LCP models of Nash-Cournot competition in bilateral and POOLCO-based power markets

Two Cournot-Nash models of imperfect competition among electricity producers are formulated as linear complementarity problems (LCPs), and a simple example is presented to illustrate their application. The two models simulate bilateral markets. The models include a congestion pricing scheme for transmission, but other transmission pricing approaches can also be represented in this framework. The two models differ from each other in that one has no arbitrage between nodes of the network, while in the other model, arbitragers erase any non-cost based differences in price. The latter bilateral model turns out to be equivalent to a Nash-Cournot model of a POOLCO system. The models differ from other Cournot power market model in the literature in that they represent both of Kirchhoff's laws (via a DC approximation) while being readily solved using efficient complementarity algorithms. The key assumption that permits their formulation as LCPs is that each producer naively assumes that its output decisions will not affect the cost of transmission.