13268 FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 38, No 3, September 2025, pp. 397 - 430 https://doi.org/10.2298/FUEE2503397G © 2025 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper PROBABILISTIC DISTRIBUTION SYSTEM PLANNING: INTEGRATING PV-BASED DG, DSTATCOM, AND RECONFIGURATION UNDER SOLAR IRRADIANCE AND LOAD UNCERTAINTIES Pragya Guru1, Nitin Malik2, Sheila Mahapatra3 1,2The NorthCap University, Gurugram-122017, India 3Alliance University, Bangalore-562106, India ORCID iDs: Pragya Guru https://orcid.org/0009-0009-5858-5463 Nitin Malik https://orcid.org/0000-0003-1484-9841 Sheila Mahapatra https://orcid.org/0000-0001-6502-0772 Abstract. Recent technological developments in power distribution networks (PDN) have triggered significant interest regarding the optimal operation of power grids. Despite the high cost of power network development and installation, there is a significant opportunity to improve voltage deviation, reduce power loss, boost efficiency, and ultimately raise system stability. This can be accomplished by reconfiguring the network and allocating distributed generations (DG) and distribution FACT devices, like distribution static compensator (DSTACOM), in the most effective way while considering the stochastic nature of solar irradiance variations, uncertainties, and load variations. The presented article enumerates the planning for optimal photovoltaic distributed generation (PVDG) and DSTATCOM device with Network Reconfiguration (NRX) using a hybrid marine predator jellyfish algorithm (HMPJA). Inspired by the coordinated movements of jellyfish and the effective hunting techniques of marine predators such as sharks, the HMPJA was created. It seeks to improve the exploration, exploitation, resilience, and flexibility of optimization algorithms in handling challenging situations by combining these tactics. Inspired by the social behavior of jellyfish and marine predators, this hybrid algorithm is used to evaluate the techno-economic benefits of installing PVDG and DSTACOM in radial PDN with reconfiguration. With multi-objective function Cost reduction, voltage stability enhancement, and voltage profile (VP) augmentation in radial PDN are the primary goals of the current study. The IEEE 33- and 69- bus systems are used to demonstrate the efficacy of the HMPJA, demonstrating notable decreases in energy and power losses and improved VP with overall net profit. A comparison of the suggested strategy with other nature-inspired alternatives demonstrates its superiority. The findings of the proposed approach provide valuable insights for distribution system planning and operation in future grids with high renewable energy source penetration. Key words: Marine Predator Algorithm, Jellyfish Search, Radial Distribution System, DSTATCOM, PVDG, Reconfiguration Received November 25, 2024; revised January 18, 2025; accepted February 03, 2025 Corresponding author: Pragya Guru The NorthCap University, Gurugram, India E-mail: pragyaguru18@gmail.com https://orcid.org/0009-0009-5858-5463 https://orcid.org/0000-0003-1484-9841 https://orcid.org/0000-0001-6502-0772 398 P. GURU, N. MALIK, S. MAHAPATRA 1. INTRODUCTION As we are transitioning toward sustainable energy technologies, it is necessary to develop innovative strategies for effective PDN planning, particularly photovoltaic systems, which present opportunities and challenges. This study investigates a probabilistic approach to optimal PDN planning that incorporates integrated photovoltaic-based distributed generation (PVDG) and Distribution Static Synchronous Compensators (DSTATCOM). To optimize system performance under fluctuating conditions, exploring network reconfiguration (NRX) strategies is crucial. This research aims to counteract uncertainties caused by solar irradiation and demand changes by optimizing the reliability and efficiency of PDN minimizing operational costs and optimizing the incorporation of sustainable energy sources through advanced probabilistic modeling. The findings will provide valuable insight into the construction of resilient PDNS that can adapt to the dynamic energy landscape and aid sustainable development initiatives. This research is intended to guarantee a more reliable and environmentally friendly energy future. 1.1. Motivation The two main components of the electrical system are the transmission and distribution networks [1]. Planning an efficient PDN is complicated by the fact that solar irradiance is unpredictable, which adds a significant amount of uncertainty to power generation. As we are transitioning to more sustainable energy models, there is a need to deploy DG sources, particularly solar PVDG. By using PVDG countries can reduce their carbon emission and become energy-independent as they work to meet renewable energy targets. To further improve power quality and voltage stability in these developing networks, DSTATCOM can be implemented. PV systems and DSTATCOM work together to maximize operating efficiency. However, this synergy makes planning more difficult and calls for creative solutions that consider dynamic variations in supply and demand. By altering the network topology, operators can increase load distribution, boost dependability, and lower losses. Reconfiguration is a potent methodology for managing the uncertainties and results brought on by renewable energy sources as it enables real- time reactions to variations in generation and demand. However, incorporating NRX into a probabilistic planning paradigm necessitates a sophisticated comprehension of how PV- based DG, DSTATCOM, and fluctuating load conditions interact. By optimal allocation of PVDG and DSTACOM in a reconfigured distribution system enhances the reliability of the grid by mitigating voltage fluctuations, and also increasing economic efficiency by reducing power losses. 1.2. Literature Review Sectionalizing lines are closed, as opposed to open tie lines which are open under normal conditions. [2]. By rearranging the sectionalizing and tie lines, the bus system can be reconfigured to its ideal state [3]. Reconfiguration aims to alleviate overload in the PDN, boost stability and dependability, decrease losses, and enhance voltage profile (VP). In [4] authors Merlin and Back found the idea of reconfiguring a PDNS. there are some old studies show the importance of the reconfigured network. In [5], a self-adaptive modified optimization algorithm was used to suggest the reconfiguration problem in terms of dependability. [6] presents a multi-step resolution process in which Harris Hawks Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 399 algorithm is essential to achieving the intended outcomes. In [7], NRX in existing networks was approached using a modified Selective Particle Swarm Optimization (PSO) while considering various loading situations. In [8], Multi-Objective Random-Key Genetic was introduced to enhance energy loss in electric PDNS by allocating meters. Traditional PDNSs have changed because of the integration of DG, particularly from renewable energy sources (RER) like solar and wind. PVDG is chosen over other RERs for numerous reasons, including There are no moving parts, exceptional reliability with a 25-year warranty, and a less visible design compared to wind turbines, space-saving and wind-resistant, as panels can be put on a roof, Environmental, economic, and electricity network performance are closely linked for this type. Several efforts have been made to integrate PVDG into the electricity supply. The authors of [9] used the Bat algorithm to optimize the integration of capacitors and distributed generation while accounting for load variations. Ref [10] uses PSO to create a voltage stability index for the ideal DG allocation. In [11], a chaotic symbiotic organism search method was created to deploy DG units in a radial system, resulting in improved VP and reduced power loss. In article [12], an improved gravitational search method was used to examine NRX using DGs. The goal was to increase transient stability, reduce loss, and lower operating costs in the PDNS. A hybrid algorithm is used in [13] to insert multiple DG units for the desired outputs. The GWO method for choosing the best for line parameter calculation by the authors is reference [14]. The optimal PVDG size and location is determined using PSO and weighted-sum method in [15]. Authors in [16] find the optimal position for PV by using voltage collapse proximity index. From a technological and financial standpoint, the best distribution of distributed generators using shunt compensators is an efficient approach. DFACTS are widely incorporated. Manuscript presented in [17] shows deployment of DFACT devices with DG in PDNS. DSTACOM is a voltage source converter, shunted to a specific bus DSTATCOM is a productive device that operates as a voltage source converter that is shunted to a specific bus and able to reduce system harmonic, balance the load, and significantly improve the system's efficiency. Additionally, by injecting a regulated voltage, it responds quickly to either absorb or inject reactive power. Furthermore, it has no operating problems such as resonance or transient harmonics, in contrast to series or shunt capacitors [18, 19, 20]. In [21] authors represent hybrid plant growth simulation PGS-PSO algorithms for NRX in the presence of the multiple DG units. The immune algorithm was used in [22] to determine the DSTATCOM's location and dimensions to minimize losses. The Harmony Search Algorithm was used in [23] to optimize the DSTATCOM location and dimensions for loss minimization. In [24], Using the Differential Evolution (DE) technique, the DSTATCOM's location and size were adjusted with the optimal network design to minimize losses. The location and dimensions of the DSTATCOM for improvement have been determined using the binary gravitational search approach [25]. Combining the operators of several metaheuristic algorithms is one sort of hybridization that performs better in several areas, such as convergence speed and solution quality [26, 27]. To find the capacity and best location for the DSTATCOM for a multi-objective function with load demand uncertainties, the authors in [28] used the imperialist competitive approach. An ant colony method and a fuzzy approach are used in [29] to determine the best distribu tion of PVDG and DSTATCOM. To reduce expenses, losses, and the VP, the DSTATCOM and DG have been assigned using the Bacterial Foraging optimization approach [30]. To 400 P. GURU, N. MALIK, S. MAHAPATRA sustain the voltage and minimize losses, the PSO has been used to distribute the DG and DSTATCOM [31]. The authors in [32] optimized the locations and dimensions of the DSTATCOM and DG using the whale optimization (WOA) method to cut expenses and losses. In [33] authors work compares WOA, DE, GWO and their quasi-opposition-based variants for reactive power planning with FACTS devices. To reduce loss and improve VP and stability, the lightning search technique is used in [34] for DG-DSTATCOM allocation. To minimize voltage variations, cost, and loss, the DSTATCOM and DG allocation has been optimized using a hybrid lightning search algorithm and the simplex approach [35]. In [36], the best PVDG, DSTATCOM, and energy storage units have been chosen to minimize costs, enhance voltage performance, and increase dependability. The Harris Hawks technique was used by the authors in [37] to determine the ideal locations and sizes at various power factor values. To achieve a resilient and effective PDNS, the synergy between the integration of the PVDG-DSTATCOM and the optimal reconfiguration plays a vital role. Numerous studies emphasize the benefits of employing probabilistic models as opposed to deterministic ones. Authors in [38] load uncertainties are considered to see the impact while placing renewable DG in the system. Results in [39] shows, the proposed MALO-based optimization framework effectively addresses the challenges of PV-DG and DSTATCOM integration in distribution systems with uncertainties, leading to a more reliable and efficient grid operation. This literature review concludes the importance of PDNS planning in the presence of PVDG and DSTATCOM under probabilistic modeling and enhances the system performance by network resilience. 1.3. Research Contribution It has been determined from previously published research that there has never been an investigation into network reconfiguration with the solar PVDG and DSTATCOM integrated into the PDN using hybridized marine predator and jellyfish search algorithms. This study adds to the published literature by utilizing the hybrid marine predator and jellyfish search technique. This hybrid approach leads to a faster convergence rate to using either individual algorithms, or enhanced exploration and exploitation processes. Hybrid algorithm has increased robustness and versatility and enhanced solution quality. This article presents the solution to the optimal power planning problem integrating PVDG and DSTATCOM, in a reconfigured network considering the uncertainties associated with four seasonal variations in solar irradiance and the load for summer, winter, spring, and autumn. The method is implemented on the widely used IEEE 33-bus standard. To determine the efficacy of the suggested technique, two case studies combining solar PVDG with and without uncertainties are studied, and the outcomes of the test are further compared to previously published results. The following is a summary of the contributions made to the article. a) Finding the optimal installation of PVDG sources and DSTATCOM, and reconfiguring the distribution network to account for the impact of load demand and solar irradiance uncertainty. b) A multi-objective optimization problem is formulated that involves minimizing cost, power losses and voltage deviation and improving the Voltage Stability Index using hybridisation of two nature-inspired algorithms. c) The load and the generation have been considered as random variables. Using historical data spanning three years, the uncertainty of the solar radiation and load Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 401 demand is modelled as gaussian distribution model and beta distribution model, respectively. d) Based on the simulation results, this research methodology for constructing large- scale PDN at all load levels is far more practical and efficient. 2. MODELLING 2.1. Line Modelling Fig. 2 displays a simplified schematic of Fig. 1. At the uth bus, the injected complicated power is provided as, u u us p jq= + (1) Where, qu and pu is real and reactive power load at the uth bus, respectively. Eq. 2 represents current injected at the uth bus (iu), * u u u u p jq i v − = (2) Where the voltage at uth bus is denoted by vu. Eq. (3) gives the real power loss in a branch connecting nodes u and u+1. 2( , 1)loss up u u i r+ =  (3) 2 * ( , 1) u u loss u p jq p u u r v  − + =     (4) 2 2 2 ( , 1) u u loss u p q p u u r v  + + =     (5) 2.2. Integrated Photovoltaic-Based Distributed Generation Positioning the PV unit at an ideal site and size facilitates reducing real power losses, enhancing VPs, minimizing environmental consequences, improving overall energy system performance, and alleviating PDN overload. Due to the random nature of solar PV-based plants, the network experiences an increase in uncertainty. As a result, precisely calculating PV power is difficult. Solar radiation intensity, absorption capacity, panel surface, and cell temperature all affect how much power PV systems can produce. Because solar radiation is stochastic, the related output power fluctuates. The PV output power (PrPV ) is given by 2 0 < 0 < S rated S C stdn C S rPV rated S C stdn rated stdn S G P for G G G G G P P for G G G P for G G            =          (6) 402 P. GURU, N. MALIK, S. MAHAPATRA where the standard solar irradiance Gstdn, is 1000 W/m2 is and shows solar irradiance W/m2. GC stands for a specific point of irradiance. Fig. 1 Illustrative PDNS Fig. 2 One-line diagram 2.3. DSTATCOM Modeling DSTATCOM modeling typically involves a voltage source converter, energy storage system, and control algorithms. DSTATCOM modeling incorporates simulating the behavior of the power electronic devices for reactive power management in electrical systems to enhance power quality, improve voltage stability, and reduce losses. Under various operating situations, DSTACOM modeling helps to ensure reliable grid operation by analyzing system dynamics and optimal integration of renewable energy sources. This technique facilitates the evaluation of performance metrics, such as response time and efficiency, which leads to effective design and deployment in contemporary power systems. DSTATCOM reactive power is expressed as follows, with real power set to zero: 2 1 cosDSTATCOM u u u u u v v v q x x +     = −       (7) 2.4. Network Reconfiguration The act of changing the structure of PDN to optimize the system performance by adjusting the switching arrangement of the nodes and branches is known as network reconfiguration. Wisely opening or closing switches during varying load conditions or during maintenance to minimize losses, redistribute power flows and to ensure uninterrupted service is an essential part of smart grid technologies as they develop and Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 403 try to regulate sophisticated distribution networks. The feeder power loss following the reconfiguration is given by   2       2 2 ( , 1) u u loss u p q p u u r v      + + =     (8) The net power losses of the new structure can be obtained by,  r Tloss Tloss Tlossp p p = − (9) 2.5. Probabilistic Modeling Probabilistic modeling in the PDN planning plays an important role for enhancing resilience and improved resource placement. This strategy is important in light of changing energy scenarios and the merging of dispersed energy resources, specifically with regard to load demand and solar irradiation. The load demand and PV unit have been modelled probabilistically using the location historical data. Three years' worth of hourly statistics on solar irradiation and load demand were taken into account in this study. Consequently, the year is divided into four different seasons. A day (24 hours) within a season is used to characterize the stochastic behaviour of the PV and load demand within that season. Every year, there are 96 time periods (four seasons, twenty-four hours). By applying the data regarding the same hours of the day, the probability density function (pdf) for each season is determined. Thus, the 270 solar irradiances and load demand for each period—three years, three months per season, and thirty days per month—are used to generate the necessary hourly PDFs. The following is a description of the PV system and probabilistic load demand model. 2.2.1. Solar irradiance modeling Using the data on solar irradiance, a beta pdf fB (gsr) has been generated for each hour, which can be explained as follows [40] [41]: ( 1) ( 1)( ) (1 ) , 0 1: , 0 ( ), ( )( ) 0, sr srsr sr sr sr sr sr sr sr srB sr g g g f g otherwise        − − +  −     =    (10) where Γ is gamma function and αsr, βsr are the beta parameters for each period. Using the historical data, these parameters can be established as follows [42], [43]: 2 (1 ) ( ) 1sr sr sr sr sr i        + = −  −    (11) 1 sr sr sr sr      = − (12) where µsr and σsr are each period's solar irradiance mean and standard deviation. The continuous beta pdfs are separated into many segments, each of which yields a mean value. A segment's probability of happening at a specific hour can be determined by: 404 P. GURU, N. MALIK, S. MAHAPATRA , 1 , ,( ) sr t sr sr t g g t B sr sr t g prob f g dg + =  (13) where gsr,t and gsr,t+1 stands for beginning and ending points of the interval, respectively for interval t. The likelihood that interval t will occur is denoted by probt gsr. The generated beta pdf of the solar irradiance for a given period can be used to calculate the output power PV for the states of that period (6). 2.2.2. Modelling of Load Dynamics At each bus, the load demand is modelled using gaussian pdf because it is stochastic. The gaussian pdf of the load demand fnl(l) is specified in eq. (14) [41]: 2 1 ( ) exp 22 ld nl ldld l f l      − =  −       (14) where the mean and standard deviation of the load demand are given by µld and σld for each period. The following is an expression for the segment's occurrence probability at a given hour: 1 ( ) t t l l t nl l prob f l dl + =  (15) where the beginning and ending points of the interval t are denoted by lt and lt+1 respectively. probt l symbolises the probability that interval t will occur. 2.6. Integrated Model of Solar Irradiance and Probabilistic Load The probabilistic solar irradiance and load model are presented in the preceding sections. An integrated probability model of the PV load is generated using these. Convoluting the probability of solar irradiance and load demand allows one to compute the integrated model of the interval t in the manner described below: , gr l int t t tP prob prob=  (16) The objective function specified in (17) should be computed for each state and proportionate to the combined probability model in terms of weight, representing the state's probability of occurrence over the planning period. An hour is represented by each time section. This indicates that each variable has several values for every period. However, we have simply displayed the variables' mean or expected values for simplicity's sake. 3. PROBLEM FORMULATION Promoting the technical and fiscal benefits of effective planning for the integration of PVDG and DSTATCOM in the power system is the primary task this work presents. Although load demand and solar irradiation is difficult to predict accurately, it should be mentioned that the planning period is three years long, with 91.25 days in each of the four seasons. The multi-objective function in (17) tends to minimize voltage deviation, cost, and VSI. Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 405 3.1. Objective Function 1 1 2 2 3 3min min( ) min( ) min( )f Obje Obje Obje  =  +  +  (17) where Obje1, Obje2 and Obje3 represents voltage deviation, cost and VSI. The weighting factors ω1, ω2 and ω3 are governed by (18). 1 2 3 1  + + = (18) and 1 W Wo TVDev Obje TVDev = 2 W WO cost Obje cost = 3 1 1 bN nn Obje VSID = =  where TVDevWo and costWO shows the total voltage deviation and total cost without insertion of the PVDG or DSTATCOM and TVDevW and costW shows the total voltage deviation and total cost with the insertion of the PVDG or DSTATCOM Enhancing the VP by reducing the voltage deviations is stated in (19) ( ) 24 1 1 1 91.25 1 sN NB ne f g TVDev V = = = =  −   (19) The total annual cost costW can be formulated as follows: W loss grid PV Recon STcost cost cost cost cost cost= + + + + (20) where costloss, costgrid, costPV, costRecon and costST represents the cost of power loss, energy loss, PV unit and DSTATCOM installation cost and cost of NRX, respectively. ( ) 24 , ,1 1 1 91.25 SN NB loss loss loss e f ge f g cost c p = = = =     (21) Where closs represents the cost of the energy loss. NS represents the number of seasons per year and is equal to 4. NB represents the number of network branches. The cost of power injection at the substation is given in (22): ( ) 24 ,1 1 91.25 SN grid grid loss e fe f cost c p = = =    (22) The cost of DSTATCOM installation is given in (23): (1 ) (1 ) 1 S S N ST ST ST N cost C Q    +  =   + − (23) where DSTATCOM’s rated kVAr, Capital cost is represented by QST; and CST; α denotes the asset rate of return DSTATCOM Ns is the lifetime of the DSTATCOM in years;. The cost of the PV system consists of fixed and variable cost given by (25) and (26). 406 P. GURU, N. MALIK, S. MAHAPATRA PV fixed Varicost cost cost= + (24) fixed PV ratedcost CRF C P=   (25) ( ) 24 & ,1 1 SN Op Mt PV e fe f CRF C p = = =   (26) where the operation and maintenance cost is denoted by COp&Mt,; PPV stands for output power of the PV unit given in eq. (6). Enhancing stability by improving the voltage stability index as given in (27): 24 1 1 1 91.25 SN NB ge f g VSID VSID = = = =    (27) where 4 2 2 1 1 14( ) 4( )g g mn n g n n n g n gVSID V P X Q R P X Q R V+ + += − − − + (28) 2.1. Constraints The equality and inequality constraints are specified below. ,1 1 1 , , pv bN N NB slack pv loss L gg g g P P g p g P = = = + = +   (29) ,1 1 1 , , pv bN N NB slack pv loss L gg g g Q Q g q g Q = = = + = +   (30) Maintaining radiality ( ) 1mainloop bN N NB= − + (31) The other operational constraints are bus voltages within ± 5%, thermal limit for ampacity, real and reactive limits, DG real and reactive power generation. The number of sectionalising switches is given by (32) 1bN NB= − (32) Nb is total no. of nodes in the system. 4. SYNERGISTIC MARINE PREDATORS-JELLYFISH SEARCH OPTIMIZATION ALGORITHM 4.1. Marine Predators Algorithm The ocean predator interactions and Levy and Brownian movement tactics in a marine predator algorithm (MPA) [44] are explained below 4.1.1. Initialization Using (33), MPA derives randomly its initial solutions in terms of lth prey's position ( )m lPry (0,1) ( )m m m m lPry lbd rand ubd lb= +  − (33) where rand is random integer between 0 and 1. The lower and upper bounds on the mth dimension are denoted by lbdm and ubdm, respectively. Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 407 4.1.2. Optimization The three stages of the algorithm mimic the methods used by predators to capture their prey. A distinct velocity ratio is considered in each of the MPA three stages. Every phase has a set number of iterations assigned to it. Phase 1 (Exploration stage): The prey moves more quickly (high velocity) than the predator. When Itr < 1/3 Maxitr, Phase 1 is chosen. (34) is used to update the solutions. .l l lPry Pry P RV stepsz= +  (34) ( )l Bl Bl istepsz RV Elite R Pry= −  (35) 21 exp 22 Bl x RV    = −    (36) where stepsz is step size, coefficient P is equal to 0.5. The matrices RV and RVBl, both of dimension 1 × dim, are composed of random values within the interval (0,1) and numbers produced by the Brownian movement, respectively. Elite is currently the best available option. Phase 2 (Exploration and Exploitation stage): Unit velocity ratios show that the predator and prey move almost simultaneously. There is an equal distribution of solutions between exploration and exploitation. Exploration is managed by the Predator, and the victim is being taken advantage of. The Levy function and Brownian motion, respectively, control the movement of the predator and the prey. Updated for the one-half of the population are the following formulae. ( )l Ll Ll lstepsz RV Elite RV Pry= −  (37) Given random walk data generated by the Levy function, RVLl is a matrix of dimension equal to that of RV. 1 ( ) a jlL Pry  −  (38) where a is in the range (1, 2) that determines the scale, which is taken to be 1.5, and ω is the flight length. The following integral shows the Levy function's probability distribution: 0 1 ( ; , ) exp( )cos( )a Lf a q q dq       − (39) (1 ) (1 )sin 2 ( ; , )L a a a f a       +    +      →  (40) where Γ represents Gamma function. The population is regulated using (41-43) for exploration. .j j jPry Pry P CVF stepsize= +  (41) ( )l Bl Bl jlstepsz RV Elite RV Pry=  − (42) 408 P. GURU, N. MALIK, S. MAHAPATRA 2 1 Itr ITR Max Itr ITR CVF Max         = −    (43) where the step size is governed by CVF. Fig. 3 Pseudocode for MPA Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 409 Phase 3 (Exploitation stage): The predator has higher velocity than the prey, making it faster. Predators are kept up to date during this phase. Eq. (44-45) provided a mathematical formulation of this phenomenon. .l lPry Elite P CVF stepsz= +  (44) ( )l Ll Ll lstepsz RV Elite RV Pry=  − (45) 4.1.3. Eddy formation This stage is similar to Fish Aggregating Devices (FAGD) which causes predators to alter their behaviour. The FAGD is expressed mathematically as below:     1 2 ( ) (1 ) ( ) l l l r r Pry CF lbd RV ubd lbd U r FAGDs Pry Pry FAGDs r r X X otherwise  +  +  −   =  +  − + − (46) (1, )U rand dim FAGDs=  (47) where Xr1 and Xr2 are two randomly chosen solutions from the population, U is a binary vector and the FAGDs is 0.2. 4.1.4. Predator memory After a successful feeding expedition, marine predators return to areas they have a good recollection of [35]. This capacity is replicated by keeping memories in MPA. To ascertain which answer is superior, the solutions from each iteration are compared to the prior one. Fig. 3 displays the pseudocode. 4.2. Artificial Jellyfish Search Algorithm 4.2.1. Initialization To replicate the movement of jellyfish in a swarm or while traveling towards the ocean current in quest of food, an artificial JFSA [45] was created. The colony of jellyfish is started at random. As a result of low population variety, there may be a risk of trapped local optima and sluggish convergence. The logistic chaotic map, as presented in Equation (54) provides a lower likelihood of early convergence and a wider range of initial populations compared to random initialization. 1 0(1 ),0 1i i iJSA JSA JSA JSA+ = −   (48) where JSAi is the logistic chaotic value; JSA0 is varied to generate the initial jellyfish population, JSA0 ∉ {0, .25, .5, .75, 1}, and 4 is the value for the parameter η. 4.2.2. Ocean current The mean of every jellyfish's vector to the one currently occupying the optimal position represents the movement of the ocean current and is represented as (49). 410 P. GURU, N. MALIK, S. MAHAPATRA *1 ( )c i JFP Direction JS e JSA N = − (49) where NJFP represents number of jellyfishes in swarm and JSA* represents the best jellyfish while attraction govern factor is represented by ec. * *i c c JSA JFP JSA Direction JSA e JSA e N = − = −  (50) where μJSA shows the mean position of all the jellyfishes in an ocean ( )0,1c JSAe rand=  (51) where βJSA is distribution coefficient whose value is taken as 3. The new jellyfish position is defined as: ( 1) ( ) (0,1)i iJSA t JSA t rand Direction+ = +  (52) *( 1) ( ) (0,1) ( (0,1))i i JSA JSAJSA t JSA t rand JSA rand  + = + −    (53) 4.2.3. Jellyfish swarm The majority of jellyfish exhibit passive motion (type A) at first around their initial sites, as the jellyfish swarm is still forming. They start to move more actively (type B) as time progresses. ( 1) ( ) (0,1) ( )i i jsJS t JS t rand ub lb+ = +   − (54) where γjs represents the motion coefficient and its value is taken as 0.1. The direction of the motion of the jellyfish in search of its food and its updated location in the search space are simulated by (43) and (44), respectively. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) j i i i i j i i JS t JS t if f JS f JS Dir JS t JS t if f JS f JS −  =  −  (55) where f (JSi) and JSi represent the objective function and jellyfish location. ( 1) ( )i iJS t JS t step+ = + (56) where ( )0,1step rand Dir=  (57) 4.2.4. The control mechanism The type of jellyfish motion and its gradual transition from one swarm to another are determined with the aid of the time control function (CF(t)) [0,1]. If the jellyfish value is more than or equal to CF0, it floats with the ocean current; if it is less than CF0 it stays with the swarm. Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 411 ( ) 1 1 (2 (0,1) 1) Itr CF t rand Max   = −  −    (58) where Maxitr represents the maximum number of iterations. 4.2.5. Boundary conditions A jellyfish will eventually return if it leaves the boundaries of the search area. As an illustration of reintegration process, ' , , , , , ' , , , , , ( ) ( ) ( ) ( ) i d i d b d b i d b d i d i d b d b i d b d JSA JSA U L d if JS U JSA JSA L U d if JS L  = − +   = − +  (59) where the ith jellyfish location in dth dimension is represented by JSAi,d and its upper and lower bounds in food search space is given by Ub,d and Lb,d, respectively. JSA'i,d is the updated position of the ith jellyfish. In Learning automata (LA), extended learning vector in is provided by the following equation:  1 2, , ,r nmP P P P= (60) 1 1 1 1 JSA nmJSA r JSNoJSA nmJSNoJSA P P P P P     =      (61) With more plausible values, the optimal motions have a higher chance of being selected. Conversely, non-optimal solution movements have smaller probability values and are therefore less likely to be selected. 1 _ (0,1) ,1' 'i nm ii p Action index find rand first p =    =      (62) where find is a searching function and the probability of ith motion is denoted by pi. JFSA pseudocode is given in Fig. 4. 4.2. LA-based Hybridization The suggested hybridization of the LA-based HMPJA will increase the algorithms’ reliability and overcome the drawbacks of the individual metaheuristic algorithms, such as insufficient jellyfish movements, scattering of jellyfishes in the search space and MP complexity, slow or premature convergence locking in local optima, and sluggish search. Fig. 5 shows the HMPJA flowchart. 412 P. GURU, N. MALIK, S. MAHAPATRA Fig. 4 Pseudocode for JSA 5. SIMULATION RESULTS AND DISCUSSION The optimal operation is simulated under uncertainty. The one-line diagram of IEEE 33- and 69-bus system are shown in Fig. 6 and Fig.7, respectively. Table 1 displays these systems' initial power flow solutions. The load flow calculations provide the bus voltages and power losses. In terms of losses and (min) voltage, the HMPJA performs better than the others in every case. For both of the situations under discussion, the optimal operation is obtained by using the recommended technique and compared with the results generated by other algorithms. The simulation is carried out on MATLAB, 64-bit operating system and 4GB RAM. The hybrid algorithm's empirical parameters are set at a maximum of 100 iterations and 10 populations. Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 413 Fig. 5 Flow chart for hybrid HMPJA 414 P. GURU, N. MALIK, S. MAHAPATRA Fig. 6 IEEE 33-bus system Table 1 The system specification and the base case results of 33-bus system System Specifications: 33-Bus 69-Bus NB 33 69 Npr 32 68 Vsys (kV) 12.66 12.66 Base MVA 100 100 Sload (MVA) 1003.802+j2.694 3.802+j2.694 PTotal Loss (kW) 202.070 225 QTotal Loss (kVAr) 142.437 102.198 Vmin (pu), bus 0.9131, 18 0.9091, 65 Table 2 The cost coefficients of the PVDG and DSTATCOM Cost Parameter Value PV CPV 770 $/kW CO&M 0.01 $/kWh 𝜏 10% NP 20 DSTATCOM CS 50 $/kVAr α 10% ND 30 Grid Closs 0.06 $/kWh Cgrid 0.96 kWh Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 415 Fig. 7 IEEE 69-bus system In this instance, the suggested methods are used to solve the optimal planning issue on the considered bus systems while accounting for the uncertainties of the linked load and sun irradiances. Cost reduction, VP, and stability index improvement are among the multi- objective functions for handling the optimum planning issue. It should be noted that this article takes into consideration three years' worth of hourly historical data on load demand and solar irradiation. This has led to the division of each year into four distinct seasons. A Day (24 hours) within each season is considered to describe the stochastic behavior of the PV and load demand throughout that season. As a result, there are 96 time periods in a year (four seasons of 24 hours). Fig. 8 and 9 show the obtained load profiles and solar irradiance under ambiguous settings. 5.1. IEEE 33-Bus system The overall cost, TVDEVev, and VSID at the base scenario (without PV or DSTATCOM or NRX included) are 2.438704E+6 $, 1.3427E+4 pu., and 2.29424E+5 pu. respectively. The suggested approach solves the optimal planning issue by including up to two PVDGs and DTSTACOMs, both separately and in an altered network. The PVDG and DSTATCOM cost parameter data are shown in Table 2. The simulation results are shown in Table 3, Table 4 and Table 5 for the optimal integration of PVDG, and DSTATCOM allocation in the reconfigured network and separately by MPA, JFSA and HMPJA for single hybrid and two hybrid system respectively. When compared to PVDG or DSTATCOM and NRX without insertion, the overall cost is significantly decreased to 1.963071E+6$, or 19.5%, and 2.398893EC6 or (1.632%) respectively when a single hybrid system is included. Additionally, the TVDev is decreased to 1.0150EC4 (24.40%) and 1.2453EC4 (7.25%) respectively for PVDG or DSTACOM placement and NRX. 416 P. GURU, N. MALIK, S. MAHAPATRA Table 3 Simulation results for IEEE 33- bus system for single hybrid systems by MPA and JFSA technique Entity Base Case MPA JFSA PV + DSTATCOM NRX PV + DSTATCOM + NRX PV + DSTATCOM NRX PV+ DSTATCOM +NRX Eloss (MWh) 1.0782 1.0647 1.0050 0.9186 1.0261 1.0257 1.0016 Egrid (MWH) 24.7293 24.4197 23.0504 21.0688 23.5321 23.5252 22.9724 Optimal loc 1 - 2 - 8 13 - 33 Psr1 (kW) - 1780 - 1527 2007 - 1769 Qds1 (kVAr) - 100 - 128 100 - 130 TVDev 1.3427 E+4 13312.3768 13545.4377 11638.5159 10912.8123 14902.0637 11584.5484 VSID 2.29424 E+5 229819.4956 229207.9052 237222.5434 241262.1909 225284.2976 239479.5715 Closs ($) 6.4692 E+4 6.3882 E+4 6.0300 E+4 5.5116 E+4 6.1566 E+4 6.1542 E+4 6.0096 E+4 Cgrid ($) 2.374012 E+6 2.344291 E+6 2.212838 E+6 2.067081 E+6 2.259081 E+6 2.258419 E+6 2.205350 E+6 Cpv ($) 0 1.93792 E+5 - 1.66247 E+5 2.18506 E+5 0 1.92594 E+5 Cds ($) 0 530.5 - 679.04 530.5 0 689.65 Ctotal ($) 2.438704 E+6 2.602495 E+6 2.273138 E+6 2.289123 E+6 2.416274 E+6 2.319961 E+6 2.458729 E+6 Tie Switches 33,34,35, 36,37 33,34,35, 36,37 35,36,25, 9, 4 35,36,25, 9, 4 33,34,35, 36,37 28,10,30, 34,5 28,10,30, 34,5 The VSID is increased to 2.41517EC5 (5.27%) and 2.32748EC5 (1.42%) respectively. Aside from that, there is a significant decrease in energy losses and the amount of energy taken from the grid when 13th bus has been designated as the ideal position for the hybrid system for PVDG-DSTACOM allocation, and the PVDG and DSTATCOM have respective sizes of 969kW and 500kVAR. When the allocation is done in the reconfigured network, total cost and voltage deviation are reduced by 24.63% and 29.93% respectively. VSID is improved by 6.78% as compared to base case condition. Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 417 Table 4 Simulation results for IEEE 33- bus system for two hybrid systems by MPA & JFSA Entity Base Case MPA JFSA PV + DSTATCO M NRX PV + DSTATCOM + NRX PV + DSTATCOM NRX PV+ DSTATCO M +NRX Eloss (MWh) 1.0782 0.8454 1.0901 0.9334 1.0041 1.0717 1.0032 Egrid (MWH) 24.7293 19.3909 25.0034 21.4086 23.0318 24.5815 23.0097 Optimal loc 1 - 2 - 11 2 - 2 Optimal loc 2 - 16 3 16 14 Psr1 (kW) - 500 - 767 100 - 736 Psr2 (kW) - 500 500 100 100 Qds1 (kVAr) - 500 - 500 100 - 100 Qds2 (kVAr) - 500 500 100 100 TVDev 1.3427 E+4 10356.0057 12804.4816 10250.9471 12766.8065 13572.8215 12764.093 VSID 2.29424 E+5 239869.656 2 231941.7684 242147.2927 231587.6083 229289.5333 231955.9914 Closs ($) 6.4692 E+4 5.0724 E+4 6.5408 E+4 5.6005 E+4 6.0251 E+4 6.4305 E+4 6.0193 E+4 Cgrid ($) 2.374012E +6 1.861526 E+6 2.400327 E+6 2.055232 E+6 2.211061 E+6 2.359825 E+6 2.208931 E+6 Cpv ($) 0 1.08872 E+5 - 1.37940 E+5 2.1774 E+4 0 9.1016 E+4 Cds ($) 0 5.305 E+3 - 5.305 E+3 1.061 E+3 0 1.061 E+3 Ctotal ($) 2.438704E +6 1.975703 E+6 2.465735 +6 2.198477 +6 2.418957 E+6 2.424130 E+6 2.361201 E+6 Tie Switches 33,34,35,3 6,37 69,70,71, 72,73 43,69,54, 61,18 43,69,54, 61,18 69,70,71, 72,73 44,17,58, 39,22 44,17,58, 39,22 The output power of the PV unit fluctuates in proportion to changes in solar radiation. In terms of cost, TVDEV, and VSID, Table 5 shows that the results produced by the suggested algorithm. The IEEE 33-bus PDN is also incorporating two hybrid systems. Table 5 shows a significant decrease in the overall cost to 18.71%, and in TVDev is 32.69% in comparison to the basic scenario. VSID is raised by 6.81%. The 11th bus and the 2nd bus are the designated ideal places for the hybrid systems in this instance, and the first PVDG and DSTATCOM have respective sizes of 908 kW and 100kVAR. DSTATCOM and the second PVDG have respective ratings of 100kVAR and 100kW. 418 P. GURU, N. MALIK, S. MAHAPATRA Table 5 Simulation results for IEEE 33- bus system for single and two hybrid systems by HMPJA technique Entity Base Case MPA JFSA PV + DSTATCOM NRX PV + DSTATCOM + NRX PV + DSTATCOM NRX PV+ DSTATCOM +NRX Eloss (MWh) 1.0782 0.82009 1.0606 0.87065 0.9246 0.8541 0.8274 Egrid (MWH) 24.7293 18.8095 24.3256 19.9691 21.2065 19.5894 18.9778 Optimal loc 1 - 13 - 13 8 - 11 Optimal loc 2 - - - - 2 - 2 Psr1 (kW) - 969 - 1115 1028 - 908 Psr2 (kW) - - - - 783 - 100 Qds1 (kVAr) - 500 - 500 100 - 100 Qds2 (kVAr) - - - - 100 - 100 TVDev 1.3427 E+4 1.0150 E+4 12453.289 9408.1626 11999.1171 9790.8691 9001.2101 VSID 2.29424 E+5 241517.2 232748.3228 244992.9943 234259.0181 242342.869 1 246198.3321 Closs ($) 6.4692 E+4 4.9205 E+4 6.3636 E+4 5.2239 E+4 5.5476 E+4 5.1246 E+4 4.9644 E+4 Cgrid ($) 2.37401 2E+6 1.805718 E+6 2.335257 E+6 1.191703 E+6 2.035830 E+6 1.880587 E+6 1.821868 E+6 Cpv ($) 0 1.05496 E+5 - 1.21392 E+5 2.16764 E+5 - 1.09742 E+5 Cds ($) 0 2.652 E+3 - 2.652 E+3 1.061 E+3 - 1.061 E+3 Ctotal ($) 2.43870 4E+6 1.963071 E+6 2.398893 E+6 1.837986 E+6 2.309131 E+6 1.931833 E+6 1.982315 E+6 Tie Switche s 33,34,3 5,36,37 33,34,35, 36,37 19,36,12, 11,28 19,36,12, 11,28 33,34,35, 36,37 9, 26, 34, 7, 16 9, 26, 34, 7, 16 Fig. 10 shows the system's VP with the DSTATCOM, PVDGs, and NRX in four seasons. It is evident from Fig. 10 that the addition of two-hybrid systems significantly improves the VP compared to the base situation. Based on Table 5, the results of applying the suggested method are superior to those of the published algorithm. 5.2. IEEE 69-Bus system The proposed approach is also applied to IEEE 69-bus system for optimal planning is PDN under uncertainties. Fig. 8 and Fig. 9 also show the system load profile and solar irradiance under uncertain conditions. By combining single and two-hybrid systems with reconfiguration, the best possible solution to the power planning problem is evaluated. Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 419 The results for the 69-bus system are listed in Table 6, Table 7 and Table 8 for single and two hybrid system by using MPA, JFSA and HMPJA respectively. The total cost and TVDev are reduced by 17.69% and 26.00% respectively for a single hybrid system. The VP is shown in Fig. 11. It is seen from the Fig. 11, that the VP is enhanced with PVDG- DSTACOM inclusion in a reconfigured network. For a two-hybrid system, the TVDev is reduced by 43.80%, along with a 21.72% reduction in total cost. The voltage stability is enhanced by 1.57% and 3.39% in single and two hybrid systems respectively. Table 9 shows the superiority of the proposed algorithm while comparing with the previously published articles. Fig. 8 The hourly load profile across seasons Fig. 9 The variations in solar irradiance throughout the seasons The following conclusions are derived by the simulation results. a) A strong and effective tool for PVDG and DSTATCOM optimal planning in the redesigned PDN is made possible by the suggested HMPJA, which outperforms the most recent algorithms. 420 P. GURU, N. MALIK, S. MAHAPATRA b) One PVDG and DSTATCOM integrated into the 33-bus system can reduce annual total costs and voltage variations by 24.63% and 28.98%, respectively. The base case voltage stability is improved by 6.35%. The total annual cost can also be reduced by optimally integrating two hybrid PVDG and DSTATCOM in the reconfigured network, with voltage deviations by 18.71 % and 32.96 %, respectively. The improvement in voltage stability over the base case is 6.81%. c) One PVDG and DSTATCOM hybrid with appropriate integration can reduce the predicted cost and voltage variations in the 69-bus system by 17.67% and 26.00%, respectively. The voltage stability is increased by 1.57% when two hybrid PVDG and DSTATCOM are implemented properly, reducing the overall annual cost and voltage deviation by 21.72% and 43.80%, respectively, and 3.39% when compared to the base scenario with one and two hybrid system respectively. To solve the challenges of optimal power planning involving the optimal integration of PVDG and DSTATCOM, future study will consider a variety of energy storage solutions, including fuel cells, batteries, hydro-pumps, compressed air, and superconducting magnetic energy storage, electrical vehicle charging stations. The effective implementation of the recommended HMPJA algorithm in the specified technical use gives an assurance to approve the coordinated functioning of FACTS controllers and expand to large-scale interconnected power networks in the future. Table 6 Simulation results for IEEE 69- bus system for single hybrid systems by MPA & JFSA Entity Base Case MPA JFSA PV + DSTATCO M NRX PV + DSTATCOM + NRX PV + DSTATCO M NRX PV+ DSTATCOM +NRX Eloss (MWh) 1.19726 1.1513 0.6680 0.5421 1.0796 0.8302 0.7036 Egrid (MWH) 27.4468 2 26.4059 15.3211 12.4355 24.7614 19.0412 16.1393 Optimal loc 1 - 13 - 17 19 - 12 Psr1 (kW) - 573 - 695 500 - 666 Qds1 (kVAr) - 500 - 500 500 - 500 TVDev 1.24867 E+4 10852.5384 11314.438 6 8278.4685 12038.1415 17790.0922 14502.1812 VSID 5.40257 E+5 559748.8951 539816.17 13 552283.9652 5.49450 E+5 516467 E+5 529179 E+5 Closs ($) 7.18361 99 E+4 6.9078 E+4 4.0080 E+4 3.2526 E+4 6.4776 E+4 4.4934 +4 4.3452 +4 Cgrid ($) 2.63489 5E+6 2.534966 E+6 1.470825 E+6 1.193808 E+6 2.377094 E+6 1.827955 E+6 1.594560 E+6 Cpv ($) - 6.2383 E+4 - 7.5660 E+4 5.44380 +5 0 7.25087 +5 Cds ($) - 2.652 E+3 - 2.652 E+3 2.652 E+3 0 2.652 E+3 Ctotal ($) 2.70673 1E+6 2.669079 E+6 1.510905 E+6 1.348458 E+6 2.988902 E+6 1.872889 E+6 2.365751 E+6 Tie Switches 69,70,71 ,72,73 69,70,71, 72,73 8,17,11, 53,21 8,17,11, 53,21 69,70,71, 72,73 4,63,19, 69,10 4,63,19, 69,10 Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 421 Table 7 Simulation results for IEEE 69- bus system for two hybrid systems by MPA & JFSA Entity Base Case MPA JFSA PV + DSTATCOM NRX PV + DSTATCOM + NRX PV + DSTATCOM NRX PV+ DSTATCOM +NRX Eloss (MWh) 1.19726 1.1513 0.6680 0.5421 1.0162 0.7489 0.7242 Egrid (MWH) 27.44682 26.4059 15.3211 12.4355 23.3073 17.1766 16.6100 Optimal loc 1 - 17 - 7 15 - 2 Optimal loc 2 - 19 25 52 46 Psr1 (kW) - 500 - 539 500 - 500 Psr2 (kW) - 825 534 500 500 Qds1 (kVAr) - 500 - 500 500 - 500 Qds2 (kVAr) - 500 500 500 500 TVDev 1.24867 E+4 10852.5384 11314.4386 8278.4685 11383.8933 11059.5843 9489.7015 VSID 5.40257 E+5 559748.8951 539816.1713 552283.9652 5.51959 E+5 5.41474 E+5 5.48543 E+5 Closs ($) 7.183619 9 E+4 6.9078 E+4 4.0080 E+4 3.2526 E+4 6.0972 E+4 4.4934 +4 4.3452 +4 Cgrid ($) 2.634895 E+6 2.534966 E+6 1.470825 E+6 1.193808 E+6 2.243808 E+6 1.648953 E+6 1.594560 E+6 Cpv ($) - 1.44255 E+5 - 1.16819 E+5 1.08872 +5 0 1.08872 +5 Cds ($) - 5.305 E+3 - 5.305 E+3 5.305 E+3 0 5.305 E+3 Ctotal ($) 2.706731 E+6 2.753604 E+6 1.510905 E+6 1.348458 +6 2.418957 E+6 1.693887 E+6 1.752718 E+6 Tie Switches 69,70,71, 72,73 69,70,71, 72,73 43,69,54, 61,18 43,69,54, 61,18 69,70,71, 72,73 44,17,58, 39,22 44,17,58, 39,22 422 P. GURU, N. MALIK, S. MAHAPATRA Table 8 Simulation results for IEEE 69- bus system for single and two hybrid systems by HMPJA Entity Base Case MPA JFSA PV + DSTATCOM NRX PV + DSTATCOM + NRX PV + DSTATCOM NRX PV+ DSTATCOM +NRX Eloss (MWh) 1.19726 1.02679 0.73328 0.68705 1.02382 0.6632 0.6306 Egrid (MWH) 27.44682 23.5502 16.8185 15.75820 23.4821 15.2126 14.4646 Optimal loc 1 - 15 - 61 11 - 2 Optimal loc 2 - - - 12 - 19 Psr1 (kW) - 2571 - 1048 1000 - 700 Psr2 (kW) - - - - 1000 - 700 Qds1 (kVAr) - 100 - 105 700 - 700 Qds2 (kVAr) - - - 700 - 700 TVDev 1.24867 E+4 1.1957 E+4 1.0553 E+4 9.236 E+3 1.07 E+03 1.0291 E+4 7.016 E+3 VSID 5.40257 E+5 5.51881 E+5 5.43531 E+5 5.48883 E+5 5.57 E+05 5.43954 E+5 5.59230 E+5 Closs ($) 7.1836199 E+4 6.1566 E+4 4.3997 E+4 4.1223 E+4 6.1429 E+04 3.3979 E+4 3.7836 E+4 Cgrid ($) 2.634895E +6 2.259082 E+6 1.61457 E+5 1.557926 E+6 2.254282 E+06 1.460409 E+6 1.388860 E+6 Cpv ($) - 2.79909 E+5 - 1.14097 E+5 2.17744 E+05 - 1.52420 E+5 Cds ($) - 5.305 E+3 - 5.586 E+3 7.427 E+03 - 7.427 E+3 Ctotal ($) 2.706731E +6 2.550452 E+6 2.222720 E+6 2.227695 E+6 2.540882 E+06 1.800208 +6 1.586543 E+6 Tie Switches 69,70,71,7 2,73 69,70,71, 72,73 13,17,21, 42,58 13,17,21, 42,58 69,70,71, 72,73 71,54,14, 64,9 71,54,14, 64,9 Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 423 Table 9 Comparative analysis for IEEE 69- bus system for single and two hybrid systems Entity Base Case MPA JFSA PV + DSTATCOM NRX PV + DSTATCOM + NRX PV + DSTATCOM NRX PV+ DSTATCOM +NRX Eloss (MWh) 1.19726 1.02679 0.6582 1.3345 1.02382 0.8136 1.1174 Egrid (MWH) 27.44682 23.5502 24.857 26.604 23.58 21.6146 Optimal loc 1 - 15 62 57 11 63 62 Optimal loc 2 - - 12 57 58 Psr1 (kW) - 2571 1113 532 1000 690 1805 Psr2 (kW) - - - 1000 1337 1316 Qds1 (kVAr) - 100 1290 2689 700 1449 935 Qds2 (kVAr) - - - 700 581 1683 TVDev 1.24867 E+4 1.1957 E+4 8.74E+03 7.61E+03 1.07E+03 6.95E+03 6.12E+03 VSID 5.40257 E+5 5.51881 E+5 5.62E+05 5.66E+05 5.57E+05 5.69E+05 5.77E+05 Closs ($) 7.1836199 E+4 6.1566 E+4 3.95E+04 8.01E+04 6.17E+04 4.88E+04 6.70E+04 Cgrid ($) 2.634895E +6 2.259082 E+6 2.39E+06 2.55E+06 2.26E+06 2.24E+06 2.08E+06 Cpv ($) - 2.79909 E+5 1.21E+05 5.72E+04 1.84E+05 2.21E+05 3.40E+05 Cds ($) - 5.305 E+3 6.84E+03 1.43E+04 7.49E+03 1.08E+04 1.39E+04 Ctotal ($) 2.706731E +6 2.550452 E+6 2.55E+06 2.71E+06 2.52E+06 2.519764E 2.50E+06 424 P. GURU, N. MALIK, S. MAHAPATRA (a) (b) Fig. 10 VP of the 33-bus system by incorporating the one and two hybrid systems PV- DSTATCOM with NRX in (a) Winter, (b) Spring (CONTD…) Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 425 (c) (d) Fig. 10 VP of the 33-bus system by incorporating the one and two hybrid systems PV- DSTATCOM with NRX in (c) Summer, (d) Autumn 426 P. GURU, N. MALIK, S. MAHAPATRA (a) (b) Fig. 11 VP of the 69-bus system by incorporating the one and two hybrid systems PV- DSTATCOM with NRX in (a) Winter (b) Spring (CONTD…) Optimizing Distribution Networks with PVDG-DSTACOM and Reconfiguration under... 427 (c) (d) Fig. 11 VP of the 69-bus system by incorporating the one and two hybrid systems PV- DSTATCOM with NRX in (c) Summer (d) Autumn 428 P. GURU, N. MALIK, S. MAHAPATRA 6. CONCLUSION This study addresses the best design and evaluation of integrating a combined system with PVDG and DSTATCOM in a reconfigured PDN while taking seasonal fluctuations in solar irradiance and load demand into account. With the use of gaussian and beta probability density functions, demand for load and solar irradiance’s random nature are accurately represented. A hybrid marine predator jellyfish search algorithm (HMPJA) has been presented based on the learning automata to improve the method's dependability. This integration aims to provide a more resilient and effective optimization method that can handle a variety of difficulties in different problem scenarios. A multi-objective function's ideal location and size have been determined by applying the suggested HMPJA, which takes into account factors including cost savings, VP, and stability index enhancement in the reconfigured network. The proposed technique has been applied to IEEE 33-bus and 69-bus systems. 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