*1.1. Literature Review*

Management of isolated HES considering the influence of renewable resources and their associated variability has been treated by many authors. In this regard, Li et al. [11] developed a procedure for sizing and managemen<sup>t</sup> of wind–BESS units. Historical wind power time series is analyzed to estimate the low-frequency component, which is the most prominent one. Using the resulting signal, charging–discharging cycles of BESS are determined considering constant power levels. During the charging period, the power to be provided by the wind–BESS unit is set to the minimum power of low-frequency component within that period. Conversely, power generation is scheduled to the highest power of low-frequency component during discharging periods. In theory, these mechanisms ensure the existence of sequential charging–discharging intervals. However, power dispatch settings could be modified to avoid the charging–discharging cycles at partial level. Other issues related to the wind power forecasting error and BESS lifetime have also been incorporated.

Luo et al. [12] created a model for the operation and sizing of wind–BESS to compensate for the forecasting error. Forecasting error is modeled by using a beta distribution, considering extreme conditions related to pessimistic and optimistic perspectives. BESS dynamic behavior, as well as its lifetime, have been also incorporated.

Mohammadi et al. [13] proposed a day-ahead scheduling model of a microgrid (MG) composed of electrical as well as hydrogen and thermal energy storage technologies. Problem formulation was based on a two-stage stochastic programming approach, while its solution was carried out using an enhanced version of cuckoo optimization algorithm. The high flexibility of the studied configuration results is useful to deal with the fact that thermal and electrical energy consumption are typically not synchronized.

O'Dwyer and Flynn [14] paid special attention to the power system operation on a daily basis, using hourly and sub-hourly time steps, under high renewable energy integration and ESS. According to the reported results, the traditional hourly analysis cannot properly estimate the ramping requirements, the number of starts of conventional generators, as well as the role and potential of ESS on the cycling reduction. Consequently, the interdependence between renewable power curtailment, CO2 emissions, and the cycling process of thermal units is not accurately described.

Wen et al. [15] presented an enhanced security-constrained unit commitment (SCUC) model, which incorporates BESS to mitigate the negative e ffects of a sudden contingency and consequently to prevent cascading outages. The methodology was formulated as a two-stage mixed integer programming problem and solved by means of Benders decomposition. The same author in [16] introduced a model based on frequency dynamic constrained unit commitment (UC) able to incorporate wind power uncertainty. Interval optimization approach was combined with mixed integer linear programming (MILP) to determine the appropriate unit schedule.

Nguyen and Crow [17] presented a scheduling model with probabilistic constraints based on stochastic dynamic programming (DP). The proposed BESS-model is inspired by the functioning of conventional fuel-based units. Thus, a detailed cost model was developed considering the electrochemical process of BESS.

Khorramdel et al. [18] proposed a UC model based on cost-benefit analysis, in which a probabilistic analysis based on a here-and-now approach was incorporated. Then, particle swarm optimization (PSO) was implemented in order to minimize total generating costs.

Li et al. [19] developed a framework to quantify the benefits of ESS incorporation to HES. The methodology is based on stochastic UC solved by means of MILP.

Jiang et al. [20] proposed a managemen<sup>t</sup> model for a residential HES provided by wind generation, micro-combined heat and power generation and smart appliances, enrolled in a real-time pricing (RTP) program. Additionally, optimal behavior of several aggregated HESs is analyzed by means of a day-ahead stochastic economic dispatch (ED) and UC model based on MILP.

Anand and Ramasubbu [21] presented a scheduling model of a system enrolled in a RTP program composed of wind and photovoltaic generation, as well as a microturbine and a fuel cell, based on anti-predatory PSO.

Wu et al. [22] proposed a methodology to solve ED and UC problems using the time-scaling transformation combined with an auxiliary continuous vector.

Dui et al. [23] proposed a two-stage scheduling methodology for BESS performance evaluation. In the first step, UC problem including the e ffects of thermal and wind generators is solved by means of second-order cone programming. Then, in the second step, the managemen<sup>t</sup> strategy for BESS is designed and evaluated using a genetic algorithm (GA).

Psarros et al. [24] investigated the operation of HESs using a MILP. BESS sizing is deeply discussed, concluding that this element is a key device for the provision of fast energy reserve. The same author in [25] proposed a model able to consider di fferent time resolutions, based on the combination of model predictive control and MILP.

Ahmadi et al. [26] presented a model for the solution of SCUC including BESS. Aging cost related to BESS operation is incorporated to the objective function. Then, MILP is combined with information-gap decision theory so that the conservatism of the strategy to be implemented can be adjusted by the system operator.

Saleh [27] created and experimentally tested the performance of an energy managemen<sup>t</sup> system (EMS) based on the solution of UC by Lagrangian relaxation. Thus, control values of permanent magne<sup>t</sup> generator of the wind turbine and the power-electronic converter are obtained.

Gupta et al. [28] formulated a SCUC model including the e ffects of BESS in order to compensate the variability of renewable power sources. The mathematical problem is solved by using Benders decomposition, determining the locational marginal price, wind power curtailment, as well as the line contingency.

Alvarez et al. [29] proposed a general purpose ESS model inspired by the behavior of hydraulic reservoirs. Using the results obtained from stochastic dual DP, carried out to determine the long-term energy schedule, the linear model of ESS cost is derived. Finally, stochastic UC, including the aforementioned ESS model, was formulated.

Chen et al. [30] developed a scheduling model based on multi-agent system for the coordination of multiple MGs. Such coordination is carried out by means of the alternating direction method of multipliers, obtaining the optimal energy managemen<sup>t</sup> of the multiple MGs. Additionally, the negative effects of uncertainty sources are compensated by using day-in rolling.

Tan et al. [31] proposed a dispatch model able to incorporate different operating perspectives related to fuel savings, carbon emissions, power generation costs, amount of renewable energy integrated, and power generation efficiency. Uncertainty of renewable generation and forecasting of carbon-trading price were included by using Monte Carlo simulations, while the associated optimization model was solved by implementing the technique for order preference by similarity to ideal solution combined with Grey relational analysis.

Yiwei et al. [32] presented a scheduling model for a HES based on renewable and thermal generation, as well as cascade hydropower and pumped ESS. The model focuses on the economy and security aspects of system operation. The optimization strategy is divided into three main stages. During the first stage, integer variables are preprocessed using heuristic rules. Then, during the second stage, ED and UC are solved. Finally, during stage three, power system feasibility was evaluated.

Once the literature review has been exposed, describing the state-of-the-art techniques used for day-ahead scheduling, the main contribution and novelty of this work are carefully explained in the next section.
