- Phasor Diagram Defined: A phasor diagram is a graphical representation of the phase relationships between different electrical quantities in an AC circuit, specifically used here for synchronous generators.
- Drawing Basics: To draw a phasor diagram for a synchronous generator, use terminal voltage (Vt) as the reference and align the armature current (Ia) phase with the excitation voltage (Ef).
- Phasor Relationships: In the diagram, the phasor for excitation voltage (Ef) is always ahead of the terminal voltage (Vt), crucial for understanding generator operations.
- Operational Conditions: The phasor diagrams vary with operational conditions—lagging, unity, and leading power factors—each affecting the voltage and current relationships differently.
- Phasor Diagram of Synchronous Motor: Understanding the phasor diagram of synchronous motors helps in predicting and managing the electrical behavior under different power factor loads.
In this article we discuss one of the easiest methods of making a phasor diagram for a synchronous generator.
Now, let’s list all the notations in one place to clarify the phasor diagram. In this diagram, we use:
- Ef which denotes excitation voltage
- Vt which denotes terminal voltage
- Ia which denotes the armature current
- θ which denotes the phase angle between Vt and Ia
- ᴪ which denotes the angle between the Ef and Ia
- δ which denotes the angle between the Ef and Vt
- ra which denotes the armature per phase resistance
To draw the phasor diagram, we use Vt as the reference point. Consider the following two important points:
- We understand that in a synchronous generator, the direction of the armature current (Ia) is in phase with the excitation voltage (Ef).
- The phasor for excitation voltage (Ef) consistently leads the terminal voltage (Vt).
These two points are essential for constructing the phasor diagram of a synchronous generator. Given below is the phasor diagram of synchronous generator:
In this phasor diagram we have drawn the direction of the Ia is in phase with that of the Ef as per the point number 1 mentioned above. Now let us derive expression for the excitation emf in each case. We have three cases that are written below:
- Generating operation at lagging power factor.
- Generating operation at unity power factor.
- Generating operation at leading power factor.
Given below are the phasor diagrams for all the operations.
(a) Generating operation at lagging power factor:
We can derive the expression for the Ef by first taking the component of the Vt in the direction of Ia. Component of Vt in the direction of Ia is VtcosΘ, hence the total voltage drop is 
along the Ia.
Similarly we can calculate the voltage drop along the direction perpendicular to Ia. The total voltage drop perpendicular to Ia is 
. With the help of triangle BOD in the first phasor diagram we can write the expression for Ef as
(b) Generating operation at unity power factor:
Here also we can derive the expression for the Ef by first taking the component of the Vt in the direction of Ia. But in this case the value of theta is zero and hence we have ᴪ = δ.
With the help of triangle BOD in the second phasor diagram we can directly write the expression for Ef as
(c) Generating operation at leading power factor:
Component in the direction of Ia is VtcosΘ. As the direction of Ia is same to that of the Vt thus the total voltage drop is .
Similarly we can write expression for the voltage drop along the direction perpendicular to Ia. The total voltage drop comes out to be 
. With the help of triangle BOD in the first phasor diagram we can write the expression for Ef as
