Modelling the effects of interconnection between electricity markets subject to uncertainty

Interconnecting distinct electricity markets by adding a new transmission line affects the outcomes in these markets in a complicated way when there is uncertainty in demand or participant behaviour. We use market distribution functions to examine the effects of interconnection using a single transmission line under the assumption that this line has a differentiable loss function and agents in each of the interconnected markets do not change their behaviour in response to the interconnection. We also show how the case with capacity constraints on flows can be represented with appropriately formulated loss functions. We give analytical formulae for computing market outcomes when the uncertain events in the markets being connected are statistically independent, and show by example how to compute these outcomes when these events are correlated.