State four types of power lines faults. With aids of phasor diagrams, explain the following: i. Positive sequence ii. Negative phase sequence iii. Zero sequence

3. (a) (i) State four assumptions made in the analysis of unsymmetrical faults.

• The system is linear.
• The system is balanced prior to the fault.
• The impedances of the system are symmetrical (i.e., self-impedances of phases are equal, and mutual impedances between phases are equal).
• The generated EMFs are balanced and sinusoidal.

3. (a) (ii) Define "operator a" as used in symmetrical components theory.
The operator a is a complex number that represents a counter-clockwise phase rotation of $120^\circ$. It is defined as $a = 1 \angle 120^\circ = e^{j