Combined heat and electricity operation with variable mass flow rates promotes flexibility, economy, and sustainability through synergies between electric power systems (EPSs) and district heating systems (DHSs). Such combined operation presents a highly nonlinear and nonconvex optimization problem, mainly due to the bilinear terms in the heat flow model—that is, the product of the mass flow rate and the nodal temperature. Existing methods, such as nonlinear optimization, generalized Benders decomposition, and convex relaxation, still present challenges in achieving a satisfactory performance in terms of solution quality and computational efficiency. To resolve this problem, we herein first reformulate the district heating network model through an equivalent transformation and variable substitution. The reformulated model has only one set of nonconvex constraints with reduced bilinear terms, and the remaining constraints are linear. Such a reformulation not only ensures optimality, but also accelerates the solving process. To relax the remaining bilinear constraints, we then apply McCormick envelopes and obtain an objective lower bound of the reformulated model. To improve the quality of the McCormick relaxation, we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned variables. We propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible solution. Case studies show that, compared with the interior point method and the method implemented in a global bilinear solver, the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.

通过电力系统 (EPS) 和区域供热系统 (DHS) 之间的协同作用，具有可变质量流量的热电联产运行提高了灵活性、经济性和可持续性。这种组合操作呈现出高度非线性和非凸的优化问题，主要是由于热流模型中的双线性项——即质量流量和节点温度的乘积。现有的方法，例如非线性优化、广义 Benders 分解和凸松弛，仍然在解决方案质量和计算效率方面实现令人满意的性能方面存在挑战。为了解决这个问题，我们首先通过等效变换和变量替换来重新构建区域供热网络模型。重新制定的模型只有一组减少双线性项的非凸约束，其余约束是线性的。这种重新公式化不仅确保了最优性，而且还加速了求解过程。为了放松剩余的双线性约束，我们然后应用 McCormick 包络并获得重构模型的客观下界。为了提高麦考密克松弛的质量，我们采用分段麦考密克技术，将双线性项的一个变量的域划分为几个不相交的区域，以便推导出增强的分区变量的下界和上界。我们提出了一种启发式紧缩方法，以进一步限制从分段 McCormick 技术得出的加强边界并恢复附近的可行解。案例研究表明，