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Towards Power FPGA: Architecture, Modeling and Control of Multiport Power Converters
Ping Wang, Minjie Chen
Power Electronics Research Lab, Princeton University
Background & Motivation
Power Rating & Convergence Analysis
Control Framework
V1 V2
y12I1 I2
y1n
y2n
Vn
In
V3, , Vn-1
y1
yn
y2
V1 V2
C1 L12 C2I1 I2
L1n
L2n
Vn
Cn
In V3, , Vn-1
V1 V2
Vn
C1 L1
CnLn
C2L2
Lm
I1 I2
In
Fig. 1: Energy system with numerous modular power converters.
➢ Future applications need multiport power converters➢ Equivalent circuit of the multi-winding transformer
➢ Control framework
Fig. 4: Equivalent circuit.
Fig. 5: Control framework.
(a) Star model (b) Inductor Delta model (c) Impedance Delta model
➢ Power rating of the multiport converters
➢ Convergence analysis
Fig. 6: Power rating analysis.
Fig. 7: Convergence analysis.
▪ Maximal and minimal power in trapezoidal mode
▪ Maximal and minimal power in resonant mode
▪ If Ci is very large: trapezoidal mode,
▪ If Ci resonates with Li: resonant mode,
V1
V2
V3
DC/AC
DC/AC
DC/AC
AC/DCVBUF
Circuit Topology for Multiport Converters
➢ Multi-stage v.s. single-stage multiport converters
Number of Devices Multi-stage Single-stage Benefits
Dc-ac cells 6 4 33% size/cost reduction
Transformers 3 1 66% size/cost reduction
Dc-ac-dc stages 2 1 50% loss reduction
Fig. 2: (a) Multi-stage dc-ac-dc; (b) single-stage dc-ac-dc.
(a) (b)
➢ Circuit topology of a generalized multiport power converter
V1
C1 L1
Port 1
V2
C2 L2
Port 2
Vn
CnLn
Port n
V3
C3L3
Port 3
Fig. 3: Example topology of a multiport power converter.
Experimental Results
➢ Experimental results of three cases
Power (w) Port 1 Port 2 Port 3 Port 4
Case I
Target -30.00 0.00 30.00 0.00
Trapezoidal -27.25 0.9 32.4 0.6
Resonant -27.90 0.30 30.90 0.90
Case II
Target -30.00 10.00 20.00 0.00
Trapezoidal -27.67 10.8 21.3 0.6
Resonant -27.40 9.30 20.40 0.90
Case III
Target -30.00 5.00 10.00 15.00
Trapezoidal -27.83 5.1 11.4 15.6
Resonant -27.23 4.80 9.90 15.30
➢ Three example cases
Fig. 11: Experimental setup.
Fig. 12: Experimental waveforms.
Passive
Network
Port 1 Port 2
Port 3Port 4
10W
20W
Passive
Network
Port 1 Port 2
Port 3Port 4
5W
10W
15W
Passive
Network
Port 1 Port 2
Port 3Port 4
30W
(a) Case I
(b) Case II (c) Case III
Fig. 13: Three typical power flow.
Simulation Results
Vo
lta
ge
(V
)V
olt
ag
e (
V)
Vo
lta
ge
(V
)V
olt
ag
e (
V)
Cu
rre
nt
(A)
Cu
rre
nt
(A)
Cu
rre
nt
(A)
Cu
rre
nt
(A)
Time (us)
Vo
lta
ge
(V
)V
olt
ag
e (
V)
Vo
lta
ge
(V
)V
olt
ag
e (
V)
Cu
rre
nt
(A)
Cu
rre
nt
(A)
Cu
rre
nt
(A)
Cu
rre
nt
(A)
Time (us)
f: 500000Delay: -1.332E-07
L1L: 1e-6
R1R: 3e-3Half Bridge1
+-PWM
f: 500000Delay: -2.464E-08
L2L: 1e-6
R2R: 3e-3Half Bridge2
+-PWM
f: 500000Delay: 5.087E-08
L3L: 1e-6
R3R: 3e-3Half Bridge3
+-PWM
f: 500000Delay: 1.04E-07
L4L: 1e-6
R4R: 3e-3Half Bridge4
+-PWM
f: 500000Delay: -2.464E-08
L5L: 1e-6
R5R: 3e-3Half Bridge5
+-PWM
f: 500000Delay: -1.962E-08
L6L: 1e-6
R6R: 3e-3Half Bridge6
+-PWM
f: 500000Delay: -4.588E-09
L7L: 1e-6
R7R: 3e-3Half Bridge7
+-PWM
f: 500000Delay: 5.087E-08
L8L: 1e-6
R8R: 3e-3Half Bridge8
+-PWM
f: 500000Delay: -7.639E-08
L9L: 1e-6
R9R: 3e-3Half Bridge9
+-PWM
f: 500000Delay: -2.464E-08
L10L: 1e-6
R10R: 3e-3Half Bridge10
+-PWM
f: 500000Delay: 5.087E-08
L11L: 1e-6
R11R: 3e-3Half Bridge11
+-PWM
f: 500000Delay: 5.087E-08
L12L: 1e-6
R12R: 3e-3Half Bridge12
+-PWM
f: 500000Delay: -1.0393E-07
L13L: 1e-6
R13R: 3e-3Half Bridge13
+-PWM
f: 500000Delay: -2.464E-08
L14L: 1e-6
R14R: 3e-3Half Bridge14
+-PWM
f: 500000Delay: 5.087E-08
L15L: 1e-6
R15R: 3e-3Half Bridge15
+-PWM
f: 500000Delay: 7.6789E-08
L16L: 1e-6
R16R: 3e-3Half Bridge16
+-PWM
f: 500000Delay: -5.0094E-08
L17L: 1e-6
R17R: 3e-3Half Bridge17
+-PWM
f: 500000Delay: -7.6396E-08
L18L: 1e-6
R18R: 3e-3Half Bridge18
+-PWM
f: 500000Delay: 5.087E-08
L19L: 1e-6
R19R: 3e-3Half Bridge19
+-PWM
f: 500000Delay: 7.6789E-08
L20L: 1e-6
R20R: 3e-3Half Bridge20
+-PWM
f: 500000Delay: -1.3933E-07
L21L: 1e-6
R21R: 3e-3Half Bridge21
+-PWM
f: 500000Delay: -2.9682E-08
L22L: 1e-6
R22R: 3e-3Half Bridge22
+-PWM
f: 500000Delay: 4.5788E-08
L23L: 1e-6
R23R: 3e-3Half Bridge23
+-PWM
f: 500000Delay: 9.8460E-08
L24L: 1e-6
R24R: 3e-3Half Bridge24
+-PWM
f: 500000Delay: -2.9682E-08
L25L: 1e-6
R25R: 3e-3Half Bridge25
+-PWM
Transformer
C1C: 10e-6
C2C: 10e-6
C3C: 10e-6
C4C: 10e-6
C5C: 10e-6
C6C: 10e-6
C7C: 10e-6
C8C: 10e-6
C9C: 10e-6
C10C: 10e-6
C11C: 10e-6
C12C: 10e-6
C13C: 10e-6
C14C: 10e-6
C15C: 10e-6
C16C: 10e-6
C17C: 10e-6
C18C: 10e-6
C19C: 10e-6
C20C: 10e-6
C21C: 10e-6
C22C: 10e-6
C23C: 10e-6
C24C: 10e-6
C25C: 10e-6
f: 500000Delay: -2.464E-08
L26L: 1e-6
R26R: 3e-3 Half Bridge26
+- PWM
f: 500000Delay: -9.599E-09
L27L: 1e-6
R27R: 3e-3 Half Bridge27
+- PWM
f: 500000Delay: 4.579E-08
L28L: 1e-6
R28R: 3e-3 Half Bridge28
+- PWM
f: 500000Delay: -8.179E-08
L29L: 1e-6
R29R: 3e-3 Half Bridge29
+- PWM
f: 500000Delay: -2.968E-08
L30L: 1e-6
R30R: 3e-3 Half Bridge30
+- PWM
f: 500000Delay: 4.579E-08
L31L: 1e-6
R31R: 3e-3 Half Bridge31
+- PWM
f: 500000Delay: 4.579E-08
L32L: 1e-6
R32R: 3e-3 Half Bridge32
+- PWM
f: 500000Delay: -1.096E-07
L33L: 1e-6
R33R: 3e-3 Half Bridge33
+- PWM
f: 500000Delay: -2.968E-08
L34L: 1e-6
R34R: 3e-3 Half Bridge34
+- PWM
f: 500000Delay: 4.579E-08
L35L: 1e-6
R35R: 3e-3 Half Bridge35
+- PWM
f: 500000Delay: 7.152E-08
L36L: 1e-6
R36R: 3e-3 Half Bridge36
+- PWM
f: 500000Delay: -5.528E-08
L37L: 1e-6
R37R: 3e-3 Half Bridge37
+- PWM
f: 500000Delay: -8.179E-08
L38L: 1e-6
R38R: 3e-3 Half Bridge38
+- PWM
f: 500000Delay: 4.579E-08
L39L: 1e-6
R39R: 3e-3 Half Bridge39
+- PWM
f: 500000Delay: 7.152E-08
L40L: 1e-6
R40R: 3e-3 Half Bridge40
+- PWM
f: 500000Delay: -1.272E-07
L41L: 1e-6
R41R: 3e-3 Half Bridge41
+- PWM
f: 500000Delay: -1.962E-08
L42L: 1e-6
R42R: 3e-3 Half Bridge42
+- PWM
f: 500000Delay: 5.598E-08
L43L: 1e-6
R43R: 3e-3 Half Bridge43
+- PWM
f: 500000Delay: 1.097E-07
L44L: 1e-6
R44R: 3e-3 Half Bridge44
+- PWM
f: 500000Delay: -1.962E-08
L45L: 1e-6
R45R: 3e-3 Half Bridge45
+- PWM
f: 500000Delay: -1.461E-08
L46L: 1e-6
R46R: 3e-3 Half Bridge46
+- PWM
f: 500000Delay: 4.251E-10
L47L: 1e-6
R47R: 3e-3 Half Bridge47
+- PWM
f: 500000Delay: 5.598E-08
L48L: 1e-6
R48R: 3e-3 Half Bridge48
+- PWM
f: 500000Delay: -7.105E-08
L49L: 1e-6
R49R: 3e-3 Half Bridge49
+- PWM
f: 500000Delay: -1.962E-08
L50L: 1e-6
R50R: 3e-3 Half Bridge50
+- PWM
C26C: 10e-6
C27C: 10e-6
C28C: 10e-6
C29C: 10e-6
C30C: 10e-6
C31C: 10e-6
C32C: 10e-6
C33C: 10e-6
C34C: 10e-6
C35C: 10e-6
C36C: 10e-6
C37C: 10e-6
C38C: 10e-6
C39C: 10e-6
C40C: 10e-6
C41C: 10e-6
C42C: 10e-6
C43C: 10e-6
C44C: 10e-6
C45C: 10e-6
C46C: 10e-6
C47C: 10e-6
C48C: 10e-6
C49C: 10e-6
C50C: 10e-6
f: 500000Delay: 5.598E-08
L51L: 1e-6
R51R: 3e-3Half Bridge51
+-PWM
f: 500000Delay: 5.598E-08
L52L: 1e-6
R52R: 3e-3Half Bridge52
+-PWM
f: 500000Delay: -9.830E-08
L53L: 1e-6
R53R: 3e-3Half Bridge53
+-PWM
f: 500000Delay: -1.962E-08
L54L: 1e-6
R54R: 3e-3Half Bridge54
+-PWM
f: 500000Delay: 5.598E-08
L55L: 1e-6
R55R: 3e-3Half Bridge55
+-PWM
f: 500000Delay: 8.211E-08
L56L: 1e-6
R56R: 3e-3Half Bridge56
+-PWM
f: 500000Delay: -4.495E-08
L57L: 1e-6
R57R: 3e-3Half Bridge57
+-PWM
f: 500000Delay: -7.105E-08
L58L: 1e-6
R58R: 3e-3Half Bridge58
+-PWM
f: 500000Delay: 5.598E-08
L59L: 1e-6
R59R: 3e-3Half Bridge59
+-PWM
f: 500000Delay: 8.211E-08
L60L: 1e-6
R60R: 3e-3Half Bridge60
+-PWM
f: 500000Delay: -1.456E-07
L61L: 1e-6
R61R: 3e-3Half Bridge61
+-PWM
f: 500000Delay: -3.474E-08
L62L: 1e-6
R62R: 3e-3Half Bridge62
+-PWM
f: 500000Delay: 4.072E-08
L63L: 1e-6
R63R: 3e-3Half Bridge63
+-PWM
f: 500000Delay: 9.295E-08
L64L: 1e-6
R64R: 3e-3Half Bridge64
+-PWM
f: 500000Delay: -3.474E-08
L65L: 1e-6
R65R: 3e-3Half Bridge65
+-PWM
f: 500000Delay: -2.968E-08
L66L: 1e-6
R66R: 3e-3Half Bridge66
+-PWM
f: 500000Delay: -1.461E-08
L67L: 1e-6
R67R: 3e-3Half Bridge67
+-PWM
f: 500000Delay: 4.072E-08
L68L: 1e-6
R68R: 3e-3Half Bridge68
+-PWM
f: 500000Delay: -8.723E-08
L69L: 1e-6
R69R: 3e-3Half Bridge69
+-PWM
f: 500000Delay: -3.474E-08
L70L: 1e-6
R70R: 3e-3Half Bridge70
+-PWM
f: 500000Delay: 4.072E-08
L71L: 1e-6
R71R: 3e-3Half Bridge71
+-PWM
f: 500000Delay: 4.072E-08
L72L: 1e-6
R72R: 3e-3Half Bridge72
+-PWM
f: 500000Delay: -1.154E-07
L73L: 1e-6
R73R: 3e-3Half Bridge73
+-PWM
f: 500000Delay: -3.474E-08
L74L: 1e-6
R74R: 3e-3Half Bridge74
+-PWM
f: 500000Delay: 4.072E-08
L75L: 1e-6
R75R: 3e-3Half Bridge75
+-PWM
C51C: 10e-6
C52C: 10e-6
C53C: 10e-6
C54C: 10e-6
C55C: 10e-6
C56C: 10e-6
C57C: 10e-6
C58C: 10e-6
C59C: 10e-6
C60C: 10e-6
C61C: 10e-6
C62C: 10e-6
C63C: 10e-6
C64C: 10e-6
C65C: 10e-6
C66C: 10e-6
C67C: 10e-6
C68C: 10e-6
C69C: 10e-6
C70C: 10e-6
C71C: 10e-6
C72C: 10e-6
C73C: 10e-6
C74C: 10e-6
C75C: 10e-6
f: 500000Delay: 6.629E-08
L76L: 1e-6
R76R: 3e-3 Half Bridge76
+- PWM
f: 500000Delay: -6.050E-08
L77L: 1e-6
R77R: 3e-3 Half Bridge77
+- PWM
f: 500000Delay: -8.723E-08
L78L: 1e-6
R78R: 3e-3 Half Bridge78
+- PWM
f: 500000Delay: 4.072E-08
L79L: 1e-6
R79R: 3e-3 Half Bridge79
+- PWM
f: 500000Delay: 6.629E-08
L80L: 1e-6
R80R: 3e-3 Half Bridge80
+- PWM
f: 500000Delay: -1.212E-07
L81L: 1e-6
R81R: 3e-3 Half Bridge81
+- PWM
f: 500000Delay: -1.461E-08
L82L: 1e-6
R82R: 3e-3 Half Bridge82
+- PWM
f: 500000Delay: 6.112E-08
L83L: 1e-6
R83R: 3e-3 Half Bridge83
+- PWM
f: 500000Delay: 1.154E-07
L84L: 1e-6
R84R: 3e-3 Half Bridge84
+- PWM
f: 500000Delay: -1.461E-08
L85L: 1e-6
R85R: 3e-3 Half Bridge85
+- PWM
f: 500000Delay: -9.599E-09
L86L: 1e-6
R86R: 3e-3 Half Bridge86
+- PWM
f: 500000Delay: 5.443E-09
L87L: 1e-6
R87R: 3e-3 Half Bridge87
+- PWM
f: 500000Delay: 6.112E-08
L88L: 1e-6
R88R: 3e-3 Half Bridge88
+- PWM
f: 500000Delay: -6.575E-08
L89L: 1e-6
R89R: 3e-3 Half Bridge89
+- PWM
f: 500000Delay: -1.461E-08
L90L: 1e-6
R90R: 3e-3 Half Bridge90
+- PWM
f: 500000Delay: 6.112E-08
L91L: 1e-6
R91R: 3e-3 Half Bridge91
+- PWM
f: 500000Delay: 6.112E-08
L92L: 1e-6
R92R: 3e-3 Half Bridge92
+- PWM
f: 500000Delay: -9.273E-08
L93L: 1e-6
R93R: 3e-3 Half Bridge93
+- PWM
f: 500000Delay: -1.461E-08
L94L: 1e-6
R94R: 3e-3 Half Bridge94
+- PWM
f: 500000Delay: 6.112E-08
L95L: 1e-6
R95R: 3e-3 Half Bridge95
+- PWM
f: 500000Delay: 8.750E-08
L96L: 1e-6
R96R: 3e-3 Half Bridge96
+- PWM
f: 500000Delay: -3.983E-08
L97L: 1e-6
R97R: 3e-3 Half Bridge97
+- PWM
f: 500000Delay: -6.575E-08
L98L: 1e-6
R98R: 3e-3 Half Bridge98
+- PWM
f: 500000Delay: 6.112E-08
L99L: 1e-6
R99R: 3e-3 Half Bridge99
+- PWM
f: 500000Delay: 8.750E-08
L100L: 1e-6
R100R: 3e-3 Half Bridge100
+- PWM
C76C: 10e-6
C77C: 10e-6
C78C: 10e-6
C79C: 10e-6
C80C: 10e-6
C81C: 10e-6
C82C: 10e-6
C83C: 10e-6
C84C: 10e-6
C85C: 10e-6
C86C: 10e-6
C87C: 10e-6
C88C: 10e-6
C89C: 10e-6
C90C: 10e-6
C91C: 10e-6
C92C: 10e-6
C93C: 10e-6
C94C: 10e-6
C95C: 10e-6
C96C: 10e-6
C97C: 10e-6
C98C: 10e-6
C99C: 10e-6
C100C: 10e-6
➢ Simulation with 4 ports ➢ Simulation with 100 ports
Fig. 8: Simulated waveforms.
Fig. 9: 100-port “Power FPGA”.
Fig. 10: 100-port power programming.
V1
V2
V3
VBUF
DC/AC
DC/AC
DC/AC AC/DC
AC/DC
AC/DC
Newton-
Raphson Solver
Port 1
Measured Pi ,Vi
Port 2
Port n
Pa
ss
ive
Ne
two
rk
PID
Controller
Vi*, θi* Pi_ref,
Vi_ref
Vi_base ,
θi_base
...
P1
P2
Pn
𝑃𝑖 =
𝑘≠𝑖
𝑉𝑖𝑉𝑘𝜔𝐿𝑖𝑘
𝜙𝑖𝑘 1 −𝜙𝑖𝑘𝜋
𝑃𝑖 =8
𝜋2
𝑘=1
𝑛
𝑉𝑖𝑉𝑘(𝐺𝑖𝑘 cos𝜙𝑖𝑘 + 𝐵𝑖𝑘 sin𝜙𝑖𝑘)
𝑃1𝑃2⋮
𝑃𝑛−1
= 𝑓: 𝑅𝑛−1 → 𝑅𝑛−1
𝜙1𝜙2⋮
𝜙𝑛−1
𝑃𝑖_ max =𝜋
4
𝑘≠𝑖
𝑉𝑖𝑉𝑘𝜔𝐿𝑖𝑘
𝑃𝑖_ min = −𝜋
4
𝑘≠𝑖
𝑉𝑖𝑉𝑘𝜔𝐿𝑖𝑘
𝑏 =8
𝜋2
𝑘≠𝑖
𝑉𝑘_ max 𝐺𝑖𝑘2 + 𝐵𝑖𝑘
2
𝑎 ≥ 0
𝑃max =
8
𝜋2
𝑘≠𝑖
V𝑘maxG𝑖𝑘2 + B𝑖𝑘
2 − V𝑖_ max G𝑖𝑘 V𝑖_ max
8
𝜋2
σ𝑘≠𝑖 V𝑘_ max G𝑖𝑘2 + B𝑖𝑘
2
2
4σ𝑘≠𝑖 G𝑖𝑘8
𝜋2
𝑘≠𝑖
V𝑘maxG𝑖𝑘2 + B𝑖𝑘
2 − V𝑖_ max G𝑖𝑘 V𝑖_ max
𝑎 = −8
𝜋2
𝑘≠𝑖
𝐺𝑖𝑘
𝑎 < 0 & −𝑏
2𝑎≤ V𝑖_ max
𝑎 < 0 & −𝑏
2𝑎> V𝑖_ max
𝑎 < 0
𝑃min =
−8
𝜋2
𝑘≠𝑖
V𝑘maxG𝑖𝑘2 + B𝑖𝑘
2 + V𝑖_ max G𝑖𝑘 V𝑖_ max
8
𝜋2
σ𝑘≠𝑖 V𝑘_ max G𝑖𝑘2 + B𝑖𝑘
2
2
4σ𝑘≠𝑖 G𝑖𝑘
−8
𝜋2
𝑘≠𝑖
V𝑘maxG𝑖𝑘2 + B𝑖𝑘
2 + V𝑖_ max G𝑖𝑘 V𝑖_ max
𝑎 ≥ 0 &𝑏
2𝑎≤ V𝑖_ max
𝑎 ≥ 0 &𝑏
2𝑎> V𝑖_ max
(a) Trapezoidal
(b) Sinusoidal▪ Solver tool in Github: https://github.com/PingWang3741/Multiport-Power-Converter.git
(a) Trapezoidal
(b) Sinusoidal
Table II: Simulation & experimental results.
Table II: Advantages of the single-stage architecture.
