Abstract The paper deals with a mathematical model of the closed loop power supply system for a remotely operated underwater vehicle with a DC transmission line via a rope-cable and the load voltage feedback. The state-space method is used to develop the mathematical model. Using differential equations in the form of Cauchy alleviates significantly the mathematical description. The results for both simulation and mathematical models of the closed loop system are compared, thus, confirming the adequacy of mathematical description and prospects for further application in the design of a versatile tool for calculating and adjusting the parameters of the control system for the power supply system under study.