Variable renewable energy sources introduce significant amounts of short-term uncertainty that should be considered when making investment decisions. In this work, we present a method for representing stochastic power system operation in day-ahead and real-time electricity markets within a capacity expansion model. We use Renders' cuts and a stochastic rolling-horizon dispatch to represent operational costs in the capacity expansion problem (CEP) and investigate different formulations for the cuts. We test the model on a two-bus case study with wind power, energy storage, and a constrained transmission line. The case study shows that cuts created from the day-ahead problem gives the lowest expected total cost for the stochastic CEP. The stochastic CEP results in 3% lower expected total cost compared to the deterministic CEP capacities evaluated under uncertain operation. The number of required stochastic iterations is efficiently reduced by introducing a deterministic lower bound, while extending the horizon of the operational problem by persistence forecasting leads to reduced operational costs.
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