power system transient stability analysis with high wind ... · power system transient stability...

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 [email protected]

2 [email protected]



2

2

i

i s

i

mi ei Di

i

d

dt

d fP P P

Hdt

(1)

Where:

D

dP 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 - jQY =

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

dv = -R ×i -ω × λ + λ

dt

dv = -R ×i +ω × λ + λ

dt

(5)

dr r dr s qr dr

qr r qr s dr qr

dv = 0 = R ×i - g×ω × λ + λ

dt

dv = 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( , ) 0x u

(9)

h( , ) 0x u

(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 Vr’= e-

jwt Vr

R

v

Grid

Gear Box

β



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 generator

The fuel cost curve is modeled by quadratic function as:

2

i i i Gi i Gif 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 h are the equality and inequality

constraints to be satisfied while searching for the optimal

solution.

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]:

, 0i di giP V P P

(13)

, 0i di giQ V Q Q (14)

h is the system inequality operation constraints that include

[11]:

min max

gi gi giP P P (15)

min max

gi gi giQ 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

2

5

24 2

3

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 1

5

1

6

2

0

1

7

1

8

1

9

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 18 15 19 20 21

22 27 28

23 24 26

25



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 : OPF RESULTS 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 80

50

100

150

200

250

t, sec

Angle

roto

rique r

ela

tif,

degre

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

2

5

24 2

3

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 1

5

1

6

2

0

1

7

1

8

1

9

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 18 15 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



0 1 2 3 4 5 6 7 80

50

100

150

200

250

t, sec

Angle

roto

rique r

ela

tif,

degre

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



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 : OPF RESULTS 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 PG

MIN

(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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power system transient stability analysis with high wind ... · power system transient stability...

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