Pareto-Based Optimization of PV and Battery in Home-PV-BES-EV System with Integrated Dynamic Energy Management Strategy

Abstract

The assessment of grid-connected systems depends on their cost efficiency, reliability, and greenhouse gas (GHG) reduction potential. This study presents a multi-objective optimization framework for designing a grid-connected photovoltaic (PV) and battery energy storage (BES) system integrated with an electric vehicle (EV) for a household in Riyadh, Saudi Arabia. The framework aims to minimize the Cost of Energy (COE) and Loss of Power Supply Probability (LPSP) while maximizing the Renewable Energy Fraction (REF). Additionally, GHG emissions are evaluated as a result of these objectives. The EV operates in Vehicle-to-Home (V2H) mode, enhancing system flexibility and energy management. The optimization process employs two advanced metaheuristic techniques, Multi-Objective Particle Swarm Optimization (MOPSO) and Multi-Objective Harris Hawks Optimization (MOHHO), to identify Pareto front solutions. Fuzzy logic is then applied to determine a balanced compromise among the economically optimal (minimum COE), renewable energy-oriented (maximum REF), and environmentally optimal (minimum GHG emissions) solutions. Simulation results show that the proposed system achieves a COE of USD 0.0554/kWh, a LPSP of 1.96%, and an REF of 92.55%. Although the COE is slightly higher than that of the grid, the system provides significant environmental and renewable energy benefits. This study highlights the potential of integrating dynamic EV management and advanced optimization techniques to enhance the performance of grid-connected systems. The findings demonstrate the effectiveness of combining Pareto-based optimization with fuzzy logic to achieve balanced solutions addressing economic, environmental, and renewable energy objectives, paving the way for sustainable energy systems in urban households.

1. Introduction

Global warming and climate change are among the global issues that emphasize the significance of sustainable energy resources and their role in reducing reliance on fossil fuels. According to the IEA, the residential and transportation sectors are responsible for 30% and 28% of worldwide energy consumption and 28% and 23% of worldwide carbon emissions, respectively [1]. In efforts to mitigate these environmental challenges, sustainable energy technologies and the use of green energy resources have been advancing and making significant progress. Hybrid systems that integrate renewable energy sources like wind turbines and photovoltaic panels are becoming increasingly popular [2,3]. Additionally, there is a significant increase in integrating distributed energy resources such as energy storage systems (ESS) and electric vehicles into the national grid. Globally, the most commonly used renewable energy sources are wind turbines and photovoltaic systems as they are environmentally friendly and cost-effective resources [4,5,6]. However, these types of renewable energy sources are well known for their intermittent character, and thus they need to be used together with battery systems to smooth power output and provide backup power [4,7].

Rooftop photovoltaic systems have quickly become a significant renewable energy source in many nations. The installation of residential PV systems along with battery storage in homes and buildings has grown rapidly in recent years, and this upward trend is expected to continue [8,9]. In 2017, PV systems contributed 114 TWh to the EU’s electricity demand, based on an installed capacity of 107 GW [10]. The share of residential and commercial rooftop systems accounted for approximately 28% and 18% of the installed photovoltaic capacity contributing to the EU’s electricity demand, respectively [10]. The installation of rooftop solar PV systems for households not only reduces harmful emissions, but also cuts electricity bills [11]. Researchers in Ref. [12] conducted a study on households in California and concluded that using solar-only systems can lower their annual lifecycle greenhouse gas emissions by 110 to 570 kg CO₂, corresponding to a 5% to 39% reduction compared to homes without solar systems.

Based on these benefits, the Saudi Arabian government has set ambitious goals to shift the economy away from dependence on fossil fuels. Among the notable goals in Vision 2030 is the incorporation of renewable energy systems into the national grid [13]. According to studies by the King Abdullah Petroleum Studies and Research Center (KAPSARC), residential buildings represent 50% of the total energy consumption in the kingdom [14]. The authorities in Saudi Arabia have taken significant steps to promote sustainability in the energy sector. Since 2018, the Saudi Electricity Regulatory Authority (SERA) and Saudi Electricity Company (SEC) issued regulations to promote the adoption of grid-connected rooftop solar photovoltaic systems (RSPV) by individuals [15,16]. Considering that the country is the largest oil exporter in the world, it is committed to the Paris Agreement. Consequently, the energy sector in Saudi Arabia is experiencing a lot of significant transformations. The target of these transformations is to have 50% of the energy consumed domestically coming from renewable sources by 2030 [17,18]. Acknowledging the possibility of decreasing emissions using a more sustainable energy mix, the government set a target to achieve 30% of electric vehicles in Riyadh city by 2030 [18]. Also, the government demonstrated its commitments towards Paris Agreement through regulations, investments in charging infrastructure and encouraged electric vehicles manufacturers to set up their facilities in Saudi Arabia. Furthermore, KSA has founded the first local EV manufacturer CEER [19,20]. Considering the transitions in the country, it is important to study the optimal planning of rooftop solar PV systems with EV, focusing on the sizing of PV panels and batteries, and managing power flow through a home energy management system (HEMS) to minimize COE, reduce LPSP, and maximize REF. Additionally, cost reductions and advancements in PV and Battery Energy Storage technologies encourage greater adoption by homeowners. Incorporating EVs into the household adds further advantages, as they can operate bidirectionally, supplying power back to the system.

The integration of rooftop solar PV systems and bidirectional EVs essentially creates a home microgrid, where optimal sizing and efficient energy management are crucial. To tackle the complexity of such systems, metaheuristic algorithms have been widely employed due to their efficiency in solving nonlinear problems and providing reasonable computational times. There are different tools that can be used for the optimization of the system such as HOMER [21], PSAT [22], and SeDuMi [23]. Furthermore, different metaheuristic algorithms are used for optimal sizing such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Cuckoo Search Algorithm (CSA) [24]. One of the recent metaheuristic optimization techniques is Harris Hawks Optimization (HHO), which was used for sizing the microgrid components (PV-WT-BES-DG) [25]. All these optimization methods can operate in MATLAB. However, the previously mentioned tools are not all suitable for solving sizing problems because of the specific characteristics of each tool [26]. The contribution of renewable energy sources in the country is very low [27]. Most solar projects are in industrial applications including hydrogen production facilities, water desalination plants, and food drying equipment [28]. Vehicle-to-home is a prominent topic in the realm of sustainable electric vehicle development [29]. V2H technology, first proposed by AC Propulsion in the early 1990s, enables electric vehicles to supply power to a home. It allows the electric vehicle to work as a mobile energy storage device. This technology can assist in managing the intermittent production of renewable energy sources (RES) [30,31]. Besides, various services can be provided by V2H technology such as: energy cost saving, peak shaving, load balancing, backup energy during outages, grid stabilization, and enhanced energy independence [30]. In summary, there are a lot of ancillary services provided to the system. Many studies combined PV/BES/EV with optimal sizing of renewable sources and batteries to ensure economic and reliable systems. In [29], the authors introduced an innovative approach for optimizing household energy costs in a grid-connected home equipped with an electric vehicle, a renewable energy source, and battery energy storage. The focus in [32] was on incorporating residential photovoltaic systems and electric vehicles into a home energy management system with an occupant-centered approach, considering factors such as occupants’ thermal comfort, clothing habits, and concerns regarding the state of charge (SOC) of EVs. To the best of the authors’ knowledge, several studies have explored EV charging, V2H systems, and PV-BES-EV systems for households. However, the majority of these studies do not emphasize the dynamic management of EVs integrated with V2H for determining the optimal sizing of PV and BES while aiming to minimize LPSP and COE and maximize REF.

In order to help the decision-makers, the authors in [33] used technical, social, economic, political, and environmental criteria to assess the sustainability of the microgrid. Similarly, in [34], the authors applied an Analytic Hierarchy Process (AHP) approach to prioritize the criteria for optimizing the hybrid energy system. The authors in [35] developed a multi-criteria decision analysis (MCDA) framework to incorporate renewable energy into the utility grid. The paper conducted techno-economic optimization considering seasonal variations to identify the optimal configuration using the Analytic Hierarchy Process (AHP) framework. Additionally, TOPSIS, along with various weighting methods, was proposed in [33] to select the final design from a range of non-dominated solutions. A review of the literature reveals that the fuzzy compromise solution method has been underexplored for decision-making problems for multi-objective optimal sizing of household components. The fuzzy logic method provides a logical and mathematical framework that helps decision-makers in determining the best compromise solution. It is a simple and effective tool because it is straightforward, computationally efficient, and provides a flexible framework for decision-makers in energy systems.

Novelty and Contribution

Despite significant research efforts on hybrid PV-BES-EV systems, several critical gaps remain unaddressed. First, most studies assume fixed EV participation without accounting for the stochastic nature of EV availability, including arrival, departure, and state-of-charge fluctuations. Second, while several works have optimized PV-BES-EV systems using single- or bi-objective methods, there is limited exploration of a comprehensive tri-objective framework that simultaneously considers COE, LPSP, and REF, thereby addressing economic, reliability, and environmental perspectives. Third, although fuzzy logic methods have been used in decision-making for energy systems, their application to multi-objective Pareto front selection in PV-BES-EV optimization is scarce. Finally, few studies have focused on Riyadh, Saudi Arabia, where the unique climatic, policy, and market conditions demand context-specific solutions. This study addresses these gaps by developing a comprehensive optimization and decision-making framework for the optimal sizing and operation of PV-BES-EV systems in Riyadh, Saudi Arabia.

This study analyzes the feasibility of a grid-connected household with PV-BES-EV configuration in Riyadh city. The objectives of this study are to minimize COE and LPSP and to maximize (REF). The study focuses on determining the optimal sizing of the PV and battery energy storage systems, employing a novel rule-based home energy management system to manage the energy flow throughout the system. This study used a set of measured data on hourly Global Horizontal Irradiance (GHI), load demand, and ambient temperature for Riyadh, Saudi Arabia. The load demand data for this location were sourced from the Saudi Electricity Company (SEC). The other data were sourced from King Abdullah City for Atomic and Renewable Energy (KACARE) [36]. The study area is located at latitude 24.7619° N and longitude 46.7539° E and benefits from abundant solar insolation.

The contributions of this paper are:

• A practical and comprehensive mathematical model employing two metaheuristic optimization techniques for optimal sizing of grid-connected PV and BES of the system with EV.
• A novel rule-based home energy management system that combines PV-BES-EV to enable the user to efficiently utilize the system. In the proposed HEMS, EV is addressed as a secondary load during charging and as an energy storage system that can supply power to the household load (V2H).
• A dynamic management of EV (charging/discharging based on SoC and TOU tariffs) in the proposed home energy management based on EV state of charge.
• Applying a fuzzy logic approach to find a compromised solution out of the Pareto fronts resulted from MOPSO and MOHHO.

2. Proposed System Configuration and Operation

The proposed home system integrates multiple power sources and components to ensure efficient energy distribution within the household, as shown in Figure 1. The primary source of power is a photovoltaic system, which generates energy during sunlight hours. This energy is fed into the DC bus, where it can either be stored in battery energy storage or converted by a bidirectional DC/AC converter for use by AC loads, including household appliances. The battery energy storage unit is a Nickel–Iron (NiFe) battery, which serves as a backup storage unit, capable of storing excess PV energy and discharging it when PV production is insufficient. The bidirectional converter allows energy to flow in both directions, enabling the battery to supply power to the home during times of need, and also to charge from the PV system when excess energy is available. An electric vehicle connected to the system can operate in both Vehicle-to-Home (V2H) and Home-to-Vehicle (H2V) modes. In V2H mode, the EV acts as a secondary energy source, supplying power back to the home when needed, while in H2V mode, the EV charges from the home’s energy sources. The system is managed by a Rule-Based Home Energy Management System (RB-HEMS) central controller, which coordinates power distribution across the different energy sources and loads. The controller monitors and optimizes the energy flow between the PV system, battery, grid, household load, and electric vehicle. In case the available energy sources are unable to meet the household’s demand, the system can import power from the grid, acting as a backup source. The RB-HEMS ensures optimal operation by controlling and balancing the power flow from all sources and managing the EV’s role as both a load and a source, thereby reducing grid dependency while maximizing the use of renewable energy and minimizing costs.

The parameters and costs of the components of the proposed system used in this study are shown in

Table 1. Technical and economic parameters.

Components	Parameters	Value		Unit
PV system [37]	Lifetime	25		y
	Rated power	0.305		kW
	Capital cost	550		USD/Unit
	O&M cost	5		USD/y
	Replacement cost	0		USD
	Temperature coefficient	$-3.7 \ast {10}^{-7}$		1/°C
	Derating factor	0.9		-
	NOCT	47		°C
Battery Energy Storage (BES) [37]	Lifetime	10		y
	Initial SOC	100		%
	${SOC}_{min}$	20		%
	${SOC}_{max}$	80		%
	Rate capacity	4.8		kWh
	Capital cost	672		USD
	O&M cost	10		USD/y
	Replacement cost	500		USD
	Self-discharge	1		%/day
	DOD	80		%
Electric Grid	Importing price	Off-peak	0.032	USD/kWh
		Mid-peak	0.048
		On-peak	0.080
	Exporting price	Off-peak	0.040	USD/kWh
		Mid-peak	0.067
		On-peak	0.11
Inverter [38]	Capacity	115		kW
	Capital cost	2500		USD
	O&M cost	1		USD/y
	Efficiency	92		%
	Lifetime	20		y
Economic parameters	Project life	25		Y
	Annual interest rate	3		%
	Annual inflation rate	8		%

. The table includes details on the photovoltaic system, battery energy storage, electric grid tariffs, and inverter specifications, along with the economic parameters governing the project’s financial outlook.

3. Mathematical Modeling of the Proposed System

Several studies have explored the mathematical equations to model grid-connected systems incorporating V2H technology with PV and BES [29,39,40,41]. These modeling equations for PV and batteries are commonly used by researchers to account for all system components [42,43,44,45]. The PV system operates at its maximum power point, while the batteries serve as storage and can operate in line with the EV battery to enhance reliability [46,47,48]. The discounted cash flow analysis method is used to calculate the cost of the energy produced by the system, considering the project’s lifetime and its components.

3.1. PV System

This research focuses on polycrystalline solar panels (LG305N1C-G4). The manufacturer’s specifications for these panels, as well as solar parameters, are detailed in [49,50,51]. The PV output power is presented for a one-year period (8760 h) in [24,43,51,52,53] and can be expressed as shown in Equation (1):

$$P_{pv}=\sum _{t=1}^{8760}\left(P_{pvr}\times N_{pv}\times {DF}_{pv}\right)\left({\displaystyle \frac{G\left(t\right)}{G_{Base}}}\right)\left(1+K_T\left(\left(T_{amb}\left(t\right)+G\left(t\right)\times \left({\displaystyle \frac{NOCT-20}{800}}\right)\times 1000\right)-T_{base}\right)\right)$$

(1)

where $P_{pvr}$ is the rated output of the module (kW), $N_{pv}$ represents the number of PV panels, and ${DF}_{pv}$ refers to the PV derating factor. G(t) denotes the global irradiance (kW/m²), $G_{Base}$ is the solar radiation under standard conditions (1 kW/m²), and the temperature coefficient for maximum power is $K_T=-3.7 \ast {10}^{-3}$ (1/°C). $T_{amb}$ is the ambient temperature in (°C), NOCT refers to the Normal Operating Cell Temperature (°C), and ${\mathrm{T}}_{\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}$ represents the temperature at reference condition (°C).

The net present cost (NPC) of the PV, denoted as ${NPC}_{pv}$, consists of the initial cost ${(IC}_{pv})$; ${IPR}_{pv}$ is investment cost per PV panel (USD/panel) operation and maintenance cost (${O\&M}_{pv}$), $I_f$ is the inflation rate (%), and $I_r$ is the interest rate (%). The PV lifetime is the same as the project lifetime, and thus there is no replacement cost. Accordingly, ${NPC}_{pv}$ is calculated as follows:

$${NPC}_{pv}={IC}_{pv}+{O\&C}_{pv}=N_{pv}\times \left[{IPR}_{pv}+\sum _{n=0}^{25}{\displaystyle \frac{{OMP}_{pv}}{{\left(1+\frac{I_r-I_f}{1+I_f}\right)}^{n-1}}}\right]$$

(2)

3.2. Battery Energy Storage (BES) System

A battery energy storage system is utilized to store energy and discharge it when the grid and PV power are unavailable. The storage system mitigates the intermittent nature of the system and improves its reliability and efficiency. The State of Charge of a battery denotes the level of energy stored in it, whereas the Depth of Discharge (DoD) indicates the amount of energy that has been consumed from the battery as illustrated in Figure 2 [54,55]. This proposed system is subjected to the following constraints:

$$E_{Bat,min}\le E_{Bat}\left(t\right)\le E_{Bat,max}$$

(3)

$$E_{Bat,max}=E_{Bat,cap}$$

(4)

$$E_{Bat,min}=E_{Bat,max}(1-DOD)$$

(5)

The energy output from the battery can be mathematically represented by Equation (6).

$$E_{Bat}(t)=P_{pv}(t)-{\displaystyle \frac{P_l\left(t\right)}{{\eta }_{inv}}}$$

(6)

where $E_{Bat}\left(t\right)$ is the energy delivered by the battery (kWh), $E_{Bat,min}$ is the minimum allowable energy in the battery, and $E_{Bat,max}$ is the maximum allowable energy in the battery, which is equal to the rated capacity of the battery bank $E_{Bat,cap}$. $P_{pv}$ is the power produced by the PV panels (kW), $P_l\left(t\right)$ is the total load demand (kW), and ${\eta }_{inv}$ is the inverter efficiency. During the charging period, when the power generated by the PV system exceeds the load demand, the battery’s energy capacity can be described in Equation (7) [24,43,56]. The energy capacity of the battery in discharging mode is utilized when the load demand surpasses the power output generated by the system, expressed in Equation (8) [24,43].

$$E_{Bat}(t)=E_{Bat}(t-1)(1-\sigma )+\left(P_{pv}(t)-{\displaystyle \frac{P_l(t)}{{\eta }_{inv}}}\right){\eta }_b$$

(7)

$$E_{Bat}(t)=E_{Bat}(t-1)(1-\sigma )-\left({\displaystyle \frac{P_l(t)}{{\eta }_{inv}}}-P_{pv}(t)\right){\eta }_b$$

(8)

where $\left(\sigma \right)$ is self-discharge of 1% per day. The battery efficiency $\left({\eta }_b\right)$ selected is 80%, and the inverter efficiency is $\left({\eta }_{inv}\right)$ 90%. The battery energy storage system is assumed to have a lifespan of 10 years, with a replacement cost of USD500 [37]. The net present cost of the battery energy storage is given as follows:

$${NPC}_{Bat}={IC}_{Bat}+{O\&C}_{Bat}=N_{Bat}\times \left[{IPR}_{Bat}+\sum _{n=0}^{25}{\displaystyle \frac{{OMP}_{Bat}}{{\left(1+\frac{I_r-I_f}{1+I_f}\right)}^{n-1}}}\right]$$

(9)

3.3. EV Charging/Discharging

When the electric vehicle is connected to a home through a bidirectional AC/DC converter, it can be utilized in Vehicle-to-Home (V2H) mode to improve household reliability. V2H operation can reduce a homeowner’s operating costs, provided there is an effective charging and discharging strategy. However, the level of EV participation in V2H mode depends on customer preferences and the availability of the State of Charge. In this study, the Nissan Leaf EV, equipped with a 40-kWh battery [57], was selected for analysis due to its prominent position in the electric vehicle market [58]. The charging/discharging capacity of the EV’s battery at any hour can be modeled in terms of its rated power as described in Equations (10) and (11), respectively [59,60]:

$${SOC}_{EV}(t)={SOC}_{EV}(t-1)+{\displaystyle \frac{{\eta }_{EV}{P}_{EV}}{C_{EV,battery}}}\times 100$$

(10)

$${SOC}_{EV}(t)={SOC}_{EV}(t-1)-{\displaystyle \frac{P_{V2H}}{{\eta }_{EV}{C}_{EV,battery}}}\times 100$$

(11)

where ${SOC}_{EV}\left(t\right)$ is the state of charge of the EV’s battery at hour (t), ${\eta }_{EV}$ is the EV charging/discharging efficiency which is 92%, $P_{EV}$ is the charging rate of EV (kW), $P_{V2H}$ is the discharging rate of EV to home (kW), and $C_{EV,battery}$ is the EV battery capacity (kWh). Additionally, the state of charge of the EV battery at each hour (t) is subject to the following constraint:

$${SOC}_{EV,min}\le {SOC}_{EV}\left(t\right)\le {SOC}_{EV,max}$$

(12)

where ${SOC}_{EV,min}$ and ${SOC}_{EV,max}$ represent the minimum and maximum allowable state of charge for the EV battery, respectively.

3.4. Inverter

The inverter is an essential component for transferring power between sources and loads, operating with an efficiency of 90% [61]. Its rating is selected to optimize the total annual cost of the system and is determined by Equation (13) [38].

$$P_{inv}={\displaystyle \frac{P_L^m\left(t\right)}{{\eta }_{inv}}}$$

(13)

where $P_L^m\left(t\right)$ represents the peak load demand (kW) and ${\eta }_{inv}$ is the inverter efficiency.

3.5. Power Grid

The electrical grid is essential for ensuring a reliable and continuous energy supply. It acts as a supplementary source of energy, especially when renewable energy sources (PV panels) and the battery energy storage are insufficient to meet the total household load demand [24,38]. The system prioritizes the use of photovoltaic generated electricity for charging EVs to optimize energy efficiency, minimize electricity costs, and maximize the use of renewable energy. When PV energy is insufficient or unavailable (e.g., during nighttime or cloudy days), the grid supplies the required energy for EV charging through the home charger. Although Saudi Arabia currently uses a flat electricity tariff, this study applies a Time-of-Use (TOU) tariff structure adapted from countries like Malaysia to simulate realistic peak demand scenarios in hot climates. The load values in

Table 2. Time zones.

Time Intervals (Hours)	00:00–8:00	8:00–11:00	11:00–12:00	12:00–14:00	14:00–17:00	17:00–22:00	22:00–00:00
Period Type	Off—Peak	Mid—Peak	On—Peak	Mid—Peak	On—Peak	Mid—Peak	Off—Peak

are allocated across three tariff periods (off-peak, mid-peak, and on-peak) to reflect typical daily household consumption patterns, especially influenced by air conditioning usage. This allows the simulation to evaluate the cost impact of grid consumption based on time-sensitive pricing and to optimize energy dispatch decisions. The grid energy consumption for EV charging is managed based on time zones, as shown in Table 2. The system will be tested for both a flat rate and TOU rates. The flat rate used for buying and selling is illustrated in the following two equations.

Integrating the grid into the system allows for strategic energy management. To calculate the revenue from selling energy back to the national grid, the following equation will be used [24]:

$$R_{grid}=\sum _{t=1}^{8760}{rate}_{feed-in}\times E_{grid\left(selling\right)}$$

(14)

where ${rate}_{feed-in}$ is the feed-in tariff rate (USD 0.0670/kWh) and $E_{grid\left(selling\right)}$ is the amount of energy sold to the grid (kWh). Furthermore, the cost of energy consumption from the grid is calculated by Equation (15) [24]:

$$C_{grid}=C_p\times \sum _{t=1}^{8760}{E}_{grid\left(purchased\right)}$$

(15)

where $C_p$ is the cost of purchasing 1 kW from the grid in Saudi Arabia, which is USD 0.0480/kWh, and $E_{grid\left(purchased\right)}$ is the energy drawn from the grid at time t (kWh). In this study, the household owner is both a buyer (purchasing energy from the grid) and a seller (selling excess PV energy to the grid). The higher feed-in tariff is a proposed rate designed to incentivize renewable energy exports, in line with net metering practices adopted in the Saudi Arabia market.

3.6. Greenhouse Gas (GHG) Emission Estimation

The analysis calculates GHG emissions for the base case scenario, where only the grid is used to meet the household and EV load. This result is then compared to the proposed system that uses PV to supply the house load and EV. This comparison is applied to calculate the net savings in GHG emissions of the entire system.

$${GHG Emissions}_{Base Case}=Total Load\times Grid electricity-specific factor\times GWP$$

(16)

Greenhouse gases vary in their impact on global warming due to their unique properties. To facilitate comparison, emissions are expressed in terms of carbon dioxide equivalents (CO₂e). This scale uses CO₂ as the reference point with a global warming potential (GWP) of 1, while all other GHGs identified in the Kyoto Protocol have higher GWP values than CO₂ [62]. As outlined in the 2014 Fifth Assessment Report (AR5) by the International Panel on Climate Change (IPCC) (Myhre et al., 2013) [63], Methane (CH4) has a GWP of 21, nitrous oxide (N₂O) has a GWP of 310, and sulfur hexafluoride (SF6) has a GWP of 23,900.

$$Grid GHG Emissions=Total Load suppied by grid\times {Grid}_{ef}\times GWP$$

(17)

where the grid emission factor specific to Saudi Arabia is 0.795591 kgCO₂/kWh [64]. It is well known that PV panels generate electricity directly from sunlight and do not have GHG emissions when they are in operation. However, the system emits some GHGs throughout its life cycle, during manufacturing, assembly, balance of system (BOS), material transport, installation, and during disposal or recycling phases [65]. The following equation can be applied to determine the emissions related to the PV system $E_{mpv}$:

$$E_{mpv} = \sum _{t=1}^{8760}{P}_{pv}\left(t\right) \times e_{pv}\times GWP$$

(18)

where $P_{pv}$ is the annual power produced by the PV system (kW), and $e_{pv}$ is the emission factor of the PV system, which equals 0.050 ($\mathrm{k}\mathrm{g}{\mathrm{C}\mathrm{O}}_2-\mathrm{e}\mathrm{q}/\mathrm{k}\mathrm{W}\mathrm{h}$) for poly-Si PV [66]. The total GHG emission reduction by the system is estimated as:

$${System}_{Total GHG} = {PV}_{GHG} \times {Grid}_{GHG}$$

(19)

$${Net}_{Saving GHG}={Base Case}_{GHG}\times {System}_{Total GHG}$$

(20)

3.7. Component Availability in the System

The reliability of a Home Energy Management System is significantly influenced by the availability of its component photovoltaic systems, electric vehicles, and the grid. These components might not be available due to planned maintenance or unexpected failures. To assess system reliability, the probability of availability (PA) for each component is considered, reflecting the likelihood that the component will be operational at any given time. The PV system’s availability is subject to factors such as weather conditions, maintenance schedules, and technical failures. Based on industry standards and studies, the PA of the PV system is typically around 96% [67].

$$P_{pv} = 0.96 \times P_{pv}$$

(21)

The availability of EVs for charging at home is less consistent than that of stationary systems like PV. It depends on the owner’s driving habits, the times of arrival and departure of the EV, and its state of charge, which are all modelled randomly. This reflects the fact that the EV might only be at home and available for charging/discharging during certain hours of the day, influenced by the user’s routine. The EV is only available for charging/discharging during this window:

$$EV Availability=\left\{\begin{array}{l}1, Arrival Time \le t\le Departure Time\\ 0, Otherwise\end{array}\right.$$

(22)

Grid availability is affected by the reliability of the utility provider, including factors like grid outages, maintenance, and failures. In this paper, the availability of the grid is assumed to be 90%, reflecting a strong grid infrastructure with rare periods of downtime [24].

4. Data Collection

This system is a grid-connected household or home microgrid that can be described as a cluster of renewable energy sources and battery units designed to manage energy consumption and generation within the household. Even though it is grid-connected system, it can operate in either on-grid or off-grid mode depending on the availability of the grid and renewable energy sources [68]. Data collected from SEC and KACARE for the system are analyzed to identify peak periods for the generation and consumption of renewable energy, allowing for the efficient scheduling of energy use and storage. The collected data correspond to the year 2024.

4.1. Solar Irradiance

Figure 3 shows the solar irradiance data for the study location. The peak monthly solar irradiance for the location is presented in

Table 3. Maximum monthly solar irradiance for the area (W/${\mathrm{m}}^2$).

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Maximum	787	904	951	1019	1029	1022	1013	1016	964	939	822	755

. The variations in solar irradiance in different days, even within the same month, can be due to several factors related to changes in weather conditions such as cloud cover and dust storms.

4.2. Ambient Temperature

The collected climatic data show significant variations throughout the year, with a notable temperature spike during the summer when the highest temperature (46 °C) is recorded. Figure 4 illustrates the ambient temperature for the studied location, while

Table 4. Maximum and minimum temperature in the area.

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Maximum	28	31	34	36	42	45	46	46	44	41	34	28
Minimum	7	8	12	12	20	26	28	28	24	19	12	6

details the monthly maximum and minimum temperatures (°C).

4.3. Electric Vehicle and Charger

The flow of electricity between the home system and EV is facilitated by the battery. EV batteries can operate as a load or storage, providing benefits such as improved power quality, reliability control, power frequency regulation, and voltage frequency regulation [6]. Various battery types are used in EV, including lead–acid batteries [69], lithium-ion batteries [70], and flywheel batteries [71]. Among these, lithium-ion batteries are the most commonly used in EV due to their advantages, such as being lightweight, reducing peak load [72], offering high specific power and energy density, and charging quickly [70]. For simulation, the electric vehicle used for this study is a Nissan Leaf. Specifications of the electric vehicle and its charger are elaborated in

Table 5. Specifications of EV model and charger.

Battery Type	Capacity (kWh)	Range (km)	Energy Consumption (Wh/km)	Charge Port	Charging Power (kW AC)
Lithium-ion	40	235	166	Type 2	3.6

[57].

4.4. Load Profile

The study area benefits from abundant solar irradiance throughout the year, with peak levels observed in June. The average solar irradiance is highest during the summer, making it the most favorable season for generating electricity from PV systems, followed by spring, autumn, and winter. In winter, most consumers use heaters, while air conditioning is prevalent during the summer. Figure 5 shows the annual load profile of the household on an hourly basis. The analysis of the seasonal data is presented in

Table 6. Seasonal analysis of data collected.

Season	Period	Mean Solar Irradiance (W/m2)	Max Solar Irradiance (W/m2)	Mean Ambient Temperature (°C)	Max Ambient Temperature (°C)	Mean Energy Demand (kW)	Peak Energy Demand (kW)	Min Energy Demand (kW)
Winter	Dec–Feb	202.7501	904	16.7392	31	1.6922	7.046	0.11
Spring	Mar–Apr	274.756	1019	23.8534	36	1.6452	6.756	0.114
Summer	May–Aug	299.5369	1029	35.9874	46	3.522	10.694	0.172
	Sep–Nov	231.5545	964	28.7840	44	2.0322	7.754	0.138

, and the daily and monthly solar irradiance data are shown in

Table 7. Daily solar irradiance and monthly data for the study area.

Months	Index Total Daily G (kWh/m2)	Mean Solar Irradiance (W/m2)	Mean Ambient Temperature (°C)	Mean Energy Demand (kW)	Peak Energy Demand (kW)
Jan	4.732	195.7608	13.7767	1.724	7.046
Feb	5.447	230.2570	18.3575	1.968	6.606
Mar	6.340	260.5621	22.5795	1.461	4.662
Apr	6.899	289.6705	25.1425	1.828	6.756
May	7.258	298.5193	32.7137	2.458	6.720
Jun	7.584	316.6078	35.8438	3.483	10.694
Jul	7.328	305.8533	37.8438	3.875	9.042
Aug	6.777	279.0879	37.6329	4.331	10.086
Sep	6.413	271.3158	34.9301	2.912	6.598
Oct	5.610	230.5851	29.3767	2.020	6.154
Nov	4.713	199.1942	22.8233	1.282	7.754
Dec	4.386	181.3545	18.0548	1.385	4.066

.

5. Objective Functions

The main goal of this research is to determine the optimal number of components (PV and battery) in a grid-connected household system. Two different metaheuristic optimization techniques are applied (MOPSO and MOHHO) and their performance is evaluated. All optimization procedures and simulations were implemented using MATLAB software. The goal is to minimize two objective functions: Loss of Power Supply Probability and Cost of Energy, while maximizing the Renewable Energy Fraction as the third objective. A trade-off exists between these three objectives, as decreasing LPSP and increasing REF typically result in higher overall system costs, which in turn increase the COE. Therefore, the decision-maker must balance these objectives to find the best solution.

The Cost of Energy is calculated using the Discounted Cash Flow (DCF) analysis method, which estimates the value of investments based on projected future cash flows [73]. The COE is expressed in Equation (23) and incorporates the Net Present Cost (NPC) in US dollars, which includes costs such as operation and maintenance (O&M), replacement, and present costs, as well as the Capital Recovery Factor (CRF). The key goal is to maximize REF while minimizing LPSP and the COE.

$$COE={\displaystyle \frac{\left(CRF\times {\sum }_x{NPC}_x\right)+C_{grid}-R_{grid}}{E_{served}+E_{grid\left(selling\right)}}}$$

(23)

where COE is the cost of energy (USD/kWh), Net Present Cost (NPC) in dollars can be calculated using Equation (24), $E_{grid\left(selling\right)}$ represents the energy sold (kWh/year), and $E_{served}$ denotes the primary load served (kWh/year) [24].

$$NPC\left(\$\right)={\displaystyle \frac{TAC}{CRF}}$$

(24)

where TAC represents the total annual system cost in $\left(\mathrm{U}\mathrm{S}\mathrm{D}/\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\right)$, and the Capital Recovery Factor (CRF) is calculated using Equation (25) [24]. Here, $i$ denotes the real interest rate, and n refers to the amortization period or system life, which is the lifetime of the solar panels.

$$CRF={\displaystyle \frac{i{\left(1+i\right)}^n}{{\left(1+i\right)}^n-1}}$$

(25)

The reliability of the system is assessed using the Loss of Power Supply Probability, which is the second objective function to be minimized and is calculated using Equation (26) [24].

$$LPSP={\displaystyle \frac{{\sum }_1^{8760}{P}_{deficit}\left(t\right)\times \Delta t}{{\sum }_1^{8760}{P}_{demand}\left(t\right)\times \Delta t}}, \Delta t=1$$

(26)

where $P_{deficit}$ is the power deficit (kW), and $P_{demand}$ is the load demand over the same period (kW) [74]. The LPSP value ranges from 0 to 1, where 1 indicates that the load is not met and 0 indicates that the load is fully met [75]. A lower LPSP value reflects higher system reliability [76].

The third objective function to be maximized is the Renewable Energy Fraction [24]. REF is the amount of energy supplied to the load generated from renewable energy sources and can be determined using Equation (27).

$$REF={\displaystyle \frac{{\sum }_1^{8760}\left(P_{pv}+V2H\right)\times \Delta t}{{\sum }_1^{8760}\left(P_{pv}+V2H+E_{grid\left(purchased\right)}\right)\times \Delta t}}, \Delta t=1$$

(27)

where $\Delta t$ indicates the time change, set to 1, and $E_{grid\left(selling\right)}$ represents the annual electricity purchased from the grid. The Grid Contribution Factor (GCF) is utilized to minimize REF. Since GCF is the inverse of REF, it reflects the grid contribution to fulfilling the energy demand and can be expressed as shown in Equation (28). By decreasing GCF, the REF value increases, thereby maximizing the use of renewable energy [24].

$$GCF=1-REF$$

(28)

5.1. Limits of Decision Variables

The objective functions are subjected to the following constraints:

$$N_x^{min}\le N_x\le N_x^{max}, x\in \left\{PV,Bat\right\}$$

(29)

where $N_x$ represents the number of component x. The setting of upper and lower limits for decision variables is highly dependent on the problem (including the complexity of the search space and the number of variables). In all optimization algorithms, these bounds have been established through a process of trial and error. For this research, the upper and lower limits of the variables are specified in Equation (30):

$$\left\{\begin{array}{l}1\le N_{PV}\le 100\\ 1\le N_{Bat}\le 25\end{array}\right.$$

(30)

5.2. Energy Balance of the System

The energy balance in the system ensures that at every time step, the total energy supplied by various sources matches the total energy demanded by the household loads and the EV load. The energy balance equation can be expressed as follows:

$$Input Energy \ge Output Energy$$

(31)

where input energy and output energy are expressed as shown in (32) and (33), respectively

$$Input Energy=E_{pv}\left(t\right)+E_{purchased}\left(t\right)+E_{discharge}\left(t\right)+E_{V2H}\left(t\right)$$

(32)

$$Output Energy=E_{House\_Load}\left(t\right)+E_{EV\_Load}\left(t\right)+E_{sold}\left(t\right)+E_{charge}\left(t\right)+E_{dump}\left(t\right)$$

(33)

where:

$E_{pv}$: energy generated by the PV system

$E_{purchased}$: energy purchased from the grid

$E_{discharge}$: energy discharged from the battery

$E_{V2H}$: energy provided by the electric vehicle to the house (vehicle-to-home energy)

$E_{House\_Load}$: household load demand

$E_{EV\_Load}$: EV load demand

$E_{sold}$: energy sold back to the grid

$E_{dump}$: energy dumped (excess energy that cannot be utilized or stored)

The Equation (31) must be true for every time step t. If there is any imbalance, it is tracked using (LPSP) metric, indicating a failure in meeting the load demand.

6. Energy Management and Optimization

6.1. Home Energy Management Strategy

The energy management dilemma is defined mathematically as the overall control method involving inputs, outputs, objectives, and constraints. There are two approaches to addressing this challenge: rule-based (RB) and optimization-based methods [77]. Even though the optimization-based approach is effective, it is limited by its high computational requirements and the complexity of the mathematical equations required, making it less favorable. Conversely, the rule-based approach, which is considered in this study, is preferred due to its advantages, such as providing exact solutions and enabling fast decision-making to meet load demand at minimal operating cost. To achieve the objectives in this study, the metaheuristic method is utilized for the sizing of the system configuration (PV-BES-EV), as outlined in the flowchart in Figure 6.

To minimize COE and LPSP while maximizing REF, the proposed rule-based home energy management system strategy exploits the TOU tariff to serve the system load demand in coordination with the PV generation, BES charging/discharging, EV charging, V2H and import/export of electricity from/to the grid, as summarized in the flowchart in Figure 7.

When PV power output exceeds household demand, the proposed energy management strategy distributes the excess power according to a defined priority sequence. First, any excessive power is allocated to charging the EV, if it is available. The EV charging process is managed based on its state of charge, categorized into scenarios A, B, C, and D. In Scenario A (critical SoC level), the EV requires the full charger rate, and if the excess PV power falls short, additional power is purchased from the grid if available. In Scenarios B, C, and D (non-critical SoC levels), the EV charging proceeds solely from the PV surplus, with no additional grid support needed. If the EV is unavailable, the excess power is directed to the Battery Energy Storage. Should the BES reach full capacity and be unable to store the excess energy, the remaining excess power is either exported to the grid if allowed, or is dumped to maintain system balance.

When PV power output falls short of household demand, the energy management strategy addresses this power deficit through a defined priority sequence. First, the system checks the Battery Energy Storage for available energy. If the BES has sufficient charge, it discharges to meet the household demand. In cases where the BES can fully cover the household demand but the Electric Vehicle is also available and requires charging, the EV is charged directly from the grid. Charging is managed based on Time-of-Use (TOU) tariffs and the EV’s state of charge. Lower SoC levels allow charging across more periods, while higher SoC levels restrict charging to off-peak times to minimize the grid costs. If the BES cannot fully satisfy household demand, the system checks if the EV is available for Vehicle-to-Home support. If the EV’s SoC is above a specified threshold (Scenarios A and B), it discharges to supply the household. Should both the BES and V2H support from the EV be insufficient to meet demand, the system imports power from the grid. Finally, if no other sources can fulfill the household load, the system accepts a temporary shortfall, marking it as a Loss of Power Supply Probability.

6.2. MOPSO and MOHHO Optimization Techniques

This section explains the implementation of MOPSO and MOHHO algorithms for optimizing the system’s configuration (Figure 8 and Figure 9). MOPSO is fast and easy, and balances exploration and exploitation, but it can get stuck in local optima and is sensitive to parameter settings. MOHHO offers better global search and avoids local traps, though it may converge slower and needs more computation.

6.3. Best Compromise Solution

Many studies have focused on developing methods to select the best compromise, or preferred solution. In this paper, the fuzzy set method is used to identify the best compromise solution from the generated Pareto front (PF). Once MOPSO and MOHHO produce their PFs, Equations (34) and (35) are applied for membership functions [78,79,80,81]:

For COE and LPSP (minimizing functions),

$${\mu }_j=\left\{\begin{array}{c}1, F_j\le F_j^{min}\\ {\displaystyle \frac{F_j^{max}-F_j}{F_j^{max}-F_j^{min}}},F_j^{min}<\\ 0, F_j\ge F_j^{max}\end{array}\right.F_j<F_j^{max}$$

(34)

For REF (maximizing function),

$${\mu }_j=\left\{\begin{array}{c}0, F_j\le F_j^{min}\\ {\displaystyle \frac{F_j-F_j^{min}}{F_j^{max}-F_j^{min}}},F_j^{min}<\\ 1, F_j\ge F_j^{max}\end{array}\right.F_j<F_j^{max}$$

(35)

where ${\mu }_j$ represents the membership function, $F_j$ is the j-th objective function, and $F_j^{min}$ and $F_j^{max}$ are its minimum and maximum values, respectively. Then, the normalized membership function is calculated as in Equation (36):

$${\mu }^k ={\displaystyle \frac{\sum _{j=1}^3{\mu }_j^k}{\sum _{l=1}^M\sum _{j=1}^3{\mu }_j^l}}$$

(36)

where M denotes the number of solutions in the Pareto front. The solution with the highest ${\mu }^k$ value is considered the best compromise solution.

7. Results and Discussions

The proposed procedure was carried out to investigate a grid-connected household system in Riyadh, consisting of PV, BES, and EV components, designed to meet household energy demands. The simulation was performed using MATLAB code with a one-hour time step, operating on one year of data (8760 samples/year). The optimization techniques were implemented using MATLAB R2022b on an Intel(R) Core (TM) i7-7700HQ CPU @ 2.80 GHz. In this section, the results are obtained for both flat rate and TOU rates and categorized into three perspectives:

• Economically optimal solution (lowest COE)
• Renewable energy usage perspective (highest REF)
• Environmentally optimal solution (lowest GHG emission)

7.1. Flat Rate

Table 8. MOPSO and MOHHO results of the sizing problem under flat rate.

Technique	Prospective	COE (USD/kWh)	NPC	LPSP (%)	REF (%)	${\mathit{N}}_{\mathit{P}\mathit{V}}$	${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}}$	Total GHG Emissions (Tone)
MOPSO	Economic	0.0210		6.87	50.70	24	1	2616
	Renewable	0.0866	108,652	1.80	97.37	100	25	1086
	Environment	0.0718	89,232	2.67	95.57	74	25	927
MOHHO	Economic	0.0217	25,588	6.08	51.35	24	2	2525
	Renewable	0.0860	107,909	1.90	97.27	99	25	1085
	Environment	0.0714	89,215	2.24	95.97	77	23	943

presents the results from the MOPSO and MOHHO analysis of the sizing problem, and

Table 9. MOPSO and MOHHO results using best compromise solutions under flat rate.

Technique	COE (USD/kWh)	NPC	LPSP (%)	REF (%)	${\mathit{N}}_{\mathit{P}\mathit{V}}$	${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}}$	Total GHG Emissions (Tone)
MOPSO	0.0468	58,452	2.10	86.87	51	13	1152
MOHHO	0.0582	73,076	1.88	93.58	66	16	972

presents the best compromise solution found for both techniques. Where the flat rate used is 0.048 USD/kWh for the buying price and 0.067 USD/kWh for the selling price.

7.2. TOU Rates

Table 10. MOPSO and MOHHO results of the sizing problem under TOU rates.

Technique	Prospective	COE (USD/kWh)	NPC	LPSP (%)	REF (%)	${\mathit{N}}_{\mathit{P}\mathit{V}}$	${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}}$	Total GHG Emissions (Tone)
MOPSO	Economic	0.0210	24,257	7.15	50.86	24	1	2595
	Renewable	0.0845	106,035	1.80	97.37	100	23	1086
	Environment	0.0683	85,292	2.19	95.35	72	23	928
MOHHO	Economic	0.0226	26,595	6.13	52.65	24	3	2379
	Renewable	0.0854	106,819	2.11	97.30	98	25	1071
	Environment	0.0689	86,069	2.24	94.98	70	25	929

presents the results from the MOPSO and MOHHO analysis of the sizing problem, where Time of Use (TOU) rates are applied.

From an economic perspective, MOPSO achieves a lower COE of USD 0.0210/kWh compared to MOHHO of USD 0.0226/kWh. Additionally, MOPSO results in a lower net present cost (NPC) of USD 24,257, while NPC of MOHHO is USD 26,595. However, this cost-saving solution is at the expense of lower REF of 50.86% and higher GHG emissions of 2595 ${tCO}_{2}e$. Moreover, MOPSO has a higher LPSP of 7.15%, compared to MOHHO at 6.13%, indicating reduced system reliability. In MOPSO and MOHHO, the same number of PV panels are used, but in MOHHO two additional battery units are used compared to MOPSO using one unit, which explains the lower capital and operational costs, but this also limits the amount of renewable energy generated or stored, leading to increased reliance on the grid and consequently higher GHG emissions.

From a renewable energy usage perspective, both MOPSO and MOHHO achieve near identical results, with a REF of 97.37% and 97.30% respectively, demonstrating that the household energy demand is almost entirely powered by renewable energy sources. The COE for MOPSO is USD 0.0845/kWh, with a significantly higher net present cost of USD 106,035 compared to the economic perspective. This high NPC is because of the system configuration, which includes 100 PV panels and 23 batteries, ensuring high renewable energy use but requiring a substantial capital investment. Additionally, both techniques show a relatively low LPSP of 1.80% and 2.11% of MOPSO and MOHHO respectively, indicating improved reliability in comparison to the economic perspective. GHG emissions are reduced to 1086 and 1071 ${tCO}_2$ in MOPSO and MOHHO respectively, making this option more environmentally sustainable. This consistency between both techniques emphasizes the robustness of the solution when considering renewable energy usage where the selection of either technique does not affect the solution.

From an environmental perspective, MOHHO and MOPSO achieve near identical results, with lower GHG emissions of 928 ${tCO}_{2}e$ of MOPSO compared to MOHHO of 929 ${tCO}_{2}e$. MOPSO slightly outperforms MOHHO across most metrics, particularly in REF, COE, and LPSP.

It is worth noting that the significant increase in system costs in both the renewable energy usage and environmental perspectives is due to the goal of increasing reliance on renewable energy sources, rather than purchasing energy from the grid, which is the most cost-effective option. The heavy dependence on photovoltaic systems directly contributes to the overall high cost of the system. The comparison between MOPSO and MOHHO highlights trade-offs depending on the perspective. MOPSO seems to be the better option for users focusing on cost-effectiveness and marginally higher reliability.

Table 11. Generated power of each element in MOPSO and MOHHO.

Technique	Prospective	${\mathit{P}}_{\mathit{P}\mathit{V}}$ (MWh)	Grid Sell (MWh)	Grid Purchase (MWh)	PV Share (%)	V2H Share (%)	Grid Share (%)	Net Saving in CO2 Emission (%)
MOPSO	Economic	12.45	3.02	13.36	45.80	5.05	49.13	30.97
	Renewable	51.89	25.43	1.40	97.37	0.00	2.62	71.09
	Environment	37.36	12.40	1.82	95.31	0.04	4.64	75.31
MOHHO	Economic	12.45	1.30	12.15	48.53	4.11	47.34	36.73
	Renewable	50.85	24.42	1.40	97.30	0.00	2.69	71.51
	Environment	36.32	11.51	1.92	94.91	0.06	5.01	75.28

provides additional insights into the system performance across each perspective, focusing on PV energy production, grid interaction, energy dumping, energy shares (PV, grid, V2H), and net CO₂ savings.

From the economic perspective, MOPSO and MOHHO produce the same PV energy (12.45 MWh), resulting in a higher PV share of 48.53% in MOHHO, while MOPSO achieves a lower share at 45.80%. Although both have lower-than-allowable shares of PV, the system still allows for some energy to be sold back to the grid (3.02 MWh) in MOPSO compared to MOHHO (1.30 MWh). However, the low PV generation leads to heavy reliance on the grid. MOPSO depends more on grid purchases (13.36 MWh in MOPSO and 12.15 MWh in MOHHO). In both techniques, Vehicle-to-Home (V2H) compensates for the energy not purchased from the grid, with MOPSO and MOHHO showing V2H shares of 5.05% and 4.11%, respectively. MOHHO achieves higher net CO₂ emission savings of 36.73% compared to MOPSO 30.97%, because MOHHO relies more on renewable energy generated or stored in the battery and less on grid power.

From the renewable energy perspective, both MOPSO and MOHHO show much better results, generating 51.89 MWh and 50.85 MWh of PV power in MOPSO and MOHHO respectively. As a result, there is a significant amount of energy sold back to the grid. The PV share is nearly full, showing that the system primarily relies on renewable energy to meet household and EV demands. Due to the high power generated by PV, it can be observed that the grid share is reduced to 2.62% and 2.69% in MOPSO and MOHHO, respectively. Both methods achieve a net CO₂ emissions savings of 71.09% in MOPSO and 71.51% in MOHHO, emphasizing the significant environmental benefits when prioritizing renewable energy usage.

From the environmental perspective, MOPSO produces a little more PV power compared to MOHHO, resulting in a slightly higher PV share of 95.31%. This additional PV generation in MOPSO also leads to more energy being sold back to the grid. Grid purchases are slightly lower in MOPSO (1.82 MWh) compared to MOHHO (1.92 MWh), indicating a marginally higher reliance on renewable energy in MOPSO. Despite these small differences, both techniques show almost similar improvements in environmental performance, with MOHHO achieving a net CO2 saving of 75.28%, compared to 75.31% for MOPSO.

It is worth noting that V2H’s share in renewable energy usage and environmental perspectives in both techniques is very low, indicating that the integration of V2H in the system is minimal. In this system, V2H’s share is influenced by several factors including EV availability, and initial SoC of EV upon arrival. The EV may not be available when the system needs energy, limiting its contribution. V2H is limited to when the EV’s SoC is between 50% and 90%. If the EV often arrives with a SoC outside this range (less than 50%), it will not contribute to V2H. In these perspectives, the system prioritizes the use of PV and battery storage first, so V2H is only used as a backup.

The Pareto front for the three objectives (COE, LPSP, and REF) is illustrated in Figure 10. It can be observed that as the REF ratio increases, the COE also increases, while the LPSP decreases. This is due to the fact that higher REF values require more PV panels, leading to higher COE and lower LPSP.

To provide a clearer understanding of the relationship between the three objective functions, Figure 11 shows the Pareto front for LPSP and COE, while Figure 12 shows the PF for LPSP and REF, and Figure 13 shows the PF of REF and COE.

Figure 11 shows that MOPSO highlights a predictable trade-off between LPSP and COE, where reducing COE increases LPSP, making it better for a highly reliable system. In contrast, MOHHO provides more flexibility and diverse low-cost solutions with acceptable reliability, making it better for a cost-effective system.

From Figure 12, it can be observed that MOPSO and MOHHO show consistent trade-off between LPSP and REF. MOPSO is concentrated at lower LPSP with high REF, making it suitable for the system where reliability is crucial. MOHHO, on the other hand, provides more flexibility in trade-offs, exploring moderate reliability solutions more effectively. This makes it suitable for the system where sacrificing reliability is tolerable for the sake of a higher renewable energy fraction.

As illustrated in Figure 13, COE increases with the increase in REF. MOPSO offers a more concentrated set of solutions, making it suitable for systems where renewable energy usage is prioritized. However, MOHHO offers more flexibility, exploring trade-offs between cost and renewable energy fractions. This makes it a better choice if the system requires balance between cost and the renewable energy fraction.

While optimizing each individual perspective provides valuable results, real-world decision-making requires a more comprehensive approach that balances the three objective functions. The Pareto front provides a set of optimal trade-offs between the conflicting objectives, but it is still a challenge for the decision-makers to select the most suitable solution based on their priorities. To overcome this, a compromise solution that effectively balances all objectives must be identified.

Table A1. F solutions and their relative normalized membership values.

MOPSO					MOHHO
Sol	LPSP	COE	REF	Normalized	Sol	LPSP	COE	REF	Normalized
1	0.0613	0.0224	0.5275	0.0067	1	0.0557	0.0238	0.5236	0.0065
2	0.0704	0.0223	0.5303	0.0058	2	0.0613	0.0227	0.5265	0.0059
3	0.0716	0.0211	0.5086	0.0056	3	0.0501	0.0427	0.5763	0.0062
4	0.0578	0.0230	0.5188	0.0069	4	0.0551	0.0244	0.5391	0.0067
5	0.0596	0.0239	0.5511	0.0071	5	0.0223	0.0685	0.9609	0.0121
6	0.0699	0.0216	0.5195	0.0058	6	0.0453	0.0351	0.6097	0.0079
7	0.0699	0.0216	0.5195	0.0058	7	0.0556	0.0392	0.5263	0.0052
8	0.0500	0.0307	0.5611	0.0076	8	0.0211	0.0483	0.8766	0.013
9	0.0186	0.0783	0.9697	0.0117	9	0.0240	0.0531	0.8345	0.0117
10	0.0716	0.0211	0.5086	0.0056	10	0.0498	0.0265	0.5733	0.0076
11	0.0541	0.0273	0.5438	0.0073	11	0.0196	0.0555	0.9256	0.0132
12	0.0225	0.0714	0.9608	0.0117	12	0.0200	0.0830	0.9718	0.0112
13	0.0704	0.0223	0.5303	0.0058	13	0.0220	0.0595	0.8929	0.0121
14	0.0461	0.0327	0.5933	0.0082	14	0.0242	0.0453	0.8592	0.0127
15	0.0216	0.0650	0.9384	0.0121	15	0.0237	0.0534	0.9154	0.0127
16	0.0204	0.0573	0.8804	0.0122	16	0.0211	0.0854	0.9731	0.0108
17	0.0699	0.0216	0.5195	0.0058	17	0.0463	0.0284	0.6312	0.0086
18	0.0229	0.0631	0.9217	0.0119	18	0.0207	0.0570	0.8865	0.0124
19	0.0469	0.0318	0.5931	0.0082	19	0.0409	0.0320	0.6882	0.0097
20	0.0213	0.0648	0.9322	0.0121	20	0.0425	0.0466	0.6403	0.0076
21	0.0340	0.0508	0.7537	0.0098	21	0.0219	0.0719	0.9643	0.0119
22	0.0242	0.0525	0.8257	0.0116	22	0.0207	0.0594	0.9087	0.0125
23	0.0699	0.0216	0.5195	0.0058	23	0.0318	0.0513	0.7650	0.01
24	0.0487	0.0332	0.5770	0.0077	24	0.0191	0.0603	0.9434	0.013
25	0.0592	0.0426	0.5077	0.005	25	0.0287	0.0437	0.7973	0.0115
26	0.0184	0.0773	0.9668	0.0117	26	0.0313	0.0376	0.7765	0.0115
27	0.0584	0.0253	0.5090	0.0066	27	0.0266	0.0511	0.8182	0.0114
28	0.0716	0.0211	0.5086	0.0056	28	0.0396	0.0343	0.7309	0.0101
29	0.0203	0.0582	0.8810	0.0121	29	0.0240	0.0447	0.8552	0.0127
30	0.0192	0.0764	0.9633	0.0117	30	0.0226	0.0610	0.9137	0.0121
31	0.0205	0.0636	0.9247	0.0122	31	0.0273	0.0398	0.8049	0.0121
32	0.0213	0.0648	0.9322	0.0121	32	0.0556	0.0392	0.5263	0.0052
33	0.0180	0.0864	0.9737	0.0111	33	0.0219	0.0589	0.9042	0.0123
34	0.0264	0.0538	0.8183	0.0111	34	0.0232	0.0586	0.9210	0.0124
35	0.0546	0.0302	0.5438	0.007	35	0.0551	0.0408	0.5430	0.0053
36	0.0250	0.0432	0.8383	0.0124	36	0.0482	0.0279	0.6203	0.0083
37	0.0212	0.0589	0.8873	0.0121	37	0.0287	0.0437	0.7973	0.0115
38	0.0541	0.0292	0.5440	0.0071	38	0.0400	0.0373	0.6714	0.0091
39	0.0220	0.0784	0.9708	0.0113	39	0.0227	0.0551	0.9234	0.0128
40	0.0457	0.0291	0.6208	0.0089	40	0.0295	0.0388	0.7929	0.0118
41	0.0267	0.0493	0.8171	0.0115	41	0.0261	0.0460	0.8642	0.0124
42	0.0180	0.0846	0.9737	0.0112	42	0.0229	0.0574	0.9130	0.0124
43	0.0205	0.0525	0.8868	0.0127	43	0.0414	0.0314	0.6769	0.0095
44	0.0207	0.0801	0.9700	0.0113	44	0.0576	0.0384	0.5281	0.005
45	0.0704	0.0223	0.5303	0.0058	45	0.0451	0.0287	0.6299	0.0087
46	0.0213	0.0648	0.9322	0.0121	46	0.0212	0.0481	0.8421	0.0126
47	0.0209	0.0794	0.9721	0.0114	47	0.0191	0.0603	0.9434	0.013
48	0.0186	0.0783	0.9697	0.0117	48	0.0409	0.0320	0.6882	0.0097
49	0.0498	0.0446	0.5760	0.0066	49	0.0502	0.0380	0.5773	0.0066
50	0.0393	0.0451	0.6554	0.0086	50	0.0242	0.0453	0.8592	0.0127
51	0.0225	0.0690	0.9498	0.0118	51	0.0492	0.0262	0.5817	0.0078
52	0.0430	0.0335	0.7158	0.0099	52	0.0216	0.0790	0.9690	0.0113
53	0.0289	0.0480	0.7758	0.0109	53	0.0223	0.0662	0.9573	0.0122
54	0.0398	0.0442	0.6558	0.0086	54	0.0265	0.0442	0.8086	0.0119
55	0.0376	0.0467	0.7008	0.0092	55	0.0205	0.0617	0.9251	0.0125
56	0.0180	0.0864	0.9737	0.0111	56	0.0492	0.0262	0.5817	0.0078
57	0.0180	0.0864	0.9737	0.0111	57	0.0556	0.0247	0.5612	0.0069
58	0.0305	0.0395	0.7855	0.0115	58	0.0200	0.0824	0.9714	0.0112
59	0.0347	0.0419	0.7421	0.0104	59	0.0256	0.0438	0.8441	0.0125
60	0.0442	0.0328	0.6252	0.0088	60	0.0430	0.0335	0.7158	0.0096
61	0.0469	0.0318	0.5931	0.0082	61	0.0232	0.0702	0.9613	0.0118
62	0.0345	0.0502	0.7423	0.0097	62	0.0555	0.0325	0.5280	0.0058
63	0.0219	0.0820	0.9711	0.011	63	0.0295	0.0388	0.7929	0.0118
64	0.0364	0.0395	0.7281	0.0102	64	0.0613	0.0227	0.5265	0.0059
65	0.0185	0.0792	0.9716	0.0116	65	0.0361	0.0497	0.7291	0.0092
66	0.0180	0.0855	0.9737	0.0112	66	0.0332	0.0365	0.7577	0.0111
67	0.0193	0.0835	0.9721	0.0112	67	0.0590	0.0233	0.5076	0.0059
68	0.0180	0.0855	0.9737	0.0112	68	0.0551	0.0244	0.5391	0.0067
69	0.0387	0.0410	0.6717	0.0092	69	0.0220	0.0595	0.8929	0.0121
70	0.0260	0.0619	0.9474	0.012	70	0.0226	0.0610	0.9137	0.0121
71	0.0180	0.0864	0.9737	0.0111	71	0.0212	0.0481	0.8421	0.0126
72	0.0215	0.0739	0.9677	0.0117	72	0.0501	0.0297	0.5608	0.0071
73	0.0227	0.0560	0.8529	0.0117	73	0.0599	0.0369	0.5091	0.0046
74	0.0487	0.0332	0.5770	0.0077	74	0.0313	0.0376	0.7765	0.0115
75	0.0224	0.0503	0.8984	0.0128	75	0.0211	0.0854	0.9731	0.0108
76	0.0186	0.0783	0.9697	0.0117	76	0.0167	0.0839	0.9724	0.0115
77	0.0537	0.0253	0.5734	0.0078	77	0.0498	0.0265	0.5733	0.0076
78	0.0180	0.0864	0.9737	0.0111	78	0.0548	0.0388	0.5431	0.0055
79	0.0180	0.0864	0.9737	0.0111	79	0.0280	0.0415	0.7760	0.0115
80	0.0556	0.0392	0.5263	0.0059	80	0.0400	0.0373	0.6714	0.0091
81	0.0180	0.0864	0.9737	0.0111	81	0.0229	0.0574	0.9130	0.0124
82	0.0180	0.0864	0.9737	0.0111	82	0.0241	0.0479	0.8253	0.0121
83	0.0182	0.0645	0.9407	0.0125	83	0.0240	0.0447	0.8552	0.0127
84	0.0219	0.0683	0.9536	0.012	84	0.0532	0.0271	0.6064	0.0075
85	0.0231	0.0738	0.9622	0.0115	85	0.0574	0.0232	0.5389	0.0065
86	0.0213	0.0775	0.9682	0.0114	86	0.0196	0.0555	0.9256	0.0132
87	0.0204	0.0653	0.9351	0.0122	87	0.0265	0.0442	0.8086	0.0119
88	0.0202	0.0576	0.8738	0.0121	88	0.0219	0.0589	0.9042	0.0123
89	0.0219	0.0820	0.9711	0.011	89	0.0532	0.0271	0.6064	0.0075
90	0.0204	0.0519	0.8588	0.0124	90	0.0580	0.0320	0.5092	0.0053
91	0.0305	0.0385	0.7831	0.0116	91	0.0377	0.0477	0.7009	0.0088
92	0.0221	0.0727	0.9669	0.0117	92	0.0266	0.0511	0.8182	0.0114
93	0.0225	0.0690	0.9498	0.0118	93	0.0223	0.0685	0.9609	0.0121
94	0.0232	0.0702	0.9613	0.0118	94	0.0396	0.0343	0.7309	0.0101
95	0.0467	0.0337	0.5935	0.0081	95	0.0366	0.0469	0.7289	0.0094
96	0.0213	0.0648	0.9322	0.0121	96	0.0451	0.0287	0.6299	0.0087
97	0.0196	0.0555	0.9256	0.0130	97	0.0596	0.0239	0.5511	0.0063
98	0.0225	0.0690	0.9498	0.0118	98	0.0216	0.0790	0.9690	0.0113
99	0.0295	0.0388	0.7929	0.0118	99	0.0557	0.0238	0.5236	0.0065
100	0.0432	0.0460	0.6247	0.0078	100	0.0225	0.0690	0.9498	0.0119

Background colors in the table highlight the solutions with the highest normalized membership values for each optimization technique—Solution 97 for MOPSO and Solution 11 for MOHHO—which represent the best compromise solutions identified in the analysis.

presents the solutions of the PF and their normalized membership values for MOPSO and MOHHO. It can be observed that the maximum values of normalized membership are on solutions 89 and 30 for MOPSO and MOHHO, respectively. These solutions represent the best compromise solutions for both techniques. The results obtained by using the best compromise solutions are given in

Table 12. MOPSO and MOHHO results using best compromise solutions under TOU rates.

Technique	COE (USD/kWh)	NPC	LPSP (%)	REF (%)	${\mathit{N}}_{\mathit{P}\mathit{V}}$	${\mathit{N}}_{\mathit{B}\mathit{a}\mathit{t}}$	Total GHG Emissions (Tone)
MOPSO	0.0554	69,503	1.96	92.55	66	13	1046
MOHHO	0.0554	69,503	1.96	92.55	66	13	1046

and

Table 13. Generated power of each element using best compromise solutions.

Technique	${\mathit{P}}_{\mathit{P}\mathit{V}}$ (MWh)	Grid Sell (MWh)	Grid Purchase (MWh)	PV Share (%)	V2H Share (%)	Grid Share (%)	Net Saving in CO2 Emission (%)
MOPSO	34.25	10.56	2.76	92.31	0.23	7.44	72.16
MOHHO	34.25	10.56	2.76	92.31	0.23	7.44	72.16

.

7.3. Performance Evaluation of MOPSO and MOHHO Techniques

The performance evaluation of MOPSO and MOHHO differed from that of single-objective PSO and HHO because there are multiple optimal solutions generated. To evaluate the performance, statistical metrics such as minimum, maximum, range, standard deviation, and mean of the Pareto solutions were used. These evaluation results are provided in

Table 14. Performance metrics of Pareto solutions obtained by MOPSO and MOHHO.

Technique	Metric	Min	Max	Range	Mean	STD	Time
MOPSO	LPSP	0.018	0.071	0.053	0.034	0.017	381
	COE	0.021	0.086	0.065	0.053	0.021
	REF	0.507	0.973	0.465	0.790	0.180
MOHHO	LPSP	0.016	0.061	0.044	0.035	0.014	664
	COE	0.022	0.085	0.062	0.045	0.016
	REF	0.507	0.973	0.465	0.757	0.158

.

7.4. Comparison with Recent Optimization Studies

A comparative analysis between this study and the work in [82] reveals both methodological distinctions and overlapping insights in the evaluation of grid-connected PV systems across various cities in Saudi Arabia. This study employs a multi-objective optimization approach that incorporates economic, reliability, and renewable energy indicators. These objectives are examined from three key perspectives (economic, renewable, and environmental) allowing for a balanced evaluation of cost, system performance, greenhouse gas (GHG) reduction, and grid interactions. In contrast, ref. [82] addresses a dual-criteria evaluation focusing primarily on REF and NPC, comparing these metrics across different cities in the Kingdom. The findings indicated that locations such as Hail, Sakaka, and Jeddah offer optimal trade-offs, with moderate NPC (USD 18.4k) and REF (47%), while other cities like Al Batin and Al Wajh show more extreme values in both cost and renewable contribution. Sensitivity analysis in [82] demonstrates that increasing GHI significantly reduces both COE (from USD 0.057/kWh to USD 0.047/kWh) and NPC (from USD 82k to USD 68k). In contrast, this study confirms that optimal PV-battery sizing combined with integrated EV-grid interaction can achieve desirable performance targets—COE below USD 0.1/kWh, LPSP under 10%, and REF exceeding 50%. While [82] provides a location-based evaluation for strategic deployment, this paper emphasizes system-level design and operational optimization. Both studies highlight the importance of renewable energy integration in improving economic feasibility; however, the present work offers a more comprehensive framework by also incorporating grid dynamics and environmental considerations, contributing to the development of smart residential energy systems.

7.5. Impacts on Urban Energy Sustainability and Resilience

The optimized Home-PV-BES-EV system discussed in this study shows important impacts in terms of economics, environment, and reliability. Economically, the system achieved a Cost of Energy of USD 0.0554/kWh, making it competitive when compared to other renewable systems and offering long-term savings by reducing the use of grid electricity. Although the COE could be slightly higher than direct grid electricity, the long-term benefits, such as energy independence and protection against price increases, prove that the system is still a good option. Policy-makers could encourage its adoption by providing subsidies or introducing net metering programs. Environmentally, the system reached a Renewable Energy Fraction of 92.55%, meaning most of the home’s energy needs were met by solar PV. This reduces dependence on fossil fuels and results in significant GHG emission reductions. The use of Vehicle-to-Home (V2H) technology further supports environmental benefits by making good use of excess PV energy stored in electric vehicles. In terms of reliability, the system achieved a low LPSP of 1.96%, showing that it can meet household energy demands with fewer power interruptions. The V2H feature makes the system more resilient by providing backup power when PV generation is low, which reduces dependence on the grid. Additionally, the optimal charging and discharging strategies employed in the system enable dynamic grid interaction, allowing households to sell excess energy and charge electric vehicles during off-peak hours. These results suggest that the system could be expanded to larger communities or microgrids. Overall, this work paves the way for sustainable, reliable, and economically viable home energy solutions in urban environments.

8. Conclusions

In conclusion, this study demonstrates the feasibility and effectiveness of a grid-connected household energy system combining photovoltaic panels, battery energy storage, and electric vehicle integration for a household in Riyadh, Saudi Arabia. Using advanced metaheuristic optimization techniques, namely Multi-Objective Particle Swarm Optimization and Multi-Objective Harris Hawks Optimization, the system was optimized to minimize the Cost of Energy and Loss of Power Supply Probability while maximizing the Renewable Energy Fraction. The results indicate that the proposed system design, supported by a rule-based Home Energy Management System, effectively meets energy demand with a COE as low as USD 0.055/kWh and an REF of approximately 92%. The integration of dynamic EV management, including Vehicle-to-Home (V2H) and Home-to-Vehicle (H2V) operations, further enhances the system’s flexibility and efficiency. The proposed system demonstrates that high renewable energy contributions can be achieved in Riyadh, supported by the region’s abundant solar resources. The use of fuzzy logic to refine Pareto front solutions ensures a balanced compromise among the competing objectives, highlighting the potential of such methodologies in advancing sustainable household energy systems.