10853 FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 36, No 1, March 2023, pp. 53-75 https://doi.org/10.2298/FUEE2301053M © 2023 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper OPTIMAL POWER MANAGEMENT OF DGS AND DSTATCOM USING IMPROVED ALI BABA AND THE FORTY THIEVES OPTIMIZER Belkacem Mahdad Department of Electrical Engineering, University of Biskra, Algeria Abstract. In this study an improved Ali Baba and the forty thieves Optimizer (IAFT) is proposed and successfully adapted and applied to enhance the technical performances of radial distribution network (RDN). The standard AFT governed by two sensible parameters to balance the exploration and the exploitation stages. In the proposed variant a modification is introduced using sine and cosine functions to create flexible balance between Intensification and diversification during search process. The proposed variant namely IAFT applied to solve various single and combined objective functions such as the improvement of total power losses (TPL), the minimization of total voltage deviation and the maximization of the loading capacity (LC) under fixed load and considering the random aspect of loads. The exchange of active powers is elaborated by integration of multi distribution generation based photovoltaic systems (PV), otherwise the optimal management of reactive power is achieved by the installation of multi DSTATCOM. The efficiency and robustness of the proposed variant validated on two RDN, the 33-Bus and the 69-Bus. The qualities of objective functions achieved and the statistical analysis elaborated compared to results achieved using several recent metaheuristic methods demonstrate the competitive aspect of the proposed IAFT in solving with accuracy various practical problems related to optimal power management of RDN. Key words: Ali Baba and the forty thieves Optimizer, Integration of distributed generation, RDN, DSTATCOM, Power losses, loading capacity Received June 12, 2022; revised July 06, 2022; accepted July 24, 2022 Corresponding author: Mahdad Belkacem Department of Electrical Engineering, University of Biskra, Al E-mail: belkacem.mahdad@univ-biskra.dz 54 B. MAHDAD LIST OF ABBREVIATIONS IAFT Improved Ali Baba and the Forty Thieves RDN Radial Distribution Network TPL Total Power Losses TVD Total Voltage Deviation LC Loading Capacity PV Photovoltaic Systems DSTATCOM Distributed Static Compensator SC Shunt Compensator DG Distributed Generation FACTS Flexible AC Transmission Systems CB Capacitors Bank GWO Grey Wolf Optmizer ABC Artificial Bee Colony ACA Ant Colony Algorithm IWHO Improved Wild Horse Optimization Algorithm SD Standard Deviation BSOA Backtracking Search Optimization Algorithm SIMBO-Q Swine Influenza Model-Based Optimization with Quarantine HHO Harris Hawks Optimization Algorithms MOIHHO Multi-Objective Improved Harris Hawks Optimization Algorithms IEO Improved Equilibrium Optimizer PM Power Management LMS Loading Margin Stability FWA Fireworks Algorithm BFOA Bacterial Foraging Optmization Algorithm HSA Harmony Search Algorithm TM Taguchi Method GA/PSO Genetic Algorithm/Particle Swarm Optimization WCA Water Cycle Algorithm TSA Tabu Search Algorithm ITSA Improved Tabu Search Algorithm EGWA Enhanced Grey Wolf Algorithm MRFA Manta Ray Foraging Algorithm JFSA Jellyfish Search Algorithm MC Margin Capacity RDN Radial Distribution Network TLBO Teaching-Learning Based Optimization QOSIMBO-Q Quasi-Oppositional Swine Influenza Model-Based Optimization with Quarantine IHHO Improved Harris Hawks Optimization Algorithms FUZZY-IAS Fuzzy And Artificial Immune System 1. INTRODUCTION Due to economic aspect, the radial distribution network (RDN) is exploited based on simple topology, as a result the energy quality delivered to consumers is greatly affected which requires urgent measures and additional costs to satisfy the desired objectives. Actually, with the large diffusion of various types of renewable sources such as wind and photovoltaic (PV) energy, the RDN becomes more flexible to exploit in terms of improving the energy quality, reducing cost investment and emission. Otherwise, the intermittent aspect of this Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 55 energy is the main drawback which affects the energy quality delivered to consumers. Recently, many smart management strategies based on the adaptation of several novel metaheuristics methods have been proposed for integration of various types of renewable sources to improve the performances of modern RDN [1].The various power management strategies developed until now aim to find the optimal solutions to the following technical and economic problems, such as: what are the best locations and size of multi types of DGs units, how to find the best locations of conventional capacitor banc (CB) and shunt compensators (SC) based FACTS devices [1], how to optimally coordinate the amount of active powers of various types of DGs units and the reactive powers of shunt compensators [2], to optimize individually and simultaneously several objective functions, and finally how to design the optimal reconfigurations of RDN under normal and abnormal situations in the presence of multi DGs and SC to reduce the total power loss (TPL), improve the total voltage deviation (TVD), reduce emission, and enhance the total cost investment of modern RDN. A deep statistical review of large number of metaheuristic methods introduced in the recent literature reveals that the success of the majority these methods depends on the structure of the diversification and intensification mechanism. Dynamic interactivity between exploration and exploitation during search process allows the algorithm to solve with accuracy various complex optimization problems [1, 2]. Among many developed strategies based recent metaheuristic methods applied with success to improve the technical and economical performances of RDN, authors in [3] proposed a hybrid technique based on combining an analytical method and metaheuristic optimization techniques for solving the optimal location of bank capacitors to improve the performances the various RDN. In [4] a water cycle algorithm is adapted and applied to solve the location and sizing of bank capacitors and DGs in RDN. In [5] an efficient Jellyfish Search Algorithm is successfully applied to solve the power management of RDN such as the location and coordination of shunt compensators based FACTS devices and DGs, and the reconfiguration operation to improve the power quality delivered to consumers such as the improvement of voltage deviation and the reduction of the TPL. In [6], three novel metaheuristic methods such as the Grey Wolf optimizer, the Dragonfly and Moth–Flame Optimization Algorithms have been applied to solve the optimal location and sizing of multi DGs and CB in RDN. In [7], a spring search algorithm is applied to solve the optimal integration of capacitor banks and various DGs; various objective functions have been treated to elevate the RDN performances. In [8] a hybrid method based on combining the GA and the PSO algorithm for optimal setting and sizing of multi DGs units, the various multi objective problems are transformed to a single objective function by employing fuzzy optimal theory. In [9], a combined technique based on Genetic Algorithm and Mathematical Optimization, is presented to improve the operating cost and reducing the TPL, the particularity of the proposed hybrid method validated on three test RDN (10-Bus, 33-Bus and 69-Bus). In [10] artificial bee colony (ABC) method is investigated for optimal location of DGs considering the operation cost and TPL in RDN. In [11] a probabilistic technique based PSO is proposed for optimal allocation of DSTATCOM based FACTS devices in coordination with renewable sources such as wind turbines and solar photovoltaic (PV) to enhance the RDN. In [12] an approach based on ant colony algorithm (ACA) for optimal location of DGs to reduce TPL and improve the voltage profile of loads. In [13] a novel quasi-oppositional chaotic Harris hawk’s optimization (QOCHHO) algorithm is adapted to solve the optimal sitting and sizing of distributed generation (DG) installed in the 33-Bus and the practical Brazil 136-bus radial distribution network (RDN) considering different types of load models at three load levels). In [14], an Improved Wild Horse 56 B. MAHDAD Optimization algorithm (IWHO) is proposed to improve the reliability of various RDN test systems, the 33-Bus, 69-Bus and the 119-Bus. In [15] a new circuit theory based branch oriented for loss allocation in RDN considering different load model and DGs units. In [16], an improved equilibrium optimizer (IEO) designed for selecting the suitable location and the most effective size of DGs based PV systems in practical RDN. Due to the robust characteristic and fast response of the STATCOM device to regulate the voltage magnitude in particular at critical situations such as severe faults, this device is also investigated by researches to improve the system loadability of multi machine based on Imperialist competitive algorithm [17] and Cuckoo Search algorithm [18]. In [19] ant lion algorithm is applied for optimal allocation and sizing of various DGs based renewable sources. In [20], an efficient reactive power management strategy based on a modern metaheuristic algorithm is proposed for reduction the TPL in RDN. In [21], a new optimization variant namely a novel opposition-based tuned-chaotic differential evolution technique designed to improve the techno-economic aspect of the optimal placement of DGs in RDN. In [22], an enhanced equilibrium optimizer (EEO) is applied for optimal planning of PV-BES units in RDN considering time-varying demand. In [23], a parallel slime mould algorithm (PSMA) is proposed for optimal reconfiguration of RDN in coordination with DGs integration. In [24], a hybrid genetic dragonfly algorithm (HGADA) is proposed and applied for optimal allocation of DGs to improve the technical performances of RDN. In [25], a planning strategy based on an improved grey wolf optimizer (IGWO) and loss sensitivity (LS) is proposed to improve the integration of DGs in RDN. In [26] an improved coyote optimization algorithm (ICOA) is proposed for optimally installing solar Photovoltaic sources in RDN. In [27], a single and multi objective technique based on an Improved Harris Hawks Optimizer (IHHO) is applied for optimal location and sizing of multi DGs. In [28], an improved meta-heuristic method is proposed to maximize the penetration level of multi DGs in RDN. In [29], a novel hybrid technique is proposed to solve the multi objective problem related to the integration of multi CBs and multi DGs in RDN. Recently, authors in [30] developed a novel optimizer tool namely Ali Baba and The Forty Thieves (AFT). The efficiency of this technique validated on many modal and multi benchmark functions [30].Results confirmed the particularity of this technique and its ability to solve complex optimization problems. The best of our knowledge there is no application of this technique to solve practical problems related to power system operation and control, otherwise, it is found that the two proposed critical values of the standard algorithm which are responsible to create balance between exploration and exploitation are not generalized and depends on the problem to be solved. The main contributions of this paper compared to existing in the literature are summarized as follows: 1. A novel variant based AFT is proposed and successfully applied to solve the power management of practical RDN. 2. The modification introduced in the standard AFT algorithm allows the mechanism search to be more flexible and interactive to locate the global solution. 3. The active power of multi DGs units and the reactive power of multi DSTATCOM devices are optimized in coordination to improve the performance of two standard RDN, the 33-Bus, and the 69-Bus. 4. Obtained results are compared to many recent metaheuristic methods demonstrate the efficiency of the proposed IAFT in solving optimal power management of various RDN. Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 57 2. FORMULATION OF THE ENERGY MANAGEMENT PROBLEM The strategy of power management (PM) consists in improving the performances of modern RDN by optimizing individually or simultaneously several objective functions formulated as follows: 2.1. TPL improvement The objective function associated to minimization of TPL is expressed as follow: 1 _ 1 ( , 1) nbr loss k Obj TPL Min P k k =   = = +     (1) where, the active and reactive power losses in lines are expressed by the following expressions: 2 2 , 1 , 1 , 12 ( , 1) k k k k loss k k k P Q P k k R U + + +  +  + =      (2) 2 2 , 1 , 1 , 12 ( , 1) k k k k loss k k k P Q Q k k X U + + +  +  + =      (3) 2.2. Improvement of Loading Capacity Margin capacity (MC) known also as loading margin stability (LMS) of RDN reflects the capability of the RD network to deliver energy quality under sever situations such as faults and load growth. Delivering power quality to consumers under this critical situation is a challenge for expert. In such situation, it is mandatory to dispatch optimally the reactive power delivered by the substation and the reactive power to be injected or absorbed by the distributed STATCOM devices. The lower reactive power delivered by the principal transformer, improves the MC of the RDN. The objective function related to the MC is expressed as follows: Obj_2 = max (MC) (4) where, MC is the margin capacity of the RDN. 2.3. Minimization of TVD The mathematical expression associated to the minimization of the normalized TVD is formulated as follow: 1 _ 3 min ( ) min ( ) Npq des i i Obj TVD V V =   = = −     (5) where; Vdes is the permissible voltage magnitude, Vi is the voltage magnitude reported at load buses, Npq is the number of load buses. 58 B. MAHDAD 2.4. Improvement the TVD and the TPL The TPL and the TVD may be two conflict objective functions. For practical planning and operation of RDN, it is mandatory to find the equilibrium balance between TPL and TVD to ensure efficient power quality. This multi objective problem may be solved using the following mathematical expression: _ 4 min ( , ) min ( (1 ) )Obj TVD TPL TPL TVD = =  + −  (6) where, α, is a balancing coefficient introduced to find the compromise solution between TPL and TVD. The two weighting coefficients are selected in the range [0 1]. 2.5. Operation constraints management 2.5.1. Active and reactive power balance To ensure reliable operation of RDN under normal and abnormal conditions, it is mandatory to ensure the following equality constraints:   = == +=+ Nl i nbr k klossiD ndg i iDGslackTr PPPP 1 1 ,, 1 ,, (7)   = == +=+ Nl i nbr k klossiD ndg i iDGslackTr QQQQ 1 1 ,, 1 ,, (8) 2.5.2. Security constraints The security constraints consist of inequality constraints associated to the secure operation of all elements of the RDN. ▪ Voltage constraint: The voltage magnitude is an important index of power quality. To satisfy consumers the voltage magnitude must be within security values. NbusiVVV iii ,,2,1, maxmin = (9) ▪ DG constraints The active power delivered by the DG units which considered as a control variable must be controlled within specified security limits. ndgiPPP iDGiDGiDG ,,2,1, m ax ,, m in , = (10) ▪ Level of DG integration Due to the stochastic and intermittent aspect of various types of DGs, the exchanged of active powers delivered by various DGs such as PV and Wind sources must be dispatched within their security range. The penetration level () to satisfy is introduced within the following operation inequality constraint:  ==  Nl j jD ndg i iDG PP 1 , 1 , (11) where,  is the level of active power penetration in the RDN. Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 59 ▪ DSTATCOM constraints The DSTATCOM device must be operated within its admissible reactive power limits. m ax ,, m in , iStciStciStc QQQ  (12) ▪ Line current transit in branches: The transit of currents in lines must be controlled without violation their permissible value. nliII lili .....1 m ax = (13) 3. MODELING OF DSTATCOM DEVICE The DSTATCOM device is a shunt compensator from the FACTS family designed principally to regulate the voltage magnitude at specified bus. Fig. 1 Model of DSTATCOM device Compared to the capacitor bank (CB) and to the SVC devices the DSTATCOM controller consists of a robust characteristic capable to regulate the voltage magnitude at critical situations. The DSTATCOM devices can regulate the voltages by injecting or absorbing reactive power from the network. Fig. 1 shows the basic structure of the DSTATCOM device. 3. DISTRIBUTED GENERATION For practical installation, as well shown in Fig 2, the DGs units are classified on three categories: Category 1: This category include al types of DGs units which can only exchange the active power with the network such as the PV sources which have been intensively integrated in many practical electrical networks in world. Category 2: This category includes DGs units which can exchange the active power with the network and absorb the reactive power. The wind sources based renewable sources are also integrated in various electrical networks. Bus k ±Q Qstc, max Qstc, min Bus i Pk+jQ k Pik+j(Qik-Qstc) 60 B. MAHDAD Category 3: This category include al the DGs units which can exchange the active power with the network and absorb or inject the reactive power. These DGs are efficient which allows to control simultaneously the active power and the reactive powers with the network. In this study an alternative solution is proposed to relieve the main drawback of the PV sources by installing shunt compensator based FACTS devices such as the DSTATCOM to ensure flexible control of reactive power in coordination of the active powers. Fig. 2 Categories of DGs units: a) DGs with only active power control, b) DGs with active power control and only reactive power absorption, c) DGs with active and total reactive power control 4. ALI BABA AND THE FORTY THIEVES OPTIMIZER The AFT mimics the human intelligence and interactivities to find the best food’s sources, materials and treasures. The current algorithm is particularly inspired from the famous tale of Ali Baba and the Forty Thieves. The following key words summarize the main strategy of the proposed AFT [30]: ▪ In the tale of Ali Baba, the thieves’ behavior tries to find the location of Ali Baba, so the thieves are the individuals in the search space (environment). ▪ The home of Ali Baba is the objective function to achieve ▪ Ali Baba location is considered as the global solution ▪ The forty thieves search within an interactive group, they travel from an initial location and try to find the best location which is the house of Ali Baba. ▪ Marjaneh is considered as an intelligent operator designed to deliver astute ways to protect Ali Baba. 4.1. Modeling of AFT optimizer ▪ Initial positions of n individuals are generated randomly in the search space characterized by d dimension. Bus i P b) DG +Q Bus i P c) DG +- Q Bus i P a) PV Pmin Pmax Pmax, Qmax Pmin Pmin, Qmin Pmax, Qmax Voltage control Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 61                 = n d nn d d XXX XXX XXX X .. ..... ..... .. .. 21 22 2 2 1 11 2 1 1 (14) i jX denotes the jth dimension of the ith thief (individual), ( ) i j j j X LB rand UB LB= + − (15) X i, is the position of the ith individual in the search space, UBj, LBj denotes the upper and lower bunds in the jth dimension, ▪ Initialize randomly the wit level of Marjaneh as follow:                 = n d nn d d mmm mmm mmm m .. ..... ..... .. .. 21 22 2 2 1 11 2 1 1 (16) Fitness evaluation: the values of control variables are evaluated during search process based on each thief’s position using the following matrix form. (   ) (   ) (   )                = n d nn n d d XXXf XXXf XXXf f .. ..... ..... .. .. 21 22 2 2 12 11 2 1 11 (17) Update locations of thieves: the new locations of thieves can be updated using the following expression: ( ) 1 1 2 3 4 ( ) ( ) sgn ( 0.5) 0.5, a ii i i i it it it it it it it it it X gbest Td best y r Td y m r rand r r Pp +  = + − + − −     (18) Where; i itX 1+ denotes the position of the ith thieve at iteration (it+1), i ity is the position of the Ali Baba at iteration it, Tdit is the tracking distance of the thieves at iteration it, Ppit is the perception potential of the thieves at iteration it, and ( )a i it m denotes the Marjaneh’s intelligence level, the parameter a is defined as: [( 1) ( 1)]a n rand n= − − (19) 62 B. MAHDAD The tracking distance and the perception potential are formulated as follow: ( ) max1 0 it it eTd it − = (20) 0 max0 log ( ) Bit itit Pp B= 21) Update Marjaneh astute plane using the following expressions: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i it it it it i i i it it it X if f X f m m m if f X f m       =   (22) where, f (.) denotes score of the fitness function. The key steps of the standard AFT algorithm [30] 1 Input setting variables of AFT: Pop_size, Iter_max, Trial_max, Dim, ubj, lbj 2 Randomly generate initial position, x, of all individuals (thieves) in the search space 3 Initialize the best position (best i it) and the global best position (gest i it)for all individuals 4 Initialize the intelligence degree of Marjaneh with respect to all individuals 5 Evaluate the position of all individuals using the appropriate fitness function (f(x)) 6 Set it  1 7 while (it < it_max) do 8 calculate Tdit using Eq.20 9 calculate Ppit using Eq.21 10 for i = 1,2,...,n do 11 if (rand  0.5) then 12 if (rand  Ppit) then 13 update i itx 1+ using Eq. 18 14 else update i itx 1+ using Eq.15 15 end if 16 else 17 update i itx 1+ using Eq.18 18 end if 19 end for 20 for i = 1,2,...,n do 21 Check the feasibility of the new position 22 Evaluate and update the new position of the individuals (thieves) 23 Update the solution best i it and gest i it 24 Update  itm using Eq. 22 25 end for 26 it=it+1 27 end while 4.2. Proposed variant The main contribution of this proposed variant is related to its ability to ensure the interactivity between the exploration phase and the exploitation phase during search process. The following are the modifications introduced to improve the performances of the original algorithm: Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 63 The first modification: The standard AFT is governed by various parameters to be well carefully identified and adjusted to achieve the near global solution. Among these parameters, the tracking distance (Td) and the perception potential (Pp).The following proposed modeling expressions are suggested to create flexible balance between diversification and intensification. Fig. 3 shows the evolution of the proposed Tracking distance (Td) and Perception potential (Pp) during search process. Fig. 3 Evolution of the proposed Tracking distance (Td) and Perception potential (Pp) during search process 4.3. Analysis methodology The following steps summarize the analysis methodology based IAFT designed to solve various single and multi objective functions: 1. Read the technical data of the RDN such as the line data, load data, 2. Select and specify the objective function 3. Introduce the initial parameters of the IAFT, such as: population size, generation max, trials. 4. Run power flow tool to determine the initial state of the RDN in terms of total power loss, low voltage magnitude, maximum current transit in lines. 5. Select preliminary buses to install DGs and DSTATCOM devices based on sensitivity power index. 6. Run IAFT to minimize the objective function 7. Save the best solution 8. Check the convergence condition based on Gmax and Tmax 9. Return the optimized solutions such as the best active of DGs, the reactive power of DSTATCOM, and the voltage profiles. 64 B. MAHDAD 5. STATISTICAL RESULTS ANALYSIS 5.1. Test 1: RDN 33-Bus This first RDN 33-Bus consists of 32 lines and 33 buses; the active and reactive power of loads to satisfy is 3.715 MW and 2.300 MVAR respectively [2, 31]. Fig 4 shows the standard topology of the RDN 33-bus. The performances of the proposed optimizer tool namely IAFT is demonstrated via experiencing the following test cases. Fig. 4 The topology of the RDN 33-Bus 5.1.1. Case 1: TPL improvement based DSTATCOM under normal condition This test case is focused to show the impact of integration only three STATCOM devices on the performances of RDN with 33-Bus. Three efficient locations are considered in buses 14, 24 and30. The maximum size of each STATCOM device is 1 MVAR. By considering the voltage limits of all PQ buses in the range [0.95 1.05] p.u, the optimized TPL found using the proposed IAFT is 126.5868 KW and by considering voltage limits in the range [0.9 1] p.u, the optimal TPL achieved is 132.2102 KW. Detailed optimized results related to decision variables of this case are shown in Table 1.The results of this case are compared to various metaheuristic methods such as: PSGA, GSA, SA, IP, FPA, MFO, GWO, DFO, PSO, and water cycle algorithm (WSA), it is absolutely clear that the proposed IAFT achieves better solution quality. The lowest voltage magnitude is 0.95 p.u reported at Bus 18. The convergence behaviour of TPL is shown in Fig. 5, it is important to mention that only 5 trails are sufficient to locate the best solution. Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 65 Fig. 5 Convergence characteristic of TPL minimization: case 1 Table 1 Optimized decision variables based three STATCOM: case 1: RDN 33-Bus Methods [3, 5] Limits of V (p.u) Location of SCs SCs size (KVAR) Min Voltage (p.u) TPL (KW) TDV (p.u) PSGA [0.95 1.05] 6 28 29 1200 760 200 0.9463 135.4 - GSA [0.95 1.05] 13 15 26 450 800 350 0.9672 134.5 - SA [0.95 1.05] 10 14 30 450 900 350 0.9591 151.75 - IP [0.95 1.05] 9 29 30 450 800 900 0.9501 171.78 - FPA [0.95 1.05] 6 9 30 250 400 950 0.9365 171.78 - MFO [0.95 1.05] 8 13 30 450 300 900 0.9400 134.0725 - GWO [0.95 1.05] 8 13 30 450 300 900 0.9400 Bus 18 134.0725 - DFO [0.95 1.05] 8 13 30 450 300 900 0.9400 Bus 18 134.0725 - PSO [0.95 1.05] 8 13 30 450 300 900 0.9400 Bus 18 134.0725 - WSA [0.95 1.05] 14 24 30 397.3 451.1 1000 0.951 Bus 18 130.912a Proposed IAFT [0.9 1] 14 24 30 361.10 547.20 1043.7 0.9389 Bus 18 132.2102 - Proposed IAFT [0.95 1.05] 14 24 30 358.70 541.90 1036.3 0.9601 Bus 18 126.5868 0.5129 66 B. MAHDAD 5.1.2. Case 2: TPL improvement based three DGs units under normal condition The main objective of this second test case is to show the impact of integration only three DGs units without considering the reactive power support of shunt compensators based DSTATCOM devices. The maximum size of each DG unit is 2 MW. It is found that by integrating three DGS at buses 14, 24 and 30, the TPL is reduced to a competitive value 70.6725KW when the voltage magnitude at all PQ buses taken in the range [0.95 1.05] p.u, and by considering the limits of voltages at PQ buses in the range [0.9 1] p.u, the optimized TPL becomes 71.4572 KW. Detailed optimized results of this case are shown in Table 2, the obtained results are compared to various competitive metaheuristic methods such as FWA, BFOA, HSA, TM, GA/PSO, PSO, GA, and Water cycle algorithm (WCA), it is clearly evident, that the proposed IAFT achieves better solution at competitive number of iteration and trials. The lowest voltage magnitude is 0.95 reported at Bus 18. The convergence behaviours of TPL are shown in Figs 6-7. Fig. 6 Convergence characteristic of TPL minimization: case 2, Vϵ [0.9 1] p.u Fig. 7 Convergence characteristic of TPL minimization: case 2, Vϵ [0.9 1] p.u Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 67 Table 2 Optimized decision variables based three DGs: case 2: RDN 33-Bus Methods [3, 5, 27] Location of DGs DGs size (KW) Min Voltage (p.u) TPL (KW) TDV (p.u) FWA 14 18 32 589.70 189.00 1014.6 0.968 88.68 - BFOA 17 18 33 633.00 90.00 947.00 0.964 98.3 - HSA 17 18 33 572.4 107.0 1046.2 0.967 Bus 29 96.76 - TM 15 25 33 587.6 195.9 783.0 0.958 Bus 30 91.305 - GA/PSO 11 16 32 925.0 863.0 1200 0.980 Bus 25 103.4 - PSO 8 13 32 1176.8 981.60 829.70 0.980 Bus 30 105.35 - GA 11 29 30 1500.0 422.8.0 1070.0 0.981 Bus 25 106.3 - WSA 14 24 30 854.60 1101.7 1181.0 0.973 Bus 33 71.052 - LSF 18 33 25 720 810 900 - 85.07 - Fuzzy-IAS 32 30 31 2071 1113.8 150.3 - 117.36 - BSOA 13 28 31 632 486 550 - 89.05 - BFOA 14 25 30 779 880 1083 - 73.53 - TLBO 10 24 31 824.6 1031.1 886.2 - 75.54 - QOTLBO 12 24 29 880.8 1059.2 1071.4 - 74.10 - SIMBO-Q 14 24 29 763.8 1041.5 1135.2 - 73.4 - QSIMBO-Q 14 24 30 770.8 1096.5 1065.5 - 72.8 - HHO 14 24 30 745.69 1022.69 1135.78 - 72.98 - IHHO 14 24 30 775.54 1080.83 1066.69 - 72.79 - Proposed IAFT 14 24 30 754.00 1099.7 1071.4 0.9687 Bus 33 71.4572 0.5872 Proposed IAFT 14 24 30 748.90 884.60 1072.3 0.9771 Bus 33 70.6726 0.3224 68 B. MAHDAD 5.1.3. Case 3: TPL improvement based DGs units and DSTATCOM under normal condition In this test case, three DGs and three DSTATCOM are integrated at buses 14, 24 and 30. The proposed IAFT is designed to optimize the amount of active powers of DGs and the reactive powers of DSTATCOM to be exchanged with the electric network. The optimal TPL achieved is 11.60 KW which is significantly improved compared to the last two cases and also compared to the results achieved using many recent methods such as, BFOA, WCA, TSA, ITSA, EGWA, MRFA, and JFSA. Details of optimized control variables are depicted in Table 3. The convergence characteristics for TPL minimization under two levels of penetration (76.72 % and 74.47 %) of DGs are shown in Figs 8-9, respectively, the lowest voltage magnitude is reported at bus 8. Fig. 8 Convergence behavior of TPL improvement considering 3 DGs and 3 DSTATCOM devices: Penetration level=76.72 %: RDN 33-Bus Fig. 9 Convergence behavior of TPL minimization considering 3 DGs and 3 DSTATCOM devices, Penetration level= 74.47 %: RDN 33-Bus Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 69 Table 3 Optimized decision variables based three STATCOM and three DGs units: case 3: RDN 33-Bus Methods [4] DGs Penetration level % Limits of V (p.u) Location of DGs DGs size (KW) Location of SCs SCs size (KVAR) Min Voltage (p.u) TPL (KW) TDV (p.u) BFOA 42.98 [0.95 1.05] 17 18 33 542 160 895 18 33 30 163 338 541 0.9783 41.41 - WCA 68.61 [0.95 1.05] 25 29 11 973 1040 536 23 30 14 465 565 535 0.98 24.68 - TSA 71.57 [0.95 1.05] 24 30 12 766 917 976 30 11 24 1060 246 566 NR 15.0 - ITSA 70.39 [0.95 1.05] 13 25 30 788 742 1085 7 15 30 603 269 834 NR 14.4 - EGWA 76.096 [0.95 1.05] 24 14 30 1094.96 767.74 964.22 25 14 30 388.75 334.77 1189.91 0.9924 12.7 - MRFA 78.5 [0.95 1.05] 13 24 30 803 1073 1040 14 24 30 300 600 900 0.992 12.572 - JFSA 77.6 [0.95 1.05] 14 24 30 748 1079 1056 14 24 30 300 600 900 0.992 12.40 - Proposed IAFT 76.72 [0.9 1] 14 24 30 743.9 1066.7 1039.7 14 24 30 348.2 510.8 1014.6 Bus 8 11.60 0.1284 Proposed IAFT 74.47 [0.9 1] 14 24 30 771.7 999.6 995.4 14 24 30 314.7 610.5 1076.5 Bus 8 12.01653 0.1287 MC 1 5.1.4. Case 4: Improvement TPL and margin capacity based DGs and DSTATCOM devices This test case is dedicated to improve the technical performances of RDN under critical situation at loading margin satiability. The TPL is optimization in coordination with the LC. For fair comparison with the third test case, three DSTATOCM and three DGs units are integrated on three optimal locations (14-24-30). The TPL optimized and the MC achieved are 71.311 kW and 2.2 p.u, respectively, the corresponding voltage deviation becomes 0.2889 p.u. The minimum voltage magnitude obtained is 0.9812 p.u reported at Bus 8. Table 4 shows the values of optimized decision variables such as the Table 4 Optimized decision variables obtained by optimizing the TPL and MC of the RDN 33-Bus Methods DGs Penetration level % Limits of V (p.u) Location of DGs DGs size (KW) Location of SCs SCs size (KVAR) Min Voltage (p.u) TPL (KW) TDV (p.u) Proposed IAFT - [0.9 1] 14 24 30 1786.10 1999.90 1999.90 14 24 30 607.30 1666.70 2661.20 0.9812 Bus 8 71.3110 0.2889 MC 2.2 70 B. MAHDAD active powers of DGs units and the reactive powers delivered by the STATCOM devices. The convergence behavior of TPL under loading margin stability is shown in Fig. 10. Fig. 10 Convergence behaviour of TPL improvement under MC maximization considering 3 DGs and 3 DSTATCOM devices 5.2. Test 2: RDN 69-Bus The proposed IAFT is also validated on a medium RDN, the 69-Bus. All data of this second test system are given in [2, 31]. This second test system consists of 69 bus and 68 branches, with 12.66 kV, the total apparent power to satisfy to loads is (3.8+j2.69) MVA. The exploitation states of this test system at normal condition without integration of compensators and without installation of DGs are: the total power loss 224.95 KW and the low voltage magnitude is 0.9092 (p.u) reported at bus 65. The one line representation of the RDN 69-Bus is shown in Fig 11. Fig. 11 Topology of the RDN 69-Bus Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 71 5.2.1. Case 5 For fair comparison with other recent technique, this test case is focused to minimize the TPL at normal condition. Three DGs and three STATCOM devices are optimally integrated at efficient locations (bus 11, bus 18 and bus 61). The sizes of DGs and STATCOM devices are 2 MW, and 1.5 MVAR, respectively. The obtained optimized variables such as the active power of DGs and the reactive power of the three STATCOM devices are recapitulated in Table 5. The best TPL achieved using IAFT is 4.2693kW, which is better than several recent techniques such as: TSA, SMA, CSO, ITAS, and JFA. The convergence behaviour of the IAFT for TPL minimization is shown in Fig 12, the distribution of voltage profile is shown in Fig 13. It is absolutely clear, that the proposed variant namely IAFT achieves the best solution quality, at a reduced time. For this test system, the population size is 10, and the maximum number of iteration is 40. Table 5 Comparison of optimized decision variables obtained using IAFT and other techniques: Case 5: RDN 69-Bus Methods [5] DGs Penetration level % Limits of V (p.u) Location of DGs DGs size (KW) Location of SCs SCs size (KVAR) Min Voltage (p.u) TPL (KW) TSA 65.97 [0.95 1.05] 9 16 61 452 555 1500 21 53 61 299 605 1148 - 6.9 SMA 58.78 [0.95 1.05] 16 30 61 497 112 1625 2 13 61 708 623 1091 - 9.0053 CSO 67.42 [0.95 1.05] 17 71 67 535 1728 299 61 67 68 1367 311 323 7.5488 ITSA 60.05 [0.95 1.05] 10 12 61 291 491 1500 9 23 61 288 292 1149 0.9944 6.8012 JFSA 67.05 [0.95 1.05] 11 18 61 495 379 1674 18 51 61 300 300 1200 0.994 4.6826 Proposed IAFT 67.15 [0.95 1.05] 11 18 61 498.8 379.3 1673.9 11 18 61 365.7 249.8 1196.3 0.9943 Bus 50 4.2693 Fig. 12 Convergence behaviour of TPL improvement considering 3 DGs and 3 DSTATCOM devices: RDN 69-Bus 72 B. MAHDAD Fig. 13 Voltage profile after integration of three DGs and three DSTATCOM: RDN 69-Bus 5.3. Statistical Analysis The performances of the proposed variant are demonstrated by elaborating a statistical analysis. The mean, the max and the standard deviation (SD) are the three well known statistical indexes used largely to identify the advantages and the drawbacks of many metaheuristic optimizers, for the first analysis five trials, and ten trials are elaborated. For all accomplished test cases, the maximum number of iterations is fixed to 40, and the population size is taken 10, the SD achieved for 10 trials is 4.3546E-6 which is remarkably better than the SD associated to a new metaheuristic namely JFSA (0.7146). Fig. 14 shows the convergence characteristics for TPL achieved for 10 trails; however the evolution of the optimized value TPL for 10 trials and 5 trials are shown in Figs.15-16, respectively. It is evident that the global solution achieved at a reduced number of trials. Table 6, depicts the statistical values achieved by using the proposed variant namely IAFT. Fig. 14 Convergence behavior of TPL minimization for 10 trials; pop_size=10 Optimal Power Manegement of DGs and DSTATCOM Using Improved Ali Baba and the Fourty ... 73 Fig. 15 Values of optimized TPL for10 trials: pop_size=10 Table 6 Robustness evaluation of optimized results: case 1: RDN 33-Bus Scenario 1: 3 DSTATCOM and 3 DGs Methods Pop_size Max_It Limits of V (p.u) Min_TPL (kW) Mean_TPL (kW) Max_TPL (kW) STD Trials Base case - - - 316.2 - - - - JFSA - - [0.95 1.05] 12.4002 13.1092 15.1889 0.7146 - Proposed IAFT 5 40 [0.9 1] 11.6366 12.0971 13.9252 0.001 5 Proposed IAFT 10 40 [0.9 1] 11.63636 11.6386 11.64734 4.3546e-06 10 MC 1 Fig. 16 Convergence behavior of TPL for 5 trials: pop_size=10 74 B. MAHDAD 6. CONCLUSION In this current study, a new variant namely IFTA is successfully adapted and applied to solve with accuracy the optimal location and setting of multi DGs units and multi shunt compensators based DSTATCOM devices. To improve the technical performances of RDN, two objective functions are optimized, the TPL and the loading margin capacity of the RDN. The TPL decreased to a competitive value 11.6473 KW when considering both three DGs and three DSTATCOM devices. The loading capacity of the RDN 33-Bus is optimized to 2.2 without affecting the operation constraints. Otherwise, the particularity of the proposed strategy is also demonstrated in optimizing the active and reactive powers of DGs and DSTATCOM devices considering the uncertainties in loads for 24 hours. It has been clearly demonstrated that the proposed power management strategy based IFTA almost gives better results in terms of solution quality and convergence behavior compared to many recent optimization algorithms. A statistical analysis demonstrated that for the RDN 33-Bus, only 5 trials are sufficient to locate the near global solution, as a result the average execution time required will be reduced at a competitive value. 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