and repetitive control of grid connected...
Post on 06-Jul-2020
8 Views
Preview:
TRANSCRIPT
H∞ AND REPETITIVE CONTROLOF GRID-CONNECTED INVERTERS
Qing-Chang Zhongzhongqc@ieee.org
Electrical Drives, Power and Control Group
Dept. of Electrical Eng. & Electronics
The University of Liverpool
United Kingdom
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 1/33
Outline
Introduction
System structure
Modelling and controller design
Experimental results
Overview of other projects
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 2/33
DC-AC converters in the contextof distributed generation
Local generator
Diode
Rectifier
DC-AC
Converter
Micro-grid
grid DC link
Gas turbines Wind-mills etc.
Fuel cells Photo-voltaic etc.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 3/33
Control problems involved
+
-
Ls , Rs va
vb
vc
ia
ib
ic
ea
eb
ec
VDC
C
vga
vgb
vgc
Circuit Breaker
Lg , Rg
Power quality control: to reduce THD
Provision of a a non-drifting neutral point/line
Power flow control: to regulate P/Q
Phase-locked loop (PLL): to synchronise with the grid
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 4/33
Power quality improvementPower quality is an important problem for renewableenergy and distributed generation. The maximum totalharmonic distortion (THD) of output voltage allowedis 5% (120V −69kV ). The maximum THD allowed incurrent is below:
Odd harmonics Maximum current THD
< 11th < 4%
11th − 15th < 2%
17th − 21th < 1.5%
23rd − 33rd < 0.6%
> 33rd < 0.3%
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 5/33
H∞ repetitive voltage-controlled VSIs
DC power source
Inverter bridge
LC filter
Transformer
PWM modulation
Internal model M and stabilizing compensator C
ia ib ic
Id* Iq*
ua ub uc
-
PI controllers
uref e
Id Iq
abc
dq + +
θ
Power controller
+
Voltage controller
PLL
abc
dq
ugb uga ugc
abc
dq
u Ud Uq
+ +
- +
- +
θ
Id Iq
An inner voltage loop to track the reference voltageuref
An outer power loop to regulate active powerP and
reactive powerQ.Q.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 6/33
Repetitive controlIncorporating an internal model, a local positivefeedback of a delay linee−τds cascaded with alow-pass filterW (s), to track or reject periodicsignals with a periodτ . Normally,τd ≈ τ .
A stabilising controller is normally needed.
uref plant
stabilizing
compensator
u
e ug
sdesW
τ−)(
+
internal model
+ w
p
P
C
M
Q.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 7/33
Poles of the internal model
−18 −16 −14 −12 −10 −8 −6 −4 −2 0−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1x 10
4
Re
Im
true poles
approximated poles * o
Resk ≈1
τd
lnτdωc
√
(τdωc)2 + (2kπ)2= −
1
2τd
ln
(
1 + (2kπ
τdωc
)2)
,
Im sk ≈2kπ − tan−1 2kπ
τdωc
τd
≈2kπ
τd
(
1 −1
τdωc
)
.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 8/33
Single-phase circuit
PWM ic Rf Lf Rg
u
grid Cf
ug
filter inductor grid interface inductor uc
Lg i1 i2
Sc
+ - VDC
neutral
uf
Rd
Inverter bridge
uo
Consists of the inverter bridge, an LC filter (Lf
andCf ), a grid interface inductorLg, and acircuit breakerSC
uf ≈ u: the PWM block and the inverter bridgecan be ignored when designing the controller.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 9/33
Modelling
States:x =[
i1 i2 uc
]T
External inputs: w =[
ug uref
]Tandu.
Output:e = uref−u0, whereu0 = uc+Rd(i1−i2)is the output voltage of the inverter.
The plantP can then be described by the state equation
x = Ax + B1w + B2u
and the output equation
y = e = C1x + D1w + D2u
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 10/33
A =
−Rf+Rd
Lf
Rd
Lf− 1
Lf
Rd
Lg−
Rg+Rd
Lg
1Lg
1Cf
− 1Cf
0
,
B1 =
0 0
− 1Lg
0
0 0
, B2 =
1Lf
0
0
,
C1 =[
−Rd Rd −1]
, D1 =[
0 1]
, D2 = 0.
The transfer function from[
w u]T
to e is then
P =
[
A B1 B2
C1 D1 D2
]
.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 11/33
Formulation as an H∞ problem
P
C u
e w
W
+
µ ξ v a
b P~
z~
y~
w~
Wd
ud
Break the loop involving the delay
Add the computational delay blockWdQ.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 12/33
W =
[
Aw Bw
Cw 0
]
=
[
−ωc ωc
1 0
]
Wd =
[
Ad Bd
Cd Dd
]
=
[
− 2T
4T
1 −1
]
P =
A B2Cd 0 0 B1 B2Dd
0 Ad 0 0 0 Bd
BwC1 BwD2Cd Aw Bwξ BwD1 BwD2Dd
DwC1 DwD2Cd Cw Dwξ DwD1 DwD2Dd
0 0 0 0 0 µ
C1 D2Cd 0 ξ D1 D2Dd
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 13/33
System stabilityThe original closed-loop system is exponentially sta-ble if the designed closed-loop system is stable andits transfer function froma to b, denotedTba, satisfies‖Tba‖∞ < 1, where
Tba =
1 −
A B2
C1 D2
WdC
−1
W
=
A B2Cd B2DdCc 0 0
0 Ad BdCc 0 0
BcC1 BcD2Cd Ac + BcD2DdCc BcCw 0
0 0 0 Aw Bw
C1 D2Cd D2DdCc Cw 0
.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 14/33
Design exampleParameters of the inverter
Parameter Value Parameter Value
Lf 150µH Rf 0.045Ω
Lg 450µH Rg 0.135Ω
Cf 22µF Rd 1Ω
42V DC voltage source
The generated three-phase voltage is connected tothe grid via a controlled circuit breaker and astep-up transformer.
The sampling frequency is5 kHz and the PWMswitching frequency is20 kHz.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 15/33
Experimental setup
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 16/33
Circuit breaker
Measure 2 Measure 1 PCB
DC power source Inverter Output
filter
Transformer
dSpace 1104
da db dc i u
Local load
ug
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 17/33
Controller design
W =
[
−2550 2550
1 0
]
for f = 50Hz and
Wd =
[
−10000 20000
1 −1
]
.
ξ = 2.5 andµ = 0.8.
Using the MATLABhinfsyn algorithm, theH∞ con-troller C which nearly minimises theH∞ norm of thetransfer matrix fromw to z is obtained as
C(s) =735.2737(s + 1e004)(s2 + 9132s + 4.058e008)
(s + 1.109e004)(s + 2550)(s2 + 9515s + 4.232e008).
The resulting‖Tba‖∞ is 0.8426.Q.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 18/33
Controller reduction
C(s) =735.2737(s + 1e004)(s2 + 9132s + 4.058e008)
(s + 1.109e004)(s + 2550)(s2 + 9515s + 4.232e008).
It can be reduced to
C(s) =735.27
s + 2550= KpW (s)
with Kp = 735.272550 without causing noticeable per-
formance degradation, after cancelling the poles andzeros which are close to each other. This leads to‖Tba‖∞ = 0.8222, which still maintains the stabilityof the system.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 19/33
Resulting controller
uref plant
u
e ug
sde τ−
+
internal model
+ w
P
C
M
)(sW)(sW
pK
)(sW
uref plant
stabilizing
compensator
u
e ug
sdesW
τ−)(
+
internal model
+ w
p
P
C
M
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 20/33
Steady-state responses
-20
-10
0
10
20
Vo
ltag
e [V
]
0.00 0.01 0.02 0.03 0.04 0.05
Time [sec]
#1:1
#1:2
-4
-2
0
2
4
Vo
ltag
e er
ror
[V]
0.00 0.01 0.02 0.03 0.04 0.05
Time [sec]
#1:1
(a) voltageuA and its referenceuref (b) voltage tracking errore
-4
-2
0
2
4
Cu
rren
t [A
]
0.00 0.01 0.02 0.03 0.04 0.05
Time [sec]
#1:1
#1:2
(c) output currentiA and its reference
The recorded current THD was2.47%, while the output voltage
THD was1.74% and the grid voltage THD was2.11%.Q.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 21/33
Transient responses
-4
-2
0
2
4
Cu
rren
t [A
]
3.60 3.65 3.70 3.75 3.80 3.85 3.90
Time [sec]
#1:1
#1:2
-20
-10
0
10
20
Vo
ltag
e [V
]
3.60 3.65 3.70 3.75 3.80 3.85 3.90
Time [sec]
#1:1
#1:2
(a) current outputiA and its referenceiref (b) voltage outputuA and its
referenceuref
-4
-2
0
2
4
Vo
ltag
e er
ror
[V]
3.60 3.65 3.70 3.75 3.80 3.85 3.90
Time [sec]
#1:1
(c) voltage tracking errore
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 22/33
H∞ repetitive current-controlled VSIsProposed control algorithms to improve total harmonic distortion usingH∞ and repetitive control.
Phase-lead low-pass
filter
DC power source
Inverter bridge
LC filter
Transformer
PWM modulation
Internal model M and stabilizing compensator C
Id* Iq*
iref e
abc
dq θ
Current controller
PLL
ugb uga ugc
u
+ +
+ +
+ +
u’gb u’ga
u’gc
u’
u’gb u’ga
u’gc
ia ib ic
- +
- +
- +
H∞ repetitive current-controlled VSIs
-3
-2
-1
0
1
2
3
Cu
rren
t [A
]
0.00 0.01 0.02 0.03 0.04 0.05
Time [sec]
#1:1
#1:2
The recorded current THD
was0.99%, while the grid
voltage THD was2.21%.
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 23/33
Synchronverters(Patent pending)
Synchronverters are inverters that are operated according
to the mathematical model of synchronous generators and
thus are grid-friendly.
Can work alone or in parallel without an external
communication channel.
Can work in grid-connected mode and island mode. In the
grid-connected mode, they can easily take part in the
regulation of real power and reactive power.
Time (Second)
P(W
)an
dQ
(Var
)
PXXy
Q
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 24/33
AC Ward Leonard drive systems (Patent pending)
Extended the concept of Ward Leonard drive systems to AC machines.
Constant speed
Variable speed
Controllable field Fixed field
Prime mover
Load
Variable speed
Variable speed
Fixed field
SM/IM Load
SG Prime mover VDC
Inverter
(a) Conventional (DC) Ward Leonard drive systems (b) AC WardLeonard drive systems
(c) Experimental results when reversing the motor: speed (left) and current (right)Q.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 25/33
Parallel Operation of Inverters
Ro1 Ro2
1 1E δ∠ 2 2E δ∠1 1 1S P jQ= +0V∠
Z
2 2 2S P jQ= +
0 0.5 1 1.5 20
1000
2000
3000
P/ W
0 0.5 1 1.5 20
500
1000
1500
Q/ V
ar
t/s
P1
P2
Q2
Q1
(a) Joining of Inverter 2
0 0.5 1 1.5 20
1000
2000
3000
P/ W
0 0.5 1 1.5 20
500
1000
1500
Q/ V
ar
t/s
P2
P1
Q1
Q2
(b) Change of loadsQ.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 26/33
Inverter-dominated Power SystemsGenerator 1
RenewableEnergy Source
EnergyStorage
Inverter
CircuitBreaker
Generator 2 Generator nRenewable
Energy Source
EnergyStorage
Inverter
CircuitBreaker
RenewableEnergy Source
EnergyStorage
Inverter
CircuitBreaker
AC BUS
Public Grid
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 27/33
A demonstration wind power system
Patented by Nheolis, France, installed on the department’srooftop
Control panelQ.-C. ZHONG: H
∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 28/33
Buck Converter
Boost Converter
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 29/33
Regulation of induction generatorsfor wind power
Q
P
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 30/33
Energy recovery from landing aircraft
Coils
Risen slope to fall when energy recovery is activated
Aircraft
Runway Magnets with alternative poles (N, S, N, …)
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 31/33
Voltage and current (zoomed)
0 0.1 0.2 0.3 0.4 0.5-6000
-4000
-2000
0
2000
4000
6000
Pha
se A
vol
tage
0 0.1 0.2 0.3 0.4 0.5-1
-0.5
0
0.5
1x 10
5
Time
Pha
se A
cur
rent
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 32/33
0 5 10 15 20 25 30-6000
-4000
-2000
0
2000
4000
6000P
hase
A v
olta
ge
0 5 10 15 20 25 30-2000
-1000
0
1000
2000
Time
Pha
se A
cur
rent
(a) Phase current andthe generated voltage
(phase)
0200400600800
d
0
50
100
v
-10
-5
0
a
0
1
2x 10
7
p
0 5 10 15 20 25 300
5
10x 10
7
Time
E
(b) Distance, speed,deceleration, power and
energy
Q.-C. ZHONG: H∞ AND REPETITIVE CONTROL OF GRID-CONNECTED INVERTERS– p. 33/33
top related