Chinese Library Classification Number: TM48 Document Identification Code: A
The LCL parameter's researching in arctive power filter of three-phase three-wire system simulation
JI Xiao-chun, LIU Jian-chun, ZHAO Gao, LI Wei-jiang
( Acrel Electrical co. LTD, Shanghai 201801, China )
Abstract : Three-phase three-wire active power filter (APF) can compensate power system harmonics,when APF compensating the harmonic,the APF's inverter also has switching frequency of the high order harmonics,by analyzing LCL filter mathematical model can build a three-phase three-wire system active power filter system simulation model.We can compare the active power filter without LCL and with LCL,what effect can they have,the simulation results show that three-phase three-wire APF with LCL filter can filter out the converter of APF's high-frequency switching harmonics.
Keywords : three-phase three-wire system;APF;simulation-model; high-frequency;
harmonic
1 Introduction
Three-phase three-wire active power filters (APFs) can compensate for harmonics in modern power systems. However, the converters of active power filters themselves use PWM modulation technology, which generates high-frequency switching harmonics. These high-order harmonics can cause significant electromagnetic interference to some equipment, affecting its normal operation [1-3] . When active power filters compensate for harmonic currents, they need to track the command current in a timely manner. When the inductance of the output reactor is very small, although the current tracking effect is guaranteed, the switching ripple of the current is very large. The inductance of the output reactor of the APF should not be too large either, otherwise the bridge arm output current will lag behind the command current, resulting in a poor compensation effect. It can be seen that while selecting a small inductance reactor to ensure the current tracking effect, an LCL filter stage needs to be added at the grid connection point to filter out the high-frequency switching ripple [4] .
When an active power filter is connected to the grid, the selection of parameters after adding an LCL filter stage will affect the filtering effect and may even cause system resonance. Therefore, it is necessary to first analyze and understand the mathematical model of the active power filter with LCL, find the resonance point and appropriate parameters, so as to ensure the best filtering effect.
2. Mathematical Model of Three-Phase Three-Wire APF-LCL
The structure diagram of the three-phase three-wire APF using the LCL grid connection method is shown in Figure 1 [5-6] .
Figure 1. APF LCL parallel connection method
In Figure 1, represents the phase voltage on the grid side, represents the AC side voltage of the converter bridge, represents the output reactance inductance of the APF, represents the grid-side reactance inductance of the LCL, C represents the capacitance value of the LCL, and R represents the resistance value. The three-phase structural model in Figure 1 is equivalent to a single-phase structural model as shown in Figure 2. The damping resistor R is used to suppress resonance. Based on Figure 2, the mathematical model of the LCL is the equation set (1):
Figure 2. Equivalent single-phase LCL model
(1)
The structural block diagram of equation system (1) after Laplace transformation is shown in Figure 3.
Figure 3. Block diagram of the equivalent single-phase LCL model
The transfer function can be obtained.
The resonant frequency can be determined as:
2. Parameter Analysis of the APF-LCL Mathematical Model
Based on the selection method of LCL parameters in references [7-8], and considering that the LCL capacitance value has a significant impact on the uncontrolled rectification pre-charging process of APF (for example, the current limiting resistor is 51Ω when APF starts up, and the DC side voltage stabilizes at 473V after rectification when the capacitor is 40uF, and the DC side capacitor charging process during rectification is shown in Figure 4), the LCL parameters in the APF simulation model are respectively taken as shown in Table 1, and the impact of changing electrical parameters on system performance is analyzed.
Figure 4 shows the voltage curve across capacitor C when C is 40uF in the LCL.
Table 1 LCL parameter values
L 1 (mH) | L 2 (mH) | C(uF) | R (Ω) |
0.35 | 0.08 | 40 | 1 |
0.35 | 0.08 | 50 | 1 |
0.35 | 0.08 | 60 | 1 |
0.35 | 0.1 | 50 | 1 |
0.35 | 0.08 | 50 | 0 |
0.35 | 0.08 | 50 | 2 |
Group comparison analysis of the impact of each parameter:
(1) L1 = 0.35mH, L2 = 0.08mH, R = 1Ω. Compare the Bode plots of the transfer function H(S) when the value of C is changed to 40uF, 50uF and 60uF (as shown in Figure 5).
Figure 5. Bode plots for different capacitance parameters
As shown in Figure 5, the amplitude-frequency characteristic C increases, the resonant frequency f <sub>res</sub> decreases, and the frequency shifts to a lower frequency range. There is little attenuation in the low-frequency range, but in the high-frequency range, the high-frequency portion (above the resonant frequency) is attenuated by 25 dB per decade, resulting in a slight increase in attenuation. The phase-frequency characteristic also shows that the phase angle shift starting frequency shifts to a lower frequency range.
(2) When L1 = 0.35mH, C = 50uF, R = 1Ω, compare the Bode plot of the transfer function H(s) when the value of L2 is changed to 0.08mH and 0.1mH (as shown in Figure 6).
Figure 6. Bode plots for different reactance parameters
As shown in Figure 6, the amplitude-frequency response indicates that as L2 increases, the resonant frequency f <sub>res </sub> decreases, shifting towards the lower frequency domain. In the low-frequency domain below the resonant frequency, the gain is 0 dB, indicating no attenuation. Attenuation begins in the high-frequency domain above the resonant frequency, with a significant attenuation effect at high frequencies. The degree of attenuation can be observed by examining the resonant point to determine the extent to which i2 deviates from i1 . The phase-frequency response also shows that the initial frequency of the phase angle shift also shifts towards the lower frequency domain.
(3) L1 = 0.35mH, C = 50uF, L2 = 0.08mH, compare the Bode plot of the transfer function H(S) when the value of R is changed to 0Ω, 1Ω, and 2Ω (as shown in Figure 7).
Figure 7. Bode plots for different damping resistance parameters
As shown in Figure 7, the amplitude-frequency response indicates that increasing the damping R strengthens the ability to suppress resonance. However, while a large damping R value significantly suppresses resonance peaks in the high-frequency domain, it also degrades the filtering performance in that domain. Conversely, a small damping R value results in insufficient resonance suppression. The phase-frequency response shows that increasing the damping R value leads to a slower phase angle shift at higher frequencies.
3. APF-LCL Simulation Results
A three-phase three-wire APF simulation model was established. The harmonic load current is shown in Figure 8. It is a typical nonlinear resistive load harmonic with a THD content of 16.6%, mainly including the 5th, 7th, 11th and 13th harmonics.
Figure 8 Typical resistive harmonic load
Without the LCL grid-connected filtering function, the compensated THD content is 1.59%, as shown in Figure 9.
Figure 9. Grid-side current after APF compensation without LCL
It can be seen that the 200th harmonic content at 10kHz is relatively high. The filtering effect after using LCL is shown in Figure 10. The THD content after compensation is 0.95%, which attenuates the 200th (10kHz) and 400th (20kHz) high-frequency switching harmonics.
Figure 10. Grid-side current after APF compensation with LCL
4. Conclusion
This paper analyzes the mathematical model and resonant frequency of adding an LCL grid-connected filter to a three-phase three-wire APF system. By analyzing the Bode plot of the transfer function of the APF-LCL mathematical model, it derives the impact of adjusting various electrical parameters on the APF filtering effect. The influence of having or not having an LCL component on the filtering effect is compared in the APF-LCL simulation model. The conclusion is that adding an LCL component, while avoiding resonance, has a good effect on filtering out harmonics of higher switching frequencies in the APF system.
Source: Building Electrical Engineering, 2014, Issue 2 - Supplement
References
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About the author:
Zhao Gao (1987-), from Ningguo, Anhui, holds a master's degree and his research interests are power electronics and harmonic control.
