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There is growing interest in the use of energy storage systems (ESS) to create combined ''renewable energy plus storage'' power plants. ESS based on lithium-ion batteries have drawn much attention due to their high energy density and low self-discharge. However, as lithium-ion batteries are still costly, a power producer should determine ESS capacity in a sophisticated manner to ensure profitability of the PV plus storage projects. During the project horizon, lithium-ion batteries undergo severe capacity degradation, which must be considered in ESS planning. The degradation rate depends on various stress factors which are affected by ESS sizes and operation. Therefore, this paper aims to propose an advanced framework for calculating the capacity of an ESS supplementing a photovoltaic system considering the effect of the size and operation of ESS on battery degradation while maximizing profitability. Depending on how batteries are used during the project horizon, two scenarios are discussed and an ESS sizing framework for each scenario is suggested. To deal with non-convexity and black-box parameters of the optimal ESS sizing problems, we introduce an iterative algorithm that finds a solution by accessing battery degradation and optimizing profitability repetitively. We adopted the South Korean market for analysis and simulation of the frameworks. INDEX TERMSBattery degradation, energy storage system (ESS), ESS sizing, economic analysis. HUNYOUNG SHIN (Member, IEEE) received the B.S. degree in radio and communication engineering and the M.S. degree in electrical engineering from Korea University, Seoul, South Korea, and the Ph.D. degree from the Electrical and Computer Engineering Department, The University of Texas at Austin, Austin, TX, USA, in December 2017.In 2018, he joined LG CNS as a Managing Consultant and has participated in energy storage system planning projects. He is currently an Assistant Professor at Sangmyung University, Seoul. His research interests are primarily in optimization of power systems, risk-hedging strategies, and pricing rule in electricity markets.