Demand and Supply Curve Forecasting using a Monotonic Autoencoder for Short-Term Day-Ahead Electricity Market Bid Curves

Abstract

This paper proposes a novel short-term forecasting model for day-ahead electricity market demand and supply price/volume curves. These curves are intrinsically monotonic. The model decomposes the curves into three structurally meaningful and interpretable components. These components are two specific points $\mathbf{A}_t$ and $\mathbf{B}_t$ on the volume axis at a given time $t$, and the vector $\mathbf{C}_t$ of the prices corresponding to the volumes laying between $\mathbf{A}_t$ and $\mathbf{B}_t$. This approach purposely separates the time variations of the curves in the price and volume axes, to an advantage. The $\mathbf{A}_t$ and $\mathbf{B}_t$ points are separately forecasted using an introduced variant of the Echo State Network (ESN), which will be termed Enhanced ESN (EESN).  

For forecasting $\mathbf{C}_t$, a spatiotemporal model incorporating a monotonic autoencoder is used, in order to eliminate redundant information from the curves before forecasting individual encoding elements with the EESN. The autoencoder is called monotonic because a distance-weighted average of the five nearest neighbors of the autoencoder output is used to construct an approximate version of the curve which is guaranteed monotonic.

To evaluate the forecasting performance of the model, a novel loss function called the Heterogeneous Curves Mean Absolute Error (HCMAE) is proposed. The forecasted $\hat{\mathbf{A}}_t$, $\hat{\mathbf{B}}_t$, and $\hat{\mathbf{C}}_{t}$ components are optimally glued together into curves using a model that takes into account curve information at times $t - 1$ and $t - 7$ to produce a curve forecast aimed at minimizing HCMAE. The model is tested on data coming from the Italian IPEX market NORD zone. It is numerically shown that the proposed model significantly outperforms traditional PCA-based models and other benchmarks.

Keywords: day ahead electricity market, short term forecasting, demand and supply curves, autoencoders, machine learning