- Electrical Machines Tutorial
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- Basic Concepts
- Electromechanical Energy Conversion
- Energy Stored in a Magnetic Field
- Singly-Excited and Doubly Excited Systems
- Rotating Electrical Machines
- Faraday’s Laws of Electromagnetic Induction
- Concept of Induced EMF
- Fleming’s Left Hand and Right Hand Rules
- Transformers
- Electrical Transformer
- Construction of Transformer
- EMF Equation of Transformer
- Turns Ratio and Voltage Transformation Ratio
- Ideal and Practical Transformers
- Transformer on DC
- Losses in a Transformer
- Efficiency of Transformer
- Three-Phase Transformer
- Types of Transformers
- DC Machines
- Construction of DC Machines
- Types of DC Machines
- Working Principle of DC Generator
- EMF Equation of DC Generator
- Types of DC Generators
- Working Principle of DC Motor
- Back EMF in DC Motor
- Types of DC Motors
- Losses in DC Machines
- Applications of DC Machines
- Induction Motors
- Introduction to Induction Motor
- Single-Phase Induction Motor
- Three-Phase Induction Motor
- Construction of Three-Phase Induction Motor
- Three-Phase Induction Motor on Load
- Characteristics of 3-Phase Induction Motor
- Speed Regulation and Speed Control
- Methods of Starting 3-Phase Induction Motors
- Synchronous Machines
- Introduction to 3-Phase Synchronous Machines
- Construction of Synchronous Machine
- Working of 3-Phase Alternator
- Armature Reaction in Synchronous Machines
- Output Power of 3-Phase Alternator
- Losses and Efficiency of 3-Phase Alternator
- Working of 3-Phase Synchronous Motor
- Equivalent Circuit and Power Factor of Synchronous Motor
- Power Developed by Synchronous Motor
- Electrical Machines Resources
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- Electrical Machines - Discussion
Concept of Induced EMF
According to principle of electromagnetic induction, when the magnetic flux linking to a conductor or coil changes, an EMF is induced in the conductor or coil. In practice, the following two ways are used to bring the change in the magnetic flux linkage.
Method 1 − Conductor is moving in a stationary magnetic field
We can move a conductor or coil in a stationary magnetic field in such a way that the magnetic flux linking to the conductor or coil changes in magnitude. Consequently, an EMF is induced in the conductor. This induced EMF is known as dynamically induced EMF. It is so called because the EMF induced in a conductor which is in motion. Example of dynamically induced EMF is the EMF generated in the AC and DC generators.
Method 2 − A stationary conductor is placed in a changing magnetic field
When a stationary conductor or coil is placed in a moving or changing magnetic field, an EMF is induced in the conductor or coil. The EMF induced in this way is known as statically induced EMF. It is so called because the EMF is induced in a conductor which is stationary. The EMF induced in a transformer is an example of statically induced EMF.
Therefore, from the discussion, it is clear that the induced EMF can be classified into two major types namely,
Dynamically Induced EMF
Statically Induced EMF
Dynamically Induced EMF
As discussed in the above section that the dynamically induced EMF is one which induced in a moving conductor or coil placed in a stationary magnetic field. The expression for the dynamically induced EMF can be derived as follows −
Consider a single conductor of length l meters located in a uniform magnetic field of magnetic flux density B Wb/m2 as shown in Figure-1. This conductor is moving at right angles relative to the magnetic field with a velocity of v m/s.
Now, if the conductor moves through a small distance dx in time dt seconds, then the area swept by the conductor is given by,
$$\mathrm{\mathit{A\:=\:l\times dx\:}\mathrm{m^{\mathrm{2}}}}$$
Therefore, the magnetic flux cut by the conductor is given by,
$$\mathrm{\mathit{d\phi }\:=\:\mathrm{Flux\:density\times Area\: swept}}$$
$$\mathrm{\Rightarrow \mathit{d\phi }\:=\:\mathit{B\times l\times dx}\:\mathrm{Wb}}$$
According to Faraday’s law of electromagnetic induction, the EMF induced in the conductor is given by,
$$\mathrm{\mathit{e}\:=\:\mathit{N}\frac{\mathit{d\phi }}{\mathit{dt}}\:=\:\mathit{N}\frac{\mathit{Bldx}}{\mathit{dt}}}$$
Since, we have taken only a single conductor, thus N = 1.
$$\mathrm{\mathit{e}\:=\:\mathit{Blv}\:\mathrm{volts}\cdot \cdot \cdot (1)}$$
Where, v = dx/dt, velocity of the conductor in the magnetic field.
If there is angular motion of the conductor in the magnetic field and the conductor moves at an angle θ relative to the magnetic field as shown in Figure-2. Then, the velocity at which the conductor moves across the magnetic field is equal to "vsinθ". Thus, the induced EMF is given by,
$$\mathrm{\mathit{e}\:=\:\mathit{B\:l\:v}\:\mathrm{sin\mathit{\theta }}\:\mathrm{volts}\cdot \cdot \cdot (2)}$$
Statically Induced EMF
When a stationary conductor is placed in a changing magnetic field, the induced EMF in the conductor is known as statically induced EMF. The statically induced EMF is further classified into following two types −
Self-Induced EMF
Mutually Induced EMF
Self Induced EMF
When EMF is induced in a conductor or coil due to change of its own magnetic flux linkage, it is known as self-induced EMF.
Consider a coil of N turn as shown in Figure-3. The current flowing through the coil establishes a magnetic field in the coil. If the current in the coil changes, then the magnetic flux linking the coil also changes. This changing magnetic field induces an EMF in the coil according to the Faraday’s law of electromagnetic induction. This EMF is known as self-induced EMF and the magnitude of the self-induced EMF is given by,
$$\mathrm{\mathit{e}\:=\:\mathit{N}\frac{\mathit{d\phi }}{\mathit{dt}}}$$
Mutually Induced EMF
The EMF induced in a coil due to the changing magnetic field of a neighboring coil is known as mutually induced EMF.
Consider two coils X and Y placed adjacent to each other as shown in Figure-4. Here, a fraction of the magnetic flux produced by the coil X links with the coil Y. This magnetic flux of coil X which is common to both coils X and Y is known as mutual flux ($\mathit{\phi _{m}}$).
If the current in coil X is changed, then the mutual flux also changes and hence EMF is induced in both the coils. Where, the EMF induced in coil X is known as self-induced EMF and the EMF induced in coil Y is called mutually induced EMF.
According to Faraday’s law, the magnitude of the mutually induced EMF is given by,
$$\mathrm{\mathit{e_{m}}\:=\:\mathit{N_{Y}}\frac{\mathit{d\phi _{m}}}{\mathit{dt}}}$$
Where,$\mathit{N_{Y}}$ is the number of turns in coil Y and $\frac{\mathit{d\phi _{m}}}{\mathit{dt}}$ is rate of change of mutual flux.