Nonconvex multicommodity near equilibrium models: Energy markets perspective

Abstract

In this paper we explore the application of the minimum total opportunity cost (MTOC) model of Fuller and Celebi (2017) to multicommodity market planning models containing binary variables and price sensitive demands, with or without substitution among commodities. We present a greatly simplified derivation of the MTOC approximation of Fuller and Celebi (2017), here called the near equilibrium (NE) model, a mixed integer program with nonlinearities only in the objective function. For some models, the NE solution achieves the MTOC solution exactly, as in an example. We provide a simple example of capacity expansion in gas and electricity markets that are linked through substitution in demand and in the possibility of using gas to produce electricity. In several cases, we compare the NE solution to the social welfare (SW) maximization solution calculated by a sequential optimization algorithm. In one case, the sequential optimization algorithm fails to converge, due to the binary variables. For the other cases, the NE model has smaller producer opportunity costs – in particular, in most cases, smaller make whole payments that bring negative producer profits up to zero – at some sacrifice of social welfare. We suggest that the NE model could be useful to government regulators as a supplementary tool along with SW models, as the NE solution usually reduces subsidies needed for make whole payments, and sometimes benefits consumers compared to the SW solution.