Co-optimization planning of integrated electricity and district heating systems based on improved quadratic convex relaxation

The rapid growth of combined heat and power (CHP) units has led to the development of integrated electricity and district heating systems (IEHS). To support the design of a highly efficient energy supply system, this paper proposes a long-term co-optimization planning model for an IEHS. Not only CHP units, non-CHP thermal generators, wind farms and electric boilers but also transmission lines and heat pipelines are considered as investment candidates to meet electricity and heat demands. Nonlinear hydraulic conditions and thermal conditions are adopted to precisely capture the characteristics of the heating system. To make the planning model tractable, the nonlinear hydraulic conditions are approximated through piecewise linearization. Based on the introduction of auxiliary variables, the nonconvex thermal conditions are reformulated into linear constraints through quadratic convex relaxation. Hence, the planning model is converted into a large-scale mixed integer linear programming (MILP) problem. Since the planning model is formulated based on independent load blocks, a parallel Benders decomposition algorithm combined with the sequential bound-tightening procedure is proposed to efficiently obtain high-quality solutions. Numerical cases are studied based on two IEHSs of different scales to validate the effectiveness of the proposed co-optimization planning model and the feasibility of the proposed solution methods for solving this complicated planning model for an IEHS.