4.1 Write down the typical line voltage value of a three-phase supply for the end user - NSC Electrical Technology Power Systems - Question 4 - 2022 - Paper 1

The standard international colour code is as follows:

• L1: red
• L2: yellow/white
• L3: blue.

The phasor diagram represents the three-phase voltages as vectors rotating at 120° apart from each other. The diagram should show:

• L1 at 0°
• L2 at 120°
• L3 at 240°.

The three network stages of the national power grid in order are:

1. Generation
2. Transmission
3. Distribution.

Line voltage is measured between any two lines. It can be expressed as L1 & L2, L2 & L3, or L1 & L3.

Phase voltage is measured between any of the lines and neutral, which can be represented as L1 & N, L2 & N, or L3 & N.

Reactive power is the power that is transferred back and forth between the supply and the inductor or capacitor, and it does not perform any real work in the system.

To calculate the line voltage (VL), use the formula: $V_L = \\sqrt{3} \, V_{ph}$ Substituting the values: $V_L = \\sqrt{3} \, \times 230 \, V \\approx 398.37 \, V.$

The apparent power (S) in a three-phase system is given by: $S = \\sqrt{3} \, V_{L} \, I_{L}$ Substituting: $S = \\sqrt{3} \, \times 398.37 \, V \, \times 35 \, A \\approx 24149.90 \, VA \ (24.15 \, kVA).$

Reactive power (Q) can be calculated using: $Q = \\sqrt{3} \, V_{L} \, I_{L} \, \sin(θ)$ Substituting the known values: $Q = \\sqrt{3} \, \times 398.37 \, V \, \times 35 \, A \, \times \sin(18°) \approx 7466.73 \, VAr \ (7.47 \, kVar).$

True power (P) is given by: $P = \\sqrt{3} \, V_{L} \, I_{L} \, \cos(θ)$ Using the values: $P = \\sqrt{3} \, \times 398.37 \, V \, \times 35 \, A \, \times \cos(18°) \approx 22967.91 \, W \ (22.97 \, kW).$

Coil 1 of W1 is associated with the red phase (L1).

Coil 2 of W2 is associated with the yellow phase (L2).

Two advantages of using the two-wattmeter method are:

1. It can be used for both balanced and unbalanced systems.
2. The power factor can also be determined.