Fault Analysis in Power Systems Part 2b

Converting the system to base values for easy fault analysis. This is the third video in the series on fault analysis in power systems. In this video, we will proceed to step number one of our fault calculations process, which is to convert the system to base values. We will show how this simplifies our calculations considerably.

Now, let’s introduce this example. We have a three-phase synchronous generator with a short circuit capability of 600 MVA connected to a 115 kV bus. We also have a delta-wye transformer rated at 30 MVA, which connects the 115 kV bus to the 13.8 kV bus and has an impedance of 10% at 30 MVA. Additional information states that the positive sequence impedance is 10% at 30 MVA and the zero sequence impedance is also 10% at 30 MVA.

Our objective is to convert the system impedances to per unit values or per unit equivalent, which will simplify our fault calculations down the road. To do this, we need to select the base values for voltage and power, which is the first step. We will select 115 kV as our base voltage because the generator is connected to the 115 kV bus, and we will select 30 MVA as the base power value because the transformer impedance is given as a percentage of this value (10% at 30 MVA).

Given the base values of voltage and power, we can now calculate the base value for impedance. The formula for impedance base (Zbase) is the base voltage squared divided by the base power. In this case, Zbase = (115 kV)^2 / 30 MVA, which equals 440 ohms. So, 440 ohms is the base value for impedance.

Now, let’s derive the per unit impedance for both the generator and the transformer. Starting with the generator, we need to find the short circuit impedance value and convert it to the per unit value. Using the formula P = V^2 / R, rearranged to solve for R, we get the short circuit impedance = (115 kV)^2 / 600 MVA, which equals 22.04 ohms. To convert this to the per unit value, we divide 22.04 ohms by the base impedance value of 440 ohms calculated earlier. The per unit value of the short circuit impedance at 30 MVA is therefore 22.04 ohms / 440.83 ohms = 0.05 per unit. Considering the resistive part is very small compared to the inductive part, we write this as Z short circuit at 30 MVA = 0 + j0.05 per unit. For simplicity, we assume this per unit value represents the generator’s positive sequence, negative sequence, and zero sequence impedances.

Moving on to the transformer, the given positive sequence and zero sequence impedances are both 10% at 30 MVA. Since we selected 30 MVA as our base, the per unit values for the positive sequence and zero sequence impedances of the transformer are 0 + j0.10 per unit. We assume there is no resistive part in the impedance.

When we draw the values in a per unit

converted system, we have the generator symbol connected to an inductor representing the j0.05 impedance, connected to the 115 kV bus. This is then connected to another inductor representing the j0.10 impedance of the transformer, which is connected to the 13.8 kV bus. Please note that the buses shown are for display purposes only and do not represent the actual voltages since we are using per unit values to remove voltages from our calculations.

In our next video, we will demonstrate how to convert the sequence network into positive, negative, and zero sequence components and model the delta-wye transformer within the sequence network diagram. Thank you.