A power-flow analysis based on continuum dynamics

Based an the governing equations of continuum mechanics, a power-flow analysis is presented. In developing the mathematical model, the concept of an energy-flow density vector is introduced, which uniquely defines the energy transmission between one part of a material body/system and another. This approach allows the energy-flow line, the energy-flow potential and the equipotential surface to be defined. From this model, the local equation of energy-flow balance, the equation of energy exchange between two or many subsystems, and the time-average equations are derived to describe the characteristics of energy flow and energy exchange within the continuum. To demonstrate the applicability of the proposed mathematical model, the energy-flow relation between two simple oscillators is discussed and the concept generalized to sequential and non-sequential multiple systems. Such multiple systems are examined and for non-sequential systems, which are analogous to statically indeterminate structural systems, an approach is developed for the solution of their power flow and energy exchange. It is further shown that the 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.