Constant frequency operation of parallel resonant converter for constant-current constant-voltage battery charger applications

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1 J. Mod. Powe Syst. Clean Enegy Constant fequency opeation of paallel esonant convete fo constant-cuent constant-voltage battey chage applications Taha Nuettin GÜCN 1, Muhammet BBEROĞLU 1, Beki FNCAN 2 Abstact This pape poposes a design and contol appoach to paallel esonant convete (PRC) based battey chages. The poposed appoach is paticulaly suitable fo the constant-cuent constant-voltage (CC-CV) chaging method, which is the most commonly utilized one. Since the PRC is opeated at two diffeent fequencies fo each CC and CV chaging modes, this appoach eliminates the need fo complicated contol techniques such as the fequency-contol and phase-shift-contol. The poposed method not only simplifies the design and implementation pocesses of the convete unit but also simplifies the design of output filte configuation and deceases the numbe of the equied components fo the contol of the chage. The poposed method is confimed by two expeimental setups. The esults show that the designed chage cicuit ensued a vey stable constant cuent in CC chaging phase, whee the chaging cuent is fixed to 1.75 A. Although a voltage incease in CV phase is obseved, the chage cicuit is able to decease the chaging cuent to 0.5 A in CV phase, as depicted in CossCheck date: 5 Mach 2018 Received: 20 June 2017 / Accepted: 5 Mach 2018 Ó The Autho(s) 2018 & Taha Nuettin GÜCN tngucin@gmail.com Muhammet BBEROĞLU mbibeoglu@yalova.edu.t Beki FNCAN fincan@itu.edu.t 1 2 Enegy Systems Engineeing Depatment, Univesity of Yalova, Yalova, Tukey Electical Engineeing Depatment, stanbul Technical Univesity, stanbul, Tukey battey data-sheet. The efficiency of the chage is figued out to be in the ange of 86%-93% in the fist setup, while it is found to be in the ange of 78%-88% in the second setup, whee a high fequency tansfome is employed. Keywods Resonant convete, Paallel esonant convete, Battey chage, Constant-cuent constantvoltage (CC-CV) chaging 1 ntoduction The extensive use of batteies in small- to lage-scale powe systems, such as cell phones, plug-in and hybid electic vehicles (EVs) and enewable enegy systems (RESs), equie convenient chage cicuits. The basic expectations fom these cicuits ae that the powe electonic unit has high powe density and opeates at high efficiencies, while they ae able to keep up with the dynamic behavio of the battey pack [1]. Although thee ae vaious chaging algoithms, the constant-cuent constant-voltage (CC-CV) chaging is the most common method that is utilized fo the chaging pocess of vaious battey types [2, 3]. The CC-CV chaging algoithm is compised of two chaging modes. n the fist mode, the chage cicuit povides a constant cuent until voltage of the battey pack eaches to a cetain value. Beyond this point, the chage cicuit supplies a constant voltage output, while the chaging cuent slowly deceases. The esonant convetes offe seveal advantages such as lowe switching losses leading to highe switching fequencies and highe powe densities [4 6]. Thus, esonant convetes ae the key technology in DC powe applications [1]. Consequently, many esonant convete

2 Taha Nuettin GÜCN et al. topologies have been widely used as battey chages, especially fo EVs [7 13]. Resonant convetes ae categoized into thee basic topologies, depending on the manne by which esonant tank type the enegy is extacted fom. These ae the seies esonant convete (SRC), paallel esonant convete (PRC), and seies-paallel convete (SPRC) [1, 6]. PRCs exhibit some desied featues; easy output voltage egulation fo above the esonance fequency opeation at no load, less conduction losses, wide load vaiation (load insensitivity) and deceased ipple of the output voltage. Moeove, PRCs inheently ensue potection against shot cicuit conditions and have capability of no load opeation, with the exception of nea esonance fequencies. One majo dawback of the PRC is that the output voltage of the convete is highly dependent on the load and theefoe it can be inceased to vey high values unde no load [4, 14]. Consideing the facts mentioned above, PRCs seem to be one of the convenient topologies fo battey chage applications. The opeation of PRC is well-known [15] and the most basic appoach fo output voltage/cuent egulation is the fequency contol method. A numbe of PRC configuations with fequency contol fo battey applications have been epoted in the liteatue. Refeence [4] offeed a PRC topology fo the mobile battey chage applications, in which the lage output side inducto have been eplaced by a elatively small sized inducto. An altenative full bidge PRC fo RES has been suggested, whee the esonant tank elements have been connected in a diffeent configuation in ode to decease the voltage stess on the semiconducto devices in [16]. n [17], a PRC topology fo the gid-connected RES with educed switching fequency vaiations has been demonstated. A ecent study [18] compaes fou basic fequency-contolled esonant convete topologies opeating above the esonance in the aspect of being applicable as on-boad EV chages based on CC-CV chaging method. Thei study states that the PRC pefoms well in CC chaging mode, wheeas it has vey low efficiency in the CV chaging mode. This is caused by the fact that, at above esonance opeation, the input cuent does not significantly decease as the load deceases [18]. Although the fequency-contol method is commonly applied, the main poblem with this method is that the switching fequency must be adjusted in a wide ange. This complicates the design and optimization of cicuit elements. n addition, the change of switching fequency is actually quite shap so that it causes moe switching losses and consequently a decease in the geneal system efficiency [19 21]. n the liteatue, seveal appoaches have been poposed fo avoiding the fequency contol. One of the ealiest appoaches is the phase modulated esonant convetes (PMRC) that was published in the late 80 s. n [22], a constant fequency esonant convete is designed by implementing two conventional SRC o PRC whose outputs ae connected eithe in paallel o in seies. These convetes ae opeated at a constant fequency, wheeas the output voltage is contolled by the phase displacement at the invete stages. The disadvantages of PMRCs ae the unbalanced inducto cuents and capacito voltages at the esonant tanks. Moeove, the ciculating cuents at light loads and high component stesses ae some of the majo dawbacks [23]. n [24], clamped mode esonant convetes (CMRC) have been poposed. These convetes egulate the output voltage by contolling the pulse width of squae voltage acoss the esonant tank. The majo disadvantage of these type of convetes lies in the fact that each couple of switching elements have diffeent peak and RMS cuents. A futhe appoach is poposed in [19], whee the output voltage can be egulated by the utilization of a vaiable inducto in the esonant tank. The shotcoming of this appoach is the low efficiency due to the opeation at fa fom the esonance fequency. A classical type PRC opeating as a constant cuent souce at esonance fequency has been epoted in [25]. Refeence [26] offes anothe technique by employing a switched capacito at the esonant tank fo contolling the output voltage gain. A ecent appoach poposed by [27], is a pulse-width modulation (PWM) opeated seconday esonant tank (SRT) convete, which is compised of a conventional full-bidge PWM invete and a esonant tank connected at the seconday side of the tansfome. The voltage/cuent egulation is achieved by the closed-loop contol of the PWM geneato. As eviewed above, thee ae seveal methods fo achieving voltage and cuent egulation fo esonant convetes. The most commonly utilized technique, the fequency contol method, suffes fom the efficiency dop caused by the shap changes of the switching fequencies. Moeove, the design pocess is moe complicated since the switching fequency is not constant. Futhemoe, it is also woth mentioning that the output voltage egulation of esonant convetes ae claimed to be challenging. The majo easons fo this issue ae the load vaiations, the discontinuous and highly non-linea convete models and immeasuable state vaiables. Simila poblems also exhibit challenges in diffeent engineeing disciplines that can be ovecome with complicated techniques [28]. Thus, even adaptive contolles fo esonant convetes have been poposed in [29, 30]. As mentioned peviously, thee ae seveal poposed methods fo avoiding the fequency-contol technique, such as PMRCs, CMRCs etc. Howeve all of these techniques suffe eithe fom unbalanced cuents, deceased efficiencies o complex cicuity. Moeove, all of these

3 Constant fequency opeation of paallel esonant convete fo constant-cuent... techniques equie closed-loop contolles fo CC and CV phases. n contast to eviewed techniques, the poposed appoach in this pape utilizes two distinct inheent featues of the PRC fo achieving cuent and voltage egulation unde CC-CV chaging method. n this study, which is a moe compehensive and extended vesion of [31], the PRC is opeated unde two diffeent constant fequencies fo each chaging phase, eithe as a constant cuent souce (CCS) o a constant voltage souce (CVS). The poposed battey chage does not equie any complicated cicuity no complex contol appoaches. Moeove, this appoach diminishes the need fo closed-loop cuent / voltage contolles, when the input voltage stability is assued. Thus, the design of powe electonic unit and implementation pocess ae simplified. What is moe, the method offeed in this pape eliminates the disadvantage of the PRC, mentioned in [18], by opeating the PRC below esonance. 2 Theoetical backgound Buche et al. have investigated the steady-state chaacteistics of the PRC analyzed by seveal diffeent appoaches. They stated that thee diffeent types of solution appoach exist; exact time domain solutions, fist hamonic appoximation (FHA), and extended fist hamonic appoximation (e-fha). Thei study claimed the solutions deived by the exact time domain analysis to be vey accuate. On the othe hand, the FHA assumes that the inducto cuent and capacito voltage is sinusoidal, leading to inaccuate esults fo some opeation modes. Howeve, the e-fha assumes that only the inducto cuent is sinusoidal. Both FHA and e-fha esults ae acceptable fo switching fequencies above the esonance, wheeas the esults of the FHA ae not accuate fo discontinuous conduction mode (DCM) conditions [32]. n this study, the exact solutions of the PRC using state plane analysis (SPA) is investigated and biefly summaized. The analysis summaized hee is fo the full-bidge PRC topology including a tansfome with a tuns-atio of n ¼ 1. The details of the SPA can be found in [33, 34]. The full-bidge configuation of the PRC is illustated in Fig. 1. This cicuit can be epesented in a simple fom as V g S2 S4 S1 S3 L C n D5 D7 D6 D8 Fig. 1 Full-bidge PRC with high fequency tansfome L f C f R L V T C V C Fig. 2 Resonant tank educed to equivalent cicuit shown in Fig. 2. Please note that, the teminal voltage V T and teminal cuent T ae squae-waves with a magnitudes of V g and. The mathematical expessions deived fo the equivalent cicuit ae: d ðtþ L ¼V T V C ðtþ ð1þ dt dv C ðtþ C ¼ ðtþ T ð2þ dt Now, the cicuit paametes ae nomalized using the base values given in Table 1. The state equations in nomalized fom become: 1 dj L ðtþ ¼M T m C ðtþ ð3þ x 0 dt Table 1 Base values and nomalized paametes fo full-bidge PRC Paametes Value Base values Base impedance (X) p R base ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl =C Þ Base voltage (V) V base ¼ V g p Base cuent (A) base ¼ V g = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl =C Þ Base powe (W) P base ¼ Vg 2= p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl =C Þ p Base fequency (Hz) f base ¼ 1=2p ffiffiffiffiffiffiffiffiffi L C Nomalized paametes Nomalized load voltage M ¼ V=V base Nomalized load cuent Nomalized capacito voltage Nomalized inducto cuent Tank esonance angula fequency Tank esonance fequency Nomalized switching fequency Angula length of half switching peiod Diode conduction angle Tansisto conduction angle T J ¼ = base m C ðtþ ¼V C ðtþ=v base j L ðtþ ¼ ðtþ= base p w 0 ¼ 1= ffiffi ð L C Þ¼w base f 0 ¼ w 0 =2p F ¼ f s =f 0 c ¼ p=f a ¼ x 0 t a b ¼ x 0 t b

4 Taha Nuettin GÜCN et al. 1 dm C ðtþ ¼j L ðtþ J T ð4þ x 0 dt whee w 0 is the angula esonance fequency; M T and J T ae nomalized teminal voltage and teminal cuent values. The solutions of these diffeential equations ae: m C ðtþ ¼M T þðm C ð0þ M T Þcosðx 0 t /Þ þðj L ð0þ J T Þsinðx 0 t /Þ j L ðtþ ¼J T þðj L ð0þ J T Þcosðx 0 t /Þ ðm C ð0þ M T Þsinðx 0 t /Þ ð5þ ð6þ Using diffeential geomety techniques, the elationship of two impotant quantities V C and can be epesented geometically as a cicle centeed at the point (m C ¼ M T, j L ¼ J T ), as shown in Fig. 3. The adius of the cicle,, and / depend on the initial conditions. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðm C ð0þ M T Þ 2 þðj L ð0þ J T Þ 2 ð7þ V g V g V g L V T =V g Subinteval 3 T = L C V C <0 V g V T =V g T = V C >0 (a) Subinteval 1 (b) Subinteval 2 L V T = V g T = L C V C >0 V g V T = V g C T = V C <0 (c) Subinteval 3 (d) Subinteval 4 V T =V g V C =0 T = C V T = V g V C =0 (e) Subinteval 5 (f ) Subinteval 6 Fig. 4 Equivalent cicuit V g T = 2.1 Opeation modes Now that a geneal geometical solution fo the equivalent cicuit is obtained, solutions fo all subintevals of the cicuit can also be achieved. The PRC has 4 continuous conduction mode (CCM) and 2 additional DCM subintevals, depending on the states of the V C and Subinteval 1 The fist subinteval of CCM, shown in Fig. 4a, occus when the teminal voltage is V T ¼þV g and the teminal cuent is T ¼. n this mode, S2, S3, D6, D7 conduct and the capacito voltage is negative, V C \ Subinteval 2 The second subinteval of CCM, seen in Fig. 4b, occus when the teminal voltage is V T ¼þV g and the teminal cuent is T ¼þ. n this mode, S2, S3, D5, D8 conduct and the capacito voltage is negative, V C [ 0. j L j L (0) The thid subinteval of CCM, illustated in Fig. 4c, occus when the teminal voltage is V T ¼ V g and the teminal cuent is T ¼þ. n this mode, S1, S4, D5, D8 conduct and the capacito voltage is negative, V C [ Subinteval 4 The fouth subinteval of CCM, pesented in Fig. 4d, occus when the teminal voltage is V T ¼ V g and the teminal cuent is T ¼. n this mode, S1, S4, D6, D7 conduct and the capacito voltage is negative, V C \ Subinteval 5 (additional DCM Subinteval 1) The fifth subinteval is caused by the DCM opeation of the PRC unde heavy load. n this case, the inducto cuent, at the end of the fist subinteval is less than the teminal output cuent, T ¼. Thus, the tansition to Subinteval 2 cannot happen. Theefoe Subinteval 5 occus, whee capacito voltage, V C ¼ 0 and cuent i C ¼ 0 until the inducto cuent is chaged up to ¼. n this inteval, S2, S3 and all output diodes, D5-D6-D7-D8, conduct. This mode is epesented in Fig. 4e Subinteval 6 (additional DCM Subinteval 2) J T φ The sixth subinteval is the dual of the fifth subinteval. t occus duing the tansition fom Subinteval 3 to Subinteval 4. n this inteval, S1, S4 and all output diodes, D5-D6-D7-D8, conduct. t is illustated in Fig. 4f. 0 m C (0) M T m C Fig. 3 Nomalized state plane tajectoy fo cicuit in Fig. 1

5 Constant fequency opeation of paallel esonant convete fo constant-cuent State plane tajectoies fo CCM and DCM Since geometical solutions fo all subintevals ae obtained, they all can be intepeted in a single state plane tajectoy plot. n the CCM case, Subintevals 1 to 4 occu, whee each subinteval can be epesented as a cicle centeed at the teminal voltage and cuent values. The complete state plane tajectoy fo the CCM is illustated in Fig. 5. n case of DCM opeation, two moe additional subintevals ae obseved, whee the inducto cuent, is chaged up to the value of teminal output cuent, T. The complete state plane tajectoy fo the DCM is illustated in Fig. 6. The output voltage expessions of PRC can be deived paametically by using some aveaging techniques, esulting in the expessions fo CCM case given in (8) (10). M ¼ 2 c!! u sin u cos c 2 u ¼ accos cos c 2 þ Jsin c 2 u ¼þaccos cos c 2 þ Jsin c 2 j L!! 2 Fo above esonance Fo below esonance ð8þ ð9þ ð10þ j L (0) 1 1 j L 5 J L1 4 m C (0) whee u ¼ðb aþ=2. As it can be noticed, the value of u must be calculated fo solving the nomalized output voltage value. Since DCM and CCM tajectoies ae deived, the solutions impotant paametes, such as M, J, DCM bounday condition J cit, can be deived geometically. The DCM occus fo J [ J cit, whee J cit is expessed as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J cit ¼ 1! u 2 2 sin c þ t sin c þ 1 ðsin cþ2 ð11þ 2 4 +J +J L1 6 J Fig. 6 State plane tajectoies fo DCM m C J L1 +J The equations fo the DCM solution ae:! M ¼ 1 þ 2 ðj dþ c ð12þ m C b þ d ¼ c cosða þ bþ 2cos a ¼ 1 ð13þ ð14þ j L (0) 4 m C (0) J J L1 2sin a sinða þ bþþðd aþ ¼2J ð15þ Using these fomulas, complete output chaacteistics of the PRC is obtained as illustated in Fig. 7. These output chaacteistics descibe the elationship between J and M fo diffeent values of F. The solid lines epesent the CCM, wheeas the dashed lines epesent the DCM. Fig. 5 State plane tajectoies fo CCM

6 Taha Nuettin GÜCN et al. Nomalized load cuent J F 0.6F 0.7F 0.8F 0.9F 1.0F 1.1F 1.2F DCM-mode CCM-mode Table 2 Base values and nomalized paametes fo diffeent PRC topologies Topology Base voltage V base qffiffiffiffi Full-bidge without tansfome V g Full-bidge with 1:n tansfome, esonant tank on pimay side Half-bidge with 1:n tansfome, esonant tank on pimay side nv g nv g 2 Base impedance R base L C ffiffiffiffi qffiffiffiffi ¼ n 2 L C 00 C ffiffiffiffi qffiffiffiffi ¼ n 2 C 00 L C F 2.0F 1.3F Nomalized load voltage M Fig. 7 Exact output chaacteistics of PRC 3 Poposed method 3.1 Basic infomation on poposed method n Fig. 7, it is seen that opeation at F ¼ 1:0 esults in a staight output cuve fo M 0:3 bounday. This means that, within this bounday the PRC can act as a CCS with a nomalized output cuent of J ¼ 1. A second impotant featue is obseved fo opeation at half esonance fequency F ¼ 0:5, whee the putput cuve is appoximately a staight vetical line fo J 1:5 bounday. Thus, it can be concluded that the PRC opeates as a CVS supplying a nomalized output voltage of appoximately M ffi 1. Consideing these two distinct featues, it can be infeed that the PRC can be easily designed fo CC-CV chaging by utilizing thei inheent chaacteistics. Basically, the PRC is opeated at esonance fequency, F ¼ 1:0, fo CC chaging mode, while it needs to be opeated at half esonance fequency, F ¼ 0:5, fo CV chaging mode. 3.2 Designing PRC The fist step of the design pocedue is to detemine the maximum chaging cuent (the constant cuent value in CC phase), max, and the maximum chaging voltage (the constant voltage value in CV phase), V max. n ode to figue those out the data-sheet of the battey should be efeed Detemining esonant tank elements n the theoetical backgound section a bief analysis fo the full-bidge PRC topology with n ¼ 1 tansfome tuns atio was given. Fo diffeent PRC topologies, the base voltage and base impedance values should be alteed so that the peviously deived SPA solutions in nomalized fom emain the same. Base values fo common PRC topologies ae given in Table 2. t should also be pointed out that if a tansfome is employed, the base impedance is calculated accoding to the paametes of esonant tank efeed to the seconday side. The paametes and C00 ae the values of esonant tank elements efeed to the seconday side of the tansfome. n this study, a low powe application example is included in the last section. Theefoe, it is aimed to build a test setup with half-bidge topology in ode to decease the numbe of components and the cost of the chage cicuit. Thus, the fomulas given in this section ae obtained using ffiffiffiffi the base values V base ¼ nv g 2 and R base ¼. Fo this case C 00 the nomalized output voltage is expessed by: M ¼ V max ¼ 2V max ð16þ V base nv g The maximum voltage is achieved and maintained at CV chaging phase, whee F ¼ 0:5 and M ¼ 1:0. By eaanging (16) fo CV chaging mode, the necessay tansfome tuns atio can be obtained by (17). n ¼ 2V max MV g ¼ 2V max V g ð17þ Now, it is necessay to detemine the values of othe quantities fo obtaining the desied output cuent at CC chaging mode. The expession fo nomalized output cuent is given in (18). J ¼ max base The base cuent value is: base ¼ V base ¼ nv g ffiffiffiffi R base 2 C 00 Using (18) and (19): ð18þ ð19þ

7 Constant fequency opeation of paallel esonant convete fo constant-cuent... 2 max J ¼ ffiffiffiffi nv g C 00 ð20þ The maximum cuent, max, is achieved at CC chaging phase, whee F ¼ 1:0 and J ¼ 1:0. Now, the chaacteistic p impedance fo the esonant tank, R 0 ¼ ffiffiffiffiffiffiffiffiffiffiffiffi =C00, can be calculated. sffiffiffiffiffi R 0 ¼ ¼ njv g ¼ nv g ð21þ C 00 2 max 2 max Using (21) the value of chaacteistic impedance fo obtaining the desied output cuent at CC chaging phase is detemined. And then, one of the esonant tank elements needs to be chosen and the othe can be calculated fom the value of R 0. Mostly, a commecially available capacito is selected and then the equied value of the inducto is calculated. The esonance fequency is calculated as: 1 f 0 ¼ p 2p ffiffiffiffiffiffiffiffiffiffi ¼ C00 1 2pC 00 R 0 ð22þ f the esonance fequency is not suitable fo application, it can be adjusted by changing the values of the esonant tank elements. When a suitable capacito value and esonance fequency is achieved, the equied inductance value is calculated as follows: ¼ C00 R2 0 ð23þ Using these equations, the most cucial elements of the PRC ae detemined. The design steps explained in this section ae biefly summaized as a flowchat in Fig Choosing components One big advantage of the SPA is that the peak voltage & cuent values of the esonant tank inducto & capacito Choose max and V max Detemine n using (17) Detemine C to L atio o R 0 using (21) Choose an appopiate capacito value Check the esonance fequency using (22) f 0 easonable? Y Detemine the equied inductance using (23) Final design achieved Fig. 8 Flowchat showing design steps N Design high fequency tansfome Design inducto can be detemined fom the state plane tajectoies given in Fig. 5 and Fig. 6. f a solution fo the steady state values of the PRC has aleady been obtained, the peak values can be easily detemined using basic tigonometic pinciples. Since the details of the solutions can be found in [33] and [34], only the final solutions ae given below. Fo the CCM case the peak component stesses ae: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M CP ¼ ðm C ð0þþ1þ 2 þðj J L ð0þþ 2 1 J L ð0þ [ J ð24þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1 þðj L 1 JÞ 2 þ 1 J L ð0þ\j ð25þ M CP J LP ¼J L ð0þ M C ð0þ\1 and J L ð0þ [ 0 ð26þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J LP ¼J þ ðj L 1 JÞ 2 þ 1 M C ð0þ [ 1oJ L ð0þ\0 ð27þ whee M CP and J LP ae the nomalized peak capacito voltage and inducto cuent values, d ¼ c b (in DCM), J L ð0þ and M C ð0þ ae shown in Fig. 5 and Fig. 6. Fo the DCM case the peak component stesses can be expessed as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M CP ¼ ðm C ð0þþ1þ 2 þðj J L ð0þþ 2 1 J L ð0þ [ J ð28þ M CP ¼2 J L ð0þj ð29þ J LP ¼J L ð0þ c d\p=2 ð30þ J LP ¼J þ 1 c d p=2 ð31þ Using (24) to (31) the components can now be detemined. 3.3 Effect of tansfome on esonant tank A high fequency tansfome is often employed in esonant convete applications fo poviding galvanic isolation and adjusting the voltage and cuent levels. Geneally, the esonant tank is connected to the pimay side of the tansfome as shown in Fig. 9. Since the tansfome intoduces new elements to the esonant tank, it might be doubted whethe a PRC can exhibit close to the ideal chaacteistics o not. n this section, the effect of tansfome is investigated. A moe detailed intepetation of the influence of the tansfome can be found in [35]. Figue 9 illustates the equivalent cicuit of the esonant tank efeed to the seconday side, whee the tansfome model is compised of leakage and magnetizing inductances. As seen, the esonant tank now has moe elements compaed to the peviously analyzed ideal case. n the ideal PRC, the esonant tank consists of two elements and the output ectifie of the PRC is diven with the voltage of the

8 Taha Nuettin GÜCN et al. + V + V L C L L p L s C esonant capacitance, C. On the othe hand, the opeation of the esonant tank might be influenced due to significant inductances intoduced to the esonant tank cicuit. n ode to pevent the tansfome fom influencing the opeation of the PRC, thee ae two conditions that should be ensued. Fistly, the magnetizing inductance, L m, of the tansfome must be elatively high compaed to the esonant inductance, L, so that the esonance fequency of L m and C ae vey low compaed to esonance fequency of PRC, w 0. n this case, it can be assumed that almost no cuent is dawn by L m at the opeation fequency of PRC. Secondly, the leakage inductances, L p and L s, must be vey small compaed to L. Howeve, it might be an impossible task to achieve a tansfome design with high magnetizing inductance and vey low leakage inductances. Theefoe, it is pobable that the opeation of the PRC is influenced in this configuation, whee the convete would actually act moe like an LLC esonant convete. Fo the facts mentioned above, it is poposed to connect the esonant tank to the seconday side of the tansfome, as shown in Fig. 10. n this aangement, the magnetizing inductance is again equied to be elatively high so that it daws a minimum amount of cuent. Theefoe, it can be assumed that all the cuent flowing though the leakage inductances is also flowing though the esonant inducto. L m 1: n Fig. 9 Effect of tansfome when esonant tank is connected to pimay side + V + V 1: n L C L = n 2 L p + L s +L L =n 2 p L p L s L C L m Fig. 10 Effect of tansfome when esonant tank is connected to seconday side Consequently, the magnetizing inductance can be neglected. With this assumption, it can be seen that the leakage inductances ae connected in seies with the esonant inductance and the output ectifie of the PRC is diven by the esonant capacito voltage. This case is much moe simila to the ideal case, when compaed to the configuation given in Fig. 9. n fact, when the leakage and esonant inductance consideed to act as a single inducto, the equivalent cicuit is now same as the ideal case. Thus, the esonant tank is expected to opeate in the same manne with the ideal case. Moeove, it can be seen that the leakage inductances also contibute to the esonant inductance. Consequently, the total value of the esonant inductance efeed to the seconday side becomes: ¼ n2 L p þ L s þ L ð32þ t is also woth mentioning that the peak component stesses, given in (24) to (31), ae now changed. The voltage values should be multiplied by n, wheeas the cuent values should be divided by n. 4 Expeimental veification The pinciples of the poposed method ae veified using two pototypes. While the fist pototype does not involve a high fequency tansfome, the second pototype is built to veify that the PRC with an high fequency tansfome also opeates in the same manne. Two pototypes, shown in Fig. 11, use the same cicuity with the exception of the esonant tank and tansfome. Both setups aim to chage a 12 V 7 A battey module, Yuasa NP7-12 lead-acid battey. Using the datasheets, the max and V max values ae detemined to be 1.75 A and 14.7 V. Accoding to the datasheet, the chaging is completed when the cuent dops down to 0.5 A duing CV phase. t should be noted that, due to the paasitic esistances in the cicuit, the output chaacteistics cuves in Fig. 7 might be slightly defomed [36]. n this case, the cuve at half esonance might not be a vetically staight line anymoe. As the output cuent deceases, the voltage dops on the paasitic esistances decease and consequently the output voltage slightly inceases. Thus, the output voltage in the CV chaging mode slightly inceases as the powe deliveed to the battey deceases. Theefoe, a tansition voltage fom CC to CV phase, V tansition \V max, should be chosen consideing the effects mentioned above. Fo the expeimental setups V tansition is chosen to be 14 V. The PRC is built by using half-bidge topology. A digital contolle is used fo poducing PWM and detecting battey voltage to shift fequency fom esonance fequency, to half-esonance fequency. Only using two PWM

9 Constant fequency opeation of paallel esonant convete fo constant-cuent... DC supply Resonant inducto cuent ) ( Half-bidge paallel esonant convete Digital contolle pins and a single ADC pin ae enough fo this poposed method. The battey voltage is measued by linea optocouple in ode to sepaate powe gound and the contolle. The esonant inductance is wound by twisted litz wie. Theefoe, eddy cuent effects such as the poximity effect and skin effect ae minimized [37]. This inductance and the esonance capacito have high ac voltage ating, low ESR and high dv/dt toleance. The value of filte inductance is 0.8 mh, which is designed fo half-esonance fequency. Thus, the size and losses of filte inductance might be elatively high. The design paametes of the expeimental setups ae calculated and shown in Table Fist expeimental setup Resonant capacito voltage(v C ) Fig. 11 Schematic of expeimental setup Battey cuent A Battey V voltage Battey The fist setup does not involve a tansfome fo the sake of simplicity. Thus, it is consideed that n ¼ 1 and the input voltage is adjusted to be able to supply the desied output voltage. n spite of this fact, the idea is the same and the poposed technique can be confimed. Output cuent (A) Output voltage (V) Efficiency Time (min) Fig. 12 Results fo fist expeimental setup max and V max wee peviously chosen fom battey datasheet. Consideing the voltage dops on the diodes ( V) and paasitic esistances (not much effective in this setup), V max is inceased to be 16.2 V in ode to ensue the maximum output of the convete to be 14.7 V. The esults fo this setup ae pesented gaphically in Fig. 12. t is obseved that PRC opeated vey well in the CC chaging mode, as the output cuent is accuately fixed to 1.75 A. n the CV chaging phase, the output voltage value is inceased fom V tansition =14 V to V max =14.65 V while the output cuent deceased as pedicted. The efficiency vaies fom 86% to 93%. The total chage tansfeed to the battey is nealy 4.95 A. The wavefoms of esonant tank elements ae pesented in Fig. 13. The chage mainly stays within the CCM boundaies at CC mode, wheeas it opeates within the DCM boundaies at CV mode. Table 3 Pedetemined and calculated design paametes of expeimental setups Paametes Value Fist setup Second setup n (Pedetemined) n = 1 (no tans.) n = 40/45 V max (Pedetemined) 16.2 V V max (Pedetemined) 1.75 A 1.80 A V g ¼ 2Vmax n (17) 32.4 V 37 V R 0 ¼ nvg 2 max (21) C (Chosen) nf nf f 0 ¼ 1 (22) 2pR 0C khz khz ¼ C00 R2 0 (23) 38.1 lh 37.1 lh L L ¼ =n2 ¼ 38:1lH L ¼ n2 L p L s ¼ 27 lh

10 Taha Nuettin GÜCN et al. V ds1 V ds1 (5 A/div), V C (20 V/div) V C Time (5 μs/div) (a) At the end of CC phase, =1.75 A and V C =14 V V ds1 (10 V/div) (2 A/div) V ds1 (10 V/div) (2 A/div) Time (10 μs/div) (a) At the end of CC phase, =1.75 A and V ds1 =14 V V ds1 Time (10 μs/div) (c) At the end of CV phase, =0.5 A and V ds1 =14.63 V V ds1 (10 V/div) (2 A/div) Voltage (500 mv/div) Cuent (2 A/div) Time (10 μs/div) (b) At the beginning of CV phase, =1.75 A and V ds1 =14 V Output cuent Signal Output voltage Tansition fom CC chaging to CV chaging Time (100 ms/div) (d) Tansition fom CC chaging to CV chaging, whee =1.75 A, V ds1 =14 V (5 A/div), V C (20 V/div) (5 A/div), V C (20 V/div) V C Time (10 μs/div) (b) At the beginning of CV phase, =1.75 A and V C =14 V V C Time (10 μs/div) (c) At the end of CV phase, =0.5 A and V C =14.63 V Fig. 13 Wavefoms of and V C fo fist expeimental setup Fig. 14 Relationship between V ds1 and fo demonstating soft switching featue As it can be seen, while ZVS tun-on can be obseved in both CC and CV chaging modes, ZCS tun-off can be obseved in late phases of CV chaging mode as the output cuent deceases. Lastly, the output wavefoms of the cicuit duing the tansition fom CC to CV mode ae pesented in Fig. 14d, whee the CH2 signal denotes the time that the switching fequency is changed fom esonance fequency, x 0, to half esonance fequency x 0 =2. As shown in Fig. 14d, a vey smooth tansition fom CC to CV chaging is achieved. The most of the losses ae caused by the diodes of the output ectifie. As an LC filte is employed at the output, the diodes ae always conducting. Moeove, the voltage dops on the diodes ae constant and they ae significant in applications with low voltage output. Thus, although the efficiency values ae good, they can impove emakably if the uncontolled output ectifie is eplaced by a synchonous ectifie cicuit at the output, especially fo low voltage applications. As it can be seen fom the esults, the voltage in CV phase slightly inceased, as the quality facto Q ¼ R=R 0 apidly changes. This is due to paasitic esistance in the cicuit, which ae mostly caused by inductances (esonant inductance and filte inductance). Howeve, despite the fact that chaging voltage inceased in CV phase, the chage was able to gadually decease the chaging cuent as equied. The soft switching featue of the PRC can be obseved in Fig. 14, whee the dain-to-souce voltage of the MOSFET and cuent of the esonant inducto illustated.

11 Constant fequency opeation of paallel esonant convete fo constant-cuent Second expeimental setup with tansfome Fo the DC-DC convetes, high fequency tansfomes ae of majo impotance since they ensue isolation and ability to change voltage and cuent levels. The second pototype is built in ode to confim whethe the PRC exhibits same chaacteistics when a high fequency tansfome is included. The second expeimental setup is pesented in two vesions. n the fist vesion, no feedback contolle is implemented. On the othe hand, the second vesion includes a feedback contolle with hysteesis contol algoithm, which is utilized only in CV chaging phase, so that a moe stict CV phase can be achieved. Fo this setup a tansfome with a tuns atio of n ¼ 40=45 is wound. The tansfome has the following paametes; L p ¼ 6:38 lh, L s ¼ 5:12 lh and L m ¼ 266 lh. Consideing the additional voltage dops acoss paasitic esistances of tansfome (nealy 0.3 X) will cause the output values to decease, V max is inceased to V and max is chosen to be 1.80 A due to fact that these esistances cause a decease of the output cuent. Since a tansfome with a pedetemined tuns atio is utilized, the input voltage of the PRC is adjusted accoding to (17). Using the pedetemined values the design paametes ae calculated as in Table Open loop opeation The esults of this test ae illustated in Fig. 15. t can be seen that PRC opeated again vey well in the CC chaging mode, as the output cuent is accuately fixed to 1.74 A. Howeve, in the CV chaging phase, the output voltage value is inceased fom V tansition ¼ 14 V to V max ¼ 14:73 V. Despite this fact, the cicuit was able to decease the output cuent as pedicted. The efficiency vaies between 78% and 88%. The chage mainly stays within the CCM boundaies at CC mode, wheeas it mainly opeates within the DCM boundaies at CV mode, as seen in Fig 16. The total chage tansfeed to the battey is nealy 4.55 A. The eason fo the less efficiency values ae due to the losses in the tansfome. The calculated esistance of the tansfome ae consideably high. t is obseved that the tansfome caused a nealy 8% dop in the efficiency. The PRC in the second expeiment also have moe voltage incease in CV phase. This is again caused by the exta paasitic esistances intoduced to the cicuit by the tansfome. n spite of that, the chage again achieved to decease the chaging cuent. Fo ensuing isolation with highe efficiency values, the opeating fequency should be inceased. This will decease the sizes of the inductos, Output cuent (A) Output voltage (V) Efficiency Time (min) Fig. 15 Results fo second expeimental setup capacitos and tansfome, which will also educe the esistances intoduced by these elements. Thus, the PRC can opeate close to the ideal chaacteistics at highe switching fequencies (also valid fo the fist setup as well) Utilizing contolle fo CV chaging phase n the pevious setups it has been demonstated that the poposed battey chage does not need any contolle at CC chaging phase, as the cuent supplied at esonance fequency emained constant. On the othe hand, thee is a voltage incease in CV chaging phase, as explained peviously. Although the convete does not exceed the pedefined maximum chaging voltage, a moe stict CV chaging phase might be equied fo some applications. Thus, it is aimed to epesent such a case by incopoating a contolle to adjust the switching fequency of the convete to nea half esonance fequency in ode to supply a constant chaging voltage in CV phase. Fo this pupose, a hysteesis contol algoithm is implemented while the est of the expeimental setup emains the same. Fo this case, a tansition voltage is not necessay, so that the tansition fom CC to CV phase will occu when the battey voltage is equal to 14.7 V. Aftewads, the implemented algoithm will keep the voltage aound 14.7 V fo the est of the CV chaging peiod. The esults ae shown at Fig. 17. The total chage tansfeed to the battey is nealy 4.49 A. The esults show that the contolle was able to achieve a constant voltage output at CV chaging phase by adjusting the switching fequency fom khz to khz. The egulation of the switching fequency is nealy 2.25% of the esonance fequency, which is quite small.

12 Taha Nuettin GÜCN et al. (5 A/div), V C (20 V/div) (5 A/div), V C (20 V/div) (5 A/div), V C (20 V/div) V C Time (5 μs/div) (a) At the end of CC phase, =1.75 A and V C =14 V V C Time (10 μs/div) (b) At the beginning of CV phase, =1.74 A and V C =14 V V C Time (10 μs/div) (c) At the end of CV phase, =0.5 A and V C =14.75 V Fig. 16 Wavefoms of and V C fo the second expeimental setup Output cuent (A) Output voltage (V) Efficiency Fequency (khz) Time (min) Fig. 17 Results fo second expeimental setup with contolle at CV phase 5 Conclusion n this study, a simple design and contol appoach fo CC-CV chaging application of PRC was pesented. The PRC was opeated at two diffeent fequencies, which ae F ¼ 1:0 and F ¼ 0:5, as CCS and CVS, espectively. Thus, the need fo closed-loop contolles with the pupose of output cuent and voltage egulation wee eliminated. The electical design of the chage and implementation pocedue wee simplified. The output filte design was also simplified due to the constant fequency opeation. Shap changes of switching fequency, which is claimed to decease the oveall efficiency, ae avoided. The numbe of equied components and elated costs wee deceased. What is moe, the opeation of the PRC at half esonance fequency inheently constitutes an output voltage limitation at no load condition. Futhemoe, the poo pefomance of the PRC in CV chaging phase, as claimed by the study [18], was also avoided by opeating the PRC at half esonance fequency, in DCM. The pefomance of the poposed cicuit is evaluated with two expeimental setups. t is shown that the designed pototypes opeate at easonably good efficiency values: the fist setup achieves efficiency values between 86% and 93%, while the efficiency values of the second setup ae found to be in the ange of 78%-88%. Moeove, it is also shown in Fig. 14d that the tansition fom CC to CV chaging do not esult in any kind of oscillations.

13 Constant fequency opeation of paallel esonant convete fo constant-cuent... The esults appove the validity of the poposed method, as the designed chages ae able to opeate without closed loop contolles fo a wide ange of load values in both CC and CV chaging phases. The designed chages ae able to supply a constant cuent output, which ae well fixed to nealy 1.75 A. t is shown that high paasitic esistances in the cicuit affects the pefomance especially in CV phase, whee a nealy 0.7 V incease is obseved. Despite this fact, the poposed chage is able to educe the chaging cuent to 0.5 A in CV phase, as desied. Although the esults ae quite good, an expeimental setup with a contolle at CV phase is also pesented fo compaison with open-loop opeation. n this setup it is shown that the convete is able to assue a constant output voltage with a little amount of fequency adjustment, which coesponds to a change of nealy 2.25% of the esonance fequency. On the othe hand, pecautions must be taken in the design pocess, since the poposed chage equies input voltage stability fo achieving constant voltage/cuent output, when no contolle is employed. Moeove, the values of esonant tank elements, L and C, have a diect effect on the output cuent value in CC phase. Additionally, the voltage incease in CV phase is caused by the paasitic esistances in the cicuit. The CV tacking pefomance of the cicuit can be impoved by inceasing the esonance fequency of the convete fo deceasing the sizes of magnetic elements and thei paasitic esistances. The majo loss mechanism of the pesented low voltage output expeiments ae caused by the voltage dops on the ectifie diodes. This is due to fact that the diode voltage dops ae elatively lage in low voltage output chage cicuit. Thus, employing a synchonous ectifie cicuit at the output would incease the oveall efficiency. n contast to low voltage chages, the diode voltage dops ae not a big concen fo high voltage chage applications, whee the efficiency of the poposed chage cicuit is expected to incease damatically. Open Access This aticle is distibuted unde the tems of the Ceative Commons Attibution 4.0 ntenational License ( ceativecommons.og/licenses/by/4.0/), which pemits unesticted use, distibution, and epoduction in any medium, povided you give appopiate cedit to the oiginal autho(s) and the souce, povide a link to the Ceative Commons license, and indicate if changes wee made. Refeences [1] Chuang YC, Ke YL, Chang SY (2009) Highly-efficient battey chages with paallel-loaded esonant convetes. n: Poceedings of EEE industy applications society annual meeting, Houston, USA, 4 8 Octobe 2009, 10 pp [2] Schalkwijk WAV, Scosati B (2002) Advances in lithium-ion batteies. 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