carlson, O.; Pierik, J.; 

Estanqueiro, A.; Sørensen, P.; O’Malley, M.; Mullane, A.; 

Anaya-Lara, O.; and Lemstrom, B.; “Dynamic models of 

wind farms for power system studies–status by IEA Wind 

R&D Annex 21,” European Wind Energy Conference & 

Exhibition (EWEC), London, U.K., November 22−25, 

2004. 

[5] Petersson, A.; Thiringer, T.; Harnefors, L.; Petru, T.; 

"Modeling and Experimental Verification of Grid 

Interaction of a DFIG Wind Turbine", IEEE Transactions 

on Energy Conversion, Volume 20, Issue 4, Dec. 2005 

Page(s): 878 – 886. 

[6] Hughes, F.M.; Anaya-Lara, O.; Jenkins, N.; Strbac, G.; 

”A Power System Stabilizer for DFIG-Based Wind 

Generation,” IEEE Transactions on Power Systems, 

Volume 21, Issue 2, May 2006, Page(s):763 – 772. 

[7] Behnke, M.R.; Muljadi, E.; Reduced Order Dynamic 

Model for a Variable-Speed Wind Turbine with a 

Synchronous Generator and Full Power Conversion 

Topology, presented at the International Conference on 

Future Power Systems, November 16-18, 2005, 

Amsterdam, The Netherlands, Page(s): 1 – 6. 

Figure 14. Low-speed shaft, high-speed shaft rotational speed, 

and pitch angle for a VSWTG at PF = 1 

HSS rotor speed

LSS rotor speed

Pitch angle

5

7

9

11

13

15

Pitch Angle (degree)

-0.25

-0.15

-0.05

0.05

0.15

0.25

Rotor Speed (p.u.)

0 2 4 6 8 10

Time (seconds)

HSS rotor speed

LSS rotor speed

Pitch angle

5

7

9

11

13

15

Pitch Angle (degree)

-0.25

-0.15

-0.05

0.05

0.15

0.25

Rotor Speed (p.u.)

0 2 4 6 8 10

Time (seconds)

024 68

Time (seconds)

Reactive Power (MVAR)

-200

-120

-40

40

120

200

10

-200

-120

- 40

40

120

200

Real Power (MW)

Real Power P

Reactive Power Q = 0

024 68

Time (seconds)

Reactive Power (MVAR)

-200

-120

-40

40

120

200

10

Figure 13. Real power and reactive power for a VSWTG at PF = 1 

7
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Characteristics of Wind Turbines Under Normal and Fault 

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This paper investigates the characteristics of a variable-speed wind turbine connected to a stiff grid or a weak grid, 

the role of reactive power compensation in optimizing the operation of the wind turbines, and the operation of a wind 

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15. SUBJECT TERMS

wind turbine; variable-speed wind turbine; wind energy; systems integraion; utility grid connection 

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