### Abstract

Recent results for nonconservative dynamical systems involve a variational principle of the Hamilton type. In this approach the velocity of variation and the variation of velocity are not commutative as in the case of mechanics governing conservative dynamical systems. In this paper we adapt the above approach to power systems which include the effects of transfer conductances. For such power systems we show that if certain noncommutative rules (which are consistent with the ones used for the variation of velocities in nonconservative dynamical systems) are used, then it is possible to employ a variational principle of the Hamilton type to derive the classical model for power systems. Numerous simulations of specific postfault multimachine power systems have verified that the above noncommutative rules are indeed satisfied for the types of power systems which we consider. The present results give additional understanding for the types of energy functions that have recently been used in transient stability studies of power systems. In these works, several attributes of energy functions have been ascertained by means of simulations and heuristic reasoning, rather than analysis (e.g., path-dependent terms of energy functions have been approximated by making linear trajectory assumptions).

Original language | English (US) |
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Pages (from-to) | 413-424 |

Number of pages | 12 |

Journal | Circuits, Systems, and Signal Processing |

Volume | 7 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Signal Processing
- Applied Mathematics

### Cite this

*Circuits, Systems, and Signal Processing*,

*7*(3), 413-424. https://doi.org/10.1007/BF01599980