power system dynamic load identification and stability
TRANSCRIPT
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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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