The Research of Active Disturbance Rejection Control on Shunt Hybrid Active Power Filter

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1 Available online a Procedia Engineering 29 (2) Inernaional Workshop on Informaion and Elecronics Engineering (IWIEE) The Research of Acive Disrbance Rejecion Conrol on Shn Hybrid Acive Power Filer Yojie Ma a*, Jian Zhaob and Xesong Zho Tianjin Key Laboraory for Conrol Theory & Applicaions in Complicaed Sysems, Tianjin Universiy of Technology, Nankai Disric, Tianjin 3384, China asjeam@163.com, bzhaojian7@126.com Absrac This paper horoghly analysis he principles and srcres of acive disrbance rejecion conrol (ADRC), and applied i o shn hybrid acive power filer (SHAPF). Based on he principles of ADRC, his paper regards he ncerainies boh wihin and exernal of he sysem model as nknown inerference of sysem, hen esimaing hrogh exended sae observer (ESO), and compensaing by nonlinear feedback conrol (NLSEF), which makes he conrol law of he sysem is only relaed o specified inp / op, and redces deecions in conrol process, i.e. simplifies complex conrol process. Excellen resls can be achieved in sysem simlaion by selecing Parameer, which proves he possibiliy of conrol sraegy. 1 Pblished by Elsevier Ld. Selecion and/or peer-review nder responsibiliy of Harbin Universiy of Science and Technology. Open access nder CC BY-NC-ND license. Keyword: Shn hybrid acive power filer; acive disrbance rejecion conrol (ADRC); exended sae observer 1. Inrodcion Wih he rapid developmen of power elecronics echnology, all kinds of power elecronic devices have been widely sed, and also cased serios harmonic pollion o he power sysem. APF has become a very viable developing orienaion of power elecronic applicaions. Compared wih radiional passive power filer (PPF), i has he following feares: qick response and real ime dynamic seqenial compensaion. In power circi, SHAPF serves as conrolled crren, mainly sed o compensae he load * Corresponding ahor. Tel.: address: sjeam@163.com Pblished by Elsevier Ld. Open access nder CC BY-NC-ND license. doi:1.116/j.proeng

2 Yojie Ma e al. / Procedia Engineering 29 (2) reacive power and acive power, absorb crren harmonics and negaive seqence and zero seqence componens of indsrial freqency crren e al..[1] I regards he model perrbaion as inernal disrbance, and compensae ogeher wih he exernal sysem disrbance as a sysem disrbance [2]. Wih frher applicaions of modern conrol echnology in power elecronics [6], his aricle applied ADRC conrol echnology o he new objec -APF in power elecronics echnology, and condced a simlaion sdy. 2. ADRC ADRC consiss of hree pars: nonlinear racking differeniaor (TD) exended sae observer (ESO) and nonlinear feedback conrol (NLSEF) TD TD is a device which can: inp signal v (), i will op wo signals, z 1 and z 2, z 1 racks v (), while z = z, hs regards z as a differenial approximaion [7]. The role is arranging he ransiion process based on he reference inp v() and he consrains of conrolled objec, and hen ge smooh inp signal, and propose he dynamic link of his ransiion process derivaive. Discree form of TD: z11( + h) = z11() + hz22() (1) z22( + h) = z22() + hfs( z11() v(), z22(), r, h) Where ( ) v is he inp signal, h is he inegraion sep, fs( z, z, r, h) 2.2. Exended sae observer (ESO) is a nonlinear fncion. ESO is core par of ADRC. The sysem conroller reqires only inp and op as a sorce of informaion, i can no only ge all esimaes of saes, b also esimae he ncerainy model and he amon of real-ime role in oside inerference by ESO, so ha he ncerainy of he objec cold be compensaed in he feedback, in order o achieve he prpose of reconsrcing he objec. The form ESO is as following: z& = z 22 β g 1( e) : (2) z& 2 n = z 2 n + 1 β 2 n g n ( e) + b z& 2 n + 1 = β 2 n + 1g n + 1( e) e = z x( ) ( n1) So z2n+ 1is Real-ime esimaion of oal disrbance f ( xx, &,..., x, ) + w ( ) + ( bb ), b is esimae vale of b. ESO has good racking capabiliies for op saes of he observed sysem; is dynamic qaliy depends on he gain β,and he faser he response is, he higher accracy of esimaes is, however, he real-ime esimaes of he oal disrbance are resriced o cerain condiions. For example, when freqency of oside inerference is high, he capaciy of ESO o rack he oal disrbance is limied.

3 458 Yojie Ma e al. / Procedia Engineering 29 (2) NLSEF. Nonlinear sae error feedback conrol law is he non-linear combinaion of he errors beween saeesimaes generaed from racking-differeniaor and ESO, i forms conrol amon ogeher wih oal disrbance compensaion amon wih ESO. = k1fal( ε1, αδ, ) + + k n fal( ε n, αδ, ) (3) According o he characerisics of he fncion and field operaing experience, selec non-linear facor α appropriaely, his will obviosly change conrol effecs, and make he raio and he differenial play heir efficacies respecively. 3. Acive disrbance rejecion conrol of SHAPF 3.1. Principle and Modeling of SHAPF. From he poin of view of working principles, pper and sbjacen arms of SHAPF can be regarded as ideal swich, he eqivalen circi is showed in Figre1(a). Since he acion of swiches cold conrol he size of he AC side volage, he SHAPF can be considered as a conrollable volage sorce and a parallel impedance o compensae harmonic crren and reacive crren in circi, as showed in Figre 1(b). s i L L s R s i c L f S' V c + c + Z L I L (a) (b) Figre 1. Eqivalen circi of he Single-phase SHAPF Analyze from Figre (1), mahemaical model of single-phase parallel hybrid acive power filer can be expressed as: dis Lf =Ris Vc +ω() d Here ϖ () is he nknown disrbance of sysem. I can be calclaed as follows:. i = f (, ) + b + a() s i s From (5) we can ge ha if a comprehensive disrbance a () can be observed and feed forward compensaion is available, APF can be ransformed ino a firs-order linear model. 4. Design of ADRC. The conrol of sysem is showed in Figre 2. Since he response of he inner ring is mch faser han he speed of he oer ring, he DC volage is consan when he inner crren conrol is achieved. (4) (5)

4 Yojie Ma e al. / Procedia Engineering 29 (2) ϖ () * S + + a() S 22 S Figre 2. Crren loop based on ADRC Expression of TD: * ε = S11. S11 =r fal( ε, α, δ) Bilding ESO as he following eqaions: (6) ε = S. S = S 22 β 1 fal( ε, α 1, δ 1) + ( ). S = β fal( ε, α, δ ) (7) The disrbance rejecion conrol law can be obained hrogh nonlinear fncion which feedbacks by he sysem of sae error: ε1 = S11 S = β1fal( ε1, αδ, ) Toal op of ADRC is: = S b 22 Eqaion (9) illsraes ha sysem conrol law is only relaed o sysem op and a given inp, and no relaed o he parameers of he sysem and nknown disrbance. (8) (9) 5. Simlaion resls Geneic opimizaion process ses real nmber coding, afer a 1-generaion evolion, he opimal parameers obained are as follows: Opimized parameer in nonlinear racking-differeniaor are r = 9487, a =.4, δ =.1 in ESO are β1 = 47962, β2 = 76931, a =.5, δ =.15,and in NLSEF are β1 = 13, a1 = 1, δ 1 =.1. Figre 3. Spply crren before compensaion; Figre 4. Spply crren afer compensaion

5 46 Yojie Ma e al. / Procedia Engineering 29 (2) Figre 5.THD of spply crren before compensaion; Figre 6.THD of spply crren afer compensaion 6. Conclsions ADRC conroller can resolve conrol problems of a kind of ncerain objecs, and has srong adapabiliy and robsness. ADRC conrol regards sysem model and he role of oside inerference as he sysem disrbances, and hen aomaically esimaes and compensaes. This compensaion specifically realizes linearizaion of ncerain sysem feedback and deerminisic feedback. Appling ADRC ino APF cold redce he signal o be colleced, only need o sample spply crren and he DC side capacior volage, and o compensae he load crren and spply volage as nknown inerference in a sysem. Meanwhile, Parameer selecion of conrol sysem has nohing o do wih he parameers in he sysem, parameers can be seleced wihin a relaively large range, herefore, he srcre of conrol sysem is simple and easy o implemen. References [1] Akagi H. New Trends in Acive Filers for Power Condiioning. IEEE Trans on Indsrial Applicaion, 1996, 32(6): 1312~ 1322 [2] Hang Y, Zhang W G. Developmen of Acive Disrbance Rejecion Conroller [J].Conrol Theory and Applicaions, 22, 19(4): [3] Han J Q. Ao-disrbances-rejecion Conroller and is Applicaions [J].Conrol and Decision, 1998, 13(1):19-23 [4] Lei Z M, L Z D. Nonlinear Ao-Disrbance Rejecion Conroller for Spacecraf Aide Conrol Sysem [J]. Aerospace Conrol, 2, 18(4): [5] F W B, Zhao DL, Pan L. Cing-in Conrol of he VSCF Wind-power Generaor Based on Ao-disrbance Rejecion Conroller [J]. Proceedings of he CSEE, 26, 26(3): [6] W Jie, Li Mingjian, Xe Feng. An Overview of Conrol Theories in Power Elecronics Model and Linear Mehod. Conrol Theory and Ap-plicaion,1999,16(4):47~473 [7] Chen H Q. Research on Permanen Magne Synchronos Moor AC Drive Sysem Based on ADRC [D].TianJin: Tianjin Universiy,24. [8] Li X, Jiang X Z,Li D H. Ao Disrbance Rejecion Conrol for Hydro Trbine Governor [J].Jornal of Tsingha Universiy (Science and Technology),,41(1):

first-order circuit Complete response can be regarded as the superposition of zero-input response and zero-state response.

first-order circuit Complete response can be regarded as the superposition of zero-input response and zero-state response. Experimen 4:he Sdies of ransiional processes of 1. Prpose firs-order circi a) Use he oscilloscope o observe he ransiional processes of firs-order circi. b) Use he oscilloscope o measre he ime consan of