In deregulated electricity markets, minimizing the procurement costs of electricity is a critical problem for procurement agencies (PAs). However, uncertainty is inevitable for PAs and includes multiple factors such as market prices, photovoltaic system (PV) output and demand. This study focuses on settlements in multi-period markets (a day-ahead market and a real-time market) and the installation of energy storage systems (ESSs). ESSs can be utilized for time arbitrage in the day-ahead market and to reduce the purchasing/selling of electricity in the real-time market. However, the high costs of an ESS mean the size of the system needs to be minimized. In addition, when determining the size of an ESS, it is important to identify the size appropriate for each role. Therefore, we employ the concept of a "slow" and a "fast" ESS to quantify the size of a system's role, based on the values associated with the various uncertainties. Because the problem includes nonlinearity and non-convexity, we solve it within a realistic computational burden by reformulating the problem using reasonable assumptions. Therefore, this study identifies the optimal sizes of ESSs and procurement, taking into account the uncertainties of prices in multi-period markets, PV output and demand.
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