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Load Frequency Control of Multi-interconnected Renewable Energy Plants Using

Multi-Verse Optimizer

Article in Computer Systems Science and Engineering · March 2021

DOI: 10.32604/csse.2021.015543

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Computer Systems Science & Engineering Tech Science Press
DOI:10.32604/csse.2021.015543
Article

Load Frequency Control of Multi-interconnected Renewable Energy Plants

Using Multi-Verse Optimizer
Hegazy Rezk1,*, Mohamed A. Mohamed2, Ahmed A. Zaki Diab2 and N. Kanagaraj1

1
College of Engineering at Wadi Addawaser, Prince Sattam Bin Abdulaziz University, Wadi Addawaser, 11991, Saudi Arabia
2
Electrical Engineering Department, Faculty of Engineering, Minia University, Minia, 61111, Egypt


Corresponding Author: Hegazy Rezk. Email: hr.hussien@psau.edu.sa
Received: 27 November 2020; Accepted: 27 December 2020

Abstract: A reliable approach based on a multi-verse optimization algorithm

(MVO) for designing load frequency control incorporated in multi-interconnected
power system comprising wind power and photovoltaic (PV) plants is presented
in this paper. It has been applied for optimizing the control parameters of the load
frequency controller (LFC) of the multi-source power system (MSPS). The MSPS
includes thermal, gas, and hydro power plants for energy generation. Moreover,
the MSPS is integrated with renewable energy sources (RES). The MVO algo-
rithm is applied to acquire the ideal parameters of the controller for controlling
a single area and a multi-area MSPS integrated with RES. HVDC link is utilized
in shunt with AC multi-areas interconnection tie line. The proposed scheme has
achieved robust performance against the disturbance in loading conditions, variation
of system parameters, and size of step load perturbation (SLP). Meanwhile, the simu-
lation outcomes showed a good dynamic performance of the proposed controller.

Keywords: Load frequency control; multi-verse optimization; multi-area power

system; renewable energy sources

1 Introduction
The utilization of renewable energy expanded significantly everywhere throughout the world, soon after
the primary huge oil crisis in the late seventies. Besides, with the worldwide ecological contamination and
energy crisis, sustainable power sources, for example, photovoltaic (PV) and wind [1–7] have assumed an
influential role in electricity generation. In any case, the yield of PV and wind power generation is
normally oscillating because of the discontinuity and haphazardness of sun-powered and wind vitality,
and results in a vigorous effect on the grid in case of grid-connected mode. As of late, the integration of
energy storage (ES) into renewable energy sources (RES) has turned out to be a standout amongst the
most pragmatic solutions for taking care of this issue [8–17]. The principal roles of ES are to level
the variance and increment the infiltration of RES, update the transmission line capability, increment the
power quality, keep up the system dependability and soundness [18]. With the integration of RES,
the complexity of the power system operation is increasing. Moreover, the system operating point varies
instantaneously, and subsequently the system encounter deviation in frequency [19]. This deviation leads

This work is licensed under a Creative Commons Attribution 4.0 International License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original
work is properly cited.
220 CSSE, 2021, vol.37, no.2

to bothersome impacts. Load frequency control (LFC) is one of the essential auxiliary administrations which
assume a critical role in keeping up the frequency of the system at its ostensible value [20]. Due to the viral
role of LFC, optimal control-based controllers have been studied in many research. Parmar et al. [21] have
studied the two-area LFC system with diverse power generation sources. The optimal feedback controller
gains have been calculated to minimize the quadratic performance index. They have realized better
dynamic performance for the system considering shunt DC/AC tie-line in the presence of parameter
changes. The controller to the hybrid RES with Fuel Cell (FC) system has been introduced by Rawat
et al. [22]. The system consists of a Micro-hydropower system (MHP), PV, Diesel Generator (DG) and
(FC). They have proved the efficiency of the tuned proportional integral derivative (PID) rather than the
proportional-integral (PI) controller over system stability and performance. Kabiri et al. [23] have
proposed a controller to regulate thermal units and determine the amount of their generated power to
compensate PV system and regulate frequency oscillations to improve the frequency in the smart grid.
The authors in Liu et al. [24] have introduced PID and fuzzy logic controllers to the modeled hybrid
hydro systems with the synthesis of wind, thermal, solar, and diesel plants. Satisfied performance and
robustness were achieved for both controllers. Lotfy et al. [25] proposed a Polar Fuzzy (PF) control
strategy for a multi-unit energy system. In this study, the authors have utilized the electric vehicle (EV)
battery as an enormous energy storage unit to promote the system frequency stability. They have
considered the error control signal of the power supply and frequency deviation. In Zeng et al. [26] have
presented an adaptive model predictive load frequency control (MPC) method for the multi-area power
system (MAPS) in discrete time form with PV generation. They have considered a dead band for
governor and generation rate constraint for the steam turbine. They have ensured the priority of the
proposed MPC method on the conventional PI control methods over dynamic and steady-state
performance for the nominal condition, parameters uncertainties cases, load disturbance. In Mohamed
et al. [27] have proposed several frequency control techniques for variable speed wind turbines and solar
PV generators. These techniques have allowed renewable energy sources to keep a certain amount of
reserve powers and then release the reserved power according to frequency events. Mu et al. [28] have
investigated the LFC problem of a standalone microgrid with PV power and (EVs) which are used as
large-scale energy storage units. An observer-based integral sliding mode (OISM) controller has
succeeded to regulate the deviated frequency of the power system. Pandey et al. [29–31] have studied the
LFC of MAPS with multi-power generation sources utilizing HVDC link parallel to AC two areas
interconnection tie-line. They have applied differential evolution for tuning the controller parameters to
their best values to realize a satisfying system performance. Other control schemes for LFC in power
systems with or without integration of RES based on artificial intelligence and optimization algorithms
have been introduced in Golpira et al. [32,33].
In this paper, a novel optimized controller based-Multi-Verse Optimization algorithm (MVO) has
been presented to regulate the LFC. The proposed controller is applied for a single area and
interconnected multi-area MSPS. MATLAB/SIMULINK has been utilized to simulate the control system
with diverse operating conditions.

2 Controller Design
The proposed system includes hydro, thermal with reheat turbine, gas, PV, and wind power plants. Each
unit has been modeled linearly for simulation as shown in Fig. 1. The symbols of the system have been
presented in Appendix I. The following are the controller design for multi-source single area power
system (SAPS) and MAPS:
CSSE, 2021, vol.37, no.2 221

1/R3 1/R2 1/R1

Thermal power plant with reheat turbine
UT -
1 1 s kR TR 1
1 sTSG 1 sTR 1 sTT
KT +

Hydro power plant with governor PD

UH
-
1 1 sTRS 1 sTW
KH + f
1 sTGH 1 sTRH 1 0.5sTW
-

Gas turbine power plant + K PS

UG - 1 sTPS
1 1 sX c 1 sTCR 1
KG +
cg sbg 1 sYc 1 sTF 1 sTCD

PV power plant
U PV
K1 a2 s +
a1 s a3 s

Wind power plant

U wind
TWT +
1 sTWT

Figure 1: Transfer function block diagram of the SAPS with integral controllers

2.1 Controller Design for Multi-Source SAPS

The main idea in this research is to decide the optimal LFC controller gains to quickly minimize the
system frequency deviation. For this dilemma, the MVO algorithm has been applied for minimizing the
defined objective function with desired specifications and constraints. The Integral of time multiplied
squared error (ITSE) in automatic generation control (AGC) has been considered as an objective function
and the controller parameters bounds as the constraint is expressed as the following:
Z Tmax
J ¼ ITSE ¼ t ðDf Þ2 dt (1)
0

Kmin < controller parameter < Kmax (2)

where, Df is the deviation of the system frequency and Tmax is the simulation time. Kmin and Kmax are the
boundaries of the controller parameters. The control system of SAPS is shown in Fig. 2.

2.2 Controller Design of Multi-Source MAPS

The proposed procedure has been utilized to design the controller for the system described in Fig. 3.
Every system incorporates reheating thermal, gas, and hydro generating plants beside the PV and wind
power plant. The block diagram of this system integrated with RES has appeared in Fig. 4.
222 CSSE, 2021, vol.37, no.2

1/R3 1/R2 1/R1

Thermal power plant with reheat turbine
-
UT
Optimal PI 1 1 s k RTR 1
Controller 1 sTSG 1 sTR 1 sTT
KT +
Hydro power plant with governor ' PD
-
Optimal PI UH 1 1 sTRS 1 sTW
Controller 1 sTGH 1 sTRH 1 0.5sTW
KH +
-
K PS
Gas turbine power plant +
- 1 sTPS
'f
UG
Optimal PI 1 1 sX c 1 sTCR 1
Controller cg sbg 1 sYc 1 sTF 1 sTCD
KG +

PV power plant

Solar Irradiance and PV U PV K1 a2 s

Power Variation a1 s a3 s
+

Wind power plant

U wind
Wind Speed and Wind TWT
Power Variations 1 sTWT
+

Figure 2: Transfer function block diagram of SAPS with optimized controllers

AC Tie Line
Control area 1
Control area 2
Thermal, Hydro,
Thermal, Hydro,
Gas, PV and Wind
Gas, PV and Wind
Converter Converter
DC Link

Figure 3: The two-area power system interconnected through AC-DC parallel tie lines

The LFC scheme has been tested with the proposed optimized controller with two cases: one with AC
tie-line only and the other with AC/DC tie-lines. Furthermore, the control scheme has been tested under
change of load power and parameters variations. The transport delays have been neglecting for simplicity.
The following is the objective function for MAPS:
Z Tmax  
ITSE ¼ t ðDf1 Þ2 þ ðDf2 Þ2 þ ðDPtie Þ2 dt (3)
0

where, Df1 and Df2 are the deviations of system frequency, and DPtie is the power incremental change
in tie line.

3 Multi-Verse Optimizer
MVO algorithm has been inspired by the theory of multi-verse as presented in Mirjalili et al. [34,35].
The mathematical model of the MVO algorithm can be described as: firstly, the universes have to be
sorted based on their rise rates and the roulette wheel select one universe to be the white holes in every
sample, based on the following expressions:
CSSE, 2021, vol.37, no.2 223

1 1 1
R3 R2 R1
Thermal power plant with reheat turbine
B1 -
UT 1 Area 1
1 1 s k RTR 1
PI Controller
1 sTSG 1 sTR 1 sTT KT +

Hydro power plant with governor PD1

-
U H1 1 1 sTRS 1 sTW
PI Controller 1 sTGH 1 sTRH 1 0.5sTW
KH + -
+ ACE1

Gas turbine power plant + K PS

- f1
+ U G1 -
1 sTPS
1 1 sX c 1 sTCR 1
PI Controller cg sbg 1 sYc 1 sTF 1 sTCD KG +
-
PV power plant
K DC
Solar Irradiance and PV U PV 1
U PV 1 K1 a2 s
Power Variation
a1 s a3 s
+ 1 sTDC

Wind power plant UWT

TWT
Wind Speed and Wind
1 sTWT
+
Power Variation

+
2 T12
s
-

Thermal power plant with reheat turbine a12

a12
UT 2 1 s k RTR
1 1
PI Controller
1 sTSG 1 sTR 1 sTT
KT +
-
PD 2
Hydro power plant with governor
UH 2 1 1 sTRS 1 sTW
PI Controller 1 sTGH 1 sTRH 1 0.5sTW
KH + -
+ ACE2
- f2
Gas turbine power plant
- K PS
1 sTPS
+ UG2 1 1 sX c 1 sTCR 1 +
PI Controller cg sbg 1 sYc 1 sTF 1 sTCD KG +
- -
PV power plant
U PV 2 U PV 2
K1 a2 s
Solar Irradiance and
a1 s a3 s
+ K DC
PV Power Variation 1 sTDC

B2 Wind power plant

UWT
Wind Speed and Wind TWT
Power Variation 1 sTWT +

1 1 1
R1 R2 R3 Area 2

Figure 4: Transfer function block diagram of the MAPS with HVDC link
2 3
x11 x21 . . . xd1
6 x1 x2 . . . xd 7
6 2 2 17
U ¼6 6 : : : : 77 (4)
4 : : : : 5
x1z x2z . . . xdz
 j
j xk ; r1 , NlðUiÞ
xi ¼ (5)
xji ; r1 . NlðUiÞ
224 CSSE, 2021, vol.37, no.2

Start

Initialize U with dimension i*d

Define lb, ub, L and best universe

Iter=1

i=1

Calculate inflation rates of all universes

i=i+1 Perform the roulette wheel i=i+1

Update WEP and TDR

No
Last universe?
Yes Yes
Iter<L

No
Print the best universe, and inflation rate

End

Figure 5: MVO flowchart

where, d and z are the number of variables and universes, respectively. xjk specifies the j-th parameter of i-th
universe, NlðUiÞ is the normalized inflation rate of the i-th universe, r1 is a random number in [0,1], Ui
displays the i-th universe, and xji designates the j-th parameter of k-th universe nominated by a roulette wheel.
The procedure described in Fig. 6 can be described as pursues:
8  
< Xj þ TDR:ðubj  lbj :r4 þ lbj Þ r3 , 0:5; r2 , WEP
xji ¼ Xj  TDR: ðubj  lbj :r4 þ lbj Þ r3  0:5; r2 , WEP (6)
: j
xi ; r2  WEP
where, Xj demonstrates the j-th parameter of best universe so-far, lbj displays the lower bound of j-th
variable, ubj is the upper bound of j-th variable, xji demonstrates the j-th parameter of i-th universe, and
r2, r3, r4 are random numbers in [0,1]. TDR, and WEP are the rate of traveling distance and the
existence probability of wormholes, respectively and can be calculated as the following:
 
max  min
WEP ¼ min þ l: (7)
L
CSSE, 2021, vol.37, no.2 225

l 1=p
TDR ¼ 1  (8)
L1=p
where, L expresses the maximum iterations, and l specifies the recent iteration. p is the exploitation accuracy
over the iterations. Fig. 7 presents the flowchart of MVO.

Figure 6: Comparison between the convergence curves of MVO and PSO

Figure 7: Wind power and PV power variations

226 CSSE, 2021, vol.37, no.2

4 Results and Discussions

The MVO algorithm has been utilized for the simulation and validation of the proposed control scheme.
The simulation has been carried out using Core™ i5-4210U CPU, 1.7 GHz, and 8 GB RAM computer. The
MVO has been simulated with 10 independent runs to validate the proposed procedure for each case. The
obtained results by MVO are compared with PSO. The standard deviation values are 0.0565 and
0.1119 respectively for MVO and PSO methods. Also, the minimum cost values are 3.1626e-04 and 3.3e-03
respectively for MVO and PSO methods. A comparison between the convergence curves of MVO and
PSO for several runs is presented in Fig. 5. The results confirmed the robustness of the MVO algorithm.
The values of the best solution of the optimized PI controllers based on MVO and PSO have been
recorded in Tab. 1.

Table 1: Optimal gains of PI controllers using MVO and PSO

Area Plant MVO PSO
Optimized KP Optimized KI Optimized KP Optimized KI
First Area Reheat thermal 0.01 0.01 0.093304 0.007967
thermal 0.010115 5.041982 0.000148 0.00394
Hydro 0.07197 0.01 0.189913 0.013687
Second Area Reheat thermal 0.01 2.631681 0.005863 2.702066
thermal 0.662557 0.24972 0.052063 1.017917
Hydro 0.278221 0.103811 0.058338 1.900377

To test the performance of the proposed controller with parameters variation, the wind power, and PV
power variations have been assumed as shown in Fig. 7. To achieve this target, 5 cases of study have been
introduced against load disturbance, frequency variation as the following:

4.1 Multi-Source SAPS

To ponder the dynamic behavior of the Multi-Source SAPS with MVO optimized controllers, 3 cases of
study have been reproduced as the following:
4.1.1 Case#1
The 1st case has studied the performance of the control system against the integration of PV and wind
power plants into the system while maintaining the load disturbance unchanged at initial simulation at
0.01 pu. The integration of the PV and wind power plants into the system was at 10 s. The frequency
deviation response has appeared in Fig. 8. As presented in Fig. 8, the proposed MVO optimized PI
controller has quickly regulated the frequency against the penetration of the PV and wind power plants.

4.1.2 Case#2
In this case of study, a 10% SLP is applied and removed while maintaining the other system parameters
at nominal values as appeared in Fig. 9. It has proved that the proposed MVO optimized PI controller gives a
good dynamic response, however having a small peak overshoot against load disturbance in presence of
variation of PV and wind power.
CSSE, 2021, vol.37, no.2 227

Figure 8: Time-domain system frequency response: Area frequency deviations (Case#1)

Figure 9: Time-domain system response: Load disturbance variations and Area frequency deviations (Case#2)

4.1.3 Case#3
In this case, a 10% SLP is applied as shown in Fig. 10. Moreover, the time constants of all power units in
the system have been varied by +25% of their nominal values. The system performance with parameters
uncertainty is shown in Fig. 10. This figure assures the ability of the optimized PI-MVO controller to
interact with parameters variation, moreover, regulate the frequency deviation to zero.

4.2 Multi-Source MAPS

4.2.1 Case#4
In this case, a 1% SLP has been applied at t = 0 sec for area 1, and at 20 sec for the area 2 while
maintaining the other system parameters. The tie-line power and frequency deviation response have been
presented in Fig. 11. Fig. 11 has proved a good dynamic response of the proposed optimized controller,
however having a small peak overshoot against load disturbance, PV and wind plants variations.

4.2.2 Case#5
In case#5 the SLP has been applied as appeared in Fig. 12. In addition, the time constants of each power
unit have been changed by +25% of their nominal value. The simulation results, Fig. 13 validate the quality
of the proposed controller.
228 CSSE, 2021, vol.37, no.2

Figure 10: Time-domain system response with parameters uncertainty: Load disturbance variations and
Area frequency deviations (Case#3)

Figure 11: Time-domain system responses of: Area frequency deviations for the two areas and Tie-line
power (Case#4)

Figure 12: Time-domain system responses of load disturbance

CSSE, 2021, vol.37, no.2 229

Figure 13: Time-domain system responses of: Area frequency deviations for the two areas and Tie-line
power (Case#5)

5 Conclusions
An MVO algorithm has been utilized in this paper to optimize the control parameters of the LFC of a
predefined power system. This system comprises thermal, gas and hydro power plants as the conventional
sources of power generation and PV, and wind power plants as RES. The algorithm has been applied to a
single area and a two-area power system. The system performance has been observed on the basis of
dynamic parameters and frequency overshoot. The Examination of dynamic responses revealed that the
application of MVO improves the transient responses extraordinarily and enhances the frequency overshoot.
Funding Statement: This project was supported by the Deanship of Scientific Research at Prince Sattam Bin
Abdulaziz University under the research project No 2020/01/11742.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the
present study.

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Appendix

R1, R2, R3 The regulation parameters of thermal, hydro and gas units
UT, UH and UG Control outputs for of thermal, hydro and gas
KT, KH, KG Participation factors of thermal, hydro, and gas
TT (sec.) Steam turbine time constant
TW (sec.) The nominal starting time of water in penstock
TRH (sec.) Hydro turbine speed governor transient droop time constant
TF Gas turbine fuel time constant
TCD (sec.) Gas turbine compressor discharge volume-time constant
TSG (sec.) Speed governor time constant of thermal unit
Tr (sec.) Steam turbine reheat time constant
TRS (sec.) Hydro turbine speed governor reset time
TGH (sec.) Hydro turbine speed governor main servo time constant
XC (sec.) The lead time constant of gas turbine speed governor
cg Gas turbine valve positioner
TCR (sec.) Gas turbine combustion reaction time delay
KWT Wind turbine constant
YC (sec.) The lag time constant of gas turbine speed governor
bg Gas turbine constant of valve positioner
TWT (sec.) Wind turbine time constant
a1, a2, a3, K1 PV plant parameters

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