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This study introduces a fast locating algorithm for a switched shunt capacitor based on the slopes of the voltage/current space vectors at monitoring points of a power system. Compared with the other suggested slope-based methods, such as signal-processing and filter-based methods, the proposed algorithm herein offers a robuster and more reliable locating method because of using the information of all three phases, whereas other methods separately process individual phase signals. The method is training free and established based on algebraic calculations with a simple realisation algorithm, which is independent of the power system dynamics and parameters. The proposed method is analytically investigated and then verified based on the time-domain simulation of two study systems. The study systems cover various capacitor-switching scenarios, harmonic effects and measurement noise and power system dynamics including dynamics of rotating machines and power electronic converters.