A power-flow analysis based on continuum dynamics

Based an the governing equations of continuum mechanics, a power-flow analy sis is presented. In developing the mathematical model, the concept of an e nergy-flow density vector is introduced, which uniquely defines the energy transmission between one part of a material body/system and another. This a pproach allows the energy-flow line, the energy-flow potential and the equi potential surface to be defined. From this model, the local equation of ene rgy-flow balance, the equation of energy exchange between two or many subsy stems, and the time-average equations are derived to describe the character istics of energy flow and energy exchange within the continuum. To demonstr ate the applicability of the proposed mathematical model, the energy-flow r elation between two simple oscillators is discussed and the concept general ized to sequential and non-sequential multiple systems. Such multiple syste ms are examined and for non-sequential systems, which are analogous to stat ically indeterminate structural systems, an approach is developed for the s olution of their power flow and energy exchange. It is further shown that t he governing equation of energy flow is a first-order partial differential equation which does not directly correspond to the equation describing the flow of thermal energy in a heat-conduction problem.