Modeling and simulation of three-level PWM rectifier based on sliding mode control

Where:

Assuming vd and vq are the d _- axis and q-axis components of the grid-side voltage in the rotating dq coordinate system, we have _:

Where is the differential operator.

Ignoring the error between the upper and lower capacitors of the busbar, assuming that C _d1 = C _d2 = C _d , we have:

According to the above model, the equivalent circuit of the three-level PWM rectifier in the dq coordinate system is shown in Figure 2. For the DC side, the three-level rectifier bridge is equivalent to two current sources, and for the AC side, the three-level rectifier bridge is equivalent to two voltage sources.

Figure 2 Equivalent circuit of three-level rectifier in dq coordinate system

3 Design of voltage outer loop sliding mode controller

The three-level PWM rectifier has two external control variables: V _dc and i _q , where V _dc is controlled by s _d to maintain the stability of the DC bus voltage; i _q is controlled by s _q to control the system reactive current (unity power factor, leading, lagging). Taking V _dc and i _q as controllable outputs, the state space standard form is obtained as

Substituting the error between the reference value and the actual variable into equation (5) we get

In the formula, e _ig = i _qref –i _q ; e _Vdc = V _dcref –V _dc ; e _Φ = Φ _ref –Φ ; Φ is the disturbance;

According to equation (6) and the known two control degrees of freedom, the following sliding surface can be selected to ensure the robustness of the closed-loop system.

Where is a parameter related to the first-order response of DC voltage.

Formula (3) and (4) will become

In the dq rotating coordinate system, , e _q = 0, under the ideal sliding mode state, s _q is calculated by equation (5) , and the result is simplified to:

Similarly, on the ideal sliding surface, the output voltage accurately tracks the reference value, V _dc = V _dcref , and according to the power balance, we can get:

Substituting equation (10) and equation (11) into equation (9), we get:

Then sd and sq have _{little to do with the choice of sliding surface, which} simplifies the design of sliding mode controller. The sliding surface is:

The voltage outer loop controller control equation is obtained from equations (12) and (14):

[page] Therefore, the following control strategy is adopted to realize the sliding mode variable structure control of the three-level PWM rectifier: set i _qref and use PI controller to control the current loop; the voltage outer loop control adopts the sliding mode variable structure control algorithm, with the actual output voltage V _dc and the given voltage V _{dcref as the controller input, and the controller output is used as the reference current} i _dref of the current loop PI regulator , realizing the effective combination of sliding mode variable structure control and voltage oriented vector control. Its control structure block diagram is shown in Figure 3.

Figure 3 Schematic diagram of sliding mode control of three-level rectifier

4 Simulation Results

According to the mathematical model and control strategy described above, the effectiveness of the control method proposed in this paper is simulated. The simulation parameters are as follows: input inductance 20mH, DC bus upper and lower capacitors 4000/2μF, input phase voltage 220V, DC bus voltage 600V, grid frequency 50Hz, switching frequency 2kHz, output power 5kW, sudden loading at 0.135s, and at 0.25s, the system starts to work in energy feedback grid mode. Figure 4 shows the bus voltage waveform of the three-level PWM rectifier. Among them, Figure 4 (a) shows the simulated waveforms of the phase voltage ( e _a ) and current ( ia ) on the grid side of phase _a . It can be seen that the voltage and current are in phase, and the power factor is above 0.99 after calculation; Figure 4 (b) shows the grid-side current waveform and its spectrum under full load, and the harmonic distortion rate is 2.00%; Figure 4 (c) shows the AC side line voltage waveform; Figures 4 (d) and (e) respectively show the DC bus voltage ( V _dc ) waveforms using conventional PI control and sliding mode control. It can be seen that under sudden load conditions, the DC bus voltage drops under both control strategies, but the DC bus voltage changes less under sliding mode control and quickly reaches a steady state.

Figure 4. Simulation results of sliding mode control of three-level rectifier: (a) grid-side phase voltage and current; (b) grid-side current and its spectrum; (c) grid-side line voltage; (d) DC bus voltage waveform under conventional PI control conditions; (e) DC bus voltage waveform under sliding mode control conditions

The simulation results show that the sliding mode control strategy can achieve unity power factor control of the three-level PWM rectifier, and the system has good steady-state performance. From the DC bus voltage waveform, it can be seen that the dynamic response of the DC link is relatively fast, and the sudden change of load loading causes the bus voltage to drop by nearly 18V.

[page]5 Conclusion

This paper establishes a mathematical model of a three-level PWM rectifier and designs a circuit control strategy based on the sliding mode control principle. From the simulation results, it can be seen that the control strategy can achieve a stable output voltage, a sinusoidal input current, a unity power factor, and has good dynamic and steady-state response.

References

[1] Zhang Hao, Xie Yunxiang, et al. Three-phase high power factor rectifier based on sliding mode control. Electrical Applications, Vol. 27, No. 10, 2008.

[2] Zhang Yingchao. Research on control technology of neutral-point clamped three-level dual PWM inverter. Doctoral dissertation in engineering, Tsinghua University, 2008, 47-49.

[3] Zhang Haitao. Research on control system of three-level inverter based on IGCT. Doctoral dissertation in engineering, Tsinghua University, 2006, 47-49.

[4] Jin Hongyuan. Research on three-level PWM rectifier. PhD dissertation of Huazhong University of Science and Technology, 2006, 51.

[5] Hu Qing, Yu Haiyan, Xia Guiwen. Application of sliding mode variable structure control in three-phase rectifier. Journal of Shenyang University of Technology, 2002, 24(3): 139-142.