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energies Article Control Method Based on Demand Response Needs of Isolated Bus Regulation with Series-Resonant Converters for Residential Photovoltaic Systems Shu-Huai Zhang 1,† , Feng-Zhang Luo 1, *,† , Yi-Feng Wang 1,† , Jiang-Hua Liu 2,† , Yong-Peng He 2,† and Yue Dong 2,† 1 2 * † Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China; [email protected] (S.-H.Z.); [email protected] (Y.-F.W.) Tianjin Research Institute of Electric Science Co., Ltd. (TRIED), Tianjin 300301, China; [email protected] (J.-H.L.); [email protected] (Y.-P.H.); [email protected] (Y.D.) Correspondence: [email protected]; Tel.: +86-139-2090-2432 These authors contributed equally to this work. Academic Editor: Gabriele Grandi Received: 24 April 2017; Accepted: 19 May 2017; Published: 27 May 2017 Abstract: Considering the effects of isolation and high efficiency, a series-resonant DC-DC converter (L-L-C type, with two inductors and a capacitor) has been introduced into a residential photovoltaic (PV) generation and storage system in this work, and a voltage gain curve upwarp drifting problem was found. In this paper, the reason of upwarp drifting in the voltage gain curve is given, and a new changing topological control method to solve the voltage regulation problem under light load conditions is proposed. Firstly, the ideal and actual first harmonic approximation (FHA) models are given, and this drifting problem is ascribed to the multiple peaks of higher-order resonance between resonant tank and parasitic capacitors. Then the paper presents the pulse-frequency-modulation (PFM) driver signals control method to translate the full-bridge LLC into a half-bridge LLC converter, and with this method the voltage gain could easily be reduced by half. Based on this method, the whole voltage and resonant current sharing control methods in on-line and off-line mode are proposed. The parameters design and optimization methods are also discussed in detail. Finally, a residential PV system platform based on the proposed parallel 7-kW full-bridge LLC converter is built to verify the proposed control method and theoretical analysis. Keywords: full-bridge series-resonant converter; light load; parasitic parameters; high order resonant; residential photovoltaic system 1. Introduction The utilization of residential photovoltaic (PV) power systems, which provide unique advantages of flexible structures and minimal environmental pollution, has become a significant trend in renewable energy applications [1–3]. Because of parasitic capacitance between the PV panels and ground, addressing leakage current and meeting safety requirements are major operating concerns [4,5]. Therefore, electrical isolation of residential PV systems is currently recommended [6–8]. Additionally, in order to make the most of PV power, high-efficiency performance is expected as well. Among potential alternative isolated DC-DC converters, the series-resonant DC-DC converter with resonant inductor, resonant capacitor and magnetizing inductor (we call it LLC resonant converter or LLC below), which has been investigated to improve power conversion efficiency, has attracted interest recently [9–13]. When the working frequency is above the main resonant frequency, LLC can attain zero-voltage-switching (ZVS) for primary power switches. When the working frequency Energies 2017, 10, 752; doi:10.3390/en10060752 www.mdpi.com/journal/energies Energies 2017, 10, 752 2 of 21 is below the main resonant frequency, LLC can both attain ZVS for primary power switches and zero-current-switching (ZCS) for output rectifiers [14]. Additionally, the converter benefits from a narrow switching frequency range with light load and ZVS capability, even with no load [15–19]. The comparative study between the LLC resonant converter and three other isolated DC-DC converters was discussed in [20]. It is obvious that LLC has higher efficiency and less volume under the same operating conditions. However, LLC resonant DC-DC converters have several problems, as follows: (1) High voltage gain beyond regulation under light load conditions, as noted in [21]. The traditional way to solve this problem is by adopting burst mode control. Many studies on this approach have been performed. Nevertheless, in the burst mode, the output voltage ripple will be large, leading to lower efficiency; (2) A more serious problem under light load conditions is the upwarp drift of the gain curve. In [22], four factors are introduced in the first harmonic approximation (FHA) model to describe this phenomenon: metallic oxide semiconductor field effect transistor (MOSFET) output capacitance, transformer wiring capacitance, leakage inductance at the transformer secondary side, and junction capacitance of the rectifier diodes. The conclusion drawn is that the junction capacitances of the rectifier diodes are the most influential factor. On the basis of this analysis, the author proposed a method by adding parallel capacitors on the primary side. However, during experimental verification we found that the effect of this method is unsatisfactory. On the other hand, pulse width modulation (PWM) control can be adopted under light load conditions [23], but the exchange between PWM and pulse frequency modulation (PFM) is complicated, and the turn-off current will be larger; (3) In addition, because of the limited bandwidth, the dynamic performance of LLC converters is unfavorable [24]. Different control strategies for LLC resonant converters have been discussed. They are classified as variable-frequency operations and constant-frequency operations [25–27]. Recently, several improved control schemes have been proposed. A mixed control strategy in a neighborhood electric vehicle (NEV) application was proposed [28]. By combining several control strategies, both low-frequency and high-frequency current ripples on the battery are minimized while stability is maintained. Optimal trajectory control based on state-plane analysis can provide very fast dynamic performance for series resonant converters [29]. Also, a Bang-Bang charge control for LLC was proposed [24]. It is simple because it uses only the series resonant capacitor voltage and a pair of voltage thresholds to determine the MOSFETs’ switching points. It can achieve high-loop bandwidth and provide fast dynamic performance. In this study, firstly in Section 2, we describe an existing residential PV power system, and analyze the voltage regulation problem of a parallel full-bridge LLC converter in this system. In Section 3, we discuss the ideal and actual FHA model based on previous research, and aim to analyze the reason of the upwarp drifting in the voltage gain curve. Then, in Section 4, a new changing topological control method to solve the voltage regulation problem at light load condition is proposed. By adapting PFM driver signals, the full-bridge LLC converter can be changed into half-bridge LLC, and the voltage gain could be reduced by half easily for voltage regulation. Design consideration based on the new method is also given in this section. Based on this method, the whole voltage control methods and simulation verifications in on-line and off-line mode are proposed in Section 5. Finally, in Section 6, experimental results with resistive load and real household load are discussed to verify the availability of the proposed control methods. 2. A Residential PV Power System and Problem Description 2.1. System Description Figure 1 shows the architecture of a residential PV power system, which is composed of four parts. The boost maximum power point tracking (MPPT) converter and the bidirectional DC-DC converter transfer the energy from the PV and batteries to the 400 V DC bus. Compared to the systems placing batteries at the output of PV MPPT converter, the structure in this paper can easily control Energies 2017, 10, 752 3 of 21 charging/discharging state and current of batteries with bidirectional DC/DC converter, which is benefit for the life time and usage cost of the batteries. Following them, a parallel full-bridge LLC converter is connected to the next 630 V DC Energies 2017, 10, 752 3 of 21 bus, which are used to supply high-frequency isolation and voltage regulation for the system. LLC converters guarantee electrical isolation with high working frequency. As its full-load efficiency is converters guarantee electrical isolation with high working frequency. As its full-load efficiency is 98.4% and maximum efficiency is 98.7% in experiments, efficiency is not reduced largely when energy 98.4% and maximum efficiency is 98.7% in experiments, efficiency is not reduced largely when energy is transferred from PV and batteries to grid. At the end, a three-phase inverter is connected to the grid, is transferred from PV and batteries to grid. At the end, a three-phase inverter is connected to the which supplies the household load.load. The The proposed residential PV power system cancan be operated in grid, which supplies the household proposed residential PV power system be operated both on-line and off-line mode: in both on-line and off-line mode: (1) In on-line on-line mode, mode, the the LLC LLC converters converters control control the (1) In the 400 400 V V DC DC bus bus voltage. voltage. The The inverter inverter regulates regulates the 630 630 V V DC DC bus bus and and harmonics harmonics of of the The boost the the output output currents. currents. The boost converter converter adopts adopts the the MPPT MPPT algorithm. The bidirectional converter adopts current control to compensate the power difference algorithm. The bidirectional converter adopts current control to compensate the power between household load and PV. difference between household load and PV. (2) In off-line mode, the LLC resonant converters control the 630 V DC (2) In off-line mode, DC bus bus voltage. voltage. The inverter inverter regulates the AC output voltage. The boost converter adopts the MPPT algorithm and the regulates the The boost converter adopts bidirectional converter adopts voltage control to regulate the 400 V DC bus voltage. bidirectional Figure 1. Architecture of residential photovoltaic photovoltaic system. system. 2.2. Existing Problem Description In the proposed residential PV system, the energy generated by PV is delivered to the batteries, little poweris is transmitted to inverter through theresonant LLC resonant DC-DC converters, when the little power transmitted to inverter through the LLC DC-DC converters, when the household household load is light. The LLC converters maywork always workload at light load condition. So the problem load is light. The LLC converters may always at light condition. So the problem of the of the upturn thevoltage LLC voltage gain at high frequencies given in [21] be inescapable. According upturn of the of LLC gain at high frequencies given in [21] willwill be inescapable. According to to experiments, the light load gain is so high that the required voltage (630 V DC or 400 V DC) cannot experiments, the light load gain is so high that the required voltage (630 V DC or 400 V DC) cannot be be restrained. Thus, voltage regulation problem could be described as following: restrained. Thus, thethe voltage regulation problem could be described as following: (1) In DC bus bus voltage, voltage, U U400,, will be lower than 400 V, and a steady-state (1) In on-line on-line mode, mode, the the 400 400 V V DC 400 will be lower than 400 V, and a steady-state error exists, as the 630 V DC bus voltage is constant and with error exists, as the 630 V DC bus voltage is constant and regulated regulated by by the the following following inverter inverter with closed-loop control. closed-loop control. (2) In V DC bus voltage, voltage, U U630,,will be higher than 630 V normally. Burst mode (2) In off-line off-line mode, mode, the the 630 630 V DC bus 630 will be higher than 630 V normally. Burst mode is adopted, too large voltage ripple exists, as the 400 DC bus voltage is stable and controlled is adopted, too large voltage ripple exists, as the 400 VVDC bus voltage is stable and controlled by by the bidirectional DC-DC converter, as shown in Figure 1. the bidirectional DC-DC converter, as shown in Figure 1. (3) Too slow voltage regulation when the load changes, and too large a voltage spike or sink when (3) Too slow voltage regulation when the load changes, and too large a voltage spike or sink when the load is changing suddenly. the load is changing suddenly. 3. Ideal and Actual FHA Model FHA modeling method is widely used due to its simple and effectiveness. In this paper, FHA modeling process is based on previous research [30,31] and we just used it to analyze and explain the difference between ideal and actual gain of the LLC converter. Figure 1 shows the topology of the proposed full-bridge LLC resonant converter. The input voltage is Uin, the output voltage is Uo. The resonant tank is formed by the resonant capacitor Cr, the Energies 2017, 10, 752 4 of 21 3. Ideal and Actual FHA Model FHA modeling method is widely used due to its simple and effectiveness. In this paper, FHA modeling process is based on previous research [30,31] and we just used it to analyze and explain the difference between ideal and actual gain of the LLC converter. Figure 1 shows the topology of the proposed full-bridge LLC resonant converter. The input voltage is Uin , the output voltage is Uo . The resonant tank is formed by the resonant capacitor Cr , the resonant inductor Lr and the magnetizing inductor Lm of the transformer. The turn ratio of the Energies 2017, 10, 752 4 of 21 transformer is n:1. The switches on the primary side of the transformer (Q1 , Q2 , . . . , and Q8 ) are MOSFETs. In the output rectifier, D1 , D2 , . . . , and D8 are the rectifier diodes. The DC voltage gain in MOSFETs. In the output rectifier, D1, D2, …, and D8 are the rectifier diodes. The DC voltage gain in this paper refers to the ratio of output voltage: Uo /Uin . this paper refers to the ratio of output voltage: Uo/Uin. 3.1. Ideal FHA Model Analysis 3.1. Ideal FHA Model Analysis Firstly, several assumptions are made here: Firstly, several assumptions are made here: (1) Waveforms in resonant tank are perfect sinusoidal waves under any working frequency. (1) Waveforms in resonant tank are perfect sinusoidal waves under any working frequency. (2) All the energy is conveyed by the fundamental component of the input voltage: uin,FHA . (2) All the energy is conveyed by the fundamental component of the input voltage: uin,FHA. (3) (3) All All the the parasitic parasitic parameters parameters are are neglected. neglected. (4) (4) Figure Figure 22 shows shows the the ideal ideal equivalent equivalent circuit circuit of of the the proposed proposed full-bridge full-bridge LLC LLCconverter converterusing usingthe the FHA modeling method [31]. FHA modeling method [31]. Figure2. 2. Ideal Ideal equivalent equivalent circuit circuit of ofLLC LLCresonant resonantconverter converter Figure As is known, LLC converter has two resonant frequencies, in this paper we define the higher As is known, LLC converter has two resonant frequencies, in this paper we define the higher resonant frequency fr1 as the main resonant frequency fr, that means: fr = fr1. fr2 is the secondary or resonant frequency fr1 as the main resonant frequency fr , that means: fr = fr1 . fr2 is the secondary or lower resonant frequency: lower resonant frequency: 1 1 f r1 = , fr 2 = (1) 1 1 f r1 = 2π√ Lr Cr , f r2 = 2πp ( Lr + Lm )Cr (1) 2π Lr Cr 2π ( Lr + Lm )Cr and uin can be expressed with the Fourier series as: and uin can be expressed with the Fourier series as: 4Uin uin ( t ) = ⋅ 4U uin (t) = ∞ 1 sin 2π Nft ) 1 ( in π · N =∑ 1,3,5, N sin(2πN f t ) ∞ (2) (2) π N N =1,3,5,··· t is the time parameter, N is the integer parameter for the Fourier series expansion, and f is the t is thefrequency. time parameter, N is the parameter for the Fourier series expansion, andresonant f is the switching According to integer the above assumptions, the input voltage of LLC switching frequency. According to the above assumptions, the input voltage of LLC resonant of network network can be regarded as its fundamental component, thus the fundamental component uin is: can be regarded as its fundamental component, thus the fundamental component of uin is: 4U uin, FHA ( t ) = in ⋅ sin ( 2π ft ) (3) π 4U in uin,FH A (t) = · sin(2π f t) (3) π be calculated as: The root mean square (RMS) value of uin,FHA can The root mean square (RMS) value of uin,FHA can2 be as: 2Ucalculated in Uin, FHA (t ) = √ π 2 2Uin Uin,FH A (t) = Likewise, the output voltage of the resonant network, π can be expressed as: ∞ 4U 1 Likewise, the output voltage of the resonant network, can be expressed as: uro ( t ) = o ⋅ sin ( 2π Nft − φ ) π N =1,3,5, N (4) (4) (5) where φ is the time shift compared to the input voltage, and the fundamental component of uro is shown as: 4U o Energies 2017, 10, 752 5 of 21 uro (t) = ∞ 4Uo 1 · ∑ sin(2πN f t − φ) π N =1,3,5,··· N (5) where ϕ is the time shift compared to the input voltage, and the fundamental component of uro is shown as: 4Uo uro,FH A (t) = · sin(2π f t − φ) (6) π The RMS value of uro,FHA can be calculated as: Uro,FH A √ 2 2Uo = π (7) The fundamental component of the rectifier current irct can be expressed as: irct,FH A = √ 2Irct,FH A sin(2π f t − φ) (8) where Irct,FHA is the RMS value of irct,FHA . Thus the average output current Io can be obtained: 2 Io = Ts T 2 Z 0 √ 2 2 I |irct,FH A (t)| dt = π rct,FH A (9) and the equivalent output resistance of the resonant network can be expressed as follows: Ro,e U = ro,FH A = Irct,FH A √ 2 2 π Uo π √ I 2 2 o = 8 Ro π2 (10) In order to simplify the calculation, the equivalent output resistance in the secondary side of the transformer can be converted to the primary side: R0 o,e = n2 Ro,e (11) With all the given parameters, φ can be calculated as: " φ = arctan 2π f Lm n4 Ro,e 2 + (2π f Lr − 2 1 4 2π f Cr )( n Ro,e 4π 2 f 2 Lm 2 n2 Ro,e + 4π 2 f 2 Lm 2 ) # (12) The forward transfer function of the resonant network can be derived as follows: H (s) = Uo,FH A (s) sL · R0 o,e m i = h Uin,FH A (s) n (sLm + R0 o,e ) sLr + sC1 r + sLm · R0 o,e (13) Finally, the ideal voltage gain of the LLC resonant converter can be calculated as: Gid = = n q Uo Uin = Uo,FH A Uin,FH A ( R0 o,e −( j2π f ) 2 = k H ( j2π f )k (14) ( j2π f )2 Lm Cr R0 o,e 2 2 3 Lr Cr R0 o,e −( j2π f ) Lm Cr R0 o,e ) +(( j2π f ) Lm −( j2π f ) Lm Lr Cr ) 2 3.2. Actual FHA Model Analysis Including Parasitic Capacitors In order to illustrate the upwarp drifting of the voltage gain curve, the junction capacitances of the rectifier diodes and the wiring capacitance of the transformer are added. Its equivalent FHA circuit is shown in Figure 3. Cpc represents the total parasitic capacitances of the rectifier diodes and transformer windings. Cr_PC represents parasitic capacitance of resonant inductor, which has not been considered Energies 2017, 10, 752 6 of 21 in former work [21]. In our LLC converter, Cr_PC = 0.2 nF. Cr_PC is so small, and the impact of the parameter of Cr_PC can be neglected, so the parameter will not appear in the actual FHA model and analysis in the whole article. From Figure 3, it can be obtained that the reason of the upwarp drifting should be ascribed Energies 2017, 10, 752 to the high order resonance between the resonant tank and parasitic capacitors6 C ofpc 21. Energies 2017, 10, 752 6 of 21 Figure 3. Equivalent model of LLC resonant converter considering parasitic parameters. Figure 3. Equivalent model of LLC resonant converter considering parasitic parameters. 3. Equivalent of LLC considering parasiticas: parameters. AfterFigure considering Cpc, themodel voltage gainresonant of LLCconverter converter can be rewritten After considering Cpc , the voltage gain of LLC converter can be rewritten as: ′ f ⋅ Cr ⋅ B ( f ) o , e ⋅ 2πconverter After consideringGCpcpc=, the voltage gain ofRLLC can be rewritten as: 2 2 R0 o,e · 2π f · Cr · B ( f ) G pc = q n A ( f ) ⋅ B ( f ) + {RR′o′ , e⋅2Aπ(ff ⋅)C⋅ 2π⋅ Bf (⋅ fC)pc + B ( f ) ⋅ 2π f ⋅ Cr } o,e r 2 G npc =[ A( f ) · B( f )]2 +2 R0 o,e A( f ) · 2π f · C pc + B( f ) · 2π f ·2 Cr n A (as: f ) ⋅ B ( f ) + { Ro′ , e A ( f ) ⋅ 2π f ⋅ C pc + B ( f ) ⋅ 2π f ⋅ Cr } where A(f) and B(f) are defined where A(f ) and B(f ) are defined as: A ( f ) = 4π 2 f 2 Lr C r − 1 where A(f) and B(f) are defined as: 2 2 A(ABf()(ff= C − π 22fff 22LLmrC −111 44π Cpcr − )) ==4π r r (15) (15) (15) (16) (16) (17) (16) 2 As shown in Figure 4, the full line parasitic parameters with(17) (15), f ) 4π =gain 4π2 2f 2fcurve −− 1 1 B(isfB)the LLmmCCpcpcconsidering (17) (= the dash line is the ideal gain curve. The straight dot dashed line is the expected voltage gain (630 V As shown in Figure 4, the full line is the curve considering parasitic parameters with (15), the gain gain curve DC/400 V DC = 1.575). Those curves are given under the considering same output resistance (5 kΩ), and fr is 78.8 the dash line is the ideal gain curve. The straight dot dashed line is the expected voltage gain (630 V kHz. Therefore, the expected voltage gain cannot be obtained under the model considering actual DC/400 VDC DC==1.575). 1.575).Those Those curves given under same output resistance (5 kΩ), fr is DC/400 areare given thethe same output resistance (5 kΩ), andand fr is 78.8 parasiticVparameters, which iscurves the same as the under experimental result. 78.8 kHz. Therefore, the expected voltage gain cannot be obtained under the model considering actual kHz. Therefore, the expected voltage gain cannot be obtained under the model considering parasitic parasitic parameters, parameters, which which is is the the same same as as the the experimental experimental result. result. Figure 4. Voltage gain curve of full-bridge LLC converter at light load condition. Figure 4. gain Load curve Conditions of full-bridge full-bridge LLC LLC converter converter at at light light load load condition. condition. 4. New Control Method at Light Figure 4. Voltage Voltage gain curve of AsControl shown in Figureat 3, Light there is an additional Cpc in the actual FHA model, which is parallel with 4. New New Method Load Conditions 4. Control Method at Light Load Conditions the transformer. Therefore, the reason of upwarp drifting of the voltage gain curve can be ascribed pc in the actual FHA model, which is parallel with As higher-order shown in in Figure Figure 3, there there is is an an additional additional to the resonance between resonant tank parasitic capacitors, there is an As shown 3, CCpc in theand actual FHA model, whichand is parallel with the transformer. Therefore, the reason of upwarp drifting of the voltage gain curve can be ascribed additional resonant bottomthe where the is higher than the main resonant in the transformer. Therefore, reason of frequency upwarp drifting of the voltage gain curve canfrequency be ascribedfr to to the higher-order resonance between parasitic capacitors, and there is an Figure 4. But it isresonance hard to calculate the realresonant value Ctank pc parasitic dueand to the uncertainty ofthere parasitic the higher-order between resonant tankofand capacitors, and is anparameters. additional additional resonant bottom where the frequency higher main resonant frequency fr in In order towhere solve thisfrequency non-monotonic problem simply andthe effectively, this paper presents resonant bottom the is higher thanisthe mainthan resonant frequency fr in Figure 4. But ita Figure 4. But it is hard to calculate the real value of C pc due to the uncertainty of parasitic parameters. topological method. adapting PFM driverofsignals, theparameters. full-bridge LLC converter ischanging hard to calculate thecontrol real value of CpcBy due to the uncertainty parasitic In changed order to into solve this non-monotonic problem andbe effectively, this paper presents a can be half-bridge LLC, and the voltage simply gain could reduced by half. changing topological control method. By adapting PFM driver signals, the full-bridge LLC converter can changed into half-bridge LLC, andMethod the voltage gain could be reduced by half. 4.1. be Proposed Changing Topological Control As shown in Figure 5, a full-bridge LLC can be simply transformed into a half-bridge LLC by 4.1. Proposed Changing Topological Control Method turning off Q3 and turning on Q4 (as shown in Figure 1) incessantly. The input voltage of resonant in Figure a full-bridge LLCUcan be simply transformed into a half-bridge LLC by tankAs in shown full-bridge LLC, 5, uAB_F , ranges from in to −Uin in one period, each voltage lasts 50% of the Energies 2017, 10, 752 7 of 21 In order to solve this non-monotonic problem simply and effectively, this paper presents a changing topological control method. By adapting PFM driver signals, the full-bridge LLC converter can be changed into half-bridge LLC, and the voltage gain could be reduced by half. 4.1. Proposed Changing Topological Control Method As shown in Figure 5, a full-bridge LLC can be simply transformed into a half-bridge LLC by Energies 2017, 7 of 21 turning off10, Q3752 and turning on Q4 (as shown in Figure 1) incessantly. The input voltage of resonant tank in full-bridge LLC, uAB_F , ranges from Uin to −Uin in one period, each voltage lasts 50% of the 50% of period, the whole Thus, the RMS fundamental harmonic of period, uAB_F in each full-bridge whole but period. that in half-bridge LLC,value uAB_Hof , ranges from Uin to 0 in one voltageLLC, lasts U AB_F , can be displayed as: 50% of the whole period. Thus, the RMS value of fundamental harmonic of uAB_F in full-bridge LLC, 1/ f UAB_F , can be displayed as: R 1/ f u AB _ F ⋅ dt 2 2√ 0 (18) U AB _ F = 0 u AB_F · dt= 2 U2in U AB_F = =π Uin (18) 1/ f 1/ f π And value of fundamental harmonic of uAB_H in half-bridge LLC, UAB_H, can be displayed Andthe theRMS RMS value of fundamental harmonic of u AB_H in half-bridge LLC, UAB_H , can be as: displayed as: R 1/1/f f √ ·dtdt 1 2 0 uuAB_H ⋅ AB _ H U AB_H = = 2 U U=in1= U (19) (19) U AB _ H = 0 1/ f = U π 2 AB_F π in 2 AB _ F 1/ f By adopting (10), (11) and (15), we can conclude that given the same output resistance Ro , By adopting (10), (11) and (15), we can conclude that given the same output resistance Ro, the the voltage gain of the half-bridge LLC mode GH_pc is half of that of the full-bridge mode: voltage gain of the half-bridge LLC mode GH_pc is half of that of the full-bridge mode: 11 G pc ( f , Ro ) G ( ff,,RRo ) = GH_pc = ( ) 2Gpc ( f , Ro ) H _ pc o 2 (a) (20) (20) (b) Figure signals of the proposed changing topological LLC:LLC: (a) Full-bridge LLC; and HalfFigure 5.5.Drive Drive signals of the proposed changing topological (a) Full-bridge LLC;(b) and (b) bridge LLC. LLC. Half-bridge To verify the above analysis, an open loop experimental based on a half-bridge LLC converter To verify the above analysis, an open loop experimental based on a half-bridge LLC converter has been carried out. As shown in Figure 6, the solid line is the voltage gain curve calculated by the has been carried out. As shown in Figure 6, the solid line is the voltage gain curve calculated by the actual FHA model with (15), and the dashed line is the experimental results, which are obtained by actual FHA model with (15), and the dashed line is the experimental results, which are obtained by changing the operating frequency under the same input voltage and output resistance (5 kΩ), and fr changing the operating frequency under the same input voltage and output resistance (5 kΩ), and fr is is 78.8 kHz. The straight dot dashed line (the same with Figure 4) is the expected voltage gain. 78.8 kHz. The straight dot dashed line (the same with Figure 4) is the expected voltage gain. Therefore, Therefore, by utilizing the proposed changing topological control method, the expected voltage gain by utilizing the proposed changing topological control method, the expected voltage gain can be can be obtained under very light load condition, and even the switching frequency could be reduced. obtained under very light load condition, and even the switching frequency could be reduced. Compared to the full-bridge LLC, conduction loss and core loss in the half-bridge LLC increases due to the larger RMS of the resonant current. As the switching frequency becomes lower, and MOSFETs in switching mode decrease from 4 to 2, the turn-off loss declines largely. To conclude, at light load condition, the fall of turn-off loss is larger than the rise of conduction loss and core loss. Overall, the efficiency under half-bridge mode is a little higher than that under full-bridge mode. Figure 6. Voltage gain curve of half-bridge LLC. has been carried out. As shown in Figure 6, the solid line is the voltage gain curve calculated by the actual FHA model with (15), and the dashed line is the experimental results, which are obtained by changing the operating frequency under the same input voltage and output resistance (5 kΩ), and fr is 78.8 kHz. The straight dot dashed line (the same with Figure 4) is the expected voltage gain. Therefore, by utilizing the proposed changing topological control method, the expected voltage8gain Energies 2017, 10, 752 of 21 can be obtained under very light load condition, and even the switching frequency could be reduced. Energies 2017, 10, 752 8 of 21 4.2. Design Consideration Based on the New Method As is discussed above, to track the required gain of the LLC converter in all load range, it is important to find the required gain in full-bridge mode when load is normal. It is also important to find the required gain in half-bridge mode when load is so there are several restrictions. In the Figure gain curve curve of light, half-bridge LLC. Figure 6. 6. Voltage Voltage gain of half-bridge LLC. following Section 4.2.1, the design procedure of the resonant tank parameters and power devices will be discussed. The andLLC, design approach of the voltage gain and working frequency range Compared torequirement the full-bridge conduction 4.2. Design Consideration Based on the New Method loss and core loss in the half-bridge LLC increases for the changing topological LLC converter, whichAs arethe used to meet the voltage gain requirements of due to the larger RMS of the resonant current. switching frequency becomes lower, and As is discussed above, to track the required gain of the LLC converter in all load range, it is the whole load range, will be analyzed in Section 4.2.2. MOSFETs in switching mode decrease from 4 to 2, the turn-off loss declines largely. To conclude, at important to find the the required in full-bridge mode when is normal. It isloss alsoand important to light load condition, fall ofgain turn-off loss is larger than the load rise of conduction core loss. 4.2.1. Resonant Parameters and Rated Operationg Point Design find the required gain in half-bridge mode when load is light, so there are several restrictions. In the Overall, the efficiency under half-bridge mode is a little higher than that under full-bridge mode. following Section 4.2.1, the design procedure of the resonant tank parameters and power devices will In this paper, the design procedure of the resonant tank parameters and power devices which is be discussed. The requirement and design approach of the voltage gain and working frequency range presented in [31] will be adopted. As shown in Figure 7, Uin_max, Uin_min, Uout_max and Uout_min are the for the changing topological LLC converter, which are used to meet the voltage gain requirements of maximum and minimum of input and output voltage respectively, Pout_max is the maximum output the whole load range, will be analyzed in Section 4.2.2. power, n, np, ns, Lr, Lm is the turn ratio, turns of primary and secondary, resonant inductor and excitation inductor of the transformer respectively,Point Cr is Design the resonant capacitor, Co is the output filter 4.2.1. Resonant Parameters and Rated Operationg capacitor, Rac is the effective resistive load reflected to the primary side, Gmax and Gmin are the required In thisand paper, the design procedure of the resonant tank parameters maximum minimum voltage gain under full-bridge LLC topology, k isand thepower ratio ofdevices Lm to Lwhich r, TD is is will be adopted. As quality shown factor in Figure 7,resonant Uin_max , tank, Uin_min ,U out_max out_min thepresented dead-timeinof[31] the bridge-arms, Q is the of the fmax and fmin isand the U feasible are the maximum and minimum of input and output voltage respectively, P is the maximum out_max maximum and minimum operating frequency under different load conditions, Ip is the current in the output power, , ns ,excitation Lr , Lm is the turn ratio, of primary and resonant inductor and resonant tank, n, Im n isp the current of theturns transformer, IQ_RMS , Usecondary, Q_max and PQ_max are the maximum excitation inductor of the transformer respectively, the MOSFET resonant capacitor, Co isID_avg the, output r is RMS current, drain-source voltage and loss powerCof each respectively, UD_max, filter PD_on capacitor, R is the effective resistive load reflected to the primary side, G and G are the required ac are the maximum average current, inverse voltage and loss power of eachmax rectifier min diode respectively, maximum and minimum voltage gain under full-bridge LLC topology, k is the ratio of Lm to Lr , TD Icr_RMS and U Cr_max are the maximum RMS current and peak resonant voltage of Cr. is theThe dead-time theoptimization bridge-arms, method Q is the quality of the resonant fmax and fmin is the design of and is basedfactor on full-bridge LLCtank, topology, because the feasible maximum and minimum operating frequency under different load conditions, I is the current p efficiency of normal load range, for example 10–100%, is the main optimization objective and the in theoperating resonant tank, Im is the of the transformer, IQ_RMS , UfQ_max PQ_max the main conditions. Onexcitation the othercurrent hand, the main resonant frequency r (or fr1and ) and rated are steady maximum RMS current, drain-source voltage and loss power of each MOSFET respectively, I D_avg , state working frequency are preset. The common setting of fr is 100 kHz, in this paper, the output U , P are the maximum average current, inverse voltage and loss power of each rectifier diode D_max per D_on power channel is up to 4 kW, so in order to strike a balance between power efficiency and power respectively, Icr_RMS of and UCr_max are the RMS current and peak resonant voltage of Cr . density, the setting fr will be nearly 80maximum kHz. Figure full-bridge LLC LLC converter. converter. Figure 7. 7. Design Design procedure procedure of of the the proposed proposed full-bridge The rated steady state working frequency setting needs to consider the limited peak voltage gain under 4 kW output condition, large DC bus voltage fluctuations caused by the transient procedures and rated conversion efficiency comprehensively. As the rated power is 4 kW in each channel, it is hard to get a high voltage gain as in [28], because the equivalent resistance Ro is too small to make the curve goes up. Thus, the peak voltage gain should be guaranteed to regulate two DC bus voltage during a large disturbance. Energies 2017, 10, 752 9 of 21 The design and optimization method is based on full-bridge LLC topology, because the efficiency of normal load range, for example 10–100%, is the main optimization objective and the main operating conditions. On the other hand, the main resonant frequency fr (or fr1 ) and rated steady state working frequency are preset. The common setting of fr is 100 kHz, in this paper, the output power per channel is up to 4 kW, so in order to strike a balance between power efficiency and power density, the setting of fr will be nearly 80 kHz. The rated steady state working frequency setting needs to consider the limited peak voltage gain under 4 kW output condition, large DC bus voltage fluctuations caused by the transient procedures and rated conversion efficiency comprehensively. As the rated power is 4 kW in each channel, it is hard to get a high voltage gain as in [28], because the equivalent resistance Ro is too small to make the curve goes up. Thus, the peak voltage gain should be guaranteed to regulate two DC bus voltage during a large disturbance. The problem Energies 2017, 10, 752 of gain upturn could be avoided by using the proposed changing topological control 9 of 21 method, so the limited voltage gain problem should be considered during rated operating point presetting. Therefore, the rated cangain be achieved the main frequency fr , point presetting. Therefore, thegain rated can be slightly achievedabove slightly aboveresonant the main resonant making fullfr,use of drop of drop gain curve. wider gain range and higher efficiency frequency making fullscope use of scope It ofcan gainguarantee curve. It acan guarantee a wider gain range and near operation higher efficiencypoint. near operation point. 4.2.2. Voltage Voltage Gain Gain and and Working Working Frequency 4.2.2. Frequency Range Range Selection Selection By using usingthe theproposed proposedchanging changingtopological topological control control method method and andthe thedesign designprocedure procedurediscussed discussed By in Section 4.2.1, the voltage gain and working frequency range selection are illustrated in Figure8.8. in Section 4.2.1, the voltage gain and working frequency range selection are illustrated in Figure When the LLC operates in full-bridge LLC mode, f is the voltage gain peak point under maximum 1-Fis the voltage gain peak point under maximum When the LLC operates in full-bridge LLC mode, f1-F load condition, condition, for for example example 4.8 4.8 kW kW (1.2 (1.2 times times of isthe theminimum minimumvoltage voltagegain gain point point 2-Fis load of rated rated power), power), ff2-F under selectable minimum load, for example 0.8 kW (0.2 times of rated power). When the load is under selectable minimum load, for example 0.8 kW (0.2 times of rated power). When the load is reduced continuously, continuously, the the circuit circuit will isthe thevoltage voltage gain gain peak peak 1-H is reduced will be be changed changed into into half-bridge half-bridge LLC, LLC, ff1-H point under maximum selectable load condition in half-bridge mode, for example 1.2 kW (0.3 times of point under maximum selectable load condition in half-bridge mode, for example 1.2 kW (0.3 times rated power), f is the minimum voltage gain point without load. Therefore, within range 2, point of rated power),2-H f2-H is the minimum voltage gain point without load. Therefore, within range 2, point 11 is the the minimum minimum frequency frequency point point and and point point 22 is is the the maximum maximum frequency frequency point point under under full-bridge full-bridge LLC LLC is topology, and within range 1, point 3 is the minimum frequency point and point 4 is the maximum topology, and within range 1, point 3 is the minimum frequency point and point 4 is the maximum frequency point point under under half-bridge half-bridge LLC LLC topology. topology. frequency Figure Figure8.8.Voltage Voltage gain gain and and frequency frequency range range selection selection in in full-bridge full-bridge and and half-bridge LLC. ItIt is is necessary necessarytoto calculate feasible minimum and maximum frequency, the calculate the the feasible minimum and maximum frequency, to select to theselect operating operating frequency range and to ensure a suitable gain can be attained, in which the gain curve is frequency range and to ensure a suitable gain can be attained, in which the gain curve is monotonic monotonic without upturn. without upturn. The first-order The first-order derivative derivative of of the the half-bridge half-bridge LLC LLC voltage voltage gain gain can can be be described described as: as: 2 2 Ro′,eCr (12π2 f 2LmCpc −1) ⋅ C( f ) +D( f ) Ro′,eCrπ fB( f ) C( f ) 6π fLmCpc A( f ) +6π fLCB r r ( f ) − GH′ _ pc ( f1_H, Ro,Cpc ) = 3 3 2 2 2 2 2nC( f ) +D( f ) 2 nC( f ) +D( f ) 2 Ro′,e Crπ fB ( f ) D ( f ) (12π f Lr Cr C pc + 12π f LmCr C pc ) 2 − 2 2 2 3 2 Ro′,e Crπ fB ( f ) D ( f ) ( C pc + Cr ) 2 + 3 (21) Energies 2017, 10, 752 G 0 H_pc 10 of 21 i h R0 o,e Cr 12π 2 f 2 Lm C pc − 1 · C ( f )2 + D ( f )2 R0 o,e Cr π f B( f )C ( f ) 6π f Lm C pc A( f ) + 6π f Lr Cr B( f ) f 1_H , Ro , C pc = − h i3 h i3 2 2 2n C ( f )2 + D ( f )2 n C ( f )2 + D ( f )2 2 2 R0 o,e Cr π f B( f ) D ( f ) 12π 2 f 2 Lr Cr C pc + 12π 2 f 2 Lm Cr C pc R0 o,e Cr π f B( f ) D ( f ) C pc + Cr − + h i3 h i3 2 2 n C ( f )2 + D ( f )2 n C ( f )2 + D ( f )2 (21) C(f ) and D(f ) are defined as: C ( f ) = A( f ) · B( f ) D ( f ) = 2π f · R0 o,e C pc · A( f ) + Cr · B( f ) (22) (23) By making G0 H_pc zero, extreme points of GH_pc are obtained. f 1_H is a local maximum value point, and f 2_H is a local minimum value point. As shown in Figure 8, the frequency range between f 1_H and f 2_H is the maximum feasible working area for the half-bridge LLC resonant converter, and range 1 should be contained within f 1_H and f 2_H . Similarly, the frequency range between f 1_F and f 2_F is the maximum suitable working area for the full-bridge LLC resonant converter, and range 2 should be contained within f 1_F and f 2_F . In Figure 8, if Gr declines to the position of G2 , the required gain cannot be tracked with the full-bridge LLC converter. Taking a margin of 0.1Gr into consideration, the selection of load or Ro should satisfy the following equation: G pc f 2_F , Ro , C pc ≤ 0.9Gr (24) The gain of the local maximum point f 1_F , should be larger than the required gain. Taking a margin of 0.2Gr into consideration: G pc f 1_F , Ro , C pc ≥ 1.2Gr (25) In half-bridge mode, the gain of the local maximum point f 1_H , should be larger than the required gain Gr . If Gr rises to the position of G1 , the required gain cannot be tracked with the half-bridge LLC converter. Taking a margin of 0.1Gr into consideration, the selection of Ro should satisfy the following equation: GH_pc f 1_H , Ro , C pc ≥ 1.1Gr (26) The gain of the local minimum point f 2_H should be smaller than the required gain Gr . Taking a margin of 0.2Gr into consideration: GH_pc f 2_H , Ro , C pc ≤ 0.8Gr (27) Considering the above design method and optimization factors, resonant tank parameters, the voltage gain and frequency range could be calculated. Furthermore, in order to realize fast dynamic response and good steady performance within the whole load conditions, a new DC bus voltage control and current sharing strategy is proposed for the parallel LLC resonant converter. By ensuring that the LLC works in full-bridge mode with normal load and in half-bridge mode with light load, the DC bus voltage is controllable in all load range. Meanwhile, with a dead-band controller, two resonant inductor currents can be shared evenly. The following Section 5 will discuss the proposed control method under on-line mode and off-line mode separately, and corresponding simulation results will be given. 5. Control of the Variable Structure LLC Converter As shown in Figure 9, a hysteresis controller is proposed to transform the mode of the proposed LLC converter. Pinv is the output power of the inverter, it is equal to the output power of LLC converter when power loss of the inverter is ignored. PU is the minimum load for the full-bridge LLC converter, and PL is the maximum load for the half-bridge LLC converter. If the output power of inverter is above PU , LLC converter operates in the full-bridge mode. If the output power of inverter is below PL , LLC converter operates in half-bridge mode. Otherwise, As shown in Figure 9, a hysteresis controller is proposed to transform the mode of the proposed LLC converter. Pinv is the output power of the inverter, it is equal to the output power of LLC converter when power loss of the inverter is ignored. PU is the minimum load for the full-bridge LLC converter, PL is the maximum load for the half-bridge LLC converter. Energies 2017,and 10, 752 11 of 21 If the output power of inverter is above PU, LLC converter operates in the full-bridge mode. If the output power of inverter is below PL, LLC converter operates in half-bridge mode. Otherwise, the the mode the same. Furthermore, is a smaller little smaller order tocontinuous avoid continuous U , into mode staysstays the same. Furthermore, PL is aPLlittle than Pthan U, in P order avoid power power fluctuations around the transition gap. fluctuations around the transition gap. Figure Figure 9. 9. Hysteresis Hysteresis controller controller for for the the transform transform signal signal generation. generation. Energies 2017, 10, 752 Scheme in on-Line Mode 5.1. Proposed Control 11 of 21 As in Figure 10,inUon-Line the reference of the 400 V DC bus voltage, IL1 and IL2 are the 5.1.illustrated Proposed Control Scheme Mode 400_ref is resonant inductor RMS currents of each channel, f 1 andoff 2the are400 theVworking frequencies of each channel. As illustrated in Figure 10, U400_ref is the reference DC bus voltage, IL1 and IL2 are the When SIGNAL_FH is 0, the converter is transformed into half-bridge mode.of The resonant inductor RMS currents of each channel, f1 and f2 are the working frequencies each frequency channel. of two LLC resonant converters change is ontransformed the basis ofinto fh_onhalf-bridge . Then a dead band When SIGNAL_FH is start 0, theto converter mode. The controller frequency is of used to control the resonant 400 V DC bus voltage. If change the 400onVthe DCbasis bus of voltage U400 is lower (U400_ref − ∆U1 ), two LLC converters start to fh_on. Then a dead bandthan controller is used to control the 400 V DC busby voltage. the 400lower V DC bus U400 is 400 lower (U400_ref − ΔU1),Ifthe the frequencies are increased ∆f 1 , toIf attain gainvoltage and higher V than DC bus voltage. U400 is frequencies are increased by Δf 1 , to attain lower gain and higher 400 V DC bus voltage. If U 400 is higher higher than (U400_ref + ∆U1 ), the frequencies are altered by ∆f 1 , to attain higher gain and lower voltage. than (U400_ref ΔU 1), the frequencies are altered by Δf1, to attain higher gain and lower voltage. In this In this paper ∆f 1+ is defined as: paper Δf1 is defined as: −k1 · U400 − U400_re f U400 − U400_re f ≥ ∆U1 − k ⋅ U − U U − U ≥ Δ U ∆ f1 = (28) 400 _ ref ) 400 _ ref 1 ( 400 400 1 Δf1 0= (28) U400 − U400_re f < ∆U1 U 400 − U 400 _ ref < ΔU1 0 When SIGNAL_FH is 1, the gate signals of Q3 and Q4 return to normal. The LLC resonant SIGNAL_FH is 1, the gatewith signals of Q3 and Q4 return to normal. The LLC isresonant converterWhen operates in full-bridge mode an initial frequency of ff_on . The controller similar; the converter operates in full-bridge mode with an initial frequency of ff_on. The controller is similar; the difference is that the step of the dead-band control scheme of DC bus voltage is ∆f 2 : difference is that the step control scheme of the dead-band is Δf2: of DC bus voltage −k2 · U400 − U400_re f − U U 400 400_re f ≥ ∆U1 − k 2 ⋅ (U 400 − U 400 _ ref ) U 400 − U 400 _ ref ≥ Δ U 1 ∆ f 2 = Δf = (29) (29) 02 − U U 400 400_re f U −U < ΔU < ∆U1 0 400 400 _ ref 1 k1 and constant, they are selected thefast fastresponse response and stability requirements. 2 are k1 kand k2 are constant, they are selectedby by considering considering the and stability requirements. Figure 10. LLC control scheme in on-line mode. Figure 10. LLC control scheme in on-line mode. Simultaneously, another dead-band controller works to balance the two LLC currents. In Figure 10, the step of Δf3 is constant and in fact very small, so the allowable error scope ΔI is 0.02|IL1 − IL2|. If resonant inductor RMS current of first channel LLC is bigger than that of second channel LLC, and the error is over ΔI, working frequency of first channel LLC is increased by Δf3 and working frequency of second channel LLC is decreased by Δf3. On the contrary, the working frequency of first channel Energies 2017, 10, 752 12 of 21 Simultaneously, another dead-band controller works to balance the two LLC currents. In Figure 10, the step of ∆f 3 is constant and in fact very small, so the allowable error scope ∆I is 0.02|IL1 − IL2 |. If resonant inductor RMS current of first channel LLC is bigger than that of second channel LLC, and the error is over ∆I, working frequency of first channel LLC is increased by ∆f 3 and working frequency of second channel LLC is decreased by ∆f 3 . On the contrary, the working frequency of first channel LLC is decreased by ∆f 3 and the working frequency of second channel LLC is increased by ∆f 3 Otherwise, when the error between two RMS currents is over −∆I and below ∆I, which means two resonant currents are almost balanced, this dead band controller of current sharing doesn’t work. By use of fixed step of ∆f 3 in dead band controller, resonant currents may not be exactly the same. However, in practical application RMS values of resonant currents need not to be identical. Also, the dead band controller is simple and can make LLC converter more stable. 5.1.1. Transfer Conditions between Half-Bridge and Full-Bridge Mode Assuming the efficiency of inverter is η, the output voltage of LLC converters is U630_ref , the equivalent output resistance for each LLC, RP could be expressed as: RP = 2U 2 630_re f · η Pinv (30) According to load range selection criteria, to make sure that the transition between half-bridge and full-bridge mode is smooth, the LLC output resistance should satisfy Equations (24)–(27), that means: 2 max{ R , R } ≤ 2U 630_re f ·η ≤ min{ R , R } 2_H 2_F 1_H 1_F PL (31) max{ R , R } ≤ 2U 2 630_re f ·η ≤ min{ R , R } 1_H 1_F PU 2_H 2_F where R1_F , R1_H are the minimum solutions to (25) and (26), and R2_F , R2_H are the maximum solution to (24) and (27). The selection of PL and PU should meet (31). 5.1.2. Initial Working Frequency Selection At beginning of each working mode (full-bridge or half-bridge mode), a proper initial operating frequency is necessary to get a smooth transition performance. As is shown in Figure 10, when the converter changes from half-bridge mode to full-bridge mode, the initial frequency ff_on is the solution ! to the following equation: 2U 2 630_re f , C pc = Gr (32) G pc f f _on , Pinv_rate Pinv_rate is the rated output power of the inverter, and 2(U630_ref )2 /Pinv_rate is the corresponding equivalent output resistance of each LLC. When the converter changes from full-bridge mode to half-bridge mode, the initial frequency fh_on could be calculated as: ! 2U 2 630_re f GH_pc f h_on , , C pc = Gr (33) PL 5.2. Simulation Results in On-Line Mode In order to verify the proposed design scheme, a simulation model is fulfilled in MATLAB. The main simulation parameters are listed in Table 1. To simplify the model and shorten the running time of simulation, only battery is used as source here. To verify the proposed current sharing strategy, the different resonant tank parameters of two channels are given deliberately. To describe the current sharing result, a parameter named current unbalance factor (CUF) is given, which can be defined as absolute value of error between two resonant RMS currents divided by average value of two resonant RMS currents. CUF = |2(IL1 − IL2 )/( IL1 + IL2 )|. The simulation results in on-line mode are shown in Figure 11. iBattery is the current of battery, iA is inverter output current of phase A. u400 , u630 are the same as 400 V DC bus voltage U400 and 630 Energies 2017, 10, 752 First channel LLC Magnetizing inductor, Lm1 Second channel LLC resonant inductor, Lr2 Second channel LLC resonant capacitor, Cr2 Second channel LLC Magnetizing inductor, Lm2 400 V DC bus capacitor 630 V DC bus capacitor AC bus voltage 228 μH 65 μH 68 nF 223 μH 200 μF 200 μF 380 V (phase to phase) 13 of 21 V DC bus voltage U , but u400 , u630 represent instantaneous values in this article. factor According To describe the sharing result, a parameter named current unbalance (CUF)toisthe 630current given,scheme, which can as absolute of errorand between resonantbyRMS control u400beisdefined controlled by LLCvalue converters, u630 istwo controlled the currents inverter.divided by average value of two resonant RMS currents. CUF = |2(IL1 − IL2)/( IL1 + IL2)|. Table 1. Simulation The simulation results in on-line mode are shownParameters. in Figure 11. iBattery is the current of battery, iA is inverter output current of phase A. u400, u630 are the same as 400 V DC bus voltage U400 and 630 V Value DC bus voltage U630, but u400, uParameter 630 represent instantaneous values in this article. According to the control scheme, u400 isLLC controlled by LLC converters, and u 630 is controlled by the inverter. main resonant frequency, fr 78.8 kHz In Figure 11a, LLC the reference the battery current s, and secondaryof resonant frequency, fr2is 3 A before 1.336.0 kHzthe two LLC resonant channel LLC resonant inductor, 60 µHwith no ripple. At 1.3 s, r1 voltage is regulated converters operateFirst in half-bridge mode. The 400 V DCLbus First channel LLC resonant capacitor, C 68 nFof the inverter increase r1 the reference of battery current increases by 12 A/s, so the output currents First channel LLC Magnetizing inductor, Lm1 228 µH accordingly. At 1.5 s, the LLC resonant converters begin to operate in full-bridge mode, and their Second channel LLC resonant inductor, Lr2 65 µH frequencies are set to ff_on . During this transition, the 400 quickly, and the Second channel LLC resonant capacitor, Cr2V DC bus voltage 68 recovers nF minimum voltage during the transition is 386 V. After approximately 3 s, the reference of the battery Second channel LLC Magnetizing inductor, Lm2 223 µH current arrives at 37.5 A, and remains 400 V DC busunchanged. capacitor The entire system is stable 200 µFand the 400 V DC bus V DCFigure bus capacitor 200 µF results at light load voltage is flat during this 630 period. 11b shows the steady state simulation 380 V (phase to phase) condition (half bridge mode), AC andbus thevoltage 400 V DC bus voltage is stable. (a) (b) Figure 11. Simulation results in on-line mode: (a) transition waveforms; and (b) steady state waveforms Figure 11. Simulation results in on-line mode: (a) transition waveforms; and (b) steady state waveforms with light load. with light load. Figure 12 shows the current sharing results of LLC resonant converters with 0 to 7 kW load in In Figure thes,reference ofLLC the transforms battery current is 3 A before 1.3 s, figure and the resonant on-line mode.11a, At 1.5 half-bridge into full-bridge LLC. The in two innerLLC box shows converters operatewaveforms in half-bridge mode. The 400 V DCthat bustwo voltage is regulated with no ripple. 1.3 s, detailed current around 2.55 s. It proves full-bridge LLC converters workAt with theworking reference of batteryabove current by 12 A/s, so thefroutput therequired invertergain increase frequencies theincreases main resonant frequency . This iscurrents becauseof the is accordingly. At 1.5 above s, the fLLC resonant in full-bridge and their achieved slightly r, making full converters use of dropbegin scopeto ofoperate gain curve, as the lastmode, paragraph in Section 4.2.1 values two LLC resonant both 9.6 A in the box, CUF frequencies areshows. set to fThe During thisoftransition, the 400 Vcurrents DC busare voltage recovers quickly, andisthe f_on .RMS minimum voltage during the transition is 386 V. After approximately 3 s, the reference of the battery current arrives at 37.5 A, and remains unchanged. The entire system is stable and the 400 V DC bus voltage is flat during this period. Figure 11b shows the steady state simulation results at light load condition (half bridge mode), and the 400 V DC bus voltage is stable. Figure 12 shows the current sharing results of LLC resonant converters with 0 to 7 kW load in on-line mode. At 1.5 s, half-bridge LLC transforms into full-bridge LLC. The figure in inner box shows detailed current waveforms around 2.55 s. It proves that two full-bridge LLC converters work with working frequencies above the main resonant frequency fr . This is because the required gain is achieved slightly above fr , making full use of drop scope of gain curve, as the last paragraph in Section 4.2.1 shows. The RMS values of two LLC resonant currents are both 9.6 A in the box, CUF is almost 0. The result indicates that in on-line mode, the proposed current sharing method can balance currents at light and full load condition, even during load transition process. Energies 2017, 10, 752 14 of 21 almost 0.2017, The result Energies 752 indicates that in on-line mode, the proposed current sharing method can14balance of Energies 2017, 10,10, 752 14 21 of 21 currents at light and full load condition, even during load transition process. almost 0. The result indicates that in on-line mode, the proposed current sharing method can balance currents at light and full load condition, even during load transition process. Figure 12. 12. Two channel LLC LLC currents currents in in on-line on-line mode mode during during load load transition transition from from 00 to to 77kW kWload. load. Figure Two channel Figure 12. Two channel LLC currents in on-line mode during load transition from 0 to 7 kW load. 5.3. Proposed Proposed Control Control Scheme Scheme in in Off-Line Off-Line Mode Mode 5.3. 5.3. Proposed Control Scheme in Off-Line Mode In off-line off-line mode, mode, the the DC DC bus bus voltage voltage control control and and current current sharing sharing strategy strategy of of the the LLC LLC resonant resonant In In off-line mode, the DC bus voltage control and current sharing strategy of the LLC resonant converter is the DC bus voltage which is controlled by the converter is similar similar to tothe thestrategy strategyininon-line on-linemode, mode,but but the DC bus voltage which is controlled by converter is similar to theisstrategy in V on-line mode, but the DC bus voltage which is bus controlled byU the LLC resonant converters the 630 DC bus voltage U 630, and the 400 V DC voltage 400 is the LLC resonant converters is the 630 V DC bus voltage U630 , and the 400 V DC bus voltage U400 is LLC resonant converters is the 630 V DCand busdischarge voltage Umanagement 630, and the 400 V DC bus voltage U400 is controlled by the forestage storage charge converter. The architecture in controlled by the forestage storage charge and managementconverter. converter.The The architecture controlled the forestage charge and discharge discharge management architecture in in Figure 13 and andbyparameters parameters of storage the entire entire simulation model are are similar similar with with on-line on-line mode, mode, so the the details details Figure 13 of the simulation model so 13 and parameters of the entire simulation model are similar with on-line mode, so the details areFigure not given given here repeatedly. repeatedly. are not here are not given here repeatedly. Figure13. 13. LLC LLC control control scheme Figure schemein inoff-line off-linemode. mode. Figure 13. LLC control scheme in off-line mode. SimulationResults ResultsininOff-Line Off-LineMode Mode 5.4.5.4. Simulation 5.4. Simulation Results in Off-Line Mode In Figure 14a, prior to 1 s, AC load is 50 W, and LLC converter works in half-bridge mode. In Figure Figure 14a, prior prior to to 11 s, s, AC AC load load is is 50 W, W, and and LLC LLC converter works works in in half-bridge half-bridge mode. In The 630 V DC14a, bus voltage is regulated with 50 no ripple. At 1 s,converter the AC load changes to 7 kW, so mode. the The 630 V DC bus voltage is regulated with no ripple. At 1 s, the AC load changes to 77 kW, kW, so the the The 630resonant V DC bus voltage is regulated with no ripple. At 1and s, the AC load changes to LLC converter begins to work in full-bridge mode, frequency is set initially. During so this LLC resonant converter begins to work in full-bridge mode, and frequency is set initially. During this LLC resonantthe converter to work in full-bridge and frequency is set During this transition, 630 V DCbegins bus voltage recovers in 50 ms,mode, the settling time is 24 ms, theinitially. minimum voltage transition, the 630 V DC bus voltage recovers in 50 ms, the settling time is 24 ms, the minimum voltage transition, thetransition 630 V DCisbus recovers in 50 voltage ms, the is settling is 24 ms, the minimum voltage during the 586voltage V, and the maximum 641 V. time The entire system is stable during during thetransition transition 586 V,and andthe the simulation maximum voltage islight 641 V. The entire system is stable during during the isis586 voltage V. The system is stable the transition. Figure 14bV,shows themaximum resultsisat641 loadentire condition (half bridgeduring mode).the the transition. Figure 14b shows the simulation results at light load condition (half bridge mode). 630 V DCFigure bus voltage is regulated smoothly.results at light load condition (half bridge mode). 630 V transition. 14b shows the simulation 630 V DC bus voltage is regulated smoothly. Figure 15 shows the current sharing results of LLC resonant converters during load transition DC bus voltage is regulated smoothly. Figure 15 shows the current sharing results of LLC resonantcurrents converters during load27.0 transition from 0 to 15 7 kW in off-line mode. sharing The peakresults valuesof ofLLC two resonant resonant are during 27.6 A and A as Figure shows the current converters load transition from 0 to 7 kW in off-line mode. The peak values of two resonant currents are 27.6 A and 27.0 A A as as from 0 to 7 kW in off-line mode. The peak values of two resonant currents are 27.6 A and 27.0 Energies 2017, 10, 752 Energies 2017, 10, 752 15 of 21 15 of 21 Energies 2017, 10, 752 15 of 21 Figure 15 15shows. shows.The Thefigure figure inner shows detailed current waveforms around RMS Figure in in inner boxbox shows detailed current waveforms around 1.23 s. 1.23 RMSs.values values of two LLC resonant currents are 11.8shows with 7 kW load. Theindicate results indicate the proposed of two LLC currents arein11.8 A with 7AkW load. The results thataround the that proposed Figure 15resonant shows. The figure inner box detailed current waveforms 1.23 s. scheme RMS Energies 2017, 10, 752 15 of 21 values ofcurrents two LLCcurrents resonant currents are 11.8 A with 7 and kW load. The results indicate that the proposed scheme can divide evenly during transition at full load condition. can divide evenly during transition and at full load condition. scheme evenly during and atcurrent full load condition.around 1.23 s. RMS Figurecan 15 divide shows. currents The figure in inner boxtransition shows detailed waveforms values of two LLC resonant currents are 11.8 A with 7 kW load. The results indicate that the proposed scheme can divide currents evenly during transition and at full load condition. (a) (a) (b) (b) Figure 14.14. Simulation ininoff-line off-line mode: waveforms;and and(b) (b)steady steady state waveforms Figure 14. Simulation results in (a) transition waveforms; and (b) steady state waveforms Figure Simulationresults results(a) off-linemode: mode: (a) (a) transition transition waveforms; state waveforms (b) with light load. with light load. with light load. Figure 14. Simulation results in off-line mode: (a) transition waveforms; and (b) steady state waveforms with light load. Figure Twochannel channelLLC LLCcurrents currentsin in off-line off-line mode during Figure 15.15.Two duringload loadtransition transitionfrom from0 0toto7 kW. 7 kW. Figure 15. Two channel LLC modeduring during load transition to 7 kW. Figure 15. Two channel LLCcurrents currentsin in off-line off-line mode load transition fromfrom 0 to 70 kW. 6. Experimental Results 6. Results 6. Experimental Experimental Results 6. Experimental Results The proposed controlscheme schemeofofthe thefull-bridge full-bridge LLC LLC converters isisverified in a a7 7kW residential The proposed control converters The proposed control schemeofofthe thefull-bridge full-bridge LLC is verified in ain 7 kW residential The proposed control scheme LLCconverters converters is verified verified in a 7 kW kW residential residential PV system. Figure 16 shows the prototype system. PV Figure 16 the prototype PV system. Figure 16 shows the prototypesystem. system. PV system. system. Figure 16 shows shows the prototype system. Figure 16. 7 kW residential photovoltaic system hardware setup. Figure16. 16.77kW kWresidential residential photovoltaic photovoltaic system Figure systemhardware hardwaresetup. setup. Figure 16. 7 kW residential photovoltaic system hardware setup. Energies Energies2017, 2017,10, 10,752 752 16 16 of of 21 21 Design criteria and key components are listed in Table 2. Design criteria and key components are listed in Table 2. Table 2. Experimental parameters. Table 2. Experimental parameters. Parameter Value Parameter Value LLC rated power 4 kW (one channel) LLC main frequency, fr1 78.8 kHz LLC resonant rated power 4 kW (one channel) LLC resonant frequency, 36.0 LLCsecondary main resonant frequency, fr1 fr2 78.8kHz kHz 60 μH LLC resonant inductor, Lr fr2 LLC secondary resonant frequency, 36.0 kHz LLC Lr Cr µH 6860nF LLCresonant resonantinductor, capacitor, LLC capacitor, Cr Lm nF LLC resonant Magnetizing inductor, 22868μH LLC Magnetizing inductor, L 228 m LLC MOSFET (primary side) IPW65R045C7 (Infineon,µH Munich, Germany) LLC MOSFET (primary side) IPW65R045C7 (Infineon, Munich,America) Germany) LLC diode rectifier (secondary side) C4D10120E (Cree, Durhmorning, LLC diode rectifier (secondary side) C4D10120E (Cree, Durhmorning, America) Battery voltage 100 V DC Battery voltage 100 V DC PV maximum power 3.5 kW PV maximum power 3.5 kW 400 DC bus capacitor 200 400 VV DC bus capacitor 200μFµF 630 V DC bus capacitor 200 630 V DC bus capacitor 200μFµF AC bus voltage 380 AC bus voltage 380VV(phase (phasetotophase) phase) 12.5 coefficient coefficient k 1 k1 12.5Hz/V Hz/V coefficient k 2 k2 62.5Hz/V Hz/V 62.5 coefficient Step3, ∆f Δf 500Hz Hz 3 3 500 Step3, The PV PVarrays arrays replaced a chroma62150H-1000S programmable DCsupply power(Chroma, supply The areare replaced by a by chroma62150H-1000S programmable DC power (Chroma, Taoyuan, Taiwan) with PV simulator. The maximum output power of the PV Taoyuan, Taiwan) with PV simulator. The maximum output power of the PV array simulator is 3.5array kW. simulator is 3.5 kW. The comparison betweenand original waveforms and the optimization The comparison between original waveforms the optimization waveforms after usingwaveforms proposed after using proposed method is also discussed. Furthermore, in order to the availability control method is also control discussed. Furthermore, in order to verify the availability ofverify the proposed control of the proposed control method under real household loads such as air conditioner, microwave and method under real household loads such as air conditioner, microwave and refrigerator, experiments refrigerator, experiments real household loads are carried out. with real household loads with are carried out. 6.1. Experimental Experimental Results Results in in On-Line On-Line Mode Mode 6.1. In this this mode, mode, the the control controlobject objectisisuu400 400. Figure with the the original original In Figure 17 shows the experimental results with controlmethod methodin inon-line on-linemode. mode.AAsteady-state steady-stateerror errorofof−−25 Vexists existsin inuu400 400. After increasing the the load load control 25 V from 00 to to 77 kW, kW,there thereisisaapulse pulseof of437 437VVand andfluctuation fluctuationduring duringtransition. transition. The The settling settling time time is is about about from 0.35 s. s. The The current current balance balance is is out out of of control control during during transition transitionprocess. process. 0.35 Figure 17. Waveforms of AC load increases from 0 to 7 kW in on-line mode with the original Figure 17. Waveforms of AC load increases from 0 to 7 kW in on-line mode with the original control method. method. control Figures 18 and 19 show the experimental results with proposed control scheme in on-line mode. Figures and 19 show the experimental results withfrom proposed control in on-line In Figure 18,18 during the transition of the LLC converters 0 to 7 kW, thescheme fluctuation of 400mode. V DC In Figure 18, during the transition of the LLC converters from 0 to 7 kW, the fluctuation of 400 V DC bus voltage is only −14 V, and the settling time can be neglected. The currents of the two LLC resonant inductors are shared evenly at last, with RMS of 12.2 A and 12.0 A. The CUF is about 1.7%. Energies 2017, 10, 752 17 of 21 bus voltage is only −14 V, and the settling time can be neglected. The currents of the two LLC resonant inductors are evenly at last, with RMS of 12.2 A and 12.0 A. The CUF is about 1.7%. Energies 2017, 10,shared 752 17 of 21 Energies 2017, 10, 752 17 of 21 Figure 18. Waveforms of AC load increases from 0 to 7 kW in on-line mode with the original Figure 18.18.Waveforms kW in in on-line on-line mode modewith withthe theoriginal original Figure WaveformsofofAC ACload load increases increases from from 0 to 7 kW control method. control method. control method. Figure 19. Waveforms of AC load transition from 7 kW to 0 in on-line mode with the new Figure 19. Waveforms Figure 19. Waveforms of of AC AC load load transition transition from from 77 kW kW to 0 in on-line mode with the new control scheme. control scheme. scheme. control Figure 19 shows a similar result when the AC load decreases from 7 kW to 0. For 400 V DC bus Figure 19 19 shows aa similar similar result result when when the the AC AC load load decreases decreases from 77 kW kW to to 0. 0. For For 400 400 V V DC DC bus bus Figure voltage, the shows maximum voltage drop is 18 V and the peak value is from 422 V. What needs illustration is voltage, the themaximum maximumvoltage voltagedrop dropisis1818 V and peak value is 422 V. What needs illustration is voltage, and thethe peak value 422 V. What needs illustration is that that u630 is controlled by inverter and V the control method isisnot optimized. As space is limited, that u 630 is controlled by inverter and the control method is not optimized. As space is limited, u630although is controlled by inverter control method notdiscuss optimized. As space is limited, although the fluctuation of uand 630 isthe a little large, we willisnot this problem here. although the fluctuation of u 630 is a little large, we will not discuss this problem here. the fluctuation of u630 is a little large, we will not discuss this problem here. 6.2. Experimental Results in Off-Line Mode 6.2. Experimental Experimental Results Results in in Off-Line Off-Line Mode Mode 6.2. In this mode, the control object of LLC is u630. Figure 20 shows experimental results with the In this thiscontrol mode,method the control control objectmode. of LLC LLC 630.. Figure Figure 20 shows shows experimental results with the original in off-line Atisis nouu630 load condition, the controller works in burstwith mode. In mode, the object of 20 experimental results the original control method in off-line mode. At no load condition, the controller works in burst mode. The voltage ripple is about 50 V, and the peak value is about 693 V. During the transition from 0 to 7 original control method in off-line mode. At no load condition, the controller works in burst mode. ThekW, voltage ripple about V, peak value 693 transition in theripple worst is case, the 50 maximum voltage is is about 211 V. V. The settlingthe time is 0.63 s.from The voltage is about 50 V, and and the the peakdrop value isabout about 693 V.During During the transition from0 0toto7 the maximum voltage isisabout time isis0.63 Figures 21case, and show the experimental results with211 the proposed control method ins.s.off-line 7kW, kW,ininthe theworst worst case,22 the maximum voltagedrop drop about 211V. V.The Thesettling settling time 0.63 mode. As shown in Figure 21, when AC load increases from 0 to 7 kW, with the proposed Figures 21 and 22 show the experimental results with the proposed control method incontrol off-line Figures 21 and 22 show the experimental results with the proposed control method in off-line scheme, the 630 V DC bus voltage declines to 589 V during the transition and recovers after 21 ms. mode. As to 77 kW, kW, with with the the proposed proposed control control mode. As shown shown in in Figure Figure 21, 21, when when AC AC load load increases increases from from 00 to The peak voltage is 642 V. The maximum CUF is about 0.7%. The experimental results are scheme, the the 630 630 V V DC DC bus bus voltage voltage declines declines to to 589 589 V V during during the the transition transition and ms. scheme, and recovers recovers after after 21 21in ms. consistent with simulation results. Figure 22 shows the experimental waveforms with AC load The peak voltage is 642 V. The maximum CUF is about 0.7%. The experimental results are in The peak voltage is 642 V. The maximum CUF is about 0.7%. The experimental results are in consistent variation from 7 kW to 2.3 kW to 0. The 630 V DC bus voltage fluctuation is only about 10 V during consistent with results. simulation results. Figure shows the waveforms experimental waveforms with AC from load with simulation Figure 22 shows the22 experimental with AC load variation transition. variation from 7 kW to 2.3 kW to 0. The 630 V DC bus voltage fluctuation is only about 10 V during 7 kW to 2.3 kW to 0. The 630 V DC bus voltage fluctuation is only about 10 V during transition. transition. Energies 2017, 10, 752 Energies 2017, 2017, 10, 10, 752 752 Energies Energies 2017, 10, 752 18 of 21 18 of of 21 21 18 18 of 21 Figure20. 20. Waveforms Waveforms of of AC AC load loadincreases increases from from000toto to777kW kWinin inoff-line off-linemode modewith withthe theoriginal original Figure Figure 20. Waveforms of AC load increases from kW off-line mode with the original Figure 20. Waveforms of AC load increases from 0 to 7 kW in off-line mode with the original control method. control controlmethod. method. control method. Figure 21. 21. Waveforms Waveforms of of AC AC load load transition transition from from 00 to to 77 kW kW in in off-line off-line mode. mode. Figure Figure Figure21. 21.Waveforms WaveformsofofAC ACload loadtransition transitionfrom from0 0toto7 7kW kWininoff-line off-linemode. mode. Figure 22. 22. Waveforms Waveforms of of AC AC load load transition transition from from 77 kW kW to to 2.3 2.3 kW kW to to 00 in in off-line off-line mode. mode. Figure Figure22. 22.Waveforms WaveformsofofAC ACload loadtransition transitionfrom from7 7kW kWtoto2.3 2.3kW kWtoto0 0ininoff-line off-linemode. mode. Figure 6.3. Experimental Experimental Results Results with with Real Real Household Household Load Load 6.3. 6.3. Experimental Results with Real Household Load 6.3. Experimental Results with Real Household Load In order order to to verify verify the the availability availability of of the the improved improved control control method method for for the the residential residential PV PV system, system, In In order to verify the availability of the improved control method for the residential PV system, experiments are conducted with real household loads. Here the 400 V DC bus voltage and the 630 V V In order to verify the availability the improved method PVthe system, experiments are conducted with real real of household loads.control Here the the 400 V Vfor DCthe busresidential voltage and and 630 experiments are conducted with household loads. Here 400 DC bus voltage the 630 V DC bus bus voltage voltage are observed observed through a real real time time sampling device, uVSIGNAL400 SIGNAL400 represents 400the V DC DC bus experiments are conducted with real household loads. Here device, the 400 u DC bus voltage and 630bus V DC are through sampling represents 400 V DC bus voltage are observed through aa real time sampling device, u SIGNAL400 represents 400 V DC bus voltage, and u SIGNAL630 represents 630 V DC bus voltage. DC bus voltage are observed through a real time sampling device, u represents 400 V DC bus SIGNAL400 voltage, and and u uSIGNAL630 SIGNAL630 represents 630 V DC bus voltage. voltage, represents 630 V DC bus voltage. voltage, and uSIGNAL630 represents 630 V DC bus voltage. 6.3.1. Experimental Experimental Results Results with with Air Air Conditioner Conditioner in in On-Line On-Line Mode Mode 6.3.1. 6.3.1. ExperimentalResults Resultswith withAir AirConditioner Conditionerinin On-LineMode Mode 6.3.1. Experimental On-Line A 4-kW 4-kW air air conditioner conditioner is is used used as as an an AC AC load load in in on-line on-line mode. mode. Figure Figure 23 23 shows shows the the transient transient A A 4-kWair airconditioner conditionerisis usedasas anAC ACload loadinin on-linemode. mode.Figure Figure2323 showsthe thetransient transient A 4-kW used an on-line shows waveforms when when the the air air conditioner conditioner is is shutdown. shutdown. During During this this transition, transition, the the currents currents of of LLC LLC and and waveforms waveforms whenslowly, theair airconditioner conditioner shutdown. During thistransition, transition, themode. currents LLC and waveforms when the isisconverter shutdown. During this the currents ofof400 LLC and inverter decline and the LLC always works in full-bridge The V and inverter decline decline slowly, slowly, and and the the LLC LLC converter converter always always works works in in full-bridge full-bridge mode. mode. The The 400 400 V V and and inverter inverter decline slowly, and the LLC converter always works in full-bridge mode. The 400 V and 630 V 630 V V DC DC bus bus voltage voltage are are flat flat and and the the entire entire system system is is stable. stable. Here Here iiL1 L1 is current of first channel LLC 630 is current current of of first first channel channel LLC LLC 630 V DC bus voltage are the flat entire and the entireissystem is stable. Here iL1 is DC bus voltage are flat and system stable. Here i is current of first channel LLC resonant resonant inductor, inductor, and and iA is is inverter inverter output output current current of of phase phase A. L1 A. resonant resonant inductor, and iiAA is inverter output inductor, and iA is inverter output current of current phase A.of phase A. Energies 2017, 10, 752 Energies 2017, 10, 752 19 of 21 19 of 21 Figure23. 23.Waveforms Waveformswhen when4 4kW kWair airconditioner conditionershutdown shutdownininon-line on-linemode. mode. Figure 6.3.2. Experimental Results with Microwave and Refrigerator in Off-Line Mode 6.3.2. Experimental Results with Microwave and Refrigerator in Off-Line Mode In order to verify the impact loading response ability of the proposed control method, a 1.5 kW In order to verify the impact loading response ability of the proposed control method, a 1.5 kW microwaveoven ovenand and a 200 refrigerator used. Figure shows waveforms during turningmicrowave a 200 WW refrigerator areare used. Figure 24 24 shows thethe waveforms during turning-on on operations of the two loads. The 630 V DC bus voltage, phase voltage of inverter and first channel operations of the two loads. The 630 V DC bus voltage, phase voltage of inverter and first channel LLC LLC working frequency, are observed through the same real time sampling device. Here uSIGNALA working frequency, are observed through the same real time sampling device. Here uSIGNALA represents represents phasef A voltage, fSIGNALs1 represents working frequency of first channel LLC. During this phase A voltage, SIGNALs1 represents working frequency of first channel LLC. During this period, period, LLC transforms from to full-bridge as its workingshows, frequency shows, uto630 LLC transforms from half-bridgehalf-bridge to full-bridge mode as itsmode working frequency u630 declines declines 555 V and after 30 ms, the steady about 60 V. current the distorted current 555 V andto recovers afterrecovers 30 ms, the steady fluctuation is fluctuation about 60 V. is The distorted is caused by is caused by the microwave and refrigerator, which don’t have power factor correction ability. The the microwave and refrigerator, which don’t have power factor correction ability. The entire system entire system is stable. is stable. Figure 24. Waveforms when turn on microwave oven and refrigerator in off-line mode. Figure 24. Waveforms when turn on microwave oven and refrigerator in off-line mode. 7. Conclusions 7. Conclusions In this work, a new method to regulate voltage for a full-bridge LLC resonant converter under In this work, a new method to regulate voltage for a full-bridge LLC resonant converter under light load conditions is proposed to solve the voltage gain curve upwarp drift problem. This method light load conditions is proposed to solve the voltage gain curve upwarp drift problem. This method transforms a full-bridge LLC resonant converter into a half-bridge LLC resonant converter by transforms a full-bridge LLC resonant converter into a half-bridge LLC resonant converter by adapting adapting PFM driver signals simply. Ideal and actual FHA models are analyzed based on previous PFM driver signals simply. Ideal and actual FHA models are analyzed based on previous reference reference method. Furthermore, a new voltage and current sharing control scheme in on-line and offmethod. Furthermore, a new voltage and current sharing control scheme in on-line and off-line mode line mode to enhance LLC performance in a residential PV system is implemented. Based on this to enhance LLC performance in a residential PV system is implemented. Based on this control scheme, control scheme, the DC bus voltage is regulated smoothly in all load range, and the two LLC resonant the DC bus voltage is regulated smoothly in all load range, and the two LLC resonant inductor currents inductor currents are shared well. are shared well. Matlab simulation and experimental results, based on resistive load, are performed in the Matlab simulation and experimental results, based on resistive load, are performed in the laboratory. In on-line mode, steady-state error of 400 V DC bus voltage is eliminated under light load laboratory. In on-line mode, steady-state error of 400 V DC bus voltage is eliminated under light load conditions. During load transition from 0 to 7 kW, the 400 V DC bus voltage has a drop of 14 V in conditions. During load transition from 0 to 7 kW, the 400 V DC bus voltage has a drop of 14 V in simulation and stays stable in the experiments. The settling time declines from 0.35 s to almost 0 in simulation and stays stable in the experiments. The settling time declines from 0.35 s to almost 0 in the experiments. CUF is almost 0 in the simulation and 1.7% in the experiments. In off-line mode, the experiments. CUF is almost 0 in the simulation and 1.7% in the experiments. In off-line mode, burst mode is eliminated and ripple is restrained. During load transition from 0 to 7 kW, 630 V DC bus voltage has a drop of 42 V and a rise of 11 V in simulation, while it has a drop of 41 V and a rise Energies 2017, 10, 752 20 of 21 burst mode is eliminated and ripple is restrained. During load transition from 0 to 7 kW, 630 V DC bus voltage has a drop of 42 V and a rise of 11 V in simulation, while it has a drop of 41 V and a rise of 12 V in the experiments. The settling time declines from 0.63 s to 21 ms in the experiments. CUF is almost 0 in simulation and 0.7% in the experiments. Furthermore, the experimental results have also been carried out with real household loads. The waveforms show that the improved residential PV system can work stably with real household loads such as an air conditioner, microwave oven and refrigerator. Acknowledgments: This research was supported by the National High Technology Research and Development Program (863 Program) of China (Grant: 2015AA050603). The authors would also like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. 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In Proceedings of the International Symposium on Power Electronics, Electrical Drives, Automation and Motion IEEE, Taormina, Italy, 23–26 May 2006; pp. 200–207. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).