2.1 Name the instrument that is used to measure electrical energy - NSC Electrical Technology Power Systems - Question 2 - 2016 - Paper 1

1. Three-phase systems can be operated in star or delta configurations, which allows for flexibility in applications and systems.

2. Three-phase systems can supply both three-phase and single-phase installations, making them versatile for various electrical needs.

A diagram representing the voltage waveforms of a three-phase AC generation system would show three sine waves, each 120 degrees out of phase with each other. The peaks should be labeled +Vmax and -Vmax, and the voltage values should be shown clearly to differentiate each phase (e.g., Ph₁, Ph₂, Ph₃, etc.).

To calculate the line voltage (Vₗ), we use the formula:

S = rac{\sqrt{3} Vₗ Iₗ}{S}

Solving for Vₗ, we have:

$Vₗ = \frac{S}{\sqrt{3} Iₗ} = \frac{20000}{\sqrt{3} \times 25} = 461.88 \, V$

To find the phase voltage (Vₚ), we can use the relationship between line and phase voltage in a star connection:

$Vₚ = \frac{Vₗ}{\sqrt{3}} = \frac{461.88}{\sqrt{3}} = 267.67 \, V$

The total input power (Pₜ) is calculated by summing the wattmeter readings:

$Pₜ = P₁ + P₂ = 8 \, kW + 4 \, kW = 12 \, kW$

To find the line current (Iₗ), we use the formula:

$P = \sqrt{3} Vₗ Iₗ \cos φ$

Rearranging to solve for Iₗ gives us:

$Iₗ = \frac{P}{\sqrt{3} Vₗ \cos φ} = \frac{12000}{\sqrt{3} \times 380 \times 0.8} = 22.79 \, A$