### 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) |
---|---|

Pages (from-to) | 413-424 |

Number of pages | 12 |

Journal | Circuits, Systems, and Signal Processing |

Volume | 7 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing

### Cite this

*Circuits, Systems, and Signal Processing*,

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

**A variational principle for nonconservative power systems.** / Vittal, Vijay; Michel, A. N.

Research output: Contribution to journal › Article

*Circuits, Systems, and Signal Processing*, vol. 7, no. 3, pp. 413-424. https://doi.org/10.1007/BF01599980

}

TY - JOUR

T1 - A variational principle for nonconservative power systems

AU - Vittal, Vijay

AU - Michel, A. N.

PY - 1988/9

Y1 - 1988/9

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0024136068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024136068&partnerID=8YFLogxK

U2 - 10.1007/BF01599980

DO - 10.1007/BF01599980

M3 - Article

AN - SCOPUS:0024136068

VL - 7

SP - 413

EP - 424

JO - Circuits, Systems, and Signal Processing

JF - Circuits, Systems, and Signal Processing

SN - 0278-081X

IS - 3

ER -