Power capacitors are widely used in power systems, and any internal capacitor failures will affect the safe operations of the systems. The most common failures include humidity, partial discharge, aging, or insulating material degradation and structural damage. The purpose of this study is to detect the types of power capacitor failures by using a humanmachine interface diagnostic system in order to determine the real-time status of the power capacitors. Partial discharge data measurement and diagnostic analysis were mainly conducted on power capacitors operating at a low voltage for a long time. Defects were pre-processed before capacitance measurement, and then, an electric testing machine was used to conduct a partial discharge test for capacitor enclosures and to continuously apply voltage until the occurrence of a partial discharge. A high frequency oscillograph was used to capture the voltage and partial discharge signals. Subsequently, the empirical mode decomposition (EMD) was applied to identify the characteristics of the discharge signals and to build the chaos and error scatter map by combining the chaotic synchronization detection and analysis method. Moreover, eyes of chaos were taken as the characteristics of fault diagnosis, and an extension algorithm was used to identify capacitance failures. The advantages of this method are to reduce the characteristics' captured data and to effectively detect the minimum movement of the voltage signal discharged from power capacitors, so that the operating states of the power capacitors can be detected and determined, in order to carry out emergency measures in advance and prevent major disasters. After verification through actual measurement, the proposed method has a detection rate of 84% based on the extension theory, which proves that the method used in this study is applicable to partial discharge detection of power capacitors.