 Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 Multi-Objective Optimization of EV Charging for Cost and Loss Minimization Under TOU Tariff Suwimon Techanok, Keerati Chayakulkheeree* Institute of Electrical Engineering, Suranaree University of Technology, Nakhonratchasima, Thailand Received 19 November 2024; received in revised form 17 March 2025; accepted 18 March 2025 DOI: https://doi.org/10.46604/aiti.2024.14520 Abstract This study proposes an optimal electric vehicle (EV) charging (OEVC) management methods to minimize electricity costs and energy losses in the distribution system, which arise from the growing demand for EV charging. a multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the OEVC multi-objective optimization (MOO). Additionally, the time-of-use (TOU) tariff is used to coordinate between the distribution system operator and EV users, which can help increase the efficiency of the charging schedule. Monte Carlo Simulation (MCS) is used to model virtual EV user behavior and create EV charging load profiles. The proposed MOPSO-based OEVC approach is verified on the modified IEEE 33-bus distribution test system, using MATLAB software, under both uncontrolled and controlled charging case studies. The simulation results demonstrate that the proposed method optimizes EV charging efficiently, achieving reductions of approximately 7.60% in electricity costs and 28.73% in energy losses compared to the uncontrolled charging case. Keywords: optimal EV charging (OEVC), multi-objective optimization (MOO), electricity cost minimization, energy loss minimization, time-of-use (TOU) tariff 1. Introduction Global warming poses a critical threat to ecosystems and human well-being. Many countries aim to achieve net zero emissions (NZE) as the solution under the Paris Agreement, with a key strategy being the transition from internal combustion engines (ICEs) to electric vehicles (EVs). Fuel combustion in ICEs is a major source of CO2, and studies indicate that widespread EV adoption can reduce emissions by up to 20% [1-2]. Under the most ambitious scenarios, EVs could account for up to 65% of all light car sales globally by 2030, driven by strong policy support, advancements in battery technology, and market expansion in major regions. This projection aligns with the NZE by 2050 Scenario outlined in the Global EV Outlook 2024 [3]. However, the rapid increase in EV adoption also presents significant challenges for electricity grid management. As EV users typically charge their vehicles after returning home, this coincides with peak electricity demand from other daily activities, leading to elevated peak electricity loads. Without proper planning, this can result in significant negative impacts on the grid, such as voltage instability, increased power losses, and transformer overloading. For instance, studies [4] analyzing the impact of uncoordinated EV charging on grid performance, have shown that peak demand can increase by up to 53%. To address these challenges, implementing strategies such as smart charging, time-of-use (TOU) tariffs, and vehicle-to-grid (V2G) technology is crucial for ensuring the sustainable integration of EVs into the energy system [5]. Fig. 1 demonstrates the impact of EV charging on the load profile. * Corresponding author. E-mail address: keerati.ch@sut.ac.th Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 221 Fig. 1 The impact of EV charging on the load profile Consequently, many studies are being conducted to find the management approaches to the rapid increase in EV numbers within the electricity system. In [5], an efficient and accurate predictive model for EV charging demand is proposed, specifically designed for use in the management and planning of urban transportation infrastructure. In [6], the authors propose sequential heuristic (SH) and global heuristic (GH) approaches to solve the optimal EV charging (OEVC) scheduling problem to minimize charging costs. In [7-8], centralized EV scheduling problems are proposed to minimize grid load imbalance through valley filling. In [9], the optimization of EV charging and discharging primarily aims to decrease energy costs by shifting loads to low-cost periods and regulating power system demand more efficiently. Various algorithms have been studied and developed to optimize charging scheduling. Heuristic rule-based algorithms have been proposed in [10-11] to handle a variety of scheduling challenges considering variables such as the number of instances, the available limitations, and computational, including the scheduling of EV charging sessions at charging stations while solving an optimal power flow problem. However, heuristic rules are applied to problems with a small number of decision variables and lower computational complexity. In contrast, metaheuristic algorithms are better suited for handling complicated problems, especially when it comes to scheduling optimization and power system challenges. In [12], the crow search algorithm (CSA) is used to optimize the energy control system and minimize operating costs. In [13], the focus is on minimizing the peak-to-valley difference in grid load and reducing user charging costs, proposing the use of genetic algorithms (GA) for optimal scheduling schemes for electric vehicles. In [14], the particle swarm optimization (PSO) algorithm can be employed to optimize EV charging scheduling to effectively minimize power loss, although it does not account for the uncertainty in user charging behavior. However, in [15], the uncertain behavior of EVs using a Markov decision process, with optimal charging management achieved through the bounded real- time dynamic programming (BRTDP) algorithm. In [16], GA and monte carlo simulation (MCS) are used to minimize distributed generators' investment costs. Adjusting EV users' charging behavior is crucial for optimizing charging schedules for maximum efficiency. Demand side management (DSM) is an alternative solution for controlling electricity demand, including the demand for EV charging. DSM has been successfully applied in large-scale buildings through various demand response programs, such as real-time demand reduction, load shifting, and energy efficiency enhancement, as demonstrated in real-world case studies proposed in [5]. Dynamic pricing is important for managing conflicting energy demands from EV charging. In [17], it was demonstrated that the dynamic real-time demand electricity pricing mechanism can significantly reduce electricity costs. The TOU considered in [18] was applied for optimal energy scheduling to reduce system costs and minimize CO2 emissions, utilizing the multi-objective grasshopper optimization algorithm (MOGOA). Meanwhile, [19] introduced a model developed using the learnable partheno-genetic algorithm (LPGA) to determine the optimal EV routes to minimize total distribution costs under the TOU framework. Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 222 However, MOGOA is still a relatively new algorithm with limited development and improvements, and LPGA is susceptible to becoming caught in local optima in the absence of a well-thought-out methodology. By contrast, multi-objective particle swarm optimization (MOPSO) is a widely used algorithm with several improved versions, making it highly effective for solving specific problems. MOPSO also has a strong capability to explore solution spaces efficiently and avoid local optima while offering flexibility in various applications. In [20], MOPSO has been used to optimize the power flow. Many studies focus on solving multi-objective scheduling problems, such as [21-22] minimizing grid load imbalance and focusing on reducing EV users' charging prices. However, many studies primarily target reducing costs for the benefit of EV users. From the perspective of solving scheduling issues to minimize the distribution system operator's (DSO) expenses, this aspect is one of the most challenging issues. In large-scale EV charging, power losses from extensive electricity transmission impose significant challenges that are comparable to other grid impacts. Insufficient electricity to meet rising demand may also force the DSO to procure additional power, often from international sources, which could elevate costs due to fluctuating global energy prices. Moreover, both escalating costs and rising power losses have substantial and interconnected impacts on the grid’s sustainability. Therefore, both issues should be considered simultaneously in any comprehensive optimization strategy. The study in [5] focuses on developing a predictive model to accurately forecast EV charging demand by leveraging advanced deep learning techniques, primarily emphasizing long-term planning and resource allocation for charging station operators. However, it does not address the critical challenges associated with large-scale EV integration into the power grid, such as increased power losses and higher operational costs for DSOs. Meanwhile, this study aims to address this gap by focusing on optimizing EV charging to minimize both electricity costs and energy loss in the distribution system for the benefit of the DSO. Based on the discussion above, this study proposes an integrated approach for OEVC that uses the MOPSO algorithm to minimize electricity costs and energy losses, achieving a balanced optimization between both objectives. In the methodology presented in this article, dynamic pricing is incorporated by integrating a TOU tariff as a representative example of price-based demand response actively used in Thailand in conjunction with MOPSO. Moreover, the versatility of MOPSO allows adaptation to other pricing schemes, which provides a flexible framework for diverse market conditions. While accounting for the uncertainty in the user charging behavior, the MCS generates EV load profiles based on actual usage data. The proposed MOPSO-based OEVC algorithm was tested on the IEEE 33-bus distribution system using the central Thailand household load profiles. The simulation results show that the proposed OEVC method effectively minimizes electricity costs and energy losses compared to charging profiles generated by MCS. This study is structured as follows: Section 2 addresses the OEVC problem formulation, Section 3 presents the MOPSO method for solving the OEVC, Section 4 presents the simulation results and discusses the results of the MOPSO base OEVC, and Section 5 presents the conclusions. 2. Problem Formulation In this section, objective functions are formulated to minimize electricity costs and energy losses. The MCS is used to model EV user behavior and handle the variability resulting from EV user behavior uncertainty. This part will also cover the TOU tariff, which is a time-based program that encourages response to the OEVC scheduling. 2.1. Time of Use (TOU) Tariff The TOU rate is an electricity rate that represents the cost of generating power over two periods. Electricity costs are calculated based on the user's electricity usage period. As shown in Fig. 2, electricity costs during peak hours (from 9:00 AM to 10:00 PM) are higher than those during off-peak hours (from 10:00 PM to 9:00 AM). Implementing the TOU tariff encourages EV users to adjust their charging times to take advantage of the lower rates. Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 223 Time (Hours) E n e r g y c h a r g e ( B a th /k W h ) Off-Peak Off-Peak On-Peak 00.00 09.00 10.00 24.00 Fig. 2 Typical TOU tariff pattern 2.2. The probabilistic modeling of the EV user's behavior For the behavior of EV users, MCS is applied to address the uncertainty of EV users' behavior. The random variables considered include the time at which EVs depart from home (𝑇𝑒𝑑𝑟), the duration from home to work (𝑇ℎ𝑡𝑤), the duration back from work to home (𝑇𝑒𝑏ℎ), and the duration EVs are parked at work without being connected to the grid (𝑇𝑒𝑜𝑝). Additionally, the model considers battery capacity and distance. The probability distributions and parameter values used for these variables were derived from empirical studies on real-world EV user behavior in European countries, which investigated travel patterns, parking durations, and charging preferences. These findings provided the basis for determining the means and standard deviations for each parameter, as presented in Table 1 from [23]. The lower and upper bounds of random variables are 0-24 hours. Fig. 3 illustrates the EV user activity model generated using MCS. This model creates an EV charging load profile, which is combined with the household load profile. These inputs and network data are provided to the MOPSO algorithm to solve the OEVC. ATV1 ATV2 ATV3 ATV4 ATV5 Time step % S O C MOPSO Optimal EV Charging EV Charging EV Charging Input Load profile household Load profile EV Charging Network data Monte Carlo simulation EVs stay at home The owner drives to work EVs stay at work The owner drives to home The EVs arrive home Maximum SOC Decreasing SOC Constant SOC Increasing SOC Input Fig. 3 Framework of MOPSO-based OEVC with probabilistic EV user activity model Once these random time variables are obtained from the MCS, they serve as inputs to model the EV usage activities of users. The model for EV usage activities is based on the assumption that EVs are primarily used for commuting within urban areas, where they only travel from home to work and do not account for regional variations in user behavior or external factors Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 224 such as traffic conditions or weather. Therefore, the activities of EV users include the time of departure from home, the time of return to home, the travel duration, and the duration of parking without charging, as described in Eqs. (1)–(6).      [ ], 1 2 3 4 5 n n n n n n ATV ATV ATV ATV ATV ATV day = + + + + (1)        {1: -1}, 1 n n ATV T edr = (2)            { : ? }, 2 n n n n ATV T T T edr edr htw = + (3)                { 1: ?   }, 3 n n n n n n ATV T T T T T edr htw edr htw eop = + + + + (4)                    { ?  1: }, 4 ? n n n n n n n n ATV T T T T T T T edr htw eop edr htw eop ebh = + + + + + + (5)              { ?        1: }, 5 n n n n n ATV T T T T np edr htw eop ebh = + + + + (6) 1, , , 1, ,for n NC t np=  =  where, 𝐴𝑇𝑉𝑑𝑎𝑦 𝑛 represents the daily activities of the 𝑛𝑡ℎ EV usage. The 𝑛𝑡ℎ EVs stay at home before leaving for work in activity 𝐴𝑇𝑉1 𝑛. 𝐴𝑇𝑉2 𝑛 is the owner who drives the 𝑛𝑡ℎ EVs to work. The user of the 𝑛𝑡ℎ EV parks the EVs at work without connecting to the grid by 𝐴𝑇𝑉3 𝑛 is the activity in which the user of the 𝑛𝑡ℎ EV parks the EV at work without connecting to the grid. The owner, 𝐴𝑇𝑉4 𝑛 takes the 𝑛𝑡ℎ EVs home. Lastly, 𝐴𝑇𝑉5 𝑛 represents the owner of the 𝑛𝑡ℎ EVs after they get home from work. In order to estimate the electricity consumption from EV charging and create the load profile for uncontrolled charging of EVs, it is necessary to calculate the state of charge (SOC). Based on the assumption that EV usage begins in the morning after overnight charging, it is initially considered that the battery is fully charged, as indicated in Eq. (7) [24]. Considering only the charging state, it is assumed that the 𝑆𝑂𝐶𝑡 is limited to a minimum depth of discharge (DOD), determined by the fraction 𝑃𝑑𝑜𝑑 and the maximum SOC when fully charged, denoted as 𝑆𝑂𝐶𝑚𝑎𝑥 , as shown in Eq. (8).          0 max n n SOC SOC= (7)               min max   n n n p SOC SOC SOC dod t   (8) The level of SOC changes according to EV usage activities. It increases when the EV is charged at home and decreases when the user drives the EV. For the time step of the SOC at time increases from its initial state according to the charging power when the EV is charged. It decreases according to the energy consumption when the EV is driven, as calculated in Eq. (9).      , arg mod            - , mod 1   , Δ Δ nSOC P t for ch ing e t c n n tSOC SOC C t for driving e t t nSOC else t  +   =+    (9) 1, , , 1, ,for n NC t np=  =  Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 225 Time period % S O C   max nSOC       1   Δ- n n t t tSOC SOC C t+ =     1 n n t tSOC SOC+ =       1    Δn n t t cSOC SOC P t+ +=     m0 ax n nSOC SOC= At home Parking at work Fig. 4 The SOC varies over time under different EV charging strategies Fig. 4 illustrates the SOC profiles of an EV under different charging strategies across key activity periods, including staying at home, driving to work, parking at work without charging, EV driving back home, and charging at home. Each segment reflects the change in SOC based on the corresponding activities, where SOC decreases during driving, remains constant while parked at work, and increases when charging at home, following Eqs. (7)-(9). The EV charging load profile 𝑃𝑒𝑣,𝑖,𝑡 𝑛 will be equal to or dependent on 𝑃𝑐 following the vehicle usage activities at that time initially, as shown in Eq. (10). The total EV charging load profile is determined by summing the charging loads of all EVs, as described in Eq. (11).     , arg mod     , ,   0, P forch ing en cP ev i t else =    (10)           , , , , 1 NC total n P P ev i t ev i t n =  = (11)     1, , , 1, ,for n NC t np=  =  The power EV charging 𝑃𝑒𝑣,𝑖,𝑡 𝑛 must be taken into account hourly in the data analysis to ensure that the information is in line with the objective function, understandable, and adheres to standard procedure. The outcome of changing the time step from one minute to one hour is displayed in Eq. (12).           , , , , 1 NC total n P P ev i h ev i h n =  = (12)     1, , , 1, , 24for n NC h=  =  2.3. Objective functions This research focuses on managing the increasing electricity demand resulting from EV charging by searching for the OEVC time with two objectives. The first objective is to reduce electricity costs, and the second is to minimize energy losses in the system. The objective functions of the electricity cost minimization problem are presented in Eq. (13) and the energy loss minimization problem is presented in Eq. (14).  24             1 total h MinimizeC C ep ep h =  = (13) Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 226  24           1 total h Minimize E P loss loss h =  = (14) where the hourly electricity cost can be calculated by:                          1 , , , h h h hNBC C C Ciep en i Ft i vat i = + + = (15)                    ( ? ) , , , h h h h C P P r en i hh i ev i tou = +  (16)                ( ) ? , , , h h h C P P Ft Ft i hh i ev i = +  (17) ( )                , , , h h h C C C VAT vat i en i Ft i = +  (18)   1, , , 1, , 24for i NB h=  =  The hourly loss can be calculated using Eqs. (19)-(20), the equations are referred from the load flow equations in [25].                      -( )1 , , , h h h hNBP P P Piloss G i hh i ev i = + = (19)           [ cos( - ) sin( - )] 1 NB h P V V G B loss i j ij i j ij i j j    = + = (20) 1, , , 1, , 24for i NB h=  =  2.4. Constraints According to the MCS of EV user behavior, EVs are not charged from the moment they leave home until they return. Thus, 𝑃𝑒𝑣,𝑖 ℎ,𝑜𝑛 represents the charging power at the time h at bus i when the EV is charging, with its value ranging between a maximum, the total power charge of all EVs at bus i, and the minimum is a percentage of the total number of cars (pnc). While 𝑃𝑒𝑣,𝑖 ℎ,𝑜𝑓𝑓 indicates the total power charge at the time h at bus i when the EV is not charging, which equals 0. According to Eqs. (21)-(22).      , ( ) ( ),1 1, , , , , h h on hNC NCpnc P P Pn nc i n ev i c i n    = = (21)  ,    0, ,   h off P ev i = (22)    1, , , 1, , , 1, , 24for i NB n NC h=  =  =  The equality constraints, which represent the load flow equations, are as follows in Eqs. (23)-(24)[25].  - - [ cos( - ) sin( - )] 0 1 NB P P V V G B Gi Di i j ij i j ij i j j    + = = (23) Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 227  - - [ sin( - ) - cos( - )] 0 1 NB Q Q V V G B Gi Di i j ij i j ij i j j     = = (24)    1, , , 1, , 24for i NB h=  =  The inequality constraints establish the system's operational bound, as follows. Generator constraints, including voltage, active power, and reactive power at the 𝑖𝑡ℎ bus, are restricted between their upper and lower bounds, as shown in min max           min max          , min max         V V V Gi Gi Gi P P P Gi Gi Gi Q Q Q Gi Gi Gi       (25) Transformer tap settings are confined within specified limits, as detailed in min max      ,T T T i i i   (26) Shunt compensations are subject to their respective limits, as outlined in min max         ,Q Q Q ci ci ci   (27) and line flow constraints in   max    f f l l  (28) 3. Multi-Objective Particle Swarm Optimization (MOPSO) In this section, the MOPSO algorithm designed for the problem considered in this article is discussed. Furthermore, the concept of Pareto dominance, which is important for the operation of MOPSO for handling multi-objective optimization (MOO) problems, is explained. 3.1. Basic Concept of Pareto Dominance Problem-solving with multiple objectives, as presented in this article, targets reducing electricity costs and minimizing energy losses. Therefore, it requires carefully balancing conflicting goals. The Pareto dominance concept is applied to analyze and solve the MOO problem. The Pareto dominance helps identify solutions in which an improvement in one objective cannot be achieved without causing a deterioration in another. In other words, if a solution 𝑥1 is better than a solution 𝑥2, then the solution 𝑥1 is said to be the dominating one. Thus, the set of non-dominated solutions, which is known as the Pareto frontier, naturally represents a balanced trade-off between the two objectives. Coello and Salazar Lechuga were among the first to extend the PSO algorithm to handle multi-objective problems by incorporating the principle of Pareto dominance. The key advancements include using an external repository to store and update non-dominated solutions and employing a leader selection mechanism based on Pareto criteria. These modifications guide the swarm toward less crowded regions of the objective space, promoting diversity and ensuring that the final set of solutions maintains a balanced trade-off between minimizing electricity costs and reducing energy losses. This method is known as MOPSO [26]. Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 228 3.2. MOPSO algorithm Start Specify the parameter for MOPSO Initialize search population with random position and velocity Initialize the repository for the Pareto frontier and set of non–dominated solution Does MOPSO fulfill the convergence criteria? Loop each particle p = 1, NP Update the velocity and position of each particle as follows in (29) and (30), respectively. Enhance diversity by using a mutation rate to prevent getting stuck in local optimal. Evaluate the objective function of each particle according to (13) and (14). p = NP ? Update the repository of non-dominated solution and discard points with the lowest crowding distance. Calculate spread and quadratic mean distance according to (31) and (32). p = p+1 No Yes Yes No Post processing End Pareto frontier (Repository) Fig. 5 The proposed MOPSO-based OEVC computational procedure MOPSO is an extension of the PSO concept, maintaining the fundamental principles of PSO while incorporating the core concept of Pareto dominance to manage MOO [27-28]. Therefore, in each iteration, the equations for velocity and position updates remain as defined in Eqs. (29)-(30), respectively. 𝑉𝑖,𝑡 is the velocity at iteration t and 𝑉𝑖,𝑡+1 is the updated velocity at iteration t+1 of particle i. 𝑥𝑖,𝑡 is position at iteration t, and 𝑥𝑖,𝑡1 is the updated position at iteration t+1 of particle i. w is the inertia weight. Parameters 𝑐1 and 𝑐2 are the cognitive constant and the social constant respectively. 𝑟1 and 𝑟2 are the random numbers uniformly distributed between 0 and 1. 𝑥𝑖,𝑡 𝑃𝑏𝑒𝑠𝑡 is the best position of particle i at an iteration. This is the best solution that the particle has found till the current iteration. 𝑥𝑖,𝑡 𝐺𝑏𝑒𝑠𝑡 is the global best position across all particles up to the current. This is the non-dominated solution or best solution found by the swarm.     , 1 , 1 1 , , 2 2 , ,      ( - ) ( - )Pbest Gbest i t i t i t i t i t i tV wV c r x x c r x x+ = + + (29) , 1 , , 1          i t i t i tx x V+ += + (30) The MOPSO algorithm has been developed and detailed in [29] and is called the multiple design option (MDO)-MOPSO. In this research, the MDO-MOPSO algorithm has adapted to suit the specific characteristics of the problem in this article while still considering the spread and the mean of the crowding distances (quand mean) as convergence criteria according to Eqs. (31)-(32). Fig. 5 illustrates the methodology of the MDO-MOPSO algorithm.    spread Qd    + = + (31) Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 229 21             k k quand mean d Q =  (32) where 𝜇 is the parameter that quantifies whether the extreme values of the Pareto frontier have changed between two consecutive iterations. 𝜎 and 𝑑 are the standard deviation and the arithmetical average of the crowding distances of point k, and Q is the number of points on the Pareto frontier. This modified version of the MOPSO algorithm integrates performance metrics and includes a post-processing step to identify MDO. The iterative process stops when one of the following three conditions. The first is when the maximum number of iterations is reached. The second is that the change in the spread measure falls below a specified relative and absolute tolerance of, or the final, the change in the quadratic mean of crowding distances falls below a specified absolute and relative tolerance. In the post-processing section, a process is conducted to identify the optimal solutions according to predefined criteria. The steps are as follows: (1) Identify the search area for selecting extreme values and conducting trade-off analysis based on the Pareto frontier. (2) Remove any outliers to ensure only relevant and feasible solutions are considered. (3) Select extreme designs that maximize energy shares, focusing on solutions that provide the best balance between objectives. (4) Calculate key performance indicators (KPIs). KPIs are computed to evaluate and compare the diversity characteristics among the original Pareto frontier, the enhanced Pareto frontier, and the selected MDO points. The calculation of KPIs is based on the Manhattan measure. Details of this calculation are presented in [29]. (5) Plot the trade-offs and results to visually assess and compare the final solutions. 4. Simulation Results and Discussion 1 2 3 4 5 6 7 8 9 10 11 12 14 15 1613 17 18 23 24 25 19 20 21 22 26 27 29 30 3128 32 33 Fig. 6 The modification IEEE 33-bus distribution test system with EV charging devices This section discusses the simulation of a system modified from the IEEE 33-bus distribution test system by adding EV connections at each bus, as shown in Fig. 6. According to this research study, the OEVC scheduling controls the increasing demand for electricity to minimize electricity costs and energy losses in the system. The MOPSO algorithm is used for OEVC scheduling, and the simulation is performed with MATLAB software. 4.1. IEEE 33-bus distribution system without EV charging device The IEEE 33-bus distribution system is used as the base system for this study, as shown in Fig. 6. In the base case, the simulation is performed without connecting any EV charging devices to the system, while other cases include EV charging Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 230 devices. The load profile used as the system's base load for households is the central Thailand load profile for July, as shown in Fig. 7. This case study contrasts the outcomes of the OEVC scheduling for objective functions of different purposes. 4.2. IEEE 33-Bus distribution system with EV charging device The IEEE 33-bus distribution system with the integration of EV charging devices, as shown in Fig. 6. This system is used for the simulation under uncontrolled and controlled charging conditions. For the controlled scenario, three case studies are presented to assess and compare the performance of the proposed algorithm in solving the OEVC problem. 4.2.1. Uncontrolled EV charging devices Fig. 7 The Load Profiles of the System without and with EV Charging IEEE 33-bus distribution system with EV charging device, as shown in Fig. 6. EV charging input parameters are as in [24] and the BYD Atto 3 model, as shown in Table 2. The load profile for EV charging follows user behavior as suggested by the MCS, which is shown in Fig. 7. The uncontrolled EV charging load profile, location status based on user activities and SOC by considering the time period np = 1440 minutes, is shown in Fig. 8. Simulation results indicate that without controlling EV charging, the daily electricity cost for the entire system is 105.6815 kTHB/kWh, and the daily energy loss is 6.16 MWh. Fig. 8 Uncontrolled EV charging simulation Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 231 Fig. 9 Comparison of real-world EV charging and MCS results Fig. 9 presents the comparison of the EV charging load profile from the MCS and the real-world EV charging data from the Denmark study [30]. The outcomes indicate that the load profile generated by the MCS agrees with the real-world data. In particular, the peak electricity demand is close to real-world values and occurs between 8:00 PM and 9:00 PM. Table 1 Mean and variance of EV usage patterns Random variable Mean (μ) Variance (𝜎2) 𝑇𝑒𝑑𝑟 7:15 AM 30 min 𝑇ℎ𝑡𝑤 30 min 15 min 𝑇𝑒𝑜𝑝 9 h and 20 min 50 min 𝑇𝑒𝑏ℎ 30 min 15 min Table 2 Input parameters of EV charging Parameter values 𝑆𝑂𝐶𝑚𝑎𝑥 60.48 kWh 𝑃𝑐 3.7 kWh 𝑃𝑑𝑜𝑑 0.6 𝐶𝑠 𝑡 of un-Aug 1.1 𝑣𝑚 60 km/h 𝑐𝑚 0.257 kWh/km ∆𝑡 1/60 h 𝑝𝑛𝑐 0.1 4.2.2. Controlled EV charging devices In this article, household consumption at a voltage level lower than 12 kV is used, using the TOU pricing of Thailand as indicated in Table 3. In this study, the OEVC scheduling is proposed in three case studies to assess the effectiveness of optimal charging planning, including using the algorithms differently to solve the problem. The three case studies are as follows: Table 3 Time of Use rate (TOU rate) for type 1 residential households Voltage level Energy charge (Bath/kWh) Peak (09:00 a.m.-10:00 p.m.) Off-Peak (10:00 p.m.-09:00 a.m.) At voltage level 12 – 24 kV 5.1135 2.6037 At voltage level lower than 12 kV 5.7982 2.6369 (1) Case I: Single objective for minimizing Electricity cost In this case, the PSO and GA determine the OEVC scheduling, considering the single objective function of minimizing the electricity cost of the system. The result of the PSO achieved a minimum daily electricity cost of 96.92823 kTHB, leading to a daily energy loss of 5.4966 MWh. In comparison, the result of the GA produced a minimum daily electricity cost of 98.1728 kTHB, leading to a daily energy loss of 5.5542 MWh. Across 30 trials in this case, the resulting averages of PSO and GA were 97.1056 kTHB and 98.4532 kTHB. (2) Case II: Single objective for minimizing Energy losses In this case, the PSO and GA determine the OEVC scheduling, considering the single objective function of minimizing the energy loss of the system. The result of the PSO achieved a minimum daily energy loss of 4.0900 MWh, leading to a daily electricity cost of 97.752 kTHB. In comparison, the result of the GA produced a minimum daily energy loss of 4.208 MWh, leading to a daily electricity cost of 100.442 kTHB. Across 30 trials in this case, the resulting average of PSO and GA was 4.3195 MWh and 4.3560 MWh. Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 232 (3) Case III: Multi-objective for minimizing Electricity cost and Energy losses The MOPSO will be used to determine the OEVC scheduling in this case, considering both the objective function that minimizes electricity cost and minimizes energy loss. The results of the MOPSO indicate that in the system with controlled charging, the daily electricity cost for the entire system is 97.651 kTHB, and the daily energy loss is 4.39 MWh. Table 4 Objective function values from 30 trials by PSO and GA (Case I and Case II) Objective function values Case studies Case I Case II Electricity cost (kTHB) Energy loss (MWh) Algorithm PSO GA PSO GA Max 99.3399 101.8907 4.8523 4.5714 Avg. 97.6148 099.5013 4.3196 4.3560 Min 96.2823 098.1728 4.0900 4.2085 Table 4 and Fig. 10 show the results of the objective function values of the maximum, minimum, and average obtained from 30 PSO and GA trials for case I and case II. The comparison of the performance of PSO and GA for Case I and II, as shown in Fig. 10(a) and Fig. 10(b). Each figure includes the results of 30 trials, showing the average trend line across trials, with the best result marked by a red diamond and the worst result marked by a black circle. The simulation results show that PSO is better than GA in both cases, with the PSO achieving a minimum daily electricity cost of 96.2823 kTHB and a minimum daily energy loss of 4.09 MWh. The EV charging scheduling results by PSO and GA for case I and case II are the minimum electricity cost and energy loss obtained from the simulation results for 30 trials, as indicated in Table 5. (a) Case I (b) Case II Fig. 10 The results from 30 trials of the PSO and GA algorithm Fig. 11 Pareto Frontier of the proposed MOPSO-based OEVC Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 233 Fig. 11 shows the results from MDO-MOPSO for case III. The history of fitness values evaluated during the MOPSO process, including optimal and suboptimal solutions, is represented by black points. The blue points indicate the MDO solution set selected after post-processing analysis. The red line shows the Pareto frontier, representing the optimal trade-offs between electricity cost and energy loss. The most suitable set of solutions is derived from the Pareto frontier after further filtering using a diversity criterion based on crowding distance and a post‐processing step that retains only the solutions within a predefined tolerance. This process indicates that the final solutions reflect a balanced trade-off between minimizing electricity costs and reducing energy losses. Table 5 EV load profiles and minimum objective function values for the IEEE 33-Bus system Hours Power consumption (kWh) Uncontrolled charging Controlled charging Case I Case II Case III PSO GA PSO GA MOPSO 1 0 229.40 331.27 231.58 265.42 296.96 2 0 346.16 173.09 221.73 106.09 282.31 3 0 379.73 468.63 255.62 089.09 221.05 4 0 459.64 225.38 194.35 133.60 143.07 5 0 570.91 224.49 211.49 187.90 241.65 6 0 138.92 105.90 373.12 652.74 372.80 7 0 222.69 249.58 740 408.66 675.08 8 0 0 0 0 0 0 9 0 0 0 0 0 0 10 0 0 0 0 0 0 11 0 0 0 0 0 0 12 0 0 0 0 0 0 13 0 0 0 0 0 0 14 0 0 0 0 0 0 15 0 0 0 0 0 0 16 0 0 0 0 0 0 17 0 0 0 0 0 0 18 332.445 103.23 074.66 292.30 382.40 135.02 19 740.000 080.39 074.66 121.54 076.07 138.28 20 740.000 074.01 074.66 074.69 369.62 138.72 21 740.000 074.00 108.62 088.67 175.42 135.02 22 740.000 122.09 339.17 150.63 155.40 222.82 23 096.015 132.41 482.71 212.92 226.21 203.80 24 0 454.92 455.67 219.86 159.88 181.92  total epC (kTHB) 105.682 96.2823 98.1728 97.752 100.442 97.651  total lossE (MWh) 6.16 5.4966 5.5542 4.0900 4.2085 4.3917 Table 5 presents the results of EV charging scheduling in the three cases compared to uncontrolled EV charging schedules. The results of all three cases show that optimized charging schedules reduce electricity costs and energy loss. In case I, the best result among PSO and GA is a daily electricity cost of 96.922 kTHB, but the energy loss remains relatively high at 5.4966 MWh. In case II, the best result among PSO and GA is a daily energy loss of 4.0900 MWh, but the electricity cost remains relatively high at 97.752  kTHB. The obtained solution in case III is the OEVC. It achieves a daily electricity cost of 97.651 kTHB and an energy loss of 4.3917 MWh. Cases I and II, which consider minimizing a single objective function, using the PSO and GA, achieve the minimum value for that specific objective function. However, the values for the other objective function are higher. Furthermore, the PSO shows slightly superior performance compared to GA. Conversely, OEVC scheduling with MOPSO considers the balance between the two objective functions in that the results for the obtained objective values are not minimum. But these are the optimal results for both objectives. Therefore, the electricity cost and energy loss values in case III fall between cases I and II. The comparison of the EV load profile, electricity Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 234 cost, and energy loss for each hour is shown in Fig. 12. The simulation results in Fig. 12(a) compare the system load profiles, showing that the system with charging control under TOU pricing results in lower on-peak energy demand, which helps reduce electricity costs and energy loss, as shown in Fig. 12(b) and Fig. 12(c). (a) Comparison system load profile (b) Comparison of electricity cost (c) Comparison of power loss Fig. 12 Comparison of results from all cases 5. Conclusions This study proposed a method for OEVC that uses the MOPSO algorithm to solve the multi-objective optimization problem. The goal is to minimize electricity costs and energy losses in the system caused by the large increase in EVs. MCS is used to model the uncertain behavior of EV usage. Additionally, a TOU tariff was used to promote OEVC. The experiments were conducted using MATLAB software and tested on the IEEE 33-bus distribution system. According to the simulation results, the conclusions are summarized: (1) MCS has effectively modeled the uncertain behavior of EV users, which can create realistic EV charging load profiles. This shows that the energy demand during peak periods increases, leading to higher electricity costs and energy losses. (2) The MOPSO algorithm is designed to explore a balanced set of solutions using the Pareto frontier. This approach enables it to effectively address the multi-objective challenge of OEVC by reducing both electricity costs and energy losses. However, MOPSO cannot minimize either aim to the lowest possible level because it operates with the Pareto frontier, which focuses on balancing both objectives without allowing one to outperform the other. Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 235 In the future, improvements might include adaptive tuning of parameters, combining MOPSO with other techniques, or using real-time data to boost specific performance while still maintaining the overall balance. Acknowledgment The authors sincerely want to thank the Suranaree University of Technology for their invaluable support throughout the project. Appendix 1 Abbreviations and Symbols BEV Battery Electric Vehicle DiP The real power demand at bus i DOD Depth of Discharge GiP The real power of the generator at bus i EV Electric Vehicle min GiP The minimum real power of the generator at bus i MOPSO Multi-Objective Particle Swarm Optimization max GiP The maximum real power of the generator at bus i MDO Multiple Design Option DiQ The reactive power demand at bus i MOO Multi-Objective Optimization GiQ The reactive power of the generator at bus i NB The total number of buses min ciQ The minimum shunt VAR compensator NC The total number of cars max ciQ The maximum shunt VAR compensator PSO Particle Swarm Optimization ?h tour The electricity pricing at hour h SOC State of Charge   0 nSOC Initial State of charge of n cars TOU Time of Use   max nSOC The maximum state of charge of n cars ijB The susceptance on branch 𝑖𝑗   min nSOC The minimum state of charge of n cars  total epC The total daily electricity prices  n edrT The time the n-th EV departs from its residence ?h epC The total hourly electricity prices  n htwT The duration of time it takes for the n-th EV to travel from home to the workplace ? , h en iC The electricity energy prices at bus i and hour h  n eopT The duration of time the n-th EV is parked in the garage at the workplace ? , h Ft iC The electricity fuel adjustment charge prices at bus i and hour h  n ebhT The duration of time it takes for the n-th EV to travel from workplace to the home ? , h vat iC The electricity value added tax prices at bus i and hour h min iT The minimum transformer tap settings lf The MVA flow of line l max iT The maximum transformer tap settings l maxf The maximum limit of line l Vij The voltage of bus i and j Ft The fuel Adjustment Charge (at the given time) VAT The value-added tax ijG The conductance on branch 𝑖𝑗 𝛿𝑖𝑗 The phase difference of voltages between bus i and j  total lossE The total daily energy losses  t sC Season coefficient   , , total ev i hP The total charging power at bus i and hour h mc Electricity consumption in distance (kWh/km)   , , n ev i hP The charging power of n cars at bus i and hour h cP Charging power (kWh)  h lossP The hourly power loss dodp Depth of discharge fraction  h hhP The hourly power of the household load carp Vehicle usage probability , , , h on ev i nP The charging power of n cars at bus i that is charging t Time step length (hr) , , , h off ev i nP The charging power of n cars at bus i that is not charging mv The average velocity for a private vehicle trip Advances in Technology Innovation, vol.10, no.3, 2025, pp.220-237 236 Conflicts of Interest The authors declare no conflict of interest. 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