Increasing reliability of price signals in long term energy management problems

Determining reliable price indicators in the long-term is fundamental for optimal management problems in the energy sector. In hydro-dominated systems, the random components of rain and snow that arrive to the reservoirs have a significant impact on the interaction of the low-cost technology of hydro-generation with more expensive ones. The sample employed to discretize uncertainty changes certain Lagrange multipliers in the corresponding optimization problem that represent a marginal cost for the power system and, therefore, changes the price signals. The effect of sampling in yielding different price indicators can be observed even when running twice the same code on the same computer. Although such values are statistically correct, the variability on the dual output puts at stake economic analyses based on marginal prices. To address this issue, we propose a dual regularization that yields sample-insensitive indicators for a two-stage stochastic model. It is shown that the approach provides the minimal-norm multiplier of the energy management problem in the limit, when certain parameter is driven to zero. The new method is implemented in a rolling horizon mode for a real-life case, representing the Northern European energy system over a period of one year with hourly discretization. When compared to SDDP, an established method in the area, the approach yields a significant reduction in the variance of the optimal Lagrange multipliers used to compute the prices, with respect to different samples.