Hydraulic-Thermal Cooperative Optimization of Integrated Energy Systems: A Convex Optimization Approach

The integrated energy systems (IESs) that combine multiple heterogeneous energy systems such as power, natural gas, and district heating systems, are believed to have high potentials in future energy systems owing to their advantages in economy, energy efficiency, and promoting renewable energy consumption. The complicated hydraulic and thermal operating conditions of the district heating network (DHN) render the dispatch of IESs a nonlinear and nonconvex optimization problem that is computationally intractable. To address this problem, firstly, we propose a hydraulic-thermal cooperative optimization (HTCO) model for the operation of IESs. Secondly, the DHN model is reformulated by introducing auxiliary variables to reduce the complexity, based on which the HTCO model is converted into a nonconvex quadratically constrained programming (NCQCP). Thirdly, a second-order conic relaxation model is proposed for the NCQCP model, and a penalty model is introduced based on the convex-concave procedure to reduce the relaxation errors. Finally, an iterative algorithm with efficient stopping criteria is developed for the HTCO model to find a local optimum, in which low optimality gaps (similar to 5.3% for the small case and similar to 2.4% for the big case) are numerically observed. Case studies verify the effectiveness of the proposed methods.