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The method of fault position is useful for characterising power-system performance in the presence of voltage dips due to faults. It is based on short-circuit simulations repeated for all the system nodes and for many points along the system lines: fault voltages that are below a preset threshold are the required voltage dips. These dips are stored in so-called dip matrices which contain only the dips in all the system nodes when faults occur at points along the lines. The paper proposes a new compact analytical formulation of dip matrices for balanced and unbalanced faults in terms of bidimensional vector relations and for site- and system-voltage dip indexes. Compact formulations are very useful tools when several sensitivity analyses have to be conducted to estimate variation of site- and system-voltage dip indexes in relation to possible reinforcement and/or compensation devices. Graphical presentation of dip matrices is also proposed as a valuable tool to ascertain the critical area for system performance. Numerical applications to an actual transmission system are presented to demonstrate the easy applicability of the model.