## 2 Benefits Assessment of ESS Introduction in the F/R Market
### Probabilistic Long-Term SMP Forecast  
To assess effectively the economic benefit of ESS for F/R over a given horizon (typically 10-15 years), we propose the novel probabilistic weighted average to predict future annual SMP profiles for the horizon. Because the SMP is the most expensive fuel cost of the generator that is last committed to  
Figure 1: Economic benefits of ESSs for F/R in the electricity market [25; 26]. meet the forecasted demand at a given hour, the estimation for an hourly marginal plant profile across the operating horizon is the key element in predicting annual SMPs. To this end, the current study proposes a probabilistic method by which to forecast a long-term marginal plant profile associated with hourly SMP, to assess the economic benefit of ESS for F/R. To obtain the annual SMP profiles--that is, annual marginal plant probability profiles in electricity markets--we used a 15-year national long-term supply and demand projection plan published by a South Korean energy agency [24]. Detailed descriptions of the development of a probabilistic annual SMP forecast, based on the estimation of a long-term marginal plant profile, are given below. First, the annual generation capacity of each fuel type for the next 10 years can be obtained from the national plan for long-term electricity supply and demand. However, this capacity cannot be identified as real generation capacity, because it does not take into account the operational unavailability of generators owing to events such as forced and maintenance outages. The forced outage rate (FOR) and maintenance outage rate (MOR) speak to the unavailability of generating units associated with unplanned and planned outages, respectively. When assessing the annual generation capacity for each fuel type, the unavailable generation capacity should therefore be extracted from the nominal generation capacity. In addition, given the fluctuating output of renewable energy, we use estimations of actual generation capacity from the national plan, rather than installed capacity data. Second, we obtain from the hourly demand average the past demand profiles that are assumed to be identical to estimated peak demand. However, these profiles can also be divided into two different demand profiles--weekdays and weekends. Annual peak demand for the next 10 years is used to determine the annual hourly demand. The methodology is as follows. Equations (1) and (2) represent the idea that the sum of the hourly average demand is the product of hourly peak demand and \(\alpha_{t}\) (rate of hourly demand on the basis of peak demand), which transform to Equation (3). Applying this notion, annual peak demand satisfying average demand is calculated by Equation (4). Peak demand is calculated as:  
\[d_{t}=d_{\text{peak}}\times\alpha_{t} \tag{1}\]  
\[\sum_{t=1}^{24}d_{t}=\sum_{t=1}^{24}d_{\text{peak}}\times\alpha_{t}=d_{\text{ peak}}\sum_{t=1}^{24}\alpha_{t} \tag{2}\]  
\[d_{\text{peak}}\sum_{t=1}^{24}\frac{\alpha_{t}}{24}=d_{\text{average}} \tag{3}\]  
\[d_{\text{peak}}=\frac{d_{\text{average}}}{\sum_{t=1}^{24}\alpha_{t}} \tag{4}\]  
where \(d_{t}(0\leq t\leq 24),~{}d_{\text{average}}\), and \(\alpha_{t}(0\leq\alpha_{t}\leq 1)\) are the demand at each time, peak demand, and rate of past demand for each time on the basis of peak demand, respectively. Third, the annual demand clustering pattern can be obtained from the peak demand for each year, as drawn from past data. This means that estimated demand is equal to the movement of the past demand pattern, in line with peak demand. Therefore, the annual demand pattern is estimated by multiplying annual peak demand by each value of the percentage of demand for every hour, based on peak demand from the past demand clustering pattern. We compare the annual generation mix from generation capacity and the demand clustering for every hour to identify the marginal plant resources used on weekdays, weeknights, and weekends.