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• True power and power factor.
• Fourier transforms.
• Three-phase systems and harmonic problems.
• Pulse Width Modulated Motor Drives.
• IEC Standards. Harmonics & Flicker.
• Solutions and Measurements.
Real and apparent power
 Instantaneous power is the product of instantaneous voltage and current.
 Resistive load.
– instantaneous W is always (+)ve
– W = V x A

 Inductive load
– current is phase shifted
– instantaneous W sometimes (-)ve
– W ¹ V x A
 Apparent Power = V x A
 Power Factor = Cosq
Power factor and cosq
The power factor is reduced . Not by phase displacement, but by shape distortion.
Why is this important?
Power factor of <1 means generation and transmission must be oversized:
• Power lines and transformers sized to supply VA, not Watts.
Power factor <1 due to harmonic distortion:
• Cannot be corrected by capacitors. (Capacitors may be damaged).
• Distorts Voltage which increases the losses in motors.
• Creates electromagnetic interference. EMI.
• Neutral burn-out in 3 phase 4 wire systems.
Distortion is measured and controlled in terms of harmonics.