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The integrated electricity and heating system (IEHS) can improve energy efficiency and promote renewable energy consumption. When quality-quantity regulation (QQR) is adopted, namely adjusting hydraulic and thermal conditions of heating system, the increase in operation flexibility is more remarkable. However, present IEHS dispatch models considering QQR overlook hydraulic characteristics of valves and variable frequency pumps resulting in inexecutable dispatch results easily and hindering IEHS's flexibility potential. Furthermore, loop networks and the access of multiple heat sources in heating systems may lead to flow reversal, but current research adopts a fixed flow direction which suppresses the potential of flow reversal to improve flexibility. In this paper, we propose an IEHS dispatch model considering QQR to promote renewable energy consumption, which considers hydraulic characteristics of valves and variable frequency pumps, and flow reversal. Specifically, we introduce two binary flow direction labels for every branch in heating system model and then the IEHS dispatch model which can deal with flow reversal is established. A sequential solution process combining linear and nonlinear optimization is formulated to overcome the non-convex feature of IEHS dispatch model. Specifically, piecewise linearization and piecewise McCormick relaxation are combined to handle complex nonlinear terms in the dispatch model. Therefore, a mixed integer linear programming model is obtained and solved, of which results are used as initial values for nonlinear optimization. Results in the case study show that operation cost is decreased by 0.97 % and renewable power consumption rate is increased from 83.31 % to 84.42 % after considering valve adjustment. Operation cost is further decreased by 6.06 % and renewable power consumption rate is increased to 94.04 % after considering flow reversal. • IEHS dispatch model with quality-quantity regulation of heating systems is proposed. • Operation characteristics of pumps and valves in heating system is considered. • Heating system model with flow reversal is constructed. • A sequential method combining linear and nonlinear optimization is formulated. • Impact of valve adjustment and flow reversal on IEHS dispatch is investigated. [ABSTRACT FROM AUTHOR]