Three phase voltage is the most widely used AC power system in the world. It forms the backbone of electric power generation, transmission, distribution, and industrial applications. Compared to a single-phase supply, a three-phase system delivers higher efficiency, smoother torque, lower conductor cost, and constant power transfer. Because of these advantages, almost all industrial machinery, motors, power plants, and high-power equipment operate on three-phase systems.
Three Phase Voltage Waveform (Diagram)
The following waveform illustrates three sinusoidal voltages spaced by 120°.
At any instant, each phase reaches a different voltage level, and when one phase is at its peak, the other two are below peak. This property ensures continuous and nearly constant power delivery.
Definition of Three Phase Voltage
A three-phase voltage system consists of three alternating voltages of the same magnitude and frequency, but displaced from each other by 120 electrical degrees. These voltages are usually identified as:
- Phase-R (Red)
- Phase-Y (Yellow)
- Phase-B (Blue)
Mathematically, the instantaneous voltages are expressed as:
\[
v_R = V_m \sin(\omega t)
\]
\[
v_Y = V_m \sin(\omega t – 120^\circ)
\]
\[
v_B = V_m \sin(\omega t – 240^\circ)
\]
or equivalently,
\[
v_B = V_m \sin(\omega t + 120^\circ)
\]
Here, \(V_m\) is the maximum (peak) phase voltage and \(\omega\) is the angular frequency.
Generation of Three Phase Balanced Voltage
Three-phase voltage is generated by placing three identical stator coils in an alternator, spaced 120° apart. When the rotor rotates in a uniform magnetic field, sinusoidal EMF is induced in each coil.
The three induced voltages are:
- Equal in magnitude
- Same frequency
- Displaced by 120°
This forms a balanced three-phase system. If one phase differs in magnitude or angle, the system becomes unbalanced.
Note: In practice, power plants always try to maintain perfectly balanced phase voltages to avoid heating, vibration, and losses in motors and transformers.
Mathematical Derivation of Three Phase Voltage
Consider three coils placed mechanically 120° apart in a rotating magnetic field. The instantaneous EMF induced in coil-R is:
\[
v_R = V_m \sin(\omega t)
\]
Since coil-Y is displaced by \(120^\circ\):
\[
v_Y = V_m \sin(\omega t – 120^\circ)
\]
Similarly, coil-B is displaced by \(240^\circ\):
\[
v_B = V_m \sin(\omega t – 240^\circ)
\]
Phasor Form Representation
In polar (phasor) form:
\[
V_R = |V|\angle 0^\circ
\]
\[
V_Y = |V|\angle -120^\circ
\]
\[
V_B = |V|\angle +120^\circ
\]
Sum of Three Phase Voltages
The phasor sum of the three voltages in a balanced system is:
\[
V_R + V_Y + V_B = 0
\]
This is a unique and powerful property of three-phase systems which ensures constant power transfer to the load.
Line Voltage and Phase Voltage Relationship Star (Y) Connection
In a star-connected system:
\[
V_L = \sqrt{3}\,V_{ph}, \qquad I_L = I_{ph}
\]
Delta (Δ) Connection
In a delta-connected system:
\[
V_L = V_{ph}, \qquad I_L = \sqrt{3}\,I_{ph}
\]
Where:
- \(V_L\) = Line voltage
- \(V_{ph}\) = Phase voltage
- \(I_L\) = Line current
- \(I_{ph}\) = Phase current
Working of Three Phase System
A three-phase supply may use:
- 3-wire system (without neutral)
- 4-wire system (with neutral)
In three-phase power transmission and industrial supply, the 3-wire system is preferred because it saves conductor material. In domestic distribution, the 4-wire system allows users to draw single-phase loads from any one phase and neutral.
The key characteristics of three-phase power include:
- Power delivered is nearly constant
- Power factor is better compared to single phase
- Three-phase motors produce smooth torque
- Voltage regulation is better
Advantages of Three Phase Voltage System
- Higher efficiency in power transmission
- Requires less conductor material for the same power
- Three-phase motors are self-starting
- Produces constant and smooth torque
- Lower copper and core losses
- Voltage drop is smaller
- More economical for long-distance power transfer
- Able to handle large industrial loads
- Flexible star and delta configurations
- Better performance in rotating machines
Disadvantages of Three Phase System
- Initial installation cost is higher
- Requires skilled supervision and maintenance
- Fault analysis is more complex
- Unbalanced loads cause voltage imbalance
- Insulation and protection systems are more expensive
- Short-circuit currents are higher compared to single phase
Applications of Three-Phase Voltage
- Electric power transmission and distribution networks
- Industrial factories and manufacturing plants
- Induction and synchronous motors
- Power plants and alternators
- HVAC compressors and refrigeration systems
- Electric traction and metro rail systems
- Wind turbines and renewable power systems
- Data centers and UPS systems
- Large-scale welding and furnaces
- Pumps, conveyors, cranes, and machine tools
Difference Between Single Phase and Three Phase
| Parameter | Single Phase | Three Phase |
|---|---|---|
| Conductors | 2 wires | 3 or 4 wires |
| Power Delivery | Pulsating | Constant |
| Efficiency | Low | High |
| Motor Starting | Not self-starting | Self-starting |
| Application Area | Homes | Industry & Power Systems |
Conclusion
The three-phase voltage system is the foundation of modern electrical engineering. Its 120° phase displacement enables constant power transfer, smooth motor torque, reduced conductor requirements, and superior efficiency compared to single-phase systems. Because of these unique advantages, three-phase power is universally used in generation, transmission, distribution, and industrial applications.
A clear understanding of three-phase theory, waveform analysis, phasor representation, and voltage relationships is essential for students, engineers, technicians, and professionals working in the electrical and power sector.