Influence of forecasting electricity prices in the optimization of complex hydrothermal systems. (English) Zbl 1189.91169
The paper deals with short-term hydrothermal scheduling (STHS) known as one of the most important optimization problems of the power systems. In traditional centralized markets, the aim of STHS is to determine the optimal operation schedule of thermal units and hydro-plants which minimizes the total thermal production costs over a short-term period, taking into account the operating constraints. The model considered in the paper concerns the current problem of competitive deregulated electricity market. In the presented approach, the company maximizes profit over a period of up to one week. In such a framework, the authors propose a new method for addressing the short-term optimal operation of a generation company. The paper generalizes a sequence of papers (among others: L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez [Appl. Math. Comput. 184, No. 1, 12–22 (2007; Zbl 1108.76019)]; L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez [J. Comput. Appl. Math. 192, No. 1, 11–19 (2006; Zbl 1088.49010)] ; L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez [Int. J. Comput. Math. 86, No. 2, 237–249 (2009; Zbl 1155.91441)]; L. Bayón, J. M. Grau and P. Suárez [Math. Probl. Eng. 8, No. 3, 181–196 (2002; Zbl 1130.80304)]). The contribution of the paper is threefold. Firstly, the authors present a novel method for next-day price forecasting based on a functional approach that considers the hourly price time series as a series of hourly observation of daily price functions. They model the functional time series with a linear autoregressive functional model which describes the relationships between each daily function of prices and the functions of previous days. Secondly, they formulate the optimization problem (within the framework of nonsmooth analysis using Pontryagin’s maximum principle), and propose a new method that uses diverse mathematical techniques (the shooting method, Euler’s method, the cyclic coordinate descent method) adapted to the case of functionals. Finally, the results of applying the method to a price-taker company in the Spanish electricity market are presented.
Reviewer: Malgorzata Doman (Poznań)
MSC:
| 91B99 | Mathematical economics |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 91B84 | Economic time series analysis |
Keywords:
optimal control; electricity markets; shooting method; cyclic coordinate descent; forecasting; functional models; time series analysisSoftware:
fda (R)References:
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