Decentralized Continuous-Time Power Dispatch for Integrated Heat and Power Systems via Bernstein-Galerkin Equivalent Projection

Abstract

Decentralized power dispatch for integrated heat and power systems (IHPSs) involves coordinating electric power systems (EPSs) and district heating networks (DHNs) while preserving privacy. The existing methods rely mainly on discretetime DHN models and constant-flow operations, limiting the ability to exploit thermal flexibility. Enabling variable-flow and variable-temperature (VF-VT) operations requires thermal-hydraulic coupling to be addressed together with continuous-time thermal dynamics. However, the simultaneous variations in mass flows and temperature lead to a nonconvex IHPS model, for which conventional decomposition methods are difficult to apply. This paper proposes a decentralized continuous-time dispatch framework using Bernstein-Galerkin equivalent projection. For a prescribed mass flow trajectory, DHN thermal dynamics are formulated in the Bernstein space and projected onto boundary variables, yielding an equivalent feasible-region model without disclosing the internal DHN topology or states. The equivalent model and DHN subproblem are derived from a unified Bernstein-Galerkin formulation, ensuring a consistent thermal state representation throughout the EPS-DHN coordination procedure. A safeguarded Anderson prediction scheme further accelerates the alternating coordination process by using historical updates and fixed-point residuals to predict the next input without additional subproblem solving steps. Numerical results show the proposed method preserves thermal state consistency, exploits VF-VT flexibility, and improves economic and computational performance.