# Prediction of Intraday Electricity Supply Curves
## 2 State of the Art for Supply Curve Prediction  
Most of the published works in this field focus on directly predicting the energy price and demand or other scalar variables. Three recent reviews on the techniques used for such purposes can be found in [8; 9; 10]. Our objective is to predict an offer curve, which is a more complex task. Nonetheless, obtaining this prediction is, indirectly, a prediction of the energy price, which is achieved by obtaining the intersection point of the forecasts of the supply and demand curves, as proposed by [11]. The two main challenges in predicting a supply curve are that it is not a prediction of a scalar quantity and it is not a continuous function. An approach that addresses the first challenge is the procedure proposed by [12], which uses functional data nonparametric techniques to model residual demand curves. Since they use nonparametric kernel-type estimators, they are limited by the problem known as the curse of dimension and, therefore, only consider a single functional regressor. These authors assume that the curves are sufficiently smooth with up to two derivatives, which contradicts the second challenge. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **1 st Session** & **2 nd Session** & **3 rd Session** & **4 th Session** & **5 th Session** & **6 th Session** \\ \hline Market opening & 14:00 D-1 & 17:00 D-1 & 21:00 D-1 & 1:00 D & 4:00 D & 9:00 D \\ Market close & 15:00 D-1 & 17:50 D-1 & 21:50 D-1 & 1:50 D & 4:50 D & 9:50 D \\ Matching & 15:00 D-1 & 17:50 D-1 & 21:50 D-1 & 1:50 D & 4:50 D & 9:50 D \\ PISCA program publication & 15:07 D-1 & 17:57 D-1 & 21:57 D-1 & 1:57 D & 4:57 D & 9:57 D \\ PHF publication of the OSs & 16:20 D-1 & 18:20 D-1 & 22:20 D-1 & 2:20 D & 5:20 D & 10:20 D \\ Market horizon & 24 h & 28 h & 24 h & 20 h & 17 h & 12 h \\ (Time period) & (1–24 D) & (21–24 D-1 \& 1–24 D) & (1–24 D) & (5–24 D) & (8–24 D) & (13–24 D) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Schedules and horizons of intraday markets. Information available at: [[https://www.omies.es](https://www.omies.es)]([https://www.omies.es](https://www.omies.es)) [7], accessed on 6 September 2024. In [11], LASSO regression is used to forecast a short number of bid classes obtained from the supply and demand curves in the EPEX market. This paper used the term \"X-model\" to denote the process of obtaining the price as a result of crossing the supply and demand curves. This is the first work that addresses both challenges since it takes into account the fact that the functions to be predicted are stepwise. In [13], a modification of the X-model is proposed, where transformed versions of the curves are used by assuming a perfectly inelastic demand. Both methods use a small number (only 16) of bid classes, which makes their approximation of the curves imprecise. In fact, as the motivation of [11; 13] is price prediction, the authors do not study the behavior of the procedure as a curve predictor. Parametric and nonparametric functional autoregressive models were used in [14] to model the supply and demand curves of the Italian electricity market. Again, the techniques used assume smoothness conditions that are not satisfied by step functions. Another approach is to approximate the curves using others from a parametric family and predict the relevant parameters. In the literature, various procedures of this kind can be found, such as using radial basis functions in [15] or using polynomials and sigmoid functions [16]. In [15], univariate autoregressive models were used for each of the parameters, and weekly seasonality was modeled using dummy variables. The authors of [16] used vector autoregressive models with seasonal harmonic component periods of 24 and 168. This approach has the attraction that the number of parameters to be predicted is small, but it does not solve the challenge regarding the non-continuity of the curves. In [17], a continuous piecewise version of the supply curve is used to approximate it with great precision.