Index Terms Current stress, Dual active bridge (DAB), Particle swarm optimization (PSO), Triple phase shift (TPS).

Transcription

1 Generic Closed Loop Conroller for Regulaion in Dual Acive Bridge DC/DC Converer wih Curren Sress Minimizaion O. Hebala, A.A. Aboushady, K.H. Ahmed, I. Abdelsalam Absrac This paper presens a comprehensive and generalized analysis of he bidirecional dual acive bridge (DAB) DC/DC converer using riple phase shif (TPS) conrol o enable closed loop power regulaion while minimizing curren sress. The key new achievemens are: a generic analysis in erms of possible conversion raios/converer volage gains (i.e. Buck/Boos/Uniy), per uni based equaions regardless of DAB raings, and a new simple closed loop conroller implemenable in real ime o mee desired power ransfer regulaion a minimum curren sress. Per uni based analyical expressions are derived for converer AC RMS curren as well as power ransferred. An offline paricle swarm opimizaion (PSO) mehod is used o obain an exensive se of TPS raios for minimizing he RMS curren in he enire bidirecional power range of -1 o 1 per uni. The exensive se of resuls achieved from PSO presens a generic daa pool which is carefully analyzed o derive simple useful relaions. Such relaions enabled a generic closed loop conroller design ha can be implemened in real ime avoiding he exensive compuaional capaciy ha ieraive opimizaion echniques require. A deailed Simulink DAB swiching model is used o validae precision of he proposed closed loop conroller under various operaing condiions. An experimenal prooype also subsaniaes he resuls achieved. Index Terms Curren sress, Dual acive bridge (DAB), Paricle swarm opimizaion (PSO), Triple phase shif (TPS). I. INTRODUCTION DUAL acive bridge (DAB), originally proposed in he 199s [1], significanly araced researchers among several bidirecional DC/DC converers [2] such as dualflyback, dual-cuk, Zea-Sepic, forward-flyback, dual-pushpull, push-pull-forward, push-pull-flyback and dual-halfbridge. This is mainly due o is high power handing capabiliy, zero volage swiching (ZVS) characerisics, high power densiy, galvanic isolaion in ransformer based versions and he possibiliy of cascaded or modular configuraion o enable higher power/higher volage designs [3-7]. Due o hese advanages, DAB DC/DC converers have araced more aenion in power energy conversion applicaions, such as dc microgrids, medium volage dc (MVDC) and high volage dc (HVDC) ransmission sysems [8-1]. In addiion, DAB DC/DC converers have been widely used in disribued generaing sysems incorporaing variable-naure energy resources, such as PV or wind, for volage maching/sepping and accommodaing power regulaion beween energy sorage sysems, energy sources and load demands [11-14]. Sudies have been on going o analyze, conrol and improve he overall performance of he DAB converer. Phase shif conrol echniques are he mos common modulaion schemes in lieraure due o heir implemenaion simpliciy, fundamenal frequency operaion which reduces swiching losses, uniform conducion of swiching devices, enabling of ZVS operaion and non-acive power circulaion conrol wihin converer [2, 3, 14]. The convenional phase shif (CPS), or single phase shif (SPS), was he firs proposed echnique [1] where he phase shif angle beween he wo acive bridges conrols he power flow. Then, dual phase shif (DPS) modulaion echnique was inroduced in [15] by adding he same inner phase shif o he bridge volages o overcome he phenomenon of backflow power ha appeared when using CPS. Exended phase shif (EPS) was proposed [16] in order o exend he ZVS range of he DAB converer, by conrolling he duy cycle of one of he bridge volages. The above menioned modulaion echniques (SPS, DPS and EPS) share a common drawback which is no exploiing all possible conrol variables which resuls in reduced efficiency of DAB operaion. In his regard, Triple phase shif (TPS) [17-19] inroduces an addiional conrol variable which can lead o furher improvemen of ZVS range and reducing he overall losses hence increasing he efficiency. TPS conrol uilizes he phase shif angle beween he bridges in addiion o inner phase shifs a boh bridges separaely which makes TPS he mos general modulaion conrol (hree degrees of freedom) [2]. A full performance analysis of DAB under TPS conrol as well as deailed analyical derivaions and operaional consrains for all possible swiching modes were presened in [2, 21] where he volage conversion is no included in he proposed model which is a major drawback. Considering he aforemenioned lieraure, generalized per uni TPS-based DAB model including he converer volage conversion raio is overlooked. Currenly, here is a srong rend oward improving he DAB DC/DC converer efficiency while mainaining he power ransfer flow conrol. Differen echnical aspecs can be considered for minimizing overall DAB losses such as nonacive power losses [22, 23] and curren sresses [16,18,24, 25]. Non-acive power loss minimizaion was ackled in [22] for DAB where he inducor curren was analyzed o obain an operaing range where phase shifs achieving minimum nonacive power loss can be realized for ligh and heavy loads in boos operaion. However he model was based on he exended phase shif (EPS) modulaion echnique which resul in local opimal operaing poins a ligh loads. An ieraive algorihm has been proposed in [23] o search for TPS conrol variables ha saisfy he desired acive power flow while achieving minimum reacive power consumpion. The proposed conroller works in an open loop approach wih no feedback informing wheher acual desired power level is achieved or no. In

2 addiion, he mehod is no generalized for buck and boos DAB operaing modes. Auhors in [24] used Lagrange Muliplier mehod o calculae he opimal phase shif raios for any given power level argeing minimum curren sresses defined as RMS inducor curren. However, he hree proposed converer swiching modes do no cover he enire bidirecional power range bu only cover operaion from -.5 o 1 pu, herefore he proposed scheme canno be considered universal. An analyical mehod based on Karush-Kahn-Tucker mehod was developed in [18] o ge he global opimal conrol parameers achieving minimum RMS curren sresses for DAB under a modified TPS conrol where he ouer phase shif beween he fundamenal componens of bridges volage is inroduced. However, he analysis is based on fundamenal frequency analysis where he square bridge volages of he DAB are replaced by he fundamenal frequency componens. This ignores he effec of higher order harmonics on effecive increase of RMS curren. In oher cases, he researchers focused on minimizing he per uni peak curren in [16] and [25]. Considering he aforemenioned lieraure, RMS inducor curren can be considered o be he mos effecive amongs oher minimizaion objecives such as non-acive power loss, peak or average inducor curren. This is due o he fac ha RMS curren sresses have a direc impac on he conducion losses which are considered o be he dominan porion of losses [26, 27]. In addiion, conducion and copper losses are proporional o he square of he RMS curren [28]. Now, i is a quie clear from lieraure ha he shorcomings in previous DAB curren opimizaion researches can be summarized as follows: non-generalized per uni analysis, discarding he effec of converer volage gain wih bidirecional power flow, cumbersome analysis in some cases, achieving local minimal soluions in some cases due o resricing opimizaion o a specific conrol echnique or load range and finally impracicaliy of some derived conrollers for real ime implemenaion. I is obvious ha no work has compleely ackled all challenges simulaneously and mos imporanly wihou compromising on level of conrol complexiy and implemening opimizaion in real ime. This paper has idenified his research gap herefore proposing an all-round universal soluion o he menioned shorcomings. The paper comprises 7 secions. Secion 2 covers he generalized per uni DAB model under TPS conrol. Secions 3 and 4 presen he offline opimizaion process ha was carried ou by applying PSO o he derived per uni DAB model o obain he global opimal phase shif raios for minimizing RMS curren a full power range for differen converer volage gains. The oucome from he opimizaion process is a generalized relaion beween desired power ransfer and he opimal phase raios as a funcion of he volage conversion raio. This generalized relaion is used for designing a novel simple closed loop conroller which is discussed in deail in secion 5. Aferwards, Simulaion resuls using he proposed closed loop conroller are presened in secion 6. Finally, secion 7 presens a low scaled experimenal prooype which confirms he simulaion resuls. II. GENERALIZED PER UNIT ANALYSIS OF DAB UNDER TPS CONTROL The DAB circui diagram is presened in Fig. 1. Transformerless version is sudied in his paper o simplify analysis which will no change if ransformer is insered as magneizing inducance is usually negleced and equivalen leakage inducance plays he same role as inerface inducor L in Fig. 1. Fig. 2 shows he ypical AC volage/curren waveforms of DAB under TPS conrol. D 1, D 2 and D 3 are he hree phase shif raios obained using classical phase shifing of gae signals S 1-S 4 and Q 1-Q 4 such ha D 1 1, D 2 1, 1 D 3 1. The raios are normalized wih respec o half he swiching cycle (T h). The raio D 1 represens he pulse widh of he firs bridge volage waveform (v br1), and similarly, raio D 2 represens he pulse widh of he second bridge volage waveform (v br2). Raio D 3 is he phase shif beween posiive going edge of v br1 and posiive going edge of v br2. Based on all possible combinaions beween D 1, D 2 and D 3 ha would resul in differen inducor curren waveforms in he bidirecional power range, a oal of welve swiching modes can be derived. The welve operaing modes are generically considered in his paper and heir ypical operaing waveforms are illusraed in Table I. A facor K is used o describe he volage conversion raio (or converer volage gain) where K=V dc2/v dc1 and K<1 represens buck/boos mode. In he proposed generalized DAB analysis, all expressions derived are funcion of (D 1, D 2, D 3 and K). For generalized per uni analysis, base values are seleced as volage V base=v dc1, impedance Z base=8f sl where f s is he swiching frequency and ime of T h (half period). I dc1 S 1 S 3 Q 1 Q 3 R ac L V dc1 C 1 v br1 v br2 C 2 D 3 T h S 2 Bridge 1 Bridge 2 S 4 Fig. 1. DAB Circui Diagram. Fig.2. Examples of volage and currens waveforms for TPS conrol: Forward (ve) power flow, and Reverse (-ve) power flow. A. Transfer Characerisic DAB converer s equivalen circui model is shown in Fig. 3. Average power ransferred by he DAB converer can be calculaed a eiher bridge by assuming a lossless inducor. Per uni power for each mode is presened in Table I which is obained from (1) wih piecewise consideraion of he volage Q 2 Q 4 I dc2 V dc2

3 and curren waveforms over half he period. The operaional consrains for each mode in Table I are applied o he derived power equaions and he power ranges associaed wih he modes are herefore achieved. T h P = 1 v T br1 (). ()d (1) h Fig. 3. DAB equivalen circui. B. RMS Inducor Curren Taking I base=v base/z base, he normalized posiive half cycle curren insans for each mode are shown in Table II o be used for power and RMS curren calculaions. A generalized expression for squared RMS inducor curren can be developed from (2) by examining he waveforms of inducor currens in he welve swiching modes shown in Table I. RMS 2 = 1 T h T h i 2 L () d (2) Considering inducor curren half-wave symmery hen RMS2 is achieved from (2) as oulined by (3). Consequenly, RMS curren can be calculaed by subsiuing he ime insans ( 1, 2, 3, 4) from Table I and curren insans from Table II ino (3). RMS 2 (K, D 1, D 2, D 3 ) = 1 3 { ( )2. ( ) ( 1 ) 2. ( 2 ) ( 2 ) 2. ( 1 3 ) ( 3 ) 2. ( 2 1) ( ). ( 1 ). ( 1 ) ( 1 ). ( 2 ). ( 2 1 ) ( 2 ). ( 3 ). ( 3 2 ) ( ). ( 3 ). ( 1 3 ) } (3) III. PROPOSED CURRENT STRESSES MINIMIZATION ALGORITHM A. Formulaion of he Minimizaion Problem In his paper, he minimizaion objecive is he squared RMS inducor curren obained from (3). Mahemaical formulaion of he proposed muli-consrained minimizaion problem is given as follows: Minimize (for given K) Subjec o br1 Obj. Fun. = RMS 2 (K, D 1, D 2, D 3 ) (4) Equaliy consrain: P = 1 T h v T br1 (). ()d h And he inequaliy consrains: D 1 1, D 2 1, 1 D 3 1 where 1 18º Operaional consrains of each swiching mode (see Table I) B. Opimizaion Technique Due o is capabiliy o handle muli-consrain opimizaion problems, paricle swarm opimizaion (PSO) mehod [29] is chosen o be applied off-line o he DAB model o calculae he opimal phase raios. PSO imiaes he swarm behavior and he individuals represen poins (soluions) in he N-dimensional search space. In his case, N is 3, such ha each individual (paricle) is composed of a hree values (D 1, D 2 and D 3). PSO L br2 involves wo model equaions as oulined by (5) and (6), where X is defined as individual posiion (soluion TPS raios) and V is defined as he velociy (deviaion) needed o change he individual posiion X (soluion) in each ieraion. The velociy of each paricle in he N-dimensional space is obained by (5). The velociy depends on hree parameers: he previous velociy, personal experience of he paricle and he global experience of he whole swarm. Then each individual s posiion X in he N-dimensional space is updaed using (6) depending on he previous posiion (soluion) and he curren velociy. V i m1 = w V i m c 1 r 1 (Pbes i m X i m ) c 2 r 2 (Gbes m X i m ) (5) X i m1 = X i m V i m1 (6) Where m is he ieraion index. c 1 and c 2 are wo posiive consans, such ha c 1 = c 1 = 2, as he common pracice of PSO [29]. r 1 and r 2 are wo randomly generaed numbers, such ha r 1 1, r 2 1 w is he ineria consan, such ha w=.9-(.5*m). Pbes i m is he bes posiion paricle based on is own experience Gbes m is he bes posiion based on overall swarm s experience. The flowchar of he PSO algorihm is presened in Fig. 4. Before execuing he ieraions, a vecor of paricle posiions X is randomly generaed (random TPS soluions). In each ieraion he following seps are carried ou: Each paricle X i m is evaluaed a ieraion m. The oupus of his evaluaion are (power ransfer evaluaed ax i m ) and (Obj. Fun. evaluaed ax i m ). The evaluaion of (Obj. Fun. a X i m ) i.e. ( RMS 2 ) for individual X i m is compared o he evaluaion of he same individual from he previous ieraion; hence he paricle posiion X i m achieving he minimum evaluaion value is defined as personal bes value Pbes i m. The previous comparison is done wih respec o he equaliy consrain defined in secion III-A. Then he Pbes achieving he minimum I L RMS 2 value beween all paricles (he enire swarm) is idenified as he global bes value Gbes. Then using (5) and (6), he velociy and posiion of individuals are updaed respecively wih respec o he inequaliy consrains defined in secion III-A. YES Sar Generae a random swarm & Sar ieraion Evaluaed all ieraions? NO Evaluae he obj. fun. Updae Pbes and Gbes Updae swarm s posiion and velociy(wihin consrains) END

4 TABLE I DAB MODES OF OPERATION & PER UNIT POWER EQUATIONS USING TPS CONTROL Mode 1 Mode 1' Mode 2 Mode 2' Waveforms D 3 T h D 3 T h Normalized ime insans o Th Operaional Consrains Transfer Range =, 1 = D 3, 2 = D 2 D 3 3 = D 1, 4 = 1 =, 1 = D 3 1, 2 = D 2 D = D 1, 4 = 1 =, 1 = D 1, 2 = D 2 D = D 3, 4 = 1 =, 1 = D 1, 2 = D 2 D 3 3 = D 3 1, 4 = 1 D 1 D 2 D 1 D 2 D 2 D 1 D 2 D 1 D 3 D 1 D 2 D 3 1 D 1 D 2 (1 D 1 D 2 ) D 3 1 (1 D 1 D 2 ) D P = 2K(D 2 2 D 1 D 2 2D 2 D 3 ) P = 2K(D 2 2 D 1 D 2 2D 2 (D 3 1)) P = 2K(D 2 1 D 1 D 2 2D 1 2D 1 D 3 ) P = 2K(D 2 1 D 1 D 2 2D 1 D 3 ) P max =.5K pu, P min =.5K pu P max =.5K pu, P min =.5K pu P max =.5K pu, P min =.5K pu P max =.5K pu, P min =.5K pu Mode 3 Mode 3' Mode 4 Mode 4' Waveforms D i 3 T h L D 3 T h Normalized ime insans o Th Operaional Consrains Transfer Range =, 1 = D 1, 2 = D 3 3 = D 2 D 3, 4 = 1 =, 1 = D 1, 2 = D = D 2 D 3 1, 4 = 1 =, 1 = D 2 D 3 1, 2 = D 1 3 = D 3, 4 = 1 =, 1 = D 2 D 3, 2 = D 1 3 = D 3 1, 4 = 1 D 2 1 D 1 D 1 D 3 1 D 2 D 2 1 D 1 D 1 D D 2 D 1 D D 3 D 2 1 D 3 D 1 D 1 D D 3 D 2 D 3 D 1 P = 2K(D 1 D 2 ) P = 2K(D 1 D 2 ) P = 2K( D 2 2 D 2 3 2D 2 2D 3 P = 2K( D 2 2 (D 3 1) 2 2D 2 D 3 D 1 D 2 1) 2D 3 2D 2 D 3 D 1 D 2 1) P max =.5K pu, P min =. pu P max =. pu, P min =.5K pu P max =.667K pu, P min =. pu P max =. pu, P min =.667K pu Mode 5 Mode 5' Mode 6 Mode 6' Waveforms D 3 T h i L D 3 T h Normalized ime insans =, 1 = D 3, 2 = D 1 3 = D 2 D 3, 4 = 1 =, 1 = D 3 1, 2 = D 1 3 = D 2 D 3 1, 4 = 1 =, 1 = D 2 D 3 1, 2 = D 3 3 = D 1, 4 = 1 =, 1 = D 2 D 3, 2 = D = D 1, 4 = 1 o Th Operaional Consrains Transfer D 1 D 3 D 2 1 D 3 D 3 D 1 P = 2K( D 2 1 D 2 3 D 1 D 2 2D 1 D 3 ) D 1 D 3 1 D 2 D 3 D 3 1 D 1 P = 2K( D 2 1 (D 3 1) 2 D 1 D 2 2D 1 (D 3 1)) 1 D 2 D 1 1 D 2 D 3 D 1 P = 2K( D 1 2 D 2 2 2D 3 2 2D 3 2D 2 D 3 D 1 D 2 2D 1 D 3 2D 2 1) 1 D 2 D 1 1 D 2 D 3 1 D 1 P = 2K( D 2 1 D 2 2 2(D 3 1) 2 2D 3 2D 2 D 3 D 1 D 2 2D 1 (D 3 1) 1) Range P max =.667K pu, P min =. pu P max =. pu, P min =.667K pu P max = K pu, P min =. pu P max =. pu, P min = K pu Fig. 4. Flow char of PSO. The previous seps are carried ou for all he possible swiching modes according o he reference power. Afer all ieraion are execued, he Gbes is idenified which includes he opimal TPS raios hence minimum I L RMS 2 is obained wih accompanied swiching mode.

5 TABLE II PER UNIT INDUCTOR CURRENTS (I L) FOR POSITIVE HALF CYCLE SWITCHING INTERVALS NORMALIZED TO IBASE Modes il() il(1) il(2) il(3) 1 (D 1 KD 2 ) ( D 1 2D 3 KD 2 ) ( D 1 2D 2 2D 3 KD 2 ) (D 1 KD 2 ) 1 (D 1 KD 2 ) ( D 1 2(D 3 1) KD 2 ) ( D 1 2D 2 2(D 3 1) KD 2 ) (D 1 KD 2 ) 2 (D 1 2K KD 2 2KD 3 ) (D 1 2KD 1 KD 2 2K 2KD 3 ) (D 1 KD 2 ) (D 1 KD 2 ) 2 (D 1 2K KD 2 2K(D 3 1)) (D 1 2K 2KD 1 KD 2 2K(D 3 1)) (D 1 KD 2 ) (D 1 KD 2 ) 3 (D 1 KD 2 ) (D 1 KD 2 ) (D 1 KD 2 ) (D 1 KD 2 ) 3 (D 1 KD 2 ) (D 1 KD 2 ) (D 1 KD 2 ) (D 1 KD 2 ) 4 (D 1 2K KD 2 2KD 3 ) ( D 1 2 2D 2 KD 2 2D 3 ) (D 1 KD 2 ) (D 1 KD 2 ) 4 (D 1 2K KD 2 2K(D 3 1)) ( D 1 2 2D 2 2(D 3 1) KD 2 ) (D 1 KD 2 ) (D 1 KD 2 ) 5 (D 1 KD 2 ) ( D 1 2D 3 KD 2 ) (D 1 2KD 1 KD 2 2KD 3 ) (D 1 KD 2 ) 5 (D 1 KD 2 ) ( D 1 2(D 3 1) KD 2 ) (D 1 2KD 1 KD 2 2K(D 3 1)) (D 1 KD 2 ) 6 (D 1 KD 2 2KD 3 2K) ( D 1 2D 2 2D 3 KD 2 2) ( D 1 2D 3 KD 2 ) (D 1 2KD 1 KD 2 2KD 3 ) 6 (D 1 KD 2 2K(D 3 1) 2K) ( D 1 2D 2 2(D 3 1) KD 2 2) ( D 1 2(D 3 1) KD 2 ) (D 1 2KD 1 KD 2 2K(D 3 1)) IV. PSO OFF-LINE ALGORITHM ANALYSIS The off-line opimal phase shif calculaions were carried ou using MATLAB sofware, based on he proposed per uni DAB equaions and consrains. Assuming ha K=V dc2/v dc1 and K 1, he oher condiion K>1 can be analyzed similarly. The buck/boos mode is included in his paper as bi-direcional power a K<1 inherenly includes buck mode for operaion in forward power flow and boos mode for operaion in reverse power flow. The values of volage conversion raio (K) used in his secion were: K=.25,.4 and.6 represening buck/boos mode. K=1 represening uniy gain operaing mode. The opimal soluions of he hree phase raios are presened in Fig. 5 pars o (c) and Fig. 6 where he full per uni power range is from K o K; such ha P max-pu =K. This is calculaed by normalizing he DAB maximum power ransfer from (7) o he base power expressed in (8). The PSO is applied in he enire power range for boh power flow direcions; such ha posiive power ransfer indicaes power flow from bridge 1 o bridge 2 and vice versa. A general paern for he opimal phase shifs raios in buck/boos mode is developed in Fig. 5 (d) where he enire power range is divided ino four secions. P max = V dc1 V dc2 8 f s L P base = V base 2 Z base, Where V dc2 = KV dc1 (7) = V 2 dc1 8 f s L Regarding he opimal soluions in buck/boos mode shown in Fig. 5 pars o (c): If desired power P. 5K, opimal soluions were aained by (TPS) where minimum RMS is achieved by he swiching modes 2 as shown in Fig. 5 (d). If desired power P. 5K, exended phase shif (EPS) [16] and convenional phase shif (CPS) achieved he opimal soluion, as shown in Fig. 5 (d), where he minimum RMS is realized by swiching modes 6 and 6 for posiive and negaive power ransfer respecively. On he oher hand, Fig. 6 shows ha he convenional phase shif (CPS) [1] fulfills opimal soluions for uniy gain operaing mode a he enire loading range a boh power flow direcions. In his special case, he opimal soluions were aained by mode 6 or mode 6 wih D 1=D 2=1. (8) -K D1, D2 &D3 D1, & & D2 &D3 D1, D2 &D K= [pu] K= [pu] K=.6 [pu] (c) D1 D2 D3 -.2 D1 -.4 D2 D K<<-.5K D1 D2 D K<< [pu] <<.5K.5K<<K CPS, EPS TPS TPS EPS, CPS Mode 6' Mode 2' Mode 2' Mode 6 D 1 D 1 D 1 D 1 D 2 = 1 D 2 = D 1 / K D 2 = D 1 / K D 2 = 1 (d) Fig. 5. Applicaion of PSO o he DAB for buck/boos mode: -(c) Opimal phase shif raios a K=.25,.4 and.6 respecively (d) General paern of opimal TPS a buck/boos mode. K

6 D1, D2 &D Fig. 6. Opimal phase shif raios uniy gain mode K=1. V. CLOSED LOOP CONTROL DESIGN The exensive se of opimal TPS raios, presened in previous secion, presens a generic daa pool. This daa is carefully analyzed o derive simple relaions which are used o design he generalized closed loop conrol scheme presened in Fig. 7. In buck/boos mode, D 1 can be regulaed hrough a PI conroller as he relaion beween power and D 1 is almos linear hroughou which can be noiced in Fig. 5 pars o (c). Whereas he relaionship beween he oher conrol parameers (D 2 and D 3) and power is non-linear and dependen on he power level. The following relaions can be concluded from Fig. 5 pars o (c): For P. 5K: opimal value of D 2 is (D 2=1). The value of D 3 is highly non-linear and herefore can only be calculaed from re-arranging mode 6 and mode 6 power equaions in Table I. For forward power flow his is shown in (9.a), and for reverse power flow his is shown in (9.b). For P <. 5K: opimal value of D 2 is D 2=D 1/K. The value of D 3 is highly non-linear and herefore can only be calculaed from re-arranging mode 2 power equaion in Table I. The calculaion of D 3 in his secion is shown in (9.c) for boh forward and reverse power flow. ( 1 D 2 D 1 ) 2D 1 2D 2 D 1 2 D 2 2 P K 1 2 K=1 [pu], for P.5K D 3 = (1 D 2 D 1 ) 2D 1 2D 2 D 2 1 D 2 2 P K 1, for P.5K 2.5 (D { 1 D 2 P ), for.5k < P <.5K 2KD 1 (9.a) (9.b) In uniy gain mode, Fig. 6 shows ha boh DAB bridge AC volages are full square waves (D 1=D 2=1) for he enire bidirecional power range and he only conrol needed o regulae power flow is on D 3. This can be implemened using a PI conroller because he relaion beween he power level and value of he hird phase shif D 3 is almos linear as depiced in Fig. 6. The close-loop variable is he sending end power (P se) such ha P se=p br1 for posiive power flow while P se=p br2 for negaive power flow, where P br1 and P br2 are he H-bridge powers measured a he DC sides of bridges 1 and 2 respecively. D1 D2 D3 (9.c) P * - Buck/Boos Mode YES D 2=1 D 3 is calculaed from (9.b) PI D 1 K NO P * -K/2 P * > NO D 2=(D 1/ K) D 3 is calculaed from (9.c) Phase Shif Calculaion Ge K, P *, PI Oupu Operaing Mode? D 1=PI Oupu YES Fig. 7. Proposed conrol scheme for he DAB. VI. SIMULATION RESULTS To confirm he presened analysis, deailed simulaions using SIMULINK/MATLAB plaform sofware were performed. The simulaions were carried ou for he buck/boos/uniy operaing modes using he DAB parameers described in Table III. TABLE III PARAMETERS OF THE EXPERIMENTAL SETUP Parameer value Bridge 1 DC Volage V dc1 1V Bridge 2 DC Volage V dc2 K*1V Swiching Frequency fs 2.5kHz Base P base 5W Inerface inducor L 1mH A. Effeciveness of he proposed conrol scheme YES D 2=1 D 3 is calculaed from (9.a) The effeciveness of he proposed conrol algorihm o rack reference power level while mainaining minimum curren sresses is verified in his secion by applying bidirecional sep changes of reference power level a various volage conversion raios. The resuls are presened in Fig. 8, where he sending end power is measured and ploed agains he reference power level. In addiion, associaed measured RMS inducor curren ( ac ) is shown along wih he minimum possible RMS inducor curren ( min ) calculaed offline by he PSO. I can be noiced ha he proposed power flow conroller is capable of racking he bidirecional reference power level a differen volage conversion raios. Moreover ( ac ) is mainained very close o ( min ) which confirms minimum losses. K<1 D 2 D 3 K=1 NO D 2=(D 1/ K) D 3 is calculaed from (9.c) Send D 1, D 2 & D 3 o TPS Modulaor TPS Modulaor Uniy Gain Mode D 1=D 2=1 D 3=PI Oupu P * K/2 Swiching Signals S1 S2 S3 S4 Q1 Q2 Q3 Q4 DAB

7 (pu) min=1.21 pu ac=1.23 pu K=.4 min=.38 pu ac =.41 pu (pu) min=.91 pu ac=.919 pu Fig. 8: Response of power ransfer wih curren sresses a differen power levels for differen volage conversion raios: K=.4 K=.6 (c) K=1. K=.6 min =.28 pu ac =.285 pu min =.66 pu -.2 min =1.59 pu i -.3 ac=.68 pu L min=.57 pu -.7 ac =1.64 pu ac =.581 pu (c) (pu) min =.99 pu ac =1.1 pu K=1 min =.43 pu ac =.44 pu RMS [pu].85 CPS[1].45 DPS[15] EPS[16] EDPS[22] TPS[28] UPS[24] Proposed TPS Conroller (±)[pu] il RMS [pu].85 CPS[1].45 DPS[15] EPS[16] EDPS[22] TPS[28] UPS[24] Proposed TPS Conroller (±)[pu] (c) Fig. 9: Curves of curren sress RMS wih respec o and K in CPS[1], DPS[15], EPS[16], EDPS[22], TPS[28], UPS[24] and proposed TPS conroller a: K=.2, K=.3, (c) K=.4. il RMS [pu].85 CPS[1].45 DPS[15] EPS[16] EDPS[22] TPS[28] UPS[24] Proposed TPS Conroller (±)[pu] B. Comparaive analysis wih oher phase shif mehods A comprehensive comparison beween he proposed phase shif echnique and oher phase shif echniques in lieraure is provided in his secion. The phase shif echniques o compare he proposed phase shif echnique wih are: Convenional phase shif (CPS) [1], Dual phase shif (DPS) [15], Exended phase shif (EPS) [16], Exended dual phase shif (EDPS) [22], Triple phase shif [28] and Unified phase shif [24]. The enire per uni bi-direcional power range (-K pu o K pu) is considered in all echniques. The RMS inducor curren is compared for all menioned echniques a differen volage conversion raios K as shown in Fig.9. The curren is he main facor affecing he efficiency; hence i is displayed firs where he proposed phase shif echnique is achieving he lowes curren sresses. Moreover, efficiency calculaions, oulined by (1), have been carried ou in simulaions a he DC side o include swiching and copper losses. The DAB circui diagram shown in Fig.1 is used in he simulaion where he variables used for efficiency calculaion (V dc1, I dc1, V dc2, I dc2) are shown along wih he parasiic resisance (AC link) resisance (R ac). The values for his resisance is chosen carefully o produce reliable resuls such ha R ac=.6pu, where Z base =8f swl. The efficiency curves, presened in Fig.1, show ha he proposed mehod achieves beer performance han oher exising phase shif schemes. efficiency = P if P > hen { re = P se if P < hen { { P se = V dc1 I dc1,avg P re = V dc2 I dc2,avg P se = V dc2 I dc2,avg P re = V dc1 I dc1,avg (1) Efficiency (%) Efficiency (%) Transferred [pu] Fig.1. Efficiency curves using exising phase shif echniques and he proposed TPS conroller: K=.2, K= Transferred [pu] CPS[1] DPS[15] EPS[16] EDPS[22] TPS[28] UPS[24] Proposed TPS Conroller CPS[1] DPS[15] EPS[16] EDPS[22] TPS[28] UPS[24] Proposed TPS Conroller

8 (Wa) (c) (Wa) 2 (Wa) (Wa) 1-1 (Wa) 1-1 (Wa) 1-1 (Wa) (d) (e) (f) (Wa) (g) (h) (i) Fig. 11. Robusness of he proposed conrol algorihm o differen sysem condiions K=.4, L=1mH, R ac=1.2ω, K=.4, L=1mH1%,R ac=1.2ω 1%, (c) K=.4, L=1mH-1%, R ac =1.2Ω -1%, (d)k=.6, L=1mH, R ac=1.2ω, (e) K=.6, L=1mH1%,R ac=1.2ω 1%, (f) K=.6, L=1mH-1%, R ac =1.2Ω -1%, (g)k=1., L=1mH, R ac=1.2ω, (h) K=1., L=1mH1%,R ac=1.2ω 1%, (i) K=1.,L=1mH-1%, R ac=1.2ω -1%. (Wa) C. Robusness of he proposed conrol scheme In order o es proposed conroller robusness, simulaions have been implemened wih values of inducor and is parasiic resisance (L and R ac respecively) changing by ±1%. The proposed conroller is applied on he DAB circui shown in Fig.1, and simulaed, for hree cases: L=1mH, R ac=1.2 Ω, P raed = V dc1 V dc2 = 5 Wa 8 f s L L=1mH 1%, R ac =1.2 Ω1%, P raed = V dc1 V dc2 = Wa 8 f s L L=1mH-1%, R ac =1.2 Ω-1%, P raed = V dc1 V dc2 = Wa 8 f s L The proposed conroller response in erms of sending end power P se ploed agains ref. power for he hree cases lised above are shown in Fig. 11. The simulaion is carried ou a hree differen volage conversion raios K (K=.4,.6 and 1) for each of he hree cases of parameer variaion described. The DAB response while parameers change show ha he conrol algorihm is sable and robus and can be applied o any DAB converer regardless of raing and parameers. This is because he proposed analysis is all per uni and generically sandardized. VII. EXPERIMENTAL RESULTS A low scaled experimenal DAB seup was developed according he schemaic shown in Fig. 12 in order o validae he proposed closed loop conroller. The parameers used for designing he es rig are lised in Table III. The enire analysis in he paper is based on ransformer-less DAB, as he main scope is he derivaion and implemenaion of new conroller. The DAB is based, in heory and experimen, on an AC inducor which is fundamenally he equivalen model of a ransformer s leakage inducance. Based on his, a 1mH air core inducance is employed in he experimenal rig while he semiconducor swiches used are MOSFETs (MOSFET IRF25). A. Seady sae response Proposed conrol scheme is verified in his secion a seleced seady sae reference power levels for various volage conversion raios K. Boh bridge volage (V br1, V br2) and insananeous inducor curren () are measured a he AC side presened in Fig. 13 where he RMS inducor is measured and displayed on he righ hand side of he scope screensho.

9 S 1 S 3 Q 1 Q 3 R ac L V dc1 C 1 v br1 v br2 C 2 S 2 S 4 Q 2 Q 4 V dc2 AC link readings (V br1, V br2, and RMS) a hese differen condiions are presened in Fig.14, where he RMS curren sresses using he proposed echnique is lower han curren sresses resuling from oher exising echniques proving he significance of proposed echnique. S 1 S 2 TPS S 3 Modulaor S 4 V D 1 D 2 D 3 dc1 Conroller I dc1 Q 1 Q 2 Q 3 Q 4 V dc2 I dc2 Fig. 12. Schemaic of he experimenal DAB opology. il RMS=2.5 A =.5 pu il RMS=1.81 A =.362 pu CH4 CH3 CH1 CH4 CH3 CH1 il RMS=1.42 A =.284 pu il RMS=1.5 A =.21 pu CH1=iL, CH3= Vbr1, CH4= Vbr2 CH1=iL, CH3= Vbr1, CH4= Vbr2 CH3 CH4 CH1 CH3 CH4 CH1 (c) il RMS=1.78 A =.356 pu (d) il RMS=1.74 A =.348 pu (c) CH1=iL, CH3= Vbr1, CH4= Vbr2 (d) CH1=iL, CH3= Vbr1, CH4= Vbr2 Fig. 13. Volage of boh bridges and inducor curren (V br1,v br2,) readings a he AC link from he experimeal seup: K=.2, P * =-.8 pu, K=.4, P * =.15 pu. (c) K=.6, P * =-.24 pu, (d) K=1, P * =.5 pu. Comparison beween experimenal seup and opimal offline resuls in erms of phase shifs and he RMS inducor curren is shown in Table IV. I can be observed ha he oupus of he proposed conroller (D 1, D 2 and D 3) are closely maching he opimal phase shifs provided in secion IV. (e) il RMS=1.39 A =.278 pu (f) il RMS=.94 A =.188 pu TABLE IV COMPARISON BETWEEN EXPERIMENTAL SETUP AND OPTIMAL OFFLINE RESULTS Phase shifs/inducor curren K, P * From experimenal seup From PSO offline (opimal) D1=.263, D2=1, D3=-.74 D1=.246, D2=1, D3=-.78 K=.2, P * =-.8pu RMS =2.3 A =.46 pu Min RMS =.44 pu D 1=.36, D 2=.9, D 3=. D 1=.35, D 2=.89, D 3=. K=.4, P * =.15pu RMS =2.7 A =.414 pu Min RMS =.412 pu D1=.57, D2=.95,D3=-.32 D1=.54, D2=.91, D3=-.36 K=.6, P * =-.24pu RMS =2.39 A =.478 pu Min RMS =.471 pu D 1=1, D 2=1, D 3=.148 D 1=1, D 2=1, D 3=.146 K=1, P * =.5pu RMS =2.79 A =.558 pu Min RMS =.555 pu B. Comparaive analysis wih oher phase shif mehods The proposed echnique and oher exising phase shif mehods are applied o he experimenal DAB a differen condiions (volage conversion raio K) and a differen power levels. The (g) Fig. 14. Experimenal comparison beween he proposed echnique and oher exising phase shif mehods (CH1= Vbr1, CH2= Vbr2, CH3=iL) -(d) K=.4, P * =.8 pu, in CPS, DPS, EPS and Proposed echnique respecively. (e)-(h) K=.6, P * =.12 pu, in CPS, DPS, EPS and Proposed echnique respecively. C. Experimenal and heoreical comparaive analysis For furher verificaion of he heoreical analysis/conroller, comparaive efficiency curves in experimenal and heoreical (simulaion) using he proposed echnique are provided as depiced in Fig. 15. The efficiency calculaion, oulined by (h)

10 (1), is carried ou using he DAB parameers illusraed in Table III. Efficiency (%) Experimenal Theoreical Transferred [pu] Fig.15. Efficiency calculaed in experimenal and simulaion using he proposed echnique: a K=.2, a K=.4 CONCLUSION In his paper, a generalized per uni model of dual acive bridge (DAB) converer based on he riple phase shif modulaion (TPS) was developed. On he basis of his generic model which can be applied o any DAB converer regardless of raings and parameer values, paricle swarm opimizaion (PSO) echnique was used offline a firs o generae he opimal phase shif raios for he converer a differen values of power levels and conversion raios. The opimal phase shif raios obained from his offline opimizaion exercise were analyzed and useful paerns were idenified and uilized o design a simple closed loop conroller for real ime power regulaion of he DAB converer. 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