Short-run economic dispatch with mathematical modelling of the adjustment cost

In a typical liberalised wholesale power market, an optimisation process ensures the economically efficient utilisation of the controllable resources every few minutes. But electricity networks are subject to constant shocks to the available generation, load, or transmission assets. The response to these shocks is through a variety of ad hoc mechanisms which do not involve an optimisation process and therefore cannot achieve economically efficient utilisation of the available assets. But the higher the cost of responding to contingencies ex post the greater the need there is to distort the ex ante operation of the power system. In cases where the power system cannot respond at all to a particular contingency ex post, the power system must often be operated ex ante as though the contingency has already happened. This significantly reduces the efficiency with which the available assets can be utilised ex ante. In this paper the concept of short-run economic dispatch is introduced and mathematically modelled. The concept of short-run economic dispatch is formulated through three stages: (1) the initial steady-state equilibrium, (2) transition to a new steady-state equilibrium, and (3) final steady-state equilibrium. These three stages model the state of power system before, during, and after contingency occurred. The derived mathematical model is a linear programming problem. The approach is illustrated using the IEEE 24-node example system.