Economic assessment of battery energy storage systems for frequency regulation reserve provision: A case study of the Dominican Republic

Contents lists available at ScienceDirect Energy for Sustainable Development journal homepage: www.journals.elsevier.com/energy-for-sustainable-development Economic assessment of battery energy storage systems for frequency regulation reserve provision: A case study of the Dominican Republic Emely Cruz-De-Jesús ∗, José Luis Martínez-Ramos , Alejandro Marano-Marcolini , Antonio Gómez-Expósito Dept. of Electrical Engineering, Universidad de Sevilla, Camino de los descubrimientos, Seville, 41092, Andalusia, Spain A R T I C L E I N F O Keywords: Battery energy storage system Economic dispatch Frequency regulation Unit Commitment A B S T R A C T This paper presents an economic assessment of the integration of battery energy storage systems for providing frequency regulation reserves in island power systems that are undergoing a transition to a decarbonized energy mix. The Dominican Republic system is used as a paradigmatic case study. The study employs actual data from 2022 and multiple mixed-integer linear programming optimization models to evaluate the operational and frequency regulation provision costs in different scenarios, both with and without accounting for the contribution of the storage systems to primary and secondary frequency regulation. The findings indicate that the integration of battery energy storage systems can lead to a reduction in annual operational costs of 10%, and enhance the penetration of renewable energy by 12% for 2030. Moreover, the economic analysis reveals that currently, the payback period for such investments is less than one year for primary frequency regulation and less than two years for secondary frequency regulation. The results highlight the dual benefits of storage systems in enhancing grid stability and supporting the integration of renewable energy, thus contributing to a more sustainable and resilient power system. Abbreviations BESS Battery Energy Storage System ESS Energy Storage System FR Frequency Regulation ICE Internal Combustion Engine ISO Independent System Operator MILP Mixed Integer Linear Programming NIES National Interconnected Electrical System PFR Primary Frequency Regulation RES Renewable Energy Sources SFR Secondary Frequency Regulation UC Unit Commitment ∗Corresponding author. E-mail address: [email protected] (E. Cruz-De-Jesús). Introduction Conventional power plants have traditionally been used to provide frequency regulation services in electric power systems. By offering this ancillary service, these plants are required to operate below their maximum generation capacity in order to maintain a regulation reserve band. As the proportion of Renewable Energy Sources (RES) in the global electricity generation mix continues to grow, Battery Energy Storage Systems (BESS) are emerging as promising candidates to provide frequency regulation services (Datta, Kalam, & Shi, 2021). These systems enable optimal operation of RES and conventional plants by fully leveraging their ability to supply demand without the need for dedicated frequency regulation reserves (Gomez & Hermana, 2019). BESS for frequency regulation (general case studies) The rapid responsiveness of BESS, characterized by activation times less than one second, along with their ability to manage significant power fluctuations, are attributes that make them attractive for frequency regulation applications (Prakash et al., 2022), as well as for additional fast response services (He, King, Luo, Dooner, Li, & Wang, https://doi.org/10.1016/j.esd.2025.101749 Received 27 January 2025; Received in revised form 7 May 2025; Accepted 8 May 2025 Energy for Sustainable Development 88 (2025) 101749 Available online 4 June 2025 0973-0826/© 2025 The Authors. Published by Elsevier Inc. on behalf of International Energy Initiative. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ). E. Cruz-De-Jesús et al. 2021). For example, in Shin et al. (2022), a BESS is integrated with a steam turbine generator to improve the primary frequency control, leading to a better response under load changes. The study in Arrigo, Bompard, Merlo, and Milano (2020) assesses how BESS influences the primary frequency control within the electrical system. The performance of BESS, measured by an effectiveness index reliant on the inertia level of the system and the type of frequency fluctuation, was determined to compare favorably to fast turbine governors and surpass that of traditional power plants. Economic viability assessments of BESS Numerous research papers have explored the use of BESS for frequency regulation, energy arbitrage, and various ancillary services. In Rancilio, Filippo, and Merlo (2022) analyzed the techno-economic evaluation of a BESS participating in the Fast Reserve, also a multiservice case, where the BESS participates in the balancing market for the provision of replacement reserve in the Italian market with positive benefits for the grid operator, and the author suggested as promising future the participation of BESS in the Automatic Frequency Restoration Reserve. Also, in Yu, Zhu, Liang, Chen, and Xiong (2023), the BESS is used to participate in an ancillary emergency backup service, which has proven to be more profitable than participating in the spot market for real-time balancing. In Maluenda, Córdova, Lorca, and NegretePincetic (2023), a chance-constrained stochastic model is presented for the optimal operation scheduling of a PV-BESS-Electrolyzer system contributing to energy and ancillary services markets. BESS integration within island grid systems Island power systems present unique challenges and opportunities to integrate renewable energy with the aid of BESS (Amiruddin, Liebman, Dargaville, & Gawler, 2024). In Pombo, Martinez-Rico, and Marczinkowski (2022) evaluated three scenarios of renewable energy integration and generation and storage expansion planning, defined as business as usual, optimal, and 100% renewable scenario, using a diversified energy mix including BESS, using São Vicente Island, Cape Verde in Africa as a case study. The objective was to minimize investment costs, emissions, and operation and maintenance. Among the results, it is mentioned that the optimal scenario is better compared to the others in terms of cost and emissions reduction and avoids oversizing. Similarly, the study in El-Bidairi, Nguyen, Mahmoud, Jayasinghe, and Guerrero (2020) explores the optimal size of a BESS on Flinders Island, demonstrating that the extent of RES penetration depends on the size of the BESS. Unit Commitment (UC) as a tool for optimal operation Several studies have used UC as a key tool to analyze the provision of frequency regulation reserves in power systems. For example, in Zhang et al. (2021), a frequency response model is proposed for the purpose of analyzing frequency stability. The model incorporates conventional units (hydro and thermal plants), wind generation, and BESSs. The UC is explicitly modeled to reflect the critical dependence of system inertia on the committed conventional units during each programming period. The results demonstrate the computational efficiency and utility of this model for the behavioral analysis of frequency response. Similarly, in Hao et al. (2020), UC is employed to assess the impact of incorporating a significant share of wind generation in the PFR. The results of the UC analysis were used to identify highrisk scenarios involving demand, generation, and disturbances, which were then evaluated in terms of frequency stability under specific commitments, taking into account load shedding and wind generation curtailment as part of the PFR strategies. This integrated UC model guarantees the safe and cost-effective operation of the power grid in light of the findings presented in the study. Contributions and organization This study investigates the economic impact of BESS in providing PFR and SFR reserves within a medium-sized islanded power system, focusing specifically on the Dominican Republic’s National Interconnected Electrical System (NIES). The analysis considers BESS participation in frequency reserve provision, exploring two scenarios: standalone participation in PFR and SFR, and concurrent participation in both services. The BESS analyzed are stand-alone devices, not associated with generation plants. A UC model is utilized to evaluate the economic benefits to power system operations from various BESS configurations providing regulation reserves. The assessment encompasses multiple weekly demand and RES generation scenarios, considering the generation technologies currently employed in the NIES. The network is represented using a single-bus model. The principal contributions of this work, in comparison to the existing state of the art, are outlined below. •Economic Evaluation of BESS in Frequency Regulation with full Technical and Operational Constraints: In contrast to Lee and Kim (2019), a UC model is employed that includes all technical and operational constraints of thermal units, representing demand and renewable generation variations across different typical weeks of the year. Also this study analyzes the economic impact of BESS participation in frequency regulation services within the specific context of the NIES. •Perspective of the System Operator: Unlike López-Grajales et al. (2023) and Braeuer, Rominger, McKenna, and Fichtner (2019), which focus on benefits for individual agents or external investors, this study considers the independent system operator responsible for storage investment, evaluating the economic impact on weekly operating costs and the dispatch of all system units. •Reduction of System Operating Costs: Contrary to Pusceddu, Zakeri, and Castagneto Gissey (2021), which do not address the reduction of operating costs from a system-wide perspective, this work evaluates how BESS participation can decrease overall system operating costs. In Li, Xu, and Huang (2023), the combined use of BESS for peak and valley regulation and frequency regulation is investigated. A technical-economic evaluation is performed to select the best combination in technical and economic terms. In this model, the environmental benefits of BESS participation in frequency regulation are considered. •Real-World Application in an Island System: The island electricity system of the Dominican Republic is used as a case study, analyzing the inclusion of storage for frequency regulation and its contribution to system stability and the transition to a cleaner energy mix. To summarize, the aim is to assess the cost-effectiveness, from the Independent System Operator (ISO) perspective, of integrating BESS into island systems for PFR and SFR participation, with the Dominican Republic serving as a case study. The Dominican Republic is currently publishing regulations on BESS, specifically on its participation in the arbitrage service (Comisión Nacional de Energía, 2024a; Comisión Nacional de Energía, 2024b). In addition, at the end of 2024, it published a regulation on the participation of BESS in the frequency regulation, in which it sets a fixed annual incentive to reward investors for participating in this service (Superintendencia de Electricidad, 2024). While it is too early to assess the real reaction of investors to this incentive, this article presents another alternative in which the ISO itself installs BESS for frequency regulation, thereby fostering cost reductions in the operation of the system. This approach serves to encourage regulators and energy policymakers to explore other ways to diversify the energy matrix and reduce operating costs. Energy for Sustainable Development 88 (2025) 101749 2 E. Cruz-De-Jesús et al. The rest of the paper is organized as follows: Section ‘‘Business model’’ describes the business model of BESS participating in frequency regulation reserve provision, Section ‘‘Methodology’’ presents the methodology and mathematical formulation of the optimization problem; Section ‘‘Results and Discussion’’ explains how the case studies are selected and defined, and provides the results of the simulations and Section ‘‘Conclusions’’ summarizes the main conclusions of this work. Business model The energy and power ratings of the different storage technologies range between 1 kWh and more than 1 GWh, with power capacities between 1 kW and 300 MW (Energy Transition Expertise Centre (ENTEC), 2023). In particular, for ancillary services and transmission grid support applications, the capacities are between 1 MWh and 1 GWh. The provision of ancillary services, particularly reserve containment service, is the second most popular application of BESS, the first being energy arbitrage. Revenues from the participation in the ancillary service markets in countries such as Austria (76,000 euros/MW in 2020, and 190,000 euros/MW in 2021) make this applications attractive. Also in Hameed, Træholt, and Hashemi (2023) evaluated the prices of different frequency regulation service products in the Nordic countries from 2015 to 2020, including the hours and months when it is most profitable to participate in these services. They also estimate the revenues that would be received by BESS participating in frequency regulation services. Order 755, as issued by the US Federal Energy Regulatory Commission (FERC), requires that Independent System Operators (ISOs) and Regional Transmission Operators (RTOs) consider both speed and accuracy when designing compensation rates for frequency regulation services. It introduced the concept of ‘‘mileage’’, where service providers are paid based on the cumulative distance of upward and downward adjustments made during a service period. Recognizing the importance of speed and accuracy can significantly enhance the deployment of storage systems within the power grid (Tabari & Shaffer, 2020). An illustrative example can be found in You et al. (2022),where the primary frequency regulation revenues of the Energy Storage Systems (ESS) are calculated using the mileage concept. Secondary regulation compensation is performed using frequency control capacity compensation and frequency control mileage compensation. The results show that the addition of ESS reduces the investment cost of frequency regulation. In Lee and Kim (2019), a method is proposed to estimate the benefits of introducing ESSs to provide frequency regulation services in the Korean electricity markets. They also suggest that the compensation of ESSs for participating in frequency regulation should be calculated differently from conventional technologies, since BESSs have superior performance. The study examines three cases: daytime benefits for a one-year period, nighttime benefits, and all-day benefits. As in the preceding case, the results demonstrate that the involvement of ESSs in frequency regulation confers benefits to the system. Another approach is illustrated in Merten, Olk, Schoeneberger, and Sauer (2020). In this instance, a BESS linked to a virtual power plant (VPP) is employed to contribute to automatic frequency restoration reserve (aFRR) solely to provide upward reserve. The TSO initiates the BESS activation request according to a merit order list, which is sorted in accordance with the power bid price. The BESS also performs energy arbitrage while not participating in the aFRR. An estimation of the time series of aFRR requests is performed using SARIMA prediction models. The results showed that the strategies used are not economically feasible for the 2019 data, since the savings do not compensate for the costs of the BESS; for the 2025 predictions, the results seem to be economically viable for BESS working in conjunction with the VPP, but not as an independent resource. In Pusceddu et al. (2021), an economic evaluation of a BESS participating in Enhanced Frequency Response (EFR) and energy arbitrage is conducted using historical data from 2015 to 2018 of the power system in Great Britain. The findings indicate that a BESS with a capacity of 10 MW engaged in both markets generates profits that are 25% higher than those generated by participation in EFR alone. Furthermore, the results indicate that one of the key determinants of the profitability of BESS in this configuration is the energy-to-power (E/P) ratio, rather than the discharge efficiency. It was concluded that the optimal E/P ratio is between 1.5 and 2 h. Finally, in Nitsch, Deissenroth-Uhrig, Schimeczek, and Bertsch (2021), the profitability of BESS participation in the Day-Ahead (DA) market and aFRR is evaluated using a case study in the German market with data for 2019 and estimated prices for 2030. The results demonstrated that battery efficiency contributes only a minimal amount to annual revenue. Nevertheless, the capacity to provide energy in the short term represents the most lucrative opportunity, with revenue increasing in proportion to the simultaneous participation of BESS in different markets. Methodology This section is dedicated to the presentation of the models employed to quantify the cost associated with FR reserves and the savings that can be achieved through the utilization of distinct BESS configurations. Three dispatching models are employed. The first model seeks to meet demand while accounting for the technical limitations of generators, excluding the FR requirement (resulting in CM1 costs). The second model incorporates the PFR and SFR constraints, resulting in CM2 costs. Finally, the third model computes the total cost, considering the contribution of BESS to FR (resulting in CM3 costs). A weekly study horizon with hourly resolution is considered, with the objective of minimizing operating costs. Three optimization problems are constructed to describe the dispatching models. Each of these leads to a Mixed Integer Linear Programming (MILP) problem, which is implemented in GAMS using the CPLEX solver. The choice of MILP as an optimization methodology is mainly justified by its ability to handle complex problems involving both continuous and discrete decisions, which are common in energy, design and operation problems. Unlike other approaches such as Linear Programming (LP), which only deals with continuous variables, MILP allows the modeling of binary or integer variables, which is crucial in UC problems. In contrast, Non-Linear Programming (NLP) can struggle to find globally optimal solutions due to the presence of multiple local optima. MILP solvers, such as CPLEX and Gurobi, have been shown to be highly efficient at solving large problems in terms of variables and constraints, even in relatively short time. More details can be found in Putz, Schwabeneder, Auer, and Fina (2021) Alex et al. (2024), Olivos and Valenzuela (2025). Fig. 1 depicts the proposed methodology. The cost of implementing FR reserve constraints is calculated as the difference between the CM2 and CM1. System savings from implementing FR with the support from BESS are calculated as the difference between CM3 and CM2. Model assumptions and limitations The following assumptions and limitations have been considered for this study: •A single-bus model has been considered, which does not include the network constraints that can affect the daily operation of the system and increase operating costs. Additionally, power plants of the same technology have been grouped, which may imply a percentage of error with the actual scheduling that contains all the details of the network and individual generating units. Energy for Sustainable Development 88 (2025) 101749 3 E. Cruz-De-Jesús et al. Fig. 1. Methodology for evaluating savings in FR costs using BESS. •Deterministic demand and renewable generation profiles have been considered, so the impact of uncertainty on the model is not evaluated. •This study does not include the charging and discharging model of the BESS, as the objective is to evaluate the impact of BESS on the reserve for frequency regulation. According to Sargent (2024), a Li-ion battery typically degrades by 1.5% per year, assuming a full daily charge–discharge cycle. However, when regulating frequency, a BESS may not complete a full daily cycle, and the depth of discharge for this service is usually small, both of which positively affect the device’s degradation. Additionally, considering the projected reduction in battery energy costs presented in Sachs (2024), the impact of degradation costs will also gradually decrease over time. Mathematical formulation The three models are subject to a different block of constraints, contingent on the FR requirements of each case. Outlined below are the specific attributes of each model: •Model 1: Fig. 1 shows the constraints of CM1 and the choice of these constraints is due to the fact that this model aims to quantify only the cost of meeting the demand of the system, since this is an ideal case in which no power reserve is needed for the possible frequency variation. The decision variables of this model are the generator status of the conventional generator (𝑢𝑝𝑔 𝑡) whether it is on or off, the variable (𝑦𝑝𝑔 𝑡) that indicates the start-up of the traditional generator, variable (𝑧𝑝𝑔 𝑡) that indicates shut-down, the power output of each conventional generator (𝐺𝑝𝑔 𝑡) that includes the reservoir hydropower plant. •Model 2: The objective of the constraints of CM2 is to evaluate the cost of the system including the reserve constraints for the PFR and SFR, which are included in the system operation schedules for regulatory and system security reasons. The decision variables of this model are the generator status of the conventional generator (𝑢𝑝𝑔 𝑡), the variable (𝑦𝑝𝑔 𝑡) that indicates the start-up of the traditional generator, the variable of the 𝑧𝑝𝑔 𝑡 that indicates shut-down, the generation of each conventional generator 𝐺𝑝𝑔 𝑡 including the reservoir hydropower plant, the regulation reserve of conventional generators and reservoir hydropower plant participating in PFR (𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡) and the regulation reserve of the run-of-river hydropower plant (𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡) participating in PFR, and the regulation reserve of conventional generators participating in SFR (𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡) and the regulation reserve of the run-of-river hydropower plant (𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡) participating in SFR but in this case there are not plants of this type with available power for the SFR. •Model 3: The objective of the constraints of CM3 is to evaluate the impact of the BESS on the system reserve constraints, and how the operating cost is reduced by including the BESS. The objective is to evaluate the feasibility of the BESS in this service and whether it is of interest to the system. The decision variables of this model are the generator status of the conventional generator (𝑢𝑝𝑔 𝑡), the variable (𝑦𝑝𝑔 𝑡) that indicates the start-up of the traditional generator, the variable of the 𝑧𝑝𝑔 𝑡 that indicates shut-down, the power output of each conventional generator 𝐺𝑝𝑔 𝑡 that includes the reservoir hydropower plant, the regulation reserve of conventional generators and reservoir hydropower plant participating in PFR (𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡) and the regulation reserve of the run-of-river hydropower plant (𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡) participating in PFR, and the regulation reserve of conventional generators participating in SFR (𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡) and the regulation reserve of the run-of-river hydropower plant (𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡) participating in SFR but in this case there are not plants of this type with available power for the SFR. As it can be seen, the decision variable that directly affects in the objective function is the power output of the conventional power plant (𝐺𝑝𝑔 𝑡), as at the same time is affected for the variable of the power reserve that each power plant has for the frequency regulation (𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡), participating in PFR, and the regulation reserve of conventional generators participating in SFR (𝑅𝑟𝑠𝑓 𝑔𝑝𝑔 𝑡) in Model 2 and Model 3. Also, 𝐺𝑝𝑔 𝑡 is affected by the generation of renewable plants (𝐺𝑤𝑟𝑛 𝑡) in the three models. Due to the way frequency regulation compensation is handled in the Dominican Republic, these variables were not included in the objective function with an assigned price. A detailed formulation of the equations and description of each model is explained in the following paragraphs. •Sets 𝑡∈𝑇Hours of the study horizon where 𝑇= {𝑡𝑖∣𝑖∈Z,0≤𝑖≤168} ℎ𝑡∈𝑇Subset of hours of the study horizon where 𝑇= {𝑡𝑖∣𝑖∈Z,1≤ 𝑖≤168} 𝑑∈ℎ𝑡Where d is an alias of ℎ𝑡 𝑝𝑔 ∈𝑃 𝑔 Conventional generator where 𝑃 𝑔 = {𝑝𝑔𝑖∣𝑖∈Z,1≤𝑖≤19} 𝑟𝑛 ∈𝑅𝑛 Renewable generation technology where 𝑅𝑛 = {𝑟𝑛𝑖∣𝑖∈ Z,1≤𝑖≤4} •Parameters 𝐿𝑡Demand load at hour t [MW] 𝐶𝑟𝑟𝑛 𝑡Availability of renewable resources at hour t [MW] 𝑉 𝑃 𝐶𝑝𝑔 Variable production costs of generation plants [$/MWh] 𝑃 𝑚𝑖𝑛𝑝𝑔 Minimum power of generation plants [MW] 𝑃 𝑚𝑎𝑥𝑝𝑔 Maximum power of generation plants [MW] 𝑅𝑢𝑝𝑝𝑔 Ramp up rate [MW/h] 𝑅𝑑𝑤𝑝𝑔 Ramp down rate [MW/h] 𝑆𝑢𝑝𝑔 Start-up ramp [MW/h] 𝑆𝑑𝑝𝑔 Shut-down ramp [MW/h] 𝑂𝑛𝑝𝑔 Minimum up time [h] 𝑂𝑓 𝑓 𝑝𝑔 Minimum down time [h] 𝑈𝑎𝑝𝑔 Number of operating hours of the power plant 𝑝𝑔 at the beginning of the study [h] 𝑈𝑓𝑝𝑔 Number hours the power plant 𝑝𝑔 is out of operation at the beginning of the study [h] 𝑈𝑖𝑛𝑖𝑝𝑔 Initial condition of generators 𝑊𝑝𝑔 Number of hours that the plant must remain online during the first hours of the study horizon [h] Energy for Sustainable Development 88 (2025) 101749 4 E. Cruz-De-Jesús et al. 𝑁𝑝𝑔 Number of hours to be offline during the first hours of the study horizon [h] 𝐽Total hours of study horizon [h] 𝑀𝑟𝑝𝑓𝑝𝑔 Maximum generator PFR reserve [MW] 𝑀𝑟𝑠𝑓𝑝𝑔 Maximum generator SFR reserve [MW] 𝑀ℎ𝑝𝑓𝑟𝑛 Maximum run-of-river hydropower PFR reserve [MW] 𝑀ℎ𝑠𝑓𝑟𝑛 Maximum run-of-river hydropower SFR reserve [MW] 𝑃 𝑔𝑟𝑝𝑝𝑔 Generators’ participation in the PFR 𝑃 𝑔𝑟𝑠𝑝𝑔 Generators’ participation in the SFR 𝑃 ℎ𝑟𝑝𝑟𝑛 Participation of run-of-river hydropower in the PFR 𝑃 ℎ𝑟𝑠𝑟𝑛 Participation of run-of-river hydropower in the SFR 𝑃 𝑟𝑝𝑓 Total percentage of reserve for PFR [%] 𝑃 𝑟𝑠𝑓 Total percentage of reserve for SFR [%] 𝑃 𝑑𝑠𝑝 Battery power for PFR [MW] 𝑃 𝑑𝑠𝑠 Battery power for SFR [MW] 𝐶𝑚𝑔𝑐𝑡Short-term marginal cost at hour t [$] •Variables 𝑂𝐶 Total operating cost [$] 𝑢𝑝𝑔 𝑡Variable equal to one if the generator is in operation or zero if it is idle at hour t 𝑦𝑝𝑔 𝑡Variable equal to one if the generator is started up at hour t 𝑧𝑝𝑔 𝑡Variable equal to one if the generator is shut-down at hour t 𝐺𝑝𝑔 𝑡Power output of power plants at hour t [MW] 𝐺𝑤𝑟𝑛 𝑡Power output of renewable generator at hour t [MW] 𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡Maximum operating power of generators at hour t [MW] 𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡Regulation reserve of generators participating in PFR at hour t [MW] 𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡Regulation reserve of generators participating in SFR at hour t [MW] 𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡PFR regulating reserve of run-of-river hydropower plant at hour t [MW] 𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡SFR regulating reserve of run-of-river hydropower plant at hour t [MW] Constraints The objective function for the three models is specified in (1), while the constraints are elaborated upon subsequently. The objective function for the three models is as follows, 𝑂𝐶 =∑ 𝑡∈𝑇⧵{𝑡0}∑ 𝑝𝑔∈𝑃 𝑔 𝑉 𝑃 𝐶𝑝𝑔 ⋅𝐺𝑝𝑔 𝑡,(1) where 𝐺𝑝𝑔 𝑡 is the generation of each conventional plant 𝑝𝑔 at hour 𝑡, and 𝑉 𝑃 𝐶𝑝𝑔 is the variable production cost associated with each conventional plant. In models 2 and 3, the costs associated with the FR are implicitly included in Eq. (1) as the production of conventional plants is significantly constrained by FR requirements. •Generation-demand balance The balance between demand and generation for models 1 and 2 is established as follows: ∑ 𝑝𝑔∈𝑃 𝑔 𝐺𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛 𝐺𝑤𝑟𝑛 𝑡=𝐿𝑡,∀𝑡∈𝑇⧵{𝑡0},(2) Where 𝐺𝑤𝑟𝑛 𝑡 is the renewable generation at hour t, this generation belongs to the photovoltaic, wind, biomass and run-of-river hydropower plant, and 𝐿𝑡 is the hourly demand load. •Operating status of generation units The on or off status of each conventional power plant is determined by the variable 𝑢𝑝𝑔 𝑡, and 𝑦𝑝𝑔 𝑡 for the start-up, and 𝑧𝑝𝑔 𝑡 for the shut-down: 𝑦𝑝𝑔 𝑡−𝑧𝑝𝑔 𝑡=𝑢𝑝𝑔 𝑡−𝑢𝑝𝑔 𝑡−1,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (3) 𝑦𝑝𝑔 𝑡+𝑧𝑝𝑔 𝑡≤1,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔. (4) •Minimum up time constraints Likewise, Eq. (5) allows calculating the time that the plant must remain online if it has been in operation consecutively before the beginning of the study horizon. If the plant is started, it must remain online consecutively for 𝑂𝑛𝑝𝑔 hours; this dynamic is modeled in (6). In case it receives a startup during the last 𝑂𝑓 𝑓 −1 h, it must remain in operation until the final hour (7) (Arroyo & Conejo, 2000; Xie, Pinson, Xu, & Chen, 2024). Here, 𝑊𝑝𝑔 is the number of hours that the plant must remain online during the first hours of the study horizon, it follows that 𝑊𝑝𝑔 =𝑀𝑖𝑛 [𝐽, (𝑂𝑛𝑝𝑔 −𝑈𝑎𝑝𝑔)⋅𝑈𝑖𝑛𝑖𝑝𝑔]. 𝑂𝑛𝑝𝑔 is the minimum up time, 𝐽 is the total hours of the study horizon, 𝑈𝑎𝑝𝑔 is the number of hours that the conventional plants have been on operation at the beginning of the study, and 𝑈𝑖𝑛𝑖𝑝𝑔 is the initial condition of generators at 𝑢𝑝𝑔 𝑡0, for example, the plant can be in operation or offline at the beginning of the study. Also in the model, the output power of the generator at the beginning of the study 𝐺𝑝𝑔 𝑡0 can be specified, but this is not mandatory, it depends on the assumptions of the initial conditions. 𝑊𝑝𝑔 ∑ ℎ≥1[1 − 𝑢𝑝𝑔 ℎ]= 0,∀𝑝𝑔 ∈𝑃 𝑔, 𝑊 𝑝𝑔 ≥1,(5) ℎ+𝑂𝑛𝑝𝑔 −1 ∑ 𝑑≥ℎ[𝑢𝑝𝑔 𝑑]≥𝑂𝑛𝑝𝑔 ⋅𝑦𝑝𝑔 ℎ, ∀ℎ=𝑊𝑝𝑔 + 1...𝐽 −𝑂𝑛𝑝𝑔 + 1, 𝑊 𝑝𝑔 + 1 ≤𝐽−𝑂𝑛𝑝𝑔 + 1,∀𝑝𝑔 ∈𝑃 𝑔, (6) 𝐽 ∑ 𝑑≥ℎ[𝑢𝑝𝑔 𝑑−𝑦𝑝𝑔 ℎ]≥0,∀ℎ=𝐽−𝑂𝑛𝑝𝑔 + 2...𝐽 , 𝑂𝑛𝑝𝑔 ≥2,∀𝑝𝑔 ∈𝑃 𝑔. (7) •Minimum down time constraints Similarly, Eqs. (8)–(10) have the same objective as Eqs. (5)–(7), but in this case, it is the minimum time that the plant must be down when it goes offline (Arroyo & Conejo, 2000; Xie et al., 2024). Here, 𝑁𝑝𝑔 is the number of hours to be offline during the first hours of the study horizon, it follows that 𝑁𝑝𝑔 =𝑀𝑖𝑛 [𝐽 , (𝑂𝑓 𝑓 𝑝𝑔 −𝑈𝑓𝑝𝑔 )⋅(1 − 𝑈𝑖𝑛𝑖𝑝𝑔 )] where 𝑂𝑓 𝑓 𝑝𝑔 is the minimum down time, and 𝑈𝑓𝑝𝑔 is the number of hours the plant has been out of operation at the beginning of the study. 𝑁𝑝𝑔 ∑ ℎ≥1[𝑢𝑝𝑔 ℎ]= 0,∀𝑝𝑔 ∈𝑃 𝑔, 𝑁𝑝𝑔 ≥1,(8) ℎ+𝑂𝑓 𝑓𝑝𝑔 −1 ∑ 𝑑≥ℎ[1 − 𝑢𝑝𝑔 𝑑]≥𝑂𝑓 𝑓 𝑝𝑔 ⋅𝑧𝑝𝑔 ℎ, ∀ℎ=𝑁𝑝𝑔 + 1...𝐽 −𝑂𝑓 𝑓 𝑝𝑔 + 1, 𝑁𝑝𝑔 + 1 ≤𝐽−𝑂𝑓𝑓 𝑝𝑔 + 1,∀𝑝𝑔 ∈𝑃 𝑔 (9) 𝐽 ∑ 𝑑≥ℎ[1 − 𝑢𝑝𝑔 𝑑−𝑧𝑝𝑔 ℎ]≥0, ∀ℎ=𝐽−𝑂𝑓 𝑓 𝑝𝑔 + 2...𝐽, 𝑂𝑓 𝑓 𝑝𝑔 ≥2,∀𝑝𝑔 ∈𝑃 𝑔. (10) •Thermal power plant operational limits The maximum power of the generators depends on their previous and following status. For renewable plants, the minimum power is zero, and the maximum power depends on the hourly power availability of the resource. Here, the 𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡 is the variable that indicates the maximum operating power of generators, and 𝑃 𝑚𝑎𝑥𝑝𝑔 is a parameter that indicates the maximum technical power of generation plants, 𝑆𝑑𝑝𝑔 Energy for Sustainable Development 88 (2025) 101749 5 E. Cruz-De-Jesús et al. is the shut-down ramp of each generator, 𝑅𝑢𝑝𝑝𝑔 is the ramp up rate of each generator and 𝑅𝑑𝑤𝑝𝑔 is the ramp down rate, 𝑆𝑢𝑝𝑔 is the startup ramp, 𝑃 𝑚𝑖𝑛𝑝𝑔 is the minimum power of generation plants. The power output of the renewable generator is indicated by 𝐺𝑤𝑟𝑛 𝑡, and the availability of the resources each hour is indicated by 𝐶𝑟𝑟𝑛 𝑡. These constraints are established by 𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡≤𝑃 𝑚𝑎𝑥𝑝𝑔 [𝑢𝑝𝑔 𝑡−𝑧𝑝𝑔 𝑡+1]+𝑆𝑑𝑝𝑔 ⋅𝑧𝑝𝑔 𝑡+1, ∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (11) 𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡≤𝐺𝑝𝑔 𝑡−1 +𝑅𝑢𝑝𝑝𝑔 ⋅𝑢𝑝𝑔 𝑡−1 +𝑆𝑢𝑝𝑔 ⋅𝑦𝑝𝑔 𝑡, ∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (12) 𝐺𝑝𝑔 𝑡−1 −𝐺𝑝𝑔 𝑡≤𝑅𝑑𝑤𝑝𝑔 ⋅𝑢𝑝𝑔 𝑡+𝑆𝑑𝑝𝑔 ⋅𝑧𝑝𝑔 𝑡, ∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (13) 𝐺𝑝𝑔 𝑡≤𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (14) 𝐺𝑝𝑔 𝑡≥𝑃 𝑚𝑖𝑛𝑝𝑔 ⋅𝑢𝑝𝑔 𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (15) 𝐺𝑤𝑟𝑛 𝑡≤𝐶𝑟𝑟𝑛 𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, (16) When the reserve constraints for PFR and SFR are introduced, the minimum and maximum dispatch power of the operating plants change, respecting the technical limits of each plant, so that in models 2 and 3 (14)–(16) are changed to (17)–(20) respectively (Lagos & Hatziargyriou, 2021). Here 𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡 and 𝑅𝑟𝑝𝑓ℎ𝑝𝑔 𝑡 are the regulation reserve of generators participating in PFR, and 𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡 and 𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡 are the regulation reserve of generators participating in SFR. 𝐺𝑝𝑔 𝑡≤𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡−𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡−𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡, ∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (17) 𝐺𝑝𝑔 𝑡≥𝑃 𝑚𝑖𝑛𝑝𝑔 ⋅𝑢𝑝𝑔 𝑡+𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡+𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡, ∀𝑡∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, (18) 𝐺𝑤𝑟𝑛 𝑡≤𝐶𝑟𝑟𝑛 𝑡−𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡−𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡, ∀𝑡∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, (19) 𝐺𝑤𝑝𝑔 𝑡≥0 + 𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡+𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡,∀𝑡∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛. (20) •Generation reserve for frequency regulation The reserve for PFR and SFR that each generator can contribute is limited by its maximum reserve margin. The maximum generator PFR reserve is indicated by 𝑀𝑟𝑝𝑓𝑝𝑔 , and the maximum generator SFR reserve is indicated by 𝑀𝑟𝑠𝑓𝑝𝑔 , the same is for the renewable generator specifically run-of-river plants that are the one that participate in the frequency regulation with 𝑀ℎ𝑝𝑓𝑟𝑛 and 𝑀ℎ𝑠𝑓𝑟𝑛. This behavior is represented by, 𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡≤𝑀𝑟𝑝𝑓𝑝𝑔 ⋅𝑢𝑝𝑔 𝑡, 𝑡 ∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, 𝑃 𝑔𝑟𝑝𝑝𝑔 ≥1,(21) 𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡≤𝑀𝑟𝑠𝑓𝑝𝑔 ⋅𝑢𝑝𝑔 𝑡, 𝑡 ∈𝑇⧵{𝑡0},∀𝑝𝑔 ∈𝑃 𝑔, 𝑃 𝑔𝑟𝑠𝑝𝑔 ≥1,(22) 𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡≤𝑀ℎ𝑝𝑓𝑟𝑛, 𝑡 ∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, 𝑃 ℎ𝑟𝑝𝑟𝑛 ≥1,(23) 𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡≤𝑀ℎ𝑠𝑓𝑟𝑛, 𝑡 ∈𝑇⧵{𝑡0},∀𝑟𝑛 ∈𝑅𝑛, 𝑃 ℎ𝑟𝑠𝑟𝑛 ≥1.(24) The sum of the reserves of all generators must satisfy the minimum total margin required by the system for the PFR and the SFR where 𝑃 𝑟𝑝𝑓 and 𝑃 𝑟𝑠𝑓 are percentages imposed to maintain the reserve for the PFR and SFR at a certain level, that is, ∑ 𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑝𝑝𝑔 ≥1 𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑝𝑟𝑛≥1 𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡≥ 𝑃 𝑟𝑝𝑓 ⋅(∑ 𝑝𝑔∈𝑃 𝑔 𝐺𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛 𝐺𝑤𝑟𝑛 𝑡),∀𝑡∈𝑇⧵{𝑡0}, (25) ∑ 𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑠𝑝𝑔 ≥1 𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑠𝑟𝑛≥1 𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡≥ 𝑃 𝑟𝑠𝑓 ⋅(∑ 𝑝𝑔∈𝑃 𝑔 𝐺𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛 𝐺𝑤𝑟𝑛 𝑡),∀𝑡∈𝑇⧵{𝑡0}. (26) The contribution of the batteries to the primary and secondary regulation is described by (27)–(28), where the BESS is modeled with constant power, its contribution to the reserve for frequency regulation is added on the left-hand side of these equations. Here, the 𝑃 𝑑𝑠𝑝 is the contribution of the BESS to the PFR, and the 𝑃 𝑑𝑠𝑠 is the contribution of the BESS to the SFR. 𝑃 𝑑𝑠𝑝 +∑ 𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑝𝑝𝑔 ≥1 𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑝𝑟𝑛≥1 𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡≥ 𝑃 𝑟𝑝𝑓 ⋅(∑ 𝑝𝑔∈𝑃 𝑔 𝐺𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛 𝐺𝑤𝑟𝑛 𝑡), 𝑡 ∈𝑇⧵{𝑡0},(27) 𝑃 𝑑𝑠𝑠 +∑ 𝑝𝑔∈𝑃 𝑔,𝑃 𝑔𝑟𝑠𝑝𝑔 ≥1 𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛,𝑃 ℎ𝑟𝑠𝑟𝑛≥1 𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡≥ 𝑃 𝑟𝑠𝑓 ⋅(∑ 𝑝𝑔∈𝑃 𝑔 𝐺𝑝𝑔 𝑡+∑ 𝑟𝑛∈𝑅𝑛 𝐺𝑤𝑟𝑛 𝑡),∀𝑡∈𝑇⧵{𝑡0}.(28) •Short-term marginal cost This is not exactly a constraint, it is a calculation after the model has been run. For each hour of the scheduling horizon, the marginal cost is calculated as the VPC of the most expensive plant dispatched. The VPC of the most expensive thermal unit dispatched in each hour is given by Eq. (29), 𝐶𝑚𝑔𝑐𝑡=𝑀𝑎𝑥 [𝑃 𝑔, (𝐺𝑝𝑔 𝑡>0), 𝑉 𝑃 𝐶𝑝𝑔 ],∀𝑡∈𝑇⧵{𝑡0}.(29) To summarize, Model 1 is made up of the Eq. (1)–(2), (3)–(16) and (29). Model 2 is made up of the Eq. (1)–(2), (3)–(13), (17)–(26) and (29). Finally, Model 3 is made up of the Eq. (1), (2)–(13), (17)–(24) and (27)–(29). •Variable Domains 𝑂𝐶 ∈R 𝑢𝑝𝑔 𝑡∈ {0,1} ∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝑦𝑝𝑔 𝑡∈ {0,1} ∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝑧𝑝𝑔 𝑡∈ {0,1} ∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝐺𝑝𝑔 𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝑃 𝑚𝑎𝑥𝑝𝑔 𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝑅𝑟𝑝𝑓𝑔𝑝𝑔 𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝑅𝑟𝑠𝑓𝑔𝑝𝑔 𝑡∈R+∀𝑝𝑔 ∈𝑃 𝑔, ∀𝑡∈𝑇 𝐺𝑤𝑟𝑛 𝑡∈R+∀𝑟𝑛 ∈𝑅𝑛, ∀𝑡∈𝑇 𝑅𝑟𝑝𝑓ℎ𝑟𝑛 𝑡∈R+∀𝑟𝑛 ∈𝑅𝑛, ∀𝑡∈𝑇 𝑅𝑟𝑠𝑓ℎ𝑟𝑛 𝑡∈R+∀𝑟𝑛 ∈𝑅𝑛, ∀𝑡∈𝑇 Energy for Sustainable Development 88 (2025) 101749 6 E. Cruz-De-Jesús et al. Table 1 Key Statistics for the Dominican Republic in 2022. Population Load (GWh) Capacity (GW) GDP (M$) 10,760,028 22,143.59 5.08 114 Results and discussion This section presents the main characteristics of the data from the NIES system in the Dominican Republic used in this study. First, the NIES and its main figures are described. Then, the main results obtained for each case study are presented. Several case studies are proposed to investigate the impact of BESS on the cost of providing regulatory reserves. The case studies are evaluated using a combination of median demand and median availability profiles for solar, wind, and run-of-river hydro generation. These profiles are calculated for periods that include different months of the year (i.e., January–February, March–April, May–June, July–October, November–December). The Dominican Republic power system The National Interconnected Electricity System (NIES) of the Dominican Republic, an island in the Caribbean, has experienced a significant increase in renewable energy generation in recent years due to the commissioning of new projects. In 2021, wind and solar technologies accounted for 7.40% and 6.10% of the total installed capacity, respectively. By 2022, these figures had increased to 8.22 % and 7.99%, and by 2023 these figures changed to be 7.3% and 11.9% respectively (Organismo Coordinador, 2022a, 2023a, 2024). Table 1 presents key data for the system, including the total electricity generated in 2022 and the total installed capacity. The gross domestic product (GDP) grew by 4.9% in 2022, indicating a similar increase in energy consumption (Banco Central, 2023). Demand For this study, the actual delivered demand in 2022 was provided by the Organismo Coordinador del Sistema Eléctrico Nacional Interconectado of the Dominican Republic (Organismo Coordinador, 2023a). One week of demand was selected from each subset of months with similar demand profiles to create realistic scenarios. The months were grouped as follows: January–February, March–April, May–June, July–October, and November–December. In accordance with General Electricity Law No. 125-01 and its Application Regulation, 3% of the total generation per period was modeled as a reserve for primary and secondary frequency regulation (PFR and SFR) (Superintendencia de Electricidad, 2001, 2007). Fig. 2 shows the monotonic load curve for 2022, where the peak power is 3,161.48 MW. The prominent negative peak corresponds to September 19, hour 24. On this day, multiple transmission line trips occurred due to Tropical Storm Fiona, affecting several 69 kV lines. Fig. 3 illustrates the average hourly demand over the course of a week, beginning on Monday and concluding on Sunday. It is evident that the daily demand displays similar trends, with peak consumption occurring roughly between 20:00 and 22:00, and reduced demand observed between 5:00 and 7:00. Notably, a decrease in demand is observed during the weekend. Power plants The maximum power availability declared for each power plant during 2019–2020 was used as the maximum power for the simulations. PFR and SFR margins were also considered. For plants without ramp-up and ramp-down data, these values were calculated based on maximum and minimum power and ramp-up and ramp-down times, expressed in MW/min. The ramp-up and ramp-down values were limited to the maximum power of the plant to avoid inconsistencies. Fig. 2. Monotonic load curve in MW. Annual demand 2022. Fig. 3. Weekly presentation of average hourly demand (Monday to Sunday). Table 2 Installed capacity by technology in 2022. Technology Capacity (MW) Solar 405 Wind 417 Hydroelectric 623 Combined cycle 1,129 Gas Turbine 134 Internal combustion engine 1,209 Steam turbine 1,158 The start-up ramp of each plant was calculated using the minimum power and hot start-up time in hours, limited by the minimum and maximum power to ensure that all plants reach the technical minimum during the start-up period. For the shutdown ramp, the maximum power and the time to reach standby condition were considered, similarly limited by the minimum and maximum power. In some cases, the start-up and shutdown ramp were considered the same. Plants were grouped by technology, with the minimum power assumed to be the lowest minimum power in the group. For the variable production costs (VPCs), the average dispatch costs from Organismo Coordinador (2023b) were used. Table 2 shows the installed capacity by technology for 2022 (Organismo Coordinador, 2023a). Hydropower plants were categorized into reservoir and run-of-river types. All reservoir plants were grouped into a single entity, modeled as thermal, with 𝑃𝑚𝑎𝑥 calculated considering the median generation of 2020. PFR and SFR margins were included. For run-of-river plants, 2020 data were used, incorporating their PFR and SFR margins into the optimization problem. In the case of the biomass plant, actual average hourly generation in 2020 was used. For wind and solar plants, 2022 hourly actual generation data were used. Energy for Sustainable Development 88 (2025) 101749 7 E. Cruz-De-Jesús et al. Table 3 Parameters of thermal power plants and reservoir hydropower plants. Unit Fuel Technology VPC Pmin Pmax Rup Rdw Mrpf Mrsf Su Sd $/MWh (MW) (MW) (MW/h) (MW/h) (MW) (MW) (MW/h) (MW/h) P1 Water Hydropower 0 0 113 113 113 13 10 113 113 P2 Coal Steam turbine 42 150 375 160 174 10 0 155 150 P3 Coal Steam turbine 43 142 375 135 213 8 0 142 148 P4 Natural Gas Combined cycle 50 66 218 169 218 14 16 66 218 P5 Coal Steam turbine 51 100 120 18 63 0 0 100 100 P6 Natural Gas Combined cycle 53 66 90 16 90 3 7 66 86 P7 Coal Steam turbine 54 94 120 18 57 0 0 94 94 P8 Natural Gas Combined cycle 54 66 90 17 90 3 7 66 81 P9 Natural Gas Combined cycle 55 66 224 183 224 21 24 86 224 P10 Natural Gas Combined cycle 57 66 90 14 90 3 9 66 90 P11 Coal Steam turbine 64 29 52 46 39 0 0 41 29 P12 Natural Gas Combined cycle 82 150 300 267 300 14 45 150 242 P13 Natural Gas Combined cycle 95 185 315 189 137 20 0 185 185 P14 Natural Gas Combined cycle 103 49 110 110 110 4 5 110 110 P15 Fuel Oil No. 6 ICE 126 6 423 254 372 19 31 344 423 P16 Fuel Oil No. 6 ICE 128 14 34 34 34 2 9 34 34 P17 Natural Gas ICE 129 14 25 25 25 2 6 25 25 P18 Fuel Oil No. 6 ICE 139 5 135 135 135 6 12 95 119 P19 Fuel Oil No. 2 Gas turbine 292 60 85 85 85 5 0 85 85 Table 4 Comparison between the operating costs obtained with model 2 (CM2) and the average weekly operating costs reported by the Dominican system operator. Months CM2 (M$) Report 2022 (M$) Report 2023 (M$) Jan–feb 18.32 23.94 25.18 Mar–Apr 18.46 25.28 20.59 May–jun 22.38 34.47 26.62 Jul–oct 23.29 32.77 30.49 Nov–dec 19.07 27.76 24.99 Table 3 provides the main parameters for thermal power plants and reservoir hydropower plants, with VPCs referring to 2023 values. Results for case study 1. Calculation of the cost of provision of FR in the NIES The objective of this case study is to compute the cost of provision of FR according to the rules of the NIES system. The methodology involves a comparison of the costs obtained using Model 1 and Model 2. As previously stated, Model 1 solely considers the energy balance, whereas Model 2 incorporates the PFR and SFR constraints of thermal and hydro plants. Fig. 4 shows the increment in total operating cost (OC) when reserve constraints are included in Model 2. In the years 2022 and 2026, the required reserve for PFR and SFR is 3% of the system demand. In the year 2030, the reserve requirements are increased to 4% for PRF and 4.5% for SFR, as proposed in Organismo Coordinador (2020) to accommodate the anticipated rise in renewable energy integration. Consequently, a more pronounced increase is observed for 2030, reflecting a future scenario with reduced participation of coal-fired power plants. Table 4 presents a comparison of the weekly operating costs derived from our Model 2 (CM2), which incorporates both the technical constraints of the units and the FR constraints, against the average weekly operating costs reported by the Dominican system operator (Organismo Coordinador, 2023c). As can be seen, the operating costs of the actual schedule and those obtained from the simulations are of similar magnitude. The real costs are higher, which may be due to several factors, including the additional constraints that the real model considers in the network, such as generation constraints due to flow control, network maintenance, and unavailability of power plants. Results for case study 2. Evaluation of the contribution of BESS to PFR This case study aims to compare operational cost savings with and without BESS for various generation and demand scenarios. The Fig. 4. Cost of providing FR in scenarios of different years. methodology employs two models: Model 2 (without BESS) and Model 3 (with BESS). The contribution of BESS is evaluated for capacities ranging from 14 MW to 47 MW, with a storage capacity of 0.5 h. In order to evaluate the influence of incorporating BESS as a component of the PFR service, a series of storage power penetration rates were devised, with the peak demand observed in the NIES during 2022 (3,161.48 MW) of the data provided serving as a point of reference. The maximum reserve margin required by the regulation is 3% of the aforementioned maximum demand, i.e., 94.84 MW. Then, the BESS rated power was selected at four values corresponding approximately to increasing percentages (15%, 25%, 40% and 50%) of the required reserve margin. For this application, the batteries were modeled as a constant power source, since the charge and discharge cycles occur in less than one hour, which is the time frame in which the results of these models were obtained. Results for case study 3 (Evaluation of the contribution of BESS to SFR) and comparison with case study 2 Similar to Case Study 1, this study focuses on SFR instead of PFR. The methodology follows the same approach as Case Study 2, assessing BESS contributions to SFR across different hours. The evaluation of BESS involves capacities ranging from 14 MW to 47 MW, with a storage capacity of 0.5 h. Energy for Sustainable Development 88 (2025) 101749 8 E. Cruz-De-Jesús et al. Fig. 5. Change in operating costs when using BESS for PFR or SFR. In order to evaluate the impact of BESS on operating costs when it contributes to the SFR (case study 3), the same procedure was employed as that used for the PFR. Despite the identical requisite percentages for PFR and SFR, not all plants eligible for PFR are similarly qualified for SFR. Furthermore, some of the plants in question do not possess the requisite margins for participation in both SFR and PFR. Fig. 5 illustrates the percentage reduction in total operating costs when BESS with varying capacities participate in PFR (case study 2) and SFR (case study 3) separately. It can be seen that the greatest savings are obtained in the PFR. Table 5 presents the costs associated with BESSs of varying dimensions, encompassing expenditures for batteries, transformers, land, engineering, and other pertinent components. It was assumed that the costs associated with the batteries, land, BESS installation, and BESS balance of the plant are dependent on the energy capacity (MWh), while the costs related to the main transformer and electrical interconnection are contingent on the power rating (MW). Furthermore, the costs associated with engineering, procurement, and construction (EPC) are incorporated. It is expected that the batteries will have a service life of 20 years, based on the duty cycle associated with FR service only. The cost estimates for lithium-ion battery storage projects were derived from Sargent (2024) and Sachs (2024). In this study, the Energy-to-Power (E/P) ratio has been kept constant at 0.5 h for the frequency regulation application, reflecting the short duration characteristic of this type of ancillary service. By solving the UC problems corresponding to Model 2 and Model 3, the weekly operating cost savings were determined for several BESS configurations. These weekly savings were then multiplied by the number of weeks in each group of months to estimate the annual savings, as shown in Table 5. The results indicate that as the BESS power increases, the annual savings also rise. It is noteworthy that the maximum payback period for the initial investment in the PFR application was less than one year. This highlights the BESS as a profitable investment for the system operator, whose objective is to ensure reliable service at the lowest possible cost. For the SFR application, the maximum payback period was less than two years, implying that the BESS would generate benefits for the system for approximately 18 years. In summary, each of these services is profitable for the system, even when considered separately. The Net Present Value (NPV) and Internal Rate of Return (IRR) calculations presented in Table 5 show that the investment in these storage systems is profitable. For the calculation of the discount rate, we used the rate of financial return for electricity transmission and distribution for 2020 in Spain, equal to 6.003%, and considering that the investment is in the Dominican Republic, we added the risk Table 5 Operational cost savings with the inclusion of BESSs in the PFR and SFR services for 2022. Conf1 Conf2 Conf3 Conf4 Power (MW) 14 23 37 47 Energy (MWh) 7 11.5 18.5 23.5 Power cost ($/kW) 224 Energy cost ($/kWh) 448 Capital cost (M$) 3.14 5.15 8.29 10.53 Annual sav. PFR (M$) 5.13 8.02 11.86 14.17 Pay-back (years) 0.61 0.64 0.70 0.74 NPV (M$) 32 50 74 87 IRR (%) 162 153 141 132 PFR real cost 2022 (M$) 51.78 PFR real cost 2023 (M$) 56.81 Annual sav. SFR (M$) 3.65 5.81 8.16 9.27 Pay-back (years) 0.86 0.89 1.02 1.14 NPV (M$) 22 35 48 53 IRR (%) 114 111 96 86 SFR real cost 2022 (M$) 37.98 SFR real cost 2023 (M$) 36.26 premium of Mexico, equal to 7.85, due to the availability of data and the fact that this country is closer to the Dominican Republic in terms of risk premium. The discount rate used was 13% (expansion.com, 2024a, 2024b; State Agency Official State Gazette, 2019). Table 5 presents the actual expenses associated with FR for the years 2023 and 2022, obtained from Organismo Coordinador (2023a) and Organismo Coordinador (2024), along with the savings projected by our model. It is evident that the implementation of BESS into the system could lead to substantial reductions in FR costs. Additionally, it is important to account for the cost of forced dispatch, which amounted to M$ 1.24 in 2022 and M$ 0.26 in 2023 due to FR. Results for case study 4. Evaluation of the contribution of BESS to both PFR and SFR simultaneously The objective of this case study is to assess the combined impact of BESS on both PFR and SFR. The methodology uses the same median demand and generation scenarios from January to December as in Case Studies 2 and 3. The contribution of a 47 MW BESS for PFR and another 47 MW BESS for SFR is evaluated simultaneously. The impact of incorporating BESS for PFR and SFR in the NIES is evaluated in the present context and for prospective future scenarios, taking into account the long-term program of the system operator, as outlined in Organismo Coordinador (2022b). Results for 2022 This section presents the results of incorporating two 47 MW ratedpower BESS for PFR and SFR in parallel. The rated power of the BESS is approximately 50% of the reserve required for FR, which is considered a satisfactory ratio. The total annual savings amount to $23.6 million. Based on the data presented in Table 5, the payback period is calculated to be 0.89 years. BESS for PFR and SFR in future scenarios A series of future scenarios were evaluated by increasing the total load, as well as the capacities of the PV and wind parks, and by also considering the potential addition of a 190 MW natural gas plant (Organismo Coordinador, 2022b). It is again assumed that 47 MW of BESS is used for PFR and a further 47 MW for SFR. Table 6 illustrates the impact of BESS on renewable energy integration for the future scenario of the year 2026. The inclusion of BESS results in increased energy generation across all renewable sources. Specifically, the total increase in RES integration is of 3%, with the highest impact on Hydro generation integration. Table 6 includes both reservoir and run-of-river hydropower plants. Additionally, Table 7 Energy for Sustainable Development 88 (2025) 101749 9