infonet-economy

We present a medium-term planning model for hydropower production based on multistage stochastic programming (MSP). The model determines a production schedule for a planning horizon of one year where decisions are made on generation, pumping or spillover. While in reality a production schedule must be determined with (at least) hourly time resolution, the MSP model cannot decide in hourly steps due to the curse of dimensionality. To overcome this issue, we exploit a special aggregation technique based on occupation levels for prices.

The system under consideration consists of several interconnected seasonal reservoirs and produced electricity is sold on the spot market. Thus, we consider stochastic inflows and stochastic electricity prices which are modeled with a regime-switching approach to take also extreme price movements (spikes) into account. Scenario paths are generated with Monte Carlo simulation and then aggregated to scenario trees which serve as input for the stochastic optimization problem.

In an extension, we use the approach for the valuation of non-standard power contracts by means of indifference pricing. In a first step, an optimal production schedule is determined where the objective function consists of a mix of risk and return that can be weighted according to the decision maker's preferences. In a second step, another optimization model is solved that includes also one or more contracts for the delivery of electricity. The model minimizes the price the producer must demand for the delivery of electricity subject to the constraint that the resulting mix of risk and return with inclusion of the contracts is not worse than without (for the case that electricity is sold only at the spot market). The demand for the contracts may depend on price levels and can be stochastic, which requires also a corresponding model for the load. Results are presented for a multi-reservoir system located in the Alps.