To address the challenges about high computational burden

poor privacy and reliability in centralized scheduling of large-scale electric vehicles (EVs)

this paper proposes a real-time EV charging scheduling strategy based on the distributed approximate dynamic programming (ADP). First

a polytope-based EV charging model is constructed

and a corresponding EV aggregation and disaggregation method based on polytope approximation is proposed

which can reduce computational complexity while ensuring sufficient optimization accuracy. Furthermore

a centralized scheduling model for aggregated EVs is established

where the model is reformulated under the Markov decision process so as to align with the practical real-time scheduling process. Next

this study proposes a distributed ADP algorithm to solve the scheduling model under stochastic environments. The value function is approximated using piecewise linear functions

and a consensus theory incorporating power limitation factors is applied for distributed optimization. Moreover

by integrating the ADP algorithm with consensus theory

a distributed piecewise linear function slope update method is proposed

which can embed empirical information about the system’s stochastic factors into the value function

assisting decision-making by only utilizing local information and communication between neighboring elements. As a result

the approximate global optimal real-time EV scheduling strategy is obtained in a distributed manner. Finally

case studies on the modified IEEE 6-bus system and IEEE 118-bus system validate the effectiveness of the proposed polytope-based aggregation method

consensus-based distributed optimization method

and distributed ADP stochastic solving method.