Predictive Current Control of a Three-Phase High-Frequency PWM Rectifier

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Predictive Current Control of a Three-Phase High-Frequency PWM Rectifier [Copy link]

The mathematical model of three-phase high-frequency PWM rectifier is studied, the basic principle of predictive current control method is analyzed, and the method of voltage control loop calculation is given. Finally, the experimental results are given.

Keywords: three-phase high-frequency PWM rectifier; predictive current control; principle and calculation

　

0 Introduction

Traditional phase-controlled rectifiers and diode rectifiers have disadvantages such as low power factor, high current harmonic content, and serious pollution to the power grid. The power factor of high-frequency PWM rectifiers can reach 1, the input current is sinusoidal, and energy can be fed back to the power grid, overcoming the shortcomings of traditional rectifiers. High-frequency PWM rectifiers generally adopt a voltage and current dual-loop design in the control algorithm to control the stability of the DC output voltage and make the input current sinusoidal. In the current control algorithm, the method of converting the model to a synchronously rotating dq coordinate system is often used to achieve the decoupling control of the d and q axis currents. This algorithm often requires a phase-locked loop and other links to achieve the positioning of the d and q axes, which is relatively complex. This paper studies a predictive current control method that can achieve a fast response to the current and is simple to implement.

1 Three-phase high-frequency PWM rectifier model and basic principles of predictive current control

The main circuit of the three-phase voltage type high-frequency PWM rectifier is shown in Figure 1. From Figure 1, we can get

U _Si - U _Ci = L , i = a , b , c (1)

Where: U _Sa , U _Sb , U _Sc are the three-phase power supply voltages respectively;

i _Sa , i _Sb , i _Sc are the corresponding three-phase currents;

U _Ca , U _Cb , U _Cc are the voltages at points A, B, and C respectively, which are three control quantities and are determined by the duty cycle of each bridge arm and the DC output voltage;

L is the inductance of the series inductor of each phase.

Using the forward difference quotient instead of the differential to discretize equation (1), we get

U _Ci ( k ) = U _Si ( k ) - L , i = a , b , c (2)

Where: Ts _is the sampling period.

In order to reduce the influence of time delay, the known state can be used to predict the control voltage U _Si ^* required to reach the current i _Si ^* at the next sampling moment . Therefore, from formula (2), we can get

U _Ci ^＊ ( k ) = U _Si ( _k ) - L ,

i = a , b , c (3)

_The meaning of formula (3) is to predict the voltage U _{Ci *} ( k ) required to make the current reach i Si * ( k + 1) in the k + 1th step based on the currently known state variables U Si ( k ) and i Si ( k ) and the parameter values TS and L as well as the next step command current value i _Si ^* ( k + 1 ) . _If the voltages required by _formula ( 3 ⁾ can be obtained at points ^A , B , and C in Figure 1 at this moment, then the required current i _Si ( k + 1) can be obtained in the k + 1th step.

Figure 1 Three-phase high-frequency rectifier main circuit

The predicted current value in formula (3) is obtained by formula (4):

i _Si ^＊ = U _Si , i = a , b , c (4)

Where: I ^* is the command value of the DC output current, which is a constant DC value in steady state.

In steady state, U _Sa ² + U _Sb ² + U _Sc ² and U _o are also constant DC quantities, so i _Si ^* is proportional to U _Si . Since U _Si is sinusoidal, the predicted current value (i.e., current command) i _Si ^* has the same shape as the input voltage, both are sinusoidal, and the phase is also the same, achieving a control with a power factor of 1. From formula (4), we get

i _Sa ^＊U _Sa＋i _Sb ^＊U _Sb＋i _Sc ^＊U _Sc = U _o I ^＊ (5)

This shows that formula (4) ensures the balance between input and output power, that is, the current prediction value given by formula (4) can control both the waveform of the input current and its magnitude (and thus also the magnitude of the output power).

2 Control loop design

After adopting the predictive current control method, the response of the current loop is very fast and can be replaced by a first-order inertia link. Although the three-phase currents are sinusoidal, from the perspective of power balance, they are equivalent to the changes in DC voltage and current. Therefore, the control loop of the entire system can be equivalent to the structure of Figure 2.

Figure 2 Three-phase high-frequency rectifier voltage control loop diagram

In Figure 2, C is the capacitance value of the electrolytic capacitor. The DC output current command I ^* is obtained by amplifying the difference between the output DC voltage command U _o ^* and the feedback value U _{o , which is} e = U _o ^* - U _o .

I ^* = Kp (6 ₎

The open-loop transfer function of the entire system is:

G = K _p = (7)

It can be seen from equation (4) that in order to ensure the sinusoidal shape of the input current, the fluctuation of the command current I ^* should be as gentle as possible. In other words, the bandwidth of the output voltage controller determined by equation (6) should be as narrow as possible. Since the grid frequency is 50Hz, the bandwidth of the voltage loop should be much lower than 50Hz. However, in order to prevent the dynamic response time from being too slow, the bandwidth is required to be as wide as possible. Combining the above two factors, the turning frequency in the actual system is taken as _{ω =} 1 / τ =2π5s - ¹ . Since the sampling period Ts is very small and the bandwidth is very low, the high-frequency filtering link has little effect. Therefore, equation (7) can be simplified to G =( Kp / τC )(1+ sτ )/ s2 , and its Bode diagram is shown in Figure 3. In Figure 3, _τ = 30ms, _the voltage loop magnification Kp = C /(2τ ) , and the phase margin is about 45°. The PI regulator parameters designed in this way can make the system absolutely stable.

Figure 3 Bode plot of the voltage loop open-loop transfer function

3 Vector Control Algorithm

By comparing the voltage values of each phase calculated by equation (3) with the triangular wave, the switching time of each bridge arm can be obtained. This is the general SPWM method, as shown in Figure 4(a).

Vector control can also be used, which is essentially the control of the zero state. For example, the three-phase line voltage in a PWM cycle can be set to zero (i.e., zero vector state) and all upper bridge arms can be fixed to be fully turned on, as shown in Figure 4(b). At this time, the three-phase modulation voltage becomes

(a) SPWM method (b) Vector control method

Figure 4 Schematic diagram of comparison between SPWM method and vector control

(12)

And

=(2/3)( U _Ca ′＋e ^j2π/3 UCb ′＋e ^－j2π/3 U _Cc ′)

=(2/3)〔( U _Ca＋x )＋e ^j2π/3 ( U _Cb＋x )＋e ^－j2π/3 ( U _Cc＋x )】

=(2/3)( U _Ca＋e ^j2π/3 U _Cb＋e ^－j2π/3 U _Cc )

It can be seen that after the three-phase modulated voltage is simultaneously offset by a certain value, the synthesized space voltage vector remains unchanged, and thus the control effect remains unchanged. However, this treatment brings many benefits, such as reduced switching times, increased bus voltage utilization, and improved conversion efficiency.

4 Experimental Results

In order to verify the correctness of the proposed minimum loss control method for three-phase high-frequency rectifier, a 3kW prototype was trial-produced and experimental research was carried out. The filter inductor is 6mH, the filter capacitor is 500μF, and the switching frequency is 10kHz. The control circuit is a fully digital controller with DSP (TMS320LF2407A) as the core, as shown in Figure 5. The current loop, voltage loop and space vector PWM algorithm are all implemented by software. Figure 6 (a) shows the input voltage, current and DC output voltage waveforms when the AC input voltage is three-phase 250V and the output DC voltage is 500V. Figure 6 (b) shows the corresponding waveforms when the AC input voltage is three-phase 380V and the output DC voltage is 600V. It can be seen that the input current is a sine wave and is consistent with the input voltage phase. When the input voltage and output voltage are different, the current control is better.

Figure 5 Experimental setup

(a) Input is three-phase 250V, output is 500V

(b) Input is three-phase 380V, output is 600V

Figure 6 Input AC voltage, current and output DC voltage waveforms

5 Conclusion

This paper studies a current control method for a three-phase high-frequency PWM rectifier, which can achieve fast and accurate control of the grid current. The loop transfer function of the system is analyzed and the design method is given. It is pointed out that the use of vector control can reduce the number of switching times and switching losses and improve the operating efficiency of the system. Finally, the experimental results are given.

　

About the Author

Wan Shanming, male, graduated with a Ph.D. from Huazhong University of Science and Technology in 1998, and has been engaged in academic research and product development in the field of power electronics and motor control for a long time.