Analytical model of a dynamic system "long cable - submersible induction motor with fixed rotor" in a polar coordinate system

Relevance. The stock of oil wells in the Russian Federation, where production is carried out with the help of electric centrifugal pumps or electric-driven vane pumps, is expanding every year. This trend will continue for at least a couple of decades. In its turn, the number of wells with readily available oil products in the commissioned stock is decreasing. This leads to the need to improve production quality and reduce energy consumption to maintain profitability and production volumes. This can be achieved by implementing vector energy-efficient control systems for submersible motors based on observers of induction motor state variables. In this case one should take into account transients in the supply cable of considerable length, which transmits energy from a frequency converter to a motor. The observers are based on adjustable mathematical models that describe electrical, electromechanical and mechanical processes in electric drive and related process automation systems as reliably as possible. Using complex and cumbersome adjustable mathematical models in digital signal processors due to limited performance and memory causes objective difficulties in obtaining solutions of increased accuracy in real time. On this basis, the development of an analytical model of the dynamic system "long cable - submersible induction motor with fixed rotor" in the polar coordinate system is an urgent task. Aim. Development of analytical description of the mathematical model of the induction motor with a fixed rotor in the polar coordinate system taking into account the influence of a long cable. Methods. Electric drive theory, electric machine theory, mathematical models of submersible induction motors and reduced long cable model, Vandermonde's determinant, analytical methods for solving differential equations. Result and conclusions. The authors have developed an analytical model of the regulated induction motor with a fixed rotor in the polar coordinate system taking into account the supply cable of considerable length. The developed analytical model is recommended for use in vector energy-efficient electric drive with application of phase discrimination principles taking into account the influence of processes in the supply cable line. Such electric drive has a potential for increasing the profitability of oil production from low- and medium-debt wells.