Abstract
Optimal power flow (OPF) is a non-linear and non-convex problem that seeks the optimization of a power system operation point to minimize the total generation costs or transmission losses. This study proposes an OPF model considering current margins in radial networks. The objective function of this OPF model has an additional term of current margins of the line besides the traditional transmission losses and generations costs, which contributes to thermal stability margins of power systems. The model is a reformulated bus injection model with clear physical meanings. Second order cone program (SOCP) relaxations for the proposed OPF are made, followed by the over-satisfaction condition guaranteeing the exactness of the SOCP relaxations. A simple 6-node case and several IEEE benchmark systems are studied to illustrate the efficiency of the developed results.
Highlights
The Optimal power flow (OPF) problem is widely researched in the many fields of power systems, such as energy management, economic dispatch, congestion management, demand response, etc. [1].In Carpentier’s research about economic dispatch, this optimization problem is firstly raised [2].Dommel and Tinney make the contribution of making OPF a complete optimization model [3].Constrained by Kirchhoff’s law, the OPF problem is a nonlinear mathematical program, being non-convex and NP-hard [4]
OPF 3 model metioned in the paper of which the semidefinite program (SDP) relaxations have been changed into Second order cone program (SOCP) ones
The model mentioned in [31] is in a complex number field and our model is illustrated in a real number filed, and as is shown in Table 7, the model proposed in this paper calculates faster than the bus injection model with SOCP relaxation of each branch, which is especially obvious in the large systems
Summary
The Optimal power flow (OPF) problem is widely researched in the many fields of power systems, such as energy management, economic dispatch, congestion management, demand response, etc. [1]. [19] firstly transforms the power flow model in a quadric format with SDP relaxations This model processes superlinear convergence but it is not exactly equal to the original problem. [20] reveals that SDP relaxation is exact only if the duality gap is zero This method is based on the bus injection model, relaxing the nonconvex rank-1 constraint of network’s voltage matrix. By relaxing the constraints of apparent power, branch current and node voltage, the OPF is shown in a convex optimization model. It calculates faster than the SDP method with colossal matrices In this model, the physical relationship is no longer clear due to the squared algorithm of the power flow equation and the direction in which the line should be defined. We use different weight coefficients to make the current margins, active power losses and generation costs an objective function.
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