High-bandwidth control of unfolding-based AC-DC converters
An apparatus includes an unfolder with three input terminals connected to a three-phase AC power source and three output terminals, p-terminal, o-terminal, and n-terminal, and a three-port converter connected to the unfolder and feeding a direct current (“DC”) load. The three-port converter includes input capacitors. A feedback control loop includes outputs of a p-terminal modulation index derived from a difference between p-terminal current and a p-terminal reference current and an n-terminal modulation index derived from a difference between n-terminal current and an n-terminal reference current. A feedforward control loop outputs an emulated p-terminal current and an emulated n-terminal current derived from differences between DC-link voltages and ideal DC-link voltages. A duty cycle controller is configured to generate duty cycles controlling switches of the three-port converter derived from the modulation indexes and the emulated currents.
1 . An apparatus comprising:
an unfolder comprising three input terminals that connect to a three-phase alternating current (“AC”) power source with grid inductances and comprising three unfolder output terminals comprising a p-terminal, an n-terminal and an o-terminal;
a three-port converter connected to the three output terminals of the unfolder, the three-port converter configured to feed power to a direct current (“DC”) load connected to converter output terminals of the three-port converter, wherein the three-port converter comprises input capacitors across three three-port converter input terminals;
a feedback control loop comprising outputs of a p-terminal modulation index m p derived from a difference between p-terminal current i p and a p-terminal reference current i p-ref and an n-terminal modulation index m n derived from a difference between n-terminal current i n and an n-terminal reference current i n-ref ,
a feedforward control loop comprising outputs of an emulated p-terminal current i p-emu derived from a difference between a p-terminal direct current (“DC”)-link voltage v po measured across the p-terminal and the o-terminal and an ideal p-terminal DC-link voltage v po-ideal and an emulated n-terminal current i n-emu derived from a difference between an n-terminal DC-link voltage v on measured across the o-terminal and the n-terminal and an ideal n-terminal DC-link voltage v on-ideal ; and
a duty cycle controller configured to generate duty cycles controlling the switches of the three-port converter, the duty cycles derived from the p-terminal modulation index m p , the emulated p-terminal current i p-emu , the n-terminal modulation index m n , and the emulated n-terminal current i n-emu .
2 . The apparatus of claim 1 , wherein the feedforward control loop is configured to emulate damping resistors configured to damp a resonance formed between grid inductances and the input capacitors.
3 . The apparatus of claim 1 , wherein the feedforward control loop is configured to maintain a positive control phase margin and a stable feedback control loop at bandwidth values lower than the resonant frequency of grid inductances and the input capacitors of the three-port converter.
4 . The apparatus of claim 1 , wherein the feedforward control loop is configured to maintain a positive control phase margin and a stable feedback control loop at bandwidth values higher than the resonant frequency.
5 . The apparatus of claim 1 , wherein the ideal p-terminal DC-link voltage v po-ideal and the ideal n-terminal DC-link voltage v on-ideal comprise two ideal unipolar piece-wise sinusoidal DC voltage waveforms offset from each other by a half of a period.
6 . The apparatus of claim 5 , wherein the unfolder converts bipolar AC voltages into two unipolar piece-wise sinusoidal DC voltage waveforms offset from each other by a half of a period, which are present at the three output terminals of the unfolder, wherein the two unipolar piece-wise sinusoidal DC voltage waveforms are affected by oscillating voltages and currents caused due to a resonance associated with grid inductances of the three-phase AC power source and the input capacitors.
7 . The apparatus of claim 5 , wherein the ideal two unipolar piece-wise sinusoidal DC voltage waveforms offset from each other by a half of a period comprise a scaled representation of an idealized positive portion of each of three line-voltages of the three-phase AC power source realized across the p-terminal and the o-terminal and across the o-terminal and the n-terminal without oscillations caused by a resonance between grid inductances from the three-phase AC power source and the input capacitors.
8 . The apparatus of claim 1 , wherein the p-terminal reference current i p-ref and the n-terminal reference current in-ref comprise a scaled representation of an idealized p-terminal current i p and an idealized n-terminal current i n without oscillations caused by a resonance between grid inductances from the three-phase AC power source and capacitance of the input capacitors.
9 . The apparatus of claim 1 , wherein the duty cycles comprise a p-terminal duty cycle d p and an n-terminal duty cycle d n wherein:
d
p
=
2
π
sin
-
1
(
m
p
(
sin
(
f
p
(
θ
g
r
i
d
)
)
-
i
p
-
e
m
u
I
g
m
)
)
;
and
d
n
=
2
π
sin
-
1
(
m
n
(
sin
(
f
n
(
θ
g
r
i
d
)
)
-
i
n
-
e
m
u
I
g
m
)
)
,
where:
θ grid is a current position in a period of a phase of the three-phase AC power source;
I gm is a peak grid current;
m p =G PI (i p-ref −i p ); and
m n =G PI (i n-ref −i n ), where GPI comprises compensation from a proportional-integral (“PI”) compensation;
i p-emu =k emu (v po-ideal −v po );
i n-emu =k emu (v on-ideal −v on );
k emu is a proportionality constant; and
f p and f n are functions according to:
Sector
θ grid grid angle
f p
f n
I
0 ≤ θ grid < π/3
θ grid + π/2
θ grid + π/6
II
π/3 ≤ θ grid < 2π/3
θ grid − π/6
θ grid + π/6
III
2π/3 ≤ θ grid < π
θ grid − π/6
θ grid − π/2
IV
π ≤ θ grid < 4π/3
θ grid − 5π/6
θ grid − π/2
V
4π/3 ≤ θ grid < 5π/3
θ grid − 5π/6
θ grid − 7π/6
VI
5π/3 ≤ θ grid < 2π
θ grid + π/2
θ grid − 7π/6
10 . The apparatus of claim 1 , wherein the three-port converter comprises a switching section, a resonant tank section, and a rectification section, the resonant tank section comprising one or more resonant tank inductors and one or more resonant tank capacitors and the rectification section comprising output terminals configured to connect to a load and the rectification section configured to rectify a waveform present at an output of the resonant tank section.
11 . The apparatus of claim 10 , wherein the resonant tank section comprises one of:
a transformer; and
a primary coil and a secondary coil separated from the primary coil by an air gap and wherein the primary coil and the secondary coil are configured for wireless power transfer.
12 . The apparatus of claim 1 , wherein the duty cycle controller further generates the duty cycles using a current position θ grid in a period of a phase of the three-phase AC power source.
13 . A power converter comprising:
an unfolder comprising an input connection comprising three input terminals that connect to a three-phase alternating current (“AC”) power source with grid inductances and comprising an output connection with three unfolder output terminals comprising a p-terminal, an n-terminal and an o-terminal;
a three-port converter connected to the three output terminals of the unfolder, the three-port converter configured to feed power to a direct current (“DC”) load connected to converter output terminals of the three-port converter, wherein the three-port converter comprises input capacitors across three three-port converter input terminals and switches that strategically operate to feed DC power to the DC load, the three-port converter comprising a switching section, a resonant tank section, and a rectification section, the resonant tank section comprising one or more resonant tank inductors and one or more resonant tank capacitors and the rectification section comprising the converter output terminals and the rectification section configured to rectify a waveform present at an output of the resonant tank section;
a feedback control loop comprising outputs of a p-terminal modulation index m p derived from a difference between a p-terminal current i p and a p-terminal reference current i p-ref and an n-terminal modulation index m n derived from a difference between an n-terminal current i n and an n-terminal reference current i n-ref ,
a feedforward control loop comprising outputs of an emulated p-terminal current i p-emu derived from a difference between a p-terminal direct current (“DC”)-link voltage v po measured across the p-terminal and the o-terminal and an ideal p-terminal DC-link voltage v po-ideal and an emulated n-terminal current i n-emu derived from a difference between an n-terminal DC-link voltage Von measured across the o-terminal and the n-terminal and an ideal n-terminal DC-link voltage v on-ideal ; and
a duty cycle controller configured to generate a p-terminal duty cycle d p controlling a first portion of switches of the three-port converter, the p-terminal duty cycle d p derived from the p-terminal modulation index m p and the emulated p-terminal current i p -emu, and an n-terminal duty cycle d n controlling a second portion of switches of the three-port converter, the n-terminal duty cycle d n derived from the n-terminal modulation index m n and the emulated n-terminal current i n-emu .
14 . The power converter of claim 13 , wherein the three-port converter comprises a T-type bridge.
15 . The power converter of claim 13 , wherein the feedforward control loop is configured to emulate damping resistors configured to damp a resonance formed between grid inductances and the input capacitors.
16 . The power converter of claim 13 , wherein the resonant tank section comprises a transformer.
17 . The power converter of claim 13 , wherein the resonant tank section comprises a primary coil and a secondary coil separated from the primary coil by an air gap and wherein the primary coil and the secondary coil are configured for wireless power transfer.
18 . The power converter of claim 13 , wherein the feedforward control loop is configured to maintain a positive control phase margin and a stable feedback control loop at bandwidth values lower than the resonant frequency of grid inductances and the input capacitors of the three-port converter.
19 . The power converter of claim 13 , wherein the feedforward control loop is configured to maintain a positive control phase margin and a stable feedback control loop at bandwidth values higher than the resonant frequency.
20 . An apparatus comprising:
an unfolder comprising an input connection comprising three input terminals that connect to a three-phase alternating current (“AC”) power source with grid inductances and comprising an output connection with three unfolder output terminals comprising a p-terminal, an n-terminal and an o-terminal;
a three-port converter connected to the three output terminals of the unfolder, the three-port converter is configured to feed power to a direct current (“DC”) load connected to converter output terminals of the three-port converter, wherein the three-port converter comprises input capacitors across three three-port converter input terminals;
a feedback control loop comprising outputs of a p-terminal modulation index m p derived from a difference between a p-terminal current i p and a p-terminal reference current i p-ref and an n-terminal modulation index m n derived from a difference between n-terminal current i n and an n-terminal reference current i n-ref ,
a feedforward control loop comprising outputs of an emulated p-terminal current i p-emu derived from a difference between a p-terminal direct current (“DC”)-link voltage v po measured across the p-terminal and the o-terminal and an ideal p-terminal DC-link voltage v po-ideal and an emulated n-terminal current i n-emu derived from a difference between an n-terminal DC-link voltage von measured across the o-terminal and the n-terminal and an ideal n-terminal DC-link voltage v on-ideal ; and
a duty cycle controller configured to generate a p-terminal duty cycle d p controlling a first portion of switches of the three-port converter, the p-terminal duty cycle d p derived from the p-terminal modulation index m p and the emulated p-terminal current i p-emu , and an n-terminal duty cycle d n controlling a second portion of switches of the three-port converter, the n-terminal duty cycle d n derived from the n-terminal modulation index m n and the emulated n-terminal current i n-emu ,
wherein the feedforward control loop is configured to emulate damping resistors configured to damp a resonance formed between grid inductances and the input capacitors,
wherein the ideal p-terminal DC-link voltage v po-ideal and the ideal n-terminal DC-link voltage v on-ideal comprise two ideal unipolar piece-wise sinusoidal DC voltage waveforms offset from each other by a half of a period, and
wherein the p-terminal reference current i p-ref comprises and the n-terminal reference current i n-ref comprises a scaled representation of an idealized p-terminal current i p and an idealized n-terminal current i n without oscillations caused by the resonance between the grid inductances from the three-phase AC power source and the input capacitors.