质量流量可调的热电联合系统可以提高能源系统的灵活性、经济性和可持续发展能力。但是，考虑质量流量可调的热电联合系统的优化运行问题是一个高度非凸非线性的问题，主要体现在热力网络模型中的双线性项，即质量流量和节点温度的乘积。现有的方法，如非线性优化、广义Benders分解方法和凸松弛技术等，在求解质量和计算性能上仍然存在不足。为了解决这一问题，本文首先建立了基于质量-流量调节的区域供热网络的基础模型，并通过等效变换和变量代换对基础模型进行了重构。该重构模型减少了非凸约束和双线性项，而且在不失去最优性的前提下，加快了求解过程。然后，文中分别建立了电力网络模型和能源模型，结合之前构造的供热网络模型，建立起热电联合系统优化调度模型。为了松弛联合调度模型中剩余的双线性项，文中采用McCormick包络的凸松弛方法，得到了联合调度模型的目标函数下界。为了提高McCormick松弛的质量，文中提出了一种紧缩McCormick的方法：首先 ，采用分段McCormick技术，将双线性项中一个变量的可行域划分为几个不相交的区域，通过求解此优化问题可以选出最优解所在的区域，从而缩小了被划分变量的可行域；然后，提出了一种启发式的边界收缩算法来进一步压缩分段McCormick技术得到的缩小版可行域，并恢复了此最优解附近的可行解。算例分析表明，与原对偶内点法和求得全局最优解的双线性求解器提供的方法相比，本文提出的紧缩McCormick方法能快速求解热电联合运行问题，得到令人满意的兼具最优性和可行性的调度结果。

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.