周 娟，徐高祥，釗翔坤，原亞雷，祝銥玉

LCL型有源電力濾波器的強魯棒性控制器優(yōu)化設(shè)計

周 娟，徐高祥，釗翔坤，原亞雷，祝銥玉

(中國礦業(yè)大學(xué)電氣與動力工程學(xué)院，江蘇 徐州 221008)

LCL型有源電力濾波器能有效補償電網(wǎng)諧波，但LCL型濾波器存在諧振問題，電容電流比例反饋有源阻尼是抑制LCL諧振的主要方式。然而，在數(shù)字控制下，諧振頻率會隨電網(wǎng)阻抗變化，導(dǎo)致反饋系數(shù)選取困難。針對該問題，研究了適應(yīng)電網(wǎng)阻抗寬范圍變化的反饋系數(shù)選取方法，推導(dǎo)不同反饋系數(shù)和諧振頻率下的系統(tǒng)穩(wěn)定條件，優(yōu)化設(shè)計適應(yīng)電網(wǎng)阻抗變化的反饋系數(shù)。此外，隨著電網(wǎng)阻抗增加，LCL諧振頻率減小，系統(tǒng)帶寬變窄，有源電力濾波器采用傳統(tǒng)準(zhǔn)PR控制補償高次諧波時，系統(tǒng)相頻曲線在控制器諧振點容易穿越-180o線，導(dǎo)致系統(tǒng)不穩(wěn)定。提出加入相位補償環(huán)節(jié)以提升控制器增益處相角，并給出詳細(xì)設(shè)計方法。理論分析表明，所提強魯棒性控制器優(yōu)化設(shè)計方法，可使有源電力濾波器在保證良好諧波補償能力的同時具有更寬的穩(wěn)定運行范圍。仿真和實驗結(jié)果驗證了理論分析的正確性。

有源電力濾波器；LCL濾波器；弱電網(wǎng)；控制延時；相位補償

0 引言

隨著電力電子技術(shù)的發(fā)展，配電系統(tǒng)中諸如整流器、電弧爐等非線性負(fù)載不斷增加，諧波污染日益嚴(yán)重[1-3]。諧波會導(dǎo)致變壓器過熱、保護設(shè)備故障、諧波諧振和通信網(wǎng)絡(luò)干擾等問題[4]。

并聯(lián)型有源電力濾波器(Shunt Active Power Filter, SAPF)能有效解決電網(wǎng)諧波污染，改善電能質(zhì)量，并且在發(fā)生故障時很容易與電網(wǎng)斷開，目前被廣泛應(yīng)用于電力系統(tǒng)中[2,5-6]。SAPF通常采用L型或LCL型濾波器濾除輸出端開關(guān)次諧波，其中LCL型濾波器具有更優(yōu)的高頻衰減能力，在SAPF中被廣泛使用[7-8]，如圖1所示。然而，LCL型濾波器存在固有諧振問題，容易造成系統(tǒng)不穩(wěn)定[9-11]。目前針對諧振問題使用較多的阻尼方法是基于電容電流反饋的有源阻尼法，將反饋環(huán)節(jié)配置成比例環(huán)節(jié)[12-13]，具有阻尼效果好、保持LCL濾波性能和實現(xiàn)簡單等優(yōu)點。

圖1 SAPF在電網(wǎng)中的應(yīng)用場景

1 LCL型APF建模和穩(wěn)定性分析

圖2 LCL型SAPF及其控制結(jié)構(gòu)

圖3 采用電容電流反饋有源阻尼的LCL型SAPF控制框圖

圖4 LCL型SAPF簡化控制框圖

由圖4與式(4)可得系統(tǒng)的開環(huán)傳遞函數(shù)如式(5)所示。

則諧振頻率為

其中

根據(jù)式(11)可列出勞斯表：

圖5 正負(fù)穿越定義

由圖5可以看出，正穿越是相頻曲線由下往上穿越-180o線，同時對應(yīng)的幅頻曲線位于0 dB上方；負(fù)穿越是相頻曲線由上往下穿越-180o線，同時對應(yīng)的幅頻曲線位于0 dB上方；兩個條件缺一不可。

表1 系統(tǒng)穩(wěn)定時的幅值裕度要求

圖6 不同諧振頻率、時的頻率響應(yīng)

圖7 不同下系統(tǒng)的穩(wěn)定條件

2 反饋系數(shù)KC優(yōu)化設(shè)計

圖8 不同下、隨著的變化情況

3 具有相位補償功能的電流控制器設(shè)計

當(dāng)采用PR控制器對SAPF電流環(huán)進行控制時，控制器可表示為

圖9 準(zhǔn)PR控制下補償25次諧波時系統(tǒng)Bode圖

表2 SAPF參數(shù)取值

求解式(33)可得到兩個解的差值為

表3 控制器參數(shù)

圖10 控制器結(jié)合控制下的Bode圖

4 仿真和實驗分析

表4 取值

Table 4 The values

表4 取值

電網(wǎng)阻抗取值/mH對應(yīng)諧振頻率 03.14 0.62.5 4.41.91 7.41.82

圖11 時，A相電網(wǎng)電壓和電流仿真波形

仿真結(jié)果表明，采用本文所提控制方案，不論是弱電網(wǎng)級別的電網(wǎng)阻抗變化，還是普通的電網(wǎng)阻抗變化，系統(tǒng)始終保持穩(wěn)定運行，對電網(wǎng)阻抗變化表現(xiàn)出很強的魯棒性。

圖13 在弱電網(wǎng)下，采用本文所提控制方案時A相電網(wǎng)電壓和電流仿真波形

圖14 時，A相電網(wǎng)電壓和電流實驗波形

圖15 時，A相電網(wǎng)電壓和電流實驗波形

圖16 在弱電網(wǎng)下，采用本文所提控制方案時A相電網(wǎng)電壓和電流實驗波形

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Optimization design of strong robust controller for an LCL-type active power filter

ZHOU Juan, XU Gaoxiang, ZHAO Xiangkun, YUAN Yalei, ZHU Yiyu

(School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou 221008, China)

The LCL-active power filter can effectively compensate for the harmonic of a power grid, but an LCL filter has a resonance problem. Capacitive current proportional feedback active damping is the main way to suppress LCL resonance. However, with digital control, the resonant point will change with the grid impedance, and this makes it difficult to select the feedback coefficient. To solve this problem, this paper researches a selection method of feedback coefficient to adapt to a wide range of grid impedance variation, derives the stability conditions of the system under different feedback coefficients and harmonic frequencies, and optimizes the design of the feedback coefficient to meet the requirements. In addition, with the increase of grid impedance, the LCL resonant frequency becomes smaller and the system bandwidth becomes narrower. When the traditional quasi PR control is used to compensate for the high order harmonics, it is easy for the phase frequency curve of the system to cross the -180oline at the resonance point of the controller. This leads to instability of the system. Phase compensation is proposed to improve the phase angle at the gain of the controller, and the detailed design method is given. Theoretical analysis shows that the proposed robust controller optimization design method can ensure good harmonic compensation ability and a wider stable operation range of active power filter. Simulation and experimental results verify the correctness of the theoretical analysis.

active power filter; LCL filter; weak grid; control delay; phase compensation

10.19783/j.cnki.pspc.211019

國家自然科學(xué)基金項目資助(51407184)；江蘇省研究生科研與實踐創(chuàng)新計劃項目資助(KYCX2_2227)

This work is supported by the National Natural Science Foundation of China (No. 51407184).

2021-08-03；

2021-12-10

周 娟(1976—)，女，通信作者，博士，教授，博士生導(dǎo)師，研究方向為電能質(zhì)量控制技術(shù)，電池管理系統(tǒng)等；E-mail: zhjcumt@126.com

徐高祥(1996—)，男，碩士研究生，研究方向為多電平變換器。E-mail: xu_gaoxiang@163.com

(編輯 魏小麗)