# Utilizing Energy Storage for Operational Adequacy of Wind-Integrated Bulk Power Systems
## 2 System Model
### Wind Generation Model  
The initial wind condition and its rising/falling trend depends on the time of day and has a significant impact on the wind speed forecast over a short future time. Past research [22] has shown that this correlation between the known initial wind speed and the future wind speed diminishes as the forecast horizon spans larger than 6-8 h. Then, the conditional probability distribution of the wind speed at the future time will be equal to the distribution obtained from the historical data for that instant of time. Such historical wind speed distribution, \(f\big{(}w_{start}^{s}\big{)}\) is, therefore, obtained and used to model the wind power at the start of an evaluation period that will occur after a planning horizon greater than 6-8 h. This distribution is used to develop conditional wind speed distribution for each interval of the evaluation period in a chronology. The wind speed model developed in this work is based upon the historical wind speed data at a 1 min interval obtained from Reference [23] for a planning horizon of a day ahead, or longer. The speed-power characteristics of a wind turbine generator (WTG), shown in Equation (1), provides the wind power probability distribution for each time interval, from which, the expected wind generation is calculated at each time interval of the evaluation period. The wind generation model is developed in the form of a series of wind power distributions associated with each time interval in the evaluation period. The probability, \(\pi_{w}\), of a state representing the \(w^{th}\) wind generation capacity between \(a_{w}\) and \(b_{w}\  
operation. These characteristics and constraints must be incorporated in an appropriate ESS model. An ESS can be operated under different ownerships, such as the utility, the wind farm owner, or an independent entity. The objectives will, therefore, differ as the owners may operate their ESS facilities to maximize profits from different electricity market components, such as energy arbitrage or reserve markets. Or, the ESS may be operated in coordination with wind power sources to maximize wind utilization, to support wind power commitment, or to provide frequency support. The owner may also want to operate their ESS to mitigate transmission congestion, defer system upgrades, avoid loss of load, mitigate reliability performance penalty, or other time-shifting benefits [24]. The ESS operating modes of charge, discharge, or idle are therefore decided by the ESS operator based on the objectives of operation, as discussed. They can be operated to acquire charge from the grid as needed, or from the wind farms when wind generation is abundant. The operation strategy of the ESS in a power system directly affects its operational adequacy and hence the operational planning. It is important to recognize the operating strategy of an ESS in the development of its model for operational adequacy evaluation. As noted earlier, the operating strategy will depend on many factors, such as the ownerships and their objectives driven by the market and regulatory policies. It should however be realized that the primary objective of inducting ESS in power systems, in the first place, is to sustain large-scale growth of renewable energy with reliable performance. The regulatory policies will be guided by this objective to exploit wind energy with the proper deployment of ESS. This paper, therefore, recognizes the need to coordinate the operation of ESS with wind power variability in the development of the ESS model. The ESS model is developed considering a coordinated operation of ESS with wind power and load variation in time chronology within the evaluation period. The accumulated energy in an ESS is generally discharged during the peak load hours. It is also discharged to mitigate loss of load during contingency events, and to support wind power commitment to the system while jointly operating with the wind resources. The maximum energy available from ESS is limited by its storage capacity, \(SOC_{max}\).