Brief Analysis of the Speed ​​Control Technology of Single-phase Motor Frequency Conversion in Asynchronous Induction Motor Speed ​​Control System

Based on the above three issues, this article will conduct a relatively detailed analysis and review of the latest developments in single-phase motor variable frequency speed regulation technology at home and abroad in terms of single-phase motor windings, main circuit structure and control technology, and on this basis, discuss its development direction.

The frequency conversion speed regulation technology of single-phase motors still faces the following problems:

1) The windings of single-phase motors are different from those of three-phase motors. The main and auxiliary windings are mostly asymmetrical windings, and the auxiliary winding is usually connected in series with a running capacitor, which brings new problems to the synthesis of a circular rotating magnetic field;

2) The frequency conversion speed regulation inverter main circuit structure for single-phase motors also has its own unique aspects, and there is a problem of how to obtain a reasonable and efficient inverter circuit;

3) Regarding the variable frequency speed regulation of single-phase motors, there is a question of what kind of control technology can be used to enable the single-phase motor to obtain the same excellent speed regulation effect as the three-phase motor or even the DC motor.

1 Single-phase motor winding analysis

According to the analysis of the synthetic magnetic field of a single-phase motor [1], a two-phase winding is embedded on the stator of a single-phase motor. Assume that the axes of the two-phase windings are spaced at an electrical angle of β. Currents with a phase difference of θ are passed through the two-phase windings. The condition for the synthetic circular rotating magnetic potential of the two phases is

 (1)

Where: FM is the magnetic potential amplitude of the main winding;

FA is the magnetic potential amplitude of the secondary winding.

In a single-phase motor, the axes of the two-phase stator windings are usually 90° apart. In order to obtain a circular rotating magnetic field, it is always hoped that the phase difference between the two-phase currents is equal to 90°.

Reference [2] gives an equivalent circuit of a single-phase motor with asymmetric windings. According to this equivalent circuit, when the spatial electrical angle β and the phase difference θ are both 90°, the motor meets the requirements of a circular rotating magnetic field under the following conditions and obtains the best performance:

=1 (2) 

Where: Imain is the main winding current;

Iaux is the secondary winding current;

a is the turns ratio between the secondary winding and the main winding.

It follows that Imain=αIaux.

In fact, it is quite difficult to keep the current ratio between the main winding and the auxiliary winding constant at all times during the operation of the motor. Usually, Vaux=aVmain is used to approximate the constant current ratio.

 Single-phase motors are mostly capacitor-operated motors. The value of the capacitor connected in series in the secondary winding enables the motor to obtain better operating performance under power frequency conditions. When the motor runs at a low frequency, as the capacitance reactance increases, the current phase flowing through the secondary winding is no longer orthogonal to the main winding, so the motor will overheat, reduce torque, increase pulsating torque and other problems [3]. Therefore, the frequency conversion circuits currently used all adopt the solution of removing the capacitor and controlling the two-phase windings separately. However, removing the capacitor also means increasing the voltage value applied to the secondary winding.

2 Inverter main circuit structure topology

2.1 Half-bridge inverter circuit

Since only two-phase voltage needs to be output, the structure of the single-phase motor half-bridge inverter circuit is simple, and only four power conversion devices are needed to form two bridge arms, as shown in Figure 1. The half-bridge inverter circuit has the advantages of simple structure, minimum number of power switching devices, low cost, and high stability.

Figure 1 Half-bridge inverter circuit

However, for single-phase motors, the use of a half-bridge inverter circuit faces the following problem: Since the two-phase currents I1 and I2 of the motor are 90° out of phase, the sum I of the two-phase currents flowing to the neutral point N is the vector sum of the two-phase currents.

 (3)

For a power supply that uses two capacitors in series to construct the midpoint, the feedback current I will increase the output voltage fluctuation of the previous inverter power supply, forcing the power supply to increase the output capacitance; at the same time, the DC bias caused by the load asymmetry will also cause the midpoint potential to continue to drift in the positive (or negative) direction, which has a great impact on the power supply. Therefore, how to obtain a high-quality bipolar DC power supply is the key to using a half-bridge inverter circuit. In reference [4], a method of using Cuk and Sepic circuits in parallel to obtain a bipolar DC power supply is proposed. However, due to the limitation of the power switch capacity, the power and output voltage need to be improved, and the practicality of the entire circuit remains to be verified. 2.2 Full-bridge inverter circuit

The ordinary full-bridge inverter circuit consists of 4 power switch devices per phase, and the two-phase winding requires a total of 8 power switch devices, as shown in Figure 2. Compared with the half-bridge inverter circuit, the ratio of the number of power switch devices is 2:1, the structure becomes more complicated, and it is not as good as the half-bridge circuit in terms of stability and economic applicability. However, the full-bridge inverter circuit no longer requires symmetrical positive and negative output power supplies, but only a single-channel regulated power supply. The current of the two-phase winding no longer causes a large interference to the power supply. At the same time, the DC voltage utilization rate of the full-bridge circuit is also higher than that of the half-bridge circuit.

In view of the large number of switching devices, in practical applications, the two middle bridge arms in Figure 2 are combined into one to form the common bridge arm of the two sets of windings, thus obtaining the two-phase three-bridge arm full-bridge inverter circuit shown in Figure 3 [5]. The common bridge arm is combined with the left and right bridge arms to form a two-phase full-bridge inverter.

Figure 2 Dual full-bridge inverter circuit

Figure 3 Upper three-bridge arm inverter circuit

The two-phase three-bridge full-bridge inverter circuit inherits the advantages of the full-bridge inverter circuit and effectively reduces the number of switching devices. Under the same DC voltage Ud, its output voltage value can reach more than 70% of the full-bridge circuit. In terms of the inverter bridge structure, the two-phase three-bridge circuit is exactly the same as the three-phase half-bridge inverter circuit. Therefore, it is easy to transplant from the existing six-unit power module for use, and its output can also be flexibly converted between three phases and two phases. At present, the development of six-unit power modules for three-phase inverter circuits has been quite mature, especially in low-power applications. 3 Control technology

When a single-phase motor adopts a half-bridge inverter circuit, due to the similar main circuit structure, speed control technologies such as SPWM and SVPWM can be easily transplanted to the single-phase motor speed control. When discussing the control technology below, for the convenience of analysis, it is assumed that the two-phase windings of the motor are symmetrical, that is, the two-phase windings are the same and perpendicular to each other in space. At the same time, it is assumed that the positive and negative power supplies are symmetrical, the amplitude is constant, and the neutral point N does not float due to the injection of current I.

3.1 Half-bridge SPWM control

When single-phase motors use SPWM control technology, the phase difference of the current in the two-phase winding must be 90°, so the phases of the two modulation signals must also be set to 90°. The advantages of SPWM control are low harmonic content, simple filter design, and easy voltage and frequency modulation functions. However, the disadvantages of SPWM are also obvious, that is, the DC voltage utilization rate is low, it is suitable for analog circuits, and it is not easy to implement digital solutions.

3.2 Half-bridge SVPWM control[6]

According to the knowledge of electrical machinery, the voltage space vector  

Same air gap magnetic field 

The following relationship exists:

 (4)

The rotation of the motor air gap magnetic field is controlled by controlling the voltage space vector, so SVPWM control is also called flux trajectory control.
The switching logic of switching devices S1 and S2, S3 and S4 are complementary, so the four switching devices can only generate four voltage vectors. According to the drawing method of reference [6], the voltage vector diagram shown in Figure 4 can be obtained.

Figure 4 Voltage vector definition

From the vector diagram, in the two-phase half-bridge inverter circuit, no zero voltage vector will be generated. In order to synthesize a voltage vector with an amplitude of Uα and a phase angle of α, when decomposing the vector, its X-axis component must be completed by E1 and E2, while the Y-axis component must be completed by E3 and E4. In a switching cycle T, the action time of E1 is t1, and the action time of E2 is T-t1. The action time of E3 is t2, and the action time of E4 is T-t2. According to the vector decomposition, we can get equations (5) and (6) (the size of vectors E1, E2, E3, and E4 are all Ud/2)

t1=

T(5)

t2=

T(6)

Since t1(t2)(<=)T

, so Ud/2. That is, when the half-bridge inverter circuit adopts SVPWM control, the maximum value of the output phase voltage is Ud/2.

3.3 Two-phase three-leg full-bridge inverter SPWM control [7]

When using SPWM control, the common bridge arm composed of N1 and N2 must be connected to the two-phase windings of the motor at the same time, so during modulation, the modulation wave of the common bridge arm is different from the modulation wave of the A and B bridge arms.

The specific modulation method of the entire inverter circuit is: under the condition of the same carrier, the modulation waves of phases A and B are sinusoidal waves, and phase A leads phase B by 90° (the motor rotates forward, and vice versa, phase B leads phase A by 90°, then the motor reverses); the common bridge arm is modulated by a constant duty cycle method, and the duty cycles of the upper and lower bridge arms are both 50%, as shown in Figure 5.

In this way, sinusoidal voltages with equal amplitude and 90° phase difference are obtained on windings A and B. The voltage amplitude is proportional to the modulation index m. When m=1, the output voltage peak reaches the maximum, which is Ud/2. Based on the V/f curve of the motor and the relationship between the output voltage and m, the variable voltage and variable frequency speed control of the two-phase motor can be realized.

3.4 Two-phase three-leg full-bridge inverter SVPWM control [5]

In the inverter circuit, each power-on mode of the power device can generate a space voltage vector in the motor. For the two-phase three-bridge-arm inverter circuit, according to the principle of complementary conduction of the upper and lower switches of the same bridge arm, the three bridge arms produce a total of 8 switch combination modes, and 8 space voltage vectors can be obtained on the motor winding, which are represented by V (A, N, B). When A=1, it means A1 is turned on and A2 is turned off; when A=0, it means A1 is turned off and A2 is turned on, and so on. The 8 vectors are listed in Table 1.

Figure 6 Definition of two-phase three-bridge voltage space vector 

4 Conclusion

1) The structure of the single-phase motor inverter main circuit is mainly divided into full-bridge and half-bridge. The half-bridge circuit has a simple structure and low cost, and requires the front-stage power supply to provide stable positive and negative symmetrical output.

2) Full-bridge inverter circuit: Since the two-phase three-bridge arm requires relatively few switching devices, it is easy to use a six-unit power module in a three-phase circuit, which has obvious advantages over the full-bridge inverter circuit composed of 8 switching devices.

3) When the half-bridge circuit adopts SPWM and SVPWM control, the maximum output voltage is the same; in the full-bridge circuit, the DC voltage utilization rate of SVPWM is 41% higher than that of SPWM. SVPWM control is easy to realize digitally, and the vector action sequence is reasonably arranged, which can effectively reduce switching losses.

4) From the above control schemes, the common problem is the low utilization rate of DC voltage. How to improve the voltage utilization rate is one of the problems that single-phase motor variable frequency speed regulation must overcome. There are low-frequency harmonics such as the 3rd and 5th order in the rotating magnetic field of the single-phase motor, so when selecting a control scheme, attention should be paid to the weakening of low-frequency harmonics. The two sets of windings of the single-phase motor are distributed vertically, and the mutual inductance between them is close to zero. When adopting more complex control strategies, such as direct torque control, it will simplify the complexity; at the same time, the sum of the currents of the two sets of windings can be used to determine the position of the magnetic field, which provides an effective way to detect the air gap magnetic field of the motor.