Three-phase voltage is not equal to three times single phase

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

11 March 2007

After reading the article on 3-phase electricity a fortnight ago, Ndung'u Kahiu remembered two questions that have been troubling him. He says, “First, if single phase is 240V, how then is 3phase 415V and not 720V? Secondly, are horse powers equal? I have noted that petrol generators have a higher rating like say 10hp yet a diesel model with around 6hp and less kVA can power more appliances. How is that possible?”

Kahiu arrives at 720V after multiplying 240V by 3 – since there are three phases. That is not the correct way to go about it. The problem is that voltage can only be measured between two wires; not three.

Now, in three-phase electricity there are four wires – three live and one neutral. If the voltage is measured between the neutral and any one of the live wires, it comes to 240V. But when it is determined using any two live wires it is found to be 415V.

To understand this, we must first remind ourselves what it is that we are measuring. Alternating current means alternating voltage. That is, the voltage varies continuous from zero to a positive value (in this case, positive 240V) then drops back to zero and onwards to a negative value (negative 240V) and so on. This alternation is at the rate of 50 times per second.

Now, if two phases were in direct opposition to each other, then when the first reaches positive 240V, the next one would be at negative 240. In that case, the difference between the two would be 480V.

To see that clearly, picture two pendulums swinging side-by-side. If they are in direct opposition, then when the first one reaches maximum on one side, the second one would also be at the other extreme end. At that point, the distance between them would be twice that from the central (“neutral”) position.

In the case three-phase electricity, the voltages are not in direct opposition. As explained in the previous article, they are separated by a duration equal to one-third of the period of an oscillation. As a result, the greatest “separation” between the voltages of any two live wires never reaches 480V. The actual difference turns out to be 415V (actually, 415.69V).

Going to the second question on petrol and diesel generators, a horse-power is a horse-power; whether it is from petrol, diesel, kerosene, gas, water or whatever, it remains the same –  approximately equal to 0.75 kilowatts.

But if Kahiu has observed that a diesel generator can power more appliances than a petrol one of greater horse-power, then my conclusion would be this: Either one manufacturer is not telling the truth, or the appliances used in the observation are not similar.

However, regardless of the fuel used, the kVA rating is always less than the kilowatts stated – even though kilowatts are found by multiplying the kilovolts (kV) by the amperes (A). The reason for the difference is a story for another day.