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. [ABSTRACT FROM AUTHOR]