| Summary: | For accurate and efficient control performance of electrical drives, precise values of phase voltages are required. In order to achieve control of the electric drive, the development of mathematical models of the system and its parts is often approached. Data-driven modeling using artificial intelligence can often be unprofitable due to the large amount of computing resources required. To overcome this problem, the idea is to investigate if a genetic programming–symbolic regressor (GPSR) algorithm could be used to obtain simple symbolic expressions which could estimate the mean phase voltages (black-box inverter model) and duty cycles (black-box compensation scheme) with high accuracy using a publicly available dataset. To obtain the best symbolic expressions using GPSR, a random hyperparameter search method and 5-fold cross-validation were developed. The best symbolic expressions were chosen based on their estimation performance, which was measured using the coefficient of determination (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula>), mean absolute error (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>A</mi><mi>E</mi></mrow></semantics></math></inline-formula>), and root mean squared error (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi></mrow></semantics></math></inline-formula>). The best symbolic expressions for the estimation of mean phase voltages achieved <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>A</mi><mi>E</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi></mrow></semantics></math></inline-formula> values of 0.999, 2.5, and 2.8, respectively. The best symbolic expressions for the estimation of duty cycles achieved <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>A</mi><mi>E</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>M</mi><mi>S</mi><mi>E</mi></mrow></semantics></math></inline-formula> values of 0.9999, 0.0027, and 0.003, respectively. The originality of this work lies in the application of the GPSR algorithm, which, based on a mathematical equation it generates, can estimate the value of mean phase voltages and duty cycles in a three-phase inverter. Using the obtained model, it is possible to estimate the given aforementioned values. Such high-performing estimation represents an opportunity to replace expensive online equipment with a cheaper, more precise, and faster approach, such as a GPSR-based model. The presented procedure shows that the symbolic expression for the accurate estimation of mean phase voltages and duty cycles can be obtained using the GPSR algorithm.
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