I am trying to investigate the Power/Energy of 3-Phase System under Different Faults.
I have a Three Phase Source and Load, Load is balanced i.e same phase angle and current (Phase-Neutral V = 230 rms, Current = 10 rms) for a power factor of unity (Ideally, typically 0.9-0.95). There is a device (Energy Meter) in between them which is measuring Power/Energy transferred from Source to Load.
Everything below is related to calculations and measurements of that Measuring device. Phase reversal/polarity does not have an effect on source /Load, only the Meter measurements will be affected.
I know about the phase sequence and Power equations of a 3-Phase Balanced System.
(Kindly forgive me if it gives you a headache, I realized after writing this question, how large it became)
I am using +ve Phase Sequence in my calculations.
So the Power Equation is like this;
P_Total = 3 * V_phase * I_phase * cosθ
The Fault Condition is like this:
"The Phase_C and Neutral are swapped or Phase C polarity is reversed".
i.e. Black Wires goes in 5 and comes out of 6, while yellow wire goes in 7 and comes out of 8 of Meter.
In this condition, Meter shows Active Power of 9.249KW, Reactive Power
of 1.89 KVAr, while power factor is still 0.9.
Now I want to measure the voltages, their phasors and ultimately the Power.
This is what I am trying to do:
V_AN will become V_AC because Phase-C is now at Neutral connection.
Here, Positive Phase Sequence is considered for calculations.
Then the Phase-A Voltage will be as following,
V_AC= V_A – V_C
∴V_AC= Phase Voltage of A,Don^' t confuse it with Line Voltage of Balanced 3 Phase System
Inserting the values…
V_AC= v_rms<0 – v_rms<-240
V_AC= v_rms (cos0+j sin0) – v_rms (cos240-j sin240)
V_AC= v_rms (1+0)- v_rms (-1/2+j √3/2)
V_AC= v_rms (1+1/2-j √3/2)
V_AC= v_rms (3/2-j √3/2)
V_AC= √3 v_rms (√3/2-j 1/2)
V_AC= √3 v_rms < 30
V_BC= √3 v_rms<-90
Now it gets tricky. To get Active Power P, i am trying to calculate Apparent POwer S = VI*.
For that, according to simple conjugate and multiplication properties of Complex numbers, Each Phase Voltage and Current will be multiplies after taking conjugate of current.
S_Total= S_Phase-A + S_Phase-B + S_Phase-C
S_Total= (V_A x I_A*) + (V_B x I_B*) + (V_C x I_C*)
S_Total=(V_A<30 × I_A<∅-30)+(V_B<-90 × I_A<∅+90)+(V_C<-60 × I_C <∅+60)
S_Total=[(√3 x v_rms x i_rms) + (√3 x v_rms x i_rms) + (v_rms x i_rms)] <∅
S_Total = 4.464 x v_rms x i_rms <∅^0
Total Active Power,
P_Total = 4.464 x v_rms x i_rms x cos∅
Total Reactive Power,
Q_Total = 4.464 x v_rms x i_rms x sin∅
From Here, assuming, Power Factor =1, Each Phase Voltage = 230 Vrms, and I = 10 A rms,
Power Comes 10.267 KW, instead of 6.9 KW.
Did i make any mistakes in calculations?
Why Power Increased?
It seems like the system is unbalanced now, but why there is no
reactive power, it seems like that reactive power only depends on the
power factor which is 1 in this case?
Please review my calculations and tell me if I am doing something wrong. Because I did measure power through Three Phase meter, it showed the phase voltages as I calculated but overall power was around 6.8KW while my calculation show 10.267KW??
If I am wrong, what will be right approach to calculate power in this
Thanks and Best regards..