Integer modelling of spinning reserve requirements in short term scheduling of hydro systems

In short term power system scheduling, reserve margins are kept in order to maintain the security of the system if a non-forecasted event occurs. The security is maintained by re-dispatch of the generators in the system. During the first seconds of the disturbance it is only possible to re-dispatch the on-line units. The maximal increase of the generation during these first seconds of the disturbance is called the spinning reserve. In hydro dominated power systems the spinning reserve is kept in the hydro system, since hydro units are easy to re-dispatch, For an on-line hydro unit the spinning reserve is the marginal between maximum generation and the actual generation. If a hydro plant has several units, only the on-line units will contribute to the spinning reserve. This means that we need to introduce integer variables to model the spinning reserve contribution from a hydro plant with several units. In the Literature there are several examples of integer models for representation of the generation of hydro plants. The contribution of this paper is that it incorporates the integer representation of the spinning reserve into an integer model of generation scheduling. To this model we apply variable splitting and Lagrange relaxation to decompose the problem into one subproblem for the hydrological constraints and one subproblem for each hydro plant. In order to find feasible solutions we use a combination of network programming and heuristic search. The dual:problem constructed by the decomposition is solved by a subgradient method. In the paper we apply the proposed method to a numerical example.