PWM–PFM hybrid controlled LCC resonant converter with wide ZVS range and narrow switching frequency variation Yiming Chen, Jianping Xu✉, Jing Cao, Leiming Lin and Hongbo Ma Variable frequency controlled LCC resonant converter suffers from wide variation of switching frequency. Although fixed frequency controlled LCC resonant converter benefits from constant switching frequency, it suffers from narrow zero voltage switching (ZVS) range of power switch and high circulating energy. A pulse width modulation – pulse frequency modulation (PWM-PFM) hybrid controlled LCC resonant converter is proposed to achieve wide ZVS range of power switch with narrow variation of switching frequency. Experiment results of a 500 W prototype are provided to verify theoretical analysis of the proposed converter.
Introduction: LCC resonant converter is widely adopted in industrial applications due to its advantages of zero voltage switching (ZVS) of power switch. However, conventional variable frequency controlled LCC resonant converter suffers from wide variation of switching frequency, and thus low utilisation of magnetic components. In order to overcome such problem, fixed frequency controlled LCC resonant converter has been proposed and studied. However, fixed frequency controlled LCC resonant converter suffers from narrow ZVS operation range and high circulating energy [1]. Although hybrid control provides a way to improve performance of LCC resonant converter, hybrid control strategies are usually complicated and lack flexibility [2]. In this Letter, a pulse width modulation – pulse frequency modulation (PWM-PFM) hybrid controlled LCC resonant converter is proposed to achieve ZVS operation of power switch under wide input voltage and load variation range. Theoretical analysis and experiment results show that the proposed converter combines the advantages of wide ZVS range of power switch of variable frequency control and high utilisation of magnetic components of fixed frequency control. PWM–PFM hybrid controlled LCC resonant converter: The schematic diagram of the proposed PWM–PFM hybrid controlled converter is shown in Fig. 1, its power stage is composed of input voltage source Vin, full-bridge inverter consisting of power MOSFETs S1–S4 with their corresponding body diodes and parasitic capacitors, resonant tank consisting of inductor Lr and capacitors Cs and Cp, transformer Tr, rectifier diodes D1 and D2, filter inductors Lf1 and Lf2, output capacitor Cf and load resistor RL. The PWM–PFM hybrid controller proposed in this Letter is illustrated in the block shown in Fig. 1. Lf1 S1
Vin
Tr
D1
n:1
D2
A
+ –
Io
S3
ir Cs
Lr
RL
+ Vo –
A/D
Cp
B S2
Cf
S4
Lf2 νo
PWM-PFM hybrid controller νgs4 νgs3 νgs2 νgs1 drive circuit
νc
– +
νδ
Σ – +
k
νfs
PI
Σ – +
CMP νsyn
νsaw
b
νref
Fig. 1 PWM–PFM hybrid controlled LCC resonant converter
The key waveforms of the proposed converter are shown in Fig. 2, where vAB is the output voltage of full-bridge inverter, ir is resonant current. vfs is the output of proportional integral (PI) compensator, and it determines the switching frequency of the proposed converter. vsaw and vδ are sawtooth waveform and conduction angle signal, respectively, and they determine the conduction angle δ of the proposed converter. vsyn and vc are synchronising signal and output of comparator CMP, respectively, and they determine the driving signals vgs1–vgs4.
As shown in Fig. 2, the driving signals of switches in the same leg are complementary to each other, and a phase difference exists between vgs1 and vgs4, and between vgs2 and vgs3. vAB is a quasi-square waveform with frequency fs and conduction angle δ. vsaw is sawtooth carrier waveform. vδ is compared with vsaw to produce vc, and vc determines the timing of vgs3 and vgs4. vsyn is a narrow pulse generated at the beginning of each cycle of vsaw and it determines the timing of vgs1 and vgs2. In PWM–PFM hybrid controlled LCC resonant converter, the relation of vδ and vfs is vd = −kvfs + b
(1)
As conduction angle δ is proportional to vδ and switching frequency fs is proportional to vfs, there exists
d = −Kfs + B
(2)
From (2) it can be known that both fs and δ are modulated simultaneously in the proposed converter.
vAB ir
θ
δ
(π – δ ) 2
ω st 2π
vfs
ω st
vδ vsaw vsyn
ω st ω st
vc vgs2 vgs1 vgs3 vgs4
ω st ω st ω st
Fig. 2 Key waveforms of proposed converter
ZVS condition: ZVS condition of LCC converter is that the zero-crossing phase of resonant current θ must be larger than the triggering phase of S4 [3], i.e.
u.
p−d 2
(3)
In fundamental harmonic approach (FHA), the zero-crossing phase of resonant current θ is also the input impedance angle of LCC resonant converter. Then θ and δ can be calculated by FHA as vs Cp Rac 1 Rac u = arctan vs Lr − − (4) vs Cs 1 + v2s Cp2 R2ac 1 + v2s Cp2 R2ac
2 Cp nVo p2 vs Cp vs vr 1+ d = 2 arcsin · − − + jQ 2Vin 2 Cs vr Cs vr vs (5) √ where ωs = 2πfs is switching angular frequency, vr = 1/ Lr Cs is resonant angular frequency, Rac = (n 2π 2RL)/2 is the equivalent ac resistance of transformer reflected to transformer primary side and
√secondary Q = 1/n2 RL Lr /Cs is quality factor. The relations of θ and δ with other circuit parameters are revealed by (4) and (5). Using similar analysis method in [4], it can be proved that θ usually increases with the increase of fs, and δ decreases with the increase of RL or with the increase of Vin in LCC resonant converter. For fixed frequency controlled LCC resonant converter, δ decreases when load decreases or when input voltage increases. The decrease of δ may lead to the failure of ZVS condition given by (3). However, for PWM–PFM hybrid controlled LCC resonant converter, the decrease of δ leads to the increase of fs, and hence larger θ. Therefore, by proper parameter design, ZVS condition given by (3) holds in wide input voltage and load range, thus a wide ZVS range can be achieved. Parameter design: The key issue of the proposed converter is to design control parameters K and B.
ELECTRONICS LETTERS 17th August 2017 Vol. 53 No. 17 pp. 1218–1220
(7)
B = Kfs(min) + d(max)
(8)
Experiment results: To verify the analysis results of PWM–PFM hybrid controlled LCC resonant converter, a 500 W prototype with 48 V output voltage, 100–200 V input voltage is built. The parameters of power stage are: Lr = 82 μH, Cs = 60 nF, Cp = 60 nF, n = 1.56, Cf = 470 μF, Lf1 = Lf2 = 80 μH. fs(min) and fs(max) are designed to be 105 and 120 kHz, respectively, and K and B are designed to be 1.086 × 10−4 and 14.313, respectively. The experimental waveforms are shown in Fig. 3. As ZVS operation of the switches in lagging leg is more difficult to realise [3], S4 is analysed to verify the ZVS operation of the proposed converter. νAB (100 V/div)
ir (10 A/div)
4.5 μs
νAB (100 V/div)
ir (10 A/div)
2.3 μs
9.6 μs νds4(100 V/div)
νgs4 (10 V/div)
2 μs/div
ZVS turn on
8.6 μs νds4 (100 V/div)
ZVS turn on
a νAB(100 V/div)
νgs4(10 V/div)
2 μs/div
b ir (10 A/div)
2.1 μs
νAB (100 V/div)
ir (10 A/div)
145 140 135 130 125 120 115 110 105 100
variable frequency controlled LCC PWM–PFM hybrid controlled LCC fixed frequency controlled LCC
145 140 135 130 125 120 115 110 105 100
variable frequency controlled LCC PWM–PFM hybrid controlled LCC fixed frequency controlled LCC
f s, kHz
d(max) − d(min) fs(max) − fs(min)
K=
From Figs. 3b and d it can be known that when load is 500 W and input voltage increases from 100 to 200 V, δ decreases from 0.53π to 0.39π, and fs increases from 116.3 to 120.5 kHz. A comparison of variable frequency controlled, PWM–PFM hybrid controlled and fixed frequency controlled LCC resonant converters is given in Fig. 4. Fig. 4 shows that when output power increases, or when input voltage decreases, switching frequency of these three LCC resonant converters decrease. Thus, when Po = 500 W and Vin = 100 V, the proposed converter operates at fs(min) = 104 kHz, and when Po = 100 W and Vin = 200 V, the proposed converter operates at fs(max) = 120 kHz. Hence, the variation of switching frequency of the proposed converter is 16 kHz, and the variation of switching frequency of variable frequency controlled LCC is 27 kHz, i.e. the proposed converter has narrower switching frequency variation than variable frequency controlled LCC resonant converter.
f s, kHz
When the proposed converter operates under minimal input voltage Vin(min) and maximal quality factor Q(max) (corresponding to the heaviest load condition), according to (4) and (5), it can be derived that the proposed converter operates at maximal conduction angle δ(max), minimal switching frequency fs(min) and minimal impedance angle θ(min). When the proposed converter operates under maximal input voltage Vin(max) and minimal quality factor Q(min) (corresponding to the lightest load condition), according to (4) and (5), it can be derived that the proposed converter operates at minimal conduction angle δ(min), maximal switching frequency fs(max) and maximal impedance angle θ(max). To design PWM–PFM hybrid controlled LCC, the first step is to design fs(min) and fs(max), then substitute fs(min), Vin(min), Q(max) into (4) and (5), δ(max) and θ(min) can be determined. Similarly, by substituting fs(max), Vin(max), Q(min) into (4) and (5), δ(min) and θ(max) can be determined. Finally, It is noted that fs(min) and δ(max) satisfy (2), and so do fs(max) and δ(min), hence K, B can be calculated as
hard switching
100
200
300 Po, W
400
a
500
hard switching
100
200
300 P o, W
400
500
b
Fig. 4 Relations of switching frequency and output power of LCC converters with different control a Vin = 100 V b Vin = 200 V
From Fig. 4 it can be also known that the proposed converter maintains ZVS operation within 100–200 V input voltage and 100–500 W output power. However, from Fig. 4a, it can be known that when input voltage is 100 V, fixed frequency controlled LCC losses ZVS operation when output power is lower than 450 W. From Fig. 4b, it can be known that when input voltage is 200 V, fixed frequency controlled LCC cannot achieve ZVS operation anymore, i.e. the proposed converter has wider ZVS operation range than fixed frequency controlled LCC resonant converter. Conclusions: A PWM–PFM hybrid controlled LCC resonant converter has been proposed to improve performance of LCC resonant converters. Theoretical analysis and experiment results show that the proposed converter benefits from wide ZVS range and narrow variation of switching frequency.
1.6 μs
8.5 μs νds4 (100 V/div) νgs4 (10 V/div)
ZVS turn on c
2 μs/div
8.3 μs νds4 (100 V/div) νgs4 (10 V/div)
ZVS turn on
2 μs/div
d
Fig. 3 Experimental waveforms of proposed converter a Vin = 100 V, Po = 500 W [δ = 2π(4.5 μs/9.6 μs) ≈ 0.94π, fs ≈ 104.2 kHz] b Vin = 100 V, Po = 100 W [δ = 2π(2.3 μs/8.6 μs) ≈ 0.53π, fs ≈ 116.3 kHz] c Vin = 200 V, Po = 500 W [δ = 2π(2.1 μs/8.5 μs) ≈ 0.49π, fs ≈ 117.6 kHz] d Vin = 200 V, Po = 100 W [δ = 2π(1.6 μs/8.3 μs) ≈ 0.39π, fs ≈ 120.5 kHz]
Figs. 3a–d show that ZVS operation of the proposed PWM–PFM hybrid controlled LCC resonant converter is realised under these four conditions of input voltage and output power. From Figs. 3a and b it can be known that when input voltage is 100 V and load decreases from 500 to 100 W, δ decreases from 0.94π to 0.53π, and fs increases from 104.2 to 116.3 kHz. From Figs. 3c and d it can be known that when input voltage is 200 V and load decreases from 500 to 100 W, δ decreases from 0.49π to 0.39π, and fs increases from 117.6 to 120.5 kHz. From Figs. 3a and c, it can be known that when load is 500 W and input voltage increases from 100 to 200 V, δ decreases from 0.94π to 0.49π and fs increases from 104.2 to 117.6 kHz.
© The Institution of Engineering and Technology 2017 Submitted: 12 June 2017 E-first: 27 July 2017 doi: 10.1049/el.2017.2248 One or more of the Figures in this Letter are available in colour online. Yiming Chen, Jianping Xu, Jing Cao, Leiming Lin and Hongbo Ma (School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, People’s Republic of China) ✉ E-mail:
[email protected] References 1 Aboushady, A.A., Ahmed, K.H., Finney, S.J., et al.: ‘Linearized large signal modeling, analysis, and control design of phase-controlled series-parallel resonant converters using state feedback’, Trans. Power Electron., 2013, 28, (8), pp. 3896–3911 2 Hiltunen, J., Väisänen, V., Juntunen, R., et al.: ‘Variable-frequency phase shift modulation of a dual active bridge converter’, Trans. Power Electron., 2015, 30, (4), pp. 7138–7148 3 Ye, Z., Jain, P.K., and Sen, P.C.: ‘A full-bridge resonant inverter with modified phase-shift modulation for high-frequency AC power distribution systems’, Trans. Ind. Electron., 2007, 54, (5), pp. 2831–2845 4 Ryu, S.H., Kim, D.H., Kim, M.J., et al.: ‘Adjustable frequency–dutycycle hybrid control strategy for full-bridge series resonant converters in electric vehicle chargers’, Trans. Ind. Electron., 2014, 61, (10), pp. 5354–5362
ELECTRONICS LETTERS 17th August 2017 Vol. 53 No. 17 pp. 1218–1220
