Proceeding of 2010 IEEE Student Conference on Reearch and Development (SCOReD 2010), 13-14 Dec 2010, Putrajaya, Malayia Comparion Study in ariou Controller in Single-Phae Inverter Shamul Aizam Zulkifli *. Md Zarafi Ahmad ** *Department of Electrical Engineering and Electronic, Univerity of iverpool, UK. Email:.aizam@yahoo.com ** Jabatan Kejuruteraan Kuaa Elektrik, Univeriti Tun Huein Onn Malayia, Malayia. Email: zarafi@uthm.edu.my Abtract-Thi paper explain the comparion of the controller that uitable to be ued in ingle phae inverter for tudying purpoe. Thi controller can eaily been developed and teted uing MATAB/Simulink and implemented on the real time application. The controller that have been developed are the Proportional Integration (PI)-d controller, Proportional Reonant (PR) controller, and PR- Repetitive controller. The controller output will be connected to the pule width modulation (PWM) generator to generate ignal to the ingle phae inverter. All thee controller have been teted with the ame load and imulation time. Keyword- PI, PR, PWM advantage in performance at the fundamental freuency and ignore other freuency [3]. For the third controller it i baed on the PR-Repetitive control that ha ability to yntheize the error to minimize the low-order harmonic to the control ignal [3,5]. Thi controller ha ability to minimize the periodic error appear in the ingle phae PWM inverter [4]. Fig. 1 how the controller diagram that have been ued in thi paper. I. Introduction Single-phae inverter are the converter which tranform the DC input to the AC output. The inverter can be cacade to be 3-phae inverter, which i uitable for grid connection. The output for the ingle-phae inverter are the voltage output ( O ) and the inductor current (I ) and by controlling the I the inverter can be ued a a grid connection. Thi paper i focued on the current control method which i ued in the renewable energy application. The current control for AC ignal i not eay to implement due to time invariant current [1]. Other iue need to be conider are to maintain the tability and power uality [8] when it i connected to the renewable energy in achieve good grid connection. The bet olution i to ha an active feedback control with current feedback. Thi feedback control can be model in many way. A been reported, it ued deadbeat control, liding control, tate feedback control, and d tranformation with the PI control a the claic approach to the control current [3]. A known, the output are the AC ignal which i related to the freuency that not uitable for PI control if no changing ha been made on the controller mode. Thi paper analye the ingle-phae inverter which i known a oltage Source Inverter (SI). Thi ha been choen becaue it i widely ued and eay to develop. The controller preented in thi paper are the PI-d controller, the PR controller and the PR-Repetitive controller. For the firt controller it i baed on Park tranformation where it i ued in three phae ytem but with ome modification in order to obtain time-invariant variable [2] in ingle phae. Thi tranformation create the new imaginary ignal [1] in the frame. It can be generated by the Phae ook oop (P) application The econd controller i the PR control and i baed on the reonant freuency of the inverter output, where it ha 50Hz freuency. Thi controller give an a) PI-d ynchronou rotating frame b) Preonant tationary reference frame c) Repetitive PR control Figure 1: ariou controller 978-1-4244-8648-9/10/$26.00 2010 IEEE
A. C filter deign II. Sytem Decription III. Controller Deign A. DQ ingle-phae current control. The circuit diagram of the ingle-phae inverter i hown in Fig. 2 which conit of full bridge inverter, inductor (), filter (C) and the load (R). The dead time effect and inevitable lo for every part have been ignored. Figure 2: Single Phae Inverter Table 1 how the value that have been ued in thi tudy. Symbol Decription alue Inverter inductance 1.5mH C Filter capacitance 10uF R oad Reitance 20 Table 1: Component The area of interet in thi paper i on the inductor current (I ). The tranfer function of the inverter form inductor current to voltage ource (I / ) i given by, I 1 2 (1) CR+ S+ R Thi tranfer function generate the bode diagram hown in Fig.3. Thi bode diagram ha a very high gain at the beginning and it will make the ytem to be untable. The tranformation to the d frame reuire the orthogonal component. The invere tranformation i hown in E. 2. d α β in( θ ) in( θ ) in( θ ) in( θ ) α β Both of thee euation cannot be applied directly to the ingle-phae inverter becaue there only ha one variable. Thi problem can be olved uing a method propoed by [1] which know a fiction input current. A been explained in the previou ection, thi ignal can be generated uing the P. P generate three output which are angle (θ ), co( ωt) and in( ω t). The lat part i known a the fiction input current [1]. The control block for the d tranformation can be modelled by following euation, di dt di d dt di dt + o pwmd pwm pwm d ω I + ω I d Thi euation how the control variable are DC uantitie (d and ). The block diagram of the controller i hown in Fig.4 with the PI controller after the d tranformation. The PI controller i ued becaue it give no teady tate current error in dc ignal. The bode diagram and the root locu of the inverter with the PI controller i hown in Fig. 5. (2) (3) Figure 3: Single-Phae Inverter bode diagram Figure 4: PI-d controller
B. P-Reonant controller a) Open loop PI bode diagram The PR controller ha been deigned baed on the freuency output of the I. A known the output i 50Hz. The aim of thi controller i to control the inuoidal variable which ha reonant freuency at 50Hz and in the ame time reject other freuencie. Uing only PI control alone which ha pole at zero which give infinite gain at zero freuency i not able to olve it. Due to thi diadvantage, the PR controller i ued where it ha high gain at the reonant freuency [3]. Fig. 6 how the PR controller block. Thi controller need to have two controller ide which repone to d and component. The reference value for d and are 1 and 0. At the end of thi control proce the d and can be um together to generate the periodic ignal that i ued to generate the PWM ignal to the inverter. b) Cloed loop PI root locu Figure 5: Bode diagram and root locu of PI control The Kp value ha been elected regarding to the cloed loop root locu hown in Fig 5b where the target damping ratio i 0.4. The value ha been elected becaue it will generate le then 5% overhoot on the tep repone of the ytem. In general the PI controller will be looked like the low pa filter by reducing the magnitude/gain of the ytem while Ki value i baed on the Fig 7 that give bigger bandwidth. Proportional (Kp) Integration (Ki) 22 150 Table 2: Kp and Ki value For PI-d bode diagram it how that the controller i behaved like the low pa freuency filter. Thi not help in reducing the THD on the overall performance. Thi controller i table becaue all the pole are located inide the circle which i range from 1 to 1. Thi value i calculated in dicrete time for eay obervation. where Figure 6 : PR controller block diagram The tranfer function of the PR controller i given by C PR K p + K i 2 + ω 2 (4) ω 2 π f The bode diagram for PR controller i hown in Fig. 7 where high gain i generated at the reonant freuency. The bet gain value i elected when it ha bigger bandwidth at the reonant freuency. Thi i becaue the bandwidth hopefully can cover the range of the reonant freuency between 48Hz to 52Hz. The value for K p and K i are the ame in Table 2. In the PR reonant control, the controller i baed on the tationary rotating frame. The tranformation between the ingle phae to the αβ i given by α co( ωt) (5) β in( ωt) Becaue thi β at the imaginary axi, the value can be ignored where it doe not affect the controller ytem.
freuency. In thi paper the value that ha been choen i 10kHz where it i expected to eliminate mot of the freuency. The repetition (1/Z N ) i baed on the ampling of the ignal where 200 point ampling ha been ued. Fig 9, how the repetitive repone at odd harmonic of the ytem. By combine with PR controller, the controller can affect more accurately. The tranfer function of the repetitive- PR control can be written in dicrete time a, 3 2 22z 63.9z + 61.81z 19.91 C z (6) 3 2 z 3z + 3z 1 Figure 7: PR reonant bode diagram Fig 7 how that the PR reonant give high peak at the 50Hz. C. PR-Repetitive Control The repetitive control provide an alternative to minimize the meaured error for the PWM generation [4]. It i able to give better performance for the teady tate when the reference input ignal i periodic. Repetitive control i able to modify the reference command by adding with the periodic compenation ignal [5] to the input command to the controller. Generally the controller can be connected with PI,.PR or PID. In thi paper the repetitive control i model baed on the low pat freuency combine with the repetition of the previou ample of the inductor current error. It calculate the correction component [5] which i hown in Fig. 8. Thi repetitive control affected to the odd freuency of the C filter. Figure 8: Repetitive PR clock diagram The value of the low pa filter i baed on the reonant freuency. Becaue of the ytem i 50Hz output and the witching freuency i 10kHz the range of the freuency mut bae on the highet THD which i 31 where it euivalent to the 1500Hz and to the witching Figure 9: Repetitive-PR bode diagram Fig 9 how the repetitive repone. It how that the reputation i happen at odd harmonic. At hi point it generated ome gain regarding to the harmonic and it make the harmonic to ha zero teady tate. Thi help in reducing the THD of the ytem where it not be dicued in thi paper. I. Simulation reult Thi ection dicued the performance of each controller on the ingle-phae inverter. Each controller ha been modelled in dicrete time model and it ready to download in real time application. Thi paper will not dicu about real time implementation. The imulation meaure three component, which are the (I ), (o) and the e (current error). All the controller mut have the ability to control the (I ) at the deired value which i 1A and to ha minimum current error. A. PI-d control For the firt imulation, the PI-d control ha been imulated. In thi imulation the component i et to be zero becaue the imaginary condition doe not affect the ytem.
Fig.11 how the imulation reult for the PR controller. It how the current i maintained at the 1A condition and the current error i limited at the range of the target. A known the PR controller i reponded to the freuency and the current error will have inuoidal affect. Thi indicate that the controller able to follow the reonant freuency. The advantage of thi controller i the current hape i moother and it i indicated the controller able to eliminate certain harmonic in the ytem. C. Repetitive-PR control Figure 10 : PI d imulation Fig. 10 how the imulation reult of the controller. The controller i able to control (I ) at the target value. For the current error graph the error i mall which indicate that the Pi-d controller can be ued to minimize the difference between the reference ignal and the meaured ignal while reducing the THD effect. B. P-Reonant control Figure 12: Repetitive PR imulation Fig. 12 how the repetitive controller repone on the ingle-phae inverter. In thi reult there ha a delay on the generate output either on the I and o. Thi i becaue in deigning the controller the delay time/ repetition ha been conidered that will have more accurate reponded to the ytem. In thi reult how the target I ha been achieved but the main advantage of thi controller i the current error i le compared to the previou controller, which it range of 0.05A to 0.05A.. Concluion A a concluion, thi paper how that ingle-phae inverter can be controlled by uing different controller topologie uch a PI-d, PReonant and Repetitive PR with the current feedback loop. The Repetitive-PR give better repone in tracking the reference value that i allowed to generate better current at the output. It alo give better output and it i uitable to ue in grid connection where it reuire le THD. I. Reference Figure 11: PR imulation [1] U.A Miranda, M.Arede, and.g.b. Rolim, A DQ Synchronou Reference Frame Control for Single Phae Converter, IEEE 36 th Power Electronic Specialit Conference, 2005, pp 1377-1381
[2] J.Salaet, S.Alepuz, A.Gilabert, and J.Bordonau, Comparion between Two Method of DQ Tranformation for Single Phae Converter Control. Application to a 3-evel Boot Rectifier, 35 th Annual IEEE Power Electronic Specialit Conference, 2004, Germany, vol.1, pp 214-220 [3] T. Hornik, Control of Grid-Connnected DC-AC Power Converter for Ditributed Power Generation Sytem, unpublihed [4] C.Rech, H. Pinheiro, H.A. Grundling, H..Hey, J.R.Pinheiro, Analyi and Deign of a Repetitive Predictive PID Controller for PWM Inverter, IEEE 32 nd Annual Power Electronic Specialita Conference, 2001, vol. 2, pp 986-991 [5] S.Duan, B.iu, Y.Kang, J.Chen, Repetitive PD control trategy with invere tranfer function compenation for CCF inverter, Journal of Control Theory and Application, vol.2, pp 121-125, 2004 [6] M.Jamil,S.M.Sharkh, M.Abuara, R.J. Boltryk, Robut Repetitive Feedback Control of a Three Phae Grid Connected Inverter, IET International Conference on Power Electronic, Machine and Drive 2010, pp 1-6 [7] Z.Xueong, S.Daichun, M. Youjie, C. Dehu, Grid-connected control and imulation of ingle-phae two-level photovoltaic power generation ytem baed on Repetitive control, International Conference on Meauring Technology and Mechatronic Automation, 2010, pp 366-369 [8] F. Alvarez, D.D. Franceco, Control of the Grid ide converter and the filter ytem in a wind turbine, unpublihed