During the operation of a motor, a rotating coordinate system with synchronous rotational speed is established by the synchronous rotation of the stator and rotor magnetic fields. This rotating coordinate system is commonly referred to as the DQ rotating coordinate system. In this rotating coordinate system, all electrical signals can be described as constants. To facilitate the study of motor vector control problems, is it possible to directly obtain the results of the DQ transformation from instruments?
The DQ transformation is a decoupling control method that transforms the three-phase windings of an asynchronous motor into equivalent two-phase windings and converts the rotating coordinate system into orthogonal stationary coordinates, thus obtaining the DC expression for the voltage and current relationship. The DQ transformation allows for independent control of each control variable, eliminating the effects of harmonic and asymmetrical voltages. Due to the application of synchronous rotating coordinate transformation, it easily separates the fundamental frequency from harmonics.
Since the main magnetic flux of a DC motor is essentially determined solely by the excitation current of the excitation winding, this is the fundamental reason why the mathematical model and control system of a DC motor are relatively simple.
If the physical model of an AC motor can be equivalently transformed into a model similar to that of a DC motor, the analysis and control can be greatly simplified. Coordinate transformation is carried out according to this idea.
When a three-phase symmetrical stationary winding A, B, and C of an AC motor is supplied with a three-phase balanced sinusoidal current, the resulting composite magnetomotive force is a rotating magnetomotive force F. It is sinusoidally distributed in space and rotates at a synchronous speed ws (i.e., the angular frequency of the current) along the phase sequence ABC. This physical model is illustrated in the figure below.
Rotating magnetomotive force (GM) does not necessarily require three phases. In addition to single-phase windings, any symmetrical multiphase windings, such as two-phase, three-phase, four-phase, etc., can generate GM when a balanced multiphase current is applied. Of course, two-phase windings are the simplest. Figure 2 shows two stationary windings a and b, which are 90° apart in space. When a balanced alternating current with a 90° time difference is applied, a rotating GM F is also generated.
When the magnitude and rotational speed of the two rotating magnetomotive forces in Figures 1 and 2 are equal, the two-phase winding in Figure 2 is considered equivalent to the three-phase winding in Figure 1. Figure 3 shows two windings d and q with equal turns and perpendicular to each other, through which DC currents id and iq are passed, respectively, generating a resultant magnetomotive force F, whose position is fixed relative to the windings. If the entire iron core, including the two windings, is rotated at a synchronous speed, the magnetomotive force F will naturally rotate as well, becoming a rotating magnetomotive force. If the magnitude and rotational speed of this rotating magnetomotive force are controlled to be the same as those in Figures 1 and 2, then this rotating DC winding is equivalent to the two fixed AC windings mentioned earlier.
Figure 3 Rotating DC winding
Therefore, based on the criterion of generating the same rotating magnetomotive force, the three-phase AC winding in Figure 1, the two-phase AC winding in Figure 2, and the overall rotating DC winding in Figure 3 are equivalent to each other. In other words, iA, iB, and iC in the three-phase coordinate system, ia and ib in the two-phase coordinate system, and DC id and iq in the rotating two-phase coordinate system are equivalent, and they can generate the same rotating magnetomotive force.
Applications of DQ coordinate transformation
The theory of motor coordinate transformation has been widely used in the field of electrical engineering. It is not only widely used in motor control and transient analysis, but also in power system fault analysis and power grid power quality detection and control. The main applications of the theory of motor coordinate transformation are as follows.
1. Motor control
2. Transient operation analysis of the motor
3. Motor fault diagnosis
Test methods
The DQ transformation is widely used in motor testing. As long as the rotor position and three-phase current signals can be accurately obtained, the algorithm can be implemented in real-time using a high-speed FPGA in parallel. The Clark transformation converts the three-phase coordinate system stationary relative to the stator into a two-phase coordinate system stationary relative to the stator, yielding the corresponding transformed outputs Iα and Iβ. Then, the Park transformation converts the two-phase coordinate system stationary relative to the stator back to a two-phase coordinate system stationary relative to the rotor, thus calculating ID and IQ. The motor control process is an inverse transformation process. First, the excitation current and torque current are set, then the transformation is performed to the two-phase coordinate system stationary relative to the stator, and then to the three-phase coordinate system stationary relative to the stator, thereby achieving motor control.
ZLG Zhiyuan Electronics is currently planning to implement this DQ conversion function in its power analyzer, which can provide a reference for motor control. The motor control process can be carried out by comparing the set values with the test results of the power analyzer, and can be used for motor control research and development, fault diagnosis, algorithm optimization, etc.
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