A Stochastic Integer Programming Model for Incorporating Day-Ahead Trading of Electricity into Hydro-Thermal Unit Commitment

Abstract

We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochastic integer program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.

Optimal Bidding Strategies for Thermal and Generic Programming Units in the Day-Ahead Electricity Market

“…It can be easily verified that for any given value of the first stage variables and , (15) and (16) correspond to the optimal bidding rules developed in (12)- (14). Equations (15) and (16) can be used to derive the expressions of the matched energy at each scenario , as functions of the first stage variables and .…”

“…In [14], the concept of price-power function, which is similar to the matched energy function defined in this paper, was used to derive the optimal offer curves of a hydrothermal system under the assumption that the spot prices for the day-ahead and reserve markets behave as a Markov chain. The mixed-integer stochastic programming model presented in [15] distinguishes between the variables corresponding to the bid energy and those representing the matched energy, although in a price-maker framework and without BCs. An earlier model [16] is found to be closely related in some aspects to the one presented in this study, where a stochastic unit commitment problem with BC is solved by maximizing the day-ahead market benefit.…”

Optimal bidding of a profit-maximizing hydropower producer in day-ahead and real-time markets

“…Further stochastic hydropower planning models are cited in the [14], [15], [16]. A stochastic hydropower planning model, which takes into account uncertainty related to the realtime market prices has been developed by Olsson in [17].…”

Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming

“…Since for applied stochastic optimization models (see, e.g., [18,19]) often the dimension m 2 of each y 2i gets large, the mixed-integer program (3) might become huge even for small numbers N of scenarios and practically unsolvable for large N . Thus, in applications, it might be desirable or even inevitable to reduce the number of scenarios such that reasonable solution times for (3) are achieved.…”