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Scientific Reports volume 15, Article number: 20755 (2025)
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The strategic integration of distributed generation (DG) units into distribution power networks (DPNs) is pivotal for augmenting system efficiency and stability. This study introduces an advanced metaheuristic optimization framework leveraging the Jellyfish Search Algorithm (JSA) for the optimal placement and sizing of solar photovoltaic (PV) DG units. The formulated multi-objective function incorporates real power loss (RPL) minimization, voltage deviation index (VDI) reduction, and voltage stability index (VSI) enhancement, employing a weighted sum approach (WSA) to ensure computational rigor. The efficacy of the proposed methodology is rigorously validated on the IEEE 33-bus radial DPN under single and multiple PV system deployment scenarios. For single PV system optimized inclusion, RPL of the DPN is cut down from 210.98 kW to 102.89 kW, total VDI is reduced from 1.8047 p.u to 0.5331 p.u, and minimum VSI is increased from 0.6671 to 0.7559. For two PV DG units inclusion, RPL is reduced to 82.99 kW, total VDI is reduced to 0.6518 p.u with a least VSI improved to 0.8848. However, better result is obtained with three units of DG placement with RPL reduced to 69.59 kW, total VDI decreased to 0.3293 p.u with a least VSI of the test system increased to 0.8916. Comparative analyses against state-of-the-art metaheuristic algorithms underscore the superior convergence efficiency and optimality of JSA in addressing nonlinearity and high-dimensionality constraints. Empirical results substantiate substantial RPL reduction, bus voltage enhancement, and system stability reinforcement, establishing JSA as an avant-garde paradigm in DG optimization.
Power system utilities supply electricity through transmission and distribution power networks. The consumers are powered through distribution power networks (DPN). DPN connects the consumers through low-potential and high-current conductors. The power losses (PL) and voltage drops along the DPN are higher than those of the transmission networks (TN), since the line resistance of the DPN is higher than that of the TN. High PL, low voltage, frequent interruptions, harmonic distortions (current and voltage), and unstable voltage limit the performance of DPN. Hence, DPN performance should be optimized for reliable and stable operation. Various approaches, including capacitor assimilation, distributed generation (DG) placement, network reconfiguration, and FACTS device placement have been adopted to increase the performance of DPN1,2. Capacitors and few FACTS such as SVC (Static VAR Compensator), STATCOM (Static Synchronous Compensator) and UPFC (Unified Power Flow Controller) inject sufficient quantities of reactive power to minimize PL and regulate bus voltages of DPN. The network reconfiguration method enhances the performance of DPN by changing the tie-line and sectionalized switches. DG is a decentralized generation system that uses modern PV technology, wind turbines or microturbines to inject real (P), reactive (Q), or both into the DPN. DG optimization is considered more effective than capacitor, SVC, STATCOM and UPFC since it can support the DPN with both real and reactive power injection. Integration of DG changes the existing radial DPN into an active system. DG can be defined as a typical small-scale power generator3. Moreover, renewable energy resource (RER) based DGs are highly recommended for optimal integration at the point of load centres because of its numerous benefits3. RER DG models especially solar and wind energy are highly recommended because of their environmental sustainability, minimum operational costs and ample accessibility. Unlike conventional fossil fuels, RER DG significantly cut down the greenhouse gas emission, support energy autonomy, and encourage decentralized power generation, which improves the reliability and resilience of the distribution power grid.
A novel short-term interval forecasting technique was proposed in4 for estimating the PV power. The meteorological element of the PV station was reconstructed using a second-order extended Markov model (HMM). A trend fusion and fluctuation clustering-based wind speed correction technique was proposed in5. First, the input feature was framed using the wind speed trend, and then the numerical weather prediction wind speed error distribution was computed to develop a precise and stable mapping relationship. A novel ultra-short-term wind power forecasting approach was proposed based on the EMD-CC Transformer6. The network model is framed, demonstrating the encoder–decoder structure. The historical wind sequence is analyzed in encoder then the wind power prediction is done using the decoder. A frequency voltage active support technique for a hybrid wind farm based on grid-following and grid-forming hierarchical subgroup control was proposed to support the premises for ensuring system stability7. A virtual external perturbance-based impedance measurement technique was implemented for grid-connected converter8. The proposed technique applied changes to the voltage and current samples at the point of common coupling.
Moreover, the modern energy systems such as microgrids encourage decentralized operation with distrusted power energy resources. Microgrid power networks employ small scale DG units and energy storage systems to operate independently and in synchronize with the main distribution grid. Microgrid with optimized integration of DG units can enhance resilience, reliability and curtail power losses. Moreover, integration of RER based DG unit play an integral part in the transition to smart grid.
A homomorphic encryption-based resilient distributed algorithm was suggested for microgrid energy management to prevent the malevolent data intrusions9. A fuel tank dispatch was included as an integral part of the mobile emergency generators for better restoration of power10. Authors have suggested a generalized Nash-in-Nash bargaining model for a building for assessing the energy loss and network usage cost in a P2P trading market11. The SSA-CNN-BiLSTM-Attention model was proposed to optimize the energy dispatch in the microgrid with enhanced prediction accuracy12. An efficient distributed optimization algorithm was developed for solving the dynamic economic dispatch problem in a hybrid microgrid network13. The economic dispatch problem was solved for minimizing the total generation expenses.
Energy management (EM) is essential in DG integrated power system networks to monitor the effective utilization of generated power. As the existing traditional power grids are shifting towards smart grid technology, Energy Management System (EMS) play a crucial part in adopting decentralized power generation and energy storage aiding to balance between generation and demand while minimizing greenhouse/carbon emissions and operational costs. EMS incorporates innovative software tools and communication technologies to monitor the operation of DG integrated electrical power networks. They help to forecast energy demand and optimize energy dispatch and make the system operator to initiate informed decision. Real-time control strategy of EM system enhances the efficiency, sustainability and reliability of conventional DPN and microgrid.
Authors have implemented an event-trigger-based resilient distributed energy management system to safeguard the smart grid from false data injection and denial of service attacks12. A complete hydrogen energy chain concept was proposed in14 to optimize the energy flows in all links of the hydrogen chain-based energy system using a bottom-up long-term investment strategy. A game-theoretic model was developed to examine the manufacturer’s optimal building strategy15. The outcome reveals that the manufacturer can build the charging stations whenever the construction cost is fairly low. A multiagent reinforcement learning technique was proposed in16 to maximize social welfare with privacy protection in a dynamic energy market. The proposed technique was executed for taking optimal decisions in the P2P energy market. A numerical simulation has been carried out to investigate the heat transfer behavior between the thermoelectric module and the environment17.
The optimized DG inclusion in the DPN/microgrid can reduce the total PL, regulate the bus voltages, and enhance the stability and reliability3. But the position and size for DG in DPN should be optimized appropriately to achieve utmost assistance from it. Meanwhile, inappropriate inclusions of DGs have led to more PL and unreliable conditions in DPNs4.
Researchers have adopted several analytical and meta-heuristic algorithms-based techniques18,19,20 for optimizing the location and ratings of compensation devices such as capacitors, few FACTS devices (SVC, STATCOM and UPFC), and decentralized power generation units. The analytical technique incorporates mathematical computation to solve the optimization problem. The heuristic technique uses randomness to solve optimization problems. Table 1 presents taxonomy of optimization techniques applied for enhancing the performance of RDPN.
Mathematical expressions based optimization methods21,22 were proposed to solve the optimal placement and sizing problem (OPSP) of DG in the radial power distribution network (RPDN). A novel analytical approach was proposed using voltage stability index (VSI) to find the best optimized solution for the OPSP23. ALO algorithm was suggested for optimizing the DG location and rating in the different DPNs24. BSOA optimization method was implemented to disperse the DG units optimally in the radial DPN. The DG’s location and sizes were optimized to minimize RPL and increase the bus voltages25. A hybrid EHO – PSO method was proposed for optimizing the different cases of DG units in IEEE benchmarks radial DPNs. The study considered three IEEE benchmark test systems, viz., 33, 69 and 118-bus RPDNs for validation. The DG locations and ratings were optimized aiming to minimize RPL and line voltage drop and improve distribution line voltage stability26. SKHA was suggested to find the solution for the DG OPSP in DPN27. The study considered RPL minimization as an objective. The effectiveness of SKHA was verified on the 33 and 69-bus IEEE benchmark RPDNs. CSA method was introduced to optimally integrate three types of DG units into the DPN. The proposed work was tested on a real Egyptian DPN for RPL minimization and operating cost savings28. A novel optimization method using OTCDE was proposed to optimize the placement and ratings for multiple units of DGs29. Likewise, DE method was proposed to optimize multiple units of DG in the distribution power grid30. A metaheuristic technique was proposed using SOA to optimize the DG sites and ratings for PL minimization, bus voltage enrichment and distribution line VS enhancement31. Hybrid TLBO-GWO optimization method was proposed to optimize PV and wind turbine systems in the IEEE 33 and 69-bus benchmark RDPNs32. The optimal positions and ratings for the DGs were optimized via ISOS algorithm to minimize PL, enhance VP and improve VS of radial DPNs33. Multiple units of DGs were optimally integrated into the IEEE 33-bus and 69-bus benchmark DPNs using CSCA method considering a single and multi-objective problems34. HHO technique35 and GWO-PSO integrated method36 were implemented to identify the locations and ratings of different type of DGs. The optimization was done to minimize PL and improve VP of DPN. LSF- SCA hybrid method was suggested to optimize PV and wind turbine (WT) systems to minimize PL and improve the bus voltages of an unbalanced 33-bus benchmark DPN37. GA38, hybrid PSO-DE39 and hybrid SFLA-PSO40 methods were proposed to optimize single solar PV system for real PL minimization and bus voltage improvement. The optimal positions and sizes for two units of solar PV systems were optimized using hybrid WIPSO-GSA41 and GWO41 methods. Likewise, BFOA42, KHA43, BA44, WOA45, and AIS46 approaches optimized the three units of PV systems locations and capacities in the 33-bus radial DPN for RPL and voltage deviation minimizations.
Analytical methods give inaccurate results and take more time to converge. But, the metaheuristic algorithm methods produced better results than analytical methods and converge in faster rate. However, metaheuristic algorithms also possess their respective limitations and weaknesses. For example, GA, BA, BSOA, ALO, GWO, BFOA, and WOA optimization algorithms are effective in solving small and simple dimensional problems, but become ineffective for large and high dimensional problems. Hence these algorithms often prematurely converge to a local optima solution because of their insufficient diversity in the population and imbalance between the exploitation and exploration. JSA is relatively a novel algorithm compared to the aforementioned algorithm, which is introduced for solving numerous complex and high dimensional problems47. JSA effectively solves the nonlinear and complex problems with its diversified search mechanism and balanced exploitation and exploration better results than the analytical methods. Also, the effectiveness of the JSA is addressed for various benchmark functions47.
The present study addresses the multi-bjective DG OPSP using JSA. The contribution of the study is highligghted below:
A multi-objective JSA optimization technique that intelligently maps the food-searching behaviors of jellyfish is implemented to optimize solar PV DG systems for achieving technological benefits, viz., RPL reduction and bus voltage deviation minimization, and VS enhancement.
The performance of the JSA metaheuristic technique is evaluated on a 33-bus RDPN for (i) single, (ii) two, and (iii) three solar PV DG unit placements.
Efficacy of the simulation findings is evaluated via a comprehensive comparison study.
The present work is detailed in different sections. Section II details the mathematical formulation of DG placement and sizing problem. Section III presents JSA mathematical modelling and implementation. Section IV explains the simulation outcomes for different cases of PV systems placement and sizing. Section V concludes the significant findings of the present work.
The identification of critical buses and ratings for DG units in the RDPN is a complex and non-linear problem. This study aims to optimize single and multiple units of PV systems as DGs to minimize RPL, minimize VD, and enhance line VS. Single line diagram (SLD) of a typical RDPN having ‘n’ number of buses and ‘k” number of distribution lines is shown in Fig. 1. The distribution lines are represented by equivalent series impedances. The power flow in the RDPN is expressed as simplified recursive equations.
Radial PDN with DG placement.
Equations (1), (2), (3) give the expression for the real and reactive power flow, and the bus voltage48.
For a bus, i = 1, 2, …., n and k = 1, 2,….n-1.
The branch current is expressed in Eq. (4).
Whenever the current passes through a distribution line, power losses occur. Equations (5) and (6) express the real (Ploss) and reactive (Qloss) power loss in a branch, respectively48.
Total Ploss and Qloss of ‘n’ bus and ‘nb’ branch RDPN are expressed in Eqs. (7), (8), respectively48.
Usually PTloss more dominant than QTloss since line resistances are higher than reactance in DPN. Hence, the present work only considers RPL minimization as the prime objective.
RPL along a branch of the RDPN after the optimal inclusion of DG units is mathematically expressed in Eq. (9).
PTlossDG after the optimal inclusion of DGs is expressed in Eq. (10).
The multiple objectives considered in this study are framed as a single objective function using weighted sum method (WSM) as expressed in Eq. (11).
Where, δ1, δ2, and δ3 are the weightage factors. The values for the weightage factors must be appropriately selected such that their sum must be unity.
Total RPL (PTloss) is the prime objective of the DG optimization study. Power loss minimization is achieved via measurement of power loss index (PLI)49. The mathematical expression for PLI is given in Eq. (12). Minimum PLI results in maximum PL reduction.
Bus VD minimization is the second of the three objectives. Bus VD cab be reduced via minimization of bus voltage deviation index (VDI)49 given in Eq. (13). Reduction of bus VDI increases bus voltage.
For i = 1, 2 ……n
Voltage stability enhancement is the third and last objective of the DG optimization study. The present work assesses the voltage stability of the DPN via VSI measurement42. Equation (14) gives the mathematical expression for the VSI.
For i = 1, 2… n and k = 1,2,….n-1
A stable DPN is the one with VSI values closer to unity at all the buses. If the VSI of any one of the buses reads zero or approaches near zero, then the DPN is considered to be an unstable system. VSI is a scalar value and is computed from load flow results data. The VSI maximization is obtained by minimizing the reciprocal value of Eq. (14).
The optimal solution to a DG placement problem should not violate any operational constraints of DPN. Equations (15)–(18) give the real power balance, bus voltage, thermal capacity, and DG power rating constraints considered in the present DG optimization study42.
Where,
The present study analyzes the impact of PV system penetration for achieving technological benefits in DPN. The PV system is modelled as a P-type DG unit and injects only real power into the RRDN. Equation (21) presents the mathematical model for a PV system49.
Since the proposed DG placement and sizing problem is solved from planning perpective, the solar radiation data for PV DG system is neglected.
JSA is a novel metaheuristic algorithm introduced47 to solve numerous optimization problems. JSA addresses complex optimization problems effectively through its diverse search ability, an adaptive search approach, and a balanced exploration-exploitation process. These unique features greatly evade local optima entrapment and fast convergence. JSA mimics the food search behaviors of jellyfish. Jellyfish adopt two types of search mechanisms, viz., diversification and intensification, to capture nutrition like fish eggs, larvae, etc., in the ocean current and jellyfish swarm. JSA switches between search mechanisms via a time control mechanism (TCM). The mathematical background of JSA implementation is presented below.
JSA adopts a unique tactic known as a chaotic map for initializing the population. Equation (22) expresses the population initialization.
And
The OC has rich quantities of nutrients. Hence, jellyfish follow the ocean current (OC) in search of nutrition. The direction of OC is discovered using Eq. (24).
Where, ‘X*’ is the best jellyfish position in the search space.
The jellyfish upgrades its location via Eqs. (25), (26).
Jellyfish swarm movement is represented as type ‘A’ and type ‘B’ motions. Type ‘A’ and type ‘b’ movements are characterized as passive and active motion, respectively. In the beginning of the optimization process, jellyfish swarms tend to follow type ‘A’ motion. But, later it follows type ‘B’ motion. Equation (27) gives the jellyfish movement following a type ‘A’ motion.
The jellyfish direction is explored in type ‘B” motion via considering a jellyfish, ‘j,’ alongside the one chosen (jellyfish, ‘i’) in a random process. If the nutrition around the jellyfish, ‘j,’ is more compared to the location of jellyfish, ‘i,’ then jellyfish, ‘i,’ directs towards jellyfish, ‘j.’ Otherwise, jellyfish, ‘i’ directs away from jellyfish, ‘j.’ Similarly, remaining jellyfish inside the swarm move and occupy the best position to consume the food. The mathematical illustration for the jellyfish movement and its updated position is given in Eqs. (28)–(30).
Where, f (X) refers to a fitness function for the location ‘X’.
OC embraces a bulk quantity of nutritious food. Therefore, the jellyfish creates a swarm to search for food in the OC. The OC changes its direction for a temperature or wind direction change. Under this circumstance, the jellyfish crafts another swarm and directs its movement towards the OC. However, JSA includes TCM to normalize the jellyfish movement inside and outside the swarm. A time control function (TCF) and constant ‘c0’ is introduced in the TCM to normalize the jellyfish movement. Equation (31) mathematically expresses TCF.
Where, (1-c(t)) signifies the movement of jellyfish inside a swarm. For ‘rand (0, 1)’ greater than (1-c(t)), the jellyfish follows type ‘A’ motion; otherwise jellyfish follows type ‘B’ motion.
The jellyfish circulates randomly inside an ocean. Hence, its position must be regularized within a specified boundary condition whenever it goes beyond the search area to have a better solution. Equation (32) illustrates the boundary condition normalization.
Where, Xi, d and X’i, d denote jellyfish’s actual position and updated position, respectively. The JSA algorithm is presented graphically as a flowchart in Fig. 2.
The JSA application for the DG placement and sizing problem is presented as algorithms below.
Input the necessary data for the 33-bus IEEE radial DPN.
Calculate PTloss, VDI, and VSI for the radial DPN without DG placement.
Initialize population size, iteration, and control parameters of JSA.
Find the initial candidate solutions using Eq. (22) and map the solution with jellyfish location.
Compute the fitness value for every candidate solution.
Fix iteration to 1.
Update the jellyfish location using Eqs. (25), (26).
Determine the fitness value for the updated jellyfish location.
Compare the fitness values of present and previous locations of jellyfish. Assign the solution that gives the minimum fitness value as the elite solution.
Check for constraint violation and iteration number. If the iteration count is less than the maximum value, increase the iteration by 1 and go to Step 7.
Print the optimized DG positions and ratings.
The proposed JSA approach for DG optimization problem is executed in MATLAB 2022b software. The simulink examination was performed on Intel i3 core processor featured personal computer. The input variables of JSA and boundary conditions for the decision variables are listed in Table 2. The optimal solution for the multi-objective function (MoF) is solved using the WSA. The fitness value for MoF is examined for different probabilities of weights as shown in Table 2. The combination weights that give the least fitness value for MoF are chosen as the feasible weights. For the present study, δ1, δ2, and δ3 values are approximated as 0.6, 0.3, and 0.1, respectively. Table 3 gives the best fitness values obtained for different combinations of δ1, δ2, and δ3.
JSA flowchart.
Figure 3 shows the SLD of IEEE 33-bus radial DPN considered in this study50. The simulation findings are investigated for three cases of solar PV-DG placements. They are: (i) single DG, (ii) two DGs, and (iii) three DGs. The impact of different cases of PV DG optimization are analyzed in terms of total RPL, bus voltage deviation, bus voltages, and line voltage stability. The real-time solar uncertainty is ignored in all cases of PV DG allocation. Further, a constant solar radiation is assumed.
33-bus radial DPN SLD.
The test system carries 33 numbers of buses and 32 numbers of branches. The balanced 33-bus radial DPN supplies 3.72 MW – PL and 2.3 MVAr – QL42.
The simulation findings of 33-bus RPDN without DG placement are essential for measuring the significance of optimized simulation findings. The simulation findings for without DG placement are obtained via backward-forward sweep (BFS) algorithm power flow execution48 and are referenced as the base case. For a base case condition, total RPL, minimum bus voltage (Vmin), and minimum voltage stability index (VSImin) are 210.98 kW, 0.9038 per unit (p.u.), and 0.6671, respectively. Figures 4, 5, 6 present base case simulation results for RPL, bus VDI, and line VSI, respectively. Figure 7 shows the bus voltages of the 33-bus RDPN without PV-DG placement. The bus voltages are presented in per unit (p.u.) on the 100 MVAbase and 12.66 kVbase. It is noticed from Fig. 5 that far-end-located buses experience more voltage deviation (VD) than the buses near the substation. The total VD of the test system is 1.8047 p.u. and the maximum VDI is 0.0962 p.u. Furthermore, 63.63% of buses (21 out of 33) have voltages below the required level (0.95 p.u.).
RPL of 33-bus radial DPN without DG.
VDI without DG placement.
VSI without DG placement.
Vbus without DG placement.
Table 4 presents the simulation findings for the optimized inclusion of a single PV system.
The optimal solution is obtained in 6 iterations and 24.4 s. Figure 8 illustrates the optimal solution for DG location, size, and objective function fitness value in each run of 50 independent runs. JSA optimizes the single PV DG in the 6th bus of the test system with a 2334.6 kW rating. JSA optimized single PV DG placement gives best solution in the 26th simulation run. The same has been highlighted in the illustration of Fig. 8. The total RPL is minimized from 210.98 kW to 102.89 kW and VDItotal is cut down to 0.533 p.u. after the optimized DG inclusion. Furthermore, the VDImin, Vmin, and VSImin are improved to 0.0393 p.u., 0.9607 p.u., and 0.7559, respectively. Figure 9 presents the RPL variation before and after the DG inclusion. Figures 10, 11,12 showcase the optimized solution of VDI, bus voltage, and VSI, respectively, for a single DG allocation. The test system has seen a significant voltage profile enhancement in all buses following the DG placement. Moreover, none of the buses of the test system records a voltage magnitude below the specified Vmin (0.95 p.u.). Figure 13 presents the convergence curve of JSA for a single DG placement.
Optimal bus selection for single DG.
33-bus radial DPN RPL after single DG placement.
33-bus radial DPN VDI after single DG placement.
Vbus of 33-bus radial DPN after single PV DG placement.
33-bus radial DPN VSI after single DG placement.
Convergence curve of JSA for a single DG placement.
The simulation findings for the two PV units optimization are presented in Table 5. Figure 14 presents the optimal solution for DG location, size, and fitness value for 50 independent runs. For two DG allocation, JSA optimizes the DGs in the 13th and 30th buses of test system. The best solution is obtained in the 42nd simulation run. The same has been highlighted in the illustration of Fig. 14. The DGs are optimized in the 13th and 30th buses of test system. The JSA converges to an optimal solution for the optimal sizes of 822.8 kW (@ 13th bus) and 1089.5 kW (@ 30th bus). JSA takes only 8 iterations and 29.4 s for convergence. Figure 15 presents the convergence plot of JSA for two units of PV system placements. The total real PL is minimized from 225 kW to 82.99 kW, and VDItotal is reduced to 0.6518 p.u. The minimum VDI is 0.0301 p.u. Consequently, the minimum Vbus and VSI are increased to 0.9698 p.u. and 0.8848, respectively. Figures 16 and 17 illustrate the simulation results for RPL and VDI without and with two PV system placements, respectively. Likewise, Figs. 18 and 19 present the optimized results for Vbus and VSI, respectively. It is evident from the illustrations that the PL and VD are substantially minimized following the optimized integration of two units of PV DG systems.
Optimal bus selection for two DGs.
Convergence curve of JSA for a two DG placements.
33-bus radial DPN RPL after two DG placements.
VDI of 33-bus radial DPN after two DG placements.
Vbus of 33-bus radial DPN after two DG placements.
VSI of 33-bus radial DPN after two DG placements.
Table 6 presents the optimized solution for the three DG unit integrations. Figure 20 illustrates the optimal solution for DG location, size, and fitness value for 50 independent runs. For three DG placement case study, JSA optimizes the DGs in the 13th, 24th, and 30th buses. The best solution is reached in the 26th simulation run. The same has been highlighted in the illustration of Fig. 20. JSA converges in 10 iterations and 42.3 s for the optimized PV systems ratings of 923.6 kW, 1028.3 kW, and 998.2 kW, correspondingly, in bus locations 13, 24, and 30. Figure 21 presents the convergence curve of JSA for the optimized three PV system allocations. The optimized inclusion of multiple PV systems reduced the PL to 69.59 kW and VDItotal to 0.3293 p.u. Also, the minimum Vbus and VSI are increased to 0.9846 p.u. and 0.8916. The optimized simulation outcomes for RPL and VDI are presented in Figs. 22 and 23, respectively. Likewise, Figs. 24 and 25 illustrate the optimized simulation results for Vbus, and VSI, respectively.
Optimal bus selection for three DGs.
JSA convergence curve for three DG placements.
RPL of 33-bus radial DPN for three DG placements.
VDI of 33-bus radial DPN for three DG placements.
Vbus of 33-bus radial DPN for three DGs placements.
VSI of 33-bus radial DPN for three DG placements.
Statistical comparison of simulation results.
The simulation findings of different cases of PV DG system placements are graphically summarized in Fig. 26. The total real PL, VDItotal, VDImin, minimum Vbus, and VSImin of the 33-bus RDPN without DG placement are 210.98 kW, 1.8047 p.u., 0.0962 p.u., 0.9038 p.u., and 0.6671, respectively. The total PL is reduced by 51.23%, 60.66%, and 67.01% for a single, two, and three units of PV system allocations, respectively. VDImin is minimized by 0.0569 p.u., 0.0661 p.u., and 0.0809 p.u. for one, two, and three PV systems placement, respectively. Minimum Vbus is increased by 0.0569 p.u. for a single PV, 0.066 p.u. for two PVs, and 0.0808 p.u. for three PV system allocations. And, VSImin is increased by 0.0888, 0.2177, and 0.2245 following a single, two, and three PV systems integration. The simulation outcomes reveal that substantial PL reduction, VP improvement, and VS enhancement have been achieved for all cases of DG placement; however, better results are obtained for three DG placements than two and single DG placements.
Additionally, the effectiveness of the JSA optimization is examined by comparing its simulation findings with other optimization methodologies. Tables 7, 8, 9 present the simulation findings of JSA and other optimization methodologies for single, two, and three PV systems allocation, respectively. The simulation results of LSF-SCA37, SCA37, BSOA25, GA38, ALO24, TLBO-GWO32, WIPSO-GSA41, GWO41, BFOA42, KHA43, BA44, WOA45, and AIS46 methodologies are compared to the JSA solutions. For a single DG optimization, JSA results outperform LSF-SCA, SCA, BSOA, GA, ALO, and TLBO-GWO methodologies by giving maximum PL reduction and better Vbus enhancement. Likewise, JSA-optimized two DG placements give better PL and VD minimization than LSF-SCA, SCA, BSOA, WIPSO-GSA, and GWO methodologies. Furthermore, JSA-optimized three units of PV systems allocation produced superior outcomes than other methodologies.
This research work successfully employs the Jellyfish Search Algorithm (JSA) for the optimal placement and sizing of solar photovoltaic (PV) distributed generation (DG) units in radial distribution power networks (DPNs). The proposed metaheuristic framework addresses multiple objectives, including real power loss (RPL) minimization, voltage deviation reduction, and voltage stability enhancement, ensuring efficient and reliable grid operation. The methodology is rigorously validated on the IEEE 33-bus radial DPN, demonstrating superior convergence characteristics and solution optimality compared to existing metaheuristic approaches. JSA optimized single PV DG optimized inclusion has cut down the total RPL by 51.23% and minimized the total VDI by 1.2716 p.u with minimum VSI 0.7559. On the other side, total RPL and VDI were reduced by 60.66% and 1.1529 p.u for two units of PV DG optimization. But, after the allocation of three units of PV DG systems, the RPL and total VDI were reduced by 67.01% and 1.4754 p.u. Minimum VSI was increased to 0.8848 and 0.8916 after the optimal inclusion of two and three units of PV DG systems, respectively. Simulation results indicate that JSA-optimized DG placements significantly improve system performance, achieving a substantial reduction in RPL while enhancing voltage stability and overall grid resilience. The comparative study highlights JSA’s superior performance over traditional optimization techniques such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimization (GWO), particularly in handling high-dimensional and nonlinear constraints. Notably, the integration of three PV-DG units yields the highest improvements in network efficiency. Overall, the findings establish JSA as an advanced optimization paradigm for DG placement in modern power systems. Future research may explore the adaptation of JSA for unbalanced distribution networks, real-world practical implementations, and hybridized metaheuristic techniques to further enhance computational efficiency and scalability.
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Real power flow along a branch
Reactive power flow along a branch
Branch current
Branch resistance
Branch reactance
Voltage
Bus voltage
Real power load
Reactive power load
Real power rating of DG
Number of branches
Number of buses
DG reactive power capacity
Real power loss
Reactive power loss
Total reactive power losses
Total real power losses without DG optimization
Total real power losses with DG optimization
Weightage factors
Objective function for RPL minimization
Objective function for VDI minimization
Objective function for VSI maximization
Nominal bus voltage
Substation real power rating
Number of DGs
Total minimum real power ratings of DGs
Total optimized real power ratings of DGs
Total maximum real power ratings of DGs
Minimum recommended bus voltage
Maximum recommended bus voltage
Biogeography Based Optimization
Voltage profile
Voltage stability
Loss sensitivity factor
Chaotic sine cosine algorithm
Improved oppositional-chaotic symbiotic organisms search
Simulated annealing
Gravitational search algorithm
Bat algorithm
Sine cosine algorithm
Genetic algorithm
Whale optimization algorithm
Weight improved particle swarm optimization
Harris hawks optimizer
Rated real power output
Actual solar irradiance
Rated solar irradiance
Logistic chaotic value of jellyfish
Constant
Distribution coefficient
Mean position of all jellyfish
Lower boundary of search space
Higher boundary of search space
Motion coefficient
Iteration
Maximum iteration
Distributed generation
Distribution power network
Jellyfish search algorithm
Photovoltaic
Real power loss
Weighted sum approach
Power losses
Transmission networks
Voltage stability index
Ant lion optimization
Backtracking search optimization algorithm
Elephant herding optimization
Particle swarm optimization
Voltage deviation
Stud krill herd algorithm
Crow search algorithm
Opposition-based tuned-chaotic differential evolution
Differential evolution
Artificial immune systems
Radial distribution power network
Power loss index
Voltage deviation index
Time control mechanism
Ocean current
Time control function
Backward-forward sweep
Multi-objective function
Bacterial foraging optimization algorithm
Krill herd algorithm
Grey wolf optimization
Teaching learning based optimization
Yuvaraj, T. & Ravi, K. Multi-objective simultaneous DG and DSTATCOM allocation in radial distribution networks using cuckoo searching algorithm. Alexandria Eng. J. 57 (4), 2729–2742 (2018).
Article Google Scholar
Agajie, T. F., Gebru, F. M., Salau, A. O. & Aeggegn, D. B. Investigation of distributed generation penetration limits in distribution networks using multi-objective particle swarm optimization technique. J. Electr. Eng. Technol. (2023).
Ackermann, T., Andersson, G. & Söder, L. Distributed generation: a definition. Int. J. Electr. Power Syst. Res. 57 (3), 195–204 (2001).
Article Google Scholar
Eshan, T., Jagadeesh, K. & Janaka, P. E.K, Optimal placement and sizing of DGs in distribution networks using MLPSO algorithm. Energies 13 (23), 61–85, (2020).
Yang, M., Jiang, Y., Zhang, W. & Li, Y. Short-term interval prediction strategy of photovoltaic power based on meteorological reconstruction with Spatiotemporal correlation and multi-factor interval constraints. Renew. Energy. 237, 121834 (2024).
Article Google Scholar
Yang, M., Che, R., Yu, X. & Xin, S. Dual NWP wind speed correction based on trend fusion and fluctuation clustering and its application in short-term wind power prediction. Energy 302, 131802 (2024).
Article Google Scholar
Li, N. et al. A novel EMD and causal convolutional network integrated with transformer for ultra short-term wind power forecasting. Int. J. Electr. Power Energy Syst. 154, 109470 (2023).
Article Google Scholar
Zhao, H. et al. Yuqing Zhou, and Frequency-voltage active support strategy for hybrid wind farms based on grid-following and grid-forming hierarchical subgroup control. CSEE J. Power Energy Syst. (2025).
Zhang, H. et al. Hancke. Homomorphic encryption based resilient distributed energy management under cyber-attack of micro-grid with event-triggered mechanism. IEEE Trans. Smart Grid (2024).
Zhang, M. et al. Supply resilience constrained scheduling of MEGs for distribution system restoration: A stochastic model and FW-PH algorithm. IEEE Trans. Smart Grid (2024).
Xia, Y., Huang, Y. & Fang, J. A generalized nash-in-nash bargaining solution to allocating energy loss and network usage cost of buildings in peer-to-peer trading market. Sustain. Energy Grids Netw. 101628. (2025).
Zhang, T., Zhao, W., He, Q. & Xu, J. Optim. Microgrid Dispatching Integrating Photovolt. Power Generation Forecast. Sustain. 17, 2 : 648. (2025).
Google Scholar
Duan, Y., Zhao, Y. & Jiangping, H. An initialization-free distributed algorithm for dynamic economic dispatch problems in microgrid: modeling, optimization and analysis. Sustainable Energy Grids Networks. 34, 101004 (2023).
Article Google Scholar
Yi, X., Lu, T., Li, Y., Ai, Q. & Hao, R. Collaborative planning of multi-energy systems integrating complete hydrogen energy chain. Renew. Sustain. Energy Rev. 210, 115147 (2025).
Article CAS Google Scholar
Feng, J., Yao, Y. & Liu, Z. Developing an optimal Building strategy for electric vehicle charging stations: automaker role. Environ. Dev. Sustain. 1–61. (2024).
Zheng, J., Liang, Z. T., Li, Y., Li, Z. & Qing-Hua, W. Multi-agent reinforcement learning with privacy preservation for continuous double auction-based p2p energy trading. IEEE Trans. Industr. Inf. 20 (4), 6582–6590 (2024).
Article Google Scholar
Miao, Z., Meng, X., Li, X., Liang, B. & Watanabe, H. Enhancement of net output power of thermoelectric modules with a novel air-water combination. Appl. Therm. Eng. 258, 124745 (2025).
Article Google Scholar
Lin, K. M., Swe, P. L. & Oo, K. Z. Combination of analytical method and heuristic technique for optimal DG allocation in practical distribution network: case study in Myingyan distribution. Acad. Educ. 124–129, (2018).
Sirjani, R. & Jordehi, R. Optimal placement and sizing of distribution static compensator (D-STATCOM) in electric distribution networks: A review. Renew. Sustain. Energy Rev. 77, 688–694 (2017).
Article Google Scholar
Agajie, T. F., Salau, A. O., Hailu, E. A., Sood, M. & Jain, S. Optimal sizing and siting of distributed generators for minimization of power losses and voltage deviation. In Proceedings of IEEE International Conference on Signal Processing, Computing and Control 292–297, (2019).
Acharya, N., Mahat, P. & Mithulananthan, N. An analytical approach for DG allocation in primary distribution network. Int. J. Electr. Power Energy Syst. 28 (10), 669–678 (2016).
Article Google Scholar
Hung, D. Q. & Mithulananthan, N. Multiple distributed generator placement in primary distribution networks for loss reduction. IEEE Trans. Ind. Electron. 60 (4), 1700–1708 (2011).
Article Google Scholar
Murty, V. V. & Kumar, A. Optimal placement of DG in radial distribution systems based on new voltage stability index under load growth. Int. J. Electr. Power Energy Syst. 69 (1), 246–256 (2015).
Article Google Scholar
Ali, E. S., Abd Elazim, S. M. & Abdelaziz, A. Y. Ant Lion optimization algorithm for optimal location and sizing of renewable distributed generations. Renew. Energy. 101 (1), 1311–1324 (2017).
Article Google Scholar
El-Fergany, A. Optimal allocation of multi-type distributed generators using Backtracking search optimization algorithm. Int. J. Electr. Power Energy Syst. 64 (1), 1197–1205 (2015).
Article Google Scholar
Singh, P., Meena, N. K., Bishnoi, S. K., Singh, B. & Bhadu, M. Hybrid elephant herding and particle swarm optimizations for optimal DG integration in distribution networks. Electr. Power Compon. Syst. 48 (6–7), 727–741 (2020).
Article Google Scholar
ChithraDevi, S. A., Lakshminarasimman, L. & Balamurugan, R. Stud Krill herd algorithm for multiple DG placement and sizing in a radial distribution system. Int. J. Eng. Sci. Technol. 20 (2), 748–759 (2017).
Google Scholar
Ismael, S. M., Aleem, S. H. & Abdelaziz, A. Y. Optimal sizing and placement of distributed generation in Egyptian radial distribution networks using crow search algorithm. In Proc. 2018 Int. Conf. Innov. Trends Comput. Eng. ITCE 332–337, (2018).
Kumar, S., Mandal, K. K. & Chakraborty, N. A novel opposition-based tuned-chaotic differential evolution technique for techno-economic analysis by optimal placement of distributed generation. Eng. Optim. 52 (2), 303–324 (2020).
Article MathSciNet Google Scholar
Huy, P. D., Ramachandaramurthy, V. K., Yong, J. Y., Tan, K. M. & Ekanayake, J. B. Optimal placement, sizing and power factor of distributed generation: a comprehensive study spanning from the planning stage to the operation stage. Energy 195 (1), 117011 (2020).
Article Google Scholar
Ali, E. S., Abd Elazim, S. M., Hakmi, S. H. & Mosaad, M. I. Optimal allocation and size of renewable energy sources as distributed generations using shark optimization algorithm in radial distribution systems. Energies 16 3983. (2023).
Nowdeh, S. A. et al. Fuzzy multi-objective placement of renewable energy sources in distribution system with objective of loss reduction and reliability improvement using a novel hybrid method. Appl. Soft Comput. J. 77, 761–779 (2019).
Article Google Scholar
Truong, K. H., Nallagownden, P. & Elamvazuthi, I. A quasi-oppositional-chaotic symbiotic organisms search algorithm for optimal allocation of DG in radial distribution networks. Appl. Soft Comput. J. 88, 106067 (2020).
Article Google Scholar
Selim, A., Kamel, S. & Jurado, F. Efficient optimization technique for multiple DG allocation in distribution networks. Appl. Soft Comput. 86, 105938 (2020).
Article Google Scholar
Selim, A., Kamel, S., Alghamdi, A. S. & Jurado, F. Optimal placement of DGs in distribution system using an improved Harris Hawks optimizer based on single and multi-objective approaches. IEEE Access. 8, 52815–52829 (2020).
Article Google Scholar
Akbar, M. I. et al. A novel hybrid optimization-based algorithm for the single and multi-objective achievement with optimal DG allocations in distribution networks. IEEE Access. 10, 25669–25687 (2022).
Article Google Scholar
Selim, A., Kamel, S., Mohamed, A. A. & Elattar., E. E. Optimal allocation of multiple types of distributed generations in radial distribution systems using a hybrid technique. Sustainability 13 (12), 6644 (2021).
Article Google Scholar
Kashyap, M., Mittal, A. & Kansal, S. Optimal placement of distributed generation using genetic algorithm approach. In Proceeding of the Second International Conference on Microelectronics, Computing & Communication Systems (MCCS 2017) 587–597, (Springer, 2019).
Naderi, E., Mirzaei, L. & Pourakbari-Kasmaei, M. Optimization of active power dispatch considering unified power flow controller: application of evolutionary algorithms in a fuzzy framework. Evol. Intel. 17, 1357–1387 (2024).
Article Google Scholar
Naderi, E., Mirzaei, L., Trimble, J. P. & Cantrell, D. A. Multi-Objective optimal power flow incorporating flexible alternating current transmission systems: application of a wavelet-oriented evolutionary algorithm. Electr. Power Compon. Syst. 52 (5), 766–795 (2023).
Article Google Scholar
Rajendran, A. & Narayanan, K. Optimal multiple installation of DG and capacitor for energy loss reduction and loadability enhancement in the radial distribution network using the hybrid WIPSO–GSA algorithm. Int. J. Ambient Energy. 41, 129–141 (2018).
Article Google Scholar
Kowsalya, M. Optimal size and siting of multiple distributed generators in distribution system using bacterial foraging optimization. Swarm Evol. Comput. 15, 58–65 (2014).
Article Google Scholar
Sultana, S. & Roy, P. K. Krill herd algorithm for optimal location of distributed generator in radial distribution system. Appl. Soft Comput. 40, 391–404 (2016).
Article Google Scholar
Yuvaraj, T., Devabalaji, K. & Ravi, K. Optimal allocation of DG in the radial distribution network using Bat optimization algorithm, In Advances in Power Systems and Energy Management; Springer: Berlin/Heidelberg, Germany, 563–569, (2018).
Chapter Google Scholar
Saleh, A. A., Mohamed, A. A. A. & Hemeida, A. Optimal allocation of distributed generations and capacitor using multi-objective different optimization techniques. In Proceedings of the 2019 International Conference on Innovative Trends in Computer Engineering (ITCE), Aswan, Egypt 377–383, (IEEE, 2019).
Meera, P. & Hemamalini, S. Optimal siting of distributed generators in a distribution network using artificial immune system. Int. J. Electr. Comput. Eng. 7, 641 (2017).
Google Scholar
Chou, J. S. & Truong, D. N. A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean. Appl. Math. Comput. 389125535, (2021).
Kawambwa, S. et al. An improved backward/forward sweep power flow method based on network tree depth for radial distribution systems. J. Electr. Syst. Inform. Technol. 8(7), (2021).
Ghosh, M., Kumar, S., Mandal, K. & S.Mandal and Optimal sizing and placement of DG units in radial distribution system using cuckoo search algorithm. Int. J. Appl. Eng. Res. 12, 362–369 (2019).
Google Scholar
Baran, M. E. & Wu, F. F. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Delivery. 4 (2), 1401–1407 (1989).
Article Google Scholar
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Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Chennai, Tamil Nadu, India
P Rajakumar
Department of ECE, Hindusthan Institute of Technology, Coimbatore, Tamil Nadu, India
P. M. Balasubramaniam
Mohan Babu University, Tirupati, India
E. Parimalasundar
Christ (Deemed to be University), Bangalore, India
K. Suresh
Mattu University, Mattu, Ethiopia
P. Aravind
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P. M. Balasubramaniam: Validation, Visualization, Writing – review & editing. P Rajakumar: Writing – original draft, Validation, Methodology, Investigation, Formal analysis, Conceptualization. Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization. Parimalasundar E Formal analysis, Methodology, Software, Validation. Suresh K: Visualization, Validation, Methodology, Investigation, Formal analysis, Conceptualization, Investigation, Methodology, Software, Validation, Visualization, Writing – review & editing. Aravind P: Visualization, Validation, Software, Methodology, Investigation, Formal analysis.
Correspondence to P. Aravind.
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Rajakumar, P., Balasubramaniam, P.M., Parimalasundar, E. et al. Optimized placement and sizing of solar photovoltaic distributed generation using jellyfish search algorithm for enhanced power system performance. Sci Rep 15, 20755 (2025). https://doi.org/10.1038/s41598-025-08227-4
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