# Nonlinear power supply model of submersible objects based on change in the cable-rope length

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3 Citations (Scopus)

## Abstract

The relevance of this work is determined by the need to develop suitable mathematical models of complex subsea process power supply equipment. Acceptable adequacy of the characteristics of the model and the actual power supply can be achieved by taking into account the variable cable-rope length and various modes of the submersible equipment operation. The use of transfer functions and operator method is an acceptable solution for adequate reflection of the voltage change on the load. By transforming the transfer function, a nonlinear mathematical model of the power supply system is written in the space of state variables. This allows solving analytically the problem of robust stabilization of immeasurable voltage on the useful electromechanical load. The main aim of the work is to build a nonlinear mathematical model of the power supply with AC power transmission via the cable-rope, taking into account the change of its length in the space of state variables. Research methods: operator method, state variable method, methods of mathematical modeling. Results. The authors have developed the method of determining parameters of the reactive power compensation device in the cable-rope to increase its transfer capacity, when transmitting power over long distances at high frequency; determined the analytical dependence, which allows calculating the inductance of the compensating device in the whole range of cable-rope length change. To construct an optimal regulator, polynomials are obtained that allow determining the coefficients of transfer functions, when changing the cable length and load resistance of the power supply system. On the basis of transfer functions obtained for different modes of the power supply operation, the authors determined the parameters of the equivalent circuit, which allows writing a nonlinear mathematical reduced order model. The paper introduces the comparative evaluation of the simulation results of the power supply with AC power transmission by cable-rope, confirming the possibility of its description by the reduced order model in the state space. Conclusions. The paper introduces the method for determining parameters of the reactive power compensation device, which allows increasing the capacity of the cable/rope. Based on the transfer functions, the authors recorded a simplified nonlinear mathematical model of the subsea process equipment power supply system. As a result, the model can be used for the subsequent synthesis of the optimal voltage regulator in the class of nonlinear control systems.

Original language English 114-123 10 Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering 329 11 https://doi.org/10.18799/24131830/2018/11/215 Published - 2018

## Keywords

• Approximation
• Mathematical model
• Power supply system of subsea equipment
• Reactive power compensation
• Transfer function
• Variable state method

## ASJC Scopus subject areas

• Materials Science (miscellaneous)
• Fuel Technology
• Geotechnical Engineering and Engineering Geology
• Waste Management and Disposal
• Economic Geology
• Management, Monitoring, Policy and Law