Forecasts of renewable energy generation are crucial to enhance the transmission power of renewable energy power plants (REPPs) with energy storage systems (ESSs). Existing forecasting methods mainly focus on reducing statistical errors and neglect the impact of forecast results on the transmission power of REPPs under stability constraints. This paper proposes a stability-constrained transmission power-oriented forecasting (TPOF) method to maximize the transmission power of REPP. To quantify the relationship between forecast errors and transmission power, a customized loss function is designed, embedding the operational dynamics of the REPP. A training algorithm based on implicit differentiation is developed to ensure the loss back-propagation of the forecasting method. Simulation results based on the model of REPP in the USA demonstrate that the proposed method significantly enhances the transmission power of REPP by precisely mitigating forecast errors during periods of lower stability margins.