How to calculate the current when a three-phase asynchronous motor operates with one phase missing?

Theoretically, a motor cannot continue to operate when there is a phase loss. During operation with a missing phase, the rotating magnetic field in the stator becomes severely unbalanced, which results in the generation of negative-sequence currents. The negative-sequence magnetic field induces a voltage of around 100 Hz in the rotor, causing the rotor current to increase sharply and leading to severe heating of the rotor. When operating with a missing phase, the motor’s load-carrying capacity drops significantly; it absorbs a large amount of active power from the power grid, which in turn causes the stator current to rise sharply. The severe unevenness of the magnetic field also leads to increased vibration in the motor, thereby damaging the bearings and the frame. Therefore, a motor operating with a missing phase under its rated load will stop immediately. If the protection system does not activate in time, the motor will be damaged. Generally, motors are equipped with protection against phase loss. Furthermore, during operation with a missing phase, electromagnetic noise increases significantly, starting becomes difficult or impossible, and the output decreases ； The winding current increases significantly when it is not connected to the phase wire with a missing phase ； The currents in the two-phase windings connected to the phase wire with a missing phase do not increase significantly, and their sum is less than that of the other phase. As for the current? The size cannot be determined; it depends on the load conditions. Generally, it increases, because if the load remains unchanged, the load that was previously distributed across three phases now has to be handled by two phases only, resulting in a significant increase in current. This will quickly cause the motor to burn out due to overheating! If we were to do the calculations, under rated load the motor would burn out when operating in two-phase mode. Why does the motor burn out at rated load? Because the voltage at this time is 1/1.732 of the original value, and there are only two phases. With such a low voltage, to maintain constant power, the current becomes 1.732*1.5 times the original value, resulting in severe heating! ! ! Actually, I think it’s basically the stall current! Real-world experience! There are also some doubts regarding the specific calculations; what are everyone’s opinions?

Yes, generally it won’t operate in the case of a missing phase, unless there is imbalance among the three phases

Now let’s discuss whether a value can be derived theoretically! :) There is a solution for this problem: The calculation involves using a triangular connection method, with each side considered as a set of coils. The voltage phases differ by 120 degrees; therefore, the current in each set of coils is 40 A. This value is determined based on the properties of an isosceles triangle, where the two sides are 20 units long and the vertex angle is 120 degrees. When one phase is missing, two sets of coils combine into one set, resulting in an internal resistance and reactive impedance that are twice the original values. As a result, the current becomes one-fourth of that in a single set, namely 10 A. Using the vector addition principle for triangles, one side is 40 A, another side is 10 A, and the angle between them is 120 degrees; the third side represents the line current, which is what we’re looking for. According to the law of cosines, we calculate the square of 40 plus the square of 10, then subtract 2 times 40 times 10 times cosine of 120 degrees. Taking the square root of the resulting value gives approximately 45.8 A. How about that?

Is this question too deep? Why are there no constructive replies?

Personal opinion: 1. This issue has no practical significance； 2. The operating current of a motor under normal conditions also depends on its load; when operating with a missing phase, it depends on the load it is carrying as well. It can operate for a while when unloaded, but it will burn out quickly if the load is heavy.

Theoretical calculations can be used as a practical approach for analyzing motor circuits, but in practice, it is important to note that a missing-phase fault in a motor can be effectively identified by a sudden increase in current. Case: The motor of a centrifugal fan in a company suddenly tripped during operation (the thermal relay activated). The electrician on duty simply reset the thermal relay, but the fan tripped again. Consequently, technical personnel were called to the site; they first checked whether there was a missing phase in the power supply. The power supply at the contactor was normal. After attempting to start the fan and measuring the current, it was found that the current exceeded the rated value, indicating a missing phase. Upon checking along the circuit, it was discovered that one of the wires in the fan motor’s wiring box was broken. The issue was resolved, and normal operation was restored.