Demand and supply curve forecasting using a monotonic autoencoder for short-term day-ahead electricity market bid curves

This paper proposes a novel short-term modeling and forecasting framework for day-ahead electricity market demand and supply price/volume curves. These economically and financially important curves are obtained daily from data derived from the full set of the price/volume bids submitted to the market, and are computed preliminarily to the market price setting phase. They contain a wealth of market information, but are difficult to forecast due to the peculiarity of their data structure. They are intrinsically monotonic, and take values on an irregularly distributed set of volume values which change in location and number each day. Unlike in the case of electricity price forecasting, only a few research groups have addressed the curve forecasting problem so far. In addition, because it is difficult to preserve monotonicity when forecasting these curves, and although its violation can result in incoherent forecasts, the existing curve forecasting models usually don’t explicitly enforce this constraint. In this paper, a modeling and forecasting framework is proposed which decomposes each curve into three structurally meaningful and interpretable geometrical entities, corresponding to macroscopic features of the curves. At a given time t, these geometrical entities are two special (price,volume) curve points At and Bt, and the price/volume vector Ct between them. On the one hand, the At and Bt points are directly and individually forecast using a variant of the Echo State Network machine learning architecture. On the other hand, the dependency on time of the Ct segment is simplified, and this simplified Ct is forecast by forecasting its reduced representation as internal to a suitably developed monotonic autoencoder network. Curve comparison, necessary for curve fitting, for the quality assessment of the forecasts, and for benchmarking the proposed framework against other available models, is made by means of a suitably developed metric algorithm which we call ‘Heterogeneous Curves Mean Absolute Error’. The three components of the curves, At, Bt and Ct, are hence optimally combined and glued together by means of optimization of this error. The framework is tested on data from the NORD zone of the Italian day-ahead IPEX zonal market. It is numerically shown that forecasting with the proposed framework outperforms forecasting with the few benchmarks available, including stochastic-functional and PCA-based models.