Enhanced Z-bus method for analytical computation of voltage sensitivities in distribution networks

Voltage sensitivity matrices are fundamental for the model-based control of the distribution networks. Here, an accurate estimation of voltage sensitivity to active/reactive power injections and tap-position of an on-load tap changer is essential for network modelling. In literature, voltage sensitivity to tap-position is computed by assuming its equivalence with voltage sensitivity to voltage magnitude of the slack bus. However, this approach provides an approximate estimation, and it leads to significant error when the external grid has a low strength. Hence, this study proposes an Enhanced Z-bus method, which comprises of analytical expressions for direct estimation of the voltage sensitivity to tap-position and active/reactive power injections. Importantly, the enhanced Z-bus method can accurately compute the voltage sensitivity to tap-position and active/reactive power injections for any strength of the external grid. The proposed method is tested in a radial (UKGDS), mesh (Case33bw) and reconfigurable (MV Oberrhein) network. Furthermore, it is benchmarked with the perturb-and-observe, Jacobian method and the proprietary methods of DigSILENT PowerFactory. Finally, the proposed method is found to be computationally competent with the existing Jacobian and Z-bus methods.