Abstract: Quarterly electricity consumption forecasting poses significant challenges due to its inherent characteristics of periodic oscillations, nonlinear fluctuations, and temporal trends, driven by seasonal variations and macroeconomic dynamics. This study proposes a seasonal grey model with time power terms (abbreviated as SPGM(1,1)) that integrates trigonometric seasonality components and time-variant power terms into the grey system framework. We rigorously derive the model’s discrete formulation and time response sequence. To enhance the model’s efficacy, a particle swarm optimization (PSO) algorithm is adopted to calibrate the model’s nonlinear parameters. To demonstrate the effectiveness and superiority of the SPGM(1,1) model, this model is applied to simulate and predict Guangzhou’s quarterly electricity consumption data (2018Q1-2023Q4). The numerical results show that the proposed model demonstrates a better performance than the other grey models, the statistical econometric model and the machine learning model. Furthermore, to validate the robustness and stability of the new model, we trained it using datasets with varying proportions. The results demonstrate that the SPGM (1,1) model can adaptively fit and predict data sequences. Therefore, the SPGM(1,1) model is utilized to predict Guangzhou’s quarterly electricity consumption by 2025, inferring that electricity consumption will continue to exhibit a growth tendency with seasonal fluctuations. Based on the attained forecasts, several suggestions are put forward to promote the sustainable development of Guangzhou’s electricity consumption, supporting the evaluation of China’s power system reform pilot programs to derive actionable insights for optimizing energy systems in similar cities globally.