## Analytical expressions for characterising voltage dips and phase-angle jumps in electricity networks

Voltage dips/sags are one of the major concerns for electricity consumers as well as utility service providers. Therefore, the characterisation of voltage dips/sags is required. This study presents a set of mathematical expressions for characterising different types of voltage dips/sags and their associated phase-angle jumps, which are typically found due to faults and/or disturbances in electricity networks. The expressions are derived analytically from the model of the power network containing generators, transmission and/or distribution lines, transformers etc. Four types of voltage dips, namely, A, B, E, and G, which are associated with four major types of faults including balanced three-phase faults, single line-to-ground, double line-to-ground, and line-to-line faults, are considered to derive the analytical expressions. Dynamic simulation results, using a test distribution system, approve the validity as well as the accuracy of the developed expressions. The influence of fault-types and fault-locations is investigated from the mathematical expressions; further, validation is conducted through a simulation study. The analytical expressions, presented in this study, are a valuable tool in the planning stage since the expressions can be employed to characterise during-fault voltage dips at different buses in electricity network without conducting a large number of repeated dynamic simulations.