Generalized linear-constrained optimal power flow for distribution networks

Optimal power flow (OPF) plays an important role in the secure and economical operation of the distribution network. This paper proposes a novel generalized linear-constrained optimal power flow (GLOPF) model for both radial and mesh distribution networks, which iteratively approaches the optimal solution to the original OPF problem. The first-order Taylor series approximation method is applied to linearize the non-linear and non-convex power flow constraints for a given Taylor expansion point (TEP). In addition, the objective function of the GLOPF model is only added with an easy-compute second-order penalty on state variables, which is at least positive semi-definite and guarantees the convexity of the quadratic optimization. Then a TEP-based iterative (TEP-I) method is proposed in the GLOPF model to construct a series of linear-constrained convex quadratic optimizations, which avoids the complex calculation of quasi-Hessian or Hessian matrices in traditional sequential programming methods. The converged solution to the GLOPF model is proved to satisfy the Karush-Kuhn-Tucker conditions of the original OPF problem. Furthermore, the GLOPF model at first and second iterations can be implemented as the 'cold-start' and 'warm-start' LOPF models, respectively. Case studies verify the super-linear convergence and high accuracy of the proposed GLOPF model.