A Conic Quadratic Format for the Load Flow Equations of Meshed Networks

Recent research has shown that the load flow equations describing the steady-state conditions in a radial network can be formulated as a second-order cone program and solved using polynomial-time interior point methods. This paper extends the conic formulation to meshed networks by including a trigonometric functional constraint for the voltage angle spread on each line in the network. In particular, it is shown that the load flow solution of a meshed network can be obtained from a sequence of conic programming solutions. The proposed formulation and iterative procedure are validated by comparing with the Newton-Raphson solution of the standard power flow model. Testing is reported on seven networks. The proposed format of equations opens the door for new implementations of energy management system functions based on efficient and numerically robust conic quadratic optimization methods.