Linear Approximations of Power Flow Equations in Electrical Power System Modelling—A Review of Methods and Their Applications

The power system is constantly changing. New elements are being added. The network structure is being changed. Existing network infrastructure is being modernised. This results in the need to perform various types of computational analyses. These analyses are designed to assess the impact of new and existing power system components on its operation. These analyses can be complicated, complex and difficult. These analyses are influenced by the size of the actual grid, technical conditions, and the specific requirements of grid operators. Therefore, there is a constant search for methods that simplify them without significantly compromising the accuracy of the obtained results. In real networks, computation time is also a crucial parameter, which can be excessive when analysing multiple operating variants. Linearisation of the computational model significantly contributes to reducing computational time but also affects their accuracy. Particular attention should be paid to two frequently used and compared linearization methods: the DC method and the first-order Taylor expansion. The DC (Direct Current) method offers relatively simple formulas. These relationships are based on simplifying assumptions. They are well suited for error analysis, at the expense of neglecting reactive power and voltage changes. Taylor linearization preserves the full AC structure around a selected operating point. It takes reactive power and voltage changes into account. Its accuracy is local and depends on the base point. It may require re-linearization for large changes in the power system operating states. This article presents a detailed literature review. It concerns the linearization of the power flow problem in the context of solving various computational problems in the power system. Selected works are grouped and categorised by topic. Linearisation methods used in the literature are presented, and the most frequently used ones are also indicated. Research gaps that may be addressed in future work are highlighted.