Improved PSO with Disturbance Term for Solving ORPD Problem in Power Systems

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER Improved PSO with Disturbance Term for Solving ORPD Problem in Power Systems Mohamed MEZAACHE 1, Omar Fethi BENAOUDA1, Hocine SEKHANE 2,3, Saad CHAOUCH 1, Badreddine BABES 1 1Research Center in Industrial Technologies "CRTI", P.O.BOX 64, Cheraga, 16014 Algiers, Algeria 2Department of Electrical Engineering, Faculty of Technology, University of 20th August 1955 Skikda, P.O.BOX 26, Street El-Hadaiek, 21000 Skikda, Algeria 3Electrical Engineering Laboratory of Constantine (LGEC), Department of Electrical Engineering, Faculty of Science and Technology, Mentouri Brothers University of Constantine 1, P.O.BOX 325, Street Ain El Bey, 25000 Constantine, Algeria mohamedmezaac[email protected], b[email protected], docsekho[email protected], saad.y[email protected], [email protected] DOI: 10.15598/aeee.v20i4.4570 Article history: Received May 24, 2022; Revised Nov 18, 2022; Accepted Dec 24, 2022; Published Dec 31, 2022. This is an open access article under the BY-CC license. Abstract. The essential purpose of an energy system is to provide electricity to its loads effectively and economically, as well as safely and reliably. Therefore, the solutions to the problems of Optimal Power Flow (OPF) and Optimal Reactive Power Dispatch (ORPD) to enable the efficient employment of various energy distributions should be found. Our work focuses on the ORPD issue; it can be formulated as a non-linear constraint and with single or multiple objectives optimization problems. Minimizing total losses is one of the main objective functions to solve the ORPD problem. This paper presents the use of an improved particle swarm optimization -with a disturbance term- (called PSO-DT) algorithm, to find the solution of ORPD in the standard IEEE 30-bus power system for reducing electrical power transmission losses. The obtained results demonstrate that the proposed method is more efficient and has a more extraordinary ability to get better solutions compared to the basic PSO method. Keywords Basic PSO, Optimal Power Flow, Optimal Reactive Power Dispatch, PSO-DT. 1. Introduction Providing a balanced and reliable source of electrical energy to consumers is the principal goal of power producers. Reactive and active powers of generators (in an interconnected electrical network) must vary within the usage limits to meet a specific load request at the lowest fuel costs. In the production station, there are two factors that must be taken into account at each variation of load, namely the load division and the economic component. Following the liberalization of the industry, Optimal Power Flow (OPF) is utilized to deal with these issues. The OPF was presented for the first time by Dommel and Tinney in 1968; it is one of the fundamental issues in the planning and operation of the energy system [1]. The main purpose of an OPF is to find the optimal settings of control variables in an electrical power system by optimizing a specific goal along with the satisfaction of certain operational constraints [2]. Solving the problem of the Optimal Reactive Power Dispatch (ORPD) is another important factor in the electrical energy management system [3]. ORPD is considered a complex, non-linear, concave, discontinuous and multi-model problem involving both discrete and continuous variables. Thus, its solution includes various objective functions such as reducing power losses, improving voltage stability and minimizing transmission costs, etc. [4] and [5]. In electrical ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 478 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER networks, the main goal of ORPD is to find the best values of control parameters including the voltage of generators, reactive power provided by shunt compensators and tap positions of transformers, so as to optimize the objective function taking into account the constraints. Moreover, dependent variables such as the voltage of charging buses, reactive power of generators and flow of apparent power in transportation lines must be within the specified permissible range [6]. Several conventional methods such as Linear Programming (LP) [7], Quadratic Programming (QP) [8] and [9] and Interior Point (IP) [10] methods have solved the problem of ORPD in certain situations. However, they are stagnating at the local optimum level in other situations, particularly to find optimal values of reactive and active power flows for large-scale systems [11] and [12]. To avoid shortages of the above methods, many optimization algorithms were applied: Particle Swarm Optimization (PSO) [13], Comprehensive Learning PSO (CLPSO) [14], Quasi Oppositional Teaching-LearningBased Optimization (QOTLBO) [15], Moth-Flame Optimization (MFO) [16], two-Archive MultiObjective Grey Wolf Optimizer (2ArchMGWO) [17], Water Wave Optimization (WWO) [18], Whale Optimization Algorithm (WOA) [19], Modified Stochastic Fractal Search Algorithm (MSFSA) [6], and PSO hybrid with Imperialist Competitive Algorithm (PSO-ICA) [20]. All of these meta-heuristic techniques have their own significance, special impact, limitations and application in solving the ORPD problem [12]. Basic PSO is a part of the various stochastic (random) search modalities. It evolved by simulating a simplified social system and has proven powerful for finding solutions to problems of nonlinear continuous optimization. This original optimization method was introduced for the first time by Eberhart and Kennedy in 1995; fundamentally grounded on the sociological behavior related to a flock of birds. Several amendments have been suggested for improving the performance of this method, such as the coordinated aggregation PSO method and parallel vector evaluated PSO method [21]. One of the best developments to improve a standard PSO performance was made by He and Han in 2007 using an improved PSO algorithm that adds a Disturbance Term (PSO-DT) to the velocity update equation by trying to avert the default value of a standard PSO [22]. For solving the problem of ORPD, the applied PSO-DT is performed on an IEEE 30-bus power system wherein the control of bus voltage of generators, tap ratio of transformers, and reactive power provided by shunt compensators are involved for reducing transmission losses in the energy system. Simulation results have shown that the PSO-DT technique was superior to the old PSO method in order to find the best solutions in terms of algorithm diversity and durability. 2. Problem Formulation of ORPD ORPD case is considered as a non-linear optimization problem that contains the constraints of inequality and equality in the electrical network. Generally, ORPD determines the loss of active power in a transport network, by setting the optimum parameters for controlling the energy system while simultaneously respecting the constraints of inequality and equality [3]. 2.1. Reduction of Total Real Power Losses Minimizing active power losses is one of the main objectives for the ORPD in a transport system Fwhich may be edited in the following form: F= min X k∈Nn Ploss = = min "X k∈Nn GkV2 i+V2 j−2ViVjcos φij#, (1) where: •P k∈Nn Ploss: total losses of active power in the transport network. •k= (i, j);i∈Nb;j∈Na. •Nb: total number of buses in a specific network. •Na: number of buses adjacent to bus i(including bus i) in a particular network. •Nn: number of network branches in a system. •Gk: conductance at the branch k. •Viand Vj: voltages at buses iand jrespectively. •φij: difference in loading angle between buses i and jin a network. 2.2. System Constraints A problem of reactive power distribution has inequality and equality constraints in processing. ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 479 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER 1) Equality Constraints In this case, there are two equality constraints that can be expressed as follows: The two equations below reveal the balance of active and reactive power needed in each normal electric grid: PGi−PDi−Vi Na X j=1 Vj(Gij cos θij +Bij sin φij)=0, (2) QGi−QDi−Vi Na X j=1 Vj(Gij sin θij −Bij cos φij)=0, (3) where PGiand PDiare the active power injected and demanded at the bus i, respectively. Gij and Bij are respectively the real and fictional parts of the admittance matrix at buses iand j.QGiand QDiare respectively the reactive power injected and demanded at the bus i in a network [13] and [23]. 2) Inequality Constraints There are several inequality constraints that must be taken into account in the ORPD formulation, such as: Equation (4) represents the voltage limits of buses Vi.Vmin iand Vmax iare the minimum and maximum voltage of the i-th bus, respectively. Nbis the overall number of buses: Vmin i≤Vi≤Vmax i, i = 1, . . . , Nb.(4) Equation (5) and Eq. (6) give the limits of active and reactive power for generators PGiand QGi, respectively. In this case, Pmin Giand Pmax Giare respectively the minimum and maximum generation of the active power of the i-th bus. Qmin Giand Qmax Giare respectively the minimum and maximum reactive power generation of the i-th bus in a system. Ngis the number of bus generators in a network: Pmin Gi≤PGi≤Pmax Gi, i = 1, . . . , Ng,(5) Qmin Gi≤QGi≤Qmax Gi, i = 1, . . . , Ng.(6) Equation (7) explains the limits of reactive power provided by capacitor banks QCi. In this case, Qmin Ci and Qmax Ciare respectively a minimum and maximum injection of reactive power of the i-th parallel compensator, while Ncis the number of capacitor banks: Qmin Ci≤QCi≤Qmax Ci, i = 1, . . . , Nc.(7) Equation (8) describes the bounds of tap positions of transformers Ti. In this case, Tmin iand Tmax iare respectively the minimum and maximum tap setting of the i-th transport line and Ntis a number of transformer branches available for tap changing: Tmin i≤Ti≤Tmax i, i = 1, . . . , Nt.(8) Finally, Eq. (9) indicates the limit of power flow for each line of transport SLi.Smax Liis the maximum flow of apparent power in the i-th line, and Nlis the number of load branches in a network [13], [20] and [23]: |SLi| ≤ Smax Li, i = 1, . . . , Nl.(9) The constraints of dependent variables are incorporated into the target function as terms of penalty. For that, Eq. (1) is replaced by Eq. (10) as follows: FGlobal = min X k∈Nn Ploss +FPenalty,(10) where FPenalty =KPf(PG1) + KV Nb=30 X i=1 f(Vi) + +KQ Ng=6 X i=1 f(QGi) + KS Nl=41 X i=1 f(SLi), (11) while the three penalty factors are defined as KP=KV=KQ=KS= 104. Calculation of the penalty value for active power violation of slack generator PG1is: f(PG1) =        0if Pmin G1≤PG1≤Pmax G1, Pmin G1−PG12if PG1< P min G1, PG1−Pmax G12if PG1> P max G1. (12) Penalty value calculation for bus voltage violation is: f(Vi) =        0if Vmin i≤Vi≤Vmax i, Vmin i−Vi2if Vi< V min i, (Vi−Vmax i)2if Vi> V max i. (13) Calculation of the penalty value for the reactive power violation of complete generators (the PV buses and the slack bus) is expressed by Eq. (14): f(QGi) =        0if Qmin Gi≤QGi≤Qmax Gi, Qmin Gi−QGi2if QGi< Qmin Gi, QGi−Qmax Gi2if QGi> Qmax Gi. (14) Penalty value calculation for line flow violations is: f(SLi) = (0if SLi≤Smax Li, SLi−Smax Li2if SLi> Smax Li.(15) ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 480 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER Therefore, the penalty function values will be zero if the whole control settings are within their bounds. Conversely, the expressions of the penalty function will be appended to the target function to punish a violation that can happen if the control variables exceed their limits. 3. Overview of the Improved PSO-DT For improving the ability of global optimization, particle diversity should be preserved throughout the iteration process; thus, the particles must not widely converge at a late stage. The velocity updating formula has been improved as follows [24]: Vt+1 id =wV t id +c1r1Pbestt id −Xt id+ +c2r2Gbestt d−Xt id+α(r3−0.5).(16) The position update equation is as follows: Xt+1 id =Xt id +Vt+1 id ,(17) where: •i∈[1,2, . . . , N];N: the number of particles in a swarm (population size). •The index tindicates the iteration counter, and d is the dimension index of the optimization search space. •Vt+1 id and Xt+1 id : the speed (velocity) value and position of the particle at the new iteration (t+1), respectively. •Vt id and Xt id: the particle’s speed value and position at the current iteration (t), respectively. •w: the inertia weight that controls a particle’s exploration for research purposes. •c1and c2: numbers greater than zero, called cognitive and social components, respectively. •r1,r2and r3: distinct indiscriminate numbers divided into a group [0,1]. •Pbestt id: the best personal position for each particle at titeration in a swarm. •Gbestt d: the best global position for all particles at titeration [25], [26] and [27]. •αis a small constant. We call the fourth part of Eq. (16): α(r3−0.5) as the disturbance term. Compared to the basic PSO, this term is not added to the velocity equation. During the first phase of the calculation, the PSO has a fairly strong global search capacity; this is due to the relatively high velocity of particles. At this moment, the disturbance term is much smaller than the previous three parts of the velocity equation and its effect on the algorithm’s search ability is small enough to be neglected. During the final or intermediate phases of the search process, the convergence property of the particles will slow down their speed. This allows the fourth element of Eq. (16) to guarantee that the particle search velocity will not drop down to zero. Consequently, the whole optimization will not allow the update for continuing and overcoming faults falling facilely into the local optimum of an basic PSO; thus, obtaining precise solutions [13]. The detailed procedure for updating individuals’ speed and position for the PSO-DT method is displayed in Fig. 1. t=t+1 No Yes End Print results: best global position and fitness Satisfying stopping criteria? Update velocity and position Update the best personal and global fitness values Start Initialize the PSO-DT algorithm parameters Randomly generate particle positions and velocities Evaluate the fitness function for each particle Fig. 1: Block diagram of suggested algorithm. 4. Results and Discussions For proving the ability of the PSO and PSO-DT methods proposed in this study, an IEEE 30-bus ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 481 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER power system is considered as a test system. This network contains 41 branches and is shown in Fig. 2. The bus load and injection data of the IEEE 30-bus system, reactive power limit of the same network and system summary are presented in Tab. 1, Tab. 2 and Tab. 3, respectively. Both methods have been implemented using the computing environment MATLAB 2014b. 29 27 28 30 26 25 23 24 15 18 19 20 21 17 22 10 1614 13 12 11 9 6 8 4 31 25 Fig. 2: IEEE 30-bus system single-line diagram [28]. Tab. 1: Bus load and injection data of the IEEE 30-bus system [28]. Bus Load (MW) Bus Load (MW) 1 0.0 16 3.5 2 21.7 17 9.0 3 2.4 18 3.2 4 67.6 19 9.5 5 34.2 20 2.2 6 0.0 21 17.5 7 22.8 22 0.0 8 30.0 23 3.2 9 0.0 24 8.7 10 5.8 25 0.0 11 0.0 26 3.5 12 11.2 27 0.0 13 0.0 28 0.0 14 6.2 29 2.4 15 8.2 30 10.6 In both algorithms, the number of populations (swarm size), maximum iteration, learning factors (C1=C2), minimum and maximum inertia weights are 40,300,2,0.4and 0.9, respectively, knowing that α= 0.04. Tab. 2: Reactive power limit of the IEEE 30-bus system [28]. Bus Qmin (p.u.) Qmax (p.u.) Bus Qmin (p.u.) Qmax (p.u.) 1−0.2 0.0 16 – – 2−0.2 0.2 17 −0.05 0.05 3– – 18 0.0 0.055 4– – 19 – – 5−0.15 0.15 20 – – 6– – 21 – – 7– – 22 – – 8−0.15 0.15 23 −0.05 0.055 9– – 24 – – 10 – – 25 – – 11 −0.1 0.1 26 – – 12 – – 27 −0.055 0.055 13 −0.15 0.15 28 – – 14 – – 29 – – 15 – – 30 – – In this work, 10 tests are performed for solving the problem of ORPD. The best results using a suggested method and those of a PSO approach are presented in Tab. 4. A set of solutions of the optimal control variables obtained from PSO-DT and PSO are summarized in Tab. 5. Convergence features of an old PSO and a proposed algorithm are presented in Fig. 3. 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Number of iterations 17.4 17.5 17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4 18.5 Total active power losses (MW) Converge characteristics of PSO and PSO-DT PSO PSO-DT 181X Y 17.5228 Fig. 3: The real power losses curve of PSO and PSO-DT. According to Fig. 3 and Tab. 4, a minimum loss of active power acquired by a suggested technique was set at 17.44 MW at the 282nd iteration. The bus data obtained by PSO is shown in Tab. 6 in App. B. The bus data obtained by PSO-DT is shown in Tab. 7 in App. B. The branch data obtained by PSO is shown in Tab. 8 in App. B. The branch data obtained by PSO-DT is shown in Tab. 9 in App. B. This value of power loss resulting from PSO-DT is less than 0.08 MW, compared with the results of basic PSO which is 17.52 MW at the 50th iteration or more (in lower simulation implementation time than the ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 482 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER Tab. 3: Summary of the IEEE 30-bus system. How many? How much? P (MW) Q (Mvar) Buses 30 Total gen capacity 900.2−125.6to 251.1 Generators 6On-line capacity 900.2−125.6to 251.1 Committed gens 6Generation (actual) 300.9 108.6 Loads 21 Load 283.4 126.2 Fixed 21 Fixed 283.4 126.2 Dispatchable 0Dispatchable −0.0of −0.0−0.0 Shunts 3Shunt (inj) −0.0 50.9 Branches 41 Losses (I2Z)17.51 67.98 Transformers 4Branch charging (inj) – 34.7 Inter-ties 0Total inter-tie flow 0.0 0.0 Areas 1 Minimum Maximum Voltage magnitude 0.962 p.u. at bus 30 1.061 p.u. at bus 1 Voltage angle −18.37 deg at bus 30 0.00 deg at bus 1 Plosses (I2R) – 5.11 MW at line 1–2 Qlosses (I2X) – 15.31 Mvar at line 1–2 Tab. 4: Power losses obtained before and after optimization. Parameters Losses before optimization Losses after optimization by PSO Losses after optimization by PSO-DT Active power losses 18.430 MW 6.124 % 17.518 MW 5.821 % 17.436 MW 5.790 % Reactive power losses 68.350 Mvar 62.937 % 67.980 Mvar 62.596 % 66.780 Mvar 61.491 % Tab. 5: Control variables obtained before and after optimization. Bus Control variables Initial values Optimized values by PSO Optimized values by PSO-DT 3QC3(Mvar) 0.000 19.9918 19.9035 10 QC10 (Mvar) 0.000 19.9666 19.9472 24 QC24 (Mvar) 0.000 15.0408 15.1290 1V1(p.u.) 1.050 1.0613 1.0619 2V2(p.u.) 1.040 1.0417 1.0465 5V5(p.u.) 1.010 1.0086 1.0104 8V8(p.u.) 1.010 1.0082 1.0205 11 V11 (p.u.) 1.050 1.0069 0.9936 13 V13 (p.u.) 1.050 1.0012 1.0216 6-9(branch 11)T1(p.u.) 1.078 1.0315 1.0344 6-10 (branch 12)T2(p.u.) 1.069 0.9827 0.9843 4-12 (branch 15)T3(p.u.) 1.032 1.0134 1.0030 28-27 (branch 36)T4(p.u.) 1.068 0.9912 0.9911 Total 65.1459 65.1470 proposed algorithm). The point of intersection of the two curves of the real power losses between the two methods is 17.52 at iteration 181, which corresponds to the lower value obtained by PSO. In order to validate the results obtained, we have compared our data with other articles already published. Authors in [33] proposed a MAS-based Reinforcement Learning (MASRL) algorithm and other algorithms such as Discrete Particle Swarm Optimization (DPSO) and Interior Point (IP) to solve the Optimal Reactive Power Dispatch (ORPD) problem for the purpose to minimize transmission active power losses in power systems. These methods were applied in the Ward-Hale 6-bus, IEEE 30-bus, and IEEE 162-bus systems. Comparing our simulation results and those obtained in the IEEE 30-bus, it was observed that our optimal value (17.436 MW) was better than their best active power values (17.94 MW, 17.93 MW and 18.15 MW), respectively. For another comparison, authors in [34] used the Hierarchically Distributed approach using a MixedInteger extension of the Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) algorithm for solving the line loss minimization problem. Their proposed method was tested on the IEEE 14-bus and 30-bus systems. The best real power value obtained was 17.999 MW on the last network ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 483 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER used. Our value (17.436 MW) was also better than theirs. This quick comparison between the different results allowed us to demonstrate the applicability and efficiency of our proposed algorithm. From Tab. 3, it may also be noticed that the proposed method achieves the least reactive power loss of 66.78 Mvar, compared to the result of PSO (67.98 Mvar). Consequently, the PSO-DT algorithm clearly appears to have a big capacity to identify optimal or near-ideal solutions and to respond efficaciously to constraints imposed by optimization issues. Including a disturbance term founded on actual structure strongly corrects faults [29]. 5. Conclusion An ORPD is a sub-group of an OPF, that has been defined as a nonlinear problem of optimization by a combination of continuous and/or discrete variables in an electrical network. In this paper, PSO and PSO-DT methods are employed to properly resolve this issue. Obtained results from simulation clearly demonstrate that a chosen method PSO-DT yields better quality of the optimal global or near-global solutions compared to other standard PSO results. It was found that PSO-DT can be more sensitive in response to changing environments and maintain greater particle diversity than basic PSO. The optimization results confirm the effectiveness of this method in providing near-optimal solutions and explain the superiority and robustness of a selected algorithm to correctly solve an ORPD issue regarding power losses. Consequently, the PSO-DT technique can be advised as a highly promising algorithm to solve several complex optimizations of engineering issues for researchers in future. Acknowledgment This research has been supported by our Research Center in Industrial Technologies "CRTI" in Algeria. Author Contributions M.M. performed the measurements, developed the theoretical formalism, performed the analytic calculations, and performed the numerical simulations. O.F.B., H.S., S.C. and B.B. contributed to the analysis of the results and to the proofreading of this manuscript. All the authors provided critical feedback, helped to shape the research and conduct the analysis and thus contributed to the final version of the manuscript. References [1] ROY, P. K. and S. DUTTA. 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ALSWAITTI, Q. AL-TASHI, M. A. SUMMAKIEH and S. MIRJALILI. Particle Swarm Optimization: A Comprehensive Survey. IEEE Access. 2022, vol. 10, iss. 1, pp. 10031–10061. ISSN 21693536. DOI: 10.1109/ACCESS.2022.3142859. About Authors Mohamed MEZAACHE (corresponding author) was born in 1985. His nationality is Algerian. He obtained the degrees of B.E., M.E. and Ph.D. in Electrical Engineering (with specialization in electrical networks) from the University of Batna, Algeria, in 2008, 2011 and 2016, respectively. He is currently a senior researcher at the Research Center in Industrial Technologies "CRTI", Algiers, Algeria. His research interests include electrical networks, power electronics, artificial intelligence techniques, welding and related techniques. Omar Fethi BENAOUDA was born on November 5th, 1984 in Tiaret, Algeria. He received a B.E. degree in electrical engineering from the University of Djelfa, Algeria in 2009, and his M.E. and Ph.D. from the University of Sciences and Technology of Oran (USTO-MB), Algeria in 2013 and 2017, respectively. He is currently a senior researcher "A" at the Research Center in Industrial Technologies "CRTI", Algiers, Algeria. He is working with the Diagnostic Group, LDEE laboratory at the University of Sciences and Technology of Oran since 2010. His research interests include electrical machines and drive control with the application of artificial Intelligence: fuzzy logic and neuron network as well as multi-level inverters and fault tolerance. Hocine SEKHANE was born in 1985 in Algeria. He received B.Sc., M.Sc. and Ph.D. degrees in electrical engineering from Mentouri Brothers University of Constantine, Algeria, in 2010, 2013 and 2019 respectively. He is currently a lecturer "B" at the Electrical Engineering Department of Skikda University and a researcher member in the laboratory "LGEC" at Constantine, Algeria. His research interests are Optimal Power Flow, modeling and control of FACTS systems, and system stability and protection systems. ©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 486