Coordinate transformation is used in motor control, power electronic inverter circuit and PQ control. When learning motor control, I feel familiar with coordinate transformation.
But when it is applied to the coordinate transformation of power electronic inverter circuit and PQ control, it is confused again.
Why does the abc three-phase voltage add up to 0, but there is a value in the dq0 coordinate system after the coordinate transformation?
Why are there constant power conversion and constant amplitude conversion, and what is the difference?
I have thought about these issues, and I have some conclusions, which I would like to share with you:
1. The difference between vector and phasor applications in power systems.
In previous circuit calculations, generally only the amplitude of current and voltage and the phase change over time are considered. In essence, it is still a function of amplitude and time, so phasors are used in circuit calculations—contains the information of amplitude and initial phase of time.
In the internal calculation of the motor, the calculation of flux linkage, magnetomotive force, etc. is carried out in space, so the vector is used—including the amplitude and its phase change in time and the difference in space phase.
At this time, just looking at one phase, the function of its amplitude and time is a sinusoidal change, as shown in the figure below:
The function of the amplitude and time of the three phases is a sinusoidal change. In the phase of time, the three-phase voltages differ by 120 degrees from each other, as shown in the figure below:
Expressed in terms of phasors, you can see that the picture below is drawn in the form of space phasors, but in essence this is a phase in time, but it is drawn in the form of space for easy understanding.
When the above-mentioned three-phase electricity is passed into the motor, the three-phase electricity will have a phase difference of 120 degrees in space in the motor, and it can be represented by a vector at this time:
The voltage represented by the vector includes the amplitude, its phase change in time, and the difference in space phase.
Therefore, all phasor calculations are linear calculations, which are essentially numerical addition and subtraction. For example, the addition of three-phase voltage phasors is equal to 0. In vector calculation, the space phase should be considered, no longer just the addition of values, but the amplitude of each phase should be considered in the abc three-phase coordinate system. For example, when the motor is connected to three-phase alternating current, its voltage The resultant vector is a space voltage vector with a fixed amplitude and rotating at an angular velocity of 2 PI f.
2. Transformation connotation of dq0 coordinate system and abc coordinate system
To undertake the first question, in the coordinate transformation from dq0 to abc or abc to dq0, the spatial phase and amplitude of three-phase electricity should be considered. The amplitude of each phase varies sinusoidally and the amplitude differs by 120 degrees in time phase, and the phases also differ by 120 degrees in space. Therefore, the vector synthesis of three-phase electricity is not zero, but a rotating vector.
For example, the figure below simply draws an example: the three-phase voltage is at the position of the asterisk marked by the black line, assuming that the amplitude of phase a (phase u) is 2 at this time, then phase b (phase v) and phase c (phase w) The magnitude is -1. If the amplitudes of the three are added directly, the sum is 0, that is, the sum of the three-phase voltages we usually understand is always 0. But put the three in the abc coordinate system, you can see that the resultant vector is not 0, but 3/2 times of the original three-phase voltage amplitude. This is also the reason why the coordinate transformation from abc to dq0 needs to be multiplied by 2/3—to ensure that the magnitude of the synthesized vector is the magnitude of the original voltage.
Therefore, the resultant vector of this rotation can be represented by other coordinate systems, and the principle of equivalence is equivalent amplitude or equivalent power. The difference between these two equivalents is reflected in the magnitude of the transformation matrix during the transformation (that is, the magnitude is equivalent when 2/3 is equivalent, and sqrt(2/3) is power equivalent). The transformation formula from the Abc three-phase coordinate system to the αβ coordinate system is as follows:
(equal amplitude transformation)
(equal power transformation)
After the coordinate transformation from abc to dq0, when the angular velocity of the rotation of the dq coordinate system is the same as the angular velocity of the synthetic rotation vector in the abc coordinate system, the vector synthesized in the dq coordinate system is directly consistent with the vector synthesized in the dq coordinate system. Equivalent to coordinate transformation.
So, why the sum of the abc three-phase voltages is 0, but there is a value in the dq0 coordinate system after the coordinate transformation? This problem is solved.
Take a record, if there is something inappropriate, please point it out.
