Question

Two balanced Y-connected loads, one drawing$\mathbf{10}\mathbf{}\mathbf{kW}$at 0.8 power factor lagging and the other$\mathbf{15}\mathbf{}\mathbf{kW}$at 0.9 power factor leading, are connected in parallel and supplied by a balanced three-phase Y-connected,$\mathbf{480}\mathbf{}\mathbf{V}$ source. (a) Determine the source current. (b) If the load nuetrals are connected to the source neutral by a zero-ohm neutral wire through an ammeter, what will the ammeter read?

Short answer

(a) The source current is$30\mathrm{A}$.

(b) The ammeter reads zero value.

Step-by-step solution

Determine the formula for active power and apparent power.

Write the formula of reactive power

$\mathrm{Q}=\mathrm{Ptan}\left({\cos }^{-1}\right(\mathrm{pf}\left)\right)$ ……. (1)

Write the formula of apparent power

$\mathrm{S}=\sqrt{3{\mathrm{V}}_{\mathrm{L}}{\mathrm{l}}_{\mathrm{L}}}$ ……. (2)

Determine the source current

(a)

Solve for the reactive power for the load 1 from equation (1).

$$\begin{gathered} \mathrm{Q}=10\times {10}^3\left({\cos }^{-1}\left(0.8\right)\right) \\ =7.5\mathrm{kVAR} \\ \mathrm{Solve}\mathrm{for}\mathrm{the}\mathrm{reactive}\mathrm{power}\mathrm{for}\mathrm{the}\mathrm{load}2\mathrm{from}\mathrm{equation}\left(2\right). \\ \mathrm{Q}=-15\times {10}^3\left({\cos }^{-1}\left(0.9\right)\right) \\ =-7.265\mathrm{kVAR} \\ \mathrm{Solve}\mathrm{for}\mathrm{the}\mathrm{total}\mathrm{complex}\mathrm{power}\mathrm{is}, \\ \mathrm{S}=(10+j7.5+15-j7.265)\mathrm{kVA} \\ =25\angle 0.{54}^{°}\mathrm{kVA} \\ \mathrm{Using}\mathrm{equation}\left(2\right),\mathrm{the}\mathrm{source}\mathrm{current}\mathrm{is}, \\ S\mathit{=}\sqrt{\mathit{3}{\mathit{V}}_{\mathit{L}}{\mathit{l}}_{\mathit{LS}}} \\ \mathit{25}\times {10}^3=\sqrt{3}\times 480\times l_{\mathrm{LS}} \\ {l}_{\mathit{L}\mathit{S}}\mathit{=}\mathit{30}\mathrm{A} \\ \mathrm{Therefore},\mathrm{the}\mathrm{source}\mathrm{current}\mathrm{is}30\mathrm{A}. \end{gathered}$$

Draw power triangle for source

(b)

In a balanced three phase load, the current through the neutral is zero if it is connected solidly to ground.

The ammeter has approximately zero resistance, hence current through it will be zero.

Therefore, the ammeter reads zero value.