### International Electrical Engineering Journal (IEEJ)

### Vol. 4 (2013) No. 1, pp. 907-913

### ISSN 2078-2365

907 Power System Transient Stability Analysis with High Wind Power Penetration

**Abstract****— Some countries did not have adequate fuel **
**and water power resources, which led them to look for **
**alternative ways of generating electricity such as wind power, **
**solar power, geothermal power and biomass power, called **
**renewable energy. Wind energy is one of the most available and **
**exploitable forms of renewable energydue to their advantages. **
**However the high penetration of wind power systems in the **
**electrical network has introduced new issues in the stability **
**and transient operation of power system. The majority of wind **
**farms installed are using fixed speed wind turbines equipped **
**with squirrel cage induction generator (SCIG). Therefore, the **
**analysis of power system dynamics with the SCIG wind **
**turbines has become a very important research issue, especially **
**during transient faults. This paper provides an assessment of **
**wind penetration effects on the power system transient **
**stability. The wind generators considered are the squirrel cage **
**induction generator (SCIG), which is a fixed speed. **

**Index Terms****— Power system, Squirrel Cage Induction **
**Generator (SCIG), Wind Penetration, Transient stability, **
**Critical Clearing Time (CCT) **

I. INTRODUCTION

Wind generators are primarily classified as fixed speed or variable speed. Due to its low maintenance cost and simple construction, squirrel cage induction generator (SCIG) is mostly used for wind power generation [1]. SCIGs directly connect to the grid and they don’t have convertor like DFIGs. Because of lack of convertor and robust control procedure, SCIGs are more sensitive to wind speed variations rather than DFIGs and mechanical parameters like wind turbine inertia constant and shaft stiffness coefficient have remarkable impact on operation of this kind of wind generators. Moreover they are more sensitive to fluctuations and faults in power system rather than DFIGs [2].

One of important issues engineers have to face is the impact of SCIGs wind turbines penetration on the transient stability of power system. Transient stability entails the evaluation of a power system’s ability to withstand large Prof. Tarek Bouktir acknowledges support from MESRS (Algeria), grant number J0203020080004

disturbances and to survive the transition to another operating condition. These disturbances may be faults such as a short circuit on a transmission line, loss of a generator, loss of a load, gain of load or loss of a portion of transmission network [3]. A number of studies have been conducted on power system transient stability with high penetration of SCIG based wind farms, but they have considered simple network

structures [4], [5], [6]. In the present work, the impact of SCIG wind farms installation and penetration on transient stability is demonstrated using the IEEE 30-bus system. Using this network, simulation has been carried out for two different cases and different penetration levels during three phases to ground fault:

*Case 1*:single SCIG wind farm has been connected
to grid.

*Case 2*: the network has been modified by
connecting two SCIG wind farms.

Simulation results show that wind farm consist of constant speed wind turbine in high penetration condition is remarkably influential in transient stability.

The paper is organized as follows. Section II briefly introduces the mathematical models of power system and wind generator. The Optimal Power Flow (OPF) formulation is presented in Section III. In section IV, the detail case studies focusing on the impacts of fixed speed grid-connected wind farms on IEEE-30 bus test system are carried out. Finally the conclusions are summarized in Section V.

II. POWER SYSTEM MODELLING

*A.* *Power System Modelling *

The power system model consists of synchronous generator, transmission network and static load models, which are presented below.

The machine classical electromechanical model is represented by the following differential equations [7]:

## Power System Transient Stability Analysis with

## High Wind Power Penetration

Amroune Mohammed 1, Bouktir Tarek 2 Department of Electrical Engineering, University of Setif 1, Algeria

1

### International Electrical Engineering Journal (IEEJ)

### Vol. 4 (2013) No. 1, pp. 907-913

### ISSN 2078-2365

908 Power System Transient Stability Analysis with High Wind Power Penetration

###

###

2 2*i*

*i*

*s*

*i*

*mi*

*ei*

*Di*

*i*

*d*

*dt*

*d*

*f*

*P*

*P*

*P*

*H*

*dt*

_{ }

_{ }(1) Where:

*P*

_{D}*Dd*

*dt*

D is the generator damping coefficient, H is the inertia constant of machine expected on the common MVA base, Pm

is the mechanical input power and Pe is the electrical output.

The transmission network model is described by the steady-state matrix equation:

*bus* *bus* *bus*
*I* *Y V*

(2) Where Ibus is the injections current vector to the network, Vbus

is the nodal voltages vector and Ybus is the nodal matrix

admittance.

The electrical power of the ith generator is given by [8]: 2 1 cos

###

*ng*

_{}

_{}

*ei*

*i*

*ii*

*ij*

*ij*

*i*

*j*

*j*

*P*

*E G*

*C*(3) Where i = 1, 2, 3…ng is the number of generators.

Cij = |Ei||Ej||Yij| is the power transferred at bus ij, E is the

magnitude of the internal voltage, Yij are the internal

elements of matrix Ybus and Gii are the real values of the

diagonal elements of Ybus.

The static model of load is represented by load admittance YL

defined by [8]:
*i* *i*
*Li* *2*
*i*
*P - jQ*
*Y =*
*V*
_{ }(4)

*B.* *Wind Generator Modelling *

The fixed-speed, squirrel cage induction generator (SCIG) is connected directly to the distribution grid through a transformer. There is a gear box which maces the generator’s speed to the frequency of the grid.

During high wind speeds, the power extracted from the wind is limited by the stall effect of the generator. This prevents the mechanical power extracted from the wind from becoming too large. In most cases, a capacitor bank is connected to the fixed speed wind generator for reactive power compensation purposes. The capacitor bank minimizes the amount of reactive power that the generator draws from the grid [3].

Fig.1. Representation of the fixed speed induction generator

The Squirrel Cage Induction generator model is shown in Fig. 2. Where Rs represents the stator resistance, Xs

represents the stator reactance; Xm is the magnetizing

reactance, while Rr and Xr represent the rotor resistance and

reactance, respectively.

Fig.2. Equivalent circuit of the Squirrel Cage Induction generator [3]

A standard detailed two-axis induction machine model is used to represent the induction generator. The relationship between the stator voltage, rotor voltage, the currents and the fluxes are given by the following equations [9]:

*ds* *s* *ds* *s* *qs* *ds*
*qs* *s* *qs* *s* *ds* *qs*
*d*
*v = -R × i - ω × λ +* *λ*
*dt*
*d*
*v = -R × i + ω × λ +* *λ*
*dt*
(5)
*dr* *r* *dr* *s* *qr* *dr*
*qr* *r* *qr* *s* *dr* *qr*
*d*
*v = 0 = R × i - g× ω × λ +* *λ*
*dt*
*d*
*v = 0 = R × i + g× ω × λ +* *λ*
*dt*
(6)
Where Vs is the stator voltage while Vr represents the rotor

voltage, λs and λr are the stator and rotor flux respectively,

while ωs is the synchronous speed. The rotor voltage is zero

because the rotor has been short-circuited in the Squirrel cage induction generator. The model is completed by the mechanical equation as given below [9]:

*r*

*m* *e*

*dω* *1*

*=* *×(T - T )*

*dt* *2H* _{ }(7)
H is the inertia constant; Tm is the mechanical torque; Te is

the electrical torque and ωr is the generator speed.

III. OPTIMAL POWER FLOW FORMULATION

The OPF problem is considered as a general minimization
problem with constraints and can be written in the following
form [10], [11]:
Minimize ( , )*f x u*
(8)
Subject to g( , )*x u* 0
(9)
h( , )*x u* 0
(10)
Where*f(x,u)* is the objective function; *g(x,u) *is the equality
constraints and represent typical load flow equation; *h(x,u) *is

*Rs* *Xs*
* Xr*
* Rr*
*Xm*
*Vs*
Vr _{ V}
r
’
= e-jwt_{ V}
r
*R *
*v*
Grid
Gear Box
*β *

### International Electrical Engineering Journal (IEEJ)

### Vol. 4 (2013) No. 1, pp. 907-913

### ISSN 2078-2365

909 Power System Transient Stability Analysis with High Wind Power Penetration

the system operating constraints and *x* is the vector of state
variables.

The objective function for the OPF reflects the cost associated with generating power in the system. The objective function for the entire power system can then be written as the sum of the fuel cost model for each generator:

1
*NG*
*i*
*i*
*f* *f*

###

(11) Where fi is the fuel cost of the ith generatorThe fuel cost curve is modeled by quadratic function as: 2

*i* *i* *i* *Gi* *i* *Gi*

*f* *a* *b P* *c P*

(12)
Where *ai*, *bi*, and *ci* are cost coefficients of the *ith* generating
unit shown in the Appendix.

The functions * g* and

*are the equality and inequality constraints to be satisfied while searching for the optimal solution.*

**h**The function * g* represents the equality constraints that are
the power flow equations corresponding to both real and
reactive power balance equations, which can be written as
[11]:

###

,###

0*i*

*di*

*gi*

*P V*

*P*

*P* (13)

###

,###

0*i*

*di*

*gi*

*Q V*

*Q*

*Q* (14)

*is the system inequality operation constraints that include [11]: min max*

**h***gi*

*gi*

*gi*

*P*

*P*

*P*

*(15) min max*

*gi*

*gi*

*gi*

*Q*

*Q*

*Q*

*(16) Where Pgi and Qgi are the active and reactive power*

generations at ith bus; Pdi and Qdi are the active and reactive

power demands at ith bus; Pi and Qi are the active and reactive

power injections at ith bus.

Several methods have been employed to solve this problem, e.g. gradient methods, Linear programming method and quadratic programming. However all of these methods they may not be able to provide optimal solution and usually getting stuck at a local optimal [12]. New optimization techniques such as genetic algorithms, particle swarm optimization, Artificial Ant Colony algorithm, and Differential Evolution Algorithm are recently introduced and also applied in the field of power systems. In this paper Differential Evolution Algorithm (DEA) is used.

Differential Evolution is a direct search method using operators: mutation, crossover and selection. The algorithm randomly chooses a population vector of fixed size. During each iteration of algorithm a new population of same size is

generated. It uses mutation operation as a search mechanism. This operation generates new parameter vector by adding a weighted difference vector between two population members to a third member. In order to increase the diversity of the parameter vectors, the crossover operation produces a trial vector which is a combination of a mutant vector and a parent vector. Then the selection operation directs the search toward the prospective regions in the search space. In addition, the best parameter vector is evaluated for every generation in order to keep track of the progress that is made during the minimization process. The above iterative process of mutation, crossover and selection on the population will continue until a user-specified stopping criterion, normally, the maximum number of generations or the maximum number of function evaluations allowed is met. The process is assumed to have converged if the difference between the best function values in the new and old population, and the distance between the new best point and the old best point are less than the specified respective tolerances [13].

IV. SIMULATION RESULTS

This section presents computer simulation studies with programs developed in MATLAB software version 7.7 to demonstrate the transient performance of the power system with high wind power integration. The Critical Clearing Time (CCT) is used as indices to evaluated transient stability and the IEEE 30-bus test system shown in Fig. 2 is employed to conduct the transient stability simulation. Detailed parameters of this system can be found in [14]. A wind farm based on Fixed Speed Induction Generator (FSIG) is used and the FSIG parameters are outlined in the Appendix.

G
G
G
G
G
G
25
24
23
2
6
2
9
3
0
2
7
1 3
2
4
5
6
8
7
9
1
0
1
1
1
2
1
4 15
1
6
20
1
7
18 19
2
2
2
1
2
8
G
G
G
G
G
G
2
5 _{7 }
8
1 3 4 6
13 9
12 10 _{11 } _{30 } 29
16 17
14 15 18 19 20 21
22 27 28
23 24
26
25

### International Electrical Engineering Journal (IEEJ)

### Vol. 4 (2013) No. 1, pp. 907-913

### ISSN 2078-2365

910 Power System Transient Stability Analysis with High Wind Power Penetration

Fig.3. Single line diagram of the IEEE 30-bus system

*A.* *Case 1: Single SCIG wind farm *

In this case the SCIG wind farm of 20 MW has been connected to bus 10 and bus 24 separately (Figure 4). The SCIG was installed in a site that has the best potential in therms of the resources itself, construction and operations and maintenance logistics as well as interconnection and potentiel permissing issues such as wildlife ampcts and local politics [15].

The Optimal Power Flow results obtained with Differential Evolution Algorithm (DEA) with and without of wind farm is listed in Table 1. According to this table connecting the wind farm at bus 24 will be a better option in terms reduction in the total costs and power losses.

Fig.4. Single line diagram of the modified IEEE 30-bus system

TABLE 1:OPFRESULTS WITH AND WITHOUT WIND FARMS

**BUS № **
**PG (MW) **
**Without **
**wind farm **
**PG (MW) **
**With wind **
**farm at bus 10 **
**PG (MW) With **
**wind farm at **
**bus 24 **
1 176.8141 167.0748 167.0383
2 48.8318 46.4729 46.4601
5 21.4853 20.7535 20.7448
8 21.6837 15.9062 15.8131
11 12.1033 10.0000 10.0215
13 12.0000 12.0000 12.0000
**P loss ** **9.51813 ** **8.80743 ** **8.67769 **
**Total ** **802.333 ** **741.518 ** **741.072 **
**cost($/h) **

A disturbance in the form of a three phase to ground fault is occurs at t = 1 second at bus 1, cleared by opening the line connecting the nodes 1–2.

The dynamic analysis of grid connected SCIG needs to know about the Critical Clearing Time (CCT) of SCIG, which determines its transient stability. If the CCT is much lower than the time setting of protective devices normally installed in network, the system is said to be stable [16].

The Figures 5 and 6 show the dynamic responses of all machines for Fault Clearing Time (FCT) equal to 170 ms and 213 ms respectively. These Figures show that the Critical Clearing Time (CCT) improved after the introduction of the wind farm of SCIG type. For FCT = 213 ms, the system with Wind Farm (WF) at bus 10 (G10) remains stable and can

return to steady state finally. However, the system with wind farm at bus 24 (G24) is unstable. Another’s simulations have

been performed for different fault locations in IEEE 30-bus system, in order to know the effect of SCIG wind farm location on transient stability. The results from the cases study are presented in Table 2. The comparative results have shown that the location of wind turbines has an effect in transient stability of power system. In our case the insertion of a wind farm at bus 10 is better than its insertion at bus 24.

0 1 2 3 4 5 6 7 8 0 50 100 150 200 250 t, sec A n g le r o to ri q u e r e la ti f, d e g re e 1-2 1-3 1-4 1-5 1-6 **** éoliennes au jb 10 --- éoliennes au jb 24 ___ sans éoliennes

Fig.5. Rotor angle differences of all machines (FCT=170 ms)

G
G
G
G
G
G
25
24
2
3
26
29
3
0
27
1 3
2
4
5
6
8
7
9
1
0
11
1
2
14 1
5
1
6
2
0
1
7
1
8
1
9
2
2
21
2
8
G
G
G
G
G
G
2
5 _{7 }
8
1 3 4 6
13 9
12 10 _{11 } _{30 } 29
16 17
14 15 18 19 20 21
22 27 28
23 24
26
25
WG
WG
_____

without wind farms ** *wind farm at bus 10 - - - wind farm at bus 24

### International Electrical Engineering Journal (IEEJ)

### Vol. 4 (2013) No. 1, pp. 907-913

### ISSN 2078-2365

911 Power System Transient Stability Analysis with High Wind Power Penetration

0 1 2 3 4 5 6 7 8 0 50 100 150 200 250 t, sec A n g le r o to ri q u e r e la ti f, d e g re e 1-2 1-3 1-4 1-5 1-6 **** éoliennes au jb 10 --- éoliennes au jb 24 ___ sans éoliennes

Fig.6. Rotor angle differences of all machines (FCT=213 ms)

TABLE 2:CCT WITH AND WITHOUT WIND FARMS

**Faulte**
**d bus **
**Open **
**line **
**CCT **
**without **
**wind **
**farms (ms) **
**CCT with **
**wind farm **
**at bus 10 **
**(ms) **
**CCT with **
**wind farm **
**at bus 24 **
**(ms) **
1 1 - 2 169 216 211
1 1 - 3 223 261 256
2 1 - 2 238 296 277
2 2 - 4 303 357 350
2 2 - 5 309 370 360
2 2 - 6 303 357 351
4 2 - 4 498 624 618
4 4 - 6 506 637 631
6 2 - 6 599 834 822
6 4 - 6 611 854 838

In order know the impact of wind penetration level on the power system Critical Clearing Time, the analysis has been carried out on 10%, 20%, 30% and 35% wind penetration levels based on the total power required (283.4 MW). Penetration level is defined as the ratio of capacity of wind electric generator to capacity of alternator. The optimal active powers generated by all generators when SCIG wind farm is connected to bus 10 and to bus 24 are shown in Fig. 7 and Fig. 8 respectively. The variation of CCT for the fault at bus 1 with opening the line 1–2 is shown in Figure 9. From these Figure, it can be seen that the system transient stability can be improved by improving penetration levels of SCIG wind turbines.

Fig.7. Power generation with wind farm at bus 10

Fig.8. Power generation with wind farm at bus 24

Fig.9. CCT variation with wind farms (fault at bus 1)

*B.* *Case 2 : Two SCIG wind farms *

In this case the two SCIG wind farms have been connected to bus 10 and bus 24 simultaneously. Both farms generate 30 MW. Table III shown the total cost obtained with three penetration level scenarios. According to this table the total cost is low when the penetration level of wind farm is high at bus 10 and low at bus 24 (scenario 3).

A three-phase short circuit has been simulated on deferent selected buses for the three previous scenarios. The

_____

without wind

farms

** *wind farm at bus 10 - - - wind farm at bus 24

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### Vol. 4 (2013) No. 1, pp. 907-913

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912 Power System Transient Stability Analysis with High Wind Power Penetration

distribution of power generation between wind farms has an effect on transient stability of power system as shown in Table IV. In our study the CCT is more improved when the penetration levels of wind farm is high at bus 10 and low at bus 24 (scenario 3).

TABLE 3:OPFRESULTS FOR DEFERENT SCENARIOS

**G10 ** **G24 ** **Total cost ($/h) **

Scenario 1 15% 15% 562.244

Scenario 2 10% 20% 664.419

Scenario 3 20% 10% 561.28

Fig.10. Power generation for deferent scenarios

TABLE I. CCT FOR DEFERENT SCENARIOS

**Faulte**
**d bus **
**Ope**
**n **
**line **
**CCT (ms) **
**for Scenario **
**1 **
**CCT (ms) **
**for scenario **
**2 **
**CCT (ms) **
**for **
**scenario 3 **
1 1 - 2 445 443 445
1 1 - 3 483 484 485
2 1 - 2 584 580 586
2 2 - 4 631 635 636
2 2 - 5 626 629 631
2 2 - 6 638 642 644
4 2 - 4 1281 1286 1288
4 4 - 6 1278 1283 1286
6 2 - 6 1576 1587 1659
6 4 - 6 1558 1561 1564
V. CONCLUSION

The impact of increased penetration of fixed speed wind generators on power system transient stability is discussed in this paper. According to the simulation results, some

preliminary conclusions and comments can be summarized as follows:

An optimal integration, location and utilization of SCIG type wind generator to the power system improved the transient stability;

Wind power plants affect voltage levels and power flows in the networks. These effects can be beneficial to the system, especially when wind power plants are located near load centers.

The location and number of SCIG based wind turbine has an effect on transient stability of power system;

The increased of penetration level of wind generation SCIG type increase the power system Critical Clearing Time;

The distribution of power between SCIG wind farms has an effect on transient stability of power system.

Appendix

TABLE 4:POWER GENERAION LIMITS AND COEFFICIENTS

**BUS № ** **Cost Coefficients ** **PGMIN **
**(MW) **
**PGMAX **
**(MW) **
**a ** **b ** **c **
1 0 2 0.00375 50 200
2 0 1.75 0.0175 20 80
5 0 1 0.0625 15 50
8 0 3.25 0.0083 10 35
11 0 3 0.025 10 30
13 0 3 0.025 12 40

TABLE 5: INDUCTION TURBINE MODEL PARAMETRS

Stator resistance (*Rs*) 0.1015 pu
Rotor resistance(*Rr*) 0.0880 pu
Stator reactance(*Xs*) 3.5547 pu
Rotor reactance(*Xr*) 3.5859 pu
Magnetizing reactance(*Xm*) 3.5092 pu
Inertia constant (*H*) 4 s
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### Vol. 4 (2013) No. 1, pp. 907-913

### ISSN 2078-2365

913 Power System Transient Stability Analysis with High Wind Power Penetration

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