1. Balanced 3-phase systems Unbalanced 3-phase systems
Three-phase Circuits
Balanced 3-phase systems
Unbalanced 3-phase systems
SKEE 1043 Circuit Theory
Dr. Nik Rumzi Nik Idris

2. Balanced 3-phase systems
POWER CALCULATION
Instantaneous power
Phase voltage of Y connected load with Z  per phase:
Phase current, lagging by :
Total instantaneous power: p = vANia + vBNib+ vCNic
Which can be re-written as:

3. Balanced 3-phase systems
POWER CALCULATION
Instantaneous power
Instantaneous power is NON PULSATING
Smoother energy conversion for electrical machine in 3-phase system
True for delta () connected load too

4. Balanced 3-phase systems
POWER CALCULATION
Complex, apparent, active, and reactive
Phase voltage
(rms)
Phase current
(rms)
The complex power per phase:
Total complex power:
For Y connection,
and
Apparent power is as before, i.e.

5. Balanced 3-phase systems
POWER CALCULATION
Power measurement using a wattmeter
wattmeter is an instrument used for measuring the average power.
The basic structure
Equivalent Circuit with load
If v(t) = Vmcos (t + v) and i(t) = Imcos (t + i)
then the wattmeter will measure the average power:
Reading on wattmeter 

6. Balanced 3-phase systems
POWER CALCULATION
Power measurement using a wattmeter
wattmeter is an instrument used for measuring the average power.

7. Balanced 3-phase systems
POWER CALCULATION
3-phase power measurement using wattmeters: two-wattmeter method
In order to measure average power in 3-phase system ONLY 2 wattmeters are needed
Reading by wattmeter1,
Reading by wattmeter2,

8. Balanced 3-phase systems
POWER CALCULATION
Reading by wattmeter1,
Reading by wattmeter2,
IT CAN BE SHOWN :
This is also true for a  connected load as well
This is also true if the load is unbalanced (ONLY for P1+P2)
Two-wattmeter method CANNOT be used for a 3-phase, 4 wire system UNLESS the neutral current = 0
P1=P2  resistive load, P2 > P1  inductive load, P2 < P1  capacitive load