In the paper there is proposed a method of differentiation with respect to an argument of direct and inverse matrices of static and differential parameters through the derivative of static parameters; the method claims to be the simplest one. The method proposes, after finding the simplest derivative, to find three more complicated derivatives on the basis of formal matrix operations. The results may be used in the theory of parametric sensitivity of first and higher degrees. As an example, the direct and inverse matrices of static and differential inductances of a saturated three-phase induction motor are considered, provided that single-phase and three-phase power supply is applied.
- V. Tchaban, The methods of analyse of the electromechanical systems. Lviv, Ukraine: Vyshcha shkola, 1985. (Russsian)
- V. Tchaban, Numerical methods. Lviv, Ukraine, 2001. (Ukrainian)
- V. Tchaban, Mathematical modeling in electrical engineering. Lviv, Ukraine: T. Soroka’s publishing house, 2010. (Ukrainian)
- V. Tchaban, S. Kostiuchko, and Z. Tchaban, “Auxi–liary model of parametric sensitivity”, Computational Problems of of Electrical Engineering, vol. 2, no. 1, pp. 129-132, 2013.
- V. Tchaban and O. Tchaban, “Derivatives of matrices of parameters over independent variables”, Tekhnichni visti, no. 1(39), 2(40), p. 51, 2014. (Ukrainian)
- V. Tchaban and S. Kostiuchko, “Mathematical model of three-phase induction motor in single-phase operation mode”, Elektrotekhnika i Elektromekhanika, no. 1, pp. 60–61, 2012. (Ukrainian)