Double-Reservoir Deep Echo State Network Architecture for short-term Electricity Demand Forecasting

This study presents a novel, streamlined and scalable deep Echo State Network (ESN) architecture for demand forecasting in electricity markets. In contemporary electricity markets, where each new day it becomes more difficult to achieve smooth technical operations and not too much volatile electricity prices, the market stakeholders face the problem of forecasting energy demand with increasingly high accuracy and computational efficiency, because knowing demand in advance helps manage coming problems. Deep ESNs demonstrated themselves to be very fitting for the forecasting endeavor. We hence propose a deep ESN architecture for demand forecasting that has higher efficiency than currently used deep ESNs, while maintaining similar forecasting accuracy. Our design strategy is based on disentangling the ESN readout matrix from the individual reservoirs that make the ESN deep, just maintaining the readout weights from the output layer reservoir only. Furthermore, we use Particle Swarm optimization (PSO) to optimize the inter-reservoir connecting weights. We will prove, by numerical testing, that this allows our architecture to achieve an accuracy close to that of current deep ESNs, while being more scalable and being based on fewer parameters than the standard deep ESNs. Specifically, we evaluate this architecture by forecasting a daily average electricity demand time series from the Spanish electricity market. Our architecture, once optimized by PSO, is shown to improve over some common benchmarks and state-of-the-art methods.