An Application of the Hamilton–Ostrogradsky Principle to the Modeling of an Asymmetrically Loaded Three-Phase Power Line

This paper presents a mathematical model of an electric power system which consists three-phase line with distributed parameters and equivalent, unbalanced RLC load cooperating the line. The above was developed on basis modified Hamilton–Ostrogradsky principle, extends classical Lagrangian by adding two more components: energy dissipative forces in work external non-conservative forces. In model, there are four types linear density. On Hamilton’s extended action functional formulated then minimized. As result, extremal derived, can be treated as solution Euler–Lagrange equation for subsystem lumped Euler–Poisson parameters. derived differential equations describes entire physical ordinary partial equations. Such regarded full dynamic object based interdisciplinary approaches. derivatives state–space analyzed approximated means finite differences, these integrated time coordinate using Runge–Kutta method fourth order. results computer simulation transient processes presented graphs discussed.