The uncertainty of new energy results in power prediction errors, causing new energy producers to bear high wind curtailment losses and deviation penalties due to bidding deviations. To address these issues, this paper proposes a feature-constrained multi-layer perception (MLP) power prediction algorithm, combined with storage-based bilateral transactions, to provide power support and reduce bidding deviations. First, the MLP model is enhanced by improving the relevancy of the hidden layers through adaptive learning, which strengthens its ability to capture nonlinear rules in input data and improves power prediction accuracy. Then, the algorithm allows for bilateral transactions between new energy producers and storage enterprise before entering the day-ahead market, helping mitigate the penalties associated with prediction errors including deviation and curtailment costs. Finally, the case study demonstrates that the feature-constrained MLP effectively improves the power prediction accuracy. Additionally, engaging in bilateral transactions with storage enterprise significantly reduces the costs incurred by new energy producers due to bid deviations.