- 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.
A phasor diagram for a synchronous generator shows the steady-state relationship between terminal voltage, armature current, internal generated emf and synchronous-impedance drop.
This article uses the following per-phase notation:
- Ef denotes internal generated or excitation voltage
- Vt denotes terminal voltage
- Ia denotes armature current, defined out of the generator
- θ denotes the power-factor angle between Vt and Ia
- ᴪ denotes the angle between Ef and Ia
- δ denotes the load, power or torque angle between Ef and Vt
- ra denotes armature resistance per phase
Take Vt as the reference phasor and apply these conventions:
- In a synchronous generator, define armature current (Ia) as leaving the stator terminals. The load power factor sets its phase relative to terminal voltage, so its angle relative to excitation voltage (Ef) varies with the operating point.
- For positive active-power generation, internal emf (Ef) leads terminal voltage (Vt) by load angle δ. At no load, the angle can approach zero.
With these references, the per-phase generator equation is internal emf equals terminal voltage plus armature current times synchronous impedance. This equation constructs the phasor diagram of a synchronous generator.
Armature current Ia must be placed at its actual power-factor angle relative to terminal voltage, not forced into phase with Ef. The following cases use the same outward-current reference:
- Generating operation at lagging power factor.
- Generating operation at unity power factor.
- Generating operation at leading power factor.
The diagrams compare the three load power-factor cases.
(a) Generating operation at lagging power factor:
Resolve Ef from the terminal-voltage components and synchronous-impedance drop. Along Ia, the component of Vt is VtcosΘ. The Ia-axis projection of Vt combines with the resistance term to give the voltage component 
along Ia.
The perpendicular voltage drop includes the synchronous-reactance component. Perpendicular to Ia, that reactive drop also depends on Ia. Under the lagging-current convention in the first diagram, the total is 
. Triangle BOD then gives the internal-emf magnitude Ef:
(b) Generating operation at unity power factor:
At unity power factor, Ef is found from the same generator equation. Terminal voltage Vt and armature current Ia are in phase, theta is zero and ᴪ = δ.
Triangle BOD in the second diagram gives Ef as
(c) Generating operation at leading power factor:
The terminal-voltage component along Ia is VtcosΘ. Combining the Vt projection with armature resistance gives the total voltage drop shown as .
For leading current, the component perpendicular to Ia changes sign relative to the lagging case. Its value is 
. Triangle BOD in the third operating case then gives Ef as
