Three-phase circuit power calculation - Database & Sql Blog Articles

1. Calculation of symmetrical three-phase circuit power (1) Average power setting The power absorbed by one-phase load in a symmetrical three-phase circuit is equal to Pp=UpIpcosφ, where Up and Ip are the phase voltage and phase current on the load. Then the total power of the three phases is:
P = 3Pp = 3UpIpcosφ
note:
1) φ in the above equation is the phase difference angle (impedance angle) between the phase voltage and the phase current;
2) cosφ is the power factor of each phase, and the three-phase power factor in the symmetrical three-phase system:
cosφA=cosφB=cosφC= cosφ;
3) The formula calculates the power delivered by the power supply (or the power absorbed by the load).
Line voltage at the load when the load is a star connection Line current In the above formula, there are:

Line voltage at the load end when the load is a delta connection Line current In the above formula, there are:

(2) The reactive power absorbed by the load in the reactive power symmetrical three-phase circuit is equal to the sum of the reactive power of each phase:

(3) Apparent power
(4) The instantaneous power of the symmetrical three-phase load is set to the voltage and current of the symmetrical three-phase load A phase:

Then the instantaneous power of each phase is:

It can be proved that their sum is:
The above equation shows that the instantaneous power of the symmetrical three-phase circuit is a constant, and its value is equal to the average power. This is one of the advantages of the symmetrical three-phase circuit. It is reflected on the three-phase motor and the balanced electromagnetic torque is obtained, avoiding the mechanical vibration. This is not available in single-phase motors.
2. Measurement of three-phase power (1) Three-table method For three-phase four-wire circuits, the average frequency can be measured with three power meters as shown in Figure 11.15. If the load is symmetrical, just one table and the reading is multiplied by 3.

Figure 11.15 Figure 11.16 (2) Two-table method For three-phase three-wire circuits, the average frequency can be measured with two power meters as shown in Figure 11.16. The connection of the measuring circuit is to string the current coils of the two power meters into any two phases, the same name end of the voltage coil is connected to the line of the current coil, and the non-identical end of the voltage coil is connected to the other phase without the string. The power meter is on the line. Obviously, in addition to the wiring of Figure 11.16, the wiring of Figure 11.17 can also be used. This method is called a two-watt meter method. Figure 11.17 In the two-watt method, if W1 reads P1 and W2 reads P2, it can be proved that the three-phase total power is:
P = P1 + P2
Proof: Let the load be Y connection. According to the working principle of the power meter, there are:

and so
because Substituting the above formula:
So the algebraic sum of the readings of the two power meters is the total power of the three phases. Since the delta connection load can become a Y-type connection, the conclusion is still true.
note:
1) The two-watt method can only be used under the condition of three-phase three-wire system, regardless of whether the load is symmetrical or not;
2) The algebraic sum of the two table readings is the total power of the three phases, and the individual readings of each table are meaningless;
3) When wiring according to the correct polarity, there may be a table reading in the second table is negative. At this time, the power meter pointer is reversed. After the current coil polarity is reversed, the pointer points to a positive number, but the reading should be recorded at this time. Negative value;
4) In the case of load symmetry, there are:


The table below shows the values ​​of the two power meters for different φ values.