Convex Relaxation of Combined Heat and Power Dispatch

TL;DR

This paper introduces a convex optimization approach for combined heat and power dispatch that enhances solution quality and computational efficiency by relaxing nonlinear constraints and employing an adaptive solution algorithm.

Contribution

It presents a novel convex model for combined heat and power dispatch that avoids simplifying assumptions and improves solution accuracy through relaxation and dynamic partitioning.

Findings

The proposed method outperforms traditional nonlinear programming solutions.

Convex relaxations significantly improve computational efficiency.

Adaptive algorithm reduces relaxation gaps effectively.

Abstract

Combined heat and power dispatch promotes interactions and synergies between electric power systems and district heating systems. However, nonlinear and nonconvex heating flow imposes significant challenges on finding qualified solutions efficiently. Most existing methods rely on constant flow assumptions to derive a linear heating flow model, sacrificing optimality for computational simplicity. This paper proposes a novel convex combined heat and power dispatch model based on model simplification and constraint relaxation, which improves solution quality and avoids assumptions on operating regimes of district heating systems. To alleviate mathematical complexity introduced by the commonly used node method, a simplified thermal dynamic model is proposed to capture temperature changes in networked pipelines. Conic and polyhedral relaxations are then applied to convexify the original problems with bilinear and quadratic equality constraints. Furthermore, an adaptive solution algorithm is proposed to successively reduce relaxation gaps based on dynamic bivariate partitioning, improving solution optimality with desirable computational efficiency. The proposed method is verified on a 33-bus electric power system integrated with a 30-node district heating system and compared to nonlinear programming solvers and constant-flow-based solutions.