Power System Dynamic Load Identification and Stability

7/26/2019 Power System Dynamic Load Identification and Stability

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Power System Dynamic Load Identification and Stability

S.

Z.

Zhu* Z. Y. Dong** K. P.

Won


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loads. Given wl , w2 nd w3 as the weighting factor of

each compone nt, the compos ite load is represented as

L

= wlLs

+ w2LG+ w3LIM, ith C

w

= 1

(2.1)

The values of wl ,

w

and w vary for different load buses

depending on their load compositions. For a load with

high concentration of industrial components, for example,

a larger value of w may be assigned.

Here we describe the loads and their aggregated

characteristics that significantly present voltage

sensibility. Details of the load m odeling are as follows,

(1) The static load is modeled as an exponential function

of voltage V

Pd = POCf Qd = QO ( f

(2.2)

where Po, Qo are static load consumptions at the rated

voltage

Vo.

The indices

a

and p are the parameters

chosen to best represent the voltage dependence of the

aggregate load, and normally have a range of a = 0.5 -

1.8,

p

=1.5 - 6 according to Kundur [8]. Xu et al.

Proposed

a =

0.31 - 1.50, p = 2.22 - 4.18 based on the

field test in [8]. The general trend is that, high

concentration of residential load exhibits larger

a

and

smaller

p;

while high concentration of commercial /

industrial loads exhibits smalle r and larger

p

[8] and [9].

For

example, their values can be chosen as a = 0.8 - 1.5,

p = 2.0

- 4.0 for

each bus depending on the load

composition. However these static load models neglect

the critical important dynamic behavior exhibited by

many loads.

(2) A number of generic dynamic load models have been

proposed recently in the literature for voltage stability

studies, see

-

[SI, [6], [lo] and [SI.

A

first-order dynamic

recovery model proposed by Hill and Karlsson in [SI and

[6]

will be used to illustrate the impact of load modeling

on

system stability. This model captures the load

restoration characteristics with an exponential recovery

process. Figure 2. shows the typical power response of

aggregate loads to a voltage step and its exponential

approximation. Some examples of this response are

provided in [Il l .

Mathematically, this model can be

expressed in state space form as,

x p = P , ( V ) - P ,

(2.3)

xq = Qs (U

Qd (2.4)

Pd = * x p

+ p , ( V ) (2.5)

Qd = t x q +Q,W (2.6)

where

Pd

and

Qd

are the load real and reactive powers,

xp and xy are the corresponding load states,

Tp

and

Tq

are

the load recovery time constants.

Qs,

,

nd

Qt,

Pl

are the

steady state and transient load characteristics respectively.

Normally they are expressed as a function of node

voltage V ither exponential as

(2.7)

=

QO

kp Q =

QO gp

or a polynomial function, such as a quadratic function;

Recovery time constants

Tp

and T, range from 60s

to

150s. The values for a; and p, will take the same values

as a nd p i n the static component, while

a

2.0 h;. .5

[61.

1.1,

Figure 2. Typical power response of aggrega te loads to

a voltage step

(3) A steady-state equivalent circuit of Induction Motor

as Figure 3 shows can be used [8]. When we neglect the

stator transients, the aggregate IM is represented by its

first order model,

(2.9)

Where s s the motor slip; H s moment of inertia; T, and

T,,, are the electromagnetic and mechanical torques

respectively;

T,a

P&,

V) in per unit if neglecting effects

of R, and T isassumed to be constant. Parameters for IM

can be taken from [8].

s = & T

s)

- T

(3,

U1

T f S

Figure

3.

IM steady-state equivalent circuit

These models will be used in load modeling and study of

modeling impact on system stability in the following

sections.

111. GA/EP

LOAD

DENTIFICATION

In this section, we propose the algorithm for load

identification. System identification and EP fitness

function for the specific purpose of load modeling

identification.

[

121

Genetic Algorithms (GAS) are heuristic algorithms,

which can locate the global optimal solution. The G A

optimization mechanism is developed from the concept of

natural evolution, where the strongest individuals survive

and the weaker ones die off during the evolution process.

Part of the work is to develop an effective modification of

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a genetic algorithm to optimally determine the load

model parameters w ith system identification algorithms.

For better GA performance, adaptively adjusted mutation

probability can be used [13], [14], [15], [16], and [17]. In

this paper

two

parallel processes are used for mutation

probability control, as follows,

P,(i,y) = P, *exp(-+i/nl)*exp(-y/n2)

(4. I )

where P, is the mutation probability, which takes the

initial value of P, , i is the fitness of the i-th individual,

y is the generation numbe r, nl an d n2 are ad justing factors

controlling the decre asing rate of P, taking into

consideration of fitness and generation number

respectively.

In our algorithm, the production mutation occurs when a

Gauss-distribution random vector is added into the parent

generation. The basic algorithm adopted in this paper is

as follows,

1. Problem Formulation: The solution

X

of the

optimization problem is represented by a d-

dimensional vectorX = [x x2 .

,

d 1 and uJ

< xJ

V j

= 1,2,-.-,

(4.3)

Where N ( O , P , + z , ) is the mutation

operation vector, and the PJ + Z J s the

determination variable based on the value of

mutation probability Z

5.

Tournament: The competence of tournament is

calculated by each individual's tournament penalty

weighting factor, weighf( i ) .This factor is calculated

by comparing with other randomly selected

individuals.

emax

e

emax

m

weight(i)

=

c w ,

/ = I

(4.4)

WJ;l ..l.Jc

0

Where ,U',, is a random vector between (0, l) , e is

the advantage.

6. Selection: According to the value of weight, all

individual (2n) are arranged

in

sequence. The first n

individuals selected as the next g eneration.

Return to 4 until the convergence condition is

satisfied.

7.

I v .

POWER SYSTEM MO EL ANALYSIS

In this section, we test out algorithm with som e real field

test data to identify load models for further stability

analysis. The data is from the field measurement from

Tong Liao Power Plant and the'neighboring area of the

North East China grid. The one line diagram of the test

system is given in Figure 4. Tong Liao Power Plant

locates in the eastern part of Inner Mongolia. The

electricity is transmitted to North East China Grid via

three 220KV transmission lines over a distance of more

than 200

km

7s

jdw

rhu ngli o

tongliao

tcngbian

176, 177

Figure 4. Power System Around Tong Liao Power Plant

1V.I. Load Model Identification

We take the population size n = 50, the number of each

individual competing with others

m

= 30. The Elite

percentage, which decides the percentage of reserved

individuals in each generation be lo , so Elite =

n*10

=

5 ;

mutation probability

z

=

0.001

and scale factor B

=

, where

step-num

is the total number of

iterations. The limits of variables to be identified are

given in Table

1.

e-O.OS*step-num

Table

1.

Variables range

of

solution vector

Lowerlimit

0

I -1

I

-3

0 -1

I -30

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These limits are used only during the initial population is

being produced. Now we give so me detailed case studies

from field test and com puter identification simulation.

Error

2.42 16307e -002

2.42 1666

1

-002

Example 1. Static load model

The active power P and reactive power Q are identified

respectively. The identification process terminates after

100

generations. The results a re shown in Table 2.

X1 x2

0.68979 14.05219

0.68653 1427952

Table 2. The identification resu lts of static load model

Active Dower

A

parameter

=

0.001 and

f l

=

e-0~08 step-num

In our

algorithm, we consider

two

aspects of modeling: (1)

order of model, A4 is often set to be 1 or 2, and (2)

linearity of the model, is Boolean variable, and

= 0

stands for linear model, = 1 for nonlinear model.

We used dynamic load model to fit the test data with

iteration number of 3000. Both first-order linear model

and se cond-order nonlinear model are identified. Figure 6

shows the simulated results of active and reactive powers.

Identification error and modeling param eters are given in

Table3 .

~~

2.42 16854e-002 0.68764 1425461

2.42 16894e-002

0.68925 1437090

2.42 17 187e-002 0.69oOo

1430551

Reactive Dower

x3

-13.95077

-14.16945

Therefore, the identification gives the static load m odel

as:

x4 X5

-7.87665 9.16634

-822913 9.47256

P

=

0.454084V1.405687

Q = 0.179435V3.206189

-14.14562

-1426829

-1420455

In our identification process, PO,

l

Qo bl are very closed

after only one identification, and all solution individuals

converged close to their final solution point very quickly.

Since the frequency f hanged very small in field tests,

the impa ct of frequency variation is ignored and the static

load model is used. The identified and measured real data

of the reactive and reactive powers are shown as Figure 5 .

~~~~

-8.05477

921439

-820608 930574

-829263 9.42222

0.48

0.46

0 45

Error

6.85621-

6.8737617MKl3

0.W 1.00 1.01 1.02 1

I3

X I x2

0.95424 535434

0.95633 5.40915

Figure

5.

The curves

of

static loads between identified

and real measured data

6.8765852dH3

6.877633W3

6 . m 3

Example 2. Dyna mic load model

Let the population size

n

= 200, the number

of

each

individual competing with others

m

=

80.

One generation

is left by IO , i.e.,

Elite = n*10 =

20, mutation

0.95445

5.46509

0.95560 539985

0.95516

m

Table 3. The identification resu lts

of

the dynamic load

~

Y

x3

-522094

-52848

-533203

-52'7143

-539731

X$

4

4 m 82027

-5.73658 7.88834

-5.75931 7.79500

-5.97893

8.031%

-5.98805

8.08046

i n

n

qn

r n

cn cm

i n n

r?n

Figure 6. The comparison curve s of reactive power:

identified and real measured

Based from the results obtained, we can conc lude-that,

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1.The results are satisfactory for the requirement of

system security analysis from field test. We also

performed Least Square identification, and it can be

seen that our G A E P based algorithm gives better

performance over the LS approach. The algorithm is

robust with different orders of linear model.

2. The initial generation of solutions can be produced by

random m odels or combining some consideration of

the actua l plant to be identified.

onstant Eq' Mod el and Constant resistance

.

Classic Eq Mod el and Constant resistance

Online Eq Model and Exponential unction

IV.11. Load Modeling and System Stability

described before. As we can see, the simulation results

fits very closely to the real field tests. This demonstrated

Based on the load identification results, simulation

of

the

power grid is carried out. The results are given in Figures

7 - 10. In the simulation, it is assumed that all

4

generators in Tong Liao Power Plant have the same

-Constan t Eq' Model and Constant resistance

.

Classic Eq Model and Constant resistance

Online Eq Model and Exponential function

2.44

,

, ,

,

, t ~ s )

0.4

0.2

0

2

4 6 8 10

Figure

7.

P at 1 Diantong transmission line after a phase

dinrnnnertinn

generation level, the network operation condition is

during later peak hours, and system loads are taken the

classical loading levels under normal operation

conditions. The system faults include: (i) disconnection

of the three phase m ain transmission line, (ii)

disconnection of the three phas e main transmission line at

-Constant Eq' Model and Constant resistance

. Classic Eq Model and Constant resistance

1 4

..

10

0 t(s)

2 4 6 8 10

Figure

9.

Power plant angle stability after Dianju

trrnsmiwinn line nn

lnnd

disrnnnertinn.

-Constant Eq' Model and Constant resistance

. Classic Eq Model and Constant resistance

Online Eq Model and Exponential unction

I I

1P

Ac

iv 3.5 1

tfs)

.51

4 .

. . . . . . . . . . .

,

0

2

i

6

10

Figure 10. #2 Generator active power behavior after Dianju line

nn-lnad 3 nhrne dismnnertinn.

In Figures

7

-

10

the solid lines in each figure stand for

constant Eq' model, dashed lines stand for Eq classical

model, and the short dashed lines stand for performances

follow ing field test for the Eq model. The load models

These stability simulations under various system

operation and loading conditions are very useful for

future

operation planning of Tong Liao Power Plant.

Algorithms used here can certainly be applied to other

systems to investigate the system load modeling and

stability conditions in a very practical and less risky way.

0 5

t(s) V. CONCLUSIONS

2

4 6 8 10

Genetic Algorithms and Evolutionary Programming

based identification is used in the paper to identify the

power system load parameters based on data from field

the terminal out of the power plant, (iii) main measurement. Several load models are used to simulate

transmission line two phase short circuit at Ju Feng the identification process. Improvements over the basic

terminal side.

genetic algorithms a re proposed including considerations

Figure

8.

Active power tra nsients of Dianling line after

3

phase

dinrnnnrrtinn nf nian tnne line.

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on m utation probability control, fitness formulation and a

progressive concept for search and optimization. Both

theoretical analytical simulation and field tests are carried

to validate the effective of the algorithm for load models

and their impact on system stability. It can be seen from

these simulations and tests the algorithms proposed in the

paper gives satisfactory results of identification for

further stability analysis. Further researches are being

carried out to develop a more comprehensive general load

model suitable for measurement based model

identification and system stability analysis.

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Power System Dynamic Load Identification and Stability