ping wang, yenan chen, youssef elasser, minjie chen power...
TRANSCRIPT
-
Small Signal Model for Very-Large-Scale Multi-Active-Bridge Differential Power Processing
(MAB-DPP) Architecture
Ping Wang, Yenan Chen, Youssef Elasser, Minjie Chen
Power Electronics Research Lab, Princeton University
Background & Motivation Systematic Small Signal Modeling Approach
➢ Large-Scale Modular DC Energy Systems
HDD Storage Server with MAB-DPP
Large-Scale MAB-DPP Simulation & Control
Load1
Load2
Load3
dc-ac
dc-ac
dc-ac
dc-ac
dc-ac
dc-ac
dc-ac
MAB-DPPDC Bus
Load4
Load5
Load6
Loadn
V1
V2
V3
V4
V5
V6
Vn
IbusΦ1
Phase Shift
Module
Φ2
Phase Shift
Module
Φ3
Phase Shift
Module
Φ4
Phase Shift
Module
Φ5
Phase Shift
Module
Φ6
Phase Shift
Module
Φn
Phase Shift
Module
V1
V2
V3
V4
V5
V6
Vn
SYSCLK
I1
I2
I3
I4
I5
I6
In
S1
S1' CB1
S2
S2' CB2
S3
S3' CB3
S4
S4' CB4
S5
S5' CB5
S6
S6' CB6
Sn
Sn' CBn
L1
L2
L3
L4
L5
L6
Ln
C2
C1
C3
C4
C5
C6
Cn
DPP Architecture Comparison
Fig. 2: An example ac-coupled differential
power processing (DPP) architecture.
➢ Large-Scale Multi-Active-Bridge Differential Power Processing
(MAB-DPP) Architecture
Load 1
Load 2
DC Bus
Load n
DC
AC
DC
AC
DC
AC
Load 1
Load 2
DC Bus
Load n
DC
AC
AC
DC
DC
AC
AC
DC
DC
AC
AC
DC
➢ Dc-Coupled v.s. Ac-Coupled DPP Architecture
Number of Devices Dc-Coupled Ac-Coupled Benefits
Dc-ac cells 2N N 50% switches reduction
Transformers N 1 1/N magnetic volume
Dc-ac-dc stages 2 1 Less conversion stages
Fig. 3: (a) Dc-coupled DPP architecture; (b) Ac-coupled DPP architecture.
(a) (b)
Table II: Advantages of the Ac-Coupled DPP Architecture.
DC AC DC DC AC
Fig. 1: Energy systems with numerous modular power converters.
➢ Improved Small Signal Model considering Power Losses
▪ Step 4. Obtaining System Transfer Function:
Fig. 4: Large-scale MAB-DPP with distributed
phase-shift control.൝𝑰 = 𝑮𝝓 × 𝝓 + 𝑮𝒗 × 𝑽
𝑽 = 𝑮𝒛 × 𝑰𝑽 = 𝑰 − 𝑮𝒛𝑮𝒗
−𝟏 𝑮𝒛𝑮𝝓 × 𝝓
Fig. 5: Small signal model for MAB-
DPP without considering losses.
Fig. 6: Simulation verification of
a 10-port MAB-DPP converter.
▪ Power losses can be modeled as an output resistance 𝑅𝑠𝑖 at each port.
▪ Output resistance 𝑅𝑠𝑖 is determined by the 𝜕𝑉𝑖
𝜕𝐼𝑖at each port.
▪ Based on the improved small signal model, the calculated bode plot
matches well with the simulation results considering power losses.
መ𝐼1መ𝐼2⋮መ𝐼𝑛
=
0 𝐺𝑣12𝐺𝑣21 0
⋯ 𝐺𝑣1𝑛⋯ 𝐺𝑣2𝑛
⋮ ⋮𝐺𝑣𝑛1 𝐺𝑣𝑛2
⋱ ⋮… 0
𝑑𝑉1𝑑𝑉2⋮
𝑑𝑉𝑛
+
𝐺𝜙11 𝐺𝜙12𝐺𝜙21 𝐺𝜙22
⋯ 𝐺𝜙1𝑛⋯ 𝐺𝜙2𝑛
⋮ ⋮𝐺𝜙𝑛1 𝐺𝜙𝑛2
⋱ ⋮… 𝐺𝜙𝑛𝑛
𝜙1𝜙2⋮𝜙𝑛
𝑉1𝑉2⋮ො𝑉𝑛
=
−𝑍1||
𝑘≠1
𝑍𝑘𝑍1𝑍2
σ𝑘=1𝑛 𝑍𝑘
𝑍2𝑍1σ𝑘=1𝑛 𝑍𝑘
−𝑍2||
𝑘≠2
𝑍𝑘
⋯𝑍1𝑍𝑛
σ𝑘=1𝑛 𝑍𝑘
⋯𝑍2𝑍𝑛
σ𝑘=1𝑛 𝑍𝑘
⋮ ⋮𝑍𝑛𝑍1
σ𝑘=1𝑛 𝑍𝑘
𝑍𝑛𝑍2σ𝑘=1𝑛 𝑍𝑘
⋱ ⋮
… −𝑍𝑛||
𝑘≠𝑛
𝑍𝑘
×
መ𝐼1መ𝐼2⋮መ𝐼𝑛
𝐼𝑖 =𝑃𝑖𝑉𝑖=
𝑗≠𝑖
𝑉𝑗
2𝜋𝑓𝐿𝑖𝑗𝜙𝑖𝑗(
|𝜙𝑖𝑗|
𝜋− 1)
𝜕𝐼𝑖𝜕𝑉𝑗
𝜕𝐼𝑖𝜕𝜙𝑗
▪ Step 1. Modeling Large Signal Current:
𝐺𝜙𝑖𝑗 =
𝑉𝑗
2𝜋𝑓𝐿𝑖𝑗1 −
2 𝜙𝑖𝑗
𝜋, 𝑗 ≠ 𝑖
𝑗≠𝑖
𝑉𝑗
2𝜋𝑓𝐿𝑖𝑗
2 𝜙𝑖𝑗
𝜋− 1 , 𝑗 = 𝑖
𝐺𝑣𝑖𝑗 =𝜙𝑖𝑗
2𝜋𝑓𝐿𝑖𝑗(𝜙𝑖𝑗
𝜋− 1)
▪ Step 2. Modeling Small Signal Current:
▪ Step 3. Considering the load structure:
𝑮𝒗 𝑮𝝓
𝑮𝒛
• 𝐺𝑣𝑖𝑖 is zero in ideal MAB.
(a)
(b)
(c)
Fig. 7: Operation waveforms
of MAB considering losses.
Fig. 8: Improved small signal model. Fig. 9: Bode plot of the improved
small signal model.
▪ Derived transfer function
matches very well with the
simulated bode plot (without
considering power losses).
▪ Power losses reduce the dc
gain of the magnitude response
and shift the phase response to
higher frequency.
Fig. 11: The calculated and simulated bode plots
of three phase to voltage transfer functions.
Fig. 10: SPICE simulation platform for a 100-port MAB-DPP system.
Fig. 12: A modular control strategy with
distributed phase-shift (DPS) module.
Fig. 14: Testbench of a HDD server with the
10-port MAB-DPP converter.▪ Experimental Measurement
Fig. 15: Measured voltage perturbation at port 10 ( ො𝑣10) with a phase perturbation ( 𝜙10).
(a) f = 1kHz (b) f = 2kHz (c) f = 5kHz
Fig. 17: Transient response of a port
voltage to a 2 A load step change.
Fig.16: Calculated and measured
transfer function from 𝜙10 to ො𝑣10.
▪ 700 uF output capacitance
▪ Overshoot : < 230 mV
▪ Settling time: < 200 us
▪ Meet hotswap requirement
of typical HDDs (5% VDD)
▪ Schematic of a 100-Port MAB-DPP Converter.
Fig. 13: A 300W 10-port MAB-DPP prototype
(with a U.S. quarter).
▪ A 10-Port MAB-DPP Prototype
▪ Differential power processing (DPP)
architecture can minimize the power
conversion stress and improve the
system performance.
▪ Ac-coupled DPP with a single multi-
winding transformer can reduce the
component count and improve the
power conversion efficiency.
• Higher power density
• Higher conversion efficiency
• Lower cost
• Power flow are closely coupled.
• Accurate modeling and scalable control
strategy is needed for very large scale
DPP system.
▪ Advantages: ▪ Challenges:
12 dB
Radius: 3.7 cm
Height: 1.2 cm
Power Density: >100w/in3