A Minimal System Cost Minimization Model for Variable Renewable Energy Integration: Application to France and Comparison to Mean-Variance Analysis

The viability of Variable Renewable Energy (VRE)-investment strategies depends on the response of dispatchable producers to satisfy the net load. We lack a simple research tool with sufficient complexity to represent major phenomena associated with the response of dispatchable producers to the integration of high shares of VRE and their impact on system costs. We develop a minimization of the system cost allowing one to quantify and decompose the system value of VRE depending on an aggregate dispatchable production. Defining the variable cost of the dispatchable generation as quadratic with a coefficient depending on macroeconomic factors such as the cost of greenhouse gas emissions leads to the simplest version of the model. In the absence of curtailment, and for particular parameter values, this version is equivalent to a mean-variance problem. We apply this model to France with solar and wind capacities distributed over the administrative regions of metropolitan France. In this case, ignoring the wholesale price effect and variability has a relatively small impact on optimal investments, but leads to largely underestimating the system total cost and overestimating the system marginal cost.