Calculation of the Rotation Speed of a Submersible Induction Motor for the Tasks of Determining the Optimal Value of the Supply Voltage

Minimizing energy costs in mechanized oil production is an urgent task. One of the ways to solve it is to determine the optimum voltage level in the power center of the oil field. Voltage regulation at the stator windings of a submersible electric motor leads to a change in the rotation speed and, as a result, to a change in the consumed active and reactive power. In turn, power consumption has an impact on losses in overhead and cable lines and transformers. Therefore, in the tasks of determining the optimal voltage in the power center of the oil field, it is important to accurately calculate the rotation speed of an induction motor with varying stator voltage. In the article an analytical solution is found, which allows calculating the rotation speed of a submersible induction motor with a small error, taking into account the characteristics of the load in the form of a centrifugal pump. It is proposed to linearize the differential equations of an induction motor and find its transfer coefficient with respect to the change in the in the value of the phase voltage. The speed calculation is based on dividing the speed drop by two components. The first component is the drop in speed under the load, and the second is under the influence of changes in supply voltage. This approach allowed us to obtain a quadratic equation relating the rotation speed of a submersible motor with the parameters of the motor and centrifugal pump, as well as with a change in the magnitude of the phase voltage. As a result, an analytical expression is obtained that allows calculating the rotation speed of a submersible motor with a high degree of accuracy, and the calculation error does not exceed 0.3% of the real value. The application of the obtained formula greatly simplifies the creation of a software product for determining the optimal voltage in the power center of the oil field, since it allows one to refuse to solve a large number of nonlinear differential equations of induction motors.