Transformer and Generator in Per Unit System

[tommyhakinen]

Homework Statement

A 3-phase generator rated 100 MVA, 13.2 kV, X = 20% is connected through a Δ/Y
transformer to a transmission line whose series reactance is 40 ohms per phase.
Assume that the base values in the line circuit are 200 MVA and 115 kV.
Find the generator and transformer reactances in pu for the following cases:
(i) The transformer is a 3-phase unit rated 100MVA, 13.8Δ/120Y kV, X = 8%.
(ii) The transformer is composed of three single-phase units, each rated 35 MVA,
13.8/69 kV, X = 8%.

 

[Valkarie]

Homework Equations X/X_base = X_pu The Attempt at a Solution(i) X_pu = 8/20 = 0.4 puX_base = (200MVA x 115kV)/(100MVA x 13.2kV) = 153.125X = 0.4 x 153.125 = 61.25 ohms(ii) For each single-phase unit,X_pu = 8/20 = 0.4 puX_base = (200MVA x 115kV)/(35MVA x 13.8kV) = 493.75X = 0.4 x 493.75 = 197.5 ohms

 

[Mene]

In the per unit system, all quantities are expressed in terms of their corresponding base values. This allows for easier comparison and analysis of different power systems. In this problem, we are given a 3-phase generator rated at 100 MVA and connected through a Δ/Y transformer to a transmission line with a series reactance of 40 ohms per phase. We are also given the base values for the line circuit, which are 200 MVA and 115 kV.

To find the generator and transformer reactances in per unit (pu), we need to first determine the per unit values for voltage and power. We can do this by dividing the actual values by their corresponding base values.

For the generator, the per unit voltage will be 13.2 kV/115 kV = 0.115 pu and the per unit power will be 100 MVA/200 MVA = 0.5 pu.

(i) For the first case, the transformer is a 3-phase unit rated 100MVA, 13.8Δ/120Y kV, X = 8%. Using the same method as above, we can calculate the per unit voltage and power for the transformer. The per unit voltage will be 13.8 kV/120 kV = 0.115 pu and the per unit power will be 100 MVA/200 MVA = 0.5 pu. To find the per unit reactance, we use the formula Xpu = Xactual/Xbase. This gives us a per unit reactance of 0.08 pu for the transformer.

(ii) For the second case, the transformer is composed of three single-phase units, each rated 35 MVA, 13.8/69 kV, X = 8%. Again, we can calculate the per unit values for voltage and power, which will be 13.8 kV/115 kV = 0.12 pu and 35 MVA/200 MVA = 0.175 pu, respectively. Using the formula for per unit reactance, we get a per unit reactance of 0.08 pu for each single-phase unit.

In both cases, we can see that the per unit reactance for the transformer is the same, despite the different configurations of the transformer. This is because the transformer ratings and voltages are the same, and the per unit system allows for easy comparison and analysis of