Frequency standardization of AC systems

The supply frequency (50 Hz or 60 Hz) was chosen not because it is best for every purpose, but because it is an acceptable middle value between requirements that pull in opposite directions. Low frequency is good for some equipment and high frequency for others.

Requirements favouring a LOW frequency

• Transmission: line reactance $X = 2\pi fL$ is lower, so voltage drop is smaller, power transfer $P = \frac{V^2}{X}\sin\delta$ and stability limits are higher.
• Charging current and Ferranti effect ($I_c = 2\pi fCV$) are smaller in long lines and cables.
• Skin effect and eddy currents are lower, so conductor resistance is lower.
• Commutator machines (traction motors, rotary converters) commutate better at low frequency; that is why railways used 16⅔ Hz and 25 Hz.
• Low-speed hydro generators need fewer poles at a low frequency.

Requirements favouring a HIGH frequency

• Lighting flicker: incandescent and arc lamps flicker visibly below about 40–50 Hz. This was a major reason to reject 25 Hz.
• Size of transformers and machines: $E = 4.44fN\phi_m$, so for the same voltage a higher $f$ needs less flux and iron; transformers and motors become smaller and cheaper.
• Speed of machines: $N_s = \frac{120f}{P}$; higher frequency gives higher speed, suitable for steam turbines and small motors.
• Aircraft and ships use 400 Hz to save weight.

Limits on very high frequency

Iron losses (hysteresis $\propto f$, eddy $\propto f^2$), higher line reactance, larger inductive voltage drop and interference with telephone lines.

Result

Early systems used many frequencies (25, 40, 50, 60, 133 Hz). Around 1900–1920 the industry settled on 50 Hz (Europe, Asia, Nepal) and 60 Hz (America), which keep flicker invisible, give reasonably small machines and transformers, and still allow acceptable reactance and losses on transmission lines. So the standard frequency is truly a compromise between contradictory requirements.