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We estimate the capacity value of concentrating solar power (CSP) plants with thermal energy storage (TES) in the southwestern U.S. Our results show that incorporating TES in CSP plants significantly increases their capacity value. While CSP plants without TES have capacity values ranging between 60% and 86% of maximum capacity, plants with TES can have capacity values between 79% and 92%. We demonstrate the effect of location and configuration on the operation and capacity value of CSP plants. We also show that using a capacity payment mechanism can increase the capacity value of CSP, since the capacity value of CSP is highly sensitive to operational decisions and energy prices are not a perfect indicator of scarcity of supply.