Real-time optimal decision-making in multi-park systems based on distributed approximate dynamic programming

• Coordinate the participation of all parks in decision-making and protect the privacy of all sides • Value function approximation via piecewise linear functions achieves exceptional accuracy • Outperform traditional myopic strategies. • Accurately describe the carbon emission flow process of energy storage devices. To address the challenges associated with the ambiguous characterization of carbon emissions due to the diversity and temporal coupling of energy storage devices, as well as the computational complexity, privacy concerns, and low reliability in multi-park scheduling arising from source-load uncertainties, a distributed approximate dynamic programming-based real-time optimization strategy for electricity-carbon synergy in multi-park systems is proposed. Initially, an extended carbon emission flow model that incorporates energy storage is developed, resulting in a multi-park optimization decision-making framework that integrates electricity-carbon synergistic decisions. This model is then reformulated as a Markov decision process, and an event-driven mechanism for a low-carbon energy consumption response strategy in parks is introduced. A distributed approximate dynamic programming algorithm is subsequently designed to solve the scheduling model under stochastic conditions. Piecewise linear functions are employed to approximate the value function, enabling distributed updates and training. The approximate dynamic programming algorithm is integrated with the Peaceman-Rachford alternating direction method of multipliers, introducing a distributed slope-updating approach for the piecewise linear functions. This integration incorporates stochastic system information into the value function, enhancing decision-making. Case studies reveal that the average deviation between the distributed approximate dynamic programming current value function update and the true slope value is 1.038 × 10 −10 , demonstrating a significant improvement in computational accuracy over the distributed myopic strategy, with a reduction in calculation error by an average of 0.0662. These findings confirm that the proposed framework effectively addresses stochastic uncertainties while preserving data privacy. © 2017 Elsevier Inc. All rights reserved.