Voltage-sensitive distribution factors for contingency analysis and topology optimization

Abstract

Topology optimization is a promising approach for mitigating congestion and managing changing grid conditions, but it is computationally challenging and requires approximations. Conventional distribution factors like PTDFs and LODFs, based on DC power flow, fail to capture voltage variations, reactive power, and losses, thereby limiting their use in detailed optimization tasks such as busbar splitting. This paper introduces generalized distribution factors derived from a voltage-sensitive linearization of the full AC power flow equations. The proposed formulation accurately reflects reactive power flows, Ohmic losses, and voltage deviations while remaining computationally efficient. We derive and evaluate generalized PTDFs, LODFs, and topology modification factors using matrix identities. We discuss potential applications including voltage-aware N-1 security analysis and topology optimization with a focus on busbar splitting. Numerical experiments demonstrate close agreement with full AC solutions, significantly outperforming the traditional DC approximation.

Figures (4)

• Figure 1: Approximation errors of the generalized DC+ approximation defined by Eq. \ref{['eq:psi-sigma']} with respect to the full AC simulation for the IEEE 14-bus test grid. AC simulations and grid data from PyPowSyBl. Branch 14 is excluded since its outage would disconnect the grid.
• Figure 2: Statistical analysis of the approximation error for three common test grids of different sizes considering all branch outages and all nodes. The approximation errors of the generalized DC+ approximation defined by Eq. \ref{['eq:psi-sigma']} (blue lines) are substantially smaller than those of the standard DC approximation (orange line).
• Figure 3: The different grid configurations used in the treatment of the opening of a switch or busbar coupler.
• Figure 4: Generalized linear approximation for bus splits. Upper panel: Elementary test grid in the unsplit state. Lower panel: Configuration of the substation 3. Opening the busbar coupler leads to voltage drop and phase angle drop at the busbar 1 (BB1). We provide numerical results for state variables and power flows. Two numbers separated by a $\vert$ compare the generalized DC+ approximation in Eq. \ref{['eq:Mo-inverse']} (left) and full AC results (right). AC computations and illustration are produced using PowSyBl powsybl2025.