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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 energy due 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 amrounemohammed@yahoo.fr

2 tbouktir@gmail.com

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

Hdt

(1)

Where:

D

d P D

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 busI 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 follo

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