The working principle and introduction of three-phase AC circuit
A circuit powered by a three-phase AC power supply. Referred to as three-phase circuit. A three-phase AC power supply refers to a power supply that can provide three voltages or currents with the same frequency but different phases, among which the three-phase AC generator is the most commonly used. In 1891, the world's first three-phase AC generator was put into operation at the Laufen power plant in Germany, and the first three-phase AC transmission line from Laufen to Frankfurt was built. Because three-phase circuits deliver power more economically than single-phase circuits, the operating performance and efficiency of three-phase AC motors are also far superior to single-phase AC motors. Therefore, power systems and power consumption in the world currently use three-phase .
Three-phase AC power The three-phase generator has three windings. They form a symmetrical three-phase power supply, each of which is called a single phase. The instantaneous value of each phase voltage is
They have the same amplitude Um and frequency 
However, the phases of the three are 120 ° different from each other (ie 1/3 cycle). The phasors of the three-phase voltage are
Where Up is the effective value of the phase voltage U (Up = Um / 匇). The instantaneous value and phasor of the phase voltage can be represented by a waveform diagram (Figure 1a) and a phasor diagram (Figure 1b), respectively.
Three-phase AC circuit The order in which the voltage of each phase in the three-phase power supply leads or lags is called the phase sequence. If the a-phase voltage leads the b-phase voltage, and the b-phase voltage leads the c-phase voltage, this phase sequence is the a-b-c phase sequence, which is called the positive sequence; otherwise, if the c-b-a phase sequence, it is Negative sequence (also called reverse sequence). The three-phase motor rotates forward when it is powered by a positive sequence voltage, and reverses when it is changed to a negative sequence voltage. Therefore, you must pay attention to its phase sequence when using a three-phase power supply. However, many production equipments that require forward and reverse rotation can change the phase sequence to achieve forward and reverse control of three-phase motors.
Three-phase power connection method There are usually two ways: one is a star connection (Y-shaped), and the other is called a triangular connection (â–³ -shaped). The three wires drawn from the beginnings a, b, and c of the three power sources are called end wires (commonly known as live wires). The voltages ab, bc, and ca between any two terminal lines are called line voltages. The wiring diagram of two different connection methods, the phasor diagram of line voltage and phase voltage are shown in Figure 2 and Figure 3. The relationship between line voltage and phase voltage is shown in the table.
Three-phase AC circuit 
Three-phase AC circuit 
Three-phase AC circuit In the star connection, the line voltage is twice the phase voltage, and the phase difference between the three line voltages is still 120 °, which is 30 ° ahead of the three phase voltages. The star connection has a common point (point n in the wiring diagram), called the neutral point. When the delta connection, the line voltage is equal to the phase voltage, and the three power supplies form a loop. Only when the three-phase power supply is symmetrical and connected correctly (at this time, a + b + b = 0) can there be no circulating current inside the power supply.
Three-phase load can be divided into symmetric three-phase load and asymmetric three-phase load according to whether the three-phase impedance is equal. Some three-phase loads, such as three-phase motors and three-phase electric furnaces, have three-phase impedances that are completely equal and belong to symmetric three-phase loads. Some three-phase loads connected by single-phase electrical equipment, such as household electricity and lighting loads, usually use one end line and a neutral line (commonly known as ground) drawn from the neutral point to provide one-phase users, and the other end line And the neutral line to another phase user. According to this connection, the loads on the three end lines cannot be completely equal, so they belong to asymmetric three-phase loads.
The three-phase load connection method is the same as the three-phase power supply, and there are two types of star connection and delta connection. The star connection and the delta connection where the neutral point is not connected to the outside world are only connected to the power supply through three end points. According to the principle of the same external characteristics, no matter whether it is a symmetric or an asymmetric three-phase load can be equivalently converted Star-triangle transformation).
Calculation of symmetrical three-phase circuit The three-phase power supply, three-phase load and three-phase terminal in the symmetrical three-phase circuit are all symmetrical. The three-phase terminal line symmetry means that the impedances of the three transmission wires are completely equal. Symmetrical three-phase power supply and three-phase load can be star or delta connection, because the star-delta transformation can always change both into an equivalent star to become a symmetrical three-phase circuit with Y-Y connection (Figure 4).
Three-phase AC circuit By applying the node voltage method, nN = 0 in Fig. 4 can be obtained, so as long as the voltage and current of one phase of the symmetric three-phase circuit are calculated, the voltage and current of the other two phases can be directly written according to the symmetry. The center line current value N = value a + value b + value c = 0, which means that the center line current of the symmetric three-phase circuit connected by YY is zero, so the presence or absence of the center line does not have any effect on the symmetric three-phase circuit. Such a three-phase system with only three wires can deliver the same power as three single-phase systems. However, the line loss of the three-phase system is only half of the three single-phase systems, because the latter must use 6 transmission conductors.
Calculation of asymmetric three-phase circuit As long as one of the three-phase power supply, three-phase load and three-phase transmission line is asymmetric, it is an asymmetric three-phase circuit. In practice, the three-phase load is mainly asymmetric. There are three common asymmetric circuits: â‘ Three-phase four-wire circuit supplying power to asymmetric star-connected loads; â‘¡Three-phase three-wire circuit supplying power to asymmetric delta-connected loads; â‘¢Power supply to asymmetric star-connected loads Three-phase three-wire circuit. When ignoring the transmission line load, the load phase voltage of the first circuit is still symmetrical, so it can be calculated according to three single-phase circuits (see star connection); for the second circuit, the load phase voltage is also symmetrical , So the load current can be calculated first, and then the line current (see triangle connection); for the third circuit, the load neutral point needs to be displaced, and the voltage and current of the three-phase load can be calculated based on the obtained neutral point voltage See neutral point).
Power of the three-phase circuit The instantaneous power of the three-phase circuit is equal to the sum of the instantaneous power of each phase. The instantaneous power of each phase is
In the formula, UΑ, UB, UC, IΑ, IB, IC are the effective values ​​of three-phase phase voltage and phase current, respectively, φΑ, φB, φC are the phase angle difference between the phase voltage and phase current of each phase. Let P denote the instantaneous power of the three-phase circuit, then
P = PΑ + PB + PC
If the circuit is a symmetrical circuit, then
at this time
φΑ = φB = φC = φ
Available
at this time
UΑ = UB = UC = Up
In the formula, Up, Ip, U and I are the effective values ​​of phase voltage, phase current, line voltage and line current, respectively.
The instantaneous power of the symmetrical three-phase circuit is a constant, so the reaction torque suffered by the prime mover driving the three-phase generator during normal operation and the output torque of the three-phase motor are stable. The instantaneous power of a single-phase AC circuit is pulsating and does not have this advantage.
The average power of a symmetrical three-phase circuit is
Its value is the same as the instantaneous power.
The reactive power of a symmetrical three-phase circuit is
Apparent power is
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