Comparison of Gray-Box and Black-Box Two-Level Three-Phase Inverter Models for Electrical Drives

The accuracy of the set voltage compared to its reference value has a high impact on the control performance of three-phase electrical drives, especially if the voltage is an input variable of integrated observers (e.g., flux observer). Voltage deviations are generally a disturbance and, therefore, they lead to a less-than-ideal control performance of the drive. In the literature, most approaches only model the basic inverter effects but do not sufficiently address its strongly nonlinear behavior at very high or low duty cycles. To enable accurate voltage estimation in the entire operation range of a given drive, a black-box inverter model utilizing machine learning is presented in this article. By means of artificial neural networks, a direct mapping of available signals in the control framework and the actual inverter output voltage is realized. For comparison, a gray-box inverter model whose parameters are identified by using half-automatized recorded datasets and a particle swarm optimization is derived. Comprehensive experimental investigations prove the effectiveness of both approaches. The gray-box model can estimate the phase voltages per switching period precisely with a root-mean-square error of less than 1.1 V at a 560 V DC-link voltage level, whereas the machine-learning-based black-box approach even achieves an error of less than 0.65 V.