In this paper, mathematical modelling of high voltage cables for power transmission line design is presented. The Finite Volume Method (FVM) is used to approximate the developed mathematical model (a system of nonlinear multi-physic differential equations) and OpenFOAM (Open source Field Operation And Manipulation) tool is used to implement the obtained parallel finite volume schemes. In order to optimize the design of power lines with respect to technological parameters, different cases of nonstationary load dynamics are investigated and the influence of system nonlinearity and external day, month and years periodical boundary conditions and the source function regimes are simulated. The main aim of this paper is to include into the mathematical model also economic requirements and to optimize sizes of cables with respect to both technologic and economic requirements. Numerical algorithms targeted to solve PDE-constrained optimization problems are developed. Results of computational experiments are presented.