Estimation of the range of energy flow

The paper relates the power engineering problem of the extremal values of effective energy flow to a well established branch of mathematics; namely, the spectral analysis of linear operators. Variation of the effective energy flow in a linear time-invariant power distribution system is studied in the light of numerical range of the operator representing the system [Eqs. (18, 19)]. A knowledge of this range and its extremal values depends on the evaluation of eigenvalues and eigenvectors of a complex network function. In most cases an exact evaluation is practically unattainable (Section V). Simple and practical estimations of the energy dissipation range are presented. The novel spectral approach to energy problems may hopefully find useful applications in power transmission and distribution.