Emissions-aware electricity network expansion planning via implicit differentiation

We consider a variant of the classical problem of designing or expanding an electricity network. Instead of minimizing only investment and production costs, however, we seek to minimize some mixture of cost and greenhouse gas emissions, even if the underlying dispatch model does not tax emissions. This enables grid planners to directly minimize consumption-based emissions, when expanding or modifying the grid, regardless of whether or not the carbon market incorporates a carbon tax. We solve this problem using gradient descent with implicit differentiation, a technique recently popularized in machine learning. To demonstrate the method, we optimize transmission and storage resources on the IEEE 14-bus test network and compare our solution to one generated by standard planning with a carbon tax. Our solution significantly reduces emissions for the same levelized cost of electricity.