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International Journal of Power Electronics and Drive Systems (IJPEDS) 
Vol. 12, No. 4, December 2021, pp. 2221~2229 
ISSN: 2088-8694, DOI: 10.1159 1/ijpeds.v12.14.pp2221-2229 O 2221 


Load frequency control of thermal system under deregulated 
environment using slime mould algorithm 


Sambugari Anil Kumar’, M. Siva Sathya Narayana’, K. Jithendra Gowd? 
Department of Electrical and Electronics Engineering, Jawaharlal Nehru Technological University, Ananthapuramu, 


Andhra Pradesh, India 


Department of Electrical and Electronics Engineering, G. Pulla Reddy Engineering College (Autonomous), Andhra 


Pradesh, India 


3Department of Electrical and Electronics Engineering, JNTUA College of Engineering, Ananthapuramu, Andhra 


Pradesh, India 


Article Info 


ABSTRACT 


Article history: 


Received May 14, 2021 
Revised Sep 22, 2021 
Accepted Sep 29, 2021 


This paper emphasizes the significance of proportional-integral-derivative 
(PID) controller parameters using a slime mould algorithm (SMA) to reduce 
load frequency control (LFC) issues in a thermal system in an open market 
scenario. The SMA is used to solve the parameterization of the PID controller, 
which was formulated as an optimization problem. The performance of the PID 


controller parameters improves the dynamic characteristics of the system as 


frequency in each area, and also deviations in tie line power after sudden load 
Keywords: violation. In order to study the efficiency of the proposed method, the system 
was tested with different power transactions for a small load disturbance and 
the comparative results were presented. The optimal value of the controller 
parameters derived from SMA based PID controller is estimated using a finite 
nonlinear optimization using a performance index based method. 


Disco participation matrix 
Load frequency control 
PID controller 


Slime mould algorithm 
This is an open access article under the CC BY-SA license. 


Corresponding Author: 


Sambugari Anil Kumar 

Department of Electrical and Electronics Engineering 
Jawaharlal Nehru Technological University 
Ananthapuramu, Andhra Pradesh 515002, India 
Email: sanil.0202 @ gmail.com 


1. INTRODUCTION 

Each plant needs to monitor load fluctuations and ensure high quality power delivery to its 
customers throughout the day. Therefore, the same power cannot be supplied constanly, and the amount of 
power generated changes according to load fluctuations. The main purpose of the control scenario is to 
generate and supply power in such a stable and economical interconnected system, but keep the frequency 
and voltage of the power supply within significant limits. Since reactive power changes as the voltage 
changes, the frequency of the system changes primarily due to load disturbances. The main purposes of the 
LFC are; i) to keep frequency within acceptable range; ii) maintain a balance between power generation and 
load; iii) to keep the power deviations within the limit. 

The vast grid of electrical systems is connected to many areas by connections. Network analysis of 
reconstructed networks faces the complexity of analysis due to its scaling. Sudden changes in the effect of the 
load on the system frequency can lead to uncertain and unstable operation. Therefore, plant working to 
maintain the load frequency variations is one of the major issues for Electrical Engineers. The problem with 
LFC is controlling the frequency and power bias between the correlation control elements [1], [2]. A very 
complex task is to ensure that the entire grid of the electrical system is in equilibrium due to the increasing 


Journal homepage: http://ijpeds.iaescore.com 


2222 O ISSN: 2088-8694 


energy demand in the current scenario. The load is always different depending on the power system. The 
main purpose of LFC is to maintain the true energy balance of the electrical system. The frequency of the 
system is determined by the generator's mechanical input force. The frequency of the system is directly 
influenced by variations in power. The frequency must be kept within safe limits by the controller. This 
frequency error is amplified and delivered to the control unit, which then sends it back to the turbine's speed 
controller and electrical system network, operating according to block and additional reserves after major 
disturbance [3], [4]. 

Deregulation of the electricity industry is the restructuring of the rules and profit incentives 
established by the government to manage and operate the electricity industry. As part of the deregulation, 
utilities were abolished as a separate entity having power generation companies (GENCO), transport 
company (TRANSCO), and distribution company (DISCO). In this open market scenario, a central authority 
called the independent system operator (ISO) governs the spot market participants. In the real-time electricity 
market, most vertically integrated utility (VIU) ancillary services play various roles in a deregulated 
environment. The ancillary services should be implemented by ISO in different ways to explain certain 
problems such as bilateral contracts between controlled areas and policies of deregulation [5]-[10]. 

Many researchers anticipated various control methods for balancing the LFC problems. A 
conventional controller used in automatic generation control (AGC) is PID controller due to their simple 
construction, consistency and ample variety of applications which are explained in [11]-[16]. The non- 
linearities like governor dead band (GDB) and generation rate constraint (GRC) also affect the performance 
of the LFC [17]-[20]. Various soft computing techniques proposed for LFC problems [21]-[27]. 


2. MULTI AREA DEREGUATED SYSTEM 
Figure 1 shows the block diagram representation of two area system under deregulation 
environment. Each area consists of two genco’s and two discom’s. 


Controller 


DISCO i 5 - : i—T DISCO 


Figure 1. Diagram of two area system under deregulation 


2.1. Traditional electric power system scenario 

The traditional electricity market consists of utilities that own and operate their own electricity. 
From production to distribution, the public service has full control. Utilities own the infrastructure and power 
lines and sell them directly to consumers. Utilities must comply with the electricity tariffs set by each state 


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utility council. This type of market is often called a monopoly due to limited consumer choice. However, its 
advantages include stable prices and long-term security. 


2.2. Deregulation power system scenario 

The term deregulation is the process of changing the rules and regulations that govern the electricity 
sector, allowing consumers to choose their electricity supplier. Free electricity market. This allows market 
participants to invest in power plants and transmission lines, allowing competitors to buy and sell electricity. 
Genco owners wholesale this electricity to retailers. Retail outlets set prices for consumers. In many cases, 
this makes profit for consumers by allowing them to compare prices and services from unlike third party 
providers and offering a special contract structure. 


2.3. Disco participation matrix 

The AGC system consists of two systems with equal area, i.e., thermal and hydro electric units. In 
each area there are two gencos and two discos. The coefficient of participation in the contract corresponds to 
the percentage of the total amount that DISCO j has concluded with GENCO i. The total number of entries in 
the column must equal to unity. Disco participation matrix is given by. 


CPhir CPfi2 cpfis cPfia 
CPf21 CPf22 CPf23 CPfoa (1) 
cPfs1 CPfs2 cCpfs3 CPfsa 
CPfar CPfa2 CPfa3 CP fag 


DPM = 


3. SLIME MOULD ALGORITHM 

The proposed algorithm (SMA) is a population-based heuristic algorithm proposed by Li et al. in 
2020. This algorithm is inspired by the nature of the behavior of mould during oscillation movements. The basic 
design of this algorithm is shown in Figure 2 which is based on the optimal food path, using both positive and 
negative feedback systems. The molecule dynamically adjusts the search path to search for food quality. The 
SMA algorithm follows three main principles: grabble, wrap and approach. Grabble prevents other molecules 
from colliding during the food fishing process. The grab phenomenon shows the same velocity of viscous 
forms. The phenomenon of the approach shows that how to move towards the center of food. 


Flowchart of SMA 


Step 1 Step 2 Step 3 Step 4 Step 5 


Compute the 
position of the 
slime mould 


Update best 
position 
& fitness 


Short the best 
& worst fitness 


Initialize the 
opulation size 


fitness of the 
slime mould 


Figure 2. Flowchart of slime mould Algorithm 


3.1. Step: 1 approach food 
The impending behaviour of slime moulds as a mathematical equation to replicate the contraction 


mode: 

reaps cea a 2% : 
vX) r = p 

p = tanh|S(i) — DF 5 

V, = [—a, a] 

a = arctan h(— G +1) = 


The weight of the slime mould is. 


Load frequency control of thermal system under deregulated environment using ... (Sambugari Anil Kumar) 


2224 O ISSN: 2088-8694 


; 1+r.log = + 1) ,condition 
W (smellindex (1)) = nee (6) 
1—r.log = + 1), other 
Smellindex = sort(S) (7) 


3.2. Step: 2 wrap foods 
The equation for updating the position of the slime mould is: 


rand.(UB — LB) + LB,rand < z 
Š = | Xo (© + X 0). (W.X10 - Xs) r < p (8) 


v-X() r> p 


where lower bound LB is 0 and upper bound UB is 1. 


3.3. Step: 3 grabble food 


The value of vb is given by the (4) and reaches to zero by increasing the iteration and V, also having 
lower bound -1 and upper bound 1 and gradually comes to zero. 


4. DESIGN OF CONTROLLERS 

The PID controller is a reliable and simple controller that can deliver good control results. The 
proportional gain (Kp), integral gain (Ky), and derivative gain (Ka) are the three primary parameters that must 
be determined while designing a PID controller. The integral square error (ISE) criterion is used as the 
objective function in this work for the paper. 


J = ISE = J” (Afi)? + (Af)? + (APrie)?.dt (9) 


For each controller the minimum value will be considered as -2 and maximum value will be considered as 2. 


5. RESULTS AND DISCUSSION 

In this paper, two area deregulated multi-source power systems to determine the efficiency of the 
proposed PID controller. It also includes the effects of non-linear factors such as GRC and GDB. The main 
reason for the inclusion of GRC is that sudden changes in power attract steam to the turbine, which leads to 
condensation of steam due to diabetic expansion or contraction. The return steam produces small droplets of 
water that corrode the turbine blades in the event of a collision. This is a long-term process that can lead to 
serious problems. The GRC limit was set at 0.05%. Similarly, GDB is defined as the sum of speed changes 
without changing the position of the steam valve. The GDB limit is set at 0.06%. Various simulation studies 
are carried out to study the efficacy of LFC will be performed. The objective function is utilized to reduce 
LFC problems by using SMA, and then the performance of SMA-based PI, PID controllers is compared to 
GWO-based PI and PID controllers. The analysis of performance is done with reference to the percentage peak 
overshoot and settling time. The simulation results are carried out in different power transactions is being as. 


5.1. Case 1: Pool CO-based transaction 

A pool co-based transaction occurs when DISCOs share a load with any of the GENCOs in the same 
region. The area participation factor is 0.5 for four values that are assumed to be equal. Figure 3 (a) shows 
the deviation of frequency in area-1, Figure 3 (b) shows the deviation of frequency in area-2 and Figure 3 (c) 
shows the deviation of tie line power by using various SMA based and GWO based controllers. Table 1 
shows that SMA based controller gives better results as compared to GWO based controller under pool co 
based transaction. 


0.5 0.1 05 05 0 0 

— |0.5 ; _ 10.1 05 05 0 0 
APF = 05 Disco = 0 | P uDPM = 0 0 0 0 
0.5 0 0 0 0 0 


Int J Pow Elec & Dri Syst, Vol. 12, No. 4, December 2021 : 2221 — 2229 


Int J Pow Elec & Dri Syst 


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O 2225 


\ 

ha i nN) 
yA Enh 
H VALA 


-0.05 


Frequency deviation in area-1 (Hz) 


-0.15 = W 


a el i 
WP vos 
IN HUR, 


3 4 
Time(Sec) 


(a) 


SMA-PID 
GWO-PID 


— — -GWO0-PI 7 
—— -SMA-PI 


Frequency deviation in area-2 (Hz) 


b 
i 


ò 
iy 
& 


H i! 


SMA-PID 


L 1 


3 4 
Time(Sec) 


(b) 


0.05 


o o o 
a Ə o 
8 3 R 


Tie-line power deviation (p.u) 


o 
2 


= — -GW0-PI 
-- -SMAPI 


SMA-PID 
GWO-PID 


Time(Sec) 


(c) 


Figure 3. These figures are; (a) deviation of frequency in area-1, (b) deviation of frequency in area-2, 
(c) deviation of tie-line power under pool-co based transaction for 1% step load disturbance 


Table 1. Comparison of peak overshoot, undershoot, and settling time using various controllers under 
pool-CO based transcation 


S. No % Peak overshoot (p.u) % Peak undershoot (p.u) Settling time (Sec) 
Af, Af, APiie Af, Af APiie Afi Af, — APi 
GWO-PI 0.05 0.12 0.055 0.18 0.28 0.01 35 3.2 3.6 
SMA-PI 0.04 0.08 0.053 0.16 0.26 0.009 3 3 3.2 
GWO-PID_ - - 0.02 0.08 0.11 - 25 18 2.8 
SMA-PID _ - - 0.018 0.06 0.09 - 18 11 2 


Load frequency control of thermal system under deregulated environment using ... (Sambugari Anil Kumar) 


2226 O ISSN: 2088-8694 


5.2. Case 2: Bilateral-based transaction 
Bilateral based transactions occur when DISCOs share the load with any of the GENCOs in another 


location. The area participation factor is 0.75, 0.25, 0.5, and 0.5 for four values that are considered to be 
uneven. Figure 4 (a) shows the deviation of frequency in area-1, Figure 4 (b) shows the deviation of 
frequency in area-2 and Figure 4 (c) shows the deviation of tie line power by using various SMA based and 
GWO based controllers. Table 2 shows that SMA based controller gives better results as compared to GWO 
based controller under bilateral based transaction. 


0.75 0.1 05 025 0 03 
—lo2s! ..... _ Jot _|o2 025 0 0 
APF =| g | Pisco = 154 | PUDPM = IG (996° 1 07 
05 0.1 03 025 0 0 

0.4} 4 al 


SMA-PID 


GWO-PID 


— — -SMA-PI 


— — -GW0-PI 4 


Frequency deviation in area-1(Hz) 


Time(Sec) 


(a) 


SMA-PID 
4 —— Gwo-Pid 
i — — -SMAPI 
1 ~~ -swo-rl 


Rati A 
= UUNID, die og 
Ie 


AIA HRA 
sek cipal Naa saci ge ENS WSs a 

+ A Jg 
Vy ININA w P See ey a u u 
e S W we Vey 


V uju y 


Frequency deviation in area-2(Hz) 


F i L I i 
o 1 2 3 4 5 6 
Time(Sec) 


(b) 


—— SMAPID 
——Gwo-ip 
—— -SMAPI 
---6w0PI 


Tie-line power deviation(p.u) 


` i 
AA AAAA 
pi A A 
\ y y A A N N Ny 

Tah ys. 


AN 4 
uN 
J 
Mi N v 
\n f i Iy v s 
u 


Time(Sec) 


(c) 


Figure 4. These figures are; (a) deviation of frequency in area-1, (b) deviation of frequency in area-2, 
(c) deviation of tie-line power under bilateral based transaction for 1% step load disturbance 


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Table 2. Comparison of peak overshoot, undershoot, and settling time using various controllers for bilateral 
based transcation 


S. No % Peak overshoot (p.u) % Peak undershoot (p.u) Settling time (Sec) 
Af, Af, APiie Af, Af APtie Af; Af, — APic 
GWO-PI 0.35 0.3 - 0.15 0.09 0.06 42 42 42 
SMA-PI 0.33 0.26 - 0.14 0.08 0.057 3.8 3.8 3.9 
GWO-PID 0.03 0.06 - 0.18 0.025 0.056 2.5 28 3.2 
SMA-PID 0.02 0.05 - 0.16 0.02 0.0055 22 21 23 


5.3. Case 3: Contract violation 
Contract violation occurs when the disco wants more electricity than the actual value, the contract is 


disrupted. There is no genco contracting out of this surplus electricity. This uncontracted electricity should be 
provided by a genco in the same area as the disco. Consider case-2, which requires additional power of 0.1 
p.u MW to a disco 1. Figure 5 (a) shows the deviation of frequency in area-1, Figure 5 (b) shows the 
deviation of frequency in area-2 and Figure 5 (c) shows the deviation of tie line power by using various SMA 
based and GWO based controllers. Table 3 shows that SMA based controller gives better results as compared 
to GWO based controller under contract violation based transaction. 


0.4 


Hl —— SMA-PID | 
——Gwo-Pip 
— —-SMA-PI 
~~ -GW0-PI 


0.3 H 


0.2} 


0.1} 


erh fy A ath A a EO RA Rn 
+ [R Lisbon LY 

Ara y 

GONE 


i 
i SMa U = 
1 A IA ent T E al 
Vow Wow G ww A 


Frequency deviation in area-1(Hz) 


-0.1 


-0.2 — 
2 3 4 5 6 
Time(Sec) 


(a) 


05 


o 
ES 
T 


SMA-PID 

ay Gwo-PID 
= — -SMA-PI 

a —-—-GwoPl 4 


o 
i 


Frequency deviation in area-2(Hz) 
o 
R 
T 


o 
o a 
T 
2 
-77 
Y 
¢ 
2 Pe 
« 
spe 
+ 
< 
7 
g 
y 
lA 
4 


Time(Sec) 


(b) 


SMA-PID 


Gwo-FID 
— — -SMA-PI 


— — -Gw0-PI 


Tie-line power deviation(p.u) 


Time(Sec) 


(c) 


Figure 5. These figures are; (a) deviation of frequency in area-1,5, (b) deviation of frequency in area- 2; 5, (c) 
deviation of tie-line power under contract violation for 1% step load disturbance 


Load frequency control of thermal system under deregulated environment using ... (Sambugari Anil Kumar) 


2228 


o ISSN: 2088-8694 


Table 3. Comparison of peak overshoot, undershoot, and settling time using various controllers for contract 


violation based transcation 


S. No % Peak overshoot (p.u) % Peak undershoot (p.u) Settling time (Sec) 
Af, Af, APtie Af, Af APie Afi Ab  APi 
GWO-PI 0.4 0.42 - 0.1 0.08 0.08 3.8 3.2 3.8 
SMA-PI 0.38 0.4 - 0.08 0.07 0.08 3.2 2.8 3.6 
GWO-PID - 0.09 - 0.2 - 0.082 22 2.5 3.3 
SMA-PID - 0.07 - 0.2 - 0.082 2 2.3 3.1 


6. CONCLUSION 


This paper examines the performance of a PID controller in deregulated market structure for various 


transactions and contract violations. In the power system, load demand is a difficult challenge to solve since it 
requires the design of various optimum controllers. The main task of the controller is to ensure that the 
frequency is maintained and the voltage magnitude is constant at all times. The DPM approach is implemented. 
A comparison of the two controllers reveals that the SMA based PI, PID controller outperforms the GWO based 
PI, PID controller in terms of settling time, overshoot, and undershoot. 


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Load frequency control of thermal system under deregulated environment using ... (Sambugari Anil Kumar)