- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Constant Flux Linkage Theorem of Synchronous Machines

A synchronous machine may be subjected to various disturbances. Any cause of disturbance will produce electrical and mechanical transients. These transients may result from switching, from sudden changes of load, from sudden short-circuits between line and ground or between double lines or between all the three lines. These disturbances produce large mechanical stresses which may damage the machine. The synchronous machine may also lose synchronism.

## Constant Flux Linkage Theorem: Statement

The *constant flux linkage theorem* is used in studying alternator transients. This theorem is stated as follows −

“The flux linkage after sudden disturbance in a closed circuit having zero resistance and zero capacitance remain constant at their pre-disturbed value. In other words, the magnetic flux linkage in an inductor cannot change abruptly.”

The armature and field windings of an alternator have no capacitance. Also, their resistances are negligibly small as compared to their inductances. Therefore, the armature and field windings may be assumed to be purely inductive and the flux linkages in the armature and field windings cannot be changed abruptly by the application of short-circuit to the armature winding. Hence, any sudden change of the current in one winding must be accompanied by a change of current in the other to keep the flux linkages constant.

## Constant Flux Linkage Theorem: Proof

For any closed circuit, the mesh voltage equations may be written as follows −

$$\mathrm{\sum π =\sum π_{π } + \sum π_{πΏ} + \sum π_{πΆ}}$$

$$\mathrm{\Rightarrow\:\sum π =\sum ππ +\sum π\frac{ππ}{ππ‘}+\sum \frac{π}{π}… (1)}$$

Also,

$$\mathrm{Flux\:linkage,\:\psi = π_{π} … (2)}$$

From Eqns. (1) & (2),

$$\mathrm{\sum π-\sum iπ -\sum \frac{π}{ π}=\sum \frac{π\psi}{ππ‘}= \frac{π}{ππ‘}\sum \psi}$$

$$\mathrm{\Rightarrow\:\frac{π}{ππ‘}\sum \psi=\sum π_{1}… (3)}$$

Where, e_{1} is the resultant voltage, which will be some function of time.

On integrating Eqn. (3), the change in linkage flux will be,

$$\mathrm{\Delta \left(\sum \psi \right)=\int_{0}^{\Delta t} e_{1}\:ππ‘ … (4)}$$

Here, $\Delta t$ is a small interval of time. When tends to zero, so will be the integral, thus,

$$\mathrm{\sum \psi= 0}$$

That is the instantaneous change of flux linkage is zero.

- Related Articles
- Blondel's Two Reaction Theory of Synchronous Machines
- Linkage Recombination
- Effect of Changing Field Excitation on Synchronous Motor at Constant Load
- Electric Flux
- In extraction of copper, the flux used isFeOSiO2CaOFeSiO3
- How to Determine Magnetic Flux Density?
- Simple Machines
- What is Synchronous Reactance & Synchronous Impedance?
- What are Architecture Flux Components in JavaScript?
- Saturated and Unsaturated Synchronous Reactance in Synchronous Generator
- Excitation System of Synchronous Machine
- Starting Methods of Synchronous Motor
- What isΒ basic proportional theorem and convers of basic proportional theorem?
- What are the advantages of simple machines ?
- Advantages of Virtual Machines over Portable Containers