Design of Multi-Objective Energy Management for Remote Communities Connected with an Optimal Hybrid Integrated Photovoltaic–Hydropower–Battery Energy Storage System (PV-HP-BESS) Using Improved Particle Swarm Optimization

Abstract

The potential for electricity distribution in power systems has significantly increased over the years. This is mainly because of the discovery of alternative electricity generation sources, such as renewable energy, coupled with distributed generation (DG), making electricity more widely accessible. However, challenges remain in distributing electricity to remote area communities (RACs), especially because of difficult terrain and the complexity of installing power plants, leaving some areas without access to electricity. In this study, we used an improved particle swarm optimization (IPSO) technique to propose multi-objective energy management for remote area communities within a hybrid integrated Photovoltaic–(PV)–Hydropower plant (HPP)–Battery Energy Storage System (BESS). The multi-objective functions enhance power quality and voltage stability to meet grid code requirements. The proposed method was applied to the IEEE 15-bus system, which is consistent with systems commonly used in remote area communities, under the following scenarios: Case I—random installation of PV-HPP-BESS and PI parameter control of BESS; Case II—optimal location of PV-HP-BESS and PI parameter control of BESS using IPSO; Case III—sudden short circuit of the transmission line in Case II. Effectiveness was verified through hardware-in-the-loop (HIL) testing. The experimental results indicate that the proposed method significantly improves power quality and stability under disturbances, demonstrating superior performance.

1. Introduction

Energy is a crucial factor for electrical systems worldwide. As human resources expand and technology advances, energy demand continues to rise. The lack of sufficient energy can have widespread consequences, potentially leading to system failures. To avoid these effects, a power system must maintain a high enough balance to satisfy demand. Even if the existing power system can maintain equilibrium, overall stability is still lacking. Demand response in remote areas remains a challenge, as the cost of transmission increases with distance, and a limited production capacity contributes to shortages in these areas [1]. When energy from the power system cannot supply remote areas, renewable energy sources (RESs) such as solar power, wind, and biofuels can serve as alternatives.

A key advantage of RESs is their ability to reduce greenhouse gas emissions. Thus, they provide clean and environmentally friendly energy solutions. As a result, many RES studies have focused on addressing energy enhancement challenges in remote areas. Irshad A. S. [2] proposed an optimal system configuration for a hybrid solar photovoltaic (PV), wind, and hydropower plant (HPP) system by using the multi-objective genetic algorithm (MOGA) optimization technique to determine the ideal size of the renewable energy system. The suggested installation methods were PV (88 kW), wind turbine (18 kW), hydropower no. 1 (215 kW), and hydropower no. 2 (197 kW). This configuration was able to enhance electrical systems in remote areas without requiring a battery energy storage system (BESS). However, this method has limitations related to the location and weather conditions required for installation; these factors need to be evaluated prior to the application of the proposed RESs. The installation space requirement of RESs is another important factor to consider. Therefore, researchers have explored the use of RESs alongside loads to reduce the demand for energy consumption in electrical systems. Eihab E.E. Ahmed et al. [3] proposed a PV system for load use with multi-objective optimization and minimal installation using loss of load probability (LLP) and life cycle cost (LCC). The particle swarm optimization (PSO) algorithm and a new Python version 3.10.5 package were used to determine the optimal number and size of PV installations to meet the load requirements. However, usage duration is still a concern in this method. Relying on PV energy requires an adequate production period to support the load. A major limitation of RESs is inconsistent energy production, which depends on local environmental conditions.

In this context, BESSs help address the limitations of RESs by storing excess energy during production periods and supplying it to the system when needed. BESSs are thus often integrated with RESs to overcome energy challenges in remote areas. Prabpal P. et al. [4] proposed a BESS based on a symmetrical concept, utilizing the symmetrical volt/var control technique for regulation. Integrating the BESS into the conventional distribution system notably influenced energy consumption. The optimal BESS solution was achieved by applying genetic algorithm (GA) optimization and the PSO technique. The simulation results demonstrated that the BESS, directly connected to the power grid using GA and PSO, effectively optimized its size and location. This optimization helped minimize the impact of load demand on total system losses and balanced energy demand within the power system network. Despite this, installing a BESS in a looped system may have a limited impact, as some systems are already designed to manage load distribution. In such cases, BESS installation may primarily contribute to reducing energy production. Installing BESSs along with RESs may cause an imbalance in energy control. Therefore, subsequent studies have focused on improving energy distribution methods combined with BESSs and RESs [5,6,7]. Following the integration of a BESS with RESs, available energy control methods include using a voltage source to supply energy through the BESS, setting multiple objectives for regulating energy injection, and designing controllers to operate alongside the BESS inverter. These methods lead to appropriate energy control outcomes when the BESS is connected to the power system. However, the time frame for injecting energy into the system remains a critical factor, and it cannot be resolved when energy cannot be drawn from the power system over the long term.

Due to this limitation, hybrid energy systems (HESs) have gained significant interest among researchers. Hybrid energy systems integrate synchronous generators powered by diesel fuel with RESs and BESSs, significantly improving power distribution stability within the grid code. A distributed generator (DG) is the primary power source, while a RES is an auxiliary generator, and a BESS serves as backup energy storage. This combined operation enhances power system stability, even in remote areas [8]. As a result, HESs have become a widely explored research topic. For instance, the authors of [9,10,11] proposed the integration of DGs with RESs and BESSs to improve the stability of a power system, with various solutions such as changing the battery type in the HES, installing capacitors alongside the BESS, and scheduling energy injection periods. While the proposed methods can address some of the issues, their objectives and constraints do not cover all the challenges identified, potentially leading to solutions that are only partially effective. To fully resolve these issues, Hosseini E. et al. [12] proposed an innovative optimal energy management system (EMS) that utilizes a nonlinear constrained multi-variable function to enhance BESS operation in an HP plant combining wind turbines (WTs) and photovoltaic (PV) plants. The hybrid system employs a battery-stored impedance-based cascaded multilevel inverter to efficiently integrate renewable energy sources, including PV plants, WTs, and BESSs, into the grid. The proposed algorithm achieved grid power while efficiently distributing excess deficit power among the BESSs. However, the rate at which excess energy is removed and injected into the system creates control limitations, resulting in delays in enhancing the power system. Despite the development of HESs via the co-installation of a DG along with RESs and BESSs, minor issues with energy distribution in remote areas persist. While the production side can meet demand during specific periods, transient power system disturbances can lead to system changes. If these issues are overlooked, they could damage sensitive devices [13].

Transient analysis is essential for solving problems in remote areas, as integrating RESs into electrical systems leads to issues such as increased inertia and a delayed recovery of system balance. To tackle this, researchers have begun to explore HES device control [14]. The authors of [15,16,17] proposed enhancing the control of HES devices by defining method objectives, constraints, and analyses through algorithms to help maintain energy balance in the electrical system. This effectively reduces power system disturbances, including inertia from RES installation and sudden disruptions in remote areas. However, improving HES equipment control is highly complex. To tackle this challenge, large electrical systems with enhanced HES control are divided into smaller sections, known as microgrid systems [18].

Microgrid systems have steadily gained popularity because of advancements in automation systems, power electronics, and small-scale power equipment, as well as a decline in the cost of energy produced by small-scale RESs. Microgrids can be viewed as a practical approach to decentralizing power systems [19]. This decentralization has been shown to positively impact the reliability of energy supply, especially in remote areas. Microgrids are effective in improving system reliability and resilience while lowering greenhouse gas emissions through the integration of HER [20]. To evaluate the concept of such microgrids, studies [21,22,23] propose solutions to the power flow challenge in remote regions by using simulations based on the standard IEEE 15-bus test system, which mirrors the load characteristics typical of these areas. They apply widely used optimization techniques—including GA, PSO, and Flower Pollination Algorithm (FPA)—to optimize the location and sizing of components in the distribution network. By simulating the test system to resemble the actual power system closely, the results can be applied to the real power system. Various approaches have been utilized to improve the efficiency of microgrid systems for more comprehensive analysis; for instance, some studies [24,25,26] have proposed optimal schedules for microgrids. The analysis of a microgrid’s power distribution schedule relies on forecasting and algorithms to determine the power distribution. Efficiency is influenced by the quality of previously collected and enhanced data and the strengths of the chosen algorithm. However, the challenge in improving efficiency through forecasting and algorithms lies in data recorded before microgrid optimization, as these data may contain transient disturbances. To achieve accurate, error-free results, collecting data from multiple points over the same period as forecasting data may be necessary. For cases in which forecasting depends on large datasets, some studies have investigated the use of algorithms to identify the optimal controller values; for example, the authors of [27,28] analyzed HES device control in microgrid systems and utilized various algorithms to improve the system’s stability during electrical disturbances in both steady-state and dynamic conditions. The results address disturbances in electrical systems under these conditions. However, these studies focus on single objectives and lack a thorough analysis, offering a solution to the symptoms rather than addressing the root cause. Thus, a comprehensive study on different factors ranging from installation to time-based control is needed to address this core issue.

This study presents a methodology for determining the optimal locations and sizing of HESs and controlling the design parameters for BESSs using improved particle swarm optimization (IPSO) to improve power quality and stability in remote communities. The analysis is guided by a multi-objective function consisting of minimizing power loss, minimizing the line voltage stability index, and minimizing fuel costs. The method involves two steps: First, steady-state analysis is performed to determine the optimal location and size of the HES during a peak RES energy production period. Then, disturbances in the power system are investigated during the transient period, utilizing the results from the first step. During this period, the BESS controller parameters are optimized using IPSO, with a hardware-in-the-loop (HIL) setup and a 5-s resolution. Our approach considers multiple factors, including load distribution, HER output variability, and grid code requirements, to provide a robust solution for various grid configurations. A summary of prior studies on the topic is provided in the table below.

2. Remote Area Communities

The distribution of energy to remote areas presents a significant challenge for a power system. As power demand continues to rise and the need for power transmission to distant locations grows, energy generation at the source must also increase [29]. This study proposes a method to address this issue and investigates potential solutions. A remote community (RAC) was simulated using the IEEE 15-bus system, as its load resembles those of remote areas, including a voltage stability index (VSI) below the acceptable range of 0.95–1.05 p.u. and considerable power losses that result in high energy production costs. The IEEE 15-bus system was thus used to test an integrated multi-objective energy management method in a remote area community, as illustrated in Figure 1.

It analyzed the challenges a remote area community faces using the backward–forward sweep (BFS) method for power flow analysis and examined problems within the power system, such as generation, transmission, and distribution. The BFS method consists of four steps, which are outlined below.

2.1. Nodal Current

The reference voltage magnitude and phase angle are set at the root node, serving as the initial voltage for all other nodes in the distribution network. The node current at bus i can be shown in Equation (1).

$$I_{i,p}^k={\displaystyle \frac{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_i+j{Q}_i}{V_i^{(k-1)}}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}for\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i\hspace{0.17em}=\hspace{0.17em}2,3,\dots ,N$$

(1)

where $P_i$ and $j{Q}_i$ are the active and reactive power consumed by loads at the $i\mathrm{th}$ nodes; $V_i^{(k-1)}$ is the complex nodes voltage of the $i\mathrm{th}$ nodes calculation round at $k-1$.

2.2. Backward Sweep

The currents through the $i\mathrm{th}$ branch are calculated starting from the last nodes and moving toward the root node, as shown in Equation (2).

$${\overline{I}}_{b{r}_l}=-{\overline{I}}_n+{\displaystyle \sum _{k\in M}{\overline{I}}_{b{r}_k}}$$

(2)

where ${\overline{I}}_{b{r}_l}$ is the current flowing through line segment $l$; $M$ is the set of branches connected downstream of node $n$.

2.3. Forward Sweep

Starting at the root node and progressing toward the outer layers of the network, the voltage at the $i\mathrm{th}$ node is calculated along with the resistance of the transmission line $\left(R\right)$ using Equation (3).

$${\overline{V}}_n={\overline{V}}_m-R_{mn}{\overline{I}}_{b{r}_h} n=2,3,\dots ,N \mathrm{and} m=1,2,\dots ,N$$

(3)

2.4. Convergence Criterion

This criterion is met as long as the maximum value of the real or theoretical value of the difference between the calculated and specified power injection exceeds the acceptable mismatch $\epsilon$, as defined in Equation (4):

$$\left|\Delta \overline{V}\right|=\left|{\overline{V}}^r-{\overline{V}}^{r-1}\right|<\epsilon$$

(4)

3. Hybrid Energy System

3.1. Mathematical Analysis of Fluctuating PV Generation

PV penetration into the distribution network has been demonstrated to enhance the voltage profile and minimize power losses [30]. Therefore, PV should be planned based on its capacity and installation point in the distribution network. PV output power data, irradiance, and temperature at the reference location of the distribution system have been used to estimate the amount of PV generated. Based on [31,32], the amount of power generated via PV is estimated using Equation (5).

$$\hspace{0.17em}{P}_{PV}=P_{R,PV}\times {\displaystyle \frac{R_{sun}}{R_{ref}}}\times \left[1\hspace{0.17em}\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}\eta \hspace{0.17em}\hspace{0.17em}\times \hspace{0.17em}\hspace{0.17em}\left(T_{PV}\hspace{0.17em}-\hspace{0.17em}{T}_{ref}\right)\right]$$

(5)

where $P_{R,PV}$ is the PV panels rated power $\left(W\right)$, $R_{sun}$ is the radiation intensity, $R_{ref}$ is the referent radiation intensity, $T_{PV}$ is the temperature of PV panels (°C), $T_{ref}$ is the corresponds to the reference test temperature for PV panels, set at 25 °C, and $\eta$ is the panel efficiency, respectively.

3.2. Mathematical Analysis of Fluctuating HPP Generation

Run-of-the-river HPP generates turbine water flow largely dependent on the upstream river level. The generated power primarily relies on key factors such as water discharge and hydraulic head. Equation (6) expresses the formula for calculating the power output of an HPP plant [33].

$$\hspace{0.17em}{P}_{HPP}=\rho \hspace{0.17em}\hspace{0.17em}\times \hspace{0.17em}\hspace{0.17em}g\hspace{0.17em}\hspace{0.17em}\times \hspace{0.17em}\hspace{0.17em}H\hspace{0.17em}\hspace{0.17em}\times \hspace{0.17em}\hspace{0.17em}Q\hspace{0.17em}\hspace{0.17em}\times \hspace{0.17em}\hspace{0.17em}\eta$$

(6)

where $P_{HPP}$ represents the output power ($\mathrm{kW}$), $\rho$ is the water density (1000 ${\mathrm{kg}/\mathrm{m}}^3$), and $g$ represents the gravitational acceleration (9.81 ${\mathrm{m}/\mathrm{s}}^2$). Additionally, $Q$ refers to the water flow rate or discharge (${\mathrm{m}}^3/\mathrm{s}$), $H$ represents the hydraulic head ($\mathrm{m}$), and $\eta$ is the plant’s overall efficiency. The power generated by the HPP is thus directly determined.

3.3. Mathematical Analysis of BESSs

The deployment of BESSs within global power electricity networks is increasing. Numerous countries have integrated BESSs to maintain grid stability and manage power balance [32]. BESSs are crucial in reducing output power fluctuations and improving voltage stability. By applying the proposed optimization model, the optimal BESS capacity and charging/discharging cycle can be determined [31]. When $P_{BESS}^t>0$, the discharge energy in the BESS for each period is mathematically expressed in Equation (7).

$$C^t=C^{t-1}-P_{BESS}^t{\displaystyle \frac{\Delta T}{{\eta }_{dis}}}$$

(7)

On the other hand when $P_{BESS}^t<0$, the discharge energy in the BESS for each period is mathematically expressed in Equation (8).

$$C^t=C^{t-1}-P_{BESS}^t\Delta T{\eta }_{chg}$$

(8)

where $t$ represents the time interval under consideration and $T$ denotes the total time horizon in hours. $P_{BESS}^t$ refers to the BESS power output at the $t\mathrm{th}$ time interval and $C^t$ is the energy stored in the BESS at the end of the $t\mathrm{th}$ interval. $\Delta T$ indicates the duration of each time interval, ${\eta }_{dis}$ is the discharge efficiency of the BESS, and ${\eta }_{chg}$ represents its charging efficiency. Additionally, the energy stored in the battery at the end of the $t\mathrm{th}$ interval must remain within the minimum state of charge (SOC) limit and the BESS energy rating, as shown in Equation (9).

$$SO{C}^{\min }{C}_{rated}\le C^t\le C_{rated}$$

(9)

4. Problem Statement

The problem outlined in this study breaks down the objective function into three separate tasks. The optimal solution must be evaluated within the given conditions of the proposed power system. The multi-objective function equations consider three objective functions: reducing active power loss, minimizing fuel costs of the grid system, and reducing the line voltage stability index (LVSI), as described below. By utilizing IPSO, more suitable and advantageous variants are selected, making IPSO an effective technique for solving optimization problems. In this method, the model starts with random solutions and progressively finds the optimal solution through iteration based on the defined objectives.

4.1. Multi-Objective Function Formulation

The optimal location and sizing of the PV, HPP, and BESS units within the distribution system are determined according to the multi-objective function defined in Equation (10).

$$F\left(x\right)=\min \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(\hspace{0.17em}{w}_1{f}_1+w_2{f}_2+w_3{f}_3\hspace{0.17em})$$

(10)

$$\mathrm{subject} \mathrm{to} \overline{g}\left(x,u\right)=0$$

(11)

$$\mathrm{and} h\left(x,u\right)\le 0$$

(12)

where $\overline{g}$ represents the equality and $h$ the inequality constraints of all objective functions, and $w_1,\hspace{0.17em}{w}_2, \mathrm{and} \hspace{0.17em}{w}_3$ are the weights for the analysis function.

4.1.1. Active Power Loss Reduction

The first objective function is the active power loss ($P_{loss}$) reduction, which is expressed in Equation (13).

$$\hspace{0.17em}{f}_1=\min \hspace{0.17em}\hspace{0.17em}(P_{loss})\hspace{0.17em}$$

(13)

where $f_1$ represents the first objective function, and $P_{loss}$ denotes the active power loss in the distribution system. The active power loss is calculated according to Equation (14).

$$\min \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_{loss}={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{a}_{ij}(P_i}{P}_j+Q_i{Q}_j)\hspace{0.17em}+\hspace{0.17em}\hspace{0.17em}}{b}_{ij}(Q_i{P}_j-P_i{Q}_j)\hspace{0.17em}\hspace{0.17em}$$

(14)

where $P_i$ and $P_j$ represent the active power at nodes $i$ and $j$, respectively; $Q_i$ and $Q_j$ denote the reactive power at nodes $i$ and $j$; $a_{ij}\hspace{0.17em}$ and $b_{ij}$ are the constants associated with each node.

4.1.2. Fuel Cost Reduction

The second objective function is to minimize fuel costs, as defined by Equation (15).

$$\hspace{0.17em}{f}_2=\min \hspace{0.17em}\hspace{0.17em}(C_f)\hspace{0.17em}$$

(15)

where $f_2$ represents the second objective function, and $C_f$ represents the total fuel cost of the power system. The total fuel cost of the power system is calculated according to Equation (16).

$$\min \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{C}_f={\displaystyle \sum _{i=i}^{N_G}\left(a_i{P}_{Gi}^2+b_i{P}_{Gi}+c_i\right)}\hspace{0.17em}$$

(16)

where $N_G$ represents the number of the power generators in the grid system; $P_{Gi}$ represents the power generated by the grid system for load; $a_i,b_i\hspace{0.17em}\hspace{0.17em}\mathrm{and}\hspace{0.17em}\hspace{0.17em}{c}_i$ represent the grid constraints of fuel cost for power generation.

4.1.3. Line Voltage Stability Index

The third objective function is LVSI reduction, expressed in Equation (17).

$$\hspace{0.17em}{f}_3=\min \hspace{0.17em}\hspace{0.17em}(LVIS)\hspace{0.17em}$$

(17)

where $f_3$ represents the third objective function, and $LVIS$ represents the line voltage stability index. The LVSI is calculated according to Equations (18) and (19).

$$\min \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}LVIS={\displaystyle \sum _{i=1}^{N_{line}}LVS{I}_i}$$

(18)

$$LVSI={\displaystyle \frac{4R{P}_r}{{\left(V_s\cos \left(\theta -\delta \right)\right)}^2}}$$

(19)

where $N_{line}$ represents the number of transmission lines connected between the nodes, $R$ represents the resistance of the transmission lines, $P_r$ represents the active power generation at the receiving nodes, $V_s$ represents the voltage at the sending nodes, $\theta$ represents the line impedance angle, and $\delta$ represents the different voltage phase angles between the start and end nodes.

4.2. Constraints of Multi-Objective Function Formulation

The constraints proposed in our study are categorized into six groups and are summarized below.

4.2.1. Power Balance Formulation

The power balance Eqn. for a power system is determined using Equations (20) and (21), while the power demand is determined using Equation (22).

$$P_{Gi}+P_{HES,\hspace{0.17em}\hspace{0.17em}i}+P_{DR,\hspace{0.17em}\hspace{0.17em}i}=P_{DR,\hspace{0.17em}\hspace{0.17em}i}^0+P_{loss,\hspace{0.17em}\hspace{0.17em}i}$$

(20)

$$P_{HES,\hspace{0.17em}\hspace{0.17em}i}=sum\hspace{0.17em}\hspace{0.17em}({\displaystyle \sum _{i=1}^{NG}{P}_{PV,\hspace{0.17em}\hspace{0.17em}i}},\hspace{0.17em}{\displaystyle \sum _{i=1}^{NG}{P}_{HPP,\hspace{0.17em}\hspace{0.17em}i}}\hspace{0.17em}\hspace{0.17em},{\displaystyle \sum _{i=1}^{NG}{P}_{BESS,i}}\hspace{0.17em}\hspace{0.17em})$$

(21)

$$P_{DR,\hspace{0.17em}\hspace{0.17em}i}=sum\hspace{0.17em}\hspace{0.17em}(P_{Gi},\hspace{0.17em}\hspace{0.17em}{P}_{HES,\hspace{0.17em}\hspace{0.17em}i})-P_{loss,\hspace{0.17em}\hspace{0.17em}i}$$

(22)

where $P_{Gi}$ represents the active power of the grid system, $P_{HES}$ represents the active power of the hybrid energy system, $P_{DR}$ represents the total active power demand in the grid system, $P_{DR}^0$ represents the total active power demand in first-time analysis, and $N_G$ represents the number of the power generator in nodes.

4.2.2. Generation Limits

Batteries store the surplus energy generated from renewable sources. If they reach their power or energy limits, any excess energy will be absorbed by the grid system (negative power). Consequently, the grid system can accommodate positive and negative power values, as indicated in Equation (23).

$$-\infty <P_{Gi}<\infty$$

(23)

The HPP generator will produce energy during periods when $P_{DR}$ is high. Since energy production from HPP cannot be continuous, it will produce energy to reduce $P_{DR}$ or be used with the BESS system. Therefore, the operational limits of the HPP generator are determined by the capacity of the equipment and the volume of fluid flowing through the turbine using Equation (24).

$$P_{HPP}^{\min }<P_{HPP}<P_{HPP}^{\max }$$

(24)

PV generators produce a minimum power of zero when there is no solar radiation, and they can generate a maximum power equal to their nominal capacity. Therefore, their operational limits are defined using Equation (25).

$$P_{PV,\hspace{0.17em}\hspace{0.17em}i}^{\min }<P_{PV,\hspace{0.17em}\hspace{0.17em}i}<P_{PV,\hspace{0.17em}\hspace{0.17em}i}^{\max }$$

(25)

Batteries can operate either as generators or as loads, producing positive or negative power, respectively, while ensuring they do not exceed their generation and consumption limits, as indicated in Equation (26).

$$P_{BESS,\hspace{0.17em}\hspace{0.17em}i}^{\min }<P_{BESS,\hspace{0.17em}\hspace{0.17em}i}<P_{BESS,\hspace{0.17em}\hspace{0.17em}i}^{\max }$$

(26)

4.2.3. BESS Limits of Charging and Discharging

Batteries have upper and lower energy storage limits that should not be exceeded to prevent damage [34]. These constraints are specified in Equation (27).

$$SO{C}_{BESS,\hspace{0.17em}\hspace{0.17em}i}^{\min }<SO{C}_{BESS,\hspace{0.17em}\hspace{0.17em}i}<SO{C}_{BESS,\hspace{0.17em}\hspace{0.17em}i}^{\max }$$

(27)

Batteries can function either as generators or as consumers, with their stored energy levels updated at each time interval based on power and operating duration, as defined by Equation (28).

$$SO{C}_{BESS,\hspace{0.17em}\hspace{0.17em}i}^t=SO{C}_{BESS,\hspace{0.17em}\hspace{0.17em}i}^{t-1}\left\{\begin{array}{c}\Delta t\times P_i^t\times {\eta }_c\\ {\displaystyle \frac{\Delta t\times P_i^t}{{\eta }_d}}\end{array}\right.\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\begin{array}{c}for\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_i^t<0\\ for\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{P}_i^t>0\end{array}$$

(28)

where ${\eta }_c$ and ${\eta }_d$ are the charging and discharging efficiencies of BESS, respectively, and $\Delta t$ is the sampled time period, defined as the entire day.

4.2.4. Voltage Constraints

The node’s voltage profile must be defined to ensure compliance with the voltage stability limits specified in the grid code, as shown in Equations (29) and (31).

$$V_{\min }^{0.95p.u.}\le V_i\le V_{\max }^{1.05p.u.}$$

(29)

$$LVS{I}_{\max }\le LVS{I}_{\lim it}$$

(30)

$$LVS{I}_{\max }=\max (LVS{I}_i);\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}i=1,2,\dots ,N_{line}$$

(31)

where $LVS{I}_{\lim it}$ represents the imposed limit of the LVSI, set to 0.9 in this study, and $LVS{I}_{\max }$ represents the maximum LVSI value within the grid system.

5. Battery Energy Storage System Controller

The BESS controller, integrated with the grid-connected PV and HPP, demonstrates effective performance in system frequency control, charging requests, and battery management through the SOC balance method described. Consequently, utilizing droop characteristics, the BESS power is regulated in response to frequency deviations ($\Delta f$):

$$P_{BESS}=\left\{\begin{array}{c}{K}_{BESS}\Delta f\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\left|K_{BESS}\right|\Delta f\le P_{\max }\\ P_{\max }\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\left(P_{\max }<K_{BESS}\Delta f\right)\hspace{0.17em}\hspace{0.17em}\end{array}\right.$$

(32)

$$K_{BESS}=K_{\max }\left(1-\left(\frac{SOC\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}SO{C}_{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{l}ow(high)}}{SO{C}_{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\max (\min )}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}SOC\hspace{0.17em}\hspace{0.17em}{SOC}_{low(high)}}\right)\right)$$

(33)

where $K_{BESS}$ represents the BESS gain, and $P_{BESS}$ represents the maximum BESS power. Additionally, $K_{BESS}$, based on Equation (33), where $SO{C}_{\hspace{0.17em}\mathrm{l}ow}$, $SO{C}_{high}$, $SO{C}_{\max }$, and $SO{C}_{\min }$ are the SOC design parameters. SOC is regulated using SOC deviation control.

6. The Proposed Improved Particle Swarm Optimization Technique

6.1. Conventional Particle Swarm Optimization Technique

Conventional PSO is inspired by swarm intelligence, mimicking the collective behavior of bird flocks and fish schools. In conventional PSO, each particle dynamically adjusts its velocity based on its own experience and the movements of its peers. The position of a particle is updated considering its current location, velocity, and relative distances to both its personal best position ($pbest$) and the global best position ($gbest$) found by any particle in the swarm. Unlike other optimization techniques, the neighborhood structure in conventional PSO remains relatively stable and does not change as frequently as in other metaheuristic algorithms [35]. In this study, we utilized conventional PSO to analyze the optimal solutions for specific objective functions. The optimal values were obtained by iteratively searching for the best particle value (individual particle′s best and global best values among all particles). The particle set is represented by Equation (34).

$$p_i=[P_{Gi},\dots ,P_{NG}\left|V_{Gi}\right|,\dots ,\left|V_{NG}\right|,P_{pi},\dots P_{NP},\left|V_{pi}\right|,\dots ,\left|V_{NP}\right|,D{R}_1,\dots ,D{R}_{NB}]$$

(34)

Conventional PSO begins by initializing the population and evaluating each particle′s fitness value. Next, it updates the $pbest$ and $gbest$ positions. In the final step, the velocity and position of all particles are adjusted. The new velocity of the particles is calculated using Equation (35).

$$v_i^{t+1}=w{v}_i^t+c_1{r}_1(pbes{t}_i^t-p_i^t)+c_2{r}_2(gbes{t}_i^t-p_i^t)$$

(35)

The process of fitness evaluation, updating $pbest$ and $gbest$, and adjusting the velocity and position is repeated iteratively until a predefined stopping condition is satisfied. The new positions of particles can be calculated as expressed in Equation (36).

$$p_i^{t+1}=p_i^t+v_i^{t+1}$$

(36)

where $p_i$ is the position of the ith particle, $V_{Gi}$ is the voltage magnitude of the generator, $P_{pi}$ is the active power of a generator, and $D{R}_{NB}$ is the actual power demand for node NB.

6.2. Improved Particle Swarm Optimization (IPSO)

Drawing inspiration from the PSO technique [36], we first performed particle discretization. In this model, the discrete operators “⊗”, “⊖”, “⊕”, and “⊙” replace the continuous operators in the PSO algorithm, defining the discretization process as follows:

$$\hspace{0.17em}{P}_i^{t+1}=P_i^t\odot v_i^{t+1}$$

(37)

During particle updates, each dimension of every particle was discretely computed asynchronously. The local modularity incremental function was then utilized to explore each node′s current local information fully. This allowed for the integration of drifting particle modeling. If the electron’s position was considered the candidate solution, and the potential energy function represented the objective function, the electron’s motion was considered similar to searching for the minimum solution. Consequently, the particle update equation was reformulated as follows:

$$P_i^{t+1}=P_i^t+v_i^{t+1}$$

(38)

$$v_i^{t+1}=\alpha \left|c_1^t-x_{i,\hspace{0.17em}j}^t\right|{\phi }_{i,\hspace{0.17em}\hspace{0.17em}j}^t+\beta \left(p_i^t-x_{i,\hspace{0.17em}j}^t\right)$$

(39)

Parameter $\alpha$ is known as the compression–expansion coefficient, while $\beta$ is referred to as the acceleration coefficient. These two key parameters can be adjusted to balance the particles’ global and local search capabilities. Higher $\alpha$ and $\beta$ values enhance the global search ability, whereas lower values improve local search performance.

In Figure 2, a comparison is presented between the traditional PSO algorithm and an improved PSO variant. The left figure illustrates the behavior of the traditional PSO, where it is observed that the particles take a longer path to converge toward the optimal solution. This limitation arises from a known flaw in the traditional PSO approach: increasing the swarm size can accelerate convergence per iteration, but it also leads to a significant increase in the amount of data that needs to be processed. To address this issue, the improved PSO algorithm introduces a partial area analysis strategy centered around the $pbest$ point, as shown in the right figure. In this approach, local searches are performed near the $pbest$ point, generating new candidate points that are closer to the optimal solution than the original $pbest$. After completing the local analysis, the algorithm proceeds with a more focused convergence phase, leading to faster and more efficient optimization.

7. Simulation Results

This study presents the simulation parameters. Consisting of the population and iteration process for the proposed method, they were determined based on bus voltage sensitivity, with the population size set to 30 and the number of iterations set to 100. The optimal location and sizing of the HES units were determined using the IPSO method. Finally, in Case III, a sudden short circuit of the transmission line in Case II was investigated. The effectiveness of the method was verified through HIL testing.

7.1. Case I: Random Installation of PV-HP-BESS and PI Parameter Control of BESS

For this test case, the initial parameters included a search population of 30 groups and an infinite number of iterations. The HES was installed at a single point; the installation size ranged from 10 to 65 kW for PV, 10 to 100 kW for HP, and f10 to 100 kW for the BESS. This setup allowed u to find the best location and size. The results of the random installation indicate that it can enhance the voltage level of the IEEE 15-bus system. However, the HES was installed on wire ends, with more than 30 iterations, as shown in Figure 3. The random installation of the PV, HPP, and BESS in locations 13, 12, and 5 had a size of 90.86, 62.41, and 65 kW, respectively. This setup reduced the power loss in the grid system to 44.23 kW and lowered the fuel cost of the grid system to 3832.1 USD/h.

The findings on the optimal location and size of the HES suggest that selecting the best location supports maintaining voltage stability in the power distribution system during periods of increased load. The voltage level in the tested scenario was higher than that in the base case. Consequently, these findings do not align with the objectives of this study.

7.2. Case II: Optimal Location of PV-HP-BESS and PI Parameter Control of BESS

In Case II, the initial parameters were kept the same as those in Case I. Additionally, the IPSO method was applied to determine the optimal location and size of the HES, with the multi-objective function weights randomly assigned values between 1 and 100. IPSO begins by adjusting the parameters in Equation (20) to determine the optimal position and size of the HES. Once these parameters are fine-tuned, the results are used to refine the solutions for the weights of the three main objectives, as outlined in Equation (10). The optimization process then aims to minimize the value according to the defined objective ($f_1,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{f}_2,\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{f}_3$). The optimization results obtained through the IPSO method, adjusted based on these weights, are presented in Figure 4. Consisting of three axes: the X-axis represents power loss, the Y-axis represents the fuel cost of the grid system, and the Z-axis represents the LVSI. When one of the objectives is assigned the least weight (or a value of 0), it results in the highest optimal value, forming a triangular area of optimal solutions. The best solution in each iteration will adjust the weights of the main objectives differently, leading to unique results. The most optimal values presented in Figure 4 are those with the adjusted weights.

The optimal locations for the PV, HP, and BESS units at locations 8, 15, and 13, with sizes of 65 kW, 100 kW, and 50 kW, respectively, reduced the power losses in the grid system to 43.873 kW and decreased the fuel cost to 3825.7 USD/h. The test results from the various cases were compared using LVSI, as shown in Figure 5.

To obtain the most appropriate results for further development in Case 3, the outcomes of various algorithms were compared with those from other studies using a similar research approach, as presented in

Table 1. Comparison of results for the IEEE 15-bus power distribution test system (Case II).

Unit	Base Case	FPA [37]	TSM [38]	IHA [39]	GA [40]	PSO [41]	IPSO
No. of HES	-	3	3	3	3	3	3
Sum of size (kW)	-	1000	1300	950	341.5	218.27	215
$P_{loss}$ (kW)	53.679	30.7112	32.4262	31.1255	51.827	44.237	43.873
$C_f$ (USD/h)	3873	5510	5873	5179	3865.10	3832.10	3825.7
Minimum Bus Voltage (p.u.)	0.9445	0.9676	0.9695	0.9658	0.9542	0.9548	0.9525

.

As shown in Table 1, the IPSO method demonstrates superior performance compared with other techniques by efficiently identifying optimal values that align with the defined objectives. This includes adjusting weights accordingly and improving voltage levels to satisfy the minimum criteria set in this study. As a result, the IPSO method was chosen to analyze the challenge in Case 3. The detailed results obtained using this method are presented in

Table 2. Comparison between Case I and Case II using IPSO.

Unit	Base Case	Case I			Case II
		PV	HP	BESS	PV	HPP	BESS
Location	-	13	5	12	8	15	13
Size (kW)	-	65	90.86	62.41	65	100	50
$P_{loss}$ (kW)	53.679	44.237			43.873
$C_f$ (USD/h)	3873	3832.1			3825.7
max LVSI (%)	<100	65.012			38.89

.

As presented in Table 2, the IPSO method confirms that the predefined objectives produce the most optimal results. In Case Study 2, we assigned random integer weights to each objective—$w_1$ = 33, $w_2$ = 32, and $w_3$ = 35. It can be explained that the highest weight, $w_3$, corresponds to the component variable LVSI. Since an LVSI greater than 1 p.u. indicates a voltage failure in the power system, minimizing LVSI becomes the top priority. To enhance clarity, LVSI values were converted from p.u. to percentages (%). The next weight, $w_1$, corresponds to the component variable power loss. Installation of the HES into the IEEE 15-bus test system reduced power losses during power transmission and, meanwhile, lowered fuel costs by decreasing upstream generation. Consequently, $w_2$ was the smallest weight. A side-by-side comparison of these outcomes is illustrated in Figure 6.

The BESS system parameters were optimally adjusted using the IPSO method within the MATLAB Simulink program version 2021b, utilizing the test model illustrated in Figure 7. Due to Case III, involving a dynamic test over a 5-s duration, it required the development of an IEEE 15-bus power distribution test system model in MATLAB Simulink for initial analysis. The optimization approach involved transmitting $\Delta f$ from the power system model to control blocks. The initial output values from these control blocks were then processed using the IPSO method to fine-tune the BESS parameters. These refined parameters replaced the previous ones, and the cycle was repeated throughout the 5-s simulation. The optimized results of the BESS parameter tuning using the IPSO method are summarized in

Table 3. Comparison of results between traditional parameters and optimal parameters.

Case	${\mathit{K}}_{\mathit{P}}$				${\mathit{K}}_{\mathit{I}}$
	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{y}}_1$	${\mathit{y}}_2$	${\mathit{y}}_3$	${\mathit{y}}_4$
Base Case	250	10,000	100	5000	250	10,000	100	5000
Case I
Case II	680	643	617	601	417	214	675	346

.

7.3. Case III: Sudden Short Circuit of Transmission Line

Case III builds upon the result of Case II, which determined the optimal location, sizing, and PI parameter control of the BESS using the IPSO method. These results were further validated through HIL testing. The OP4512 RCP/HIL FPGA real-time simulator, an internationally recognized platform for virtual hardware testing, is connected to a computer and displayed on a monitor, as illustrated in Figure 7. In this scenario, a short circuit was introduced to the IEEE 15-bus power distribution test system model for 3 s, then cleared at 3.5 s. During the fault, the BESS PI controller—tuned with the optimal PI parameters—was required to inject energy into the IEEE 15-bus power distribution test system to support voltage stability. Additionally, both the HPP and PV systems were expected to supply maximum energy throughout the testing period.

This case study aims to validate the outcomes related to Objective 3, which focuses on minimizing LVSI and ensuring voltage stability during sudden disturbances. The findings demonstrate that location and sizing, combined with PI controller parameter optimization, effectively sustain voltage stability over time, as illustrated in Figure 8.

Figure 8 displays the VSI values of buses 13 and 14, for which the voltage was reduced to below 0.95 p.u. This demonstrates that the proposed method can help mitigate the impact of a short circuit occurring at the 3 s and clearing at the 3.5 s. However, since addressing short circuits is not within the scope of this research, our method only minimizes the resulting changes rather than resolving them completely. Another key factor is that the BESS control circuit is still a basic PI controller, leading to an unbalanced response and control. As shown in Figure 8, significant voltage oscillations occurred in buses 13 and 14. Overall, however, the proposed approach helps reduce the impact of a short circuit on the power system.

8. Discussion

This study centers on evaluating three objectives: minimizing power loss, minimizing fuel costs in the grid system, and minimizing LVSI to enhance voltage stability during both steady-state and transient conditions. The approach involves determining the optimal location and size of the HES, along with fine-tuning the PI controller to support voltage stability. Using the IPSO method, the analysis was divided into three cases to identify the best configuration based on these objectives. In Case I, the HES location, size, and PI controller parameters were assigned randomly. The results, illustrated in Figure 3, show that the HES tends to be located at the end of the feeder line. While the selected HES type can inject energy and improve the voltage to an acceptable level, the solution does not align with the defined objectives. As such, Case I is not considered effective for addressing the targeted goals.

Case II involves determining the optimal location and size of the HES, along with tuning the PI controller parameters using the IPSO method. This case is divided into two main steps: Step 1 focuses on identifying the most suitable location and size for the HES, while Step 2 involves refining the PI controller parameters. In Step 1, the IPSO method is applied to determine the optimal location and sizing of the HES components, which include PV, HP, and BESS units. The convergence results, shown in Figure 4, reveal 30 potential optimal solutions, with one point identified as the most effective. The best locations for the PV, HP, and BESS units are buses 8, 15, and 13, respectively, with sizes of 65 kW, 100 kW, and 50 kW, as illustrated in Figure 4. Optimizing the location and size of the HES significantly enhances voltage stability. Additionally, when compared with other algorithms, the IPSO method proves to be the most effective in achieving the study’s objectives. Therefore, it can be concluded that the IPSO-based optimization of HES location and size successfully meets the primary goals and improves voltage stability, as shown in Figure 6. In Step 2, the results from Step 1 were used to design a test model in MATLAB Simulink to refine the PI controller parameters further, as shown in Figure 7. The IPSO method is again used to optimize these parameters. Output signals from the PI controller are analyzed to determine suitable values, which then replace the initial settings, leading to more effective PI controller performance. The optimized results obtained in Case II serve as the foundation for further validation and testing in Case III.

Case III serves to validate the analysis results through real-time testing using the OP4512 RCP/HIL FPGA simulator, focusing on Objective 3: minimizing LVSI while maintaining voltage stability during sudden disturbances. In this scenario, a short circuit is introduced to the test model for 3 s and cleared at 3.5 s. During the fault, the BESS system is required to inject energy into the test model, while both the HPP and PV systems supply their maximum available energy. The results confirm that with the optimal location and sizing of the HES, combined with PI controller parameters, the system can effectively maintain voltage stability during transient faults, as demonstrated in Figure 8. This study thus proposes the design of multi-objective energy management for remote communities connected with an optimal HES using IPSO. The approach successfully achieves the defined objectives and enhances the stability of the power system.

9. Conclusions

This study presented a multi-objective energy management method for HES units in a power distribution system suitable for RACs. Testing all three cases to determine the most effective approach for achieving the defined objectives—minimizing power loss, minimizing fuel costs, and minimizing LVSI—Case I involved random location and sizing of the HES components along with arbitrary PI controller settings. At the same time, this setup provided a basic improvement in voltage stability. Specifically, the PV, hydro, and BESS units were randomly installed at locations 13, 12, and 5, with sizes of 90.86 kW, 62.41 kW, and 65 kW, respectively. It failed to meet the key objectives. As a result, it can be concluded that this approach is not suitable for addressing the specified goals. Case II of this study focuses on determining the optimal size and location of the HES, along with tuning the PI controller parameters using the IPSO method. This process is divided into two main steps. In Step 1, the IPSO algorithm is used to identify the most suitable locations and sizes of the HES components based on the defined objectives. The optimal locations for the PV, HP, and BESS units were found to be at buses 8, 15, and 13, respectively, with capacities of 65 kW, 100 kW, and 50 kW. This configuration reduced power loss in the grid to 43.873 kW and lowered fuel costs to 3825.7 USD/h. These outcomes align well with the specified objectives and demonstrate greater efficiency compared with other methods. To validate these results, Step 2 involved simulating the system in MATLAB Simulink using the result from Step 1. The IPSO method received the target signals to optimize the PI controller parameters within the designated time frame. The findings confirmed that the refined PI parameters effectively maintained voltage stability during transient events. The successful outcomes of Case II provide the foundation for further validation and real-time testing in Case III. Finally, Case III utilizes the results from Case II to evaluate voltage stability during a simulated short circuit using the HIL testing device—specifically, the op4512 rcp/hil fpga real-time simulator. When a short circuit occurs in the test model, the BESS system, guided by the optimized PI controller, injects energy into the model testing. At the same time, both the HPP and PV systems deliver their maximum power output to support system stability. The results demonstrate that the optimal location and sizing of the HES, along with the PI controller tuning achieved through the IPSO method, effectively maintain voltage stability during sudden short-circuit events. The findings from all three cases offer valuable insights for improving active distribution systems, providing a practical approach to mitigating the impact of unexpected faults. Additionally, these results serve as a reference for future enhancements of power systems tested through HIL equipment. Future research will explore innovative control strategies for distributed generation and RES to further advance and strengthen power system performance.