Particular properties of estimation of partial capacitances of insulation of three core power cables by applying aggregate measurements

This paper presents a description of specific properties of determining the values of partial capacitances of insulation gaps in power cables with paper insulation for various ways of forming and solving the system of linear algebraic equations. Possible ways of inspection the insulation of three core power cables for the estimation of values of partial capacitances by applying aggregate measurements which are based on various ways of connection of emittance meter to tested sample of power cable are given. Estimation of partial capacitances by the direct solution of a system of linear algebraic equations, by minimizing the root mean square error of solving an overdetermined system of equations by the least squares method, as well as by finding a normal solution of an indefinite system of equations by the pseudo-inverse matrix, is also considered. It is shown that minimization of the root mean square error by the least squares method and the direct solution of system of equations show quite similar results for the case of estimation of partial capacitances by means of aggregate measurements, at the same time the solution of an indefinite system of equations by the method of a pseudo-inverted matrix allows to reproduce rather accurately only 3 out of 6 values of partial capacitances. The uneven effect of frequency on the electrical capacitance of the insulation gaps between the cores of the power cable and between its cores and the sheath is shown. It was proposed to use the frequency dependence of the electrical capacitance of insulation gaps as an informative parameter about the technical state of insulating gaps between the cores of the power cable and between its cores and its sheath.   Keywords: root mean square error; least squares method; system of linear algebraic equations; dielectric losses; dielectric permittivity.