Supply security in imperfect power markets is modelled under different market designs. In a uniform price auction for electricity with two firms, strategic behaviour may leave firms offering too few capacities and unable to supply all realized demand. Market design that relies oncapacity markets increases available generation capacities for sufficiently high capacity prices and consequently decreases energy prices. However, equilibrium capacity prices are non-competitive. Capacity markets can increase security of supply, but cannot mitigate market power, which is exercised in the capacity market instead of the energy market.