Fault Current Constraint Transmission Expansion Planning Based on the Inverse Matrix Modification Lemma and a Valid Inequality

Abstract

In the transmission expansion planning (TEP) problem, it is challenging to consider a fault current level constraint due to the time-consuming update process of the bus impedance matrix, which is required to calculate the fault currents during the search for the optimal solution. In the existing studies, either a nonlinear update equation or its linearized version is used to calculate the updated bus impedance matrix. In the former case, there is a problem in that the mathematical formulation is derived in the form of mixed-integer nonlinear programming. In the latter case, there is a problem in that an error due to the linearization may exist and the change of fault currents in other buses that are not connected to the new transmission lines cannot be detected. In this paper, we use a method to obtain the exact updated bus impedance matrix directly from the inversion of the bus admittance matrix. We propose a novel method based on the inverse matrix modification lemma (IMML) and a valid inequality is proposed to find a better solution to the TEP problem with fault current level constraint. The proposed method is applied to the IEEE two-area reliability test system with 96 buses to verify the performance and effectiveness of the proposed method and we compare the results with the existing methods. Simulation results show that the existing TEP method based on impedance matrix modification method violates the fault current level constraint in some buses, while the proposed method satisfies the constraint in all buses in a reasonable computation time.

Multistage AC transmission expansion planning including fault current‐limiting high‐temperature superconducting cables and multiple distributed generations to improve short‐circuit level and grid‐scale flexibility

“…The first stream of research concentrates on suppressing different short-circuit levels in the transmission grids [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In [8], the short-circuit level constraint was linearly modelled to restrict fault currents passing through the transmission grid buses below a prescribed safety threshold.…”

“…Relationships ( 7) and ( 8) similarly describe the investment cost of the FCL-HTS cables at stage t and the investment cost of the FCL-HTS cable n in the right-of-way (u,v) at stage t, respectively. Relationship (9) shows the investment cost of the DGs at stage t. The first and second terms of the relationship (10) explain the operation costs of the CG r and DG at stage t, respectively. Relationships ( 11)-( 13) denote the flexibility weighting factors of the transmission line h, PL-HTS cable m, and FCL-HTS cable n in the right-of-way (u,v), respectively.…”

“…Broadly speaking, there are two major streams of research concerning the TEP problem, with the target of satisfying the acceptable short‐circuit level and flexibility requirements. The first stream of research concentrates on suppressing different short‐circuit levels in the transmission grids [8–22]. In [8], the short‐circuit level constraint was linearly modelled to restrict fault currents passing through the transmission grid buses below a prescribed safety threshold.…”

Unlocking emerging impacts of carbon tax on integrated energy systems through supply and demand co-optimization

“…The branch-and-cut algorithm is derived from the branch-and-bound algorithm combined with the cutting plane method [53], whose flowchart is presented in Fig. C1.…”

Optimization-Based Formulations for Short-Circuit Studies with Inverter-Interfaced Generation in PowerModelsProtection.jl

“…A third creates linear approximations of the nonconvex constraints [42]. Last, the nonlinear constraints are relaxed in order to convexify the problem [43]. All these approaches focus on modeling positive-sequence representations of networks and do not address the additional complexities of modeling unbalanced multi-phase systems that are typical of microgrids.…”