Photovoltaic systems with battery storage: A novel and comprehensive scheduling method for high-consumption facilities

Research papers Photovoltaic systems with battery storage: A novel and comprehensive scheduling method for high-consumption facilities Carlos Gilabert-Torres a,b , Catalina Rus-Casas a,b,* , Gabino Jim´ enez-Castillo b,c , Francisco Jos´ e Mu˜ noz-Rodríguez a,b a Department of Electronic and Automatic Engineering, University of Ja´ en Las Lagunillas Campus, A3 Building, 23071, Ja´ en, Spain b Centre for Advanced Studies in Energy and Environment CEACTEMA, Universidad de Ja´ en, 23071, Ja´ en, Spain c Department of Electrical Engineering, University of Ja´ en Las Lagunillas Campus, A3 Building, 23071, Ja´ en, Spain ARTICLE INFO Keywords: Photovoltaic Battery storage system Peak shaving Energy arbitrage Scheduling method Power flow optimization ABSTRACT The increasing global energy demand and the need for efficient integration of renewable energy sources have driven the development of photovoltaic systems with battery energy storage (PV-BESS). This study proposes a novel energy-management strategy for PV-BESS in high-consumption installations. The strategy integrates a reduction of excess demand penalties, energy arbitrage, and battery aging considerations by using mixed-integer linear programming (MILP), thus addressing the limitations of traditional approaches. The results showed significant reductions in grid-imported energy, particularly during peak demand periods. For a 300-kWh BESS, grid-imported energy was reduced by 16 %, and reductions in the range of 29 % to 51 % were achieved during peak demand periods. This method also proved its ability to reduce excess power peaks, which were reduced by up to 78 % for 500 kWh batteries. As a result, annual demand expenditures decreased by up to 25 %. In addition, by considering battery aging, the strategy extended battery life by up to 9 % compared to similar methods that do not account for degradation, thus improving its profitability and sustainability. This comprehensive approach contributes to the field by optimizing economic profitability, enhancing energy efficiency, and reducing impact on the grid. 1. Introduction The rising global energy demand and the urgency to reduce greenhouse gas emissions have driven the transition toward renewable energy sources [1]. Global electricity consumption, driven by economic development and population growth, has steadily increased since 1974, with the commercial and industrial (C&I) sectors accounting for 63 % of the total consumption as of 2019 [2]. The Paris Agreement, along with national commitments to achieve carbon neutrality by 2050 and the Sustainable Development Goals (SDGs) 7, 11 and 12, has established a regulatory and social framework that fosters the widespread adoption of renewable energy sources (RES) [3,4]. Among RES, photovoltaic (PV) solar energy stands out due to its exponential growth in residential, commercial, and industrial applications in recent years. Moreover, its share in total electricity generation is expected to increase from 5.5 % to over 17 % globally between 2023 and 2030 [5]. However, the intermittent nature of PV generation poses significant challenges for energy management. Since photovoltaic power production fluctuates depending on solar irradiation, it can cause variations in the electrical grid and complicate demand management [6,7]. The growing electricity demand requires solutions that not only reduce greenhouse gas emissions but also ensure the reliability and stability of power systems. In this context, battery energy storage systems (BESS) provide an effective solution, enabling the efficient integration of RES [8]. These systems store surplus energy and release it when needed, thereby improving energy management and grid stability. Current energy management strategies primarily focus on two concepts: self-consumption maximization and energy arbitrage [9]. Selfconsumption aims to maximize the utilization of PV-generated energy by charging the battery with surplus photovoltaic power and discharging it when PV generation is insufficient to meet the demand. This leads to a reduction in the amount of energy imported from the grid and enhances the return on investment of PV systems [10]. * Corresponding author at: Department of Electronic and Automatic Engineering, University of Ja´ en Las Lagunillas Campus, A3 Building, 23071, Ja´ en, Spain. E-mail addresses: [email protected] (C. Gilabert-Torres), [email protected] (C. Rus-Casas), [email protected] (G. Jim´ enez-Castillo), [email protected] (F.J. Mu˜ nozRodríguez). Contents lists available at ScienceDirect Journal of Energy Storage journal homepage: www.elsevier.com/locate/est https://doi.org/10.1016/j.est.2025.118858 Received 4 June 2025; Received in revised form 9 September 2025; Accepted 8 October 2025 Journal of Energy Storage 139 (2025) 118858 Available online 18 October 2025 2352-152X/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/bync-nd/4.0/ ). In contrast, energy arbitrage introduces an economic dimension to battery usage optimisation, leveraging energy price fluctuations. This strategy consists of charging the battery during periods of low electricity prices and discharging it when prices are high, which generates additional economic benefits and improves the overall profitability of the system [11]. In this scenario, economic energy management strategies include peak shaving, which reduces energy consumption during peak demand periods, thereby alleviating stress on the electrical grid and minimizing costs associated with demand charges [12]. The efficacy of these strategies is affected by the type of tariff considered [13,14]. In terms of cost, energy may be charged at a fixed rate, according to a predefined time-of-use tariff (TOU), in real time (RTP), or on a tiered rate basis, proportional to consumption levels. Of particular interest are TOU tariffs, real-time tariffs, and tiered rates, as these allow the BESS to be used to consume more energy at a lower price [15,16]. Conversely, the cost of Nomenclature AAC Average annual cost AC Alternating current ATB Annual technology baseline BDI Bidirectional inverter BESS Battery energy storage system BMS Battery management system C&I Commercial and Industrial DC Demand charges DP Dynamic programming DOD Depth of discharge DP Dynamic programming DPB Discounted payback period EOL End of life GA Genetic algorithm IEC International electrotechnical commission LCOE Levelized cost of electricity LFP Lithium-ion ferro phosphate MILP Mixed-integer linear programming MINLP Mixed-integer non-linear programming MPC Model predictive control NPV Net present value NREL National Renewable Energy Laboratory O&M Operation and maintenance PEM Power-energy model PN Period Number PFO Power flow optimization PSO Particle swarm optimization PV Photovoltaic PVB Photovoltaic +BESS system RES Renewable energy sources RTP Real time pricing SCR Self-consumption ratio SDG Sustainable Development Goal SOC State of charge SOH State of health SSR Self-sufficiency ratio TOU Time of use VCM Voltage-current model Cbat Battery cost Cbd Battery degradation cost cbd Specific battery degradation cost CCP Contracted power cost CEGrid energy cost cESpecific grid energy cost CO&MAnnual operation and management cost CPE Power excess penalty cost ΔtTime resolution drAnnual discount rate E0 bat Initial capacity of the battery Eh bat Degraded capacity of the battery η bat Efficiency of the battery η BDI Efficiency of the bidirectional inverter η bat Efficiency of the battery η rt Roundtrip efficiency of the BESS fbat Battery degradation factor fpAnnual fraction of time of a TOU period HNumber of optimization horizons hOptimization horizon index iGGrid power flow binary variable irAnnual inflation rate iSBESS power flow binary variable kTime step index KpMultiplying factor of power excess penalties cost NNumber of time steps in an optimization horizon NbNumber of battery models nbBattery model index NP Number of TOU periods PAac Photovoltaic AC output η BDI Efficiency of the bidirectional inverter η rt Roundtrip efficiency of the BESS fbat Battery degradation factor fpAnnual fraction of time of a TOU period HNumber of optimization horizons simulated PCContracted power PFG Grid imported power without penalty for excess power PFGex Grid imported power with penalty for excess power PFGex,max Max. grid imported power with penalty for excess power PFPac Bidirectional inverter AC output PFPac,max Max. bidirectional inverter AC output PFS Battery discharge power PLLoad power PPVd PV generation self-consumed directly PPVbat Photovoltaic generation self-consumed through the battery PTG Grid feed-in power PTG,max Max. grid feed-in power PTPac Bidirectional inverter AC input PTPac,max Max. bidirectional inverter AC input PTS Battery charge power PTpSpecific contracted power cost pTOU period index SOCkBattery state of charge at time step k SOCmin Min. battery state of charge SOCmax Max. battery state of charge SOHEOL Battery state of health at end of life SOHhBattery state of health SCP Contracted power savings SEEnergy savings SPE Power excess savings Top Time of operation tep Specific excess power charge yEOL Years elapsed at end of life yEOL Years elapsed at end of life ykYears elapsed at time step k C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 2 demand can fluctuate based on the value of demanded power (capacitybased tariffs), the maximum power value (peak-demand charges), and the period of use. The consideration of demand charges (DC) in the optimization of BESS operation has been demonstrated to enhance profitability and mitigate the impact on the grid [17,18]. Several key aspects must be considered when analyzing the implementation of energy management strategies in PV-BESS systems. Studies have addressed aspects ranging from battery modeling and control strategies to system sizing optimization [19]. Battery modeling must account for factors such as efficiency, degradation, and charge/ discharge characteristics of the battery. Some authors opt for simplified battery models, such as the Power-Energy Model (PEM) and VoltageCurrent Model (VCM), which represent battery behavior without considering the complexity of electrochemical processes [20,21]. The PEM treats the battery as a simple energy reservoir, disregarding its internal details. Although its accuracy is limited, this model is easy to implement and computationally efficient, making it suitable for preliminary studies and for long-term planning. Regarding power flow optimization (PFO) algorithms, researchers may employ predefined rule-based methods [22,23], mathematical optimization techniques such as linear programming [24,25], heuristic methods such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) [26–28] or artificial intelligence algorithms such as machine learning and Model Predictive Control (MPC) [29,30]. These scheduling strategies seek to determine the optimal operation of PVBESS systems, considering objectives such as cost minimization, profit maximization, and grid impact reduction. Finally, studies addressing the optimal sizing of PV-BESS systems may employ deterministic methods that use mathematical models to determine the optimal system size [31] or stochastic methods that account for uncertainties in demand, PV generation, and electricity prices [32]. BESS applications have been extensively studied for various types of installations, ranging from residential households and microgrids to industrial facilities [33,34]. In commercial and industrial settings, where the stability and continuity of electricity supply are critical, BESS provides a flexible solution with significant advantages, such as electricity cost reduction and greater grid independence [35]. In addition to enhancing competitiveness, this contributes to the achievement of SDGs 7 and 11. Table 1 presents a literature review on renewable energy management with batteries, detailing the load type, the sized elements, the type of electricity tariff and the method and objective function used to solve the PFO. Energy tariffs are typically time-of-use, with or without demand charges. These tariffs, along with RTP tariffs, are particularly relevant because electricity prices vary according to the time of consumption, thereby enabling BESSs to perform energy arbitrage. However, the cost of power demand is often overlooked in the context of electricity expenses, despite its significance in the C&I sector. Capacity-based demand tariffs penalize the consumption of power exceeding the contracted level, facilitating distribution grid capacity planning and encouraging the consumption of high-power levels outside peak hours [48,49]. The most commonly used scheduling method is rule-based, which is easy to implement but provides limited results compared to other methods. The objective functions formulated using this method include self-consumption maximization and peak shaving. More advanced methods (GA, PSO, MPC, etc.) have been applied in the literature, allowing the formulation of more complex objective functions, such as minimizing energy costs and demand charges, maximizing benefits, or minimizing battery degradation costs. Regarding battery degradation, very few studies have incorporated it into PFO resolution. This aspect is highly significant, as battery degradation models allow the optimization of battery operation to minimize degradation and maximize long-term performance, considering factors such as depth of discharge (DOD), charging and discharging rates, and operating temperature [50]. However, although the strategies in Table 1 have been studied and proven effective, they may be limited when applied in isolation. There is a growing need for more comprehensive approaches that consider both the technical and economic aspects of PV-BESS systems, as well as other factors related to the achievement of SDGs 11 and 12, such as environmental impact and battery lifespan [51]. Moreover, the available literature predominantly focuses on the sizing of the PV +BESS system as a whole. This approach offers a distinct advantage, as it enables the simultaneous optimization of both systems. However, it is also of interest to design methodologies applicable to loads with existing PV systems that intend to add a BESS. This study proposes a novel energy management strategy that addresses the limitations of traditional approaches by integrating three fundamental elements: energy arbitrage, demand charge reduction, and battery aging. Unlike existing literature, this strategy not only focuses on Table 1 Main characteristics of the literature review of photovoltaic systems with storage connected to grid. Ref. Load type Sized element Electric tariff Scheduling optimization Energy cost Demand cost Method Objective [24] Residential N/A TOU Peak based Convex optimization Minimize energy and demand costs [26] Residential and commercial PV +BESS N/A N/A GA Max. self-consumption [28] Residential BESS TOU N/A PSO Maximize benefits [36] Distribution network PV +BESS N/A N/A Rule-based Peak shaving [37] Residential BESS Flat rate N/A Rule based Max. self-consumption [38] Hybrid BESS TOU N/A GA Max. self-consumption, min. payback period and min. transportation losses [39] Residential PV +BESS TOU N/A MILP Minimize energy and degradation cost [40] Commercial PV +BESS TOU Peak based DP Minimize energy and demand charges [41] Residential N/A N/A N/A MPC Minimize energy cost and battery degradation [42] Industrial PV +BESS RTP N/A MILP Minimize operational costs and CO2 emissions [43] Commercial PV +BESS TOU and flat rate N/A MINLP Minimize life-cycle costs [44] School building PV +BESS Flat rate Capacity based HOMER [45] Minimize peak load demand [46] Commercial PV +BESS RTP N/A Rule based Minimize peak demand load and energy costs [47] Commercial PV +BESS Flat rate Peak based Rule based Minimize demand capacity violation and maximize selfconsumption This work Commercial BESS TOU Capacity based MILP Minimize energy, demand and BESS degradation cost C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 3 peak shaving and self-consumption, but also incorporates an economic valuation of demand charge reduction. This approach, based on mixedinteger linear programming (MILP), enables the optimization of the contracted power, minimizing the demand-associated costs. Secondly, the methodology is applicable to facilities that already possess photovoltaic generators and wish to upgrade their facilities with a BESS of optimal size. Finally, the cost of battery degradation must be taken into consideration, for it brings key benefits in terms of environmental and economic impact. Indeed, extending the battery’s useful life will result in greater profitability and a lower environmental impact. The cost of BESS degradation is estimated based on an LFP battery degradation model that considers the non-linearities of this phenomenon. In summary, this study seeks to contribute to advancements in intelligent energy management by proposing an innovative strategy that enhances the profitability of PV-BESS systems in high-consumption facilities (C&I, hotels, etc.), incorporating the economic valuation of demand charge reduction, energy arbitrage, and battery degradation. 2. Methodology 2.1. General description This study proposes a complex energy management strategy that considers installation constraints, electricity tariff structures, and battery modeling and degradation. Fig. 1 presents a flowchart illustrating the methodology used to develop the BESS management strategy. Based on the generation and consumption data of the installation, the system was modeled using energy balances and constraints. In this case, a PEMtype BESS model was used because of its balance between accuracy and simplicity. The algorithm first verifies whether the contracted power Pc is optimal. If not, a one-year BESS operation simulation is performed (as shown by the dotted line) to determine the battery’s energy dispatch. Based on the battery operation data, the contracted power is optimized to minimize the combined cost of excess demand charges (CPE) and contracted power charges (CCP). Once the contracted power is optimal, the BESS operation is simulated for its entire lifespan (as shown by the dashed line). Simulation time is discretized in H optimization horizons and N time steps, where ∀ h=0,1,2…,H−1 and ∀k=0,1,2…,N−1. The scheduling method aims to minimize the combined cost of energy (CE), battery degradation (Cbd) and excess power penalties within a MILP optimization framework. This simulation assumes that the PV generation and consumption data are known and match the monitored values. The battery degradation model developed in [50] for lithium-ion technologies was used to estimate the loss of service life after each optimization horizon. When the BESS model nb reaches the end of its lifespan (EOL), the same steps are applied to the next battery model until the simulation of the Nb BESS models is completed. In the final part of the algorithm, a techno-economic study is conducted to analyze the key parameters of each BESS, such as the selfconsumption and self-sufficiency rates (SCR and SSR, respectively), lifespan duration, average annual cost (AAC), and net present value (NPV). These metrics are used to assess the performance of the proposed scheduling method, which is compared with other approaches to demonstrate that this integrated solution enhances investment Fig. 1. Methodology workflow. C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 4 profitability while reducing pressure on the power grid and extending the BESS lifespan. 2.2. Modeling of the system 2.2.1. Energy balances The modeled system corresponds to a high-consumption facility which includes a pre-installed PV generator and a lithium-ion battery energy storage system. The selected BESS technology is lithium iron phosphate (LFP), as this type of battery combines a competitive cost with highly advantageous technical characteristics, such as a high depth of discharge, excellent stability, and long cycle life [52]. The proposed battery coupling is implemented on the AC side through a bidirectional inverter (BDI), which is integrated into the BESS battery management system (BMS). Fig. 2 presents the system diagram. Fig. 2 also illustrates the system’s power flows, with nomenclature established according to IEC Standard 61724-1 [53]. The energy balance in the AC bus is expressed in Eq. (1), where the power demand PL equals the sum of the photovoltaic generation PAac, the net power flows of the battery (PFPac −PTPac), and the net power exchange with the grid (PFGex + PFG −PTG). The term PFGex represents the surplus imported power that exceeds the contracted capacity. Pk|h L=Pk|h Aac +Pk|h FGex +Pk|h FG −Pk|h TG +Pk|h FPac −Pk|h TPac (1) The BESS incorporates a BDI, which introduces power losses. Eqs. (2) and (3) describe the BDI’s energy balance, where the battery’s charged and discharged power in direct current is calculated based on the exchanged power in AC and the BDI efficiency η BDI. Pk|h FS =Pk|h FPac/ η BDI (2) Pk|h TS =Pk|h TPac η BDI (3) The battery’s state of charge (SOC) depends on the power it exchanges in direct current with the BDI, as well as on its inherent charging and discharging losses. The battery’s energy balance, presented in Eq. (4), accounts for these losses along with those associated with battery efficiency η bat. SOCk|h=SOCk−1|h+Pk|h FS Δt Eh bat  η bat √−Pk|h TS  η bat √Δt Eh bat (4) Eh bat =E0 bat (1−SOHh)(5) The actual battery capacity Eh bat, computed as detailed in Eq. (5), is estimated at the end of each optimization horizon based on its initial capacity E0 bat and its state of health SOHh. The roundtrip efficiency is defined as the ratio between the energy charged and the energy discharged by the battery, as expressed in Eq. (6). The battery efficiency is considered to be 90 %, while the BDI efficiency is 97 %, yielding a roundtrip efficiency of 85 %, which is an accepted value for lithium-ion batteries [54,55]. η rt =Pk|h FPac Δt Pk|h TPac Δt=Pk|h FS η BDI Δt Pk|h TS Δt/ η BDI = η bat η 2 BDI (6) The following section presents the constraints applied in this model to both power flows and battery state of charge. 2.2.2. Restrictions Regarding the power supplied by the grid, it is constrained to be lower than the contracted power PC and higher than the feed-in limitation PTG,max, as specified in Eqs. (7) and (8) respectively. Eq. (9) expresses the constraint on the excess imported power from the grid PFGex, which is limited by the maximum possible demand surplus, PFGex,max. The binary variable iG indicates whether energy is imported from or injected into the grid. 0≤Pk|h FG ≤PCik|h G(7) Pk|h TG,max (1−ik|h G)≤Pk|h TG ≤0 (8) 0≤Pk|h FGex ≤Pk|h FGex,max ik|h G(9) The power exchanged by the battery is constrained by its maximum charging power, denoted as PTPac,max, and its maximum discharging power, represented as PFPac,max. The binary variable iS, as defined in Eqs. (10) and (11), determines the charging or discharging state. 0≤Pk|h FPac ≤Pk|h FPac,max ik|h S(10) Pk|h TPac,max (1−ik|h S)≤Pk|h TPac ≤0 (11) The maximum depth of discharge of the battery is in the range of 90–100 %. However, to ensure a longer lifespan, the minimum and maximum state-of-charge are limited [56]. These constraints are expressed in Eq. (12). SOCmin ≤SOCk|h≤SOCmax (12) Additional constraints in the model arise from the type of tariff considered, including the number of TOUs and associated costs. Information regarding the tariff structure and its cost components is detailed in the following section. 2.2.3. Tariff structure Access tariffs applied to high consumption facilities are designed for high-voltage supplies, that is, those with a voltage exceeding 1 kV but lower than 30 kV. It is primarily used by companies and industries with high electricity consumption and costs vary according to different periods of use [48].The main costs associated with these tariffs are the following [57]. •Consumed energy: This refers to the amount of electricity drawn from the grid during a given period. A unit energy charge cE is applied per kWh consumed, resulting in a total energy cost CE, as expressed in Eq. (13). Ch E=∑ N−1 k=0(Pk|h FG +Pk|h FGex)ck|h EΔt(13) •Contracted power: This is the maximum electrical power that can be drawn at any given time without incurring penalties. A unit power charge PTp is applied per kW contracted annually, depending on the selected TOU period. The total contracted power cost CCP is calculated according to Eq. (14) by multiplying the annual power cost by + … S Fig. 2. Schematic diagram of the case study. C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 5 the contracted power in each period PC,p and the fraction of time that the TOU period applies on a yearly basis fp. Ch CP =∑ PN p=1 PTpPC,pfh p(14) •Power excess penalties: This tariff allows electricity consumption to exceed the contracted power. However, any excess is subject to a surcharge that depends on the excess power PFGex and the period p in which it occurs. The excess power cost CPE, calculated using Eq. (15), applies an excess power charge tep and a multiplying factor Kp that increases with grid congestion. Ch PE =∑ PN p=1 Kptep  ∑ N−1 k=0(Pk|h FGex,p)2 √ √ √ √(15) 2.3. Scheduling method Defining the objective function is essential, as it dictates the energy management strategies of the BESS. In this study, the primary strategies implemented through the MILP PFO include energy arbitrage, peak shaving, and efficient battery utilization, as expressed in objective function (16). min{Ch E+Ch PE +Ch bd}(16) Energy arbitrage enables a reduction in the cost of the consumed energy, which contributes to the amortization of the BESS. Minimizing peak power surcharges, CPE, is a key factor in the industrial sector, as this component can represent a significant portion of the total electricity bill. Furthermore, recurrent power consumption that exceeds the contracted capacity disturbs the electrical grid, and the impact becomes more detrimental as network congestion increases. Consequently, incorporating this term into the objective function enhances grid utilization efficiency. Given that the BESS is a high-cost component, its rational use is crucial. To ensure this, the battery degradation cost term, Cbd, was included and calculated according to Eq. (17) as the product of the discharged energy and the specific degradation cost, cbd. This parameter represents the average degradation cost of the BESS per unit of discharged energy from its commissioning to the optimization period h, as defined in Eq. (18). In this equation, Cbat denotes the acquisition cost of the BESS, while fbat, obtained from Eq. (19), corresponds to the fraction of the BESS’s lifetime consumed during its operational period. Ch bd =∑ N−1 k=0 Pk|h FPac ch bdΔt(17) ch bd =fh−1 bat Cbat ∑ H−1 h=0∑ N−1 k=0 Pk|h FPacΔt (18) fh bat =1−SOHh 1−SOHEOL (19) The battery’s state of health, SOHh, is determined at the end of each optimization horizon by applying the semi-empirical model developed in [50], which accounts for nonlinearities in battery degradation. This model estimates lithium-ion battery degradation due to aging and cycling based on the contribution of various operating parameters, namely the time of operation, battery temperature, number of cycles, depth of discharge and average state of charge. These cycle-related factors are calculated according to the rain-flow counting algorithm (RFC). The accuracy of the model was demonstrated by a 3 % error in capacity estimation at the end of life of the BESS, which makes it suitable for application in this work. This objective function is applied for each optimization period, a critical factor for the model. For instance, an extended optimization horizon will result in a greater computational load and an underestimation of battery degradation. On the other hand, an optimization horizon that is very limited in scope would necessitate the execution of a substantial number of loops. This would result in a diminished effectiveness of the optimization strategies, given that the PFO algorithm would operate within a very short timeframe. In this case, an optimization period of one week has been selected, a value that balances moderate computational load, minimal overestimation of battery capacity, and shortand medium-term optimization capacity. 2.4. Contracted power optimization Contracted power directly influences demand charges, including costs both contracted and excess power. However, because the contracted power cannot be modified on a weekly basis, it is not included in the scheduling method as an optimization variable. Therefore, the optimization function for contracted power is applied to a full year of BESS operation at the start of its service life. To simplify the problem, it was assumed the same contracted power for all the TOU periods. To determine the optimal contracted power for each battery model, a one-year operation should be simulated by sweeping across different contracted power levels and selecting the one that results in the lowest demand cost, as shown in Eq. (20). However, this approach would entail a very high computational time, as it would require simulating an entire year of operation for each BESS size and PC value separately. min{Ch CP +Ch PE}(20) To improve computational efficiency, we first simulated the BESS’s one-year operation using the current contracted power. Subsequently, we calculated demand charges for different contracted power levels, assuming that the power flow remained constant. This simplification is justified because the sum of energy and battery degradation costs is significantly higher than the excess power cost in the scheduling method’s objective function. Consequently, we can assume that the dispatched energy does not change significantly when the contracted power is modified. As a result, simulating a year of BESS operation proved adequate for assessing various contracted power levels. During this evaluation, the initial PC is set equal to the annual maximum value of PFG, and this value is gradually reduced in 1 kW increments until the contracted power that minimizes demand costs is identified. 2.5. Techno-economic assessment The results of the simulation of each battery model’s performance must be assessed to identify potential advantages and disadvantages of the proposed energy management method compared to other methodologies. From a technical perspective, the parameters of selfconsumption and self-sufficiency have been selected. As detailed in Eq. (21), SCR facilitates the assessment of the use of the generated photovoltaic energy, either directly (PPVd) or via the battery (PPVbat). On the other hand, SSR represents the contribution of the photovoltaic generator to the total energy consumption of the facility (PL), and its formula is described in Eq. (22). SCR =∑ H−1 h=0∑ N−1 k=0 Pk|h PVdΔt+Pk|h PVbatΔt ∑ H−1 h=0∑ N−1 k=0 Pk|h AacΔt (21) SSR =∑ H−1 h=0∑ N−1 k=0 Pk|h PVdΔt+Pk|h PVbatΔt ∑ H−1 h=0∑ N−1 k=0 Pk|h LΔt (22) C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 6 The economic assessment of the BESS can be conducted using parameters such as the levelized cost of electricity (LCOE), net present value (NPV), and discounted payback period (DPB) [58]. In this study, the NPV has been determined using Eq. (23) to assess the profitability of investing in various battery models. The initial investment is considered to be the cost of the battery, while the cash flow consists of savings from the energy component (SE), savings from peak power shaving (SPE) and savings on contracted power (SCP), which are determined according to Eqs. (24), (25) and (26), respectively. The savings are calculated by comparing the initial scenario (PV) with the solution that integrates a BESS (PVB). Annual operation and maintenance expenses (CO&M) are also considered in the profitability analysis. NPV = − Cbat −CO&MyEOL +∑ H−1 h=0 Sh E+Sh PE +Sh CP (1+dr)yh(23) Sh E=Ch E,PV −Ch E,PVB (24) Sh PE =Ch PE,PV −Ch PE,PVB (25) Sh CP =Ch CP,PV −Ch CP,PVB (26) where yh indicates the number of years elapsed since the investment in the BESS and yEOL represents the battery’s service life in years. 3. Case description The facility under study is a campsite covering an area of 5 ha, located in the province of Malaga, Spain. The site is connected to the grid and includes a monocrystalline silicon photovoltaic generator with an installed capacity of 204 kW. The photovoltaic modules are arranged in 30 strings (15 per inverter), all sharing the same orientation and tilt. The inverters lack terminals for battery connection, making it impossible to couple the BESS with direct current. The dataset analyzed in this study comprises a full year of operation, recorded in 2023 with a 5-min resolution. The photovoltaic generation Fig. 3. Average values of photovoltaic generation and consumption aggregated by hour and season. Fig. 4. Power and energy of excess demand peaks aggregated by month. C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 7 and consumption data are presented in Fig. 3, aggregated by season and hour. The average values of PV generation follow a bell-shaped curve, as is typically observed in photovoltaic fields with a fixed orientation. During spring and summer (April–September), this curve is higher and wider than in autumn and winter (October–March), as a consequence of higher irradiance and number of sunlight hours. As a result, daily photovoltaic generation is on average 50 % greater in spring and summer (1.04 MWh) compared to autumn and winter (0.69 MWh). The average daily energy consumption in winter (1.8 MWh), spring (1 MWh), summer (1.6 MWh) and autumn (1.2 MWh) varies significantly depending on the season. During autumn and winter, the consumption profile exhibits two pronounced peaks, which coincide with the hours when the guests remain on the campsite. In winter and summer, energy consumption is particularly high because of increased heating and air conditioning demand. For the remainder of the year, the consumption profile shows lower nighttime values and little variability throughout the day. The intersection of the photovoltaic generation and consumption curves depicted in Fig. 3, representing photovoltaic self-consumption, demonstrates a high self-consumption rate in winter (65 %), spring (48 %), summer (69 %) and autumn (61 %). Higher values recorded in winter and summer are due to increased energy consumption in these months. Self-sufficiency values for winter (26 %), spring (50 %), summer (45 %) and autumn (31 %), reveal that the lowest SSR is achieved in winter and autumn, as a result of lower photovoltaic generation. On the other hand, Fig. 4 illustrates the power peaks that exceed the contracted power, showing their maximum surplus and the aggregated energy demand by month. The highest consumption peaks occur from January to March, with power levels near 90 kW and energy use exceeding 200 kWh. During the remainder of the year, consumption peaks occur infrequently, and involve reduced power and energy levels. These significant excesses in the consumed power underscore the necessity of optimizing the contracted power and mitigating the penalties linked to these demand surpluses. Regarding the tariff structure, 6.1TD tariff is used, which operates with a three-phase 400 V network and a contracted power of 125 kW [57]. It is divided into six TOU periods throughout the day and month, which vary according to the season and aim to reflect different energyconsumption patterns. P1 corresponds to the period of highest demand, and P6 represents the period of lowest demand. Fig. 5 shows the hours and months in which each billing period is applied. The prices of both energy and contracted power differ across periods, being higher when the grid is more congested. Therefore, this is a timeof-use tariff with capacity-based demand charges (TOU +DC). The costs associated with the tariff, corresponding to the year 2024, are available in Supplementary Document 1 [59]. 4. Results and discussion The innovative scheduling method proposed in this study integrates the concepts of peak shaving, energy arbitrage, and power excess reduction while also considering battery degradation. The main technoeconomic parameters used in the simulation of the BESSs are shown in Table 2. Parameters and values related to the battery degradation model are available in the Supplementary Document 2. The operation of the photovoltaic system with battery storage (PV +BESS) was optimized by formulating a MILP problem in the MATLAB environment. This problem was solved with the intlinprog solver, available in the MATLAB Optimization Toolbox. To evaluate the performance of the proposed scheduling method, three case studies are considered, whose main characteristics are presented in Table 3. In the first case, the proposed algorithm (S1) was applied to a series of 8-h lithium-ion batteries, with capacities ranging from 20 to 500 kWh. These values were selected as they fall within the range of the average daily values of imported grid energy (892 kWh) and photovoltaic excess (344 kWh), both of which are significant factors in the operation of the BESS [63]. In the other two case studies, two distinct scheduling algorithms were considered: one whose objective function is to maximize self-consumption [64] and another whose objective function is to minimize the cost of energy drawn from the grid [65]. These two alternative methods (denoted S2 and S3, respectively) were evaluated Fig. 5. Distribution of TOU periods by hour and month of the electric tariff. Table 2 Main techno-economic parameters. Symbol Value Reference Cbat 2198.60 € /kW [55] CO&M6.625 € /kW [55] Δt5 min – dr5.58 % [60] ir2.80 % [61] SOCmin 20 % [62] SOCmax 80 % [62] SOH0100 % – SOHEOL 80 % – Table 3 Case studies definition. Scheduling method Optimization method Objective function BESSs size (kWh) S1 MILP min{CE,Cbd,CPE}20–500 S2 Rule-based max{SCR}200 S3 MILP min{CE}200 C. Gilabert-Torres et al. Journal of Energy Storage 139 (2025) 118858 8 for a 200 kWh BESS, with the aim of identifying how the applied PFO algorithm influences performance metrics. 4.1. Proposed scheduling algorithm The operation of 8-h BESSs with capacities ranging from 20 to 500 kWh was simulated throughout their useful life using the method developed in this study. To analyze the results, cases where the battery size was 100, 300, and 500 kWh were considered. Fig. 6 shows the distribution of the grid-consumed power throughout the useful life of the BESSs, segregated by usage time periods. A reduction in the demanded power is observed for BESSs with larger capacities, with the median decreasing between 6 % and 56 % for the 100 kWh and 500 kWh cases. However, this reduction is significantly higher during the TOU periods with higher demand: the median and mean of the demanded power decreases by 65 % and 64 % for P1, 68 % and 35 % for P2, and 100 % and 59 % for P3, for the 300 kWh BESS. These results demonstrate a modest increase in efficiency compared to the data obtained by analogous PFOs that aim to reduce energy and demand costs. Research has demonstrated that these PFOs have the capacity to reduce power demand by an average of 34 % during periods of maximum demand [66]. This figure also shows the number of excess demand peaks that exceeded the contracted power for the selected BESSs. As the battery Fig. 6. Grid power demand distribution by TOU for different BESSs sizes. Fig. 7. Grid energy demand distribution by power demand and TOU. C. Gilabert-Torres et al. 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