The substantial rise in electrical energy consumption in recent years has prompted distribution system operators to provide the required power through proper network use and design. As a result, adding DG units to distribution systems is one of the primary ways to supply loads for customers. Utilizing Renewable Energy Sources (RES) like solar and wind has been a popular choice among DG technologies because of their environmental benefits (El-Khattam and Salama, 2004; Bayod-Rújula, 2009). Optimal allocation of RES in DS is indeed a complex mathematical problem because it involves multiple objectives optimization subject to bus voltage, feeder capacity, and RES penetration constraints, considering the varying nature of loads, generation, load growth aspects, and the large scale of DS. Also, there are non-linear relations between the system variables, prompting a need to use evolutionary algorithms for solving the optimal RES allocation problem. Numerous studies are investigating the optimal placement of Distributed Generators (DGs) in the Distribution System (DS) using techniques such as Pareto-based multi-objectives using the Strength Pareto Evolutionary Algorithm (Ramsami and Ah King, 2019), PMBSA (Arubolu et al., 2024), MOPSO (Ba-swaimi et al., 2025), weighted multi-objective optimization using the Exponential Distribution Optimizer (EDO) and White Shark Optimizer (WSO) (Nassar et al., 2025), and customized GA (Maghami et al., 2025). Multi-objective Ant Lion Optimizer (Kalita et al., 2024) and the Multi-objective Moth Swarm Algorithm (Sharifi et al., 2021) are recently developed novel algorithms which can be used for RES allocation in DS. Due to nonlinear loads and inverter-based RES, harmonic problems are becoming increasingly common in DS. The harmonics these devices produce distort AC voltage and current (Wagner et al., 1993). Harmonic Power Flow (HPF) calculation methods are very important for distribution system analysis and design since they aid in determining the degree of harmonic distortion (Marti et al., 1991). Electric distribution systems commonly use power filters to lessen harmonic impacts. Power filters compensate for reactive power, raise the system power factor, lower harmonics, and decrease power losses (Ko et al., 2009; Chou et al., 2000; Chen, 2003). A DS’s performance in the presence of harmonics and unbalanced circumstances was demonstrated using an additional transient’s program (Manjure and Senior, 2002). For each bus in DS with various non-linear loads, the THD of voltage is calculated using a decoupled method in (Ulinuha et al., 2007). A multi-objective harmonic filter placement strategy based on weighted sum (Mahlalela et al., 2015) is employed in a balanced DS using a genetic algorithm (GA). Small balanced DS were used to test the proposed approach, with the loads being taken to be constant power loads alone. An overview of the evolution of APF technology is provided in (Salam et al., 2006). Additionally, the paper examines various reference signal estimate methods, which are essential to the APF. The issues of harmonic distortion and how they affect electric power quality are briefly discussed. In order to enhance the harmonic condition, voltage profile, and reduce network losses of DS, a modified Particle Swarm Optimization (PSO) technique is described in (Rezapour et al., 2024) for the simultaneous optimal allocation of capacitors and APFs. In (Jannesar et al., 2019) a GA and Monte Carlo simulation-based approach for optimal probabilistic placement and scaling of single-tuned PPFs is introduced. An evaluation of the suggested approach was conducted on an Iranian 383-bus LV unbalanced radial DS. It should be mentioned that since the modeling approach in this paper is based on measurement, harmonic interactions between nonlinear loads and PV systems have not been taken into account; thus, it is worthy to address this issue in future studies. In (Karadeniz et al., 2023) Photovoltaic-based DG units (PVDGUs) and passive harmonic filters are placed optimally in an IEEE 33-bus system to maximize hosting capacity while minimizing the bus voltages’ RMS variation and overall harmonic distortion. In (Lakum and Mahajan, 2021) adaptive grey wolf optimization algorithm is used to optimally place PVDGUs and APFs in a balanced DS to maximize cost saving. In (Karadeniz et al., 2023; Lakum and Mahajan, 2021) the authors didn’t consider varying nature of PVDGUs and load. Although load demand increases in practice, the results of earlier research did not take into consideration the growth of load for various types of loads, which is a crucial factor to consider when solving RES allocation problem. A case study on how to appropriately size and position RES in a DS to fulfil constraints and reduce overall system costs is given by (HassanzadehFard and Jalilian, 2018). The suggested method was tested on a balanced 31-bus DS.

The conclusions drawn from the literature review are summed up as.

• Majority of earlier studies optimized RES allocation considering linear loads (Arubolu et al., 2024; Biswas et al., 2019; Ramsami and Ah King, 2019; Nassar et al., 2025; Maghami et al., 2025; Ba-swaimi et al., 2025) while only few studies took nonlinear loads into consideration (Karadeniz et al., 2023; HassanzadehFard and Jalilian, 2018). RES allocation results in THD violation due to the harmonic spectrum of inverter-based DG and nonlinear loads. Hence, there is a need to place RES and power filters simultaneously for reducing THD. In earlier studies, while accounting for non-linear nature of loads during UDS planning, researchers have concentrated either on optimal allocation of power filters (Ko et al., 2009; Chou et al., 2000; Mahlalela et al., 2015; Salam et al., 2006; Rezapour et al., 2024) or optimal allocation of power filters in the presence of RES (Jannesar et al., 2019; Lakum and Mahajan, 2021). For a dependable and cost-effective system operation, both of them must be installed at the same time, albeit this has not yet been evaluated for analysis.

This work’s primary objectives, which are covered in detail below, are to address the issues described above.

• A new approach is proposed that employs PMBSA to determine the optimal size and placement of RES and power filters in UDS. RES units that rely on inverters create harmonics that negatively impact the system’s performance. The harmonic spectrum of inverter-based DG units is also taken into consideration along with non-linear loads in this work. When allocating RES, the varying nature of both generation and load is taken into consideration using Probability Distribution Functions (PDFs). This study examines load growth for the system’s available loads in order to satisfy demand, and it suggests a practical solution that expands the size of RES at their original sites.

There are eight sections further in this study apart from the introduction. Section 2 discusses RES modelling, whereas Section 3 explains power filters design. Section 4 discusses how load growth affects the performance of the DS. In Section 5, the problem formulation process is explained. The overview of PMBSA and its application to the optimal allocation studies are explained in Section 6. The PMBSA, NSGA-II and WSA results are discussed in Section 7, and the conclusion is given in Section 8.

RES in this study includes wind and photovoltaic. Generation sources and loads need to be precisely described in order for RES to be designed and distributed in UDS efficiently. Probabilistic models are used in this work for the design of RES. This section provides a basic understanding of the modelling of the RES system.

Power filters are instruments used to remove undesirable components from electrical power systems. Power filters are categorized into passive power filters and active power filters.

Distribution systems naturally experience load growth, but planning engineers face a great deal of difficulty in making the system adapt to load growth without affecting service quality. Installing a new substation or increasing the capacity of an existing substation will boost the DS capacity to handle the yearly increases in demand. Although it is very costly to install a new substation, adding RES units closer to the heavy load areas can increase the capacity of the current substation. Using the Equation 13, the effect of the annual increase on the system’s reactive power ( Q l d k \ ) and active power ( P l d k \ ) loads is assessed (Das, 2004). P l d k = P l d 0 1 + g w k   &   Q l d k = Q l d 0 1 + g w k (13)

Initially connected load ( P l d 0 \ &   Q l d 0 \ ) and yearly load increase rate (gw) are used to express load in k t h year. For a given DS, gw is usually determined using statistical data. In this instance, gw is taken as 7.5% (Das, 2004).

As daily electricity use increases and also the usage of nonlinear loads is increasing, existing DS are unable to meet the demand while satisfying THD constraints. Power filters need to be used to reduce distortion due to nonlinear loads and deployment of RES is needed to meet the demand. This study optimizes the integration of RES and power filters into UDS to reduce power loss, THD, and cost.

The RES and power filter allocation problem is being addressed by multi-objective optimization algorithm PMBSA (Arubolu et al., 2024), which is a modified version of BSA technique that can solve single-objective optimization problems. The structure of PMBSA is much simpler than that of the other multi-objective optimization algorithms, and it has a single control parameter, which makes it a suitable approach to solve even multimodal optimization problems. Unlike many evolutionary approaches, PMBSA does not suffer from premature convergence or high computation time, nor is its performance overly sensitive to its control parameter. PMBSA efficiently explores the search domain by using crossover and mutation operators. These operators are entirely distinct from those employed by evolutionary programming and genetic algorithms, among other evolutionary techniques. Another benefit of PMBSA is its memory, which establishes the search direction depending on earlier generations. The steps for using PMBSA to find Pareto optimum solutions (Arubolu et al., 2024; Brigatto et al., 2011) are provided in the Appendix section.

The proposed approach makes use of the OpenDSS and MATLAB software and is implemented in MATLAB 2017a running on a 2.9 GHz core i3 processor. Wind speed, solar irradiation, and load demand data are the inputs for estimating RES generation and load demand. The optimal placement and size of RES in a UDS are determined by taking into account the load growth, non-linear and linear load types, and the varying nature of both generation and load. This is accomplished by the use of the efficient PMBSA algorithm, while reducing THD, cost, and losses in the presence of load growth. The PMBSA algorithm settings used in this study were population size (PPS = 50) and itrmax = 200. The cost of energy supplied to the grid and purchased is estimated to be 0.077 USD/kWh (Arubolu et al., 2024). 2.7 m/s, 25 m/s, and 11 m/s are the cut-in, cut-out, and rated wind speeds of the wind turbine generator used in this work, respectively (Premono et al., 2017). 300Wp is the rated capacity of a solar PV panel (Arubolu et al., 2024). The cost information for wind turbines and solar PV is sourced from (Ahmadi et al., 2021), and it is based on an analysis of the US market. Also, cost details of all components used in this study are included in Supplementary Table A1. Equations 16–23 and these data are used to compute the annualized total cost. The cost is then divided by 8,760 to get the cost per hour.

The IEEE 123-bus test system (Distribution test feeders, 2010) is used to evaluate the performance of the proposed approach. The harmonic spectrum of the RES-based DGs with inverters is extracted from (HassanzadehFard and Jalilian, 2018), while the harmonic source data for the IEEE 123-bus system is acquired from (Ulinuha et al., 2007). RES penetration is limited to 70% of the system’s active power consumption. The power factor of RES is assumed to be 0.85 in this work. This study examines two cases to evaluate RES’s performance. Case I (C-I): DS without RES (Base case) and Case II (C-II): Optimal allocation of wind and solar RES in DS.

The objective function’s values are calculated and regarded as base case outcomes when RES is not included in the system, as in case I. Case II enhances the DS’s performance by reducing TPL, THD, and TC with the integration of wind and PV sources into UDS, whose ideal sizes and locations are acquired using PMBSA. RES penetration lowers overall costs and power losses, which improves DS behaviour, according to results presented in Table 1. The RES’s harmonic injection has led to an increase in harmonic distortion. However, the loss and cost reduction that are seen may eventually diminish as the system load increases over time. Thus, studying the impact of load growth on system performance is crucial. Table 1 shows the findings of this study’s additional analysis of the impact of load growth on RES system performance.

Table 2 shows that the objective function values increase from the first to the fifth year as the load increases over a 5-year period while maintaining the same RES size and location. Hence, this study focused on adjusting RES annually in relation to load variance in order to improve the DS’s performance under load growth. Three scenarios are outlined for C-II, which are listed below, in order to determine the best approach to be taken for RES integration:

Scenario I(S-I): Wind and solar energy resources are distributed in the UDS, with RES sites being fixed as decided in the base (0th) year, but RES sizes optimized annually.

Scenario II(S-II): Distribution of wind and solar energy resources in UDS, with RES sites being fixed as decided in the base (0th) year, but requiring a further increase in RES size beyond that determined in the base year to meet demand growth.

Scenario III(S-III): In UDS, optimal solar and wind energy resource sizes and locations are found considering the base (0th) year’s load demand. The optimal site for additional RES size is determined to accommodate load growth.

To illustrate the effectiveness of the previously suggested scenarios for optimal RES allocation under load growth conditions, the values of the objective function for each year are shown in Table 2. From a loss and cost reduction perspective, S-III is found to perform better than S-I and S-II. The RES size may decrease or increase as the load increases. This adjustment is made annually in S-I. This plan may turn out to be very costly and unfeasible because it asks for shrinking the size 1 year and then enhancing it the following, or vice versa. Even though S-III yields superior benefits, it is not logistically viable to move the additional RES sizes annually to different locations in accordance with load growth. Since S-II is a more realistic strategy that permits an expansion of RES size at the original RES sites, it was the subject of this study for further analysis.

It is observed that THD value exceeds the system’s maximum allowable limit. The fifth, seventh, and eleventh harmonic voltage levels are the most prevalent at all buses, according to the HPF results for S-II in the base year. Dominant voltage harmonics that have been normalized with respect to fundamental voltage are shown in Figure 2a for bus 40 of IEEE 123-bus system where there is large non-linear load. Therefore, in addition to RES, power filters such as PPFs and APFs are utilized in this study to reduce harmonic distortion while satisfying other objectives. As described in Section 3.1, filter parameters are computed to attenuate these prominent harmonics. The optimal RES, PPF sizes, and locations, along with objective function values obtained by PMBSA are shown in Table 3.

Normalized dominant harmonic voltages after installing PPFs are shown in Figure 2b, which illustrate the extent to which PPFs reduce harmonic distortion. The findings in Table 3 show that the simultaneous placement of RES and PPF can lower objective function values while meeting THD constraints. However, the THD value obtained in the fifth year was 4.94%, which is very close to the upper allowable limit. The THD value might be higher than 5% in the following years. Therefore, the authors of this work investigated the possibility of placing APFs in addition to RES in order to see if DS performance might be improved over that of placing PPFs with RES. As described in Section 4.2, the injection current of APFs is computed. Table 4 displays the best RES sizes and locations, APF locations found using PMBSA. Figure 2c displays the normalized dominant harmonic voltages after installing APFs. Figure comparison shows that harmonic reduction is more noticeable with APF than PPF.

Comparing the results of Scenario II in Table 2 with Tables 3, 4 makes it clear that the system’s power losses are lower and its harmonic distortion is higher than permitted limits when power filters are not present. However, THD decreases when power filters are included in the system, although power loss somewhat rises as RES sizes and placements are altered to meet THD restrictions (Tan et al., 2017). The THD comparison plot utilizes the base year and 5th year outcomes for S-II with PPF and APF, along with data for C-I and C-II, as illustrated in Figure 3. The comparative figure indicates that APF can more effectively reduce THD and voltage limit violations in addition to other objectives.

According to the results presented in Tables 3, 4, the best distribution of RES and power filters enhances DS performance by reducing power losses, total cost, and THD. Nonetheless, the power flow results show that the test system violates the voltage limit. In the IEEE 123-bus system, bus 83 consistently exhibits over voltage limit violations. In order to maintain bus voltages within permissible limits, AVRs are utilized in DS in conjunction with the existing RES and power filters. A new node, designated, <node number RG > will be created with the addition of AVR.

Purpose of AVR placement is to control voltage and maintain the system voltage within permitted bounds; however, this placement results in a lower lagging power factor condition (Arubolu et al., 2024), which may cause the THD value to rise. In this situation, it is required to install both AVRs and SCBs in together to reduce the THD and maintain the voltage within permitted bounds. When RES and PPFs are placed simultaneously, there are more voltage violations; therefore, AVRs alone are insufficient to limit violations and enhance other objectives due to low lagging power factor. For this reason, AVRs and SCBs are placed together to limit violations whose results are presented in Table 5. Table 6 presents the results of adding AVRs to a system that already has RES and APFs. Since there are fewer voltage limit violations due to the superior harmonic mitigation capabilities of APF, only AVRs are employed to solve this issue.

Sensitivity tests with 5% and 10% yearly load growth are done to highlight the robustness of the proposed approach in improving DS performance, and the respective tabulated results are included in Supplementary Appendix SB. These results presented in Supplementary Tables A3, A4 indicate that THD increases due to load growth, and there will be voltage limit violations apart from increased cost and losses. To address these issues, the proposed approach of optimal RES and APF allocation is done, whose results are presented in Supplementary Tables A5, A6. When the load growth is 10%, even after optimal RES and APF allocation, there are still some voltage violations, and to address that, AVRs are also placed. And the respective results are presented in Supplementary Table A7, based on which it can be concluded that the proposed approach works even when the system load growth rates are high.

In order to optimize the distribution of RES and power filters in an unbalanced distribution system (UDS), a novel approach is put forth that uses the Pareto front-based Multi Objective Backtracking Search Algorithm (PMBSA) to reduce Power Loss, Total Harmonic Distortion, and Cost. To ensure dependable performance, the distribution system planning process took into account both linear and non-linear load types, in addition to the varying nature of the PV and wind generating outputs, and harmonics injected by inverter-based RES. Additionally, for each type of available load, the load growth of the distribution system was considered. When the distribution system’s yearly demand increased, THD, TPL, and TC increased as well. At the same time, several buses’ voltage dropped to levels below the permitted limit. In order to enhance system performance, the proposed approach optimally increased the RES sizes to accommodate growing load demands. However, THD violations were observed, and to mitigate this issue, APF and PPFs are employed in conjunction with RES. It has been found that APF placement outperformed PPF in reducing THD, loss, and voltage limit violations. The enhanced UDS performance was demonstrated by testing the proposed approach, which combines OpenDSS and MATLAB co-simulation, on the IEEE 123-bus system. The findings show that, in comparison to the base case, i.e., without any RES, TC and TPL decreased by 27.05% and 41.06%, respectively, but THD increased by 108.8% when RES is optimally placed in the 123-bus UDS. Whereas, when RES and APF are deployed in DS, TC, THD, and TPL decreased by 29.76%, 9.28%, and 29.35%, respectively. By carefully positioning the AVR/SCBs, the proposed approach also solved the problem of voltage limit violation. The results show how well the proposed approach enhances DS performance when compared to NSGA-II, MOPSO, and WSA.