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Introduction to the Wye Wye Transformer connection: Part 2 and the introduction to the infamous square root 3.
Checkout the resources section under this video for helpful comments, suggestions, and clarifications. We introduced the YY connection in the last module – we're going to cover current and voltage quantities in this module.
We understand that the line-to-line currents flow through our lines or conductors. Our primary line-to-line current A will flow through line A, primary line-to-line current B flows through line B, and primary line-to-line current C flows through line C. On the secondary side, we have secondary line-to-line current a, b, and c which flows through the respected secondary lines.
Let's talk about phase currents. Phase current flow through transformer winding. So primary phase current A will flow through winding A, primary phase current B will flow through winding B and primary phase current C will flow through winding C. Similarly, we have secondary phase current a, b, and c that flow through their respective secondary windings.
Notice the relationship between line-to-line current A and phase current A – it's seems like they should be the same right? Well they are! For the Wye connected transformer, we should expect the primary line-to-line current on line A to be the same as the primary phase flowing through winding A. The same is true for line-to-line current on line B and phase B current and the line-to-line current on line C and phase C current.
Since the secondary windings are also connected in Wye, we should expect the secondary phase currents to be equal to the secondary line-to-line currents respectively. Let's scroll down and create a table and call it "YY transformer relationships" – Relationship #1 – line-to-line currents equal phase current.
Alright so returning back to our illustration – so now let's look at our voltages. We understand that Phase voltages are voltages across the transformer windings. The primary phase A voltage is the voltage across the polarity side of winding A and the non-polarity of winding A. Similarly, primary phase B voltage is the voltage across the polarity side of winding B and the non-polarity side of winding B. And phase C voltage is the voltage across the polarity side of winding C and the non-polarity side of winding C.
The same thing is true for the secondary side. We'll have secondary phase a, b and c voltages across the respected secondary windings. Moving on to line-to-line voltages. We understand that Line-to-line voltages are the voltage across two different lines (as the name implies).
The three most common line-to-line voltages – are:
RELATIONSHIP #1 - the voltage across line A and line B. #2 – the voltage across line B and line C and lastly #3 - the voltage across line A and line C.
We must certainly question the relationship between line-to-line voltage and phase voltages. And some of us are just itching to blurt out the answer. Our goal is to intuitively understand the relationship between line-to-line voltage and phase voltage – and discover where the root 3 comes from. We don't want to take someone's word for it right?
Okay so, we understand that voltage is a difference in potential between two points. So when we measure the line-to-line voltage between line A and line B for example, we're actually measuring the difference in potential between a particular point on line A and a particular point on line B.
Now, if we measured the voltage across the bushing of winding A and the bushing of winding B, we'd be confident that it would be the same voltage as the line-to-line voltage across line a and line b right? What if we measured the voltage across the polarity side of winding A and the polarity side of winding B, would we have the same voltage? We'd be pretty darn close since all these points are pretty the same point on the line.
So we can certainly deduce that the line-to-line voltage across line A and line B equals the voltage across the polarity side of winding A and the polarity side winding B. Ahhh now we're getting closer to our answer. So let's ask ourselves another question – what's our winding A voltage? That's right, it's our phase A voltage! That's something that we defined earlier.
Phase A voltage is the voltage across winding A and it's measured from the polarity side of the winding to the non-polarity side and for our Wye connected transformer, the non-polarity side is where the common wire is connected – and our common wire is grounded. Here's another question, what's our winding B voltage? That's right! It's our phase B voltage – again, measured from the polarity side of the winding to non-polarity side of the winding and the non-polarity side is grounded.
So let's now connect the dots now – We should expect that the line-to-line voltage across line A and line B to equal primary phase A voltage minus the primary phase B voltage – and that my friends, is our defining relationship! We should definitely commit this relationship to memory. And to add importance to it, we'll add this relationship to our relationships table.
RELATIONSHIP #2 – line-to-line voltage between two lines is equal to a phase voltage minus another phase voltage (respectively).
Okay so getting back to our equation – if the line-to-line voltage across line A and line B is equal to the phase A voltage minus phase B voltage, then what's the line-to-line voltage across line B and line C? That's right! It would equal, primary phase B voltage minus primary phase C voltage.
Similarly, the line-to-line voltage across line A and line C would equal primary phase A voltage minus primary phase C voltage. Because both the primary side and the secondary side is connected in wye, we should also expect a similar relationship on the secondary side of the transformer.
The secondary line-to-line voltage across line a and line b is equal to secondary phase a voltage minus secondary phase b voltage. The secondary line-to-line voltage across line b and line c is equal to secondary phase b voltage minus secondary phase c voltage.
And the secondary line-to-line voltage across line a and line c is equal to secondary phase a voltage minus secondary phase c voltage. Believe it or not, this is where our square root 3 comes from. We're going to look at a similar example, from a different prospective in module 3.
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