Starting a 380V three-phase cage motor is an old problem. It seems that there was an answer decades ago, but it is almost a new problem. Most of the answers now cannot stand the question of why? Or they are not practical.
Let me first talk about the existing answers (please add if you haven't said all):
The motor power is greater than 10kW;
The motor power is greater than 50kW;
The motor power is greater than 20% of the transformer capacity;
For motors that are frequently started , the voltage drop caused by starting is greater than 10%;
For motors that are started occasionally, the voltage drop caused by starting is greater than 15%.
There seems to be no basis for items 1 and 2. In reality, motors of hundreds of kilowatts are directly started at full voltage. For item 3, is the transformer unloaded? For items 4 and 5, how can they be controlled in practice? Is it through actual measurement?
In fact, the main purpose of using reduced voltage starting is to avoid affecting the normal operation of other equipment.
If there are no other equipment, only transformers and motors, then the power of the motor can be close to the capacity of the transformer. Considering factors such as power factor and efficiency, the motor power is generally 80% of the transformer capacity, and can be started directly, or the transformer and motor can be started at the same time. In reality, when most large motors are started, the transformer has more or less other loads , so the amount of other loads is also one of the factors to be considered.
Why does starting an electric motor affect the operation of other electrical equipment?
Because the starting current of the cage motor is 5-7 times its rated current, the large current will cause a large voltage drop. When the voltage drop reaches a certain value, other electrical equipment may stop working or cause failure. Therefore, it is stipulated that the voltage drop caused by frequent starting of the motor should not exceed 10%, and the voltage drop caused by infrequent starting should not exceed 15%.

Why does voltage drop occur?
This is because the transformer cannot provide the large current required for the large motor to start. If the transformer can provide the large current required for the large motor to start, there will be no voltage drop or the voltage drop will be very small. This means that the size of the transformer capacity also determines the size of the voltage drop. In practice, we must not only talk about how big a motor needs to be started at reduced voltage without talking about the size of the transformer capacity.
The size of the transformer's existing load is also one of the factors that determine the size of the voltage drop.
Imagine starting the same motor when the transformer is unloaded and fully loaded. The voltage drop will definitely be different. So it is not feasible to judge whether the motor needs to be started at reduced voltage by only saying that the motor power is a few percent of the transformer capacity without mentioning the current load of the transformer.
So far, to determine whether the motor should be started at reduced voltage, at least three factors, motor power, transformer capacity, and existing load, must be considered. None of them can be missing! So let's take a look at the various so-called judgment methods now. Do you take these three factors into consideration?
How to comprehensively consider these three factors?
For convenience, we use the parameter of current. In fact, the essence of this question is: how much current will cause how much voltage drop? That is, the problem of current and voltage drop.
As we all know, the starting current of a cage motor is 5-7 times the rated current. For a transformer, what load current will cause the voltage drop to reach 10% or 15%? This requires the use of the parameter of impedance voltage. The impedance voltage of a general power transformer is about 5%, that is, when the output current of the transformer is the rated value, the voltage drop is 5%. This is a transformer with an output of 380V. The designed output voltage is 400V, and when it is fully loaded, it is exactly 380V.
Assuming that the voltage drop of the transformer output voltage changes linearly with the increase of load current, then when the output current of the transformer is 2 times the rated current, the voltage drop is 5%, 10% when it is 3 times the current, and 15% when it is 4 times the current. Then the voltage drop allowed for frequently started motors is 10%, that is, the starting current of the motor plus the existing load current can be started directly as long as it is less than 3 times the rated current of the transformer. This is the simplest and most practical way to determine which method is used to start the motor.