Grey Systems Modeling for Energy Forecasting

Grey systems modelling has emerged as a powerful approach to predict energy consumption and production in contexts where data are scarce, incomplete or subject to uncertainty. Originating from the premise that part of the system information is known (‘white’) and part unknown (‘black’), grey models capture dynamic trends through accumulated generating operations and simple differential or difference equations. The most widely used GM(1,1) model applies a first-order differential equation to a univariate time series, thereby extracting underlying exponential patterns from limited observations. Extensions such as multivariate grey models (GM(1,N)), fractional-order accumulation, discrete formulations and nonlinear variants have significantly enhanced forecasting accuracy and robustness. These innovations allow researchers to reflect evolving priorities in new information, embed time-power terms, handle interval data and restore grey action quantities under uncertain influences. In energy forecasting, grey systems have been successfully applied to crude oil, natural gas, electricity and emissions, delivering short-term projections that inform supply planning, policy-making and grid management. The capacity to operate with minimal datasets and adapt rapidly to emerging trends renders grey models particularly valuable in regions with incomplete historical records or during periods of structural change, such as the transition to low-carbon energy systems.

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Grey Systems Modeling for Energy Forecasting publication trend

The graph below shows the total number of articles in grey systems modeling for energy forecasting across all publications each year (not limited to Nature Index journals).

Technical terms

Grey system: A system characterised by partially known information, where modelling techniques infer unknown behaviour from limited data.

GM(1,1) model: The foundational univariate grey forecasting model employing first-order accumulated generating operations and a differential equation to predict time-series trends.

Fractional-order accumulation: A generalisation of the accumulated generating operation using fractional calculus, providing flexible weighting of historical data.

Discrete grey model: A formulation of grey forecasting in discrete time, often enhanced by additional terms such as time-power or interval parameters.

Background value: The mean of adjacent accumulated data points in grey modelling, used to construct and solve forecasting equations.

References

1. Forecasting natural gas consumption of China by using a novel fractional grey model with time power term. Energy Reports (2021).
2. Modeling Method of the Grey GM(1,1) Model with Interval Grey Action Quantity and Its Application. Complexity (2020).
3. Forecasting Electricity Consumption Using an Improved Grey Prediction Model. Information (2018).