Generated current in a \$3\times450\$ VAC \$60\$ Hz \$1150\$ kVA generator

Question

Let's say I've a \$3\times450\$ VAC \$60\$ Hz \$1150\$ kVA generator. How much current will there be generated when it runs at maximum capacity?

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MY WORK:

The total Active power over a three-fase system is given by:

$$P=\sqrt{3}UI\cos\varphi\tag1$$

Where \$U\$ is the line voltage and \$I\$ is the line current.

The total Reactive power is given by:

$$Q=\sqrt{3}UI\sin\varphi\tag2$$

Where \$U\$ is the line voltage and \$I\$ is the line current.

The total Complex power is given by:

$$S=\sqrt{3}UI\tag3$$

Where \$U\$ is the line voltage and \$I\$ is the line current.

So, I know that:

$$1150\times1000=\sqrt{3}UI\tag3$$

But what is the line voltage? Is it \$450\$ volts? So, then we get: \$1150\times1000=\sqrt{3}\times450I\$ which give that the line current equals \$I=\frac{1150\times1000}{\sqrt{3}\times450}\approx1475.5\$ A.

Answer 1

Power engineers always use line-to-line rms when describing the voltage rating of three phase equipment.

So, in your case that is 450 V rms line-to-line. Your answer is correct (1,475 A).

Answer 2

There is a some information in this article of Wikipedia.

Let \$V\$ be the RMS voltage between each of the phases and the neutral, and \$V_p\$ be its amplitude: \$V_p = \sqrt{2}V\$.

Let \$U\$ be the RMS voltage between two phases, and \$U_p\$ be its amplitude:

\$U = \sqrt{3}V\$, \$U_p = \sqrt{2}U\$.

Finally, let \$P = 1150 kVA\$ be the apparent total power available from the generator: it is the sum of the powers of each dipole.

It is unclear in the question whose of these voltages is meant by 450V AC. I suppose here that that this is RMS voltage between the phases and the neutral, that is \$V\$: \$V = 450\$.

Next, the question of "how much current it runs" is ill-posed. A current flows through two terminals, but here there are 4 terminals. Is it the current flowing through the phase and the neutral? the current flowing through 2 phases (if connected), the total current flowing through the terminals in a balanced "Delta" configuration? or the total current flowing through the terminals in a balanced "Wye" configuration? This need be specified, because the answer is different in each case.

Assuming for example you demand the maximal current between two phases: Then

\$I_{max}\ (rms) = P / U\$, which is the value you have to use for your "fuse" between 2 phases. The maximum current amplitude is \$ \sqrt{2}P/U\$

If you demand the maximal current between a phase and the neutral, then \$I_{max}\ (rms) = P / V\$ and the maximum amplitude is \$\sqrt{2}P/V\$.

The other cases are processed similarly.