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Contract No. DE-AC36-08GO28308

Short-Circuit Modeling of a 

Wind Power Plant 

Preprint

E. Muljadi and V. Gevorgian

To be presented at the Power & Energy Society General Meeting

Detroit, Michigan

July 24-29, 2011

Conference Paper

NREL/CP-5500-50632

March 2011
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1 

Short-Circuit Modeling of a Wind Power Plant

E. Muljadi V. Gevorgian

Fellow, IEEE Member, IEEE

eduard.muljadi@nrel.gov vahan.gevorgian@nrel.gov

National Renewable Energy Laboratory

1617 Cole Blvd.

Golden, CO 80401, USA

Abstract - An important aspect of wind power plant (WPP) impact studies is to evaluate short-circuit current (SCC) contribution of the plant into the transmission network under different 

fault conditions. This information is needed to size the circuit 

breakers, to establish the proper system protection, and to 

choose the transient suppressor in the circuits within the WPP. 

This task can be challenging to protection engineers due to the 

topology differences between different types of wind turbine 

generators (WTGs) and the conventional generating units.

This paper investigates the short-circuit behavior of a WPP

for different types of wind turbines. The short-circuit behavior 

will be presented. Both the simplified models and detailed models are used in the simulations and both symmetrical faults and 

unsymmetrical faults are discussed. 

Index Terms — Fault contribution, induction generator, protection, short circuit, wind power plant, wind turbine. 

I. INTRODUCTION

nergy and environmental issues have become one of the 

biggest challenges facing the world. In response to energy 

needs and environmental concerns, renewable energy technologies are considered the future technologies of choice [1], 

[2]. Renewable energy is harvested from nature, and it is 

clean and free. However, it is widely accepted that renewable 

energy is not a panacea that comes without challenges. With 

the federal government’s aggressive goal of achieving 20% 

wind energy penetration by 2030, it is necessary to understand the challenges that must be overcome when using renewable energy.

In the years to come, there will be more and more wind 

power plants (WPPs) connected to the grid. With the goal of 

20% wind penetration by 2030, the WPP’s operation should 

be well planned. The power system switchgear and power 

system protection for WPPs should be carefully designed to 

be compatible with the operation of conventional synchronous generators connected to the same grid. This paper attempts to illustrate the behavior of short-circuit current (SCC)

contributions for different types of WTGs.

Conventional Power Plant versus Wind Power Plant

A conventional power plant consists of a single or several 

large (e.g., 100 MW) generators. The prime mover of the 

generator can be steam, gas, or a combustion engine. The 

generator is controllable and is adjustable up to a maximum 

limit and down to minimum limit. The power output is dispatched according to the load forecast, influenced by human 

operation, and is based on optimum operation (i.e., scheduled 

operation). The power plant is usually located relatively close 

to the load center.

The typical, conventional generator used is a synchronous 

generator. The rotational speed is fixed – no slip; and the flux 

is controlled via exciter windings. The magnetic flux and the 

rotor rotate synchronously.

A WPP consists of many (hundreds) of wind turbine generators (WTGs). Currently, available WTG sizes are between 

1 MW and 5 MW. The prime mover of the WTG is wind, 

and it is free, natural, and pollution-free. The controllability 

of the WPP is typically curtailment (spilling the wind). The 

energy production of a WPP depends on the wind variability, 

and its dispatch capability is based on wind forecasting, and it 

is influenced more by nature (wind) than human factors, with 

the goal set on maximizing energy production from renewable 

resources (i.e., unscheduled operation). Large-scale WPPs are 

located in a high-wind resource region, and these may be far 

from the load center.

Because a WPP covers a very large area, there are power 

output diversities found in a typical WPP. Each WTG in a 

WPP will be located at different electrical distances from the 

substation (diversity in line impedance). Each turbine may be 

driven by different instantaneous wind speeds. Thus, the operating condition of each turbine may be slightly different 

from others within the WPP. 

Operation of Wind Turbine Generator

The generator at each turbine should be protected individually and independently because of the electrical diversity of 

the WPP. In practice, this is an advantage of a WPP compared to a conventional power plant. During a disturbance, 

the electrical characteristics at each terminal of the turbine is 

different from the other turbines, and only the most affected 

WTGs will be disconnected from the grid. For general faults 

(distance faults at the transmission point), only 5%-15% of 

the turbines are disconnected from the grid [3]. This is partially because WPPs are required to have zero voltage ridethrough capability. Thus, the loss of generation is not as severe as in a power plant with large generators.

E
2 

At the turbine level, the WTG generates at low voltage levels (480 V to 690 V). For the Type 1 and Type 2 WTGs, it 

is typically compensated by switched capacitor banks to generate at a unity power factor. Type 3 and Type 4 generators 

are operated to generate a constant voltage at a designated 

bus, or may be operated at constant power factor or constant 

reactive power. The generator is connected to a pad-mounted 

transformer to step up the voltage to 34.5 kV. 

 Collector System 

The collector system consists of miles of line feeders connecting the high side of the pad-mounted transformer to the 

substation. Usually, wind turbines are divided into groups of 

turbines connected in a daisy chain fashion using underground cables. These groupings are then connected to the 

substation by either underground cables or overhead lines at 

34.5 kV. Since it is not practical to model hundreds of turbines in a power flow calculation or in a dynamic simulation, 

it is common to find the equivalent of the turbines as either a 

single equivalent turbine representation or multiple turbine 

representation [4],[5]. 

Organization of the Paper 

The organization of this paper is as follows; in section II, 

the SCC characteristics of different WTG types will be presented for a symmetrical fault. In section III, the characteristics of SCC for unsymmetrical faults will be discussed. Finally, in section V, the conclusion will summarize the paper’s 

findings. 

II. SHORT CIRCUIT BEHAVIOR UNDER SYMMETRICAL FAULTS

A utility-sized wind turbine is larger than non-grid wind 

turbine applications. In the early days, the turbines were 

sized from 10 kW to 100 kW. Nowadays, wind turbines are 

sized above 1000 kW (1 MW). 

A. R-L Circuits 

Short-circuit faults can occur in various locations of the 

power system in a number of different ways including line-toground and line-to-line faults. For simplicity purposes, we’ll 

consider a symmetrical three-phase fault since it is the easiest 

to analyze. A simple equivalent diagram of a power system 

under such fault conditions is shown in Fig. 1a. 

The fault in Fig. 1a is represented by a shorting switch. 

Immediately after the fault, the SCC contribution from the 

generator can be found using the following equation: 

ܮ ൌ௚ ݑ

݀݅

݀ݐ ൅ ܴ݅ ሺ1ሻ

Where ݑ ௚is the instantaneous voltage on the generator terminals, and R and L are line resistance and inductance. Solving equation (1) for current 

݅ ൌ

ܸ௚

ܼ sin ൬߱ݐ ൅ ߙ െ atan ൬ܺ

ܴ

൰൰

െ ݁ିோ

௅ ௧ ൤

ܸ௚

ܼ sin ൬ߙ െ atan ൬ܺ

ܴ൰൰൨ ሺ2ሻ

Where ܸ௚ is peak generator voltage, ܼ ൌ √ܴଶ ൅ ܺଶ - line 

impedance, and ߙ is the voltage phase. The solution (2) has 

two components; the first component is stationary and varies 

sinusoidally with time as shown in Figure 1b. It represents the 

steady SCC driven by the voltage source Eg. The second 

component decays exponentially (as shown in Figure 1c) with 

a time constant equal to ோ

௅ . It represents the DC component 

of the current and the natural response of the circuit without 

the excitation provided by Eg. 

The steady-state symmetrical fault rms value of the SCC 

ܫ௦௖ from the generator can be calculated from the first component of equation (2) and is shown in equation 3: 

ܫ௦௖ ൌ ܸ௚/√2

√ܴଶ ൅ ܺଶ

 ሺ3ሻ

Obviously, the steady-state fault current depends on the 

impedance of the line. The closer the fault occurrence loca-

(b) AC component (c) DC component 

(d) Fault current 

0 0.02 0.04 0.06 0.08 0.1 0.12 10

0

10

20

(a) Equivalent diagram of symmetrical fault 
3 

tion to generator terminals, the larger the SCC contributed to 

the fault. 

The peak magnitude of the transient component in equation 

(2) depends on line impedance as well, but it also depends on 

impedance angle φ ൌ atan ቀ௑

ோ

ቁ at the point of the fault. The 

DC term does not exist if φ = 0, and will have its maximum 

initial value of ௏೒

௓ , where ߙെφൌേ గ

ଶ . 

The worst case scenario for the SCC peak value (including 

the DC component) for the circuit presented in Figure 1a is 

shown in equation 3. 

So, depending on the time when the fault occurs and the 

circuit characteristics, the transient current waveform will be 

different. This means that in three-phase systems, the phase 

transient currents will have different peaks due to a 1200

 shift 

in voltages. 

In large power systems with many generators and transmission lines, the actual fault current at any location in the grid 

will be the sum of collective contributions from all generators, making the above described analysis extremely complicated. So, some sort of simplification is needed for the fault 

current calculation in such a case. 

B. SCC from a Type 1 WTG 

The first generation of utility-sized WTGs were a fixedspeed turbine with a squirrel-cage induction generator (SCIG) 

and is called a Type I generator in wind-related applications. 

The SCIG generates electricity when it is driven above synchronous speed. The difference between the synchronous 

speed and the operating speed of the induction generator is 

measured by its slip (in per unit or in percent). A negative 

slip indicates that the wind turbine operates in generating 

mode. Normal operating slips for an induction generator are 

between 0% and -1%. The simplified single-phase equivalent 

circuit of a squirrel-cage induction machine is shown in Fig. 2 

[6]. 

 

Fig. 2: Equivalent circuit of a Type 1 generator 

The circuit in Fig. 2 is referred to the stator where RS and 

Rr are stator and rotor resistances, Lsσ and Lrσ are stator and 

rotor leakage inductances, Lm is magnetizing reactance, and s

is rotor slip. The example single-line connection diagram of a 

Type I generator is shown in Fig. 3. In the case of a voltage 

fault, the inertia of the wind rotor drives the generator after 

the voltage drops at the generator terminals. The rotor flux 

may not change instantaneously right after the voltage drop 

due to a fault. Therefore, voltage is produced at the generator 

terminals causing fault current flow into the fault until the 

rotor flux decays to zero. This process takes a few electrical 

cycles. The fault current produced by an induction generator 

must be considered when selecting the rating for circuit 

breakers and fuses. The fault current is limited by generator 

impedance (and can be calculated from parameters in Fig. 2) 

and impedance of the system from the short circuit to the generator terminals. 

Fig. 3: Type 1 WTG 

The initial value of fault current fed in by the induction generator is close to the locked rotor-inrush current. Assuming a 

three-phase symmetrical fault, an analytical solution can be 

found to estimate the current contribution of the generator. 

The SCC of an induction generator can be calculated as [7]: 

݅ሺݐሻ ൌ √2ܸௌ

ܼௌ

ᇱ ቈ݁ି ௧

்ೄ

ᇲ

sinሺߙሻ െ ሺ1െߪሻ݁

ି ௧

்ೝ

ᇲ

sinሺ߱ݐ ൅ ߙሻ቉ ሺ4ሻ

Where α is the voltage phase angle for a given phase, σ is 

the leakage factor, ܼௌ

ᇱ ൌ ܺௌ′ ൌ ߱ܮௌ′ is stator transient reacFig. 4: Stator and rotor transient inductances. 

L’

s

L’

r

(a) AC component (b) DC component 

Fig. 5: The two components of the SCC for a Type 1 WTG 
4 

tance, and ܶௌ

′

 and ܶ௥

′

 are stator and rotor time constants 

representing the damping of the DC component in stator and 

rotor windings. The transient stator and rotor inductances ܮ௦

ᇱ

௥ܮ and

ᇱ can be determined from the circuits shown in Figure 4. 

ௌܮ

ᇱ ൌ ܮௌఙ ൅ ௅ೝ഑௅೘

௅ೝ഑ା௅೘

௥ܮ 

ᇱ ൌ ܮ௥ఙ ൅ ௅ೄ഑௅೘

௅ೄ഑ା௅೘

 ሺ5ሻ 

ܶௌ

ᇱ ൌ ௅ೄ

ᇲ

ோೄ

; ܶ௥

ᇱ ൌ ௅ೝ

ᇲ

ோೝ

 ሺ6ሻ 

ߪൌ1െ ௅೘

మ

௅ೄ௅ೝ 

 ሺ7ሻ 

ܮௌ ൌ ܮௌఙ ൅ ܮ ; ௠ܮ ௥ൌ ܮ௥ఙ ൅ ܮ ௠ሺ8ሻ

Equation 4 is different from equation 2. The first distinction is that there is no voltage source driving the fault current 

as in equation 2. The fault current is driven by the decaying 

flux trapped in the rotor winding as represented by the right 

portion of the equation 4. The second distinction is the rotor 

time constant ܶ௥

ᇱ

 governs the dynamic of the decaying rotor 

flux (AC component of the SCC as shown in Fig. 5a) and the 

decaying DC component of the fault current (refer to Fig. 5b) 

is governed by the stator time constant ܶ௦

ᇱ

. The larger the 

leakage inductances (σ), the smaller is the fault current amplitude. The third distinction is that the fault current dies out 

after the flux driving the fault current depleted to zero. Note, 

the DC and AC transient components of the SCC flowing out 

of the stator windings induce fault currents in the rotor 

winding and vice versa until the magnetic flux is depleted. 

The current calculated from equation (4) is shown in Fig. 6 

using parameters for a typical 2-MW induction generator 

when and pre fault voltage 0.7 p.u. As can be seen from Fig. 

6, the current reaches the maximum value at π (first half a 

period). Therefore, it may be a good approximation to calculate the maximum (peak) current by substituting ݐ ൌ ܶ/2 

into (4). The resulting equation for peak current will be: 

݅௠௔௫ ൌ √ଶ௏ೄ

௓ೄ

ᇲ ቈ݁ି ೅

మ೅ೄ

ᇲ

൅ ሺ1െߪሻ݁

ି ೅

మ೅ೝ

ᇲ

቉ ሺ9ሻ

 It was demonstrated experimentally in [8] that equation (9) 

gives satisfactory accuracy for peak current assessment. The 

resulting current is shown in Fig. 7. A detailed dynamic 

model of a Type 1 WTG is simulated in PSCADTM. A symmetrical three-phase fault is simulated and the resulting SCC 

is compared to the simulation result of the simplified representation as described in equation 4. It is shown in Fig. 7 

that the two traces are very closely matched. 

From equation 4, it is shown that the operating slip does not 

influence the short-circuit transient behavior. To check the 

influence of the slip, we performed symmetrical three-phase 

faults on a Type 1 WTG for two different slips using the detailed model. As shown in Fig. 8, the pre-fault current and 

the post-fault current for the two different operating slips are 

very distinct. Similarly, the frequencies of the SCC during 

the fault are not the same for two different operating slips. 

However, the peak values of the SCC of the induction generator operating at two different slips are very closely matched. 

C. SCC from a Type 2 WTG 

The variable slip generator is essentially a wound-rotor induction generator with a variable resistor connected in series 

to the rotor winding (Type 2 generator). This external resistor 

is controlled by a high-frequency switch. Below rated power, 

the resistor control is inactive, so the system operates as a 

conventional induction generator. Above rated power, the 

resistor control allows the slip to vary, so variable speed operation is possible for a speed range of about 10% [9]. If the 

blade pitch angle is kept constant at zero degrees, the rotor 

speed, and thus the slip, will vary with wind speed. However, 

operation at higher slips generate a lot of loss because of the 

rotor resistance. Thus, the heat loss can be excessive. On the 

other hand, if the blade pitch angle is controlled to keep the 

Fig. 6: SCC from a Type I WTG 

Fig. 7: SCC comparison between the output of the detailed model and the 

output of the simplified model simulated for a Type I WTG 

Figure 8: SCC comparison for two different slip. 

Min Isc-peak

Max Isc-peak
5 

rotor speeds within a small deviation from the rated slip, the 

losses in rotor resistance can be minimized. An equivalent 

electrical diagram of a variable-slip induction generator is 

shown in Fig. 9, with a variable external resistor Rext. 

The connection diagram example for this type of generator 

is shown in Fig. 10. In case of three-phase symmetrical fault, 

the same equations as for a Type I generator are applied. The 

only difference will be for rotor time constant that needs to 

account for additional external resistance. 

 Fig. 9: Equivalent circuit for a Type 2 generator 

 

Fig. 10: Connection diagram for a Type 2 WTG 

The modified rotor time constant can be calculated by adding the effect of the external resistor Rext (refer to Table II, p. 

7), where Rext is the value of external resistance that happens 

to be in the circuit at the time of the fault. The effect of such 

additional resistance on SCC is shown in Fig. 11. So, adding 

the external resistors doubles the overall rotor resistance. The 

modified equation for SCC, maximum current, and the rotor 

transient time constant can then be derived using the values 

shown in Table I (see p. 7). 

The maximum current occurs at ∆ܶ, the time after a fault 

when current reaches its first peak. In this case, this additional 

resistance decreases the overall AC component in current, but 

does not much affect the first peak value of the current since 

the increase in resistance is relatively small. The same conclusion can be made by analyzing equations (4) and (9), 

where the additional external resistance has an effect on a 

second term that represents the AC component of the current. 

As shown in Table I and Table II, the impact of the external 

rotor resistance on the SCC is two-fold: it reduces the SCC 

magnitude, and it shortens the rotor time constant (decay time 

of the SCC). 

D. SCC from a Type 3 WTG 

A Type 3 WTG is implemented by a doubly fed induction 

generator (DFIG). It is a variable-speed WTG where the rotor 

speed is allowed to vary within a slip range of +30%. Thus, 

the power converter can be sized to about 30% of rated power. The equivalent electrical diagram of a DFIG is shown in 

Fig. 12. 

It is similar to one for a regular induction generator except 

for additional rotor voltage, representing voltage produced by 

a power converter. Under normal operation, this voltage is 

actually from a current-controlled power converter with the 

ability to control the real and reactive power output instantaneously and independently. The capability to control flux 

(flux-oriented controller – FOC) in induction machines has 

been used in the motor drive industry since the seventies. 

The typical connection diagram for a DFIG (Type 3) WTG 

is shown in Fig. 12. In an ideal situation, the power converter 

connected to the rotor winding should be able to withstand the 

currents induced by the DC and AC components flowing in 

the stator winding. However, the components of the power 

converter (IGBT, diode, capacitor, etc.) are designed to handle only normal currents and normal DC bus voltage. A 

crowbar system is usually used for protecting the power electronics converter from overvoltage and thermal breakdown 

during short-circuit faults. A crowbar is usually implemented 

to allow the insertion of additional resistance into the rotor 

winding to divert the SCC in the rotor winding from damaging the power converter. Additional dynamic braking on the 

DC bus is also used to limit the DC bus voltage. 

Fig. 12: Simplified equivalent circuit of a DFIG 

Fig. 11: Effect of external resistance for a Type 2 WTG Fig. 13: Connection diagram for a Type 3 WTG 
6 

During faults, the rotor windings are essentially short circuited by an equivalent adjustable crowbar resistance RCB. 

The modified equation for SCC, maximum current, and the 

rotor transient time constant can then be derived using the 

values shown in Table I [7]. In a Type 3 WTG, however, the 

size of the crowbar is usually controlled as such that the actual fault current is more controllable than the simplified assumption. In Fig. 14, three-phase fault currents are shown to 

be well regulated by proper control of the crowbar resistance. 

In this case, the crowbar circuit installed on the rotor winding 

is controlled to maintain the DC bus voltage constant.

A dynamic braking resistor is also installed on the DC bus 

to help regulate the DC bus. Fig. 14 shows the size of the 

real power modulated in the crowbar during the faults. There 

are also dynamic braking resistors and a DC chopper installed 

on the DC bus to help regulate the DC bus voltage during 

transients. The corresponding rotor currents are also shown 

in Fig. 14. Because of differences in crowbar implementation 

from one turbine manufacturer to the other, a protection engineer should evaluate the recommended value provided by the 

manufacturers. However, if none is available, the values of 

minimum and maximum SCCs presented in Table I can be 

used.

E. Type 4 WTGs 

An example of a Type 4 direct-drive WTG with permanentmagnet synchronous generator (PMSG) is shown in Fig. 15. 

This is a variable-speed WTG implemented with full power 

conversion. Recent advances and lower cost of power electronics make it feasible to build variable-speed wind turbines 

with power converters with the same rating as the turbines.

The full power conversion allows separation between the 

WTG and the grid, thus, the mechanical dynamic can be buffered from entering the grid and the transient dynamic on the 

grid can be buffered from entering the wind turbine dynamic. 

Thus, while the grid is at 60 Hz, the stator winding of the generator may operate at variable frequencies. The temporary 

imbalance between aerodynamic power and generated power 

during a transient is handled by the pitch control, dynamic 

brake, and power converter control.

The SCC contribution for a three-phase fault is limited to 

its rated current or a little above its rated current. It is common to design a power converter for a Type 4 wind turbine 

with an overload capability of 10% above rated. Note that in 

any fault condition, the generator stays connected to the power converter and is buffered from the faulted lines on the grid. 

Thus, although there is a fault on the grid, the generator output current is controlled to stay within the current limit (e.g., 

1.1 p.u.). However, keep in mind that with a fault on the grid, 

the output power delivered to the grid is less than rated power. Although the currents can be made to balance, due to reduced voltage and/or unbalanced voltage, only a reduced output power can be delivered. In Type 4 WTGs, the SCC is a 

controlled parameter. So, such WTGs can be represented as a 

constant 3-phase balanced current source in a short-circuit 

models. The priority of the real power versus reactive power 

during the fault depends on the prior setting of the controller. 

However, the current limit of the power converter must be 

followed to protect the power switches.

 

Fig. 15: PMSG direct-drive WTG diagram

F. SCC Comparison for Symmetrical Faults

The SCCs for different types of wind turbines are not the 

same. For each turbine types, the peak value of the magnitude of the SCC is affected by the transient reactance, the prefault voltage, the effective rotor resistances, and the instant 

the fault occurs.

For turbine Types 1 through Types 3, the SCC declines as 

the fault progresses and eventually ceases as the rotor flux is 

depleted. For Type 4 WTGs, the SCC can be maintained 

constant.

The SCC transient behavior is affected by the stator time 

constant and the rotor time constant for Type 1 through Type 

3 WTGs. The Type 4 generators can generate constant current 

during the fault.

In Table I, the list parameters are shown. These parameters 

can be used to substitute the parameters from equation 4 and 

equation 6 for different types of WTGs. Table II lists the 

maximum and minimum possible values of the peak of SCC. 

Fig. 14: The fault currents, the rotor currents, and the power consumed by 

the crowbar circuits in a Type 3 WTG.
7 

It is shown that the Type 1 WTG can produce the largest 

SCC. The instant of the fault has affects on the magnitude of 

the SCC. The maximum value is based on the peak of the AC 

component and the highest value of the DC component, and 

the minimum value is based on the peak value of the AC 

component only. 

TABLE I. 

MODIFIED VALUES FOR SCC CALCULATION FOR DIFFERENT TYPES OF WTGS

WTG Type 1 Type 2 Type 3 

࢙ࢆ

ᇱ ܺௌ

ᇱ ൌ ߱ܮௌᇱ ටܺௌ

ᇱଶ ൅ ܴ௘௫௧

ଶ ටܺௌ

ᇱଶ ൅ ܴ஼஻ଶ

࢘ࢀ

௥ܮ ᇱ

ᇱ

ܴ௥

௥ܮ

ᇱ

ܴ௥ ൅ ܴ௘௫௧

௥ܮ

ᇱ

ܴ௥ ൅ ܴ஼஻

TABLE II. 

MAXIMUM AND MINIMUM POSSIBLE VALUE OF THE SCC 

WTG Type 1 Type 2 Type 3 Type 4 

Max 

ISC_PEAK '

2

2

S

s

X

V

'

2

2

S

s

X

V

'

2

2

S

s

X

V 1.1 

IRATED

Min 

ISC_PEAK '

2

S

s

X

V 2' 2 ' )9(

2

S r

s

RX

V

+

1.1 

IRATED

0 

For a Type 2 WTG, the maximum value is computed when 

ܴ௘௫௧= 0 Ω. The minimum value is computed when the slip 

reaches 10% above synchronous speed. And for a Type 3 

WTG, the maximum value is computed when the crowbar 

shorts the rotor winding and the minimum value is computed 

when the power converter can follow the commanded current 

(i.e., in case the fault occurs far away from the point of interconnection, the remaining terminal voltage is relatively high 

enough to let the power converter operate normally and 

supply the commanded currents). Note, that for a symmetrical fault, the actual fault current for each phase is different 

from the other phases due to the fact that the time of the fault 

occurs at a different phase angle for different phases, thus 

affecting the DC offset. For a Type 4 WTG, the stator current 

can always be controlled because of the nature of power converter which is based on current controlled voltage source 

converter. 

An example of SCC for Type 4 WTGs is given in the next 

section. 

In this section, the SCC is analyzed at the terminals of the 

generator. In an actual WPP, the faults will likely occur at the 

transmission side. Thus, the impact of the cable capacitance, 

plant level reactive compensation, and wind plant transformer 

connections are not included. References [10-14] provide 

good sources of information for the WPP environment. 

III. UNSYMMETRICAL FAULTS

The nature of the fault produces a different response for 

different wind turbine types. In this section, the observation 

of the short-circuit behavior for unsymmetrical faults on different types of WTGs will be presented. Note, that operating 

an induction generator under an unbalanced condition creates 

torque pulsation and unbalanced currents. If this condition 

persists for a long period of time, it may excite other parts of 

the wind turbine, and the unbalanced currents may create unequal heating in the three-phase windings, thus, shorten the 

life of the winding insulation. 

Unlike in a symmetrical three-phase fault, the positivesequence voltage source continues to drive the fault current 

until the fault or the generator removed from the circuit. The 

remaining un-faulted (normal) phases continue to maintain 

the air gap flux. The initial conditions of the fault currents 

are different for each phase. The three line currents usually 

show a different DC offset, which eventually settles out over 

time. 

To explore the short-circuit behavior of unsymmetrical 

faults presented in this section, a detailed model of the system 

is developed in PSCADTM. 

A. Single Line-to-Ground (SLG)Faults 

The single line-to-ground fault is the most likely to occur in 

the power system. The magnetic flux in the air gap, although 

smaller than normal and unbalanced, is maintained by the 

remaining un-faulted lines. Thus, the short circuit in SLG 

faults will continue to flow until the circuit breaker removes 

the fault from the circuit. 

Figure 16 shows the SCC of a Type 1 WTG for three linesto-ground (3LG) and an SLG fault. In the symmetrical fault, 

the SCC dies out rather quickly, while in a SLG fault, the 

SCC is driven by the remaining two phases and it continues to 

flow until the short circuit is removed from the circuit. The 

peak current during a SLG fault is typically higher than for a 

3LG fault (there is a quicker decay of current during symmetrical a 3LG fault due to magnetic field collapse). The differFig. 16. Voltage and SCC for 3LG and SLG for a Type 1 WTG. 

-15

-10

-5

0

5

10

15

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

CURRENT (kA)

TIME (sec)

I3a

I3b 

I3c 

-10

-5

0

5

10

15

20

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

CURRENT (kA)

TIME (sec)

I3a

I3b 

I3c 
8 

ence in peak currents for both 3LG and SLG faults depends 

on generator parameters, fault location, etc. Note also that the 

presence of the positive sequence, the negative sequence, and 

zero sequence currents in the unsymmetrical faults influence 

the size of the SCC. No comparison has been made between 

dynamic simulation results and results obtained via symmetrical component calculations (this is planned for future 

work). 

In Fig. 17, the SCC for a Type 3 WTG is shown both for 

the three-phase currents and the corresponding sequence 

components. The changes in positive sequence and the sudden appearance of the negative sequence are also shown. The 

absence of the zero sequence current is a consequence of 

transformer winding connections. 

B. Line-to-Line (LL) and Line-to-Line-to-Ground (LLG) 

Faults 

The line-to-line fault and the line-to-line-to-ground fault also maintained the air-gap flux during the fault. Output power 

of the generator will be limited and pulsating due to an unbalanced condition. The SCC will continue to flow until the 

circuit breaker removes the fault from the circuit. 

As shown on Fig. 18 and Fig. 19, the type of fault affects 

the existence of the zero sequence component in the SCC of 

the WPP. Thus, the line currents in the three phases are distributed differently based on its positive sequence, negative 

sequence, and the zero sequence magnitudes and phase angles. 

C. SCC for the Type 4 WTG under Different Faults 

In Fig. 20, the fault currents for a Type 4 WTG are shown. 

Note, that the power converter buffers the generator from the 

grid. The SCC is basically controlled by the power converter. 

Hence, the line currents are symmetrical currents at different 

types of unsymmetrical faults. The post fault recovery may 

slightly differ for different faults. 

Fig. 18. The SCC for a LL fault of a Type 2 WTG. 

Fig. 19. The SCC for LLG fault of a Type 2 WTG. 

a) 3 LG 

b) SLG 

c) LLG 

d) LL 

Fig. 20. SCC for Type 4 WTG for different types of faults 

-15

-10

-5

0

5

10

15

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

CURRENT (kA)

TIME (sec)

I3a 

I3b 

I3c 

-0.5

0

0.5

1

1.5

2

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

CURRENT (kA)

TIME (sec)

I3+ 

I3-

I3o 

-20

-10

0

10

20

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

CURRENT (kA)

TIME (sec)

I3a 

I3b 

I3c 

-1

0

1

2

3

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4

CURRENT (kA)

TIME (sec)

I3+ 

I3-

I3o 

-4

-2

0

2

4

2.95 3 3.05 3.1 3.15 3.2 3.25 3.3

CURRENT (kA)

TIME (sec)

-4

-2

0

2

4

2.95 3 3.05 3.1 3.15 3.2 3.25 3.3

CURRENT (kA)

TIME (sec)

-4

-2

0

2

4

2.95 3 3.05 3.1 3.15 3.2 3.25 3.3

CURRENT (kA)

TIME (sec)

-4

-2

0

2

4

2.95 3 3.05 3.1 3.15 3.2 3.25 3.3

CURRENT (kA)

TIME (sec)

(a) Three phase currents 

(b) Positive, negative and zero sequence currents 

Fig. 17. SCC for SLG for a Type 3 WTG 
9 

IV. CONCLUSIONS

In this paper, the SCC contributions of different WTGs for 

faults at the terminal of the generator where simulated using 

simplified model to determine SCC characteristics for symmetrical faults. The simplified model represents the size and 

the time constants governing the SCC behavior. A table 

summarizing different fault impedance and transient rotor 

time constants is provided. Another table summarizing the 

range of SCCs for different types of WTGs is presented in 

Table II. For Type 1 and Type 2 WTGs, the maximum and 

the minimum values depend on timing of the fault, and the 

parameters and the operating condition of the induction generator. For Type 3 WTGs, the control and the operation of the 

crowbar and dynamic braking affects the characteristics of the 

SCC. For Type 4 WTGs, the SCC is controllable by the power converter.

To compute unsymmetrical faults, detailed models were 

used to demonstrate the behavior of SCCs of different WTGs. 

As expected, the SCC continues to flow until the fault is 

cleared from the circuit or the generator is disconnected from 

the grid. The terminal voltage and currents are sustained 

longer because the line voltages, except from the faulted

phase, are able to sustain air gap flux. The nature of SCC is 

not only affected by the type of WTG, but also by the nature 

of the faults, and the winding connections of the generator 

and the transformers between the fault and the generator. 

Auxiliary components (reactive compensations), cable length 

and capacitance, the diversity of the WPP will contribute to 

the size and nature of the SCC, one way or another.

Each WPP is unique. Therefore, recommended practice 

from local reliability organizations, the manufacturers, transmission planners, wind plant developers, and the local utilities 

should be followed very closely.

V. ACKNOWLEDGMENT

This work is supported by the U.S. Department of Energy 

and California Energy Commission.

VI. REFERENCES

[1] U.S. Department of Energy – Energy Efficiency and Renewable Energy, “20% Wind Energy by 2030 – Increasing Wind Energy’s Contribution to U.S. Electricity Supply,” May, 2008.

[2] J. Charles Smith, Michael R. Milligan, Edgar A. DeMeo and Brian 

Parsons, "Utility wind Integration and operating impact state of the art," 

IEEE Trans. Power Systems, vol. 22, pp. 900-908, Aug. 2007.

[3] E. Muljadi, Z. Mills, A. Ellis, R. Foster, ” Fault Analysis at a Wind 

Power Plant for a One Year of Observation”, presented at the IEEE 

Power Engineering Society, General Meeting, Pittsburgh, PA, July 20-

24, 2008.

[4] E. Muljadi, S. Pasupulati, A. Ellis, D. Kosterev, “Method of Equivalencing for a Large Wind Power Plant with Multiple Turbine Representation”, presented at the IEEE Power Engineering Society, General 

Meeting, Pittsburgh, PA, July 20-24, 2008. 

[5] E. Muljadi, C. P. Butterfield, A. Ellis, J. Mechenbier, J. Hochheimer, 

R. Young, N. Miller, R. Delmerico, R. Zavadil, and J. C. Smith, “Equivalencing the collector system of a large wind power plant,” in Proc. 

2006 IEEE Power Engineering Society General Meeting.

[6] Nader Samaan, Robert Zavadil, J. Charles Smith and Jose Conto, 

“Modeling of Wind Power Plants for Short Circuit Analysis in the 

Transmission Network,” in Proc. of IEEE/PES Transmission and Distribution Conference, Chicago, USA, April 2008.

[7] J. Moren, S.W.H. de Haan, “Short-Circuit Current of Wind Turbines 

with Doubly Fed Induction Generator,” IEEE Transactions on Energy 

Conversion, Vol. 22, No. 1, March 2007.

[8] Sulawa, Zabara, et al. Short circuit current of induction generators. 

IEEE ISCAS 2007 proceedings.

[9] O. Anaya-Lara, N. Jenkins, et al. Wind energy generation: modeling 

and control. Wiley. ISBN 9780470714331

[10] IEEE PES Wind Plant Collector System Design Working Group,”Wind 

Power Plant Substation and Collector System Redundancy, Reliability 

and Economics,” Proceedings of the 2009 IEEE Power and Energy Society General Meeting.

[11] IEEE PES Wind Plant Collector System Design Working Group, ”Power Transformer Application for Wind Plant Substation,” Proceedings of 

the 2009 IEEE Power and Energy Society General Meeting.

[12] IEEE PES Wind Plant Collector System Design Working Group, “Wind 

Power Plant Grounding, Overvoltage Protection, and Insulation Coordination,” Proceedings of the 2009 IEEE Power and Energy Society 

General Meeting.

[13] WECC Modeling and Validation Work Group, “WECC Wind Power 

Plant Power Flow Modeling Guide Prepared.” May 2008.

[14] Short-circuit currents in three-phase a.c. systems–Part 0: Calculation of 

currents, IEC Standard 60909-0, July 2001.

VII. BIOGRAPHIES

Eduard Muljadi (M’82-SM’94-F’10) received 

his Ph. D. (in Electrical Engineering) from the University of Wisconsin, Madison. From 1988 to 1992, 

he taught at California State University, Fresno, CA. 

In June 1992, he joined the National Renewable 

Energy Laboratory in Golden, Colorado. His current 

research interests are in the fields of electric machines, power electronics, and power systems in 

general with emphasis on renewable energy applications. He is member of 

Eta Kappa Nu, Sigma Xi and a Fellow of the IEEE. He is involved in the 

activities of the IEEE Industry Application Society (IAS), Power Electronics 

Society, and Power and Energy Society (PES). 

He is currently a member of various committees of the IAS, and a member 

of the Working Group on Renewable Technologies and Dynamic Performance Wind Generation Task Force of the PES. He holds two patents in 

power conversion for renewable energy. 

Vahan Gevorgian (M’97) graduated from the Yerevan Polytechnic Institute (Armenia) in 1986. During 

his studies, he concentrated on electrical machines. His 

thesis research dealt with doubly-fed induction generators for stand-alone power systems. He obtained his 

Ph.D. degree in electrical engineering. from the State

Engineering University of Armenia in 1993. His dissertation was devoted to a modeling of electrical transients 

in large wind turbine generators.

Dr. Gevorgian is currently working at the National Wind Technology

Center (NWTC) of National Renewable Energy Laboratory (NREL) in Golden, Colorado, USA, as a research engineer. His current interests include 

modeling and testing of various applications of small wind turbine based 

power systems.
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Short-Circuit Modeling of a Wind Power Plant: Preprint

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This paper investigates the short-circuit behavior of a WPP for different types of wind turbines. The short-circuit 

behavior will be presented. Both the simplified models and detailed mod-els are used in the simulations and both 

symmetrical faults and unsymmetrical faults are discussed.

15. SUBJECT TERMS

Fault contribution; induction generator; electrical protection; short circuit; wind power plant; wind turbine

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