the maths behind one phase of 415V 3 phase power being 240V and not whatever 415/3 is
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The three phases can be represented as three equally spaced points on a circle. Each point is a distance of 240 from the circles center (ground). So, what is the distance between two points?
We solve this by solving the triangle with two sides of 240 and an angle of 120^o between them. We immediately see that the other two angles are 30^o each. The length of the remaining side can be solved by the law of sines.
240 * sin(120) / sin(30) = 415
The three phases can be represented as three equally spaced points on a circle. Each point is a distance of 240 from the circles center (ground). So, what is the distance between two points?
We solve this by solving the triangle with two sides of 240 and an angle of 120^o between them. We immediately see that the other two angles are 30^o each. The length of the remaining side can be solved by the law of sines.
240 * sin(120) / sin(30) = 415
The three phases can be represented as three equally spaced points on a circle. Each point is a distance of 240 from the circles center (ground). So, what is the distance between two points?
We solve this by solving the triangle with two sides of 240 and an angle of 120^o between them. We immediately see that the other two angles are 30^o each. The length of the remaining side can be solved by the law of sines.
240 * sin(120) / sin(30) = 415
I will take a shot at this… think of the symbol for a Mercedes car, 3 “spikes,” if you will. If the distance from the center of the star to any one point is 240, the distance between the points of the star will be 415. You can draw this to double-check it, 24 cm straight up from the center, 24 down and to the right, 24 cm down and to the left. I should look like the skeleton of a big Mercedes symbol. Then measure the distance between any 2 outside points, should be just over 41 cm. Your numbers times 10 show the relationship you are asking about. The insides of a three phase generator are essentially like this. If you have a generator instead of a Mercedes symbol, the distance (voltage) from one point to the center would be your 240 VAC, and measuring to any of the 2 outside points would be 415 VAC, 120 degrees “out of phase.” Essentially three generators in the space where you might only suppose there is one – a great efficiency. PS Three points on the star is just used for convenience, you could arrange pretty much any low number… getting “polyphase” AC from your generator.
I will take a shot at this… think of the symbol for a Mercedes car, 3 “spikes,” if you will. If the distance from the center of the star to any one point is 240, the distance between the points of the star will be 415. You can draw this to double-check it, 24 cm straight up from the center, 24 down and to the right, 24 cm down and to the left. I should look like the skeleton of a big Mercedes symbol. Then measure the distance between any 2 outside points, should be just over 41 cm. Your numbers times 10 show the relationship you are asking about. The insides of a three phase generator are essentially like this. If you have a generator instead of a Mercedes symbol, the distance (voltage) from one point to the center would be your 240 VAC, and measuring to any of the 2 outside points would be 415 VAC, 120 degrees “out of phase.” Essentially three generators in the space where you might only suppose there is one – a great efficiency. PS Three points on the star is just used for convenience, you could arrange pretty much any low number… getting “polyphase” AC from your generator.
I will take a shot at this… think of the symbol for a Mercedes car, 3 “spikes,” if you will. If the distance from the center of the star to any one point is 240, the distance between the points of the star will be 415. You can draw this to double-check it, 24 cm straight up from the center, 24 down and to the right, 24 cm down and to the left. I should look like the skeleton of a big Mercedes symbol. Then measure the distance between any 2 outside points, should be just over 41 cm. Your numbers times 10 show the relationship you are asking about. The insides of a three phase generator are essentially like this. If you have a generator instead of a Mercedes symbol, the distance (voltage) from one point to the center would be your 240 VAC, and measuring to any of the 2 outside points would be 415 VAC, 120 degrees “out of phase.” Essentially three generators in the space where you might only suppose there is one – a great efficiency. PS Three points on the star is just used for convenience, you could arrange pretty much any low number… getting “polyphase” AC from your generator.
Think of one phase as a wave travelling through the wire. It has peaks and troughs and the voltage varies according to where you measure on the upward or downward curve.
Then think of the second phase as the exact same thing but slightly delayed. It’s just another wave travelling through the wire slightly behind the first one. And if you were to measure the voltage again you’d get the sum of the two waves at whatever point you pick.
If there was no delay between the two waves, they would both have their peaks and troughs at the exact same time and the result of a voltage measurement would be doubled.
It’s the same idea for three phases. The result is not tripled because the peaks and troughs don’t line up. They are not in-phase with each other.
Think of one phase as a wave travelling through the wire. It has peaks and troughs and the voltage varies according to where you measure on the upward or downward curve.
Then think of the second phase as the exact same thing but slightly delayed. It’s just another wave travelling through the wire slightly behind the first one. And if you were to measure the voltage again you’d get the sum of the two waves at whatever point you pick.
If there was no delay between the two waves, they would both have their peaks and troughs at the exact same time and the result of a voltage measurement would be doubled.
It’s the same idea for three phases. The result is not tripled because the peaks and troughs don’t line up. They are not in-phase with each other.
Think of one phase as a wave travelling through the wire. It has peaks and troughs and the voltage varies according to where you measure on the upward or downward curve.
Then think of the second phase as the exact same thing but slightly delayed. It’s just another wave travelling through the wire slightly behind the first one. And if you were to measure the voltage again you’d get the sum of the two waves at whatever point you pick.
If there was no delay between the two waves, they would both have their peaks and troughs at the exact same time and the result of a voltage measurement would be doubled.
It’s the same idea for three phases. The result is not tripled because the peaks and troughs don’t line up. They are not in-phase with each other.
1 phase power has an active at 240V and a neutral of 0V. This gives you 240V.
3 phase power has three 1 phase circuits combined, but instead of moving through the sine wave at the same time, they’re offset from each other by 1/3. So one peaks at 240, then the second, then the third and then back to the first.
The 415V isn’t measured between active and neutral like 1 phase, it’s measured between two of the phases. When you draw it out, you’ll see that the difference at any one point in time is 415V.
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