4.1 Refer to FIGURE 4.1 and answer the questions that follow - NSC Electrical Technology Power Systems - Question 4 - 2022 - Paper 1

Phasor Vrn represents a phase voltage because it is the voltage between R (Line 1) and neutral (N).

Active power, also known as real power, refers to the capacity of a circuit to perform work at a particular time. It is measured in watts (W) and is the power consumed by resistive loads.

By stepping up the voltage in transmission lines, the current flowing through the lines is reduced. This reduction in current helps to minimize energy losses due to resistance in the conductors, effectively reducing copper losses.

    L1
      |
    R----N
      |
    L2
      |
    Y
      |
    L3
      |
    B

In the distribution stage, power is distributed to substations at 22 kV. It is then stepped down to 11 kV for intermediate substations, and finally to 380 V/220 V at distribution substations serving shops, offices, schools, and homes.

To calculate the phase current, we use the formula:

$I_{PH} = \frac{I_L}{\sqrt{3}}$

Thus, $I_{PH} = \frac{15 A}{\sqrt{3}} \approx 8.66 A.$

To find the impedance of the load, we use:

$Z_{PH} = \frac{V_{L}}{I_{PH}}$

Given VL = 400 V,

$Z_{PH} = \frac{400 V}{8.66 A} \approx 46.19 \Omega.$

The phase angle can be determined using the power factor:

$\cos(\theta) = pf\Rightarrow \theta = \cos^{-1}(0.85) \approx 31.79^{\circ}.$

The active power can be calculated as:

$P = \sqrt{3} \times V_L \times I_L \times \cos(\theta)$

Substituting the values:

$P = \sqrt{3} \times 400 V \times 15 A \times 0.85 \approx 8833.46 W.$

This simplifies to approximately 8.83 kW.

    R   Y   B
    |   |   |
   C1  C2  C3
    |___|___|

1. It can measure both balanced and unbalanced loads.
2. The power consumption of each phase can be determined.

Three wattmeters are required for an unbalanced load. The power factor cannot be determined if no neutral lines exist.

For a balanced load, total power is given by:

$P_T = P_1 + P_2 + P_3 = 3 \times P_1 = 3 \times 450 W = 1350 W.$