COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan, China
©2006 Tsinghua University Press & Springer
Adaptive Under-Frequency Load Shedding Scheme by Genetic Algorithm
Chinwang Lou *, Mingchui Dong, Chikong Wong
Faculty of Science and Technology, University of Macau, Macau, China
Email: [email protected]
Abstracts Under-Frequency Load Shedding (UFLS) is one technique used in the power industry for many years. The
UFLS function is to rescue the system under extreme disturbances and avoid the system collapse. Since its inception, a
large number of researches were carried out over the world. Different methodologies were presented [1-4].
Traditionally, a scheme is designed based on the projected scenarios (considering the summer and winter conditions) as
well as the worst generation deficiency that could occur in the system. Usually, when the old UFLS settings are no
longer appropriate to the new operating mode, they must be re-designed. I.e. based on the past experience in design and
operation, the new scheme and settings are assumed firstly. Then, off-line computer simulation is adopted to verify the
UFLS performance. Settings are adjusted according to the simulation result. Afterwards, the simulation and
performance are verified again under the adjusted settings. This procedure is repeated until the settings are sought such
that the UFLS demonstrates the best performance on the selected scenarios. Many efforts were devoted to simplify this
procedure. In this paper, a novel adaptive load shedding method based on Genetic Algorithm (GA) is proposed to
automate the findings of optimal settings such that the repetitive trial-error can be minimized greatly.
Keywords: Adaptive load shedding, Genetic Algorithm
INTRODUCTION
Macao is located on the southeastern coast of China with an overall area of 21 km2 and comprises of 1 peninsula and
2 islands in the Pearl River Delta. Therefore, electrically it is interconnected with south part of Guangdong Power
Grid (GPG) that is almost hundred times of Macao size. In 2004, the peak load of Macao is 422MVA. Under a
disastrous event in the GPG to provoke a frequency decline, it would decouple from GPG at 48.5Hz/0.3sec. From
the extensive studies and utilities experience, the frequency level is considered reasonable. In most of the time, its
import accounts for 20-30% of system demand. Loss of the import will definitely create a large power deficiency to
Macao system, which will cause UFLS to operate. It is obvious that a well-designed UFLS scheme is critical to
safeguard the system under the extreme situation, avoiding complete system blackout.
In tradition, UFLS settings are designed based on the selected system scenarios and the worst power deficiency.
When there are great changes in the system scenarios or network configuration, or when the new large generation
source is established, the old settings must be re-designed to cater for new requirements. Usually, the new settings
are designed with reference to the old scheme and empirical knowledge firstly. Then, off-line computer simulation is
adopted to verify the UFLS performance on selected scenarios. Settings are adjusted according to the obtained
simulation result. The new settings and performance are verified again. This procedure is repeated until the settings
are sought, with which the good performance is observed. In general, many repetitive settings adjustments and
computer simulations are required before the acceptable settings are finally sought. The method using trial-error is
quite time-consuming and tedious.
Furthermore, the scheme is verified on selected scenarios (e.g. assume the import utilization is lost by fault/
underfrequency) in design phase. But in real-time operation, it does not perform as well as design due to the
variations in the real world.
Our objective is to design a load shedding scheme such that under any system operation and major disturbance, it
could adapt itself in such a way to shed adequate amount of load automatically to avoid system blackout. This is the
key idea of our novel adaptive load shedding.
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In this paper, an adaptive load shedding is devised firstly. Then, an optimization method based on GA is proposed to
optimize the UFLS settings. The main feature of the proposed method is the powerful capability of handling multiobjective function without concerning the explicit mathematical model.
PROBLEM FORMULATION
1. Objectives
(1) Maximize the fmin to avoid generator trip due to low frequency.
(2) Minimize the final frequency overshooting and suspension.
(3) Minimize the amount of load shedding.
With above guidelines and objectives, we can formulate our multi-objective constrained optimization problem in a
simplified mathematical form:
2. Objective of Optimization
Min W1 ⋅
N
∑
i
N
N
i
i
i
i
f ∞i − f 0 + W2 ⋅ ∑ f 0 − f min
+ W3 ⋅ ∑ Pshed
where
(1) N: total number of system faults;
(2) f0: rated frequency, 50Hz;
(3) f∞i: new system steady-state frequency after disturbance in ith system fault;
(4) f imin: minimum system frequency observed after disturbance in ith system fault;
(5) W1, W2, W3: weighting factors, which are defined based on the empirical knowledge;
(6) Pished is the amount of load shed in ith system fault;
3. Subject to:
In the frequency load shedding scheme,
m
(1)
∑P = P
i
max ;
i
where
Pi: the amount of load shed at ith stage
Pmax: the maximum amount of system load that is defined to shed (such as 60% of system load)
m: total number of stages in designed frequency load shedding scheme
(2) (df/dt)1<(df/dt)2< … <(df/dt)n;
where
(df/dt)j: rate of frequency setting at jth stage and j = 1, 2, … , n
n: total number of stages for df/dt in designed frequency load shedding scheme
(3) f1>f2>f3> … >fm > 47.5Hz (generator is not allowed to operate less than the point);
where
fk: the frequency setting at kth stage and k = 1, 2, … , m
m: total number of stages in frequency load shedding scheme and m > n
Thus, it is a multi-objective optimization problem. Three objectives are competing. Therefore, we are going to seek
for an optimized solution that can coordinate and compromise all objectives.
ADOPTED LOAD MODELING AND SIMULATION SCENARIOS
Macao’s climate is moderate to hot, with an average annual temperature of over 20°C. The humidity is high with an
average range between 75%∼90%. In hot and humid weather, Macao citizens are used to work and live in a
comfortable air-conditioning environment. In winter, they are used to turn on heater for warming themselves.
Therefore, Macao load is a very complicated composite load. For the adaptability and suitability, we consider 30%,
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50% and 70% dynamic load modeling in the study. Taking into account 8 selected fault states, there are totally 24
system faults (8 faults × 3 dynamic load) for simulation.
To test the adaptability of the proposed scheme, we vary the generation dispatch and commitment to create five
scenarios and each scenario contain 24 system faults to simulate. Table 1 summarizes the five scenarios and the
corresponding minimum and maximum power deficiency:
Table1 Five scenarios to test the adaptability of the proposed load shedding scheme
Scenario
Min Power Deficiency
Max Power Deficiency
No. of Fault
1
*
5%
20%
24
2
10%
25%
24
3
15%
30%
24
4
20%
35%
24
5
25%
40%
24
Total
5%
40%
120
* generation loss / total system generation
From table 1, it is observed that there are 120 faults in total for simulation to test the adaptability of proposed UFLS
scheme. Among them, the minimum power deficiency is 5% of system generation and the maximum is 40% of
system generation.
GENETIC ALGORITHM
GA is based on the principle of the survival of the fittest strategy. It searches the solution space of a function through
the use of simulated evolution. In general, the fittest individuals of any population tend to reproduce and survive to
the next generation, thus improving successive generations. The main advantage is:
(1) It can solve linear and nonlinear problems by exploring all regions of the state space.
(2) It can solve the optimization problem without concerning explicit mathematical model. It is very favorable to our
existing problem.
(3) Since it searches the whole solution space in parallel, it has capability to find the global minima/maxima,
avoiding being tracked at local point.
Concerning the main advantages of GA, this algorithm is applied for searching the best UFLS settings as following:
Figure 1: The GA flowchart of searching the best settings of UFLS
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Remark: The stop rules are satisfied if maximum generation is exceeded or the fitness function is not changed in
pre-defined consecutive generations.
1. Coding and decoding In GA, the sequence of binary bits is called an individual, which corresponds to a set of
genes, i.e. a chromosome, in natural genetics. The coding function is used to translate the search space of actual
decision variables (11 variables in our problem) into the space of binary strings. Using16-bit strings or individuals in
our explored problem, the GA proceeds with its operational flowchart as shown in Fig. 1.
2. Fitness Function In GA, each individual is evaluated by its fitness function in each generation. The best
individuals will be remained acting as parents to produce the next generation and the bad ones will be cancelled. In
the explored problem, the fitness function is involving the calculation of dynamic frequency behavior with multimachine model.
But in this paper, we propose a single-machine model due to the following considerations:
(1) The main disadvantage of GA is its extensive computing time for finding out a global optimal point. If the multimachine model is involved, the computing time will be much burdened. For instance, one simulation cycle-time of
transient stability estimated with MTSP [5] (Mid-Term Stability Program) requires 4 seconds. In GA, each
individual needs to evaluate 120 transient stability simulations (5 scenarios × 8 fault scenarios × 3 dynamic load in
our problem). If we use 80 individuals and 80 generations, the total simulation time will be 4 × 5 × 24 × 80 × 80 =
3072000 seconds ≈853 hours.
(2) The single-machine model is appropriate with the acceptable computing accuracy for small-scale power system
like the one in Macao.
(3) The proposed method should reduce the programming work greatly.
Thus, the dynamic frequency behavior with single-machine model can be expressed by the mathematical formula
below:
t
−
P (1 + ΔPFH * ) − ( PF 0* − ΔPF * )
T
f * = f 0* − FH 0*
(1 − e f )
K pf (1 + ΔPFH * )
where:
f0*: system frequency (in p.u.) before disturbance
PFH0*: total system load (in p.u.) at f0 (50Hz)
PF0*: total system generation (in p.u.) at f0
ΔPFH*: change of system load (in p.u.) due to load shedding.
ΔPF*: change of system generation (in p.u.) due to loss of generation.
Kpf: frequency regulation factor of system load
Tf: time constant of system frequency change
DESIGN SCHEME
For solving the UFLS settings adjustment problem, we define the guidelines for devising the adaptive load shedding
scheme as following.
Guidelines:
(1) Define the maximum generation loss (importation + largest local generator) handled by the scheme. In the study,
we define as 40% of system generation.
(2) The 1st step commences at 48.5Hz, which is same as the network decoupling setting.
(3) The maximum amount of load shedding in the system is 60%, the other is important load (customers).
(4) Shed large amount of load, which is proportional to the df/dt observation in the first few steps to arrest frequency
decline promptly.
(5) The time delays of first few steps should be short enough so that to arrest frequency promptly. Considering the
required time delay for two consecutive stages, we use 0.1sec. Otherwise, it will cause the mis-coordination between
two stages. That is to say, the previous stage does not operate completely, but the next stage commences to operate
to shed load.
(6) The total number of steps should be minimized so that to reduce the extra investment.
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As shown in table 2, there are 15 variables in the formulated optimization problem. One of the main disadvantages
for GA is the extensive computing time. For improving this, we may reduce the dimension of solution space
searched by GA and consider the following empirical knowledge:
Table 2 Frame of adaptive load shedding scheme
Stage
f
P
t
df/dt
1
f1
P1
T1
D1
2
f1
P2
T1
D2
3
f1
P3
T1
D3
4
f1
P4
T1
5
f2
P5
T3
6
f3
P6
T4
Tot
-
60%
(1) Network is decoupled at 48.5Hz and generator is not allowed to operate in less than 47.5Hz [6].
(2) Within the restricted frequency, UFLS should operate immediately after network decoupling, in order to arrest
frequency decline promptly. So, f1 = 48.5Hz.
(3) According to the operation experience, 0.3Hz is short enough and sufficient for two consecutive steps. Thus, can
define f1 = 48.5Hz, f2 = 48.2Hz and f3 = 47.9Hz.
(4) According to our empirical knowledge, T1 should be short enough to arrest frequency decline promptly. So T1 =
0.1sec is considered appropriate.
With the above consideration, the 15 variables can be reduced to 11 variables as shown below (Table 2a).
Table 2a reduced variables in the frame
Stage
f
P
t
df/dt
1
48.5
P1
0.1
D1
2
48.5
P2
0.1
D2
3
48.5
P3
0.1
D3
4
48.5
P4
0.1
5
48.2
P5
T3
6
47.9
P6
T4
Tot
-
60%
SIMULATION RESULT
The proposed novel adaptive load shedding method is implemented in Matlab environment using Pentium P4 2.0G.
Different crossover and mutation rate are defined and tested. Table 3 depicts the results optimized by GA with
crossover = 0.8 and mutation = 0.01. Only around one hour is required to complete computing the 80 generations
with 80 individuals per generation, and the global optimal solution was found by GA without involving any human
interference and trial-and-error.
With these optimized settings, we use MTSP to verify the UFLS performance. Fig. 2 demonstrates the comparison
of average frequency performance, minimum frequency and the average load shed amount in two load shedding
schemes, one by conventional methodology and another optimized by GA. Here note that:
(1) The Average Frequency Performance (AFP) is defined as
N
f steady − f rated
i
f rated
AFP = ∑
× 100%
Where frated = 50Hz, fsteady = new steady state frequency after disturbance and N = 120 system faults.
(2) The minimum frequency is the lowest observed frequency over 120 system faults.
(3) The Average Load Shed amount (ALS) is the average operated load shed over 120 studied scenarios.
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N
ALS =
∑P
i
shed
i
N
× 100%
Where P ished = the amount of load shed in each system fault.
Table 3 The UFLS settings optimized by GA
Stage
f
P
t
D
1
48.5
6.98%
0.1
1.1964
2
48.5
9.19%
0.1
2.7899
3
48.5
11.92%
0.1
2.8167
4
48.5
8.26%
0.1
5
48.2
5.13%
0.8
6
47.9
8.38%
2.0
Tot
60%
Figure 2: The performance comparison in two load-shedding schemes
Remark: Old = Settings designed by conventional methodology, g60-4 = Settings optimized by GA.
Fig. 3 demonstrates the estimated computing time required for multi-machine model as compared with the singlemachine model employed in the study.
Hou r (h r
Comparison of computing time
853
900
800
700
600
500
400
300
200
100
0
1.5
mulit - machine
model
single- machine
model
Figure 3: Comparison of computing time when multi and single machine model are employed
Remark: The computing time for single-machine model includes one-hour for GA optimization and half-hour for
performance verification of sought solution in MTSP.
From above simulation results, it is obvious that:
(1) The new scheme based on GA has superior performance, compared with old scheme.
(2) The old scheme demonstrates good performance in large power deficiency but the performances are becoming
worse while the severity of power deficiencies is reducing. . As observed in scenario 1, its average frequency
performance is 4.23%. Frequency overshooting and suspension is very obvious.
(3) The new scheme reveals smooth average frequency performance over all scenarios. Frequency overshooting and
suspension is improved. The average value over 120 system faults is 1.5%. So the adaptability of new scheme under
power deficiency is better than old scheme.
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(4) The resulted minimum frequencies over all deficiencies are higher than those shown in old scheme.
(5) In old scheme, the minimum frequency in maximum power deficiency declines to 46.73 Hz that jeopardizes
seriously to the generators operation and even life cycle. In the new scheme, it is improved close to 47.5 Hz.
Although it is lower than 47.5 Hz, the sustained time is less than one second.
(6) Less amount of load is shed in new scheme. Thus, the affected customers for power interruption are reduced.
(7) The goals of our multi-objective optimization, i.e. maximize fmin, minimize the amount of load shed and
minimize the final frequency overshooting and suspension, are compromised and met.
(8) As observed from Fig. 4, frequency responses obtained from single-machine model is closed to multi-machine
model. The resulted frequency rate during frequency decline, the minimum frequency and new steady-state
frequency are similar to those from multi-machine model. Thus, adopting single-machine model is adequate in the
study.
(9) After single-machine model is adopted, the optimization time is reduced greatly as compared to multi-machine
model, i.e. from 853 hours down to 1.0 hour.
(10) Unlike the old methodology which highly depend on the trail-and-error in determining the UFLS settings, the
new methodology based on genetic algorithm proposes a systematic and normalized way in the finding the settings.
Multi-machine v.s. single-machine
model
51.0
Hz
50.0
49.0
48.0
47.0
0
10
20
30
40
50
60
70
80
Time (sec)
Multi-machine
Single-machine
Figure 4: Frequency responses from multi-machine and single-machine model
CONCLUSION
Load shedding is a last resort to avoid the complete system blackout. With one small system importing significant
power from a large power grid, an effective load shedding scheme plays the vital role to rescue the system under
extreme contingency (loss of interconnection). A novel adaptive load shedding method based on GA is proposed in
this paper to automate the searching of the best UFLS settings. From the obtained simulation results, it shows that
this novel method has superior performance than the old scheme. In addition, the time of repetitive simulation is
greatly minimized.
REFERENCES
1. Anderson PM, Mirheydar M. An adaptive method for setting underfrequency load shedding relays. IEEE
Transactions on Power Systems, 1992; 7(2).
2. Prasetijo D, Lachs WR, Sutanto D. A new load shedding scheme for limiting underfrequency. IEEE
Transactions on Power Systems, 1994; 9(3): 1371-1377.
3. Halevi Yoram, Kottick Daniel. Optimization of load shedding system. IEEE Transaction on Energy
Conversion, 1993; 8(2).
4. Al-Hasawi WM, El Naggar Khaled M. Optimum steady-state load-shedding scheme using genetic based
algorithm. IEEE Melecon 2002, May 7-9, 2002, Cairo, Egypt.
5. User Guide of MTSP (Mid-Term Stability Program). Tsinghua University, Beijing, China.
6. IEEE Guide for Abnormal Frequency Protection for Power Generating Plants. ANSI/IEEE C37.106-1987.
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