##
**Towards a theory of voltage collapse in electric power systems.**
*(English)*
Zbl 0689.93042

Summary: Several recent major power system blackouts are characterised by a progressive decline in voltage magnitude at the system buses. These events are termed ‘voltage collapses’. The mechanisms of voltage collapse are not well defined and the dynamics of the process are not well understood.

In this paper, we describe the loss of stability when a stable equilibrium point disappears in a saddle node bifurcation and present a simple model of the system dynamics after the bifurcation. The results apply generally to any generic one parameter dynamical system.

Then we use these results to propose a model for voltage collapse in power systems. The model gives an explicit mechanism for the dynamics of voltage collapse. We illustrate the model by constructing a simple power system model and simulating a voltage collapse.

In this paper, we describe the loss of stability when a stable equilibrium point disappears in a saddle node bifurcation and present a simple model of the system dynamics after the bifurcation. The results apply generally to any generic one parameter dynamical system.

Then we use these results to propose a model for voltage collapse in power systems. The model gives an explicit mechanism for the dynamics of voltage collapse. We illustrate the model by constructing a simple power system model and simulating a voltage collapse.

### MSC:

93C95 | Application models in control theory |

93C10 | Nonlinear systems in control theory |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |

34D30 | Structural stability and analogous concepts of solutions to ordinary differential equations |

PDF
BibTeX
XML
Cite

\textit{I. Dobson} and \textit{H.-D. Chiang}, Syst. Control Lett. 13, No. 3, 253--262 (1989; Zbl 0689.93042)

Full Text:
DOI

### References:

[1] | Arapostathis, A.; Sastry, S.; Varaiya, P., Global analysis of swing dynamics, IEEE trans. circuits and systems, 29, 10, 673-679, (1988) · Zbl 0496.93006 |

[2] | Barbier, C.; Barret, J.P., An analysis of phenomena of voltage collapse on a transmission system, Rev. gen. elec. CIGRE special issue, 3-21, (July 1980) |

[3] | Bergen, A.R.; Hill, D.J., A structure preserving model for power system stability analysis, IEEE trans. power apparatus and systems, 100, 1, 25-33, (July 1980) |

[4] | Calvaer, A.J.; Van Geert, E., Quasi steady state synchronous machine linearisation around an operating point and applications, IEEE trans. power apparatus and systems, 103, 1466-1472, (June 1984) |

[5] | Chiang, H.-D., Study of the existence of energy functions for power systems with losses, IEEE trans. circuits and systems, (June 1984), to appear in |

[6] | Chiang, H.-D.; Wu, F.F., On voltage stability, (), 1339-1343 · Zbl 0086.43305 |

[7] | Costi, A.; Shu, L.; Schlueter, R.A., Power system voltage stability and controllability, (), 1023-1027 |

[8] | DeMarco, C.L.; Bergen, A.R., A security measure for random load disturbances in nonlinear power system models, IEEE trans. circuits and systems, 34, 12, 1546-1557, (May 1986) |

[9] | Guckenheimer, J.; Holmes, P.J., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, (1983), Springer-Verlag Berlin-New York · Zbl 0515.34001 |

[10] | Kwatny, H.G.; Pasrija, A.K.; Bahar, L.Y., Static bifurcations in electric power networks: loss of steady-state stability and voltage collapse, IEEE trans. circuits and systems, 33, 10, 981-991, (1983) · Zbl 0621.94024 |

[11] | Liu, C.C., Analysis of a voltage collapse mechanism due to the effects of on-load tapchanges, (), 1028-1030 |

[12] | Liu, C.C.; Vu, K.T., Analysis of TAP-changer dynamics and construction of stability regions against voltage collapse, (1988), preprint |

[13] | Medanić, J.; Ilić-Spong, M.; Christensen, J., Discrete models of slow voltage dynamics for under load TAP-changing transformer coordination, IEEE trans. power systems, 2, 4, 873-882, (1988) |

[14] | Mercede, F.; Chow, J.C.; Yan, H.; Fischl, R., A framework to predict voltage collapse in power systems, IEEE trans. power systems, 3, 1807-1813, (Nov. 1988 1988) |

[15] | Narasimhumurthi, N.; Musavi, M.T., A general energy function for transient stability of power systems, IEEE trans. circuits and systems, 31, 637-645, (July 1984) |

[16] | Sastry, S.; Varaiya, P., Hierarchical stability and alert state steering control of interconnected power systems, IEEE trans. circuits and systems, 27, 11, 1102-1112, (July 1984) |

[17] | Sotomayor, J., Generic bifurcations of dynamical systems, () · Zbl 0296.58007 |

[18] | Takens, F., Partially hyperbolic fixed points, (), 134-147 · Zbl 0214.22901 |

[19] | Tamura, Y.; Mori, H.; Iwamoto, S., Relationship between voltage instability and multiple load flow solutions in electric power systems, IEEE trans. on power apparatus and systems, 97, 6, 1115-1125, (May 1983) |

[20] | Thomas, R.J.; Tiranuchit, A., Dynamic voltage stability, (), 53-58 |

[21] | Dobson, I.; Chiang, H.-D.; Thorp, J.S.; Fekih-Ahmed, L., A model of voltage collapse in electric power systems, (), 2104-2109 |

[22] | Walve, K., Modelling of power system components at severe disturbances, (), CIGRÉ Paper 38-18 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.