Equivalent Modeling of DFIG Based Wind Farm

Using Equivalent Maximum Power Curve

Feng Xue, Xiao-Fang Song, Kang Chang China Electric Power Research Institute

Nanjing, China, 210003 [xuefeng2@epri.sgcc.com.cn]

Abstract-The single-machine equivalent model (SEM) is

usually employed to represent the dynamics of wind farm,

while the accuracy of SEM decreases with the increase of

difference of the incoming wind speeds between each wind

turbine in the wind farm. In order to improve the accuracy of

SEM, an equivalent modeling method using power

characteristics curve of the wind turbine is proposed in this

paper. In this method, an equivalent maximum power curve

(EMPC) is obtained, where the wake effect is taken into

account. Using the EMPC, the calculation of equivalent wind

speed is unnecessary during equivalent modeling of the wind

farm. A wind farm with 9 wind turbines is built in MatIab, and

simulations are carried out under wind fluctuation and grid

fault to evaluated effectiveness of the proposed equivalent

modeling method.

Index Terms--DFIG; wind farm; equivalent modeling;

equivalent maximum power curve; single-machine equivalent

model

I. INTRODUCTION

A number of larger scale and grid-connected wind farms have been integrated into the power grid recently. The models of the wind farms are very important for the operation, stability analysis and control of the power system integrated with wind power. A wind farm usually consists of hundreds of wind turbines. If the detailed model of each wind turbine is integrated into the power grid simulation system, the efficiency of the simulation will be significantly decreased. However, this problem can be released when the equivalent model of the wind farm is used. [1].

Researches have been carried in the field of the equivalent modeling of the wind farm. The electrical parameters of an aggregated wind turbine generator (WTG) were estimated using optimization algorithm in [2, 3], and the single-machine equivalent model (SEM) of the wind farm was built. It was pointed in [4] that the multi-machine equivalent model is superior to SEM, when the wind distribution across the wind farm is irregular. An input­output model of the wind farm was proposed in [5, 6] based on the statistical analysis of the filed measurements of WTGs. In [7], taking the rotation speed of the DFIG as the clustering criterion, a multi-machine equivalent model of

978-1-4799-1303-9/13/$31.00 ©2013 IEEE

Tian-Ci Xu, Feng Wu, Yu-Qing Jin College of Energy and Electrical Engineering

Hohai University Nanjing, China, 211100 [ wufeng@hhu.edu.cn]

the wind farm was built, the number of the equivalent machine depends on the number of WTG groups. This model has better accuracy, while it is more complex than the SEM.

In order to increase the accuracy of the SEM of wind farm, an equivalent modeling method for DFIG based wind farm using equivalent maximum power curve is proposed in this paper. The equivalent power characteristics curve of the wind turbine (WT) is obtained. Based on which, the SEM is built. A wind farm with 9 wind turbines is built in Matlab, and simulations are carried out under wind fluctuation and grid fault to evaluated effectiveness of the SEM.

II. POWER CHARACTERISTICS OF WIND TURBINE

The wind turbine captures the wind energy and converts it into the mechanical power P willd.' It can be calculated as[8, 9]

Pwind =O.5pffR2CpV3 (1)

where, p is the density of air, 1fR2 is the area swept out by the turbine blades; V is the wind speed; Cp is the power coefficient, and it can be expressed by a model with 8 parameters:

and

11 Ai = 11 (A + C7/3) - Cs / (1 + /33) (3)

where A is the tip speed ratio; /3 is the blade pitch angle;

C1-Cs are constant coefficients. A is the function of the

wind speed and the turbine speed OJ.

A = OJR / V (4) The power characteristics curve of WT is shown in Fig. 1

[10-11]. There are three points in the power characteristics curve, namely A, B and C. When the DFIG works between A and B, the DFIG tracks maximum power from the wind.

The wind turbine rotates at an optimal turbine speed coopt, so as to make the Cp at its maximum value. The curve AB can be called Maximum Power Curve (MPC). The relationship of the turbine speed and the active power output of the WTG can be defined as:

{i(P) (P < Po) OJoP! =

OJmax (1 ;::: P ;::: Po) (5)

where P is the output active power of the WTG; f is the relationship between active power and rotating speed; Po is the active power output at B.

The DFIG keeps rotating speed constant between B and C. When the wind speed is higher than the nominal wind speed VN, the pitch angle controller is activated. The output

power of the wind turbine is kept at rated value and the wind

turbine rotates at its maximum value rotating speed, Ulnax. 1

0.8

;::: 0.6 � 0..;

0.4

0.2

c

B

A o�����--�--�--�--�--� 0.2 0.6 0.8 1.0 1.2

OJ/pu Figure I. Power characteristics curve of the wind turbine

III. EQUIVALENT POWER CHARACTERISTICS CURVE

The configuration of SEM of the wind farm is shown in Fig. 2. The voltage and current at the point of common coupling (PCC) can be measured. Using the parameters of equivalent step-up transformer and the equivalent collector network, the output power of the equivalent DFIG, PgJq, can be calculated using the power flow equation.

Figure 2. Single-machine equivalent model of wind farm

It is also need to be pointed out that the incoming wind speed, Vo, is usually measured in the wind farm. Hence, for the equivalent model of the wind farm, the incoming wind speed and the output active power are the input and output variable, respectively. The relation between the input and output demonstrates the power characteristics of the of the wind farm. If the equivalent maximum power curve can be obtained, the accuracy of the SEM can be improved.

When the WTG is running with maximum power point tracking (MPPT) mode, the pitch angle keeps to zero. Substituting (2) - (4) into (1), we have

2

P.";nd = O.5pffR2Vo3 {[CI (C2 Vo I OJR - C2CS) - C4]x

EXP[-C5 I (VO I OJR - Cs)] + C60JR I Vo}

It can be written as

(6)

P.vind = g(Vo'OJ) (7)

Ignoring the power loss in the WTG, the electrical output power, Pg, equals to the input mechanical power Pwind.

(8)

Similarly, the output of SEM, PgJ(1' can be written as

Pg _eq = g (VO' OJeq) (9)

where the subscript "_eq" demonstrates the parameters of the SEM.

Solving the nonlinear equation (9), the equivalent turbine

speed lUeq with respect to the output active power, Pg_e<J' can be obtained.

Based on the field measurements of the wind farm, a set

of relationships between Pg_e<J and COeq can be obtained.

Applying the least square method to data of (Pg_eq_i' lUecU)' the EMPC of the SEM between A' and B' can be written as

OJeq=F (Pg_eq ) (10)

Because of the wake effect [12], the wind speed decreases along the wind direction. When the wind speed of the DFIG located at the end of the wind direction reaches the nominal wind speed, all the DFIGs in the wind farm are

operating at Ulnax. In this situation, the rotating speed of

SEM between B' and C' keep constant at Ulnax_ul' and the output power of SEM at B' is Po eO" The Ulnax ea can be calculated using (10). Hence, the EMPC can be described by {F(Pg_ef/) (Pg_efl < Po_ef/)

OJ = eq OJmaX_efl (1;::: Pg _eq ;::: Po_eq)

(11)

This EMPC model can be implemented into the equivalent DFIG model of SEM as the reference of speed control.

IV. AGGREGATION OF PARAMETERS OF SEM

The other parameters of the SEM are obtained using the weighted average method [13-14]. The weight coefficients, ai, are given by

N

ai =Si IISi i=! (12)

where, Si is the capacity of the individual DFIG; N is the total number of DFIGs. The equivalent parameters can be obtained as follows: 1z' = �(a;Z,)'H, = �(a,H,),

f() ZT Deq = L.. a;Di ,Zr_eq =--i=1 N

(13)

where, H is the inertia constant, D is the damping coefficient, Z is the impedance of generators, ZT is the impedance of transformers.

The equivalent impedance of collector network is calculated using the principle that the power losses in

collector network keeps constant before and after equivalence [15].

V. SIMULATION

The DFIG based wind farm used in simulations is shown in Fig. 3. The wind farm comprises 9 DFIGs. The DFIGs in the wind farm are connected to a 25kV internal network. The wind farm is integrated into a 1l0kV power grid through two 50km feeders. The detailed parameters of this wind farm are given in Table I.

The wind direction is shown in Fig. 3. The wind farm is represented by SEM. Since the input of the SEM is the incoming wind speed, Vo' it is unnecessary to calculate the

equivalent wind speed (EWS) of the wind farm [6]. The simulations are carried out in Matlab/Simulink.

pee T

Figure 3. Structure of the simulation system

TABLE I. PARAMETERS OF THE WIND FARM USED FOR SIMULATION

Subsystem Parameters

(Label in Fig. 3)

DFIG I-DFlG9 The DFIG model is taken from "Wind Farm -

DFIG Average Model" demo in Simulink

Step-up transformer SN = 1.75MVA, 575V/25kV, R = 0.025/30(pu),

(T1-T9) X = 0.025(pu), X", = co, R", = 500(pu)

Internal network Three-Phase PI Section Line

(Zli) R = 0.1153Q/km, X = 0.3298Q/km

C= I1.33e-009F, Length: 0.6km

Power feeders Three-Phase PI Section Line

(Lio L:z) R = 0.1153Q/km, X = 0.3298Q/km

C= I1.33e-009F, Length: 50km

Step-up transformer SN = 47MVA, 25kV/llOkV R = 0.08/30(pu),

(T) X = 0.08(pu), X", = 500(pu), R", = 500(pu)

Power system IN = 60Hz, SN = 2500MVA, UN = I I0kV

A. Calculation of EMPC A 5% speed loss of wind is employed to represent the

wake effect. The dynamics of the detailed model of the wind farm are simulated, and take as the field measurements. With different incoming wind speeds, the outputs of the wind farm are listed in Table II.

From the result of the simulations, it can be concluded that when the income speed was increased to 12.4m/s, the rotating speed of DFIGs in the third column reached the maximum rotating speed. Hence, the simulation results obtained when the incoming speed is lower than 12.4m1s are

3

employed to calculate the curve between A' and B' in the EMPC.

TABLE II. OUTPUT DATA OF WIND FARM IN STEADY STATE

Vo 6.0 6.5 7.0 7.5 8.0 8.5

(m/s) 9.0

Pout 1.222 1.637 2.088 2.59 3.156 3.797 4.518

(MW)

Vo 9.5 10 10.5 I I 11.5 12 12.43 (m/s) Pout 5.32 6.206 7.181 8.252 9.422 10.66 11.74

(MW)

The genetic algorithm (GA) is applied on (9) to calculate

the equivalent rotating speed, (Oeq' In GA, the population size is set to 40, the generation gap is 0.9 and the maximum number of generations is 1000 [17]. The results of the calculation are listed in Table III.

TABLE Ill. POINTS IN THE EMPC

P/(pu) 0.0922 0.1563 0.2355 0.3366 0.4618

meq /(pu) 0.4549 0.5684 0.6623 0.7539 0.8435

P/(pu) 0.5343 0.6138 0.7008 0.7927 0.8735

me" /(pu) 0.8944 0.9336 0.9862 1.0258 1.0635

Using the least-squares method, we have

_ j(-0.5356PLeQ

+

J (PLeq < 0.8735)

Weq - 1.314P8-eq + 0.3655

1.0635 (l � PLee/ � 0.8735)

(14)

The EMPC of SEM and the MPC of individual DFIG are show in Fig. 4.

0.9 0.8 0.7

SO.6 0. if 0.5

0.4 0.3 0.2

,//./

//

/

/_�� 0 �'-;-.4-�-�----'--;:0.'co 7---;:0.'co 8 -70.CO- 9 ---:----71.�1 -----'''''1.''''''2 �c'1.3 Turbine Speedl(pu)

Figure 4. The curves of EMPC and MPC

B. Wind fluctuation The incoming wind speed as shown in Fig. 5, which is

generated by the "4-components composite model" of wind speed [16].

14

13

0012 E � 11

10 15 20 25 30 35 40 45 50 Vis) Figure 5. The curve of wind fluctation

The output of the detailed model, SEM with original MPC and SEM with EMPC are simulated and shown in Fig. 6. The errors between the dynamics of detail model and those of the equivalent models are calculated using (15).

Error =�± IYi eq-Yi IXlOO% (15) N i�1 Yi

where, N is the number of sampling points on the curve, Yi is the value of active power P or reactive power Q of detailed model, YUq is the value of P or Q of equivalent model.

From Fig.6, it can be seen that the output power of SEM

with EMPC is close to that of detailed model. The error of P is 2.55% and error of Q is 6.76%. Since the SEM with MPC

cannot take wake effect into account, the output power of the SEM with MPC has larger difference to those of the detail model, and errors in active power and reactive power are 15.53% and 36.84%, respectively. Hence, Using the EMPC, accuracy of SEM can be improved under the fluctuation of the incoming wind.

It also has to be pointed out that when the SEM with EMPC is used, the incoming wind speed is applied into the simulation system directly, while, when the SEM with MPC

is used, the EWS needs to be calculated at every simulation time step. Hence, the efficiency of the calculation can be improved using the SEM with EMPC.

0.9

0.8

-S-0.7 S Q: 0.6

0.5

-- SEM with MPC

-SEM with EMPC

-Detailed model

10 15 20 25 30 35 40 45 50 Vis)

4

0.01 r----c----r---r--.----,-----,---r-r=o======� -·_· SEM with MPC

-SEM with EMPC

-Detailed model o

·0.01

,,·0.02 Q. a '0.03

·0.04

·0.05

.0.06iOL -�-1c'c 0-�1 =-5 -2"' 0---;:2=- 5 -=30:----:3�5--;;40O---4c'c 5--:!50 Vis) Figure 6. Output of the three models of wind farm

C. G rid/a ult The grid fault of a three phase fault was applied at the

middle of the grid feeder L2 and was cleared after 0.1 second. The incoming wind speed of wind farm is set as llmls and is assumed to be constant, since the electromechanical dynamic of the DIFG is much faster than variation of the wind.

The dynamic responses of the detailed model, SEM with EMPC and SEM with MPC are shown in Fig. 7. From Fig.7, it can been seen that the dynamics of the output power of the SEM with EMPC and SEM with MPC are both close to those of the detailed model. The active power error of the SEM with EMPC is 3.24%, while that of the SEM with MPC

is 3.73%.

1.4.r----c-�-�--.---.-------.-----,=-=-=-===iI f-·_· SEM with MPC & EWS

-SEM with EMPC 1.2 -Detailed model

_0.8 it ifO.6�

0.4

0.2 �,

VI. CONCLUSION

The equivalent method of DFIG's power characteristics curve has been proposed in this paper. Using the equivalent

modeling method, the accuracy of the SEM of DFIG based wind farm has been improved, and the calculation of EWS has also been avoided. Taking the incoming wind speed and output power of the wind farm as the input and output of the equivalent model, the wake effect can be included into the EMPC. Simulations have been carried out in MatIab under the wind fluctuation and grid fault, and the results have shown the effectiveness of the SEM with EMPC.

VII. ACKNOWLEDGEMENT

This research is supported by National Natural Science Foundation

of China (51190102) and National High Technology Research and Development Program of China (863 Program) (2011 AA05A 103).

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