1. POLYPHASE CIRCUITS Three Phase Circuits
Advantages of polyphase circuits
Steady power
Less wear and tear on the lines
Fewer conductors and so more economical
Instead of two conductors (Go and Return),
a three phase supply can transmit three times
the power by using only one extra conductor.

2. THREE PHASE CIRCUITS Theorem
For a balanced three phase circuit the instantaneous power is constant

3. Proof of Theorem
For a balanced three phase circuit the instantaneous power is constant

4. THREE-PHASE CONNECTIONS
Positive sequence
a-b-c
Y-connected
loads
Delta connected loads

5. Advantages of wye
Access to two voltages, the line-to-line and line-to-neutral
Provides a convenient place to connect to ground 
Advantages of delta
Stays in balance better when serving unbalanced loads
Capable of trapping the third harmonic

6. SOURCE/LOAD CONNECTIONS
BALANCED Y-Y CONNECTION
Line voltages
Positive sequence
phase voltages
For this balanced circuit it is enough to analyze one phase

7. LEARNING EXAMPLE
For an abc sequence, balanced Y - Y three phase circuit
Balanced Y - Y
Determine the phase voltages
Positive sequence
a-b-c
The phasor diagram could be rotated by any angle
Positive sequence
phase voltages
Relationship between
phase and line voltages

8. LEARNING EXAMPLE
For an abc sequence, balanced Y - Y three phase circuit
Because circuit is balanced
data on any one phase is
sufficient
Determine line currents and load voltages
Chosen
as reference
Abc sequence

9. LEARNING EXTENSION
For an abc sequence, balanced Y - Y three phase circuit
Relationship between
phase and line voltages

10. LEARNING EXTENSION
For an abc sequence, balanced Y - Y three phase circuit
Determine source phase voltages
Currents are not required. Use inverse
voltage divider
Positive sequence
a-b-c

11. DELTA CONNECTED SOURCES
Convert to an equivalent Y connection
Relationship between
phase and line voltages
Example

12. Three-Phase Balanced AC Power Circuits
Step 1.
Convert the source/load connection to a wye–wye connection if either the source, load, or both are connected in delta since the wye–wye connection can be easily used to obtain the unknown phasors.
Step 2.
Only the unknown phasors for the a -phase of the circuit need be determined since the three-phase system is balanced.
Step 3.
Finally, convert the now known phasors to the corresponding phasors in the original system.

13. LEARNING EXAMPLE
Determine line currents and line voltages at the loads
Source is Delta connected.
Convert to equivalent Y
Analyze one phase
Determine the other phases using the balance

14. LEARNING EXTENSION
Compute the magnitude of the line voltage at the load
Source is Delta connected.
Convert to equivalent Y
Analyze one phase
Only interested in magnitudes!