<p>With the continuous growth of energy demand, the over-reliance on traditional fossil fuels has led to two major challenges: energy security and environmental degradation. The global community has reached a consensus on the need to expedite the development of renewable energy, and accurately forecasting the renewable power consumption has become an urgent problem that needs to be addressed. Starting from the inherent defects of the grey model, we refine and optimize it from three aspects: parameter estimation, accumulation calculation, and model structure. By simplifying the foundational structure of the model, the discontinuity error in parameter estimation is eliminated. An adaptation factor incorporated into the model's structure to capture the latest system changes, and the reverse accumulation operator is applied to optimize the model's accumulation. Ultimately, the RPOGM(1,1,t) model is constructed, and the optimal accumulation order is sought using the PSO algorithm. Subsequently, the modeling accuracy and robustness of the model are tested using renewable power consumption data from the US, China, and the Total World. In comparison to&#xa0;other benchmark models, the RPOGM(1,1,t) model demonstrates good modeling performance, with high accuracy and stability. The forecast results suggest that renewable power consumption in the U.S., China, and the Total World is projected to see accelerated growth under the baseline trajectory of current policy and technological development. By 2030, China's renewable power consumption is expected to reach nearly four times that of the U.S., accounting for approximately half of the global total, and China's central role in the global clean energy landscape will be further highlighted.</p>