National Renewable Energy Laboratory 

Innovation for Our Energy Future 

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

Office of Energy Efficiency & Renewable Energy

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

Comparing Single and Multiple 

Turbine Representations in a 

Wind Farm Simulation 

Preprint 

E. Muljadi and B. Parsons 

To be presented at the European Wind Energy Conference 

Athens, Greece 

February 27 – March 2, 2006 

Conference Paper 

NREL/CP-500-39510 

March 2006 
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COMPARING SINGLE AND MULTIPLE TURBINE 

REPRESENTATIONS IN A WIND FARM SIMULATION

E. Muljadi1 Brian Parsons1

Abstract—Utility system operators and engineers want a 

better understanding of the impacts of large wind farms on grid 

stability before they are interconnected to the grid. Utilities need 

wind electrical models and methods of analysis that will help 

them analyze potential problems of grid stability. Without the 

necessary tools and knowledge of the behavior of large wind 

farms, utilities are reluctant to integrate more wind power into 

the grid. 

This work compares single turbine representation versus 

multiple turbine representation in a wind farm simulation. 

While single turbine representation presents a simpler model, it 

has some disadvantages compared to multiple turbine 

representation. One disadvantage is that a single turbine 

representation does not capture the composite behavior of the 

wind farm, another, is that the single turbine represents the 

worst-case scenario when a fault occurs in the wind farm where 

the farm either stays connected to the grid or becomes completely 

disconnected from the grid. In this work, we tried to identify the 

advantages and disadvantages of the two system representations 

when simulating dynamic response of a wind farm exposed to a 

fault condition. We want to determine the impact of diversity in 

a wind farm, such as different impedances in the line feeders 

connected to each turbine, on the turbine behavior during fault. 

This paper emphasizes the dynamic behavior of the power 

system. 

Index Terms—wind turbine, wind farm, wind energy, 

aggregation, power system, variable-speed generation, renewable 

energy, low voltage ride through. 

I. INTRODUCTION

Modern wind turbines are ready for large-scale deployment 

and play an important role in the utility grid. Despite early 

stagnation, wind power has grown very fast and has become 

competitive with other types of generation. The knowledge 

base accumulated during many years of development is an 

asset as the technology moves forward. With low penetration 

of wind power, the utility was not affected by the presence of 

the wind farm. The loss of generation from a small wind farm 

was not considered a threat to the security of the overall power 

system. However, the size of wind farms is increasing, and so 

is the presence of wind energy in the power grid. More wind 

farms are being erected in more states—in part because the 

lead-time to build a wind farm is relatively short compared to 

conventional power plants. 

In the past five years, wind energy has been considered one 

of the fastest growing technology sectors and has been 

 

1

 Employees of the Midwest Research Institute under Contract No. DE-AC36-

99GO10337 with the U.S. Dept. of Energy have authored this work. The 

United States Government retains, and the publisher, by accepting the article 

for publication, acknowledges that the United States Government retains a 

non-exclusive, paid-up, irrevocable, worldwide license to publish or 

reproduce the published form of this work, or allow others to do so, for the 

United States Government purposes. 

adopted globally to fill the need of electrical energy demands. 

As the number of wind farms continues to grow and the level 

of penetration increases, utility planners need to find a method 

that they can use to predict the behavior of a wind farm. 

As the size and rating of the modern wind farm keeps 

increasing, the number of turbines within the wind farm can be 

as high 200 turbines or more. It is not practical to simulate the 

entire wind farm by representing all individual turbines in the 

simulation. To simplify, it is common to represent the entire 

wind farm by groups of turbines or a single turbine. The 

question is, how much can we simplify without compromising 

the validity of the model and which configuration is best for 

simulating a wind farm. 

In this paper, we used a large generic wind farm with many 

turbines for our simulation. Based on the available electrical 

network data, we used steady-state analysis to derive the 

equivalent circuit of the wind farm. The equivalence of the 

collector systems in the wind farm can be represented as 

single line impedance or it can be represented as several line 

impedances. Once we defined the single turbine 

representation, we could simulate various conditions and 

compare the single turbine representation to the multiple 

turbine representation. To limit the scope of this paper, only 

variable-speed wind turbines were considered. 

Although stability studies have been conducted since the 

early development of wind energy, there are still several 

important questions to be answered. Will a wind farm survive 

a fault on the grid? How far should the fault be from the wind 

farm to minimize the number of turbines disconnected from 

the grid? How do we assess the potential drop-off of a wind 

farm from the power grid? 

We describe the general concept of planning and operation 

of a wind farm in section II. In section III, we discuss single 

turbine and multiple turbine representations. In section IV, we 

simulate several aspects of wind farm diversity to understand 

the impact of the turbine and power system network under 

normal operation or under fault conditions. Finally, we 

summarize our conclusion in Section V. 

II. PLANNING AND OPERATION OF A WIND FARM 

A. Steady-State Analysis 

In planning the power system for a wind farm, there are 

several studies performed such as an interconnection 

feasibility study, an interconnection system impact study, and 

an interconnection facilities study. The system impact study, 

which is related to this paper, is generally performed to 

investigate the impact of the new wind farm on the 

surrounding power systems. 

1
 

The various studies listed above include steady-state (loadflow) and dynamic (transient and fault) analysis. The study is 

used to investigate the impact of the proposed wind farm on 

the reliability of the power system network. From this study, 

we can assess if the power system connected to the wind farm 

is adequate or if any upgrades are needed to ensure the 

reliability of the system with the connection of the new wind 

farm. 

In the steady-state analysis, load-flow simulations are 

performed with the wind farm set to generate rated output 

power to observe the impact on the loading capability of the 

transmission, distribution lines, the corresponding 

transformers, and the switchgear components. This aspect is 

normally concerned with the thermal impact of the rated 

generation of the wind farm. The reactive power adequacy is 

also assessed to determine if the grid is sufficiently ready to 

accept this particular wind farm or if additional reactive power 

compensation is necessary. The reactive power assessment 

can predict the voltage behavior of the grid under various 

conditions. A commonly used method to check the voltage 

stability is the PV and QV curves, where the output of the 

wind farm is increased from medium to high output above 

rated until the voltage collapses. This practice measures the 

stability margins of the wind farm operation. 

Steady-state analysis is also used to determine the new 

level of short circuit after the additional of the wind farm to 

the power grid. It determines if the size of the existing circuit 

breakers and other auxiliary equipment in the surrounding 

power system will be affected by the addition of the wind 

farm. If the wind farm does have an impact, what sort of 

modifications or upgrades must be made to the existing 

switchgear and power system protection, and what, if any, 

changes need to be made in the settings due to the addition of 

wind farm? These simulations were run under normal 

conditions and under a different set of contingencies 

(contingency analysis) to ensure the reliability of the power 

systems under different scenarios. 

B. Dynamic Analysis 

Dynamic analysis is performed using dynamic modeling in 

a time domain. The dynamics are created by the inputs 

exciting the wind turbine due to various events during normal, 

disturbance, or fault conditions. 

Under normal conditions, there are a few things that can be 

measured and analyzed. For example, the harmonics 

generated by each turbine, the harmonics at the point of 

common coupling, the flicker, the voltage fluctuations under 

varying wind, and the frequency variations under different 

ramp-up or ramp-down conditions. Other types of operations 

worth observing include the impact of capacitor switching on 

the wind turbines operation, the start-up behavior of the wind 

turbines, and unbalanced voltage operations of the wind 

turbines. We can analyze and simulate the characteristics of a 

wind turbine under normal conditions using dynamic models. 

The time of observation for this type of analysis normally 

varies between a few seconds to minutes. 

The analysis is important for finding out how the power 

system behaves when a fault occurs within the vicinity of the 

wind farm, and what happens to the power system when the 

wind farm is affected by faults that occur in the transmission 

network. It is also important for gauging the behavior of the 

wind farm under fault conditions. 

Under fault conditions, it is important to understand the 

transient stability of the power system to predict the post-fault 

condition. It is necessary to simulate the faults to see if the 

power systems remain stable after the fault is removed from 

the systems. Some faults are self-clearing (i.e., lines 

temporarily touching vegetation due to wind) and the network 

topology does not change after the fault is cleared. However, 

more severe faults may disconnect some lines and the network 

and the topology of the network changes after the fault. Some 

generators might get disconnected thus changing the spinning 

reserve allocation, or an island might be formed that includes 

the wind farm, several generators, and some loads. Although 

a system might be robust and stiff before the fault, it may 

become weaker in the post fault condition. Once the fault is 

cleared, any oscillations that may occur should be damped 

appropriately. Various contingencies should be simulated and 

the proper remedial action scheme (RAS) should be taken to 

ensure optimal operation of the wind farm and the power 

systems in the pre-fault and post-fault conditions. The time 

frame for this simulation normally varies from a few cycles to 

seconds. 

III. SINGLE AND MULTIPLE TURBINE REPRESENTATION 

A. Single Turbine Representation 

Within the scope of a single turbine, like many other power 

plants, a wind turbine is modeled with its individual major 

components included. Thus, different turbine types have to be 

modeled differently. Similarly, the control block diagram and 

control algorithm are modified as the new edition is 

manufactured. 

A typical module consists of the following blocks: 

• Aerodynamic 

• Pitch mechanism 

• Wind input 

• Shaft dynamic 

• Relay protections 

• Generator and power electronics 

• Control algorithm. 

The components that govern the behavior of a wind turbine 

are represented above. These components are normally built 

in modules to allow sharing of modules for different turbines 

with minimum modifications. 

Aerodynamic characterizes the aerodynamic behavior of a 

wind turbine. In this module, information about the turbine 

blade, the air density, the performance coefficient curve, and 

tip speed ratio are given as input or calculated in the module to 

compute the aerodynamic power at any wind speed. The pitch 

mechanism is included for a pitch-able turbine to represent the 

pitching activities when the wind turbine operates in the power 

regulation or speed regulation. 

The wind input is accessible through external file. Ideally, 

2
 

it is available in a time series with varying wind speed versus 

time. This time domain input wind speed can be useful to 

examine the power and voltage fluctuations due wind 

turbulence or wind gusts. The shaft dynamic is available to 

simulate a single inertia or two inertias with stiffness and 

damping specified. The shaft dynamic model can tell us about 

the mechanical damping during disturbance. 

The relay protection aspects of the wind turbine should 

reflect the capability of the wind turbine as well as the local 

regulations. If the local regulation requires that the turbine 

should always be connected to the grid under a certain voltage 

profile (low voltage ride through, LVRT), we need to test the 

turbine for this capability. The characteristics of the relay 

should be programmed based on the wind turbine 

manufacturers standard. 

B. Multiple Turbine Representation 

Within the scope of wind farm, the behavior of the wind 

farm embodies the collective behavior of all the turbines 

within the wind farm. To represent a more realistic model of 

the wind farms, the diversity in the wind farms and aggregate 

impact are included in the models. Typical aspects of 

diversity in a wind farm include the following: 

• Spatial distribution 

• Line impedance 

• Different settings of relay protections 

• Different types of wind turbines 

• Different settings and control set-points 

• Different control strategies 

• Different types of reactive power compensation. 

Although this list could be extended, if most of the listed items 

are taken into account, the modeled wind farm should be 

acceptably realistic. 

The spatial distribution has an impact on the total output of 

the wind farm because the modern large wind farm is 

normally spread across a very large area. The wind speeds 

driving each individual turbine will not be identical. Thus, the 

response of individual turbines will be different at any instant 

of time. In addition, because the wind turbines are 

geographically dispersed, the line impedance of the feeders 

and the voltage drops across the feeders will not be the same 

at each turbine. The impact of voltage drop differences among 

the turbines leads to the difference in voltage at the terminals 

of each turbine. Voltage relay protection is based on terminal 

voltage to protect the wind turbine generator against over 

voltage or under voltage. Thus, the difference in terminal 

voltage may result in different set-off times. This fact is a 

positive contribution. For example, if a wind farm is 

connected to a weak grid, and the reactive power 

compensation is not properly designed or controlled, only a 

portion of the turbines will be disconnected from the grid 

during a fault event. Thus, the wind farm does not lose 100% 

of the generation and it is still contributing to the power grid. 

In a very large area or even on the same wind farm, there 

may be several types of wind turbines installed (for example, 

in the Tehachapi, California, and McCamey, Texas, areas 

there are many wind farms connected to the same power grid 

located within the same area). The differences can be in the 

year of make, the model, the size, or the manufacturer. 

Different types of turbines are normally built differently, and 

therefore, the control mechanisms or control algorithms are 

different. Because the controllers mostly consist of 

microprocessors or microcontrollers, two identical turbines, 

can be easily set to operate differently (for example, two 

identical turbines located within proximity can be set to start 

at slightly different cut in wind speeds or have different time 

delays to avoid start-up at the same time). Similarly, two 

identical wind turbines can be operated at different control 

algorithms. This difference signifies the signature of different 

turbines or different wind farms. 

The reactive power compensation can be implemented at 

the turbine level to compensate an individual turbine. Most of 

the turbines are manufactured this way. Some wind farm 

operators add additional reactive compensation at the point of 

interconnection (POI) to improve the power quality of the 

interface at the POI. 

C. Wind Farm Representation 

 1) Load-Flow Simulation 

 How do we represent a wind farm in a power system 

steady-state simulation? For a steady-state analysis, the 

simulation is performed by using load-flow analysis. The 

wind farm is represented as a “single” conventional generator 

with output based on the characteristics of the wind farm. In 

performing the PV and QV analysis, we need to have the PQ 

characteristic of the wind farm, which can be derived from the 

generator parameters and the reactive power compensation 

characteristic at the wind farm. A better way to represent a 

PQ characteristic, however, is from the field measurement. 

Having said that, it is necessary to reevaluate this 

characteristic (repeat the measurement) when there are any 

changes in the size and the strategy of reactive power 

compensation. 

 2) Dynamic Simulation 

How do we represent a wind farm in a power system 

dynamic simulation? For the worst-case scenario in a fault 

analysis, a single turbine representation may be sufficient. 

However, a more realistic representation will include the 

unique characteristics of the wind farm. This does not mean 

that we have to represent every single turbine installed in the 

wind farm. For example, consider a wind farm that covers a 

very large area and consists of 200 turbines of 2 different 

types of turbines (fixed speed and variable speed), and the 

variable-speed turbine is deployed with two different control 

strategies (constant voltage and constant power factor). Figure 

1 shows the representation of the wind farm based on the 

unique description provided. 

The example diagram presented in Figure 1 represents five 

different groups of turbines with distinctive characteristics as 

follows: 

- Geographical dispersion causing line impedance 

difference: 

o Group 1: 40 WTGs fixed speed through line 

A (low impedance) 

3
 

o Group 2: 30 WTGs fixed speed through line 

B (high impedance) 

- Different types of turbines and different control 

algorithms: 

o Group 3: 38 WTGs variable speed with 

constant power factor control. 

o Group 4: 62 WTGs variable speed with 

voltage control. 

- Different wind resource characteristics: 

o Group 5: 30 WTGs variable speed with 

constant power factor control (same type as 

group 3) but the wind turbine is located on a 

hill with the wind resource is significantly 

better than group 3, thus group 5 turbines 

experience a higher average wind speed than 

group3. 

The above diagram and the description presented is only an 

illustration of how the wind farm can be represented by unique 

characteristics of the groups of turbines. Note that the purpose 

of separating these groups is to represent the unique signature 

of each group. Thus, the size of each group in megawatts 

must be significant enough to cause different responses at the 

POI for different excitations and events. 

IV. VARIOUS COMPARISONS OF SIMULATION RESULTS 

In this section, various comparisons will be presented. The 

impact of line impedance, the impact of reactive power 

compensation, and the impact of wind speed diversity will be 

presented to illustrate the points and assumptions made in the 

previous sections. In an attempt to clearly show the impact of 

the differences, the parameter used might be scaled up or 

down. 

A. Operation Under Normal Conditions 

In this section, normal conditions will be simulated to show 

the response of single turbine representation or multiple 

turbine representation. Let us first consider the impact of 

geographical diversity using the wind speed difference among 

the wind turbines. We will compare the power fluctuations 

and voltage fluctuations at the point of interconnection as a 

result of blades passing through the tower thus creating output 

power pulsations. We will compare the output power and 

voltage at the point of interconnection for a wind farm 

represented by a single turbine and a wind farm represented by 

multiple wind turbines. To illustrate the point, we chose a 

fixed-speed wind turbine because the tower shadow impact is 

very pronounced in a fixed-speed wind turbine generation. In 

this particular example, we assume that there are 200 fixedspeed turbines divided into 16 groups separated with a certain 

distance between consecutive groups. A time series wind 

speed stored in a file is used to drive the wind turbines. To 

simulate the wind speed on each group, it is assumed that the 

groups of wind turbines are lined up along the direction of the 

prevailing wind speed. The wind speed driving each group of 

turbines is taken from the same file, except that each group is 

driven by wind speed with a certain time delay to simulate the 

distance between each group. The time delay of the wind 

speed arriving at the location of each group is computed from 

the distance divided by the average wind speed. This method 

represents a very rudimentary approach and introduces a 

frozen turbulence. This concept introduces the phase shift in 

wind speed, simulating the geographical diversity within a 

very large wind farm. 

As shown in Figure 2, in a single turbine representation, the 

power fluctuation is merely an amplification of power 

fluctuation of a single turbine. While in the multi turbine 

representation, the wind farm’s total output power with the 

natural filtering allows for power fluctuation cancellations due 

to unequal phase shift among the turbines. Note that the 

instantaneous wind speed dictates the operating slips of 

individual turbines and thus, dictates the nature of the tower 

shadow as it appears at its output. Both real and reactive 

power varies accordingly, and the impact on the POI voltage 

Group 2 

FS, 

High Z 

Group 5 

PF = C 

VS 

Group 1 

FS, Low Z Group 3 

PF = C 

VS Group 4 

V = 1, VS 

Infinite 

Bus 

Figure 1. Methods of grouping wind turbines based 

on the unique characteristics of each group. 

Wind Farm P&Q

T ime (sec)

10 11 12 13 14 15 16 17 18 19 20

P (MW) at PCC

0

10

20

30

40

50

60 Real Power

WF1

Wind Farm Real Power (16 groups)

Time (sec)

10 11 12 13 14 15 16 17 18 19 20

P at PCC

0

10

20

30

40

50

60 Real Power (MW)

WF16

Figure 2. Power variations caused by tower shadow effect 

a) single turbine representation (WF1) 

b) multiple turbines representation (WF16) 

4
 

can be shown in Figure 3. In the longer time frame, such as 

shown in Figure 3, the fluctuation in real and reactive power is 

caused by the combination of the wind speed average, wind 

turbulence, and tower shadow effect. From Figure 3, it is 

obvious that the voltage fluctuation in a multiple turbine 

representation is significantly reduced due to cancellation 

effects among the turbines. 

 The power quality that results from using 16 groups of 

turbines will also show a better representation of an actual 

wind farm. Figure 4 shows the significant reduction of the 

flicker level as the number of groups representing the wind 

farm increases from one group to sixteen groups of turbines. 

Obviously, there are limits above which increasing the number 

of groups of turbines will no longer provide a better picture of 

the reality. For example, from Figure 4 we can see that there 

is a significant reduction in flicker level if the wind farm is 

represented as one group of turbines or four groups of turbines 

(2.2 per unit to 1 per unit). However, Figure 4 also shows that 

the difference between an eight groups turbine representation 

and a sixteen groups turbine representation is not very 

significant (0.75 per unit to 0.5 per unit). 

B. Operation Under Fault Condition 

Many types of faults may occur in a wind farm power 

system. In this paper, a three-phase symmetrical fault will be 

investigated because this fault generates the highest fault 

current and is considered to be the worst-case scenario. This 

type of analysis is necessary to properly size switchgear to 

protect the power system. 

In this section, we perform a dynamic analysis using 

models of wind turbines downloaded from the Siemens Power 

Technologies Inc. Web site. We use a variable–speed, GE 

1.5-MW turbine with its voltage control capability set to 

control its own bus. The software used is Power Systems 

Simulations for Engineers (PSS/E). Each wind farm can be 

configured to input wind speed, the number of turbines, and 

system protection (voltage and frequency relays). To include 

diversity in the analysis, a large wind farm may be split into 

several collector buses to represent a unique group of turbines 

from different perspectives (e.g., types of turbine, controller 

setting, length of line feeders, spatial diversity of wind speed 

within the wind farm). The method faults one specific bus at a 

time, then observes the response on the entire wind farm. For 

a faulted bus, the fault is designed to last 9 cycles and is then 

cleared. 

Vph at Infinite Bus and at PCC (in p.u.)

T ime (sec)

0 100 200 300 400 500 600

Per phase voltage (in p.u.)

.90

.95

1.00

1.05

1.10

1) Stiff grid versus weak grid: 

To simulate a condition of stiff grid and weak grid, the 

following single line diagram is used. As shown in Figure 5, 

five buses represent the infinite bus 1, the high voltage side of 

the main substation bus 2, the medium voltage side of the 

main substation bus 3, the medium voltage side of the group 

turbines bus 4, and the low voltage of the group turbines bus 

5. The rectangular block represents a group of turbines with 

n1 indicating the number of turbines represented by the group. 

There are two line impedances ZLINE and ZCOL. The ZLINE

represents the Thevenin impedance from the main substation 

to the infinite bus. The short circuit capability of the 

substation is determined by ZLINE. The ZCOL represents the 

collector equivalence of the line impedance. Using this we 

will simulate a fault condition that occurs at point A for both 

stiff grid simulation and weak grid simulation. For this 

condition, we set the wind speed at 13 m/sec, thus, the wind 

turbine generates rated power before and after the fault. The 

number of wind turbines n1=67 is chosen to provide 

approximately 100 MW of wind generation to the power grid. 

The wind turbine is a 1.5-MW variable-speed wind turbine 

Per phase voltage at PCC

WF1

Vph at PCC (in p.u.) - 16 groups

Time (sec)

0 100 200 300 400 500 600

Per phase voltage (in p.u.)

.90

.95

1.00

1.05

1.10 Per phase voltage at PCC

WF16

PST - Flicker Level - Votage at PCC

0

0.5

1

1.5

2

2.5

0 5 10 15 20

Number of Groups

Pst (in per unit)

Figure 3. Voltage variations at POI 

a) single turbine representation (WF1) 

b) multiple turbines representation (WF16) 

 1 

Figure 4. Flicker level of the voltage at the POI as a 

function of the number of the groups in the wind farm. 

Figure 5. A typical single line diagram of a wind 

farm power system with a single turbine 

 2 3 

ZCOL

 4 5 

ZLINE Wind1

Xfmr 

Subst.

n1 A 

Pad-mount 

Xfmr

5
 

and it is set to control the voltage at bus 4 (medium voltage 

side of the pad mount transformer. 

 a) Stiff grid (from t= 0 seconds to t = 11 seconds): 

The short circuit ratio for this particular system will be 10. 

In this simulation, the line impedance ZLINE is set up to be two 

parallel lines (line1=0.125 p.u. in parallel with line2 = 0.5 p.u.) 

and the total impedance is about 0.1 p.u. Initially, the system 

operates normally for one second. When a fault condition 

occurs at point A, at t=1sec, the fault is self-cleared after 9 

cycles. In this scenario it is assumed that none of the circuit 

breaker is opened. 

 b) Weak grid (from t=11 seconds to t = 20 seconds): 

The same grid is exposed to the same fault at t=11 seconds, 

but, this time, line1 is removed from the line at the end of the 

fault (9 cycles), thus in the post fault condition, the grid 

becomes a weak grid with line2 remains connected. The total 

impedance of 0.5 p.u. or short circuit ratio of 2.0 from the 

main substation. 

 c) Discussion: 

In this subsection, the stiffness of the grid condition is 

examined. Let us first consider the mechanical aspect of the 

wind turbine model. In this particular model, the mechanical 

shaft is modeled with its stiffness and damping characteristics 

included. The inertia of the turbine rotor including the blades 

and the generator are used as inputs. In Figure 6, the rotor 

speeds at the low-speed shaft and at the high-speed shaft are 

shown in per unit values on the same Figure. The number on 

the vertical axis indicates the slip above the synchronous 

speed of the generator. Note that the rated speed of the 

doubly-fed induction generator is about 20% above its 

synchronous speed. At this wind speed (13 m/sec), the wind 

turbine operates in region 3 (rated speed). In this region, the 

rotor speed is controlled by the pitch mechanism to stay at its 

rated speed even when the wind speed increases or fluctuates 

above its rated value. 

It is shown that when the grid is stiff, the wind turbine 

responded very well and the oscillation was damped out rather 

quickly. The LSS and the HSS seem to be out of phase as 

expected. The rotor speed HSS being connected to the lower 

inertia of the generator has a larger swing. The weaker grid 

seems to provide less electrical damping, and the oscillation 

lasts a little bit longer. 

Below the rated speed, the rotor speed (HSS) is used as a 

signal to command of the power converter so that the turbine 

will generate output power proportional to the cube function 

of the rotor speed. This region corresponds to region 2 (low to 

medium wind speed). At rated speed and above, it is used to 

control the pitch angle of the pitch mechanism to limit the 

aerodynamic power, thus, to ensuring that the rotor speed 

stays at or below rated speed to avoid a run-away condition. 

Figure 7 shows the variation of the pitch angle as the pitch 

controller works to keep the rotor speed below its rated speed. 

It shows that, for a weak grid, the pitch angle variation lasts 

longer. This time delay is due to the fact that, for a weaker 

grid, the rotor speed oscillation lingers longer. 

In Figure 8, the real power and reactive power are 

presented on the same graph. Because the commanded power 

to the power converter is based on the rotor speed (filtered), 

the electrical output power reflects the rotor speed variation. 

The filtered rotor speed shows a smoother variation in output 

power than the actual rotor speed. The reactive power is 

based on the voltage controller. The reactive power is 

modulated to maintain the voltage at the wind turbine site to 

be constant all the time (within the limit of current rating of 

the power converter). The reactive power shown in Figure 8 

is a reflection of the effort of the wind turbine generator to 

keep the terminal voltage at the wind turbine terminals 

constant. Note that there is an elevation of the reactive power 

Figure 6. Rotor speed at the low-speed shaft (LSS) and 

high-speed shaft (HSS). 

HSS 

LSS 

Stiff Weak 

less 

damping 

Figure 7. Pitch angle in degrees. 

last 

longer 

Stiff Weak 

6
 

generated by the wind turbine when the grid is weaker (t > 

11sec). This is due to the fact that there is more voltage drop 

across the weaker line impedance that must be compensated 

for by the wind turbine. It also shows that, during the fault, 

the power converter attempted to restore the voltage at the 

turbine terminals up to its current capability. 

Figure 9 shows the bus voltages at bus 2 (location of the 

fault) and at bus 5 (terminals of wind turbine). As can be 

expected, under normal conditions, the terminal output voltage 

is kept at its preset value. During the fault, the voltage at bus 

2 drops to zero, and the voltage at the terminal voltage is 

higher than zero, indicating that there is sufficient impedance 

between the fault and the terminal of the wind turbine (ZS = 

ZXFMR_SUB + ZCOL + ZXFMR_WTG). The fault current (IF) from the 

wind turbine generates sufficient voltage drop (∆V) between 

the fault and the terminal of the wind turbine as appear as the 

voltage at the terminals during the fault. 

 2) Different wind speed conditions: 

To simulate a condition of a very large wind farm, the 

simple power system network is subjected to different wind 

conditions. The purpose of this exercise is to show, at 

different wind levels, what characteristic of the wind turbine is 

important. The short circuit level of the line impedance ZLINE

is chosen to be 10. The wind farm is assumed to generate 

about 100 MW. 

There are several tests to be included in this section, as 

listed below: 

a. Wind speed is below rated (enough to generate 50% 

of rated output power of individual turbine). The 

wind speed is set to 8.5 m/sec. At this wind speed 

each turbine generates only 0.75 MW instead of 1.5 

MW. To generate 100 MW total output, the number 

of turbines in the wind farm is doubled to 134 

turbines. 

b. Wind speed is just reaching its rated value. The wind 

speed chosen is 13 m/sec. The blade pitch angle is 

very small at about 4 degrees during normal 

conditions. The number of wind turbines is 67 and 

the total output of the wind farm is 100 MW. 

c. Wind speed is above rated (about 125% rated value 

or 16.25 m/sec. With this wind speed, the output of 

the wind farm is at rated, but the blade pitch angle is 

large. The number of wind turbine is 67 and the total 

output of the wind farm is 100 MW. 

The above three cases were run, one at a time, and the 

output of each case are compared to the others. The system is 

operated normally for the first second, then, a three-phase fault 

is introduced at bus 2. The length of the fault is 9 cycles. The 

fault is self-cleared, thus, there are no changes in the short 

circuit level before and after the fault. 

Stiff Weak 

∆Q 

Pelec 

Qelec 

Figure 8. Electrical output real power (Pelec) and 

reactive power (Qelec) in p.u. 

Attempted to 

correct the voltage 

during the fault. 

Figure 9. Bus voltages (in p.u.) at bus 2 and bus 5. 

Bus 2 

Bus 5 

V5 

V2 

Noticeable voltage drop 

across the weaker line 

impedance. 

∆V = IF ZS 

Stiff Weak 

Figure 10. Rotor speed (in p.u. wrt synch. speed) 

 8.5 m/s 

13.0 m/s 

16.3 m/s 

7
 

As shown in Figure 10, for the two higher wind speeds (13 

m/s and 16.3 m/s), the rotor speeds of the turbines indicate that 

they have reached rated rotor speed. At this level, the pitch 

controller adjusts its pitch angle to keep the turbine rotor 

speed at its rated. Thus, the turbine blade angle is positioned 

not to capture maximum aerodynamic power, but it is 

positioned to avoid a run-away condition. 

For a lower wind speed (8.5 m/s), the rotor speed is below 

its rated speed and the pitch controller is basically at its 

optimum angle to capture the most optimum aerodynamic 

power. 

The responses of the turbines to the fault, shown by the 

rotor speeds, are different at different levels of wind speed. 

The turbines driven by higher wind speeds, having more 

aerodynamic power available to them, need a longer time to 

settle down, back to the pre-fault steady state condition. There 

is not a big difference in response shown by the rotor speeds 

between the turbine driven by 13 m/s and the 16.3 m/s wind 

speeds. The lower wind speed (8.5 m/s) shows smaller 

amplitude of oscillation and the time to return to pre-fault 

condition is a lot faster. 

Figure 11 shows the variation of pitch angles in response to 

the fault for different wind speed conditions. The pre-fault 

pitch angle, as can be expected, varies for different initial 

wind speeds. The higher wind speed has the highest initial 

pitch angle. Below rated wind speed, the pitch angle, 

positioned at a slightly negative pitch angle, corresponds to 

the optimum pitch angle for this wind turbine. The response 

to the transient fault also differs for different wind speeds. 

The pitch controller is driven by rotor speed error as well as a 

small contribution from the power error. The two inputs and 

the gain of the controller parameters determine the behavior of 

the pitch angle at any condition. 

Figure 12 shows the variation of the mechanical 

(aerodynamic) torque, which is based on the wind speed input 

and the performance coefficient Cp (which is affected by the 

rotor speed, wind speed, and pitch angle). The mechanical 

(aerodynamic) torques is shown to have very different 

signatures at different wind speeds. At high wind speed, the 

aerodynamic torque shows a very active variation considering 

that the wind speed average is high. The 16.3 m/s wind speed 

is about 25% higher than 13 m/s. Theoretically, at constant 

Cp, it can generate about twice the aerodynamic power as the 

13 m/s wind speed. Thus, although under normal conditions 

the aerodynamic power of the two wind speeds is equal, 

during transient conditions, very active large swings can be 

observed at 16.3 m/s wind speed. 

The aerodynamic torque of the turbine at lower wind speed 

(8.5 m/s) is very mild and it is damped out very nicely in short 

time. 

Figure 13 shows the real power output of the wind farm for 

Figure 11. Pitch angles (in degrees) for various wind speeds.

 8.5 m/s 

13.0 m/s 

16.3 m/s 

Figure 12. Aerodynamic torque (in p.u.). 

 8.5 m/s 

13.0 m/s 

16.3 m/s 

Figure 13. Real power output for various wind speeds. 

 8.5 m/s 

13.0 m/s 

16.3 m/s 

different response, 

different settling time, 

different phase shift. 

8
 

different wind speeds. Note that the number of turbines for 

the low wind speed case (8.5 m/s) is twice the number of 

turbines as for high wind speed cases. Thus the total output 

for all cases is 100 MW. It is shown that although in the prefault and post-fault steady-state conditions the wind farms 

produce the same total output power are the same at 100 MW; 

during the transient conditions there are deviations in the 

traces. Notice that the traces of real power do not seem to be 

in phase for different wind speeds. This is an important 

characteristic that will help to explain that during the fault and 

post fault oscillation, it is less likely that entire wind farm will 

synchronize to destabilize the systems. This is an important 

difference between a single large generator and a large wind 

farm consisting hundreds of wind turbines when it interacts 

with the outside power systems. 

Figure 14 shows the reactive power variation. Because the 

reactive power is used to control the terminal voltage at the 

wind turbine site, the reactive power does not resemble the 

traces of the rotor speed nor the real power. 

Figure 15 shows the voltages at bus 2 (the fault location) 

and at bus 5 (the bus terminal of the wind turbine). Look at 

the low wind speed (8.5 m/s) traces in Figures 14 and 15. 

When the wind is low, the power converter operates below its 

maximum current rating capability. Thus, there is some 

headroom to generate more current up to its rated value. 

When the fault occurs, the voltage at the wind turbine bus 

drops significantly, thus the power converter tries to correct 

the situation by injecting more capacitive current up to its 

rated current capability. As shown in Figure 14, the reactive 

power for the low wind speed is highest during the fault. In 

Figure 15, the voltage at the wind turbine bus is highest for the 

wind speed 8.5 m/s, which shows that the power converter can 

help in improving the voltage drops at the wind turbine 

terminals during the fault if there is sufficient capacity to 

generate reactive compensation. 

 3) Multiple Turbine Representation: 

To simulate a condition of a very large wind farm, 

emphasizing the diversity in the wind farm, a single line 

diagram, as shown in Figure 16, is used. The system 

simulated is similar to the one described in Section IV-2. It 

has a short circuit ratio of 10. The wind farm is divided into 5 

distinct groups and each group produces approximately 20 

MW of wind power. Each of the turbines is controlled using 

voltage control to keep a constant voltage at the high side of 

the pad mount transformer (bus 311 through bus 315). The 

wind speeds for wind1, wind2, and wind4 are set to rated 

value at 13 m/s. Wind3 is set to 8.5 m/s, and wind5 is set to 

16.3 m/s. The collector impedances are set to simulate higher 

impedance (Z1 = 0.25 p.u.) and lower impedance (Z2 = 0.0625 

p.u.). The rest of the collector impedances (Z3 through Z5) are 

set to 0.1 p.u.. Each of the group is set to generate 20 MW. 

 Figure 17 shows the voltage at the terminals of the wind 

turbines. As shown, due to the diversity listed above, there are 

differences in the voltage levels at the output terminals of the 

wind turbines under the steady-state conditions or during the 

faults. 

The behavior of the turbines has been explained previously 

based on the unique characteristics described in section IV-1 

Figure 16. Single line diagram of a wind farm 

with 5 groups of turbines. 

 300 

 100 200 

Z1

Z2

Z3

Main

ZLINE

311 90311 Wind1

312 90312

90313

n1

313

 Wind2

n2

 Wind3

n3

Z4

Z5 315 90315

314 Wind4

n4

90314

Figure 14. Reactive power output for various wind speeds. 

 8.5 m/s 

13.0 m/s 

16.3 m/s 

Figure 15. Voltages at bus 5 (in p.u.) for various 

wind speeds 

 8.5 m/s 

13.0 m/s 

16.3 m/s 

 Wind5

n5

9
 

and section IV-2, and it will not be repeated here. These 

differences can affect the behavior of the wind turbine based 

on the trigger settings of the relay protections (i.e. LVRT). 

During severe disturbances or transient events (faults), only 

some of the turbines will be disconnected instead of the entire 

wind farm. 

V. CONCLUSION

This paper presents alternatives to simulating a wind farm. 

In the past, many wind farm simulations were performed using 

a single turbine to represent the entire wind farm. It is similar 

to representing a conventional power plant with a single large 

synchronous generator. It has been very successful for 

predicting instabilities, such as sub-synchronous resonance, in 

simulating conventional large synchronous generator power 

plants. 

A wind farm is usually very large. There are diversities in 

the wind farm (wind speed, line feeder impedance etc.) that 

make individual turbines respond differently to the same fault. 

Several examples, both in normal operation and during the 

fault conditions, are described in this paper. 

In a real wind farm, there are many wind turbines 

connected to the point of interconnection. Most of the 

generators used are induction generator or combination of 

generator and power converter. Although the wind turbines 

are connected to a single point electrically, the generator 

mechanical shafts of all the turbines are not physically 

connected to each other. The mechanical and aerodynamic 

damping provided by each turbine will differ from one turbine 

to the next. Thus, unlike conventional synchronous generator, 

any mechanical oscillations at a single turbine are not 

necessarily synchronized to other turbines in the same wind 

farm. Each turbine in the wind farm is free to operate at its 

own operating condition. 

In conclusion, a single turbine representation approach 

leads to the worst-case scenario. To represent a large wind 

farm, unique attributes of the wind farms should be included 

to represent the unique characteristic of the wind turbines or a 

group of wind turbines. Thus, during transient events, 

although there may be a group of turbines disconnected from 

the wind farm, the entire wind farm will not be disconnected. 

90311 

90312 

90313 

90314 

90315 

Figure 17. Voltage at the terminals of the wind turbines. 

potential impact 

on relay settings 

and LVRT 

VI. ACKNOWLEDGMENT

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

Energy. 

VII. REFERENCES

[1] E.N. Henrichsen and P.J. Nolan, “Dynamic stability of wind turbine 

generators,” IEEE Trans. Power App. Syst., Vol. PAS-101, pp. 2640-

2648, Aug. 1982. 

[2] M.R. Behnke, W.L. Erdman, "Impact of Past, Present and Future Wind 

Turbine Technologies on Transmission System Operation and 

Performance", Report for California Wind Energy Collaborative for 

California Energy Commission’s Public Interest Energy Research 

(PIER) Program Intermittency Analysis Project (IAP), December 2005. 

[3] John Olav G Tande, Eduard Muljadi, Ola Carlson, Jan Pierik, Ana 

Estanqueiro, Poul Sørensen, Mark O’Malley, Alan Mullane, Olimpo 

Anaya-Lara, Bettina Lemstrom, ”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. 

[4] E. Muljadi, C.P. Butterfield, and V. Gevorgian, “The impact of the 

output power fluctuation of a wind farm on a power grid,” in Conference 

Record:Third International Workshop on Transmission Networks for 

Offshore Wind Farms, Royal Institute of Technology, Stockholm, 

Sweden, April 2002. 

[5] E. Muljadi and C.P. Butterfield, “Dynamic Model for Wind Farm Power 

Systems,” Global Wind Power Conference, Chicago, Illinois, 

March/April 2004. 

[6] IEC Standard 61 400-21: Measurement and Assessment of Power 

Quality of Grid Connected Wind Turbines, International Electrotechnical 

Commission. 

10
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Comparing Single and Multiple Turbine Representations in a Wind 

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This paper compares single turbine representation versus multiple turbine representation in a wind farm simulation. 

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