MISOCP Model for Reactive Power Optimization With Nonuniform Voltage Regulators in Unbalanced Three-Phase Active Distribution Networks

Reactive power optimization (RPO) is a key task in the operation and control of active distribution networks (ADNs). The nonlinear power flow constraints and the integers introduced by voltage regulator (VR) constraints make the nonconvex RPO model difficult to solve. In this paper, a RPO model is proposed considering the nonuniform tap ratios of VRs. The three phases in VRs are independently controlled and the phase coupling effects are strictly considered. Moreover, to deal with the bilinear relationship among continuous complex voltage phasors and discrete tap ratios, the voltage phasor matrix is decoupled into real and imaginary parts, and a status variable method is proposed to exactly linearize the bilinear terms. Further, the nonlinear power flow constraints are relaxed to a set of second-order cone constraints without neglecting the coupling effect among the three phases and are proved to be equivalent to the semi-definite constraints, which does not require the rank-1 verification and is more efficient and scalable. Thus, the original nonconvex RPO for three-phase unbalanced ADNs is simplified to a mixed-integer second-order cone programming (MISOCP) model. Case studies validate the model's effectiveness, and the computational efficiency meets practical requirements. Note to Practitioners-This paper simplifies the complex problem of reactive power optimization for active distribution networks with unbalanced three-phase power flows. We offer a novel RPO model improving the typically nonconvex and nonlinear optimal power flow problem, and addressing the particular challenges imposed by voltage regulators optimization with nonuniform tap ratios. Independent control of the VR phases and accurate incorporation of phase coupling effects have been realized, greatly simplifying the optimization process. The transformation of nonlinear power flow constraints into a computationally efficient set of second-order cone constraints eliminates the need for cumbersome rank-1 verification. Our mixed-integer second-order cone programming model integrates smoothly with standard optimization procedures, improving voltage regulation and network stability. The effectiveness and efficiency of the approach have been validated in case studies, offering a viable tool for industry application.