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.

I. Introduction

In today’s electrical drives, the phase voltage accuracy is mainly important due to two reasons: On the one hand, the voltage might be the control output signal, and therefore, the performance of the control (e.g., harmonics and efficiency) depends directly on the accuracy of the actual phase voltage compared to its reference. On the other hand, within a drive control framework, the voltage might be the input of integrated observers (e.g., flux observer), and since the phase voltages are generally not measured for cost reasons, the observer's performance highly depends on the modeled set voltage of the inverter. Especially at low-speed levels when only small voltage amplitudes are applied to the motor, the utilization of a voltage information that deviates only little from the true value can already result in dramatically high observation errors [1], [2]. Thus, for increasing the control performance, accurate inverter models and compensation schemes, which aim to cancel out all inverter non-ideal effects, are needed. Their integration into the standard field-oriented control (FOC) framework is visualized in Fig. 1.