## 1 Introduction  
Global electricity markets have started to use energy storage systems (ESSs) to enhance the operational performance efficiency of power systems. Compared to other existing resources such as coal and gas-fueled generators, ESSs respond to changes in demand much more quickly. This feature offers great operational flexibility in the electricity market and in system operations, particularly in the smart operation of frequency regulation (F/R). F/R is an activity through which system operations cope with excessive fluctuations in power system frequency--fluctuations that are caused by real-time mismatches in power supply and demand. Conventional coal and/or gas-type generators have been traditionally used to resolve the F/R problem, by leaving some portion of their generation capacity unused--that is, by procuring generation reserves, and by providing reserved resources in the event of excessive frequency fluctuation. Given the technical advantage of ESSs in terms of their prompt responsiveness to frequency fluctuation, electricity markets in the United States--such as Pennsylvania-New Jersey-Maryland(PJM) Interconnection, Midcontinent Independent System Operator(MISO), and New York IndependentSystem Operator(NYISO)--have already designed ESS practices in F/R markets, and they have attracted the entry of ESSs through multiple incentive mechanisms [1]. For example, some F/R markets have introduced an incentive mechanism divided into a capacity market and an energy market, to offer more benefits to those resources that respond accurately and rapidly [2; 3; 4]. Moreover, because power system frequency signals can be more frequently transmitted to ESS than conventional generators, PJM and NYISO operate single transmission systems that are separated into fast and slow-response resources [5; 6]. In addition, ESSs are being more broadly applied to electricity systems: ESSs, for example, are typically associated with connecting variable renewable energy sources to enhance the power of battery charging, as well as to effectively operate and utilize electric vehicles; both are typical recent examples of ESS applications in power system operations [7; 8; 9; 10; 11]. In some electricity markets, including that of South Korea, electricity utility companies have undertaken large-scale ESS deployment plans for F/R. To date, various studies have been conducted on F/R ESSs, covering topics such as optimal ESS capacity estimation and economic benefit assessments. Some studies [12; 13; 14] discuss the optimal capacity estimation of ESS for frequency control and evaluate the benefits thereof. Other studies [15; 16] suggest the economic dispatch methodology and the optimal sizing of ESSs from a utility operation perspective. In determining benefits, an economic assessment should precede ESS installation. [PERSON] et al. [17] propose economic analysis when an ESS is introduced as an F/R resource in an electricity market. Some studies discuss, from a utility perspective, economic benefit analyses in accordance with price arbitrage as a result of ESS application [18; 19; 20]. In economic analyses of electricity markets, the long-term system marginal price (SMP) estimation is the most important factor; however, most studies conduct short- and medium-term SMP estimation. [PERSON] et al. [21] conducted short-term SMP estimations using 24-h electricity price predictions for the day-ahead energy market, by applying various methodologies (i.e., neural network, time series, and wavelet models). [PERSON] et al. [22] propose a regime-switching model for short- and medium-term electricity price forecasting and show the superiority of the proposed model compared to an autoregressive integrated moving average and generalized autoregressive conditional heteroscedasticity models. [PERSON] et al. [23] discuss a long-term seasonal component that considers annual seasonality and estimates a future (one-year) electricity spot price by applying a wavelet-based model.