Cost-optimal power system extension under flow-based market coupling

Electricity market models, implemented as dynamic programming problems, have been applied widely to identify possible pathways towards a cost-optimal and low carbon electricity system. However, the joint optimization of generation and transmission remains challenging, mainly due to the fact that different characteristics and rules apply to commercial and physical exchanges of electricity in meshed networks. This paper presents a methodology that allows to optimize power generation and transmission infrastructures jointly through an iterative approach based on power transfer distribution factors (PTDFs). As PTDFs are linear representations of the physical load flow equations, they can be implemented in a linear programming environment suitable for large scale problems. The algorithm iteratively updates PTDFs when grid infrastructures are modified due to cost-optimal extension and thus yields an optimal solution with a consistent representation of physical load flows. The method is first demonstrated on a simplified three-node model where it is found to be robust and convergent. It is then applied to the European power system in order to find its cost-optimal development under the prescription of strongly decreasing CO2 emissions until 2050.