Modeling and Stabilization of Low-inertia Grids...Modeling and Stabilization of Low-inertia Grids...
Transcript of Modeling and Stabilization of Low-inertia Grids...Modeling and Stabilization of Low-inertia Grids...
Modeling and Stabilization of Low-inertia Grids
Brian JohnsonAssistant Professor
University of Washington
Department of Electrical and Computer Engineering
November 7th 2018
2
Collaborators
YashenLin
SairajDhople
FransescoBullo
Funding:
3
% V
aria
ble
Rene
wab
le E
nerg
y(o
f an
nual
ene
rgy)
System Size (GW)
80
5
23
Alaskan Village
Ireland Cont. USA
42
Denmark*
Actual Operating System
Maui
(*) Part of a larger synchronous AC power systemAcknowledgement: Ben Kroposki, NREL
Transforming the Grid at a Scale That Matters
10�110�210�3 1 101 102 103
25
50
75
100
14CA*
Germany*
12Texas
20
35
4
% V
aria
ble
Rene
wab
le E
nerg
y(o
f an
nual
ene
rgy)
System Size (GW)
80
5
23
Alaskan Village
Ireland Cont. USA
42
Denmark*
Actual Operating System
Maui WWSIS
CA 50%
LanaiModeled System
ERGIS
REF
(*) Part of a larger synchronous AC power systemAcknowledgement: Ben Kroposki, NREL
Transforming the Grid at a Scale That Matters
10�110�210�3 1 101 102 103
25
50
75
100
CA*
Germany*
Texas
35
14 12
20
5
% V
aria
ble
Rene
wab
le E
nerg
y(o
f an
nual
ene
rgy)
System Size (GW)
80
5
23
Alaskan Village
Ireland Cont. USA
42
Denmark*
Actual Operating System
Maui WWSIS
CA 50%
LanaiModeled System
ERGIS
REF54
DOE 2050 Goals35% Wind (404 GW)19% PV (632 GW)
Deep Decarbonization1400 GW wind900 GW Solar
78
(*) Part of a larger synchronous AC power systemAcknowledgement: Ben Kroposki, NREL
Transforming the Grid at a Scale That Matters
10�110�210�3 1 101 102 103
25
50
75
100
CA*
Germany*
Texas
35
14 12
20
6
% V
aria
ble
Rene
wab
le E
nerg
y(o
f an
nual
ene
rgy)
System Size (GW)
80
5
23
Alaskan Village
Ireland Cont. USA
42
Denmark*
Actual Operating System
Maui
Relatively Easy
Much Harder
WWSIS
CA 50%
LanaiModeled System
ERGIS
REF54
DOE 2050 Goals35% Wind (404 GW)19% PV (632 GW)
Deep Decarbonization1400 GW wind900 GW Solar
78
(*) Part of a larger synchronous AC power systemAcknowledgement: Ben Kroposki, NREL
Transforming the Grid at a Scale That Matters
Extremely Difficult
10�110�210�3 1 101 102 103
25
50
75
100
CA*
Germany*
Texas
35
14 12
20
7
Present Future
generatorinverter
generatorinverter
current source
controllable voltage source
Evolution of the Grid
�!Grid-followingcontrols
to next-generation grid-forming controls
8
Controllers Under Consideration
Grid-following:Current control with PLL
Grid-forming:Virtual oscillator control
iδoi
+ + +
PWMcurrentcontrol
powercontrol
VSI
abcdq
ld∗i
ldqio
dqiodqv
lq∗i
id∗v
iq∗v
PLL
fR
cR
fL gR gL
fCov
odv
gv
gv
iv li
li
oi
]∗q∗p[
PWM
m×÷
+ +−+
i
dcvv
−
+
vκ iκL C
iiκ
virtual oscillator
CvLi
vεκ
bv
σ
1−Cv
v
C
3αv
2/fL
2/fL
!
sinΦ−,cosΦ"
2/fR
2/fR
Grid-forming:Droop control
PWM
m×÷
+ +−+
i
ip
V q
dcvv bv
bv
v
2/fL 2/fR
2/fR2/fL
fω
fω
powercalculation
drooplaws filters
fp
fq
iω
fp
fqV
!θ
θcosV2√
Discussed today
Have similarities
9
Outline
1. How do we solve the modeling complexity problem?
2. Is there an upper limit for inverter penetration before stability is lost?
phase locked loop
grid following unit
)s(Gestθ
How many machines can we replace with
electronics?
⇡ aggregatedequivalent
8
Outline
1. How do we solve the modeling complexity problem?
2. Is there an upper limit for inverter penetration before stability is lost?
phase locked loop
grid following unit
)s(Gestθ
How many machines can we replace with
electronics?
⇡ aggregatedequivalent
10
The Scaling Problem
�
A large disparity in ratings
100’s of MVA 100’s of VA – 100’s of kVA
,
… implies a larger number of generating devices to satisfy load
From ~7,500 power plants To millions of inverters??
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An island of 950,000 people and 800,000 Enphase microinverters
“800,000 Microinverters Remotely Retrofitted on Oahu in One Day.” http://spectrum.ieee.org/energywise/green-tech/solar/in-one-day- 800000-microinverters-remotely-retrofitted-on-oahu.
>+
Motivational Example: Oahu
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Our Solution: Aggregation
Many inverters
o1i
]∗q∗p[p1κ
)v,κp1κ(
o2i
]∗q∗p[p2κ
)v,κp2κ(
oNi
]∗q∗p[pNκ
)v,κpNκ(
gvvκ+
gvvκ+
≡
)v,κ( pκ!
]∗q∗p[pκ!
oei
s
s
s
Aggregated equivalent Transmission model
13
iδoi
+ + +
PWMcurrentcontrol
powercontrol
VSI
abcdq
ld∗i
ldqio
dqiodqv
lq∗i
id∗v
iq∗v
PLL
fR
cR
fL gR gL
fCov
odv
gv
gv
iv li
li
oi
]∗q∗p[
iδoi
+ + +
PWMcurrentcontrol
powercontrol
VSI
abcdq
ld∗i
ldqio
dqiodqv
lq∗i
id∗v
iq∗v
PLL
fR
cR
fL gR gL
fCov
odv
gv
gv
iv li
li
oi
]∗q∗p[
vκpκ
vκpκ
pκ
vκ
vκ
vκpκ
vκpκ
vκpκ
pκv
2κ
pκv
2κ
pκv
2κ
pκv
2κpκv
2κ
v2κpκ
vκ vκ
vκ
vκ
vκpκ
Foundation of Aggregation Approach: Scaling Laws
§ Based on power electronics & controls rules of thumbo Fixed voltage drop across filtero Fixed total harmonic distortion across ratings:o Preserve closed-loop response with scaled control gains
Introduce power and voltage scaling factors, and
voltage
pow
er
Scalable Inverter Model
pκ
vκ
1
1
310
210
480V
35kV
]∗Q∗P[310
]∗Q∗P[1
?
p v
switching rippleIrated
=constant
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Scaling Laws and Aggregation
§ If each inverter conforms to scaling laws in [1]-[2], then
for .
]∗q∗p[pκ
)v,κpκ( gvvκ+
osi
)
o1i
]∗q∗p[p1κ
)v,κp1κ(
o2i
]∗q∗p[p2κ
)v,κp2κ(
oNi
]∗q∗p[pNκ
)v,κpNκ(
gvvκ+
gvvκ+
≡
)v,κ( pκ!
]∗q∗p[pκ!
oei
s
s
s
“equivalent”output current
bp :=NX
`=1
p`
t � to
ieo =NX
`=1
iso`
[1] Scaling laws for grid following: V. Purba, B. Johnson, S. Jafarpour, F. Bullo, and S. Dhople, “Reduced-order Structure-preserving Model for Paralleled Three-phase Grid-tied Inverters,” Workshop on Control and Modeling for Power Electronics, 2017.[2] Scaling laws for grid forming: M. Khan, B. Johnson, V. Purba, and S. Dhople, “A Reduced-order Aggregated Model for Parallel Inverter Systems Controlled with Virtual Oscillator Control,” Workshop on Control and Modeling for Power Electronics, 2018.
(a) Single grid following orgrid forming inverter
(b) System of N such parallel inverters (c) Aggregated equivalent
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Experimental Validation of Aggregation
o1i
]∗q∗p[
o2i
]∗q∗p[
o3i
]∗q∗p[ gv+
gv+
≡
]∗q∗p[
oei
1
3
1
1
1
Experiment Model
(3,1)
1kW inverter
power electronics
microcontroller for circuit-level
control
communications
120V 60Hz supply
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Experimental Validation: Grid-Following Controls
§ System of 3 grid-following inverters during power command step change.
[A]
,oi
[A]
,od i
[s]t,
o1di o2
di o3di
3X
`=1
io` ieo
V. Purba, B. Johnson, M. Rodriguez, S. Jafarpour, F. Bullo, and S. Dhople, “Reduced-order Aggregate Model for Parallel-connected Single-phase Inverters,” IEEE Transactions on Energy Conversion, Submitted.
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Experimental Validation: Grid-Forming Oscillator Controls
§ System of 3 inverters with Virtual Oscillator Control during load steps.
V. Purba, B. Johnson, M. Rodriguez, S. Jafarpour, F. Bullo, and S. Dhople, “Reduced-order Aggregate Model for Parallel-connected Single-phase Inverters,” IEEE Transactions on Energy Conversion, Submitted.
i o`,[A]
Xio` ieo
io1 io2 io3
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Outline
1. How do we solve the modeling complexity problem?
2. Is there an upper limit for inverter penetration before stability is lost?
phase locked loop
grid following unit
)s(Gestθ
How many machines can we replace with
electronics?
⇡ aggregatedequivalent
19
The Key Question
Can we get from here to here?
§ Look at this question with both grid-following and grid-forming inverters.
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An Elementary Model
A good starting point:
voltage
pow
er
Scalable Inverter Model
governor
voltagecontrol
load
primemover
exciter
pκ
vκ
1
1
310
210
480V
35kV
310
1
mioi
gv
]∗q∗p[
]∗q∗p[
Represents an aggregated collection of inverters
Prototypical steam-driven generator at fossil-fuel plant
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A Fundamental Question
Q:What happens as the ratio of inverter/machine ratings increases?
voltage
pow
er
Scalable Inverter Model
governor
voltagecontrol
load
primemover
exciter
pκ
vκ
1
1
310
210
480V
35kV
310
1
mioi
gv
]∗q∗p[
]∗q∗p[
p = inverter rating factor
m = machine rating factor
Approach: Adjust scaling concurrently such that p + m = constant
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§ Start with zero inverter penetration:
§ Find equilibrium
§ Linearize to get
§ Compute eigenvalues
§ Increase and decrease
Model Framework
voltage
pow
er
Scalable Inverter Model
governor
voltagecontrol
load
primemover
exciter
pκ
vκ
1
1
310
210
480V
35kV
310
1
mioi
gv
]∗q∗p[
]∗q∗p[
p
�x = A�x+B�u
� 2 C|x|
x = f(x, u)
x⇤
m = nominal,p = 0
m
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Results: Small-signal Stability with Grid-Following Inverter
§ Fixed machine rating = 555MVA, parameters from [1]
§ Unscaled inverter rating = 1kVA, parameters for NREL hardware
§ Instability in this example at approximately 50% [2]
§ Result varies between 40%-90%, depends on parameters
Pi
Pm
0 0.2 0.4 0.6 0.8 1
Pi / (Pi + Pm)
-2
0
2
4
6
max
(Re(λ))
[1] P. Kundur, N. J. Balu, and M. G. Lauby, Power system stability and control. McGraw-hill New York, 1994.[2] Y. Lin, B. Johnson, V. Purba, S. Dhople, V. Gevorgian, “Stability Assessment of a System Comprising a Single
Machine and Inverter with Scalable Ratings,” North American Power Symposium, 2017.
unstable
stable
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Results: Small-signal Stability with Grid-Forming Inverter
§ Now look at inverter with Virtual Oscillator Control
§ Machine same as before
§ Key finding: Instability can be eliminated with flatter Volt/VAR droop slope [1]
[1] M. Khan, Y. Lin, B. Johnson, M. Sinha, S. Dhople, “Stability Assessment of a System Comprising a Single Machine and a Virtual Oscillator Controlled Inverter with Scalable Ratings,” Industrial Electronics Conference, 2018, Submitted.
0 0.2 0.4 0.6 0.8 1
0
10
20
30
Pi/(Pi + Pm)
droop slope = 0.1⇥ Srated/Vrated
droop slope = 0.5⇥ Srated/Vrated
droop slope = 1⇥ Srated/Vrated
Thanks for your attention!
Brian JohnsonContact: [email protected]
Thanks for your attention!
Brian JohnsonContact: [email protected]
26
§ Start with zero inverter penetration
1. Solve power flow to obtain machine/inverter terminal variables
2. Compute machine/inverter equilibrium states
o Linearize, compute eigenvalues , assess stability
o Increment or replace machine with inverter of equal rating
Framework for Multi-Machine Multi-Inverter System
p
� 2 C|x|
x = f(x, u)
x⇤ = f(x⇤, u) = 0
I = Y VNetwork algebra:
Machine & inverter dynamics:
m = nominal,p = 0
m,1
m,2m,3
m,4
m,5
m,M
p,1
p,2 p,3
p,4
p,N
inverter penetration :=Pi
(Pi + Pm)