In order to enhance the precisions of grey prediction models, it is essential to address the univariate constraints of the traditional GM(1,1) model and consider the influences of data’s time delay and nonlinear mapping on system behavior. In this paper, based on the grey model with background value optimization, we propose a time-delay optimized grey BP neural network combinatorial model (BP-TDOGM(1,1)) by introducing a time-delay causal term and combining with the BP neural network. The mechanisms of time delay, nonlinear mapping and related factor sequences on system behaviour are discussed in detail. Furthermore, the modelling framework, parameter estimation methods and model resolution techniques are investigated with a view to enhancing the capture of data correlations. These endeavours are designed to extend the scope of application of neural networks in scenarios characterized by limited information and to markedly optimize the prediction accuracy of the grey forecast model. Ultimately, the proposed model's efficacy is validated through an example of forecasting China's power production. This example offers a novel approach to address the practical challenges posed by limited time-delay information. It also serves as a decision-making reference for China's power sector, ensuring the harmonious development of power supply and the economy.