Swarm Evolutionary Programming for Under-Frequency · PDF fileDepartment of Electrical and...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 18 (2016) pp. 9464-9477

© Research India Publications. http://www.ripublication.com

9464

Swarm Evolutionary Programming for Under-Frequency Load Shedding

M. Lu, W. A. W. Zainal Abidin,

PG Scholar, Associate Professor, Department of Electrical and Electronic Engineering, Department of Electrical and Electronic Engineering

Universiti Malaysia Sarawak, Universiti Malaysia Sarawak, Kuching, Malaysia. Kuching, Malaysia

T. Masri, D. H. A. Lee, S. Chen,

Senior Lecturer, Sarawak Energy Berhad, Department of Electrical and Electronic Engineering, Kuching, Malaysia. Universiti Malaysia Sarawak, Kuching, Malaysia.

Abstract

In this paper, Swarm Evolutionary Programming (SEP) method

incorporating modified System Frequency Response (SFR) model

is proposed to solve the optimal Under-frequency Load Shedding

(UFLS) scheme design problem. The objective function of this

problem is to minimize transient frequency and steady-state

frequency deviation from nominal and total quantum of load

shedding. The constrained optimization problem is transformed

into a non-constrained optimization problem by implementing the

penalty method and the proposed algorithm is tested on a nine-bus

test system. Simulation results demonstrate that SEP is a

promising solution for finding optimal settings for the UFLS

scheme.

Keywords: Swarm Evolutionary Programming (SEP), System

Frequency Response (SFR), Under-frequency Load Shedding

(UFLS), penalty method, adaptation.

INTRODUCTION

Under-frequency Load Shedding (UFLS) is a widely-used

mitigation method for arresting a power system from load-

generation imbalance in the shortest possible time. Optimal load

shedding during contingency situations is one of the most

important issues in planning, security and operation of power

systems. Due to continual changes in demand and operating

conditions, it is important that the UFLS scheme is revised

consistently with the ongoing changes in the system. The

conventional way of scheme revision using trial-and-error method

is tedious and time consuming. This problem has stirred the

interest of various researchers in this area and numerous walk-

around methods have been proposed in literature to address the

problem.

The classical System Frequency Response (SFR) model has been

used in the design of UFLS schemes to estimate frequency

behavior of power systems in the event of sudden system

disturbances. An analytic SFR model incorporating UFLS for a

multi-machine power system was introduced by Lee in 2006 [1]

and closed-form expressions of load-frequency response,

including the effect of UFLS following system contingency were

derived to compute system and UFLS parameters such as

minimum transient frequency, steady-state frequency, number of

stages and instants of activation of UFLS scheme. The use of

SFR-UFLS model has eliminated the need for computation-

intensive time-domain simulation approach. However, the

impact of load voltage was not taken into consideration in the

SFR-UFLS model and this will bring remarkable errors when

analyzing frequency dynamics in a power system with large

capacity of active power shortage as system frequency and

voltage dynamics interact with each other in the power

system following system contingencies.

Classical optimization methods have been used extensively in

literature to find optimum solutions for continuous and

differentiable functions [2]-[6]. The UFLS optimization

problem has been investigated using classical optimization

methodologies, incorporating various constraints and

objective functions. The objective was to minimize the

transient and steady-state frequency deviation from nominal

and to reduce the total quantum of load shedding to the

minimal. However, these methods are not able to handle

highly non-linear, non-continuous and non-differentiable

fitness functions which are usually the case for most power

systems-related problems such as the UFLS scheme

optimization problem.

Population-based optimization techniques such as

evolutionary and swarm methods are gaining popularity due

to its capability to alleviate limitations of classical methods in

terms of achieving global optimization, convergence speed

and robustness [7]. These population-based stochastic

approaches uses payoff information for search direction

instead of derivatives or other auxiliary knowledge, and can

therefore deal with non-smooth, non-continuous and non-

differentiable functions that are the real-life optimization

problems [8]. This has omitted the need for approximate

assumptions for a lot of practical optimization problems,

which are quite often required in traditional optimization

methods.

In addition, population-based methods are more flexible and

robust as compared to conventional methods as they use

probabilistic transition rules to select generations instead of

deterministic rules, so they can search a complicated and

uncertain area to find the global optimum. They search from

a population of points and the population is able to move

over hills and across valleys to find a globally optimal point.

mailto:[email protected]



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These methods have inherent parallel computation ability because

the computation for each individual in the population is

independent of others. These features make these methods robust

and parallel algorithms to adaptively search for the global optimal

point and offer a new tool for optimization of complex power

system problems.

Evolutionary and swarm methods are two main population-based

techniques which have been used extensively in literature since

the 1990s in various applications especially in the power system

field such as reactive power planning [9], optimal power flow

[10], maintenance scheduling [11] and dynamic economic

dispatch [12]. Evolutionary methods such as Genetic Algorithm

(GA) and Evolutionary Programming (EP) have been used most

extensively to solve both frequency- and voltage-related load

shedding optimization problems.

GA is a random optimization search method based on simulation

of biology evolutionary process. GA algorithm consists of

initialization, crossover, mutation, selection and termination. GA

is able to handle a multi-objective function without an explicit

mathematical model [13]. However, there are drawbacks to this

method eg global optimization can only be achieve after a pro-

longed period of algorithm execution time thereby limiting its

applications in complicated and highly constrained power system

problems.

EP is another optimization method within the family of

evolutionary methods. EP was introduced by L.J. Fogel in the

1960s based on finite state machine model and developed by D.B.

Fogel in four decades later. In literature, EP was used mostly in

the design of Under-voltage Load Shedding (UVLS) schemes. EP

was perceived to be better in achieving global optimum as

compared with other evolutionary methods as EP relied on

mutation rather than crossover [14]. EP is also more stable than

other methods because it relies solely on mutation in the search

process [15]. In addition, EP is able to produce optimal solutions

with the least number of generations due to flexibility in objective

functions and ease in coding. EP also has a clear search direction

relying on probability as it’s tool for running searches and has

high computation speed due to its capability in connotative

parallelity.

Nevertheless, conventional EP has some shortcomings in terms of

premature convergence resulting from mutation operator

destroying valid search pattern and search efficiency in the

aftertime of evolutionary following slowing down of competition

between search individuals. Jie and Hui in [15] has proposed to

replace the default Gauss mutation operator in conventional EP

with ladder attenuated mutation operator to improve search

efficiency and search ability in global optimization, convergence

speed and robustness. An incorporation of the concept of quantum

mechanics in EP called Quantum-Inspired Evolutionary

Programming (QIEP) was introduced in [16] to find optimal

location, quantum of load shed and sizing of DG for UVLS

schemes in radial distribution system whereby concept of

quantum mechanics such as interference and superposition were

combined with conventional EP. This method has given better

results in terms of fitness function and computation time as

compared to GA and conventional EP.

This paper proposes the incorporation of swarm-based features in

EP to address the limitations of the optimization algorithm.

Swarm methods such as the Particle Swarm Optimization (PSO),

are relatively new collaborative computation techniques and has

shorter history of application as compared to evolutionary

methods. PSO was developed by James Kennedy and Russell

Eberhart in 1995 after being inspired by the study of bird

flocking behaviour by biologist Frank Heppner. PSO is a

multi-agent parallel search technique which maintains a

swarm of particles and each particle represents a potential

solution in the swarm. All particles fly through a

multidimensional search space where each particle is

adjusting its position according to its own experience and that

of neighbors [17].

PSO has been used to solve various complicated optimization

problems which are nonlinear, non-differentiable and

multimodal due to its simplicity and fast convergence speed

[18]. PSO is not highly impacted by the size and nonlinearity

of the problem and can converge to the optimal solution in

many problems [19]. However, unlike evolutionary methods

whereby crossover allows leaps from one region to another,

PSO has "memory" of past successes and has the tendency to

converge upon regions of the search space from previous

searches with no mechanism for catastrophic leaps from one

region to another. In literature, PSO was used to solve

various power system problems such as optimization of

Under-voltage Load Shedding (UVLS) scheme, design of

optimum islanding scheme and congestion management

strategies.

The contribution of this paper is three-fold. Firstly, analysis

is done on the impact of load voltage on system frequency

response during contingency situations. Different types of

system loads such as exponential voltage load, ZIP load,

exponential voltage frequency dependent load, mixed load

and constant power load are used for this purpose. A

modified System Frequency Response (SFR) model taking

into consideration the impact of load voltage on system

frequency is used to compute system and UFLS parameters.

Secondly, a modified EP method incorporating swarm

features is proposed to solve the optimization problem. In the

advanced approach, UFLS scheme must take into account

different influencing factors such as frequency variation,

magnitude of disturbance, voltage profile of the system and

so on leading to identify number of steps, the amount of load

shed in each step and delay in each step. Thirdly, an

adaptation framework consisting of several methods is

proposed to further improve the optimization results. The

validation methods and their results are presented. Based on

the results, the conclusions and future work are drawn.

IMPACT OF LOAD VOLTAGE ON SYSTEM FREQUENCY

The frequency and voltage dynamics interact with each other

in the power system following system contingencies. The

SFR model without considering the impact of system voltage

would bring remarkable errors when analyzing frequency

dynamics in a power system with large capacity of active

power shortage.

There are obvious differences for frequency and voltage at

different buses due to space-time distribution characteristics.

Studies on the effect of voltage on frequency dynamics are

still lacking. Load characteristics or load-voltage effects

poses negative impacts to the effectiveness of load shedding.



9466

The frequency-voltage coupling effect enhances with the increase

of values of two factors namely initial reactive power deficit and

ratio of induction motors in loads [20]. When the values exceed a

certain threshold, the imbalance active-power would change sign.

Although severe low-frequency will be predicted, the system

actually occur high frequency due to strong frequency-voltage

coupling effects. Traditional last line defense in power grids

would fail to prevent system collapse when the coupling effect is

significant.

The frequency response of a power system is determined by the

active power balance of the generators and loads within the

system. System frequency response is affected by load voltage

through changing of absorbed active power.

Yang, Cai, Jiang and Liu defined total active power deficit as the

equivalent of the summation of active power deficit from

frequency response of generators and active power loads

changing due to voltage deviations [21]:

∆𝑃 = ∆𝑃𝑔 + 𝑃𝐿 (1)

Yang, Cai, Jiang and Liu defined total active power deficit as the

equivalent of the summation of active power deficit from

frequency response of generators and active power loads

changing due to voltage deviations. Disturbance power was

computed from initial rate of frequency change measured by

PMU and the swing equation of the ith generator was used to

compute the total active power deficit from frequency response of

generator whereby frequency response of from all generators was

summed up as:

∆𝑃𝑔 = 𝑃𝑚 − 𝑃𝑒 = ∑2𝐻𝑖

𝑓𝑛

𝑑𝑓𝑖

𝑑𝑡

𝑁𝑔

𝑖=1=

2𝐻𝑐

𝑓𝑐

𝑑𝑓𝑐𝑜𝑖

𝑑𝑡 (2)

There are three main types of loads usually used in

power system dynamic analysis namely static loads, dynamic

loads and composite loads. Analysis on the impact of load

characteristics on computation of load-generation imbalance

following disturbance is available in literature.

Characteristics of static load models can be expressed

using voltage and frequency dependent algebraic models [22].

The exponential and polynomial representation of static loads has

been widely used in literature:

𝑃𝐿 = ∑ 𝑃𝐿,𝑗𝑀𝑗=1 (3)

𝑄𝐿 = ∑ 𝑄𝐿,𝑗𝑀𝑗=1 (4)

where 𝑃𝐿 and 𝑄𝐿 are the current total active and reactive power

load of all the load buses, 𝑃𝐿,𝑗 and 𝑄𝐿,𝑗 are the current active and

reactive power load of the jth load bus.

In this paper, the polynomial model or commonly known

as the "ZIP model" consists of constant impedance (Z), constant

current (I) and constant power (P) properties is assumed. This

model is represented as:

𝑃𝐿,𝑗 = 𝑃𝐿0,𝑗 × [𝑝1 (𝑉𝑗

𝑉0,𝑗)

2

+ 𝑝2 (𝑉𝑗

𝑉0,𝑗) + 𝑝3] (1 + 𝐾𝑝𝑓∆𝑓) (5)

𝑄𝐿,𝑗 = 𝑄𝐿0,𝑗 × [𝑞1 (𝑉𝑗

𝑉0,𝑗)

2

+ 𝑞2 (𝑉𝑗

𝑉0,𝑗) + 𝑞3] (1 + 𝐾𝑞𝑓∆𝑓) (6)

where 𝑝1, 𝑝2 and 𝑝3 are the load parameters for constant

impedance, constant current and constant power. The

summation of 𝑝1, 𝑝2 and 𝑝3 is equivalent to 1. Linearizing

Equation (5), imbalance active power supplied by load at bus

j is determined as:

𝑃𝐿,𝑗 = 𝑃𝐿0,𝑗 × [(2𝑝1 + 𝑝2) (𝑉𝑗

𝑉0,𝑗)] (1 + 𝐾𝑝𝑓∆𝑓) (7)

whereby ∆𝑉𝑗 = 𝑉𝑗 − 𝑉0,𝑗. Therefore, the total active power

imbalance for a polynomial model is:

∆P = ∑2Hi

fn

dfi

dt+

Ng

i=1

∑ PL0,j× [(2p1+p

2) (

Vj

V0,j

)]

NL

i=1

(1+Kpf∆f)

= 2Hc

fc

dfcoi

dt+ ∑ PL0,j× [(2p

1+p

2) (

Vj

V0,j)]

NL

i=1 (1+Kpf∆f)

= ∆𝑃0+ ∑ PL0,j× [(2p1+p

2) (

Vj

V0,j)]

NL

i=1 (1+Kpf∆f) (8)

Assuming ∆f to be negligible,

∆P = ∆𝑃0+ ∑ PL0,j× [(2p1+p

2) (

Vj

V0,j)]

NL

i=1 (9)

According to [1], free load-frequency dynamic

response following contingency is defined as:

∆ω(s) =−∆𝑃(𝑠)∏ (1 + 𝑠𝑇𝑖)

𝑁𝑖=1

(2𝐻𝑠 + 𝑑)∏ (1 + 𝑠𝑇𝑖) + ∑ [𝐾𝑚𝑗

𝑅𝑗(1 + 𝐹𝑗𝑇𝑗𝑠)∏ (1 + 𝑠𝑇𝑖)

𝑁𝑖=1,𝑖≠𝑗 ]𝑁

𝑗=1𝑁𝑖=1

= ∆𝑃 ∑𝐴𝑖

𝑝𝑖∙ (

1

𝑠−

1

𝑠−𝑝𝑖

𝑁+1𝑖=1 ) (10)

The time response for N+1th-order SFR model was given as:

∆ω(t)=∆𝑃 ∑𝐴𝑖

𝑝𝑖∙ (1 − 𝑒𝑝𝑖𝑡𝑁+1

𝑖=1 ) ∙ 𝑈(𝑡) (11)

Substituting (8) into (11) gives:

∆ω(t)= [∆𝑃0+∑ PL0,j× [(2p1+p

2) (

Vj

V0,j

)]

NL

i=1

] ∙ ∑𝐴𝑖

𝑝𝑖

∙ (1 − 𝑒𝑝𝑖𝑡

𝑁+1

𝑖=1

) ∙ 𝑈(𝑡)

(12)

Equation (12) shows that load characteristics could

significantly affect the frequency dynamics through change

of system voltage and when the percentage exceeds a certain

threshold, the system could go into over-frequency despite

severe initial active-power deficit, ∆𝑃0. Voltage decreases as

reactive-power deficit, ∆𝑄0 increases during which ∆P

decreases as well. When ∆𝑄0 increases over a certain

threshold, ∆𝑃 drops sharply due to the voltage decline.

The severity of frequency-voltage coupling is influenced by

magnitude of initial reactive power deviation and system load

characteristics [20]. According to Yang & Zhang in [20], the

frequency-voltage coupling effect enhances with the increase



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of values of ∆𝑄0 and the percentage of induction motor in load

which represents majority of electrical loads. Voltage recovery

following contingencies is delayed by load dynamics of induction

motors in loads [23].

System voltage decreases when the percentage increases and

motor becomes unstable due to voltage drop whose active-power

reduces steeply and reactive-power increases when the percentage

exceeds a certain limit.

LOAD VOLTAGE IN SFR MODEL

Most of the loads in a power system are voltage-dependent and

the occurrence of a major outage causes severe decline in system

voltage which will lead to reduction of active and reactive

demands of these loads. This will affect the total active power

imbalance between load and generation in the SFR model and

lead to considerable error in the computation of system and UFLS

parameters.

A modified value of total active power imbalance, ∆𝑃𝑚 is

considered in this paper whereby the effect of voltage on loads is

incorporated into the SFR model in computation of system

frequency response. ∆𝑃𝑚 can be computed by running a simple

power flow program such as PSAT whereby imbalance between

load and generation is compensated by slack bus. The slack bus

generation will give the ∆𝑃𝑚 for the entire system.

UFLS OPERATION PHILOSOPHY

The impact of load voltage on power imbalance is investigated

using a nine-bus test system with simplified synchronous machine

models, as shown in Figure 1 [24].

Figure1. Nine-bus Test System

In this model, constant power loads are connected at buses 5, 6

and 8. Slack bus is connected at bus 1 to portray quantum of load-

generation imbalance in the system. A three phase fault is applied

at time equals 1s, at bus seven. The fault is then cleared by

opening line 4-7 at time equals 1.083s and re-closed at time

equals 4s. The magnitude of disturbance was estimated using

different types of loads such as exponential voltage load, ZIP

load, exponential voltage frequency dependent load, mixed

load and constant power load. The results are as shown in

Tables 2A and 2B.

Table 2A. Simulation Results for ZIP, Exponential Voltage

and Mixed Loads

Bus

ZIP Load Exponential

Voltage Load Mixed Load

V P gen V P gen V P gen

[p.u.] [p.u.] [p.u.] [p.u.] [p.u.] [p.u.]

1 1.04 0.372 1.04 -0.097 1.04 -2.345

2 1.025 1.63 1.025 1.63 1.025 1.63

3 1.025 0.85 1.025 0.85 1.025 0.85

4 0.982 0 1.01 0 1.026 0

5 0.928 0 0.979 0 1.029 0

6 0.928 0 0.98 0 1.038 0

7 0.99 0 1.015 0 1.046 0

8 0.953 0 0.995 0 1.055 0

9 0.998 0 1.02 0 1.048 0

Table 2B. Simulation Results for Voltage-Frequency

Dependent Load and Constant Power Loads

Bus

Voltage-Frequency

Dependent Load Constant Power Load

V P gen V P gen

[p.u.] [p.u.] [p.u.] [p.u.]

1 1.04 -2.345 1.04 0.716

2 1.025 1.63 1.025 1.63

3 1.025 0.85 1.025 0.85

4 1.026 0 1.026 0

5 1.029 0 0.996 0

6 1.038 0 1.013 0

7 1.046 0 1.026 0

8 1.055 0 1.016 0

9 1.048 0 1.032 0

Figure 2 shows the bus voltage for all nine buses when the

four different types of loads are used. Simulation results

show that load voltage has significant impact on power

imbalance during disturbance. Therefore disregarding impact

of load voltage will give inaccurate results of the actual

condition of a power system and render load-shedding efforts

ineffective. It is observed that mixed load and voltage-

frequency dependent load resulted in same quantum of

imbalance during disturbance.



9468

Figure 2. Power Imbalance Versus Bus Voltage

PROBLEM FORMULATION

The optimal design of UFLS scheme is a highly non-linear and

non-convex constrained optimization problem to devise a robust,

practical and optimal UFLS scheme that captures the trade-off

between minimizing the frequency deviations, Δωts, steady-state

frequency, ∆𝜔𝑠𝑠 the amount of total load shed, ΔPj [1]:

Minimize fobj = Cts ∙ |∆ωts| + Css ∙ |∆ωss| + Cls ∙ ∑ |∆Pj|Mj=1

(13)

whereby 𝑔𝐽 (𝑥) ≤ 0, for 𝐽 = 1, … ,𝑚J, ℎ𝐾 (𝑥) = 0, 𝑓𝑜𝑟 𝐾 =

1, … , 𝑙𝐾 , 𝑙 (𝐼) ≤ 𝑥𝐼 ≤ 𝑢(𝐼) , 𝐼 = 1, … , 𝑛 𝐼 with fobj being the

objective function, gJ(x) and hK(x) the inequality and equality

equations, and l(I) and u(I) the lower and upper bounds of the

decision variables respectively. Cts and Cls are the constant cost

coefficients for transient frequency and load shed.

A few design and performance criterions for optimal design of

UFLS scheme were developed in literature [1]:

i. Number of load-shedding stages, kmin ≤ k ≤ kmax.

ii. Allowable range of frequency thresholds, 𝜔𝑡ℎ_𝑚𝑖𝑛 ≤ 𝜔𝑡ℎ (𝑗) ≤ 𝜔𝑡ℎ_𝑚𝑎𝑥.

iii. Allowable range of load shed sizes, ∆𝑃𝑚𝑖𝑛 ≤ ∆𝑃𝑗 ≤ ∆𝑃𝑚𝑎𝑥 . iv. Allowable range of time delays, 𝑡𝑑_𝑚𝑖𝑛 ≤ 𝑡𝑑 (𝑗) ≤ 𝑡𝑑_𝑚𝑎𝑥 .

v. Minimum margin between two frequency thresholds,

|𝜔𝑡ℎ (𝑗) − 𝜔𝑡ℎ (𝑗+1)| ≥ 𝜎𝑤.

vi. Maximum allowable total load shed, ∑ |∆𝑃𝑗| ≤ ∆ 𝑃𝑠_𝑚𝑎𝑥𝑘𝑗=1 .

vii. Requirements for maintaining stability and dynamic security.

viii. Allowable minimum steady state frequency.

ix. Allowable minimum transient frequency.

x. Over-loadshedding criteria.

Items (i) through (iv) are the bounds constraints, items (v)

through (vi) are the linear inequality constraints and items (vii)

through (x) are the non-linear inequality constraints.

The non-linear inequality constraints can be summarized as:

gJ(x) =

[ ωss_min- ωss(u)

ωts_min- ωts(u)

real (pi)+ ε

ωss<0 ]

≤0 (14)

where Mu is the number of UFLS stages activated and Mmax(u)

is the maximum allowable stages for contingency u. ωss(u) and

ωts(u) are the steady-state and transient frequency

respectively, following the occurrence of contingency u.

A simple way to penalize infeasible solutions is to apply a

static penalty parameter to those solutions which violate

feasibility in any way [25]:

𝑓𝑝 = ∑ 𝑟𝑘𝑐 ∙ 𝑔𝐽

𝑚𝐽

𝐽=1 (15)

where r are the penalty weights for the multiple constraints, J = 1,…, mJ with number of penalty weights, kc.

Static penalty method albeit simple requires prudent

definition of weighing parameters in order to control the

amount of penalty added when multiple constraints are

violated. These parameters are usually problem-dependent

and prior knowledge about the degree of constraint violation

in a problem is needed to be able to find the most suitable

penalty parameter [26]. By penalizing the infeasible points

with static penalty function, the inequality constraints,

fp = r1[g (ωss)]+r2[g (ωts)] + r3+ r4+r5+r6 (16)

is adopted to deal with all operating limits. r1, r2, r3 and r4 are

penalty weights of minimum steady-state frequency,

minimum transient frequency, transient stability limit and

over-loadshedding criteria for contingency scenarios such as

tripping of generating units in the system; [g(ωss)] and [g(ωts)] are the penalty function for the related variables. The

original constrained optimization problem is transformed to

an unconstrained one as follows:

Fobj= { fobj, if gJ

(x) ≤ 0

fobj+fp, Otherwise, where J=1,…, mJ (17)

PROPOSED METHOD

UFLS scheme is a popular mitigation method used to arrest a

power system from load-generation imbalance in various

parts of the world such as Asia, Europe, Australasia, Africa,

Middle East and the Americas. UFLS in these continents

differ in terms of total load shed, number of UFLS blocks,

average block size and trip frequency deviation thresholds

depending on their system size, system inertia and generation

mix.

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1 2 3 4 5 6 7 8 9

Bu

s V

olt

age

[p.u

.]

Bus Number

ZIP Load Exponential Load

Mixed Load Voltage-Frequency Dependent Load

Constant Power Load



9469

A. Classical Evolutionary Programming (CEP)

Step 1: Initialization

The initial control variable population is selected by randomly

selecting vi = [ωth(j)T, ΔPj

T, tdjT] where T = 1, 2, .., m where m is the

population size from sets of uniform distribution ranging over

their upper and lower limits, [ωth_min, ωth_max], [ΔPmin, ΔPmax] and

[td_min, td_max]. The free load dynamic response following a

contingency for a N+1th order SFR model is as follows [1]:

∆ ω (s) = ∆ P0 ∑Ai

pi

N+1i=1 (

1

s -

1

s-pi ) (18)

whereby Ai is real or complex, pi is a root or pole of the

denominator and may be a real or a complex conjugate-pair. From

Equation (18), the value of gain, Ai and poles, pi can be

determined. These values are important to compute the basic

indicators that define system and UFLS performance such as

minimum frequency deviation, steady-state frequency, minimum

transient frequency deviation, the number of load shedding stages

and the time instant activation of the UFLS scheme [1].

Step 2: Statistics

The maximum fitness, minimum fitness, sum of fitnesses and

average fitness of this generation are calculated as follows:

fmax = {fi | fi ≥ fj fj , j=1, …, m} (19)

fmin = {fi | fi ≤ fj fj , j=1, …, m} (20)

f = ∑ fimi=1 (21)

favg= f

m (22)

Step 3: Mutation

Each pi is mutated and assigned to vi+m in accordance with the

following equation:

vi+m, j = vi, j+ N (0, β (xj, max- xj, min ) fi

fmax) , j=1, 2, …, n (23)

where vi,j is the jth element of ith individual, N(μ,σ2) is the

random Gaussian variable with mean, μ and variance, σ2, fmax is

the maximum fitness of old generation which is obtained in

Statistics, xj,max is the maximum limits of the jth element, xj,min is

the minimum limits of the jth element and β is the mutation scale

where 0 ≤ β ≤ 1. A combined population is formed with the old

generation and the mutated old generation.

Step 4: Competition

Each individual vi in the combined population has to compete

with some other individuals to get its chance to be transcribed to

the next generation. A weight value, 𝑤𝑖 is assigned to the

individual according to Equation (24).

𝑤𝑖 = ∑ 𝑤𝑡𝑞𝑡=1 (24)

Where q = competition number; wt = number of {0 ; 1}which

represents win, 1 or loss, 0 as vi competes with a randomly

selected individual pr in the combined population

= {1, if u1<

fr

fr+fi

0, Otherwise (25)

where fr = fitness of randomly selected individual vr; fi =

fitness of vi and u1 is randomly selected from a uniform

distribution set, U(0,1).

When all individuals, vi, i = 1, 2, …, 40 get their competition

weights, they will be ranked in descending order of their

corresponding value, wi. The first m individuals are

transcribed along with their corresponding fitness, fi, to be the

basis of the next generation. The maximum, minimum and

average fitness and also sum of fitness of this generation are

then calculated in the Statistics process.

Step 5: Determination

The convergence of maximum fitness to minimum fitness is

checked. Convergence describes limiting behavior,

particularly of an infinite sequence or series toward some

limit. The convergence criterion is specified as:

maximum fitness – minimum fitness ≤ 0.0001 (26)

If the convergence condition is not met, the loop will repeat

from Competition. The full program will terminate after the

convergence condition is met.

B. Swarm Evolutionary Programming (SEP)

In the proposed method, a different mechanism to reproduce

and generate new individuals or new alternatives in different

position in space is used whereby Step 3 in CEP is replaced

with a different operation called particle movement. This

operator is more effective than mutation in generating

solutions that approach the optimum. In addition, Step 4 in

CEP was replaced with a different selection method which

tournament method based on priority selection. The

procedures of Swarm Evolutionary Programming for the

optimal design of UFLS scheme are as follow:

Step 1: Initialization

Initialization stage for SEP is identical to that of CEP in

Section 6.1.

Step 2: Mutation

The population of clones then undergo maturation process

through generatic operation eg mutation. The inertia weights

determine the impact of previous history of velocities on

current velocity and are important for the convergence of

SEP. Large weight factor should be chosen for initial

iterations to facilitate global exploration and gradually

reduced weight factor in successive iterations to facilitate

local exploration. The weights of the particles are mutated

according to w∗𝑖𝑘 = 𝑤𝑖𝑘 + 𝜏𝑁(0,1), whereby 𝜏 is a learning

parameter and N(0,1) is a random variable with Gaussian

Distribution with mean zero and variance one.

The mutation operator which alters one or more component

of a selected structure randomly, provides the way to

introduce new genetic materials. Mutation ensures



9470

reacheability of all points in the search space, preventing

premature convergence [27].

Step 3: Reproduction

Each particle generates an offspring according to the movement

rule of conventional PSO. The replicated particles make use of

the mutated weights. The offspring is held separately for the

original particles and the mutated ones,

vik+1=w*

i0vik+w*

i1×(pbest-xik)+w*

i2×(gbest*-xi

k) (27)

gbest*=gbest+τ'N(0,1) (28)

where 𝜏′is a learning parameter. 𝑣𝑖,𝑚𝑎𝑥 determines the resolution,

or fitness, with which regions between the present position and

target position are searched and is often set at 10-20% of the

dynamic range of the variables of each dimension [28]. 𝑤∗𝑖0, 𝑤∗

𝑖1

and 𝑤∗𝑖2 are often set to 0.8, 2 and 2 respectively.

Step 4: Evaluation/Competition

Each particle is evaluated according to their current position.

Step 5: Selection/Determination

The best particles are selected by priority selection method to

form a new generation. The convergence of maximum fitness to

minimum fitness is checked. This is similar to Step 5 in Section

6.1.

SIMULATION RESULTS

The SFR model has been widely used in computation of load-

frequency response of a power system during system

contingency. However in the classic SFR model, only inertia

constant of generator and frequency information are considered

and the impact of voltage dependence of loads is not taken into

account although load characteristics have been proven to have

significant influence on the dynamic behaviour of power systems

during low frequency oscillation and severe faults. In more recent

literature, SFR model incorporating frequency and voltage

dependence load models is proposed and used in the design of

optimal UFLS scheme.

To verify the effectiveness of the proposed method, the

optimization algorithm is tested on the nine-bus test system as

shown in Figure 1. An optimal load-shedding scheme is designed

assuming a three phase fault at bus 7 at time equals 1s on the

nine-bus test system with fault clearing time of 0.083s and line re-

closing at time equals 4s. This is a critical contingency for a small

system and comprises 30.80% of the total system loading.

UFLS performance for two different algorithms which are CEP

and SEP are compared in this paper. Three cases are considered:

Case 1: UFLS scheme using trial-and-error method.

Case 2: UFLS scheme implementing CEP algorithm.

Case 3: UFLS scheme implementing SEP algorithm.

The UFLS scheme derived using conventional trial-and-error

method is available in Table 3. Table 4 shows a summary of

results showing the performance of CEP and SEP that has been

tested using the nine-bus test system in Figure 1 for the three

cases above.

Table 3. UFLS Scheme Trial-and-Error Method

J ωth(j) (Hz) ΔP (p.u.) td (s)

0 50.0 0.3080 0.0

1 49.0 -0.05 0.1

2 48.8 -0.05 0.1

3 48.6 -0.10 0.1

4 48.4 -0.10 0.1

Table 4A. Summary of Results for Cases 1, 2 and 3

Case

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-

state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

1 2.3332 48.387 49.955 0.3000

2 0.4518 48.530 49.645 0.4153

3 0.3445 48.605 49.940 0.3154

Table 4B. Nonlinear Constraint Violations

Case Nonlinear Constraint Violations

r1 r2 r3 r4 r5 r6

1 0 0 0 0 0 1

2 0 0 0 0 0 0

3 0 0 0 0 0 0

The percentage of results improvement for Case 2 and 3 are

80.636% and 85.235% respectively. The minimum transient

frequency observed in Case 2 and 3 when SEP is applied as

the optimization saw an improvement of 0.296% and 0.451%

from 48.387Hz to 48.53Hz and 48.605Hz respectively.

Hence, SEP method has lower transient frequency deviation

from nominal as compared with CEP. From this perspective,

using the SEP has positively impacted the power system,

with no constraint violations.

The algorithm is repeated for 30 iterations and the results are

tabulated in Figure 3. The indicated a maximum objective

function of 0.4003 obtained over the 30 iterations with an

average of 0.3588.

Figure 3. Objective Function Vs Iteration

ADAPTATION FOR UFLS

A combination of sensitivity algorithms and adaptation

methods are investigated to determine the sensitivity of SEP.

These methods include varying of penalty function, mutation

method, selection method and replacing static penalty

function with adaptive penalty function.

0.30

0.32

0.34

0.36

0.38

0.40

0.42

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Ob

ject

ive

Fu

nct

ion

, fo

bj

Iteration



9471

Method 1: Varying Penalty function

The first type of static adaptation method is the varying the values

of static penalty function. In order to determine the link between

parameter values and algorithm performance, numerous tests are

run by changing the value of the static penalty function in Step 1

of Figure A-2 from a value as small as 0.001 to a maximum of

10,000 upon each run of the algorithm.

Recommended parameter values are presented based on

experimental results from changing strategy parameters such as

increasing or decreasing penalty factor for violated constraints.

The findings are shown as in Table 5A and 5B.

Table 5A. Varying Penalty Function Value

Penalty

Factor,

r

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-

state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

0.001 0.2390 50.000 50.700 0.2240

0.01 0.2465 50.000 50.715 0.2222

0.1 0.3397 50.000 50.680 0.2260

1 0.3973 48.725 49.545 0.3627

2 0.3445 48.605 49.940 0.3154

5 0.3630 48.715 49.790 0.3332

10 0.3608 48.670 49.815 0.3305

25 0.3608 48.670 49.815 0.3305

50 0.3608 48.670 49.815 0.3305

75 75.2397 50.000 50.685 0.2260

100 0.3973 48.725 49.545 0.3627

200 0.3445 48.605 49.940 0.3154

300 0.3538 48.670 49.865 0.3245

400 0.3630 48.715 49.790 0.3332

500 0.3630 48.715 49.790 0.3332

600 600.2362 50.000 50.720 0.2218

700 0.3608 48.670 49.815 0.3305

800 800.2397 50.000 50.685 0.2260

900 0.3973 48.725 49.545 0.3627

1000 0.3445 48.605 49.940 0.3154

10,000 0.3538 48.670 49.865 0.3245


Penalty Factor, r Nonlinear Constraint Violations

r1 r2 r3 r4 r5 r6

0.001 0 0 0 0 0 1

0.01 0 0 0 0 0 1

0.1 0 0 0 0 0 1

1 0 0 0 0 0 0

2 0 0 0 0 0 0

5 0 0 0 0 0 0

10 0 0 0 0 0 0

25 0 0 0 0 0 0

50 0 0 0 0 0 0

75 0 0 0 0 0 1

100 0 0 0 0 0 0

200 0 0 0 0 0 0

300 0 0 0 0 0 0

400 0 0 0 0 0 0

500 0 0 0 0 0 0

600 0 0 0 0 0 1

700 0 0 0 0 0 0

800 0 0 0 0 0 1

900 0 0 0 0 0 0

1000 0 0 0 0 0 0

10,000 0 0 0 0 0 0

It is observed that there is one constraint violation of g6 for

value of r equals 0.001, 0.01, 0.1, 50, 75, 600 and 800, hence,

eliminated from the selection of possible best values of r with

respect to the objective function. There are no constraint

violations for other values of r within the range of 0.001 to

10,000.

Figures 6 to 8 show the objective function value, total load

shed, minimum transient frequency and minimum steady-

state frequency for all possible best values of r. The objective

value is the lowest at r equals two, 200 and 1000 whereby

𝑓𝑜𝑏𝑗 is equal to 0.3445. At these values of r, the total quantum

of load shed is the least which is 0.3154p.u. The minimum

transient frequency and the minimum steady-state frequency

are recorded at 48.605Hz and 49.940Hz which meets the

minimum acceptable value of 48.6Hz and 49.5Hz

respectively.

Figure 6. Objective Function Vs Penalty Value

Figure 7. Total Load Shed Vs Penalty Value

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.40

0.41

Ob

ject

ive

Fu

nct

ion

, fo

bj

Penalty Value, r

0.29

0.30

0.31

0.32

0.33

0.34

0.35

0.36

0.37

Tota

l L

oad

Sh

ed [

p.u

.]

Penalty Value, r



9472

Figure 8. Minimum Transient Frequency, 𝜔𝑡𝑠 and Steady-state

Frequency, 𝜔ss

Method 2: Varying Mutation Method

The second type of static adaptation method is the varying of

algorithm mutation method. The weight factor to compute

algorithm velocity is mutated incorporating several types of

random distributions such as Cauchy, Poisson, Chi-square,

Gamma and Rayleigh. Table 6A and 6B show the results obtained

from varying mutation methods from Gaussian to Cauchy,

Poisson, ChiSquare and Gamma. It is observed that varying the

mutation method did not improve the results in terms of objective

function albeit all nonlinear constraints are met.

Table 6A. Varying Mutation Method

Mutation

Method

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-

state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

Gaussian 0.3445 48.605 49.940 0.3154

Cauchy 0.3647 48.635 49.790 0.3332

Poisson 0.3753 48.600 49.720 0.3417

ChiSquare 0.3454 48.705 49.920 0.3179

Gamma 0.3630 48.715 49.790 0.3332


Mutation Method Nonlinear Constraint Violations

r1 r2 r3 r4 r5 r6

Gaussian 0 0 0 0 0 0

Cauchy 0 0 0 0 0 0

Poisson 0 0 0 0 0 0

ChiSquare 0 0 0 0 0 0

Gamma 0 0 0 0 0 0

Method 3: Varying Selection Method

The third type of static adaptation method is the varying of

algorithm selection method. Selection is an important part of an

evolutionary algorithm. Without selection directing the algorithm

towards fitter solutions there would be no progress. Selection

must favor fitter candidates over weaker candidates but

beyond that there are no fixed rules. Furthermore, there is no

one strategy that is best for all problems. Some strategies

result in fast convergence, others will tend to produce a more

thorough exploration of the search space. An evolutionary

algorithm that appears ineffective with one selection strategy

may be transformed by switching to a strategy with different

characteristics.

There are several selection methods namely truncation

selection, roulette wheel selection, tournament selection and

so forth. Truncation selection is the simplest and most

straight-forward whereby a certain percentage of the fittest

population is selected to be copied to the next generation.

These fittest individuals are cloned to maintain the original

number of individuals in the population. This selection

strategy is easy to implement but may result in premature

convergence as less fit candidates are ruthless culled without

being given opportunity to evolve into something better.

Roulette wheel selection is one type of fitness-proportionate

selection whereby every individual is given a chance to be

selected for breeding although fitter candidates are more

likely to be chosen as compared to weaker individuals. In

roulette wheel selection, the fitness function is evaluated for

each individual, providing fitness values, which are then

normalized. Normalization means dividing the fitness value

of each individual by the sum of all resulting fitness values

equals one. The population is sorted by descending fitness

values and accumulated normalized fitness values are

computed. A random number between zero and one is

chosen. The selected individual is the first one whose

accumulated normalized value is greater than the random

value.

Tournament selection is very commonly used in evolutionary

algorithms as the method works well for a wide range of

problems and is amendable to parallelization. At its simplest

tournament selection involves randomly picking two

individuals from the population and staging a tournament to

determine which one gets selected. Equation (24) and (25)

are used to compute the weight value, 𝑤𝑖 assigned each

individual in the population.

Table 7A and 7B show the results obtained from varying the

selection method. It is observed that replacing priority

selection with truncation selection improves the results in

terms of objective function computed from minimum

transient frequency, steady-state frequency and total load

shed. The objective function is reduced by [0.3445-

0.3387=0.0058]. The minimum transient frequency deviation

from nominal is improved by [(48.620-48.605) Hz = 0.015

Hz] or 0.0309% and the steady-state frequency is improved

by [(49.98-49.94)Hz = 0.04Hz] or 0.08%. The total quantum

of load-shedding is also reduced by [(0.3154-

0.3106)p.u.=0.0048p.u. or 1.5219%. Hence, this is a possible

adaptation method to obtain the best improved simulation

results. Replacing priority selection with roulette wheel and

tournament method did not improve the objective function,

hence, not recommended.

48.5

48.7

48.9

49.1

49.3

49.5

49.7

49.9

50.1

Fre

qu

ency

[H

z]

Penalty Value, r

wts wss



9473

Table 7A. Varying Selection Method

Selection

Method

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

Priority

Selection

0.3445 48.605 49.940 0.3154

Roulette

Wheel

0.3984 48.665 49.545 0.3626

Tournament 4.4299 48.425 49.355 0.3855

Truncation 0.3387 48.620 49.980 0.3106


Selection Method Nonlinear Constraint Violations

r1 r2 r3 r4 r5 r6

Priority Selection 0 0 0 0 0 0

Roulette Wheel 0 0 0 0 0 0

Tournament 1 1 0 0 0 0

Truncation 0 0 0 0 0 0

Method 4: Replacing Fixed UFLS Scheme with Adaptive UFLS

Scheme

The adaptive scheme makes use of the frequency derivative and is

based on the SFR model [33]. This model is obtained from the

complete block diagram representation of a generic generating

unit, along with its governor. A reduced order SFR model for the

whole electrical system can be obtained on the basis of commonly

adopted hypotheses [34] and from the reduced order SFR model,

it is possible to obtain a relation between the initial value of the

rate of frequency change and the size of the disturbance 𝑃𝑠𝑡𝑒𝑝 that

caused the frequency decline. This relationship is:

df

dt⌋

t=0=

1

2H (Pstep) (29)

where f is expressed in per unit on the base of the nominal system

frequency (50 or 60 Hz) and 𝑃𝑠𝑡𝑒𝑝 is in per unit on the total

apparent power of the whole system. The initial value of the rate

of frequency change is proportional to the size of the disturbance

through the inertia constant H.

An adequate countermeasure in terms of load-shedding

can be operated as follows [10]:

Load Shed = {∆𝑃0̇, if |

𝑑𝑓

𝑑𝑡⌋𝑡=0

| ≥ �̇�𝑡ℎ > 0

0, if | 𝑑𝑓

𝑑𝑡⌋𝑡=0

| < �̇�𝑡ℎ

(30)

whereby �̇�𝑡ℎ is the pre-defined threshold value for initial rate of

frequency change and ∆𝑃0̇ is the quantum of initial load shed. �̇�𝑡ℎ

is usually set to a minimum of 0.04 p.u./s and ∆𝑃0̇ has a typical

range of between 0 p.u to 0.5 p.u [10] which is larger than the

typical range of a fixed type UFLS scheme of between 0.05 p.u

and 0.2 p.u. This is necessary to effectively and quickly stop rapid

frequency decline when critical contingency situation arises.

Hence, for a power system with a loading of 1000 MW, for

instance, the �̇�𝑡ℎ will be 40 MW/s and ∆𝑃0̇ will have a range

of between 0 MW and 500 MW.

Therefore, if the system impact at the onset of disturbance is

∆�̈�0, then the net system impact is given as [10]:

∆P0 = ∆P0̈- ∆P0̇ (31)

This scheme considers power system characteristics,

generator dynamic behavior under large disturbance as well

as nonlinear interacting generators [35 - 37] and can achieve

rapid removal of loads in case of severe power outages. If the

system frequency continues to decline after initial load is

shed, the fixed scheme is activated [10].

Table 8A and 8B show the simulation results of using an

adaptive UFLS scheme instead of the fixed scheme. It is

observed that using adaptive UFLS scheme has given

improved results whereby objective function is reduced by

[0.3445-0.3182=0.0263]. The minimum transient frequency

deviation from nominal is improved by [(48.615-48.605) Hz

= 0.01 Hz] or 0.02% and the steady-state frequency is

improved by [(49.96-49.94)Hz = 0.02Hz] or 0.04%. The total

quantum of load-shedding is also reduced by [(0.3154-



results.

Table 8A. Fixed Vs Adaptive UFLS Scheme

Type of

UFLS

Scheme

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-

state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

Fixed

UFLS

Scheme

0.3445 48.605 49.940 0.3154

Adaptive

UFLS

Scheme

0.3182 48.615 49.960 0.3128


Type of UFLS Scheme Nonlinear Constraint Violations

r1 r2 r3 r4 r5 r6

Fixed UFLS Scheme 0 0 0 0 0 0

Adaptive UFLS Scheme 0 0 0 0 0 0

Method 5: Replacing Static Penalty Function with Adaptive

Penalty Function

Replacing the static penalty function with an adaptive one is

one way of performing dynamic adaptation whereby the

direction and/or magnitude of the penalty parameter is

changed adaptively in every generation by the selection of

two constants, β1 and β 2 (β 1> β 2>1). The objective function

is altered by increasing or decreasing the penalty coefficients

for violated constraints based on feedback from the search

process whereby information from the current generation is

used to control the amount of penalty added to the infeasible

individuals in the next generation [68]. rk+1 is updated as a



9474

multiple of r (t) with β2 (> 1) if the best individual do not reside

inside the feasible region and if the best individual is an element

in the feasible region, the penalty parameter r(k + 1) are updated

to be smaller than r(t) by dividing it with β1 (> 1).

Table 9A and 9B show the results obtained from using an

adaptive UFLS scheme instead of a fixed scheme. It is observed

that the objective function value is increased by [1.2720-

0.3445=0.9275] or 72.9167% with one nonlinear constraint

violation, 𝑟6 for increase of steady-state frequency exceeding

nominal. Hence, this adaptation method is not recommended.

Table 9A. Static Vs Adaptive Penalty Function

Type of

Penalty

Function

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-

state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

Static

Penalty

Function

0.3445 48.605 49.940 0.3154

Adaptive

Penalty

Function

1.2720 49.530 50.455 0.2535


Type of Penalty

Function

Nonlinear Constraint

Violations

r1 r2 r3 r4 r5 r6

Static Penalty Function 0 0 0 0 0 0

Adaptive Penalty

Function 0 0 0 0 0 1

Method 6: Varying Swarm Size

To evaluate the performance of SEP, swarm size is varied from

20 to 500. Table 10A and 10B show the results obtained from

applying this adaptation method. It is observed that there are no

constraint violations for all swarm sizes tested in the simulation.

Table 10A. Impact of Swarm Size

Swarm

Size

Objective

Function,

𝑓𝑜𝑏𝑗

Minimum

Transient

Frequency,

𝜔𝑡𝑠

Steady-

state

Frequency,

𝜔𝑠𝑠

Total

Load

Shed,

ΔPj

20 0.3871 48.615 49.635 -0.352

40 0.3674 48.610 49.775 -0.3351

60 0.3362 48.655 49.990 -0.3091

80 0.3470 48.605 49.990 -0.3189

100 0.3426 48.605 49.950 -0.3138

120 0.3478 48.670 49.905 -0.3193

140 0.3489 48.660 49.900 -0.3201

160 0.3528 48.645 49.875 -0.3231

180 0.3799 48.685 49.675 -0.3471

200 0.3637 48.685 49.790 -0.3332


Swarm Size

Nonlinear Constraint Violations

r1 r2 r3 r4 r5 r6

20 0 0 0 0 0 0

40 0 0 0 0 0 0

60 0 0 0 0 0 0

80 0 0 0 0 0 0

100 0 0 0 0 0 0

120 0 0 0 0 0 0

140 0 0 0 0 0 0

160 0 0 0 0 0 0

180 0 0 0 0 0 0

200 0 0 0 0 0 0

Figure 9 shows the impact of varying swarm size on the

objective function value. Swarm size equals 60 has given the

best results in terms of objective function with minimum

transient frequency of 48.655Hz, steady-state frequency of

49.990Hz and 0.3091p.u. It is observed that using a swarm

size of 60 has reduced the objective function by [0.3445-

0.3362=0.0083]. The minimum transient frequency deviation

from nominal is improved by [(48.655-48.605) Hz = 0.05

Hz] or 0.103% and the steady-state frequency is improved by

[(49.990-49.940)Hz = 0.05Hz] or 0.1%. The total quantum of

load-shedding is also reduced by [(0.3154-



results.

Figure 9. Varying Swarm Size

Figure 10 shows the comparison plots for all adaptation

methods. It is obvious that adaptation methods 1, 3, 4 and 6

are possible adaptation methods that will improve objective

function values of SEP and the best objective function value

is obtained through adaptation method 4.

0.33

0.34

0.35

0.36

0.37

0.38

0.39

20 40 60 80 100 120 140 160 180 200

Ob

ject

ive

Fu

nct

ion

, fo

bj

Swarm Size



9475

Figure 10. Best Objective Function for Adaptation Methods

The SEP optimization framework is repeated using different

combination of the recommended four adaptation methods and

the results obtained are shown in Table 11A, 11B and 11C. It is

observed that combining adaptation methods does not give better

results with respect to the objective function, hence, hybridization

of these methods is not recommended.

Table 11A. Combination of Adaptation Methods

Adaptation Method Combination

1 Combination 2

1 Varying Penalty Value r=2 r=2

2 Varying Mutation

Method NA NA

3 Varying Selection

Method Truncation Truncation

4 Adaptive UFLS Yes No

5 Adaptive Penalty NA NA

6 Varying Swarm Size 60 60

Objective Function 2.2358 0.3781

Table 11B. Combination of Adaptation Methods

Adaptation Method Combination

3

Combination

4


2 Varying Mutation Method NA NA

3 Varying Selection Method Truncation Priority

4 Adaptive UFLS Yes Yes

5 Adaptive Penalty NA NA



Table 11C. Combination of Adaptation Methods

Adaptation Method Combinatio

n 5

Combinatio

n 6


2 Varying Mutation

Method NA NA

3 Varying Selection

Method Truncation Truncation

4 Adaptive UFLS Yes Yes

5 Adaptive Penalty



CONCLUSION

A Swarm Evolutionary Programming (SEP) method

incorporating modified System Frequency Response (SFR)

model has been presented to solve the optimal UFLS

problem. In order to show the effectiveness of the proposed

method, the performance of the proposed method has been

tested on a nine-bus test system. Analysis on the simulation

results show that SEP incorporating adaptation method 4 is

able to produce an UFLS scheme which will respond

optimally to system disturbance in terms of minimizing

transient and steady-state frequency deviation from nominal

and also reducing total quantum of load shedding to the

minimal.

ACKNOWLEDGEMENT

The authors would like to thank Universiti Malaysia Sarawak

who has funded this research work.

List of Symbols and Abbreviations SFR System Frequency Response

SEP Swarm Evolutionary Programming

UFLS Under-frequency Load Shedding

UVLS Under-voltage Load Shedding

GA Genetic Algorithm

EP Evolutionary Programming

ΔPj Total Load Shed

𝑓𝑜𝑏𝑗 Objective Function

𝜔𝑡𝑠 Minimum Transient Frequency

𝜔𝑠𝑠 Minimum Steady-state Frequency

r1, r2, r3, r4, r5, r6 Nonlinear Constraint Violations

QIEP Quantum-Inspired Evolutionary

Programming

DG Distributed Generation

PSO Particle Swarm Optimization

ZIP Combination of constant impedance,

constant current and constant power load

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1 2 3 4 5 6

Ob

ject

ive

Fu

nct

ion

, fo

bj

Adaptation Method



9476

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