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Multi-objective Optimal Power Flow Using Improved Multi-objective Multi-verse Algorithm


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This study proposes an improved multi-objective multi-verse optimization (IMOMVO) algorithm for solving multi-objective optimal power flow (MOOPF) problem with uncertain renewable energy sources (RESs). Cross and self-pollination steps of flower pollination algorithm (FPA) along with crowding distance and non-dominating sorting approach is incorporated with the basic MOMVO algorithm to further enhance the exploration, exploitation and for well-distributed Pareto-optimal solution. To confirm the effectiveness of the proposed IMOMVO algorithm, modified IEEE 30-bus system with security constraints is utilized by considering the total generation cost and active power loss minimization. The simulation results obtained with IMOMVO is compared with MOMVO, NSGA-II, and MOPSO, which reveals the capability of the proposed IMOMVO in terms of solution optimality and distribution.
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Multi-objective Optimal Power Flow
Using Improved Multi-objective
Multi-verse Algorithm
Muhammad Abdullah1, Nadeem Javaid1(B
), Annas Chand2,
Zain Ahmad Khan2, Muhammad Waqas1, and Zeeshan Abbas1
1COMSATS University Islamabad, Islamabad 44000, Pakistan
2COMSATS University Islamabad, Abbottabad 22010, Pakistan
Abstract. This study proposes an improved multi-objective multi-verse
optimization (IMOMVO) algorithm for solving multi-objective optimal
power flow (MOOPF) problem with uncertain renewable energy sources
(RESs). Cross and self-pollination steps of flower pollination algorithm
(FPA) along with crowding distance and non-dominating sorting app-
roach is incorporated with the basic MOMVO algorithm to further
enhance the exploration, exploitation and for well-distributed Pareto-
optimal solution. To confirm the effectiveness of the proposed IMOMVO
algorithm, modified IEEE 30-bus system with security constraints is uti-
lized by considering the total generation cost and active power loss min-
imization. The simulation results obtained with IMOMVO is compared
with MOMVO, NSGA-II, and MOPSO, which reveals the capability of
the proposed IMOMVO in terms of solution optimality and distribution.
1 Introduction
The optimal power flow (OPF) is considered a vital optimization tool for efficient
operation and planning of the power system. The OPF is used to determine the
control variables at a specific time for the power system operation in order
to optimize (maximize or minimize) different objective functions (OFs) while
assuring the technical feasibility of the solution [1].
Limited reserves of fossil fuels and environmental protection issues have
raised the concern to integrate renewable energy resources (RESs) into the grid.
Wind power plants and solar photovoltaic are amongst the most common RESs.
A lot of research work has been done on classical OPF, which consider only
thermal generators. Classical OPF, which is by itself non-linear and non-convex
and large scale optimization problem because of different OFs and constraints,
however, by incorporating uncertain RESs further increase the complexity of the
problem [2].
The OPF was firstly introduced in 1962 by Carpentier. Since the inception of
OPF, many optimization methods have been introduced to the solution of OPF
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L. Barolli et al. (Eds.): WAINA 2019, AISC 927, pp. 1071–1083, 2019.
1072 M. Abdullah et al.
problems. These approaches can be divided into classical numerical analysis and
modern metaheuristics algorithms. The classical method includes linear pro-
gramming, quadratic programming, interior point, and dynamic programming
etc. These techniques are inadequate for large-scale problems because they are
comprised of complex, lengthy calculation and they are excessively dependent on
initial guess values. In the past few years, different metaheuristic algorithms have
been developed to overwhelm the deficiencies of the classical methods [2,3]. Some
of these algorithms are; whale optimization algorithm (WOA), particle swarm
optimization algorithm (PSO), moth-swarm algorithm (MSA), modified firefly
algorithm (MODFA), non-dominating sorting genetic algorithm (NSGA), differ-
ential evolution (DE), elephant herding optimization (EHO) technique, Teaching
learning-based optimization (TLBO) technique etc. In any case, due to the incon-
sistency of the OPF solution for different objectives, no heuristic algorithm can
be proven optimal for solving all these objectives, Hence, there is always a room
for new techniques and algorithms that can effectively solve multiple objectives
of OPF.
The OPF problem is considered as single-objective if only one objective func-
tion is reckoned to be optimized. However, OPF problem needs to optimize
conflicting objectives in real world, simultaneously. For solving multi-objective
optimization (MOO) problems, two techniques are used in the literature: a pri-
ori and a posteriori [4]. In the first MOO technique, the MOO problem is con-
verted into a single objective (SO) by assigning weight to different objectives and
aggregating them. The importance of each objective is dictated by the weights
assigned to it, which is generally set by an expert. Solving the problem with this
approach does not require any modification in the algorithm. In posteriori MOO
approach, there is no need to define the weights by an expert. In this method,
different solutions are there for the decision maker as compared to the former
one. There is no need to define weights for each objective by an expert and the
Pareto frontier is approximated, even in a single run [5,6].
Increasing the participation of consumers in the electrical network operations
and accommodation of RESs are the most important features of smart grids. The
role of OPF in smart grids is very vital in order to decrease the transmission,
distribution losses, emission of fossil fuels, and the energy generation cost. Sub-
sequently, decreasing the electrical power consumption and prices, concurrently,
enabling consumers and electrical utilities to regulate the demand [711].
2 Problem Formulation of MOOPF
The main goal of solving OPF problems is to optimize different objectives by
adjusting control parameters. In MOOPF problems, two are more objectives are
optimized simultaneously subject to the constraints. The MOOPF mathematical
formulation can be described as below [12,13].
fobj =min
Multi-objective Optimal Power Flow 1073
subject to:
gkx, ´v)=0 k=1,2,...,G (2)
hlx, ´v)0l=1,2,...,L, (3)
where, fobj are the OFs to be minimized, gkx, ´v)isthekth equality constraint
(EC) which actually represent the load flow equations [14]. The inequality con-
straints (IC) are expressed by hx, ´v). ´xand ´vare the vectors of state (dependent)
variables and control (independent) variables respectively [15].
The state variables are:
(1) Real power at swing bus (PG1).
(2) Reactive power output of generators (QG).
(3) Voltage at P-Q (Load) buses (VL).
(4) Loading of transmission lines (SL).
The vector of static variables can be written as:
The Control variables are:
(1) Voltages at generation buses (VG).
(2) Generation buses active power output (PG).
Besides these, tap settings of transformer, and compensation of shunt VAR (reac-
tive power) compensators can also be considered as control parameters.
Accordingly, vector ´vcan be expressed as:
NT ].
2.1 Objective Functions
Two OFs are considered in this paper, i.e. minimization of generation cost and
power loss, whose details are provided subsequently.
2.1.1 First Objective: Minimization of Generation Cost
Total generation cost comprises of the operation cost of thermal generators and
RESs along with penalty and reserve cost, which are described below.
Thermal Power Generator Cost Model
For realistic cost model of thermal generators, valve point effect is considered
[16]. In a thermal generating unit steam is regulated by valves to run the turbine
through a separate nozzle group. To achieve maximum efficiency, every nozzle
group operate at its full output [21].For the required output, the valves are
1074 M. Abdullah et al.
operated in sequence, which results in the non-continuous cost curve. The cost
model of thermal generators considering valve loading effect is given by [17]:
where, NTG is the number of thermal generators. ´ai,´
bi, and ´ciare the cost
coefficient of ith generator, producing output power PTG
diand ´eiare the
coefficients of valve point loading effect. The values of thermal units coefficients
are listed in Table 1.
Table 1. Thermal generators coefficient
Cost coefficients ´a ´
b´c ´
GTh10 2 0.00375 18 0.037
GTh201.75 0.0175 16 0.038
GTh803.25 0.00834 12 0.045
Cost Model of Renewable Energy Sources
Generation from RESs does not require any fuel source for its operation. There-
fore, cost function does not exist, except maintenance cost, if the RESs are owned
by independent system operators (ISO). However, in the case when RESs are
operated by private bodies, the ISO pays to them accordingly to the scheduled
power contractually agreed [18].
The direct cost function of the kth wind farm in terms of scheduled power is
given by [19]:
where PWis the scheduled power and gwis the direct cost coefficient of the wind
power unit. Similarly, the direct cost for the solar PV unit with scheduled power
PPV , and cost coefficient hpv is given by:
CPV (PPV )=hpvPPV .(6)
The third renewable energy resource that is considered in this study is the
combination of wind and run of river small hydro generation plant. The scheduled
power is jointly delivered by wind and hydro generators. The hydro generation
considered in this work is of 5 MW, which is proportional to the river’s flow rate
[20]. The direct cost of the combined wind and hydro plant is described as:
CWH(PWH)=gwhPWH =gwPWH,w +ghPWH,h,(7)
Multi-objective Optimal Power Flow 1075
where, PWH represent the scheduled real power from the combined plant, PWH,w
and PWH,h are the electrical energy contribution from the wind and hydro units
respectively. gwis the direct cost coefficient of wind unit and ghis that of hydro
As wind energy is stochastic in nature, the actual power produced may be less
or more than scheduled power. Therefore, the ISO must have reserve generating
capability to meet the demand. Reserve cost for the wind unit can be calculated
as [21]:
CRW,i (PWsh,i PWac,i)=krw,i(PWsh,i PWac,i)
=krw,i PWsh,i
(PWsh,i pw,i )fw(pw,i)dpw,i.(8)
In the case when the output power of the wind generators is greater then the
scheduled power, the ISOs pay penalty cost if the surplus power is not utilized
by them by reducing the power of thermal generators.
The penalty cost of wind plant can be mathematically described as:
CPW,i (PWac,i PWsh,i)=kpw,i(PWac,i PWsh,i)
=kpw,i PWr,i
(pw,i PWsh,i)fw(pw,i)dpw,i,(9)
where, PWsh,i is the scheduled power, PWac,i is the available power from wind
plant, PWr,i is the rated power, and fw(pw,i)is the probability density function
of wind power. Similarly the reserve and penalty cost of solar and combined
wind and hydro can be calculated. The values of direct, reserve, and penalty
cost coefficients for RESs are provided in Table 2.
The output power of wind power units is directly proportional to wind speed.
Wind speed probability is predominantly represented by Weibull, probability
distribution function (PDF) [17,21,22].
The power given by PV arrays depends on solar irradiance. The probability
distribution of solar irradiance Gsis represented by lognormal PDF [21,23].
Gumbel distribution correctly represent the river flow rate [24,25]. Summary of
the number of turbines, the rated power output from RESs, and the values of
PDF parameters are listed in Table 3.
2.1.2 Second Objective: Minimization of Real Power Loss
The active power loss in the branches of the power system is unavoidable because
of inherent resistance of lines. The real (active) power loss can be mathematically
written as,
f2(x, u)=Ploss =
Gij [V2
j2ViVjcos(δij )] (10)
Where nL is the number of branches, Gij is the conductance of the branch which
linked together the ith and jth bus, and δij is the voltage angle between them.
Viand Vjare the voltages of bus iand bus j. The magnitude of these voltages
are calculated through newton-Raphson load flow equation.
1076 M. Abdullah et al.
Table 2. RESs direct, reserve, and penalty cost coefficient
Direct cost coefficient
Wind (at bus number: 5, 13) gw1=1.6,
Solar PV (at bus number 11) hs=1.6
Small hydro (at bus number 13) gh=1.5
Reserve cost coefficient
Wind (at bus number 5) krw =3
Solar PV (at bus number 11) krs =3
Combined wind and hydro (at bus number 13) krwh =3
Penalty cost coefficient
Wind (at bus number 5) kpw =1.5
Solar PV (at bus number 11) kps =1.5
Combined wind and hydro (at bus number 13) kpwh =1.5
2.2 System Constraints
MOOPF is a non-linear, non-concave optimization problem, which requires to
satisfy different equality constraints (ECs) and inequality constraints (ICs).
These constraints are described as follow.
2.2.1 Equality Constraints
The ECs in MOOPF comprising of real and reactive power load flow equations
[26], which stipulates that the real and reactive power generation must be equal
to the load demand and power losses in the network. The ECs can be mathe-
matically described as:
Vl[Gij cos(δij +βij sin(δij ))] = 0 iNB, (11)
Vl[Gij cos(δij +βij sin(δij ))] = 0 iNB. (12)
2.2.2 Inequality Constraints
ICs are actually the active, reactive power generation limits, security constraints
of lines, and voltage limits of generation and load buses [17,27].
The constraints of generators are:
Multi-objective Optimal Power Flow 1077
Table 3. PDF parameters for uncertain RESs.
Wind power generator Solar PV unit
Tota l w ind
Cumulative rated
power (MW)
Weibull PDF
rated power
25 75 k=2, c=9 60 μ=6,
Combined wind+small-hydro
Tota l w ind
Rated wind
power (MW)
Weibull PDF
Small hydro
rated power
Gumbel PDF
15 45 k=2, c=10 5λ= 15,
TG,i PTG,i Pmax
TG,i i=1,...,N
WG,j PWG Pmax
WG ,(14)
PV,k PPV Pmax
PV ,(15)
WHG,j PWHG,j Pmax
TG,i QTG,i Qmax
PV ,(19)
G,i VG,i Vmax
G,i ,i=1,...,N
where, PTG,i is the active power generation of ith thermal unit, PWG,PPV,and
PWHG is the real power of wind farm, solar PV array, and combined wind and
hydro generators, respectively. Similarly, QTG,i,QWG,QPV,andQWHG are the
reactive power output of the thermal, wind, solar, and combined wind and hydro
generators. VG,i is the voltage of the ith generation bus.
Security constraints includes the voltage limits of P-Q buses and the trans-
mission lines loading capability, which are described as follow:
Lp VLp Vmax
Lp p=1,...,N
LB ,(22)
Slq Smax
lq q=1,...,N
Equation 22 represents the voltage limits for NLB number of load buses and
the line loading constraint is described in Eq. 23 for Nlbranches.
1078 M. Abdullah et al.
Table 4. Best results of two-objective for Case 1 of 30 bus power system at 500
2(MW) 23.6459 23.8473 20.0000 57.9310 20.6786 29.3117 24.8195 31.9106
5(MW) 42.5207 63.1317 46.3870 75.0000 44.7182 101.0292 44.7238 94.7263
8(MW) 10.0000 10.1696 10.0000 34.6162 10.1694 48.4191 10.1382 39.9864
11 (MW) 41.4415 54.7171 44.9287 60.0000 43.0685 66.2612 40.5211 68.7966
P(W+H)G13(MW) 36.4134 35.9545 32.5331 48.6378 34.8491 36.4088 32.1291 35.9207
1(p.u) 1.1000 1.1000 1.1000 1.1000 1.1137 1.0808 1.3422 1.2794
2(p.u) 0.9500 1.0921 1.0913 1.1000 1.0747 1.0813 1.2014 1.1614
5(p.u) 1.1000 1.0731 1.0989 1.0995 1.1697 1.0735 1.3208 1.2728
8(p.u) 1.1000 1.1000 1.1000 1.0958 1.1882 1.1506 1.3124 1.2888
11 (p.u) 1.1000 1.0975 1.0822 1.1000 1.1006 1.1565 1.3652 1.3513
V(W+H)G13 (p.u) 1.1000 1.0780 1.0999 1.0982 20.6786 1.0881 1.4777 1.2716
Cost ($/hr) 776.400 818.017 777.777 942.171 776.882 979.451 770.917 954.880
Power los s (MW) 5.526 3.515 5.275 1.760 5.166 1.376 3.572 0.999
3 IMOMVO Algorithm and Its Application to MOOPF
Many real-world optimization problems entail optimizing different objectives
simultaneously while meeting the constraints. These objectives are often con-
flicting in nature and the optimal value of all these objectives cannot be achieved
at the same time.
3.1 Basic MOMVO Algorithm
MOMVO optimization algorithm is based on the theory of the existence of multi-
verse, recently proposed by Mirjalili [28]. The inspiration of MOMVO is the inter-
action between universes through black, white, and worm wholes. The objects
from one universe move to another via tunnels (black, white holes), and move
within the universe or even from one universe to another through worm hole
3.2 IMOMVO Algorithm
The PF obtained by the MOMVO algorithm at higher times (iteration) is not
well distributed. Therefore, to further increase the exploration and exploitation
of MOMVO, levy flight and self-pollination steps of flower pollination algorithm
[30], is used to create a new set of universes. After finding the inflation rates of
both sets of universes, they are merged together. The solutions are sorted and
selected on the bases of domination level, and crowding distance approach is
Multi-objective Optimal Power Flow 1079
used to maintain the diversity of the non-dominated solution. The solutions are
truncated to the size of the archive to reduce computation time. The new solu-
tions are compared to the stored results in the archive and the better solutions
are replaced in the archive.
4 Simulation Results and Discussions
Modified IEEE 30-bus test system is considered to varify the effectiveness of the
proposed IMOMVO for the solution of MOOPF and its performance is compared
with the results of MOPSO, MOMVO, and NSGA-II optimization algorithm.
The codes of these algorithms are written in the MATLAB environment and
MATPOWER (MATLAB package) is used for power flow calculation. All the
simulations are performed on Intel Core i7, 2.00 GHz processor with an 8 GB
RAM personal computer. For the fair comparison of the proposed IMOMVO
with MOPSO, MOMVO, and NSGAII in terms of obtaining the best PF. The
size of the population (Np = 50) and numbers of iterations are taken the same
for all of these algorithms. The summary of the adapted 30-bus is provided in
Table 5.
Two conflicting objectives, total generation cost minimization, and power
loss minimization are solved simultaneously using proposed IMOMVO and its
performance is compared with other optimization algorithms. The PF obtained
from the simulation of these algorithms for solving MOOPF problem of modified
Fig. 1. Pareto optimum front obtained at 20 iterations.
1080 M. Abdullah et al.
Fig. 2. Pareto optimum front obtained at 100 iterations.
Fig. 3. Pareto optimum front obtained at 500 iterations.
Multi-objective Optimal Power Flow 1081
Table 5. Summary of the modified IEEE-30 bus system.
Item Quantity Details
Buses 30 6 generators buses and 24 load
Branches 41
Thermal generators Buses (TG
3 At bus number: 1,2, and 8. Bus
number 1 is a slack bus
Wind generator 1At bus number 5
Solar PV array 1At bus number 11
Wind generator+small hydro unit 1 At bus number 13
Control variables 11 The real power of generator buses
except for the slack bus and
voltages of all generator buses
Allowed range of load bus voltage 24 0.95 to 1.05 p.u.
Connected load 283.4 MW, 126.2 MVAr
IEEE 30-bus system is shown in Figs. 1,2,and3for 20, 100, and 500 runs. From
the simulation results, it is obvious that the PF obtained from IMOMVO per-
formed better than MOPSO, MOMVO, and NSGA-II, both at lower and higher
iteration (times) in term of solution optimality and distribution. The values of
the control variables for the best cost, best power loss, and the resultant OFs are
provided in Table 4. The PF obtained by MOMVO is better than MOPSO and
NSGA-II at lower iteration, however, at higher iteration, the PF obtained by
MOMVO is not well distributed. The proposed IMOMVO eliminated the limi-
tation of PF distribution of MOMVO algorithm by incorporating the crowding
distance and non-dominating sorting approaches and displayed the best results
both at lower and higher iteration.
4.1 Conclusion
In this study, IMOMVO algorithm has been proposed and applied to solve
MOOPF problem. The proposed algorithm was successfully implemented on
modified IEEE 30-bus power systems. The simulation results reveal the superi-
ority of the IMOMVO over NSGA-II, MOPSO and MOMVO algorithms. The
IMOMVO eliminated the limitation of PF distribution of MOMVO algorithm
and displayed the better results both at lower and higher iteration. Therefore,
the IMOMVO provides better PF. The PF obtained by multi-objective algo-
rithms helps the decision maker to take a better informed-decision, concerning
the compromise between the conflicting objectives.
1082 M. Abdullah et al.
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... erefore, this paper focuses on the evaluation of six voltage stability indices: VCPI, LVSI, Lmn, FVSI, line stability factor (LQP), and the novel line stability index (NLSI) in the multiobjective OPF of a system incorporating intermittent renewable energy sources. A modified IEEE 30bus consisting of wind, solar photovoltaic (PV), and hybrid wind-small hydro generators taken from [39] is utilized to assess the performance of the VSIs based on voltage stability improvement, generation cost minimization, transmission loss reduction, and simulation speed for each VSI. A multiobjective Mayfly algorithm (MOMA) is used to obtain the Pareto optimal solutions from all case studies. ...
... However, only operation and maintenance costs are incurred if an independent system operator owns the RES. erefore, the ISO must pay according to the contractually agreed scheduled power [39]. Hence, there is a direct cost associated with each renewable generator, expressed in equations (2)-(4) for wind, solar PV, and hybrid wind-small hydro. ...
... e modified IEEE 30-bus presented in Figure 4 and Table 4 was obtained from [39,55]. e system comprises thirty buses, six generators, forty-one branches, and four transformers. ...
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The performance of voltage stability indices in the multiobjective optimal power flow of modern power systems is presented in this work. Six indices: the Voltage Collapse Proximity Index (VCPI), Line Voltage Stability Index (LVSI), Line Stability Index (Lmn), Fast Voltage Stability Index (FVSI), Line Stability Factor (LQP), and Novel Line Stability Index (NLSI) were considered as case studies on a modified IEEE 30-bus consisting of thermal, wind, solar and hybrid wind-hydro generators. A multiobjective evaluation using the multiobjective mayfly algorithm (MOMA) was performed in two operational scenarios: normal and contingency conditions, using the MATLAB–MATPOWER toolbox. Fuzzy Decision-Making technique was used to determine the best compromise solutions for each Pareto front. To evaluate the computational efficiency of the case studies, a preference selection index was used. The results indicate that VCPI and NLSI yielded the best-optimized system performance in minimizing generation costs, transmission loss reduction, and simulation time for normal and contingency conditions. The best-case studies also promoted the most scheduled reactive power generation from renewable energy sources (RES). On average, the VCPI index contributed the highest penetration level from RES (13.40%), while the Lmn index had the lowest. Overall, VCPI and Lmn index provided the best and worst average performance in both operating scenarios, respectively. Also, the MOMA algorithm demonstrated superior performance against the multiobjective harris hawks algorithm (MHHO), multiobjective Jaya algorithm (MOJAYA), multiobjective particle swarm algorithm (MOPSO), and nondominated sorting genetic algorithm III (NSGA-III) algorithms. In all, the proposed approach yields the lowest system cost and loss compared to other methods.
... Generally, the aim of OPF problem is to optimize one or more objective functions by optimally adjusting power system control parameters subject to some equality and inequality constraints [31,32]. Summary of some optimization algorithms used for the solution of different OPF problems in recent literature (since 2014) are decomposition-based algorithms [33], evolutionary algorithms (EA) [34], improved multi-objective ABC algorithm [35], multi-hive bee foraging algorithm (MHBFA) [35], modified TLBO [36], an improved adaptive DE [37], hybrid fuzzy PSO and Nedler-Mead algorithm (HFPSO-NM) [38], learning DE-APSO-PS [39], an adapted GA with adjusting population size [40], adaptive biogeography based PPO [41], adaptive clonal selection algorithm [42], PSO [43], PSO, EP, GA, GWO and DE [44,45] backtracking search optimization algorithm (BSOA) [46], opposition based GSA [47], a semidefinite programming-based model [48], a probabilistic multi-objective algorithm [49], improved ABC (IABC) [50][51][52][53], parallel NSGA-II [54]; a new Sine-Cosine algorithm (SCA) [55], safety barrier interior point [56], an improved gravitational search algorithm (EGSA) [57], improved group search optimization (IGSO) [58,59], chaotic invasive weed optimization (CIWO) algorithms [7], a modified bacteria foraging algorithm (MBFA) [60], chanceconstrained framework [61], the social spider optimization (SSO) algorithm [62], a modified Jaya algorithm [63], an improved DE algorithm integrated with effective constraint handling techniques [64], biogeography-based optimization (BBO) [65,66], an enhanced strength Pareto evolutionary method [67], BAT [68], MOPF solution methodology [69,70], an improved multi-objective multi-verse optimization (IMOMVO) algorithm [71], a quasi-oppositional cuckoo search (QOCS) [72], chaotic KHA [73], non-dominated sorting hybrid CSA [74], a hybrid algorithm of MSA with GSA [75], interior search algorithm (ISA) [76], forced initialized DE [70], a quasi-oppositional improved Jaya algorithm [77], glowworm swarm optimization (GSO) [78], multi objective ant lion algorithm (MALA) [79], improved colliding bodies optimization (ICBO) [80], a new mixed-integer nonlinear programming model [81], an improved firefly algorithm [82], a new TLBO using L evy mutation strategy [83], a hybrid PSO with MVO [84], improved bat algorithm [85], DSA [86], hybrid PSOGSA [87], stud KHA [88], fuzzy harmony search (FHS) [89], adaptive FFA [90], modified MOEA/D [67,91], electromagnetism-like algorithm (ELA) [92], enhanced self-adaptive DE [93] and moth swarm algorithm (MSA) [94]. ...
The teaching-learning-based optimizer (TLBO) algorithm is a powerful and efficient optimization algorithm. However it is prone to getting stuck in local optima. In order to improve the global optimization performance of TLBO, this study proposes a modified version of TLBO, called teaching-learning-studying-based optimizer (TLSBO). The proposed enhancement is based on adding a new strategy to TLBO, named studying strategy, in which each member uses the information from another randomly selected individual for improving its position. TLSBO is then used for solving different standard real-parameter benchmark functions and also various types of nonlinear optimal power flow (OPF) problems, whose results prove that TLSBO has faster convergence, higher quality for final optimal solution, and more power for escaping from convergence to local optima compared to original TLBO.
... So, there is only maintenance cost present without any cost function involved in it, in the event of RESs being owned by Independent System Operators (ISO) [26]. But when the private bodies operate RESs, then ISO has to pay them as per the contract which mutually brought the parties involved towards agreement for the scheduled power [27]. ...
The current research study proposes a multi-objective optimal power flow (OPF) solution using a modified Interior Search Algorithm in which Levy Flight feature with two different strategies is incorporated to accelerate the convergence speed and to enhance solution quality. In traditional OPF problems, the thermal generation units alone are accounted, whereas the security challenges faced by the network are mostly ignored. In other terms, the emission needs to be significantly reduced in terms of environmental sustainability aspects. So, the electrical grid must be infused with power generated from different renewable energy sources. Consequently, the current research article proposes an approach in order to accomplish OPF through a combination of stochastic wind and solar power coupled with traditional thermal power generators in the system. The authors leveraged modified IEEE 30-bus system, IEEE 118-bus system and real-time electrical network 62-bus Indian Utility System in order to validate the Levy Interior Search Algorithm proposed in the study by incorporating renewable energy sources. During implementation, the researchers considered different factors such as network security limitations, for instance transmission line capacity, bus voltage limits and restricted operation zones for thermal units. The simulation results obtained using the proposed LISA Strategy-II algorithm are compared with the results obtained using LISA Strategy-I, ISA and other optimization algorithms reported in the literature. The results achieved from the implementation infer that the proposed method has inherently good convergence characteristic and affords better exploration of the Pareto front.
... Table 9 shows a comparative analysis of different optimization techniques in the literature and the proposed IGWO with AHP. Remarkably, the results obtained using the proposed IGWO-AHP are compared to the corresponding results obtained using SMODE [39], MOEA/D [27], MODA [66], MOFA-CPA [67], PSO-SSO [21], and MVO [68]. The AHP-ETED model presented in this work can significantly minimize fuel costs to 902.4951 $/h, lower emission levels as 0.09785 t/h, and achieve a lower power loss of 2.4110 MW. ...
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This paper presents an economical-technical-environmental dispatch (ETED) model for an adapted IEEE 30-bus system incorporated with thermal and a mix of renewable energy sources (RESs). Total fuel costs, active power losses, and emissions level minimization is the main aim. Different equality and inequality limits involving prohibited operating zones (POZs) are considered as system restrictions. Metaheuristic optimization techniques-moth-flame optimization, salp swarm algorithm, improved grey wolf opti-mizer, and multi-verse optimizer-are employed to find the best solution for the generation cost, losses, and emissions. Various scenarios are examined to approve the ability of the formulated optimization model in solving the problem. A weighted sum strategy using the analytic hierarchy process (AHP) is used to convert the multi-objective problem into a normalized single-objective one. The AHP-ETED model presented in this work can significantly minimize fuel costs to 902.4951 $/h, lower emission levels as 0.09785 t/h, and achieve a lower power loss of 2.4110 MW. The results attained validate that the IGWO outperforms the other considered algorithms in finding the best solution to the ETED problem. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.
... In which, The MOMVO is a novel algorithm proposed by Professor Mirjalili in 2016, which divides the search process into two aspects: exploration and development. It has been successfully applied in many optimization problems [40]- [42]. Based on the characteristics of MOMVO and MODE algorithm, in order to avoid a lot of modification of invalid coding in the evolution process, these two algorithms only update the OS part of chromosome iteratively, and use random key coding to generate the mapping with the jobs, while MS and WS parts are automatically generated according to scheduling rules and various constraints. ...
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The classical hybrid flow shop scheduling problem (HFSP) only treats machines as the only resource constraint, ignoring the dominant role of workers in production and manufacturing. Considering the dual flexibility of machine and worker, this paper studies the multi-objective hybrid flow shop scheduling problem with dual resource constraints (DHFSP). Firstly, according to the characteristics of DHFSP and various constraints, the model is built to minimize the maximum completion time (makespan), total tardiness time and workload balance of worker. Then, an improved multi-objective memetic algorithm (IMOMA) is proposed to solve the DHFSP, which mainly includes the improvement of initial population, crossover, mutation and local search. In addition, Taguchi method is used to set parameters. Finally, through numerical experiments, IMOMA is compared with NSGA-II, MODE and MOMVO algorithms. The experimental results show that IMOMA can solve the multi-objective hybrid flow shop scheduling problem with dual resource constraints effectively. In terms of convergence, diversity and dominance of non-dominated solutions, IMOMA is significantly superior to other algorithms, but the distribution uniformity of non-dominated solutions of the four algorithms are not significantly different.
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In this paper, a modified equilibrium algorithm (MEA) is proposed for optimally determining the position and capacity of wind power plants added in a transmission power network with 30 nodes and effectively selecting operation parameters for other electric components of the network. Two single objectives are separately optimized, including generation cost and active power loss for the case of placing one wind power plant (WPP) and two wind power plants (WPPs) at predetermined nodes and unknown nodes. In addition to the proposed MEA, the conventional equilibrium algorithm (CEA), heap-based optimizer (HBO), forensic-based investigation (FBI), and modified social group optimization (MSGO) are also implemented for the cases. Result comparisons indicate that the generation cost and power loss can be reduced effectively, thanks to the suitable location selection and appropriate power determination for WPPs. In addition, the generation cost and loss of the proposed MEA are also less than those from other compared methods. Thus, it is recommended that WPPs should be placed in power systems to reduce cost and loss, and MEA is a powerful method for the placement of wind power plants in power systems.
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Demand Response Management (DRM) is considered one of the crucial aspects of the smart grid as it helps to lessen the production cost of electricity and utility bills. DRM becomes a fascinating research area when numerous utility companies are involved and their announced prices reflect consumer’s behavior. This paper discusses a Stackelberg game plan between consumers and utility companies for efficient energy management. For this purpose, analytical consequences (unique solution) for the Stackelberg equilibrium are derived. Besides this, this paper presents a distributed algorithm which converges for consumers and utilities. Moreover, different power consumption activities on the basis of time series are becoming a basic need for load prediction in smart grid. Load forecasting is taken as the significant concerns in the power systems and energy management with growing technology. The better precision of load forecasting minimizes the operational costs and enhances the scheduling of the power system. The literature has discussed different techniques for demand load forecasting like neural networks, fuzzy methods, Naïve Bayes, and regression based techniques. This paper presents a novel knowledge based system for short-term load forecasting. The algorithms of Affinity Propagation and Binary Firefly Algorithm are integrated in knowledge based system. Besides, the proposed system has minimum operational time as compared to other techniques used in the paper. Moreover, the precision of the proposed model is improved by a different priority index to select similar days. The similarity in climate and date proximity are considered all together in this index. Furthermore, the whole system is distributed in sub-systems (regions) to measure the consequences of temperature. Additionally, the predicted load of the entire system is evaluated by the combination of all predicted outcomes from all regions. The paper employs the proposed knowledge based system on real time data. The proposed scheme is compared with Deep Belief Network and Fuzzy Local Linear Model Tree in terms of accuracy and operational cost. In addition, the presented system outperforms other techniques used in the paper and also decreases the Mean Absolute Percentage Error (MAPE) on a yearly basis. Furthermore, the novel knowledge based system gives more efficient outcomes for demand load forecasting.
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Nowadays, automated appliances are exponentially increasing. Therefore, there is a need for a scheme to accomplish the electricity demand of automated appliances. Recently, many Demand Side Management (DSM) schemes have been explored to alleviate Electricity Cost (EC) and Peak to Average Ratio (PAR). In this paper, energy consumption problem in a residential area is considered. To solve this problem, a heuristic based DSM technique is proposed to minimize EC and PAR with affordable user’s Waiting Time (WT). In heuristic techniques: Bacterial Foraging Optimization Algorithm (BFOA) and Flower Pollination Algorithm (FPA) are implemented.
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With the emergence of smart grid (SG), the consumers have the opportunity to integrate renewable energy sources (RESs) and take part in demand side management (DSM). In this paper, we introduce generic home energy management control system (HEMCS) model having energy management control unit (EMCU) to efficiently schedule household load and integrate RESs. The EMCU is based on genetic algorithm (GA), binary particle swarm optimization (BPSO), wind driven optimization (WDO) and our proposed genetic WDO (GWDO) algorithm to schedule appliances of single and multiple homes. For energy pricing, real time pricing (RTP) and inclined block rate (IBR) are combined, because in case of only RTP there is a possibility of building peaks during off peak hours that may damage the entire power system. Moreover, to control demand under the capacity of electricity grid station feasible region is defined and problem is formulated using multiple knapsack (MK). Energy efficient integration of RESs in SG is a challenge due to time varying and intermittent nature of RESs. In this paper, two techniques are proposed: (i) energy storage system (ESS) that smooth out variations in renewable energy generation and (ii) trading of the surplus generation among neighboring consumers. The simulation results show that proposed scheme can avoid voltage rise problem in areas with high penetration of renewable energy and also reduce the electricity cost and peak to average ratio (PAR) of aggregated load.
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Generations from several sources in an electrical network are to be optimally scheduled for economical and efficient operation of the network. Optimal power flow problem is formulated with all relevant system parameters including generator outputs and solved subsequently to obtain the optimal settings. The network may consist of conventional fossil fuel generators as well as renewable sources like wind power generators and solar photovoltaic. Classical optimal power flow itself is a highly non-linear complex problem with non-linear constraints. Incorporating intermittent nature of solar and wind energy escalates the complexity of the problem. This paper proposes an approach to solve optimal power flow combining stochastic wind and solar power with conventional thermal power generators in the system. Weibull and lognormal probability distribution functions are used for forecasting wind and solar photovoltaic power output respectively. The objective function considers reserve cost for overestimation and penalty cost for underestimation of intermittent renewable sources. Besides, emission factor is also included in objectives of selected case studies. Success history based adaptation technique of differential evolution algorithm is adopted for the optimization problem. To handle various constraints in the problem, superiority of feasible solutions constraint handling technique is integrated with success history based adaptive differential evolution algorithm. The algorithm thus combined and constructed gives optimum results satisfying all network constraints.
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Demand Side Management (DSM) will play a significant role in the future smart grid by managing loads in a smart way. DSM programs, realized via Home Energy Management (HEM) systems for smart cities, provide many benefits; consumers enjoy electricity price savings and utility operates at reduced peak demand. In this paper, Evolutionary Algorithms (EAs) (Binary Particle Swarm Optimization (BPSO), Genetic Algorithm (GA) and Cuckoo search) based DSM model for scheduling the appliances of residential users is presented. The model is simulated in Time of Use (ToU) pricing environment for three cases: (i) traditional homes, (ii) smart homes, and (iii) smart homes with Renewable Energy Sources (RES). Simulation results show that the proposed model optimally schedules the appliances resulting in electricity bill and peaks reductions.
This paper introduces the multi-objective cuckoo search (MOCS) method for solving the multi-objective optimal power flow (MOOPF) which is a multi-variable, multi-constraint and nonlinear programming problem. In order to speed up convergence and enhance the quality of solution, the quasi-opposition based learning mechanism is adopted to propose the multi-objective quasi-oppositional cuckoo search (MOQOCS) algorithm in this paper. In MOCS and MOQOCS methods, the feasibility-prior domination principle (FDP) is presented to ensure the feasibility of simulation result which is based on the objective values and the sum of constraint violation values. The crowding-distance sorting is considered to enhance the diversity of Pareto-optimal solutions and obtain better distributed Pareto optimal front. IEEE 30-bus and IEEE 57-bus systems have been considered to check the performance of the proposed methods. The simulation results confirm that MOQOCS algorithm obtains superior compromise solution and produces better distributed Pareto optimal front compared to other methods.
This paper presents the application of a novel algorithm, which is based on a modified Sine-Cosine technique for solving the optimal power flow (OPF) problem. It is a highly coupled non-linear constrained optimization problem. The modified Sine-Cosine algorithm (MSCA) aims at reducing the computational time with a sufficient improvement in finding the optimal solution and feasibility. Levy flights are added to the original Sine-Cosine algorithm to enhance the ability to focus on optimal and avoids local optima. Decreasing search agents number based on the objective function speeds up the MSCA. The MSCA presents a simple and robust solution for the OPF problem under different objective functions. The MSCA is validated with solving the OPF problem for a number of benchmark test systems, namely the IEEE-30 bus and IEEE 118-bus systems under selected objective functions, which are based on operational and economic performance indices of the power system. The proposed MSCA is compared with other optimization methods to illustrate the effectiveness and potential of the SCA and MSCA algorithms.
This work proposes two novel optimization algorithms called Salp Swarm Algorithm (SSA) and Multi-objective Salp Swarm Algorithm (MSSA) for solving optimization problems with single and multiple objectives. The main inspiration of SSA and MSSA is the swarming behaviour of salps when navigating and foraging in oceans. These two algorithms are tested on several mathematical optimization functions to observe and confirm their effective behaviours in finding the optimal solutions for optimization problems. The results on the mathematical functions show that the SSA algorithm is able to improve the initial random solutions effectively and converge towards the optimum. The results of MSSA show that this algorithm can approximate Pareto optimal solutions with high convergence and coverage. The paper also considers solving several challenging and computationally expensive engineering design problems (e.g. airfoil design and marine propeller design) using SSA and MSSA. The results of the real case studies demonstrate the merits of the algorithms proposed in solving real-world problems with difficult and unknown search spaces.
This work proposes the multi-objective version of the recently proposed Multi-Verse Optimizer (MVO) called Multi-Objective Multi-Verse Optimizer (MOMVO). The same concepts of MVO are used for converging towards the best solutions in a multi-objective search space. For maintaining and improving the coverage of Pareto optimal solutions obtained, however, an archive with an updating mechanism is employed. To test the performance of MOMVO, 80 case studies are employed including 49 unconstrained multi-objective test functions, 10 constrained multi-objective test functions, and 21 engineering design multi-objective problems. The results are compared quantitatively and qualitatively with other algorithms using a variety of performance indicators, which show the merits of this new MOMVO algorithm in solving a wide range of problems with different characteristics.
In this paper, a novel two-archive Multi-Objective Grey Wolf Optimizer (2ArchMGWO) is proposed for solving Multi-Objective Optimal Reactive Power Dispatch (MORPD) problems. The optimizer has been improved from its original Multi-Objective Grey Wolf Optimizer (MGWO) by modifying the reproduction operator and adding the 2-archive concept to the algorithm. It is then implemented on solving MORPD with objective functions being active power loss minimization and voltage profile improvement (voltage deviation minimization). The generator bus voltages, tap setting transformers and shunt reactive power sources or flexible alternating current transmission systems are set as design variables. The proposed algorithm along with other existing multiobjective optimizers are applied to solve three test problems with the standard IEEE 30-bus, IEEE 57-bus, and the IEEE 118-bus power systems. The optimum results obtained from the various optimizers performance are compared based on the hypervolume indicator and they reveal that 2ArchMGWO is clearly superior to the others.