Forecasting Electricity Production, Consumption, and Price: Three Novel Fractional Grey Models of a Complex System

Effectively forecasting electricity generation, consumption, and pricing enhances power utilization efficiency, safeguards the stable operation of power systems, and assists power generation enterprises in formulating rational generation plans and dispatch schedules. The electricity generation, consumption, and pricing system exhibits complex chaotic dynamics. Establishing effective predictive models by leveraging the strong coupling and multi-scale uncertainty characteristics of nonlinear dynamical systems is a key challenge in grey modelling. This study leverages grey differential information to effectively transform differential equations into difference equations. Fractional-order cumulative generation operations enable more refined extraction of data characteristics. Based on the coupling and uncertainty features of electricity generation–consumption–pricing dynamics within complex power systems, three types of fractional-order multivariate grey models are established. These models both reflect the system’s dynamic relationships and expand the conceptual framework for grey prediction modelling. Simultaneously, the effectiveness of these three models is analyzed using data on generation, consumption, and prices from both new and traditional power sources within China’s electricity system. Employing identical annual data, the models are evaluated from two distinct perspectives: variations in the numbers of simulated and predicted variables. Experimental results demonstrate that all three novel models perform well. Finally, the most effective predictive application of the three models was selected to forecast electricity generation, consumption, and pricing in China. This provides a basis for China’s power system and supports national macro-level intelligent energy dispatch planning.