# Electrical network stability theory

#### Miguelec

Joined Mar 8, 2006
6
Hi,

Could someone please recommend me a good website or text book on the subject of electrical network stability? (i.e. parameters that define stability, instability mechanisms, etc). Ideally with a focus on aircraft electrical systems.

Thank you!

#### Papabravo

Joined Feb 24, 2006
18,840
Originally posted by Miguelec@Apr 18 2006, 11:36 AM
Hi,

Could someone please recommend me a good website or text book on the subject of electrical network stability? (i.e. parameters that define stability, instability mechanisms, etc). Ideally with a focus on aircraft electrical systems.

Thank you!
[post=16287]Quoted post[/post]​
Could you possibly mean sensitivity in place of stability?

#### Miguelec

Joined Mar 8, 2006
6
Thank you for your reply. Possibly; I am not sure I know the difference between sensitivity and stability. I found the following discussion, which is exactly what I want to know more about. If you could recommend a textbook or article on this subject it would be much appreciated.

"For studying stability, the common approach is to linearize the system around its operating point and obtain the small-signal linearized model of the system. Then, the stability of the system can be determined using linear system stability analysis methods such as: Routh-Hurwitz, root locus, Bode plot, and Nyquist criterion. Although small-signal stability can be governed using this linearized approach, large-signal stability of the system cannot be determined. In other words, absence of small-signal instability does not guarantee large-signal stability of the system.

Large-signal stability refers to the ability of the system to move from one steady state operating point following a disturbance to another steady state operating point. In the large-signal stability assessment, the way the aircraft power system responds to the various types of disturbances, such as: change in power demand; loss of generations; short circuits; and open circuits, is important. In addition, the dynamics of the system are affected by interconnection between the components.

Stability analysis of the aircraft power systems is best performed via time domain simulation using large-signal models. It depends on the actual control and protection circuit dynamics which may include, but are not limited to: undervoltage; overvoltage; and overcurrent protections; switching effects of power electronic converters; nonlinearities due to magnetic saturation; leakage; semiconductor operation; temperature variations; and aging.

Dynamic behavior of an aircraft power system can be improved and its stability margins can be increased by considering the following issues:

- Using suitable fast-response protection devices.
- Avoiding heavily loaded connections.
- Overrating the sources to ensure an appropriate reserve in power generation.
- Overrating the power distribution system as an appropriate reserve in the ability to deliver power to the loads.
- Avoiding long links.
- Managing the loads properly according to the operating conditions of sources and distribution system to avoid overloading.
- Controlling the loads via the control commands of the management center in such a way that the system always operates around its nominal power.
- Avoiding overvoltage and undervoltage.

Source: "Aircraft Power Systems: Technology, State of the Art, and Future Trends", Emadi, A., Ehsani, M., Aerospace and Electronic Systems Magazine, IEEE
Volume 15, Issue 1, Jan. 2000 Page(s): 28 - 32.

#### Miguelec

Joined Mar 8, 2006
6
Thank you for your reply! Possibly, I am not sure I know the difference between sensitivity and stability. I found the following discussion, which is exactly what I want to know more about. If you could recommend a textbook or an article on this subject it would be much appreciated.

"For studying stability, the common approach is to linearize the system around its operating point and obtain the small-signal linearized model of the system. Then, the stability of the system can be determined using linear system stability analysis methods such as: Routh-Hurwitz, root locus, Bode plot, and Nyquist criterion. Although small-signal stability can be governed using this linearized approach, large-signal stability of the system cannot be determined. In other words, absence of small-signal instability does not guarantee large-signal stability of the system.

Large-signal stability refers to the ability of the system to move from one steady state operating point following a disturbance to another steady state operating point. In the large-signal stability assessment, the way the aircraft power system responds to the various types of disturbances, such as: change in power demand; loss of generations; short circuits; and open circuits, is important. In addition, the dynamics of the system are affected by interconnection between the components.

Stability analysis of the aircraft power systems is best performed via time domain simulation using large-signal models. It depends on the actual control and protection circuit dynamics which may include, but are not limited to: undervoltage; overvoltage; and overcurrent protections; switching effects of power electronic converters; nonlinearities due to magnetic saturation; leakage; semiconductor operation; temperature variations; and aging.

Dynamic behavior of an aircraft power system can be improved and its stability margins can be increased by considering the following issues:

- Using suitable fast-response protection devices.
- Avoiding heavily loaded connections.
- Overrating the sources to ensure an appropriate reserve in power generation.
- Overrating the power distribution system as an appropriate reserve in the ability to deliver power to the loads.
- Avoiding long links.
- Managing the loads properly according to the operating conditions of sources and distribution system to avoid overloading.
- Controlling the loads via the control commands of the management center in such a way that the system always operates around its nominal power.
- Avoiding overvoltage and undervoltage.

Source: "Aircraft Power Systems: Technology, State of the Art, and Future Trends", Emadi, A., Ehsani, M., Aerospace and Electronic Systems Magazine, IEEE
Volume 15, Issue 1, Jan. 2000 Page(s): 28 - 32

#### Papabravo

Joined Feb 24, 2006
18,840
Yes you were correct. Any introductory book on control systems will cover the techniques which are applicable to linear systems. I recommend:

Kuo, B.C., Automatic Control Systems, Prentice Hall, 1967

For a general introduction to non-linear systems, I recommend:

Strogatz, S.H., Nonlinear Dynamics and Chaos, Perseus, 1994

You might also be interested in:

McRuer, D., Ashkenas, I., Graham, D., Aircraft Dynamics and Automatic Control, Princeton University Press, 1973

It's not electrical systems but it is a fascinating read nonetheless.

Hope this helps