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NOTE: If the transformer is out of service use Z = 100000 to simulate open circuit , transformer current should be almost zero. If there are only two parallel transformer, set Z3 and Z4 to 1000000
I 1 + I 2 + I 3 + I 4 = Equation 1
I 1 + I 2 + I 3 + I 4 = Equation 2
I 1 + I 2 + I 3 + I 4 = Equation 3
I 1 + I 2 + I 3 + I 4 = Equation 4
For SCENARIO ANALYSIS, assume all transformers have the same % Z value. You only need one through fault current from one transformer to get the constant voltage = IZ across the four banks of transformer. Then you can do quick adjustment of voltage to approximate the known through fault current from one faulted transformer. You can get this through fault current from PMU data, DFR, or SEL 87T relay.
Z 1 = 10 Ω
Z 2 = 30 Ω
Z 3 = 10 Ω Z 4 = 10 Ω
V L-G = 303 V Voltage adjustment to approximate the known through fault current. Next you apply the appropriate % Z of each transformer and you will get the approximate through fault current for the remaining three banks of transformer.
Practice : Z 1 = 0.092 Ω
Z 2 = 0.092 Ω
Z 3 = 0.092 Ω
Z 4 = 0.092 Ω
V L-G = 303 V
Given PMU through fault for Transformer T2 = 1054 A. What is the adjusted voltage to simulate a 1054 A through fault assuming all transformers have the same % Z of 0.092? ANSWER = 97 V. Using the 97 V as your voltage source to let through fault current of 1054 A flow through Transformer T2. Now you are ready to estimate the through fault current passing through Transformer T1, T3, and T4 using their actual nameplate impedance value.
What is the estimate thru fault current for T1 at Z1 = 0.096 ; T3 at Z3 =0.065 ; T4 at Z4 = 0.0623
Using back substitution to find value of I 1, I 2 and I 3.
INITIAL CONDITION :
Answer, I 1 = 101.00
Transformer T 1 Load current; I 1 - I 2 = 30.30 Equal load sharing if the transformer impedance are all equal. If they don't have equal impedance, you need to do new impedance calculation base on the lowest impedance value. The reason is to make sure the load current are equally share so you don't overload a transformer.
Answer, I 2 = 70.70
Transformer T 2 Load current; I 2 - I 3 = 10.10
Answer, I 3 = 60.60
Transformer T 3 Load current; I 3 - I 4 = 30.30
Answer, I 4 = 30.30
Transformer T 4 Load current; I 4
Important definition to remember about row echelon. The process of reducing augmented matrix in row echelon form is called Gaussian elimination
1. The first nonzero entry in each row is always 1
2. A row with more leading zero entries compare to the previous row must be located below.
3. A row with all zero entries must be below the rows having nonzero entries.
Gaussian elimination will not work properly if one of the definition is violated.
Operation 1 - The order in which any two equations are written may be interchanged.
Operation 2 - Both sides of the equation may be multiplied by the same nonzero real number.
Operation 3 - A multiple of one equation may be added to another equation.
IEEE-2800 DFR data and event duration capture of 5 seconds seems to be unreasonable and questionable. Why? Because 5 seconds time range is equivalent to 300 cycles at 60 Hz.
Most of the relay will trip the breaker during fault event at 2.5 to 7 cycles. If because of stuck breaker the primary breaker did not trip then the secondary back-up relay will trip the breaker and the total trip time
will be about 15 cycles allocating another 8 cycles for secondary back-up relay to clear the fault. Again assuming the secondary back-up did not trip the circuit the third back-up relay will trip the breaker. Allocating another 15 cycles for third relay to trip the faulted circuit then it is reasonable
to use 30 cycles to capture the pre-trigger event and the post event as required by IEEE-2800 for DFR event waveform captured.
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