<p>The costs associated with electricity generation include costs that are independent of their marginal output, such as the cost of starting their units, and constraints such as minimum generation levels. Modelling these costs and constraints requires integer formulation of the units, and so they have typically been ignored in electricity market modelling and simulation to date. We present a stochastic equilibrium model to include these costs and constraints in a Cournot game. We solve it using the Gauss-Seidel diagonalization algorithm and apply it to a model of the power system of the island of Ireland for varying levels of variable renewable power generation. We find that the impacts of integer modelling are non-trivial, and are heterogeneous across firms and wind levels. Furthermore, excluding integer modelling exaggerates the impact of price-making behaviour. We conclude that neglecting integer constraints in power system market models leads to inaccurate results, particularly at high penetrations of renewable energy sources.</p>