Power capacitors are extensively used in power systems; thus, any internal capacitor fault can affect their safe operation. The most common faults include dampness, partial discharge, aging or insulation deterioration, and structural deterioration. The purpose of this study is to use a human–machine interface diagnosis system to detect the type of power capacitor fault, so as to determine the real-time status of the power capacitor. Partial discharge data are measured and diagnosed for the power capacitors that are functional and remaining in long-term high-voltage operation. The defects are handled before the capacitor is measured by a high-frequency current transformer (HFCT) sensor, and one power platform tester is used to measure partial discharge in the capacitor case. The voltage is increased until the partial discharge phenomenon stops, and the voltage and partial discharge signals are visualized by using a high-frequency oscillograph. Afterwards, the feature of the discharge signal is determined by the empirical mode decomposition (EMD) method, combined with the chaos synchronization detection analysis method to establish the chaotic error scatter map of the discharge voltage. Then, the chaos eyes are used as the features of fault diagnosis, and the extension neural network (ENN) algorithm is used for capacitor fault recognition. The advantages of this method are that the feature extraction data volume can be reduced, subtle changes in power capacitor discharge voltage signal can be detected effectively so as to detect the power capacitor’s operating state, and emergency measures can be executed in advance to prevent severe disasters. The proposed method is validated by actual measurements. The detection rate of the ENN fault detection method is 95%, proving that this method is applicable to power capacitor partial discharge detection.