Power Conrol of Resonan Converer MPPT by Pulse Densiy Modulaion Akif Karafil 1, Harun Ozbay 2, and Selim Oncu 3 1,2 Bilecik Seyh Edebali Universiy, Bilecik, Turkey akif.karafil@bilecik.edu.r, harun.ozbay@bilecik.edu.r 3 Karabuk Universiy, Karabuk, Turkey soncu@karabuk.edu.r Absrac This paper presens he simulaion of series resonan converer sysem wih proposed 32 pulse densiy modulaion (PDM) paerns which ransfer he elecrical energy obained from PV panels o load wih high power densiy. Maximum power poin racking (MPPT) is achieved by deleing some conrol pulses. Therefore, zero curren swiching (ZCS) is achieved a 1 khz resonan frequency. The average oupu power changes of series resonan converer are given according o he proposed 32 PDM paerns. Boh he MPPT algorihm and he high frequency series resonan converer are conrolled by TMS32F28335 DSP. In he 6 W PV sysem, sof swiching condiion is achieved by using he proposed 32 PDM echnique. 1. Inroducion Phoovolaic sysems have gained imporance since hey conver he solar energy ino elecrical energy direcly, hey work silenly wihou giving harm o he environmen and hey are fas, reliable and have easy se-up. However, he efficiency of he PV panels is very low. Moreover, he oupu power of he panels varies coninuously because of he changing environmenal facors. Therefore, MPPT dc-dc converers are used o have he maximum oupu power of PV panels [1-3]. Many conrol mehods such as frequency conrol, pulse widh modulaion (PWM), phase-shif conrol and duy conrol are used o conrol he dc-dc converers. However, hese conrol mehods resul in an increase of swiching losses since hard swiching is achieved in all hese mehods. Swiching losses occur when eiher he curren passing hrough he power swich during he swiching or he volage of swich ends is no zero. Therefore, elecromagneic inerferences (EMI) also increase due o high curren and volage spikes occurring during he swiching. As a resul, operaing frequency is limied, efficiency is decreased and he swiches are forced due o high swiching losses [4-7]. In his sudy, a series resonan converer MPPT is operaed in order o avoid he hard swiching condiions and EMI problems occurring in he radiional PWM swiched MPPT and o increase he limied operaing frequency. The sysem is operaed a higher frequencies compared o PWM conrolled converers by providing sof swiching condiions. As a resul of high operaing frequencies, he componen sizes and herefore he coss can be reduced. Moreover, PDM echnique is more convenien o rack he maximum power poin a fixed operaing frequency for conrol mehods used wih resonan converers since he power generaed by he PV panels is no same hroughou he day. Therefore, i is required for resonan converer sysems o operae a frequencies differen from he operaing frequency. In his sudy a series resonan converer MPPT circui is conrolled by phase locked loop (PLL) and PDM is simulaed in order o have a maximum power poin racking by achieving he sof swiching condiions a each power poin of 6 W PV sysem. Therefore, an MPPT circui operaing a sof swiching condiions and fixed operaing frequency are achieved. The operaing frequency of he designed sysem is 1 khz and Perurb & Observe (P&O) algorihm is chosen as he MPPT algorihm. P&O algorihm is conrolled wih a TMS32F28335 DSP. This paper is organized as follows: Secion 2 presens he sysem design and analysis. This secion includes he design of series resonan converer, he analyzed PDM conrol sraegy and power conrol wih PDM. In secion 3, he principle of P&O MPPT is presened. Secion 4 gives informaion abou he PSIM simulaion of he sysem and analyses resuls. Finally, some conclusions are drawn in he conclusion par. 2. Sysem Design and Analysis Today s elecronic circuis are expeced o be ligh, small and wih high efficiency. PWM echnique is generally used in dc-dc converer conrol. However, he swiching losses of PWM conroller converers are very high. High swiching losses limi dc-dc converer operaing frequency, reduce he efficiency and may damage power swiches. To overcome hese drawbacks, resonan converers are used. Resonan converer is a dc-dc or dc-ac converer obained by adding he resonan circui o PWM swiching power converer [8-1]. Square wave curren is obained in he inverer oupu when he power swiches of he inverer circui are swiched in a sequence. Sinusoidal load curren/volage wave form is obained from square wave volage produced by inducor (L) and capacior (C) componens (resonan circui). Sinusoidal volage is recified by recifier circui and ransferred o he oupu o have dc volage. Series resonan converer circui is obained by adding he Lr and Cr componens o he converer circui in series. Resonan frequency (fr), an imporan parameer in he conrol of he circui, is calculaed by he following equaion [11, 12]. 1 fr = (1) 2π LrCr A full bridge converer consiss of a dc volage source and four MOSFET power swiches. +Vd dc inpu volage is obained in load ends when S1 and S4 swiches are urn on simulaneously. On he oher hand, he volage in he load ends
is negaive and has Vd value when S2 and S3 swiches are urn on simulaneously. The circui configuraion of he sysem and he operaing modes are shown in Figure 1 and 2, respecively. 2.1. Analysis of PDM Conrol Sraegy PDM is among he mos suiable conrol echniques for resonan opologies [16]. PDM is a command sequence. Power conrol is provided by deleing some of he on pulses in accordance wih he command sequences wihou making any change in he urn on duraion of he swich. Power decreases as he number of he deleed pulses increases. The PDM conrol principle is given in Figure 3. Fig. 1. The circui configuraion of he sysem Fig. 3. The basis of PDM conrol (a) (c) Fig. 2. The operaing modes of he simplified circui: (a) he equivalen circui (b) Mode I, (c) Mode II and (d) Mode III S1 and S4 swiches are urn on in Mode I while S2 and S3 swiches are urn on in Mode II. The oupu volage of he inverer (VAB) is zero in Mode III. The curren passing hrough D4 diode when S2 swich is urn on and he curren passing hrough D2 diode when S4 swich is urn on are in damped oscillaion form. The swiching modes and he posiions are shown in Table 1. Table 1. Operaing modes (b) (d) Swiching Modes Off On Mode I S2 and S3 S1 and S4 Mode II S1 and S4 S2 and S3 Mode III S1 and S3 S2 and D4 S4 and D2 While he oupu volage of he inverer is VAB = +Vd (Fig. 2.b) in Mode I, i is as VAB= -Vd (Fig. 2.c) in Mode II. The oupu volage of he inverer is VAB= (Fig. 2.d) in Mode III when he load is disconneced from he source [4, 13-15]. As seen in he figure, unil he sevenh resonan cycle square wave volage (Mode I and II operaing) is applied as Vd value. In he 8 h cycle on pulse is deleed and zero volage (Mode III operaing) is applied o he inverer. The oupu volage of he inverer is in periodic wave form in he eighh resonan cycle. The average oupu power is 28/32 when compared o he full power operaing. Tha is, he oupu power of he inverer is conrolled by adjusing he pulse densiy of he square wave volage. Turn on and urn off duraions of he swiches are calculaed by he following equaion. T T = NT, 1, 2, on r = Ton + Toff Ton = N Tr Toff = N Tr D = (2) T Where; N is he oal resonan cycle, N1 is normal resonan cycle number, N2 is he conrolled (deleed pulse) resonan cycle number. The following equaions are obained when examining he mahemaical analysis of he full bridge series RLC resonan circui shown in Fig. 2.a. dires 1 Lr + iresd + Rires = V d() (3) d Cr 2Lr 2Q τ = = (4) R ωr Where, τ is ime consan, Q is he qualiy facor of he series resonan circui and ωr is angular resonan frequency. The following equaion is obained when he Vd () principle componen is wrien using Fourier analysis. 4V V() d d = sin( ωr) (5) π
The following equaion is obained when he general soluion of he equaion is wrien. R 2L 4V i d res() = Acos( r) Bsin( r) e r ω + ω + sin( ωr) (6) π R When he iniial condiions are considered, he resonan curren is as follows: R 4Vd 2L i r res() = 1e sin r π R ( ω ) Figure 4 shows he resonan curren (ires) and he envelope of he resonan curren (ie). When he resonan curren is wrien a his condiion, he following equaions are obained. (7) i res( ) = i E( )sinωr, (8) i E( ) = A(1 e τ ) + B, < < T on, (9) T on i E( ) = Ce τ, Ton < < T (1) If PDM period (T=NTr) is smaller han he ime consan (T<<τ), he ampliude of he resonan curren is proporional o he pulse densiy. Therefore, when he relaionship beween he oupu power and he pulse densiy is wrien, he following equaion is obained: 2 lim P = PmaxD (15) τ If PDM period (T=NTr) is bigger han he ime consan (T>>τ), he oupu power is [4, 13]: 2.2. PDM and PLL Conrol Basics lim P = PmaxD (16) τ The block diagram of he PDM conrol circui designed wih PLL is shown in Figure 5. The conrol circui consiss of wo pars. The firs par is he PLL circui where resonan curren (ires) and he inverer oupu volage (VAB) phase are locked. As a resul, zero ransiion poins are deeced a resonan frequency and he sof swiching condiions are achieved. On he oher hand, PLL circui consiss of hree pars. These are as follows: phase deecor, low pass filer and volage conrolled oscillaor (VCO). In he las par of he PLL circui VCO oupu signal is compared wih a riangular signal comparaor and PWM pulses are obained. The obained PWM pulses are sen o frequency divider and parallel inpu serial oupu (PISO) regiser of he PDM logic circui, which is he second par of he conrol circui. The parallel inpus required for he shif regiser are he proposed 32 PDM pulses and obained from he digial oupu of he DSP. Fig. 4. PDM curren wave form When he ie curren is rewrien using he A, B and C coefficiens, he following equaions are obained: i E( ) = I( 1 e τ ) + Imine τ, < < T on, (11) T on i E( ) = i E(T on )e τ, Ton < < T (12) Fig. 5. The block diagram of he designed PDM conrol circui A able is prepared o choose he proposed PDM paerns for he PDM conrol uni in order o generae swich driving signals. Figure 6 shows he proposed PDM swiching forms for N=32. Table consiss of and 1 bies. The average oupu power is obained by he following equaions: 1 T P = V AB()i res()d, (13) T T on Ton T T on τ 1 e τ P = Pmax + e τ e τ T T T 1 e τ (14) Fig. 6. The proposed 32 PDM paerns
In he able, N represens he lines and 2*N represens he columns. On he oher hand, 32 lines represen he differen levels for PDM (N=1/32 32/32). The columns represen he 32 resonan cycles generaed o conrol he inverer swiches. The duraion of each cycle is equal o he resonan duraion (T=NTr). 3. MPPT wih PDM Conrol MPPT is compleely an elecronic sysem racking he maximum power by racking he maximum power of PV panel. In MPPT algorihm, inpu volage and curren are racked coninuously and simulaneously, he changes are calculaed and he necessary seps are followed o obain he maximum power poin (MPP) [17]. In his sudy, P&O mehod, which is one of he mos used mehods, was preferred due o is simpliciy and high efficiency. In P&O mehod, PV panel power is measured when he change is applied o he conrol parameer and i is compared o he previous measured power. The flow char of he PDM conrolled P&O MPPT algorihm is shown in Figure 7. Figure 8 shows he overall block diagram of he proposed sysem consising of he PV generaor, he P&O MPPT conrol algorihm, PLL, PDM, resonan converer and he DSP uni. In he designed sysem, he generaed power is calculaed wih DSP by using he measured PV volage and curren. DSP provides he conrol of he sysem by deleing some of he conrol pulses of he resonan converer according o he P&O algorihm. Therefore, PV panels are operaed a heir maximum power. 4. PSIM Simulaion Resuls The proposed 32 PDM conrolled series resonan converer MPPT circui simulaed a PSIM is shown in Figure 9. Fig. 9. The proposed 32 PDM conrolled series resonan converer MPPT circui Fig. 7. The flow char of PDM conrolled P&O MPPT algorihm If he power and volage increases, he change is applied in he same direcion in he nex sep. Therefore, PDM swiching signal also increases. If he power decreases and he volage increases or he power increases and he volage decreases, hen PDM signal decreases. On he conrary, if boh he power and he volage decrease, PDM signal increases. Figure 8 shows he resonan converer MPPT sysem. When he maximum PDM lengh N=32 (T=32Tr) is chosen, pulse densiy D will change from 1/32 o 32/32. While he minimum power is obained a 1/32 condiion, maximum power is obained a 32/32 condiion. The pulse densiy changes depending on he power amoun obained from PV panels. In his sudy, P&O MPPT algorihm and 32 cycled PDM able are wrien ino he simplified C block. The average oupu power of he full bridge series resonan converer circui simulaed and calculaed according o he PDM signals is shown in Figure 1. THE AVERAGE OUTPUT POWER OF CONVERTER Solar radiaion (W/m2) 1 8 6 4 2 5 4 3 2 Power (W) 1 Simulaion Resuls Calculaion Resuls 32 28 24 2 16 12 Pulse densiy 8 4 Fig. 8. The block schema of he resonan converer MPPT sysem Fig. 1. The average oupu power of converer according o he pulse densiy and solar radiaion variaions
To es he proposed sysem, solar radiaion level is changed rapidly sep by sep as 25-5-75 and 1 W/m 2 in PSIM program and P&O MPPT algorihm is examined. The heoreical PV power (Pref) and he obained PV power (Ppv) from he proposed sysem are shown in Figure 11. Fig. 11. P&O MPPT algorihm resuls Figure 12 shows he ZCS condiion while he sysem is racking he MPP by PDM. 1 5 I(Mos 2) Vds2/1.492969.493359.49375.494141 Time (s) Fig. 12. ZCS condiion 5. Conclusions In his sudy, he proposed 32 PDM conrolled full bridge series resonan converer obained by using P&O MPPT algorihm is simulaed a PSIM. The required power for MPPT algorihm is conrolled by deleing some conrol pulses of series resonan converer operaing a resonan frequency. Therefore, he oupu power is conrolled a wide range wih 1 khz resonan frequency depending on he deleed conrol pulses and ZCS is provided coninuously. The changes in he proposed 32 PDM paerns occurring depending on he power values obained from PV panels and herefore he average oupu power changes of he series resonan converer are also examined. Validiy of he PDM conrolled MPPT converer is esed in 6 W PV generaion sysem and sof swiching condiions a 1 khz are presened from 25 o 1 W/m 2 radiaion levels. 6. Acknowledgmen This research was suppored by Karabuk Universiy Research Projecs Fund (No: KBU-BAP-15/2-DR-5). The auhors would like o hank for suppor. 7. References [1] O. Deveci, and C. Kasnakoglu, "Performance improvemen of a phoovolaic sysem using a conroller redesign based on numerical modeling" Inernaional Journal of Hydrogen Energy, vol. 41, no. 29, pp. 12634-12649, Aug. 216. [2] M. A. Enany, M. A. Faraha, and A. Nasr, "Modeling and evaluaion of main maximum power poin racking algorihms for phoovolaics sysems", Renewable and Susainable Energy Reviews, vol. 58, pp. 1578-1586, Feb. 216. [3] S. Borekci, E. Kandemir, and A. Kircay, "A simpler singlephase single-sage grid-conneced PV sysem wih maximum power poin racking conroller", Elekronika Ir Elekroechnika, vol. 21, no. 4, pp. 44-49, Apr. 215. [4] H. Fujia, and H. Akagi, "Pulse-densiy-modulaed power conrol of a 4 kw, 45 khz volage-source inverer for inducion meling applicaions", IEEE Trans. on Indusry Applicaions, vol. 32, no. 2, pp. 279-286, Mar./Apr. 1996. [5] R. L. Seigerwald, R. W. De Doncker, and M. H. Kheraluwala, "A comparison of high-power DC-DC sofswiched converer opologies", IEEE Trans. on Indusry Applicaions, vol. 32, no. 5, pp. 1139-1145, Sep./Oc. 1996. [6] B. Nagarajan, and R. R. Sahi, "Phase locked loop based pulse densiy modulaion scheme for he power conrol of inducion heaing applicaions", Journal of Power Elecronics, vol. 15, no. 1, pp. 65-77, Jan. 215. [7] S. Oncu, and S. Nacar, "Sof swiching maximum power poin racker wih resonan swich in PV sysem", Inernaional Journal of Hydrogen Energy, vol. 41, no. 29, pp. 12477-12484, Aug. 216. [8] M. K. Kazimierczuk, and D. Czarkowski, "Resonan Power Converers", John Wiley & Sons Inc, Chap. 19, 1995. [9] S. Tian, F. C. Lee, and Q. Li, "A simplified equivalen circui model of series resonan converer", IEEE Trans. Power Elecronics, vol. 31, no. 5, pp. 3922-3931, 216. [1] S. Oncu, and H. Ozbay, "Simulink model of parallel resonan inverer wih DSP based PLL conroller", Elekronika Ir Elekroechnika, vol. 21, no. 6, pp. 14-17, Sep. 215. [11] M. Z. Zainol, N. A. Rahim, and J. Selvaraj, "Design and analysis of conacless ransformer using series resonan converer", Przegląd Elekroechniczny, vol. 89, no. 5, pp. 192-195, 213. [12] M. Mohammadi, and M. Ordonez, "Fas ransien response of series resonan converers using average geomeric conrol", IEEE Trans. Power Elecronics, vol. 31, no. 9, pp. 6738-6755, Sep. 216. [13] V. Eseve e al., "Improving he efficiency of IGBT seriesresonan inverers using pulse densiy modulaion", IEEE Trans. Indusrial Elecronics, vol. 58, no. 3, pp. 979-987, Mar. 211. [14] S. Oncu, and A. Karafil, "Pulse densiy modulaion conrolled converer for PV sysems", Inernaional Journal of Hydrogen Energy, vol. 42, no. 28, pp. 17823-1783, 217. [15] J. Essadaoui, P. Sicard, E. Ngandui, and A. Cherii, "Power inverer conrol for inducion heaing by pulse densiy modulaion wih improved power facor", in Proc. IEEE Canadian Conference on Elecrical and Compuer Engineering (CCECE), 23, pp. 515-52. [16] P. Kowsubha, K. Krishnaveni, and K. R. Reddy, "Review on differen conrol sraegies of LLC series resonan converers", in Proc. IEEE In. Conf. Advances in Elecrical Engineering (ICAEE), 214, pp. 1-4. [17] M. A. Elawil, and Z. Zhao, "MPPT echniques for phoovolaic applicaions", Renewable and Susainable Energy Reviews, vol. 25, pp. 793-813, May 213.