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 

Model Validation at the 204 MW 

New Mexico Wind Energy Center 

Preprint 

E. Muljadi and C.P. Butterfield 

National Renewable Energy Laboratory 

A. Ellis and J. Mechenbier 

Public Service Company of New Mexico 

J. Hochheimer and R. Young 

FPL Energy LLC 

N. Miller and R. Delmerico 

General Electric International, Inc. 

R. Zavadil and J.C. Smith 

Utility Wind Interest Group

To be presented at the American Wind Energy Association 

WindPower 2006 Conference 

Pittsburgh, Pennsylvania

June 4–7, 2006 

Conference Paper 

NREL/CP-500-39048

June 2006 
NOTICE

The submitted manuscript has been offered by an employee of the Midwest Research Institute (MRI), a 

contractor of the US Government under Contract No. DE-AC36-99GO10337. Accordingly, the US

Government and MRI retain a nonexclusive royalty-free license to publish or reproduce the published form of

this contribution, or allow others to do so, for US Government purposes. 

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any 

warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or

usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not 

infringe privately owned rights. Reference herein to any specific commercial product, process, or service by

trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement,

recommendation, or favoring by the United States government or any agency thereof. The views and

opinions of authors expressed herein do not necessarily state or reflect those of the United States

government or any agency thereof. 

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from: 

U.S. Department of Energy

Office of Scientific and Technical Information 

P.O. Box 62 

Oak Ridge, TN 37831-0062

phone: 865.576.8401 

fax: 865.576.5728 

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from: 

U.S. Department of Commerce 

National Technical Information Service 

5285 Port Royal Road 

Springfield, VA 22161 

phone: 800.553.6847 

fax: 703.605.6900 

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/ordering.htm

Printed on paper containing at least 50% wastepaper, including 20% postconsumer waste
Model Validation at the 204 MW New Mexico Wind Energy Center 

A. Ellis J. Mechenbier 

Public Service of New Mexico

Alvarado Square, MS 0604 

Albuquerque NM 87104

E. Muljadi C.P. Butterfield

National Renewable Energy Laboratory

1617 Cole Blvd

Golden, CO 80401 

J. Hochheimer R. Young

FPL Energy LLC

700 Universe Blvd. 

Juno Beach, FL 33408

N. Miller R.Delmerico

General Electric International, Inc. 

1 River Road, Bldg. 2-605

Schenectady, New York 12345

R. Zavadil J.C.Smith

Utility Wind Interest Group 

2004 Lakebreeze Way

Reston, VA 20191

Abstract—Wind energy continues to be one of the 

fastest growing technology sectors. This trend is expected 

to continue globally as we attempt to fulfill a growing

electrical energy demand in an environmentally 

responsible manner. As the number of wind power plants

continues to grow and the level of penetration reaches high

levels in some areas, there is an increased interest on the 

part of power system planners in methodologies and 

techniques that can be used to adequately represent wind 

power plants in the interconnected power systems. 

Wind power plants can be very large in terms of

installed capacity. The number of turbines within a single 

wind power plant can be as high 200 turbines or more, and

the collector system within the wind power plant can have

several hundred miles of overhead and underground lines. 

It is not practical to model in detail all individual turbines 

and the collector system for simulations typically

conducted by power system planners. To simplify, it is a

common practice to represent the entire wind power plant

with a small group of equivalent turbine generators or a

single turbine generator. The question is how much can a

model be simplified and still preserve its faithfulness? 

In this presentation, we will describe methods to derive

and validate equivalent models for a large wind farm.

FPL Energy’s 204-MW New Mexico Wind Energy Center,

which is interconnected to the Public Service Company of

New Mexico (PNM) transmission system, was used as a 

case study. The methods described are applicable to any 

large wind power plant. We will illustrate how to derive a

simplified single-machine equivalent model of a large wind

power plant (which includes an equivalent collector system

model), preserving the net steady state and dynamic

behavior of the actual installation. We use steady state as

well as the dynamic analysis to derive the equivalent 

model. To verify the derivations, we compare the steady 

state and dynamic performance of the equivalent model 

against a detailed model of the wind power plant, which

contains all the wind turbine generators and associated 

collector system. 

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

wind energy, dynamic transient, aggregation, equivalence,

collector system, distribution network, power systems

renewable energy. 

I. INTRODUCTION

The Taiban Mesa wind power plant is the most

technically advanced wind plant in the country today.

Built in 2003, it employs the latest advances in variable

speed machine technology, incorporating low voltage

ride through capability and controllable reactive power

output. The plant employs 1.5 MW variable speed

machines manufactured by General Electric Company

(GE), is owned and operated by FPL Energy, LLC 

(FPLE), and sells its entire output to Public Service

Company of New Mexico (PNM), on whose

transmission system it is interconnected. 

The interconnection of the Taiban Mesa plant overcame

unique engineering technical challenges. Located in

eastern New Mexico, the plant interconnection

substation is tapped into a 223 mile 345 kV transmission 

line. One terminal of the line is at Albuquerque, N.M.,

while the other end connects to the Blackwater HVDC 

converter station in Clovis, NM. The Blackwater HVDC

station interconnects the Western and Eastern 

Interconnections. 

During the plant design phase, two of the unique 

engineering challenges included: 

• Consideration for low-voltage ride-through for faults

on the PNM 345 kV transmission system. Since the plant

nameplate represents a significant fraction of the PNM

control area load, loss of the plant in response to

transmission network faults would pose a severe

operating challenge. At the time however, the industry

discussion of low-voltage ride through for wind turbines 

was just beginning, so there was little precedent upon 

which to base the engineering design. 

• The advanced turbines at the wind plant are capable of

dynamic reactive power control and coordinated

regulation of the interconnect bus voltage. There was

concern about this autonomous system interacting with

the HVDC converter station voltage control scheme, and

detailed engineering studies were conducted prior to

plant commissioning to investigate this potential. 

1
Validated positive-sequential computer models (power 

flow and transient stability) for the Taiban Mesa wind

plant are critical for PNM transmission studies given the

potential for the Taiban Mesa to interact with and

influence the PNM transmission network. PNM has 

accumulated significant operating experience with the

Taiban Mesa wind power plant and has pro-actively

worked to refine its planning models used in GE –

Positive-Sequence Load Flow (PSLF) program.

However, wind power plant modeling, particularly

model validation, remains an area of concern for the

industry in general. NREL, in cooperation with the Wind 

Plant Modeling and Interconnection User Group of the

Utility Wind Interest Group, seeks cooperation with

PNM, FPLE, and GE to conduct a model development

and verification effort in order to advance the state of the

art in the development and use of wind plant models for

power system applications ("Joint Study"). 

In the next few sections, we will present our work in

progress up to this point. In section I we have presented 

the background of this work. In section II the Taiban 

Mesa wind power plant equivalent circuit derivation will

be briefly discussed. In section III dynamic simulation

with low voltage ride through will be presented. In

section IV, single turbine representation will be 

discussed and in section V, the full system

representation will be presented. The conclusion and 

summary of the work will be presented in Section VI. 

II. TAIBAN MESA WIND POWER PLANT EQUIVALENT

CIRCUIT

A. General overview and general assumption

In this section the background of circuit simplification

Caliente

Artesia

Blackwater

Guadalupe

B-A

Norton

Ojo

San Juan

Four Corners

Springerville

Greenlee

West Mesa

Belen

Hernandez 

Taos

Sandia

Socorro

Elephant Butte

Picacho

Hollywood

Alamogordo 

Holloman AFB

Newman

Diablo

Luna

Hidalgo

Dona Ana

Las Vegas 

Storrie Lake

Bravo Dome

Springer

York Canyon

Los Alamos

Algodones Santa Fe

Blue Water 

Ambrosia

Bisti 

Pillar

Shiprock

Amrad

HVDC tie

HVDC tie

Moriarty

Willard

Arroyo

Deming 

Phelps Dodge 

McKinley

Yah-tah-ey

PEGS

Central

Salopeck

Rio Grande

WECC PATH 48 

345 kV

230 kV

115 kV

Bernardo

Black Lake

Taiban Mesa

Figure 1. Power System Network Transmission lines under Public Service of New Mexico service territory. 

2
will be described. Figure 1 shows the power system

network transmission lines under Public Service of New 

Mexico service territory. Only the transmission level

voltage interconnections were shown on the map. The

Taiban Mesa wind power plant is indicated at a green 

star with label “Taiban Mesa” under the star. 

The wind power plant collector system consists of

underground cables and overhead lines. The system

distribution can be described by referring to Figure 2. It

is shown here that the lowest level of grouping of the

wind turbines is shown in blocks. 

In the planning stage, the power system designer will

compute the collector system requirement for the wind 

power plant. Normally, there are many considerations in

placing the turbines on each site, which contributes to 

the diversity of impedances intra-turbines, and between

the turbine and the substation transformer. Among 

many others, are, the wind resource of the site (micro

siting strategy), the minimum distance between two 

turbines to avoid the turbulence wake caused by one

turbine affecting another turbines, the voltage drop along

the line feeders, the line losses within the collector 

system. 

Taiban Mesa

Infinite Bus

10999 

345 kV

10995

345 kV

10998

34.5 kV

Each wind turbine generates a three-phase output power

at 570 Volt at 60 Hz. This voltage is stepped up by a 

pad-mount-transformer to a higher voltage at 34.5 kV.

A group of turbines (2 to 6 in a group) are connected

together as a daisy chain connection at the high side of

the pad mount transformer, and it is represented by a

block shown in Figure 2. Figure 3 shows the content of

each block where a string of turbines are connected in

daisy chain fashion. 

The collector system data consists of intra-nodes

impedances and line shunt capacitances in the wind 

power plants. From here, we have two choices to make. 

One is to simulate the entire wind power plant with each 

of the 136 turbines represented. Another one is to find 

an equivalent circuit representation of the 136 turbines.

In simulating the entire wind power plant as a single

turbine, we essentially observe the collective behavior

predicted by a single turbine. Obviously, we loose some

aspects of observation especially if the wind power plant

is a very large one covering a very large area. 

There are two types of processes to be considered here

for finding the equivalent circuit of a large wind power

plant. The first one will be called Analytical Approach

is based on the data of collector system provided by the

power system designer. Another one will be called 

Deduction Approach deduced from load flow calculation

of a complete full system representation (136 turbines). 

B. Analytical approach 

At first, lets considered the analytical approach where

the entire wind power plant can be considered as a single

wind turbine. The final equivalent circuit representation

of the entire 136 wind turbines is given in Figure 4. 

The equivalent of all the turbines and the collector

D2

D3

D4

D5

D1

D7

D8

D9

D10 

D6

D15 

D16 

D14 

D13 

D12 

D11 

D23 

D22 

D19 

D20 

D18 

D17 

N8

D21 

N3

N1 N2

N4 N6

N5 N7

Figure 2. Complete collector system in the wind farm.

D1

 

Figure 3 a) single series daisy-chain physical diagram

 b) equivalent representation of circuit (a) 

(a) (b)

34.5 kV 345kV

10998 10995

(0.01345 + j0.0497) 

B= -j 0.1004 Wind Farm 10999

(0.002+j0.002) 

Taiban Mesa

Infinite Bus

10997 10996

0.570 kV 34.5kV

(0.0014+j0.0828)

(0.0026 + j0.0245) 

Figure 4. A single turbine equivalent circuit of

Taiban Mesa wind farm. 

3
system infrastructure within the wind power plant can be 

approached using power line losses equivalence. 

Detailed of this approach is described in paper reference

[1], (paper submitted to the IEEE-PES 2006). 

The process of equivalencing the Taiban Mesa wind 

power plant is started from the lowest level of turbine

connections (daisy-chain connected turbines). The

equivalent circuit of these turbines (as shown in Figure

2) is represented as D1 through D23. First find the

equivalent circuit of the block (e.g. D1 through D23).

This simplification process converts the daisy chained 

wind turbines into a single impedance representation. 

Then the next step is to find the equivalent circuit of the

parallel D1, D2, D3, D4, and D5 connected to N1. The 

same process is followed for the rest of the wind power

plant collector system. And then we find the equivalent

circuit of the parallel impedances connected to N1 

through N8. Finally, the collector system of the wind

power plant can be represented by the single line 

diagram shown in Figure 4. 

C. Deduction approach 

In this approach, the entire 136 turbines are modeled in

the load flow analysis. The load flow calculation is

performed for the base case scenario. The real power

loss, reactive power loss, and the currents in the

branches are calculated by load flow and available in 

tabular form. The total loss in all of those branches 

within the collector system is then added. From the total

loss and the main line current, we can find the equivalent

impedance. From here, the equivalent impedance of the

distribution power system network can be deduced. The

shunt admittance is difficult to separate in the calculation 

of reactive power loss, however, we can use the same

techniques developed in the previous section to find the

approximate value of B. 

Table 1. Equivalent Circuit of Collector system

Circuit Impedance-Shunt Admittance

Representation R X B

Analytical 0.01345 0.0497 0.1004

Deduction 0.0104 0.0388 0.1004

A comparison between the results from the analytical

approach and the result from the deduction approach are

tabulated in Table 1. It is shown that the result from the

two approaches is in a good agreement. The small

difference between the two concepts is caused by the

fact that in the analytical approach the output currents of

the wind turbines are assumed to be identical, while in 

reality, due to the differences in the impedances, the

phasor currents are not identical. With identical currents

the sum of the currents at any summing junction will be 

maximized, and so will the total losses. 

III. DYNAMIC SIMULATION WITH LVRT VOLTAGE

PROFILE FOR MODEL VALIDATION 

A. General Description 

To check the validity of model equivalencing, we use

dynamic simulation. Based on the same transient

condition, the two systems Single Turbine

Representation (STR) and the Full System

Representation (FTR) of 136 turbines are compred. 

In the next few sections we attempted to recreate a 

fictitious fault at the Taiban Mesa 345kV substation 

using a guidelines provided by AWEA. According to

the AWEA-LVRT, the wind power plant must be

connected to the grid as long as the voltage at the point

of interconnection is at or above the specified voltage

profile. The voltage profile starts at 1.0 p.u. at t = 0 and

drops to 0.15 p.u. at t = 625 msecs, and the voltage 

slowly ramps up to 0.9 p.u. at t = 3.0 secs. The wind

turbine must be connected indefinitely as the voltage 

drops down to 0.9 p.u. The low voltage ride through

voltage profile provided can be shown in Figure 5. This

Figure 5. Test Voltage Profile (Ref. From FERC NOPR

Jan 24, 2005)

10999 

Taiban Mesa

345 kV 

Full System Representation 

or 

Single Turbine Representation 

 10995 345 kV 

 Taiban Mesa

 10998 34.5 kV 

 Taiban Mesa

Figure 6. Single line diagram of the wind farm for 

two types of collector system configuration. 

4
voltage profile is proposed by AWEA as appear in the 

FERC NOPR January 24, 2005. The purpose of 

applying this voltage profile is more to test the wind

turbine behavior than to test the power system integrity.

Under normal circumstances, this type of fault will be

cleared within 4-5 normal clearing cycles. 

Voltage

Since the relay protection of most of generators installed 

in the field is not set to survive this voltage profile, we

will temporarily disable the protection systems for

under/over voltage protection and under/over frequency 

protection. The voltage profile is applied at Taiban

Mesa substation by using a generator classic (GNCLS)

PSLF model with a voltage profile readable from an

input file. This LVRT requirement does not consider

frequency changes, thus, only the voltage magnitude is

modulated according to this voltage profile shown. 

Real power 

B. Circuit Representation Reactive power

The power system network can be simplified and it is 

shown in Figure 6. The single turbine representation is a

wind power plant representation, where, all of the 136

wind turbines are represented by a single turbine. The

equivalencing process is described in Section II. In

Figure 6, the equivalent circuit to replace the CDNC

block is shown in Figure 4 for a single turbine 

representation, or, it can be replaced by the circuit shown 

in Figure 2 for the full system representation. 

Figure 7. Voltage, real power and reactive power 

response to the fault at the Taiban Mesa 345 kV. 

IV. SINGLE TURBINE REPRESENTATION (STR)

A. Bus 10999 (Taiban Mesa –345 kV)

Figure 7 shows the result of the simulation. The voltage

profile representing a fictitious fault based on AWEA –

LVRT proposed voltage profile is shown. The real

power and reactive power traces are also shown on the 

same figure. The direction of the power flows shown in 

this figure is Taiban Mesa to the wind power plant, thus 

the actual flows from the wind power plant to Taiban 

Mesa is the mirror image of the traces shown. 

B. Bus 10701 (Wind Turbine – 0.57 kV)

Figure 8 shows the traces of voltage, real power, and 

reactive power output of the wind turbines represented 

by a single turbine. Since this simple circuit is a single

series circuit connecting the wind turbine and Taiban

Mesa substation, the traces shown in Figure 7 and Figure

8 are very similar with the exception of the collector

system power loss. 

This point of measurement is the wind turbine terminals

connected to the utility at the low voltage side. By 

looking at the range of the variables plotted, the voltage

range is between 0.23 pu to 1.03 pu. The terminal

voltage shows a second swing after the fault. Note, that

although the voltage at the fault (Taiban Mesa

substation) goes down to 0.15 pu, but the impedance

between the fault and the wind turbine terminals is

sufficient as such that the lowest voltage during the fault,

at the turbine terminals is about 10% higher. This is due

to the voltage drops along the lines between the wind

power plant and the substation. The turbine is able to

Voltage

Real power 

Reactive power

Figure 8. Voltage, real power and reactive power 

response to the fault at the wind turbine terminals. 

5
correct the voltage in the post fault condition although

the voltage at Taiban Mesa substation stays at 0.9 p.u. 

The real power output of the wind turbine drops to –

35.68 MW for a short period of time, and in the

upswing, it reaches 228.49 MW. Note that this very

short transient indicates the changes of the phasors

voltages and currents with respect to the reference.

While the current limit of the power converter is

controlled very strictly, the voltage phase shift during

transient is not controllable. During transient, the phase

angle changes can create an impression as if the power

(real or reactive) limit is exceeded. The post-fault

(steady state) condition of the real power returns the 

terminal voltage, and output power (real and reactive) to

the same level as its pre-fault condition, as expected.

Note, that both the real and reactive power output of the

wind turbine is the mirror image of the real and reactive 

power shown at the Table Mesa. 

The reactive power, in an attempt to regulate the voltage

during the fault, it shows the correct trend, and the

turbine produces reactive power that swings between

8.95 MVAR and 130.5 MVAR. It is also shown that the

post-fault condition of the reactive power does not stay

at the same level of output as the pre-fault condition due

to the voltage at Taiban Mesa that stays at 0.9 pu

indefinitely, three seconds after the fault occurs. Thus it

is obvious that the reactive power trace reacts to the

changes in voltage as planned. 

To observe the mechanical aspect of the turbine, the

rotor speed, the pitch angle and the mechanical

(aerodynamic power) are shown in Figure 9. It is shown 

there that the speed fluctuates significantly creating the

speed range between 1.0 pu and 1.26 pu. It is a bit

difficult to predict the response of the rotor speed to this

severe fault, because the speed variation is affected by 

both the mechanical and electrical systems. Electrical

output torque is the restraining torque and the

mechanical output torque is the driving torque. The

electrical torque is affected by the available voltage at

the turbine terminals and the output current (i.e. the 

power that can be generated) at any instant (including

during the fault). The mechanical torque depends on the 

mechanical power and the rotor speed. The mechanical

power variation is affected by the pitch angle of the

blades, the rotational speed, and the wind speed itself at

any moment. At any pitch angle, there is a valid Cp

versus tip speed ratio applicable for solving aerodynamic 

power. And at any pitch angle, it is possible that the Cp

goes to negative values when the tip speed ratio is too

low or too high. The tip speed ratio, is the ratio of the 

tip speed with respect to the wind speed. Since the wind

speed in this case study is assumed to be constant, the tip

speed ratio is only affected by the rotor speed. It is

interesting to note that the mechanical output variation 

goes between -1.1 p.u. (during the fault) to about 1.5 p.u. 

The pitch angle is controlled to maintain the rotor speed 

constant when the rotor speed reaches its rated speed. 

The pitch angle shown in Figure 9 varies significantly

from low to high values with the swing of about 25 

degrees. All in all, even with this severe fault, the 

turbine does not go into run-away condition, and the

rotor speed is still controllable. Note, how the pitch

angle variation has strongly affects the mechanical

power output. 

Rotor speed 

Mechanical power 

Pitch angle 

Figure 9. Rotor speed, mechanical power and pitch angle 

variation pre-fault and post-fault condition.

C. Frequency comparison among Buses

In Figure 10, the frequency of several buses are shown. 

Although in steady state the frequency is more or less

constant, instantaneously, the frequency is proportional

to the rate of change of the phase angle of the voltage

phasor at the buses. The frequency at the Taiban Mesa

(10999) and the frequency at the HV of the substation

transformer (10995), have a similar trend because the

impedance between the two buses is very small. There

is a significant difference between the frequency of bus 

10995 and bus 10998 (LV of the substation transformer). 

Although the two buses are separated by the leakage 

inductance of substation transformer, however the

impedance of the transformer is significantly larger than

the impedance of other components in the power system

network under consideration. Also, note that the nature

of the voltage variations (rate of change, control methods

etc.) affect the frequency difference. As mentioned

before, the bus voltage at Taiban Mesa (10999) is

controlled by preset voltage profile, while the bus 10998

6
is controlled by the wind turbine generator at bus 10701. 

Of course, the voltage at bus 10998 is first affected by 

bus 10999, however, the response of the generator at bus

10701 to correct that voltage changes that makes the bus

at 10998 looks different from the bus 10999 (or 10995).

The voltage drops along 10998 to 10701 creates the

different in the frequency traces between the two buses.

D. Comparison between sending end (WTG at Bus 10701)

and the receiving end (Taiban Mesa 345 kV or bus 10999)

To help with focusing the observation, dashed circles are

drawn on the traces. Figure 11a shows comparison of

the two traces of real power at two different buses (wind 

turbine bus and HV substation transformer bus. From

the scales located at the bottom of the plot, we can see

the range of the traces within the window of observation. 

It is shown that the arriving power at Taiban Mesa 345 

kW is about 10 MW less than when it is generated at the

wind turbine terminals. The real power flow difference

between the sending and receiving end is accounted for

the losses. 

Figure 12 shows the two traces of reactive power at two 

different buses (wind turbine bus and HV substation

transformer bus). The two traces show a significant

difference in the sense that the difference is nonlinear.

The wind turbine output reactive power stays in the

positive region indicating the flow from turbine to the

substation. The reactive power arriving at the substation

changes in direction during the fault. For example

during the recovery of the voltage (between t = 1.5sec to 

t = 3.0 sec) the reactive power flowing from the

substation. This significant difference is probably

caused by the effect of Ldi/dt, which has a non-linear

impact during transient on reactive power consumed by

the impedances along the line between bus 10999 and 

bus 10701 

at the turbine

Wind Turbine 

HV Substation XFMR 

at the substation 

LV Substation XFMR 

Taiban Mesa 345 kV

Figure 11. Real power comparison. Figure 10 Bus frequencies comparison. 

at the turbine

at the substation 

Figure 12 Reactive power comparison.

7
V. FULL SYSTEM REPRESENTATION (FSR)

A. General Description

In this section, the entire wind power plant is

represented. Each turbine, each line connecting turbine 

to turbine, each pad mount transformer are represented. 

The same fault condition applied to the STR, is also

applied to this FSR. The fault is applied to the same bus 

Taiban Mesa 345 kV (10999) by generating the voltage

profile as in the single turbine equivalent. The same

setting is applied to the relay protection to disable them

during this simulation. From the simulation results, we 

can observe the behavior of individual turbines as well

as the collective behavior of the entire wind power plant. 

The dynamic model of each generator consists of the

wind turbine prime mover model, the generator-power

converter model, and the relay protection model must

each be represented in the dynamic file. Thus for the

entire 136 turbines, these models must be repeated and 

represented creating many variables that must be 

computed at each time step. One disadvantage of

representing all the turbines installed in the wind power

plant is the computing time can be very long. 

B. Bus 10999 (Taiban Mesa 345 kV):

At the pre-fault condition, there is a 204MW wind power

generation from the wind power plant. When the fault

occurs, the severity of the fault shows how the power

flow is affected. Figure 13a illustrates the behavior of

the voltage, real and reactive power at bus 10999

(Taiban Mesa Substation) when subjected to a voltage

profile (AWEA-LVRT). For an easy comparison 

between FSR and STR, Figure 13b is brought here from

the previous section (at the right hand side). The voltage 

waveform is the same preset voltage read from an input

file. From Figure 13a, it is shown that the traces for

real and reactive power for an FSR is rounder or 

smoother than the traces for the STR, indicating that

there is some cancellation effect among the 136 turbines. 

Note that in the FSR, the wind speed driving each

turbine is the same, thus the only diversity considered 

here is the impedance of the collector system. The range

of variation of real power for an FSR is narrower than 

the range of variation for an STR. Table 2 is used to

compare the range of real and reactive power variations. 

TABLE 2. Power flow at bus 10999 for an FSR and STR

FSR STR

Max Min Max Min.

Real Power (MW) 13 -218 46 -217 

Reactive Power 

(MVAR) 65 -60 107 -62

From this table, we can see that the use of STR assumes 

that all turbines respond instantaneously and are in sync

with the rest of the turbines in the wind power plant, thus

there is no cancellation or no smoothing effect in place.

Sharp rise of high ramp rates is amplified by 136 times.

On the other hands, for FSR, the diversity in the wind 

Voltage Voltage

Real Real power power 

Reactive power Reactive power

(a) Full System Representation (136 WTGs) (b) Single Turbine Representation

Figure 13. Voltage, real power and reactive power at Bus 10999. 

8
power plant collector system is fully employed. 

From this table we can also see that the range of real

power exceeds the allowable range of wind power plant

output. For example, the output ranges of wind power

plant for real power output is 0 MW to 204 MW, and the

reactive power output ranges from –70 MVAR to

+70MVAR. This deviations occur during the fault

where only the magnitude of the power converter

currents are restrained by the current capability of the

power converter by its system protection, while the 

phase angle of the voltage during transient can swing 

unpredictable. 

C. Comparison among the turbines 

All of the 136 turbines are simulated with the same wind 

speed input, the same initial conditions of the pitch 

angle, real input power etc. The difference in conditions

among the turbines, are strictly based on their line

impedances among the turbines. 

To observe the impact of line-impedances among the

wind turbines, we compare one turbine with index

number 10701 with another turbine with an index

number 10836. This choice of turbines observed here is

random with consideration based only on the index

number (the first one and the last one). It is neither

based on the electrical distance nor physical distance. It

is neither based on the choice of line impedances nor the

choice of bus voltage magnitude and phase angle.

Having said that, we must be aware that there is a

difference in the Thevenin line impedance (between the

turbine and the infinite bus) of the turbines being

compared that warrant significant behavior differences

observable on the traces shown.

Considering that the only diversity considered is the

collector system impedances, it is expected that the

electrical behavior of the turbines will be different.

First, lets consider the voltage at the terminals of two 

buses mentioned above. Note, that the two turbines are

set to control the voltage at the low voltage side of the

substation transformer (bus 10998). Figure 14 shows 

that the two wind turbines experience different voltage at

any instant of time. The dashed circles indicate the 

notable difference in the electrical characteristics

between the two turbines. The voltage difference is

reflected by the difference in reactive power. The 

reactive power changes with the voltage as a

consequence of the control systems trying to fix the

deviation of the voltage away from the reference value. 

Note, that the voltage controller indicates that the PID 

(both the voltage error and the rate of voltage error)

components in controlling the reactive power. The real

power trace has a very subtle difference between the two 

turbines. The shape is very similar between the two 

traces, with the exception that there is some time delay 

between the two traces. 

Figure 15 shows the mechanical aspects of the two 

turbines (i.e. the rotor speed, the mechanical power, and 

the pitch angle). Since in this simulation, we considered

only constant wind speed the mechanical power is

influenced by the rotor speed (tip speed ratio) and the

pitch angle (power curve). There are several

connections can be made between the mechanical and

electrical variables that may influence each other. 

Under normal condition, the electrical power is

controlled to follow the rotor speed. Under abnormal

Voltage Voltage

Real power Real power 

(a) wind turbine at 10701 (b) wind turbine at 10836 

Reactive power Reactive power

Figure 14. Voltage, real power and reactive power at two turbines 

9
conditions (fault, under voltage), the output power is

affected by the available voltage at the grid and the

current capability of the converter.

Rotor speed depends on the balanced between the input

mechanical power and electrical power. Rotor speed 

influences the mechanical driving (aerodynamic) power

of the turbine and in addition, the blade pitch angle also

influence the mechanical power. Once the balance of

electrical and mechanical power is disturbed (fault,

changes in blade pitch), the rotor speed will respond

accordingly.

Thus, there is a strong interaction between electrical and 

mechanical characteristics within a single turbine. Let

us observe the wind turbine at bus 10701 alone. We can 

observe the interaction within turbine shown. When 

there is a fault on the electrical lines, the voltage drops

significantly, the electrical output power drops

significantly, the balanced of mechanical and electrical

power is disturbed. The rotor speed changes with this

balance. The rotor speed changes is further complicated

by the fact that the shaft and dual inertia of the wind 

turbine and generator interacts to produce the rotor speed

shown in Figure 15. As the rotor speed changes, the 

blade pitch mechanism becomes active to keep the rotor

speed stabilized. The combination of electricalmechanical balance, the shaft stiffness, the blade pitch

action, all of them creates the total and final response of

the rotor speed. 

Lets compare the mechanical aspects of the two turbines

(Figure 15a and Figure 15b). With a known constant

wind speed and relatively constant rotor speed, it is easy

to relate the relationship between the pitch angle and 

mechanical power. The mechanical power is shown 

mainly as a response to the pitch angle. Increase pitch

angle means decrease in mechanical power, and decrease

pitch angle means an increase in mechanical power. The

control of pitch angle is an attempt to keep the rotor

speed constant. 

Rotor speed Rotor speed 

Mechanical power Mechanical power 

(a) wind turbine at 10701 (b) wind turbine at 10836 

Pitch angle Pitch angle 

Figure 15. Rotor speed, mechanical power and pitch angle variations. 

Comparing the mechanical power, the rotor speed, and

the pitch angle between the two turbines are very similar

both in the shape and in the magnitude. Some of the

differences are shown in the area encircles by the dashed

lines. 

VI. CONCLUSION

This paper describes methods of equivalencing

collector system in a large wind power plant. We

simplified a wind power plant with a 136 wind turbines

into a single turbine representation. There are two 

methods we use in the process of simplification from

136 turbines into single representation. The analytical

approach is strictly based on circuit concepts. The

deduction approach is based on deduction derived from

load flow analysis. From the results, we conclude that

both methods are very compatible especially the value of

X/R. 

The full system representation (FSR) and the single

turbine representation (STR) are compared in dynamic. 

performance. To verify the resulting equivalent circuit,

we compare the two different turbine representations by 

using dynamic analysis. A simple low voltage ride

through (LVRT) voltage profile proposed by AWEA is

used as a test case. Both system representations are

10
subject to this voltage profile and the responses are

compared. 

What we find advantageous to the STR is that we

have the advantage of representing the entire wind farm

as a simple single turbine. The dynamic model of the

turbine can be represented as one set of turbine models

(we need only three sub-models per turbine, rather than

3x136 sub-models for the entire 136 turbines). This

type of simplification tends to be on the conservatives

side, especially when the relay protection is included in

the simulation run. Thus, if the there is a severe fault,

the choice is only two, either the wind power plant is

disconnected or the wind power plant stays connected.

With the FSR, the entire wind power plant is

represented in detail. Thus the wind power plant

diversity in the line impedances, relay protection setting,

wind speed on each individual turbine can be

represented. When severe fault occur, we can find out

how many turbines will be disconnected from the grid

and how many turbines will stay connected to the grid. 

 

VII. ACKNOWLEDGMENT

We acknowledge the support of the U.S. Department

of Energy. We also thank William Price from General

Electric International Inc., for help and discussions

during the development of this project. 

VIII. REFERENCES

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

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

Zabadil, J.C. Smith, ”Equivalencing the Collector System

of a Large Wind Power Plant,” presented at the IEEE 

Power Engineering Society, General Meeting 2006,

Montreal, Quebec, Canada, June 18-22, 2006. 

[2] 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. 

[3] Y.A. Kazachov, J.W. Feltes, and R. Zavadil, “Modeling 

wind farms for power system stability studies,”Power 

Engineering Society General Meeting, 2003, IEEE, Vol.

3, July 2003. 

[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.

11
F1147-E(12/2004) 

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing the burden, to Department of Defense, Executive Services and Communications Directorate (0704-0188). Respondents 

should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a 

currently valid OMB control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.

1. REPORT DATE (DD-MM-YYYY)

17-06-06 

2. REPORT TYPE

conference paper 

3. DATES COVERED (From - To)

June 4-7, 2006 

5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE

Model Validation at the 204 MW New Mexico Wind Energy Center: 

Preprint 

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

NREL/CP-500-39048 

5e. TASK NUMBER

6. AUTHOR(S)

E. Muljadi, C.P. Butterfield, A. Ellis, J. Mechenbier, J. Hochhiemer, 

R. Young, N. Miller, R. Delmerico, R. Zavadil, and J.C. Smith 

5f. WORK UNIT NUMBER

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

National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden, CO 80401-3393 

8. PERFORMING ORGANIZATION 

REPORT NUMBER

NREL/CP-500-39048 

10. SPONSOR/MONITOR'S ACRONYM(S)

NREL 

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

11. SPONSORING/MONITORING 

AGENCY REPORT NUMBER

12. DISTRIBUTION AVAILABILITY STATEMENT

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

13. SUPPLEMENTARY NOTES

14. ABSTRACT (Maximum 200 Words)

In this paper, we describe methods to derive and validate equivalent models for a large wind farm. FPL Energy’s 

204-MW New Mexico Wind Energy Center, which is interconnected to the Public Service Company of New Mexico 

(PNM) transmission system, was used as a case study. The methods described are applicable to any large wind 

power plant. 

15. SUBJECT TERMS

wind energy; wind farm; wind power plant; FPL Energy; New Mexico Wind Energy Center; wind farm model 

16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON 

a. REPORT 

Unclassified 

b. ABSTRACT 

Unclassified

c. THIS PAGE 

Unclassified

17. LIMITATION 

OF ABSTRACT

UL 

18. NUMBER 

OF PAGES 

19b. TELEPHONE NUMBER (Include area code)

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18