Fault analysis in Power Systems Part 2c

In this, we will learn how to draw the sequence networks for each of the positive, negative, and zero sequences based on the systems converted in Part 2b. The network diagram we previously drew represents a loose representation of a positive sequence network, which already integrates the delta-y transformer sequence model. However, we have yet to represent the zero sequence and negative sequence network diagrams, which will be the focus of this video.

The delta-y transformer connection is the most complex part of the sequence network analysis, so we will dedicate most of our time to discussing it in this tutorial. If the transformer is a delta-y transformer with the neutral of the y side (or the low voltage side) solidly grounded, then the transformer’s positive and negative sequence networks can be represented by a single impedance, as shown below. However, the zero sequence network is more complex.

Now, let’s talk about the zero sequence network side of the delta-y transformer model. The delta side is treated as an open circuit because the delta winding traps the zero sequence current and does not allow it to flow. This means that if there is a high voltage fault, the zero sequence current cannot be reflected on the low voltage side, and vice versa for a low voltage fault. The y side of the transformer can be represented by a series impedance (Zt) connected to ground at one end only, due to the neutral terminal of the low voltage side being connected to ground. The ground connection causes the zero sequence current to flow into the ground, allowing the fault to circulate but remain on the low voltage side. This is because the zero sequence current will not be reflected on the high voltage side, as we discussed earlier, due to the delta connection being modeled as an open circuit for the zero sequence network. However, it’s important to note that this concept applies only to the zero sequence current, as the transformer will have positive and negative sequence currents reflected on the high voltage side.

It’s also important to keep in mind that different transformer connections will require different zero sequence network diagrams, as the positive and negative sequence networks remain the same regardless of the transformer connection. This applies to both two-winding and three-winding transformers.

Now, let’s draw the positive sequence network. In the positive sequence network, the generator’s voltage source per unit values will be one per unit at an angle of zero degrees. This is fairly simple since we conveniently selected 115kV as the base voltage, which matches our generator source. The voltage source, sometimes called the pre-fault voltage, is commonly selected as one per unit at zero degrees for fault analysis. We add the short circuit impedance of the generator (j 0.05 per unit) in series, followed by drawing a line to mark the 115kV bus. Next, we draw the positive sequence representation of the delta-y transformer with a series impedance of j 0.10 per unit. Finally, we draw a line for the 13.8kV bus. It’s important to note that the voltage on this line is only for reference and serves as a guide. It does not reflect the actual voltages on the circuit.

Now, let’s move on to the negative sequence network. The negative sequence network is essentially the same as the positive sequence network, with the exception that there is no voltage source. This is because the generator does not produce negative sequence currents and, therefore, does not inject negative sequence current into the system during a faulted condition. However, negative sequence currents will still flow through the winding for both balanced and unbalanced faults. So, we still represent 25 per unit but do not represent the actual voltage source of one per unit at zero degrees. The negative sequence network diagram is very similar to the positive sequence network diagram.

Now, let’s discuss the zero sequence network diagram. Similar to the negative sequence diagram, there is no voltage source in the zero sequence network. We include the same generator impedance of j 0.05 per unit, followed by a line indicating the 115kV bus. We then reach the transformer and pick up the zero sequence model for the delta-y transformer, which was discussed earlier in the video, and insert it into the network with an impedance of 0.10 per unit. Finally, we draw a line to indicate the 13.8kV bus, and the network is complete. Note that for the transformer network diagram, there is an open connection for the high voltage side, representing the delta, and a short immediately before the 0.10 per unit impedance, representing the low voltage y side of the transformer connected to ground.

In the next video, we will demonstrate how to connect these three individual sequence networks in the event of a fault and use them to calculate fault currents and voltages easily.