Why we use 50Hz, 60Hz or 400Hz frequency?

Why the frequency of power supplies in European and Asian countries is 50Hz, while American countries use 60Hz power supplies? What is the basic of the standard? What are the advantages and disadvantages of 50Hz and 60Hz power supply? In addition, why the airport and aircraft use 400Hz frequency?

In fact, there is no big difference between 50Hz and 60Hz, only the generator speed has slightly difference. Choose 50Hz or 60Hz, it's almost always the same in a country except Japan (Japan has both 50Hz and 60Hz power supplies).

We should be aware that why use 50Hz or 60Hz, rather than lower or higher frequency.
In electrical system, frequency is a very important basic element, not arbitrarily determined. It looks like simple, but in fact, it is a much complex issue, involve with many aspects. From the principle, we should mention the classical electromagnetic theory found by Maxwell, Hertz added a critical point for Maxwell's theory, Faraday's law of electromagnetic induction and the world's first electromagnetic induction generator, the British engineer Ward King made the electromotor first, the French Pixie made generator, Siemens found the generator principle, the invent the power generation machine, which is the first case in practical application.

Since then, it was found and summed up the theorem that the cyclical changes in the direction of the current is called alternating current, the time of the current in one cyclical change called the cycle, the cycle times of the current changes in one second called frequency, the unit is Hertz (in order to commemorate the contribution of German physicist Heinrich Rudolf Hertz). The frequency of alternating current is 50(60) Hz, the current direction changes 50(60) cycles, 100(120) times per second.

The electric motor is made according to the basic principle of the rotating coil in the magnetic field. If connect two copper slip rings respectively to the ends of the motor coil and two brushes connect with the slip rings, it becomes an alternator (principle). Generator is a device to achieve the conversion from mechanical energy to electrical energy.

Frequency value is related to the structures and materials of generator, motor and transformer.
50Hz generator synchronous speed is 3000rpm, if the frequency is 100Hz, then the synchronous speed will be 6000rpm. Such a high speed will bring a lot of troubles to manufacture the generators, especially the rotor surface speed is too fast which will limit the generator capacity greatly. In actual applications, the high frequency will make the reactance increase, electromagnetic loss, and increase the reactive power. Motor, for example, the current will decrease greatly, the output power and torque will decrease evidently, which does not has any benefit. In addition, if use a lower frequency such as 30Hz, transformer efficiency is too low, not benefit for AC power transformation and transmission.

The frequency in modern power system is the frequency of the sinusoidal fundamental voltage generated by the synchronous generator. Frequency is the unified operating parameter in the whole power system. A power system has one frequency only. Most Asian and European countries use 50Hz frequency. American countries use 60Hz. Most countries regulate the frequency deviation between ±0.1~0.3 Hz. In China, the frequency deviation of 3 million kW and higher power systems shall not exceed ±0.2Hz; lower than 3 million kW power systems shall not exceed ±0.5Hz.

The difference in grid frequency depends on different calculation habits.
The large-scale power generations in America are earlier than other continents. At that time, the calculation tool was British (duodecimal number system) slide rule. For easy calculation, they used 60Hz. And then later, the power grids use decimal calculation, 50Hz is more convenient.

List of worldwide mains frequencies:

The special circumstances in airport: aircraft generators require small size, light weight, the only way to meet the power requirements is to increase the frequency, so the corresponding electrical equipment on airplanes should be 400 Hz, and aircraft-related power supplies is 400 Hz, military uses even higher frequency.

Aircraft power supply uses 400Hz is in order to reduce the size and weight, it is a complex system. 400Hz being used on military and avionics is mainly depending on the following: 1, High frequency generator or electro motor has small size and light weight due to the high rotating speed and low torque; 2, The aircraft generator is driven by the aero engine, it has high speed; 3, Aircrafts have lots of DC machines, high frequency is benefited for reducing the rectification ripple.

In case of same voltage, what are the differences of 50Hz, 60Hz and 400Hz power supplies in transmission and efficiency?
The reason of not using 100Hz or 120Hz is due to the high frequency, on the one hand, the transmission will be difficult; on the other hand, it's inadvisable to increase the speed or poles of the generator and electro motor. 400Hz power cannot be transmitted for long-distance, the user needs to regulate the transmission distance and method before ordering a 400Hz generator, and the rectifier efficiency will be poor, but the rectifier ripple is smaller, the ripple frequency is higher and good for handling.