In a photovoltaic power plant (PVPP), the DC-AC converter (inverter) is one of the components most prone to faults. Even though they are key equipment in such installations, their fault detection techniques are not as much explored as PV module-related issues, for instance. In that sense, this paper is motivated to find novel tools for detection focused on the inverter, employing machine learning (ML) algorithms trained using a hybrid dataset. The hybrid dataset is composed of real and synthetic data for fault-free and faulty conditions. A dataset is built based on fault-free data from the PVPP and faulty data generated by a digital twin (DT). The combination DT and ML is employed using a Clarke/space vector representation of the inverter electrical variables, thus resulting in a novel feature engineering method to extract the most relevant features that can properly represent the operating condition of the PVPP. The solution that was developed can classify multiple operation conditions of the inverter with high accuracy.