Convex Optimal Power Flow Based on Second-Order Cone Programming: Models, Algorithms and Applications

Optimal power flow (OPF) is the fundamental mathematical model to optimally operate the power system. Improving the solution quality of OPF can help the power industry save billions of dollars annually. Typical applications of OPF include economic dispatch, locational marginal pricing (LMP), power loss minimization, maximizing renewable energy penetration and network planning. Past decades have witnessed enormous research efforts on OPF since J. Carpentier firstly published the fully formulated alternating current OPF (ACOPF) model which is nonlinear and nonconvex. These research efforts lead to promising developments regarding modelling techniques, solution algorithms and expanding applications.
This thesis firstly proposes three convex OPF models based on SOCP (SOC-ACOPF). Conic relaxations and McCormick envelopes are used to derive our SOC-ACOPF models. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. Feasible region relationships between the proposed SOC-ACOPF models are analytically proved. A heuristic algorithm to recover feasible OPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through several IEEE case studies under various load scenarios. The quality of solutions with respect to global optimum is evaluated using MATPOWER and LINDOGLOBAL. A computational comparison with other SOC-ACOPF models in the literature is also conducted. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm. We then propose to speed up solving large-scale SOC-ACOPF problem by decomposition and parallelization. Firstly, we use spectral factorization to partition large power network to multiple subnetworks connected by tie-lines. Then a modified Benders decomposition algorithm (M-BDA) is proposed to solve the SOC-ACOPF problem iteratively. Taking the total power output of each subnetwork as the complicating variable, we formulate the SOC-ACOPF problem of tie-lines as the master problem and the SOC-ACOPF problems of the subnetworks as the subproblems in the proposed M-BDA. The feasibility of the proposed M-BDA is analytically proved. A GAMS grid computing framework is designed to compute the formulated subproblems in parallel. The numerical results show that the proposed M-BDA can solve large-scale SOC-ACOPF problem efficiently. Accelerated M-BDA by parallel computing converges within few iterations. The computational efficiency can be improved by increasing the number of partitioned subnetworks. Finally, various applications of our SOC-ACOPF models and M-BDA are demonstrated by real power network test cases and numerical results. These applications include distribution locational marginal pricing (DLMP), stochastic optimal operation of voltage-source converter based multi-terminal DC transmission (VSC-MTDC) and flexible AC transmission system (FACTS) to integrate wind power, and coordinated energy dispatch in European super grid.