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I₁ + I₂ + I₃ = Equation 1

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I₁ + I₂ + I₃ = Equation 2

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I₁ + I₂ + I₃ = Equation 3

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INITIAL DATA

Given Z₁ = 10

Given Z₂ = 30

Given Z₃ = 10

V_L-G = 303



Now use the factory test report short circuit impedance value to estimate the short circuit for each transformer during bus fault

Transformer 1, factory test report short circuit impedance value is Z₁ = 0.092 or 9.2 %

Transformer 2, factory test report short circuit impedance value is Z₂ = 0.097 or 9.7 %

Transformer 3, factory test report short circuit impedance value is Z₃ = 0.095 or 9.5 %

To validate your answer substitute the values of I₁, I₂, and I₃ to your original equation 1 , equation 2, and equation 3. The answer must satisfy all the equations or with very small error.

Answer, Loop Current I₁ = 70.70 Bus fault along segment HG to ground Transformer Bank 1 XF ₁ GB through fault current; I ₁ - I ₂ = 30.30

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Answer, Loop Current I₂ = 40.40 Bus fault along segment GF to ground Transformer Bank 2 XF ₂ FC through fault current; I ₂ - I ₃ = 10.10

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Answer, Loop Current I₃ = 30.30 Bus fault along segment FE to ground Transformer Bank 3 XF ₃ ED through fault current; = I ₃

Result of Pivot 1, which means making column 1 = [ 1, 0, 0 ]

Result of Pivot 1, eliminating and in column 1.

I₁ + I₂ + I₃ = Equation 1 (derived)

Divide Equation 1 (see above, original equation 1) by 10

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I₁ + I₂ + I₃ = Equation 2 (derived). Eliminating (see above, original equation 2).

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I₁ + I₂ + I₃ = Equation 3 (derived) . Eliminating if it is not zero value.

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Result of Pivot 2, which means making column 2 = [ CI₂, 1, 0 ] where C is the constant of I₂.

Result of Pivot 2 eliminating in equation 3 (derived) above.
Then converting in equation 2 to one (1) in column 2.

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ANSWER: I₃ = = .
Using back substitution , substitute I₃ = in equation 2 below, you will get I₂ = .
Finally substitute I₃ = , I₂ = in equation 1 below, you will get I₁ = .

I₁ + I₂ + I₃ = Equation 1

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I₁ + I₂ + I₃ = Equation 2

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I₁ + I₂ + I₃ = Equation 3

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See Detailed Explanation of Calculation

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.