low inertia for power system frequency control · embracing low inertia for power system frequency...
TRANSCRIPT
![Page 1: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/1.jpg)
Embracing Low Inertia for Power System Frequency ControlA Dynamic Droop Approach
Enrique Mallada
4th Grid Science Winter School and ConferenceJanuary 14, 2021
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Acknowledgements
Yan Jiang Richard Pates Fernando PaganiniHancheng Min Petr VorobevEliza Cohn
Enrique Mallada JHUJan 14 2021 2
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Dynamic Degradation
Jan 14 2021 Enrique Mallada JHU 3
In the United States:
[FERC, Nov. 16]
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Dynamic Degradation
Jan 14 2021 Enrique Mallada JHU 3
In the United States:
[FERC, Nov. 16]
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Inverter‐based Control
Challenges• Measurements with noise and delays• Stability + robustness (plug & play)• Lack of incentives
Jan 14 2021 Enrique Mallada JHU 4
Virtual Synchronous Generator
Controller
Telecom Analogy
Current approach: Use inverter‐based control to mimic generators response
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Inverter‐based Control
Challenges• Measurements with noise and delays• Stability + robustness (plug & play)• Lack of incentives
Jan 14 2021 Enrique Mallada JHU 4
Virtual Synchronous Generator
Controller
Telecom Analogy
Current approach: Use inverter‐based control to mimic generators response
It works, but perhaps there is
something better…
![Page 7: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/7.jpg)
Inverter‐based Control
Challenges• Measurements with noise and delays• Stability + robustness (plug & play)• Lack of incentives
Jan 14 2021 Enrique Mallada JHU 4
Dynamic Droop Control (iDroop)
Our approach: Design and tune of controllers rooted on sound control principles
Dynamic Droop
Design Objectives:
• Exploit power electronics capabilities• Improve Dynamic Performance• Minimize control effort• Stability and Robustness
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Merits and Trade‐offs of Inertia
Jan 14 2021 Enrique Mallada JHU 5
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Merits and Trade‐offs of Inertia
Jan 14 2021 Enrique Mallada JHU 5
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Merits and Trade‐offs of Inertia
Pros: Provides natural disturbance rejection Cons: Hard to regain steady‐state
Jan 14 2021 Enrique Mallada JHU 5
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Merits and Trade‐offs of Low Inertia
Cons: Susceptible to disturbances Pros: Regains steady‐sate faster
Jan 14 2021 Enrique Mallada JHU 6
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• Performance Specification
•Limits of Virtual Inertia and Droop Control
•Dynamic Droop Control: iDroop
Roadmap to Low Inertia Frequency Control
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IEEE Transactions on Automatic Control, October 2020
arXiv preprint arXiv:1910.04954 (2019)
IEEE Transactions on Automatic Control, July 2020
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• Performance Specification
•Limits of Virtual Inertia and Droop Control
•Dynamic Droop Control: iDroop
Roadmap to Low Inertia Frequency Control
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Power System Performance
Depends on several factors: generators, network, disturbancegood performance metric must identify the source of the degradation!
Enrique Mallada JHUJan 14 2021 8
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Frequency Response Control Effort
Performance Specification
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Decomposition of Step Response
Jan 14 2021 Enrique Mallada JHU 9
Synchronization Error
Center of Inertia: Kundur ‘94
System Frequency
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Center of Inertia: Kundur ‘94
System Frequency
Step Disturbance Performance
Jan 14 2021 Enrique Mallada JHU 10
RoCoF
Nadir
Nadir RoCoF
Deviation from Mean
Synchronization Cost
Steady‐state
Steady‐state
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Frequency Response Control Effort
Performance Specification
RoCoF
Nadir
Steady‐state
Sync. Cost
System Freq. :
Sync. Error :
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Control Effort
Jan 14 2021 Enrique Mallada JHU 11
Inverter Power
Power Rating
Power Rating Max Energy
Injected Energy
Steady‐State Effort
Steady‐State Effort
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Frequency Response Control Effort
Performance Specification
RoCoFSteady‐state
Sync. Cost
System Freq. :
Sync. Error :
Power Rating
Injected Energy:
Injected Power:
Steady‐State
Benchmark: Quantify control ability to eliminate overshoot in the Nadir
NadirMax Energy
![Page 22: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/22.jpg)
• Performance Specification
• Limits of Virtual Inertia and Droop Control
• Controller Design: iDroop
Roadmap to Low Inertia Frequency Control
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Power Network Model
Jan 14 2021 Enrique Mallada JHU 12
Laplacian Matrix
Step:
[Bergen Hill ‘81]
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Bus DynamicsGenerator:
Jan 14 2021 Enrique Mallada JHU 13
Model: Swing Equations Turbine
inverter
generator
ci
+ ! i
power imbalance
frequency
gi
piBus Dynamics
+
+
xiinverter
power injection
ui − pe,i
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Bus DynamicsGenerator:
Jan 14 2021 Enrique Mallada JHU 13
Model: Swing Equations Turbine
inverter
generator
ci
+ ! i
power imbalance
frequency
gi
piBus Dynamics
+
+
xiinverter
power injection
ui − pe,i
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Bus DynamicsInverter:
Jan 14 2021 Enrique Mallada JHU 13
inverter
generator
ci
+ ! i
power imbalance
frequency
gi
piBus Dynamics
+
+
xiinverter
power injection
ui − pe,i
Droop Control and Virtual Inertia:
Closed-loop Bus Dynamics:
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Control of Low Inertia Pendulum
Cons: Susceptible to disturbances Pros: Regains steady‐sate faster
Jan 14 2021 Enrique Mallada JHU 14
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Control of Low Inertia Pendulum
Pros:Provides disturbance rejection
Cons: Hard to regain steady‐state + excessive control effort
Jan 14 2021 Enrique Mallada JHU 14
Virtual Mass Control:
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Control of Low Inertia Pendulum
Jan 14 2021 Enrique Mallada JHU 14
Pros: Provides disturbance rejection, quickly restore steady‐state, with reasonable control effort.
Virtual Friction Control:
Cons?None, at least for pendulum
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Frequency Response Control Effort
Performance Specification
RoCoFSteady‐state
Sync. Cost
System Freq. :
Sync. Error :
Power Rating
Injected Energy:
Injected Power:
Steady‐State
Benchmark: Quantify control ability to eliminate overshoot in Nadir
NadirMax Energy
![Page 31: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/31.jpg)
Modal Decomposition for Multi‐Rated Machines
Assumption: Let be the machine relative inertia ( ), and assume
Swing Equations + Turbine Virtual Inertia
Enrique Mallada JHUJan 14 2021 15
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia ( ), and assume
Swing Equations + Turbine Virtual Inertia
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let be the machine relative inertia ( ), and
F -12 V Tu u
Change of Vars.
F -12V
w w
Change of Vars.
[Paganini M ‘17 , Guo Low 18’]Enrique Mallada JHUJan 14 2021 15
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let be the machine relative inertia ( ), and
System Frequency
Sync Error
[Paganini M ‘17 , Guo Low 18’]
Eigenvalues of:
Enrique Mallada JHUJan 14 2021 15
F -12 V Tu u
Change of Vars.
F -12V
w w
Change of Vars.
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Frequency Response Control Effort
Performance Specification
RoCoFSteady‐state
Sync. Cost
System Freq. :
Sync. Error :
Power Rating
Injected Energy:
Injected Power:
Steady‐State
Benchmark: Quantify control ability to eliminate overshoot in Nadir
NadirMax Energy
![Page 36: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/36.jpg)
System Frequency w/ Virtual Inertia
Nadir Overshoot Elimination:
Jan 14 2021 Enrique Mallada JHU 16
requires 𝝂 𝟎 in low inertia systems (low 𝒎)
Virtual Inertia Droop ControlNo Control
System
Freq.
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Frequency Response Control Effort
Performance Specification
RoCoFSteady‐state
Sync. Cost
System Freq. :
Sync. Error :
Power Rating
Injected Energy:
Injected Power:
Steady‐State
Benchmark: Quantify control ability to eliminate overshoot in Nadir
NadirMax Energy
![Page 38: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/38.jpg)
Control Effort
Jan 14 2021 Enrique Mallada JHU 17
System
Freq.
Control Effo
rt
Virtual InertiaNo Control Droop Control
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• Performance Specification
•Limits of Virtual Inertia and Droop Control
•Dynamic Droop Control: iDroop
Roadmap to Low Inertia Frequency Control
![Page 40: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/40.jpg)
Pros: Provides disturbance rejection, quickly restore steady‐state, with reasonable control effort.
Control of Low Inertia Pendulum
Jan 14 2021 Enrique Mallada JHU 18
Virtual Friction Control:
Cons? Large steady‐state effort in power systems
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iDroop: Dynamic Droop Control
Instead of Virtual Inertia:
Jan 14 2021 Enrique Mallada JHU 19
Virtual Inertia
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iDroop: Dynamic Droop Control
Instead of Virtual Inertia:
We use
Jan 14 2021 Enrique Mallada JHU 19
iDroop – Lead iDroop – Lag
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Bus Dynamics /w iDroopInverter:
iDroop Control:
inverter
generator
ci
+ ! i
power imbalance
frequency
gi
piBus Dynamics
+
+
xiinverter
power injection
ui − pe,i
Closed-loop Bus Dynamics w/ iDroop:
iDroop
Enrique Mallada JHUJan 14 2021 20
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Control of Low Inertia Pendulum
Jan 14 2021 Enrique Mallada JHU 21
Dynamic Friction Control:
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Control of Low Inertia Pendulum
Jan 14 2021 Enrique Mallada JHU 21
Dynamic Friction ControlNo Control
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Frequency Response Control Effort
Performance Specification
RoCoFSteady‐state
Sync. Cost
System Freq. :
Sync. Error :
Power Rating
Injected Energy:
Injected Power:
Steady‐State
Benchmark: Quantify control ability to eliminate overshoot in Nadir
NadirMax Energy
![Page 47: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/47.jpg)
Overshoot Elimination w/ iDroop
Jan 14 2021 Enrique Mallada JHU 22
Whenever and
System
Freq.
Control Effo
rt
Virtual Inertia Droop Control iDroop
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Overshoot Elimination w/ iDroop
Jan 14 2021 Enrique Mallada JHU 22
Whenever
first order step response
and
1ms + d
r − 1g
⌧s + 1
�s + δr − 1r
s + δ
- -1
ms + d
r − 1g
⌧s + 1
r − 1r + r − 1
g −r − 1
g
⌧s + 1
- -1
ms + d
r − 1r + r − 1
g
-
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System Frequency w/ iDroop
iDroop can reduce system frequency step‐response to a first order system ‐ no Nadir!
Nadir Cancellation
1ms + d
r − 1g
⌧s + 1
�s + δr − 1r
s + δ
- -
first order step response
1ms + d
r − 1g
⌧s + 1
r − 1r + r − 1
g −r − 1
g
⌧s + 1
- -1
ms + d
r − 1r + r − 1
g
-
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Step Disturbance
Base Case: No Inverter Control
Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)
Jan 14 2021 Enrique Mallada JHU 23
Icelandic Grid
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Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)• Droop equally set for inverters in all cases• Virtual inertia tuned for critically damped response 𝝂 𝝂𝒎𝒊𝒏• iDroop tuned for Nadir elimination
Jan 14 2021 Enrique Mallada JHU 23
Icelandic Grid
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Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100 0 50 100
Icelandic Grid
iDroop Benefit Summary• Overshoot Elimination in Nadir• Noise Attenuation• Disturbance Rejection• Reduce Inter‐area Oscillations
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Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100 0 50 100
Icelandic Grid
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Step Disturbance ‐ Frequency
iDroop Tuning
• Droop equally shared between gens. and inverters.• Virtual inertia tuned for critically damped response 𝝂 𝝂𝒎𝒊𝒏• iDroop tuned for Nadir elimination
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Step Disturbance – Control EffortInertia parameters of iDroop and VI are set to achieve zero overshoot.
Zero Nadir Tuning
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100 0 50 100
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Parameter Uncertainty
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2-224
-222
-220
-218
-216
-214
-212
-210
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Other Benefits of iDroop
Benefits Summary• Overshoot Elimination in Nadir• Noise Attenuation• Disturbance Rejection• Reduce Inter‐area Oscillations
iDroop – Lead
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Thanks!Related Publications:• Paganini and M, “Global analysis of synchronization performance for power systems: bridging the theory‐practice gap,” IEEE TAC 2020
• Jiang, Pates, M, “Dynamic Droop Control for Low Inertia Power Systems,” IEEE TAC 2021• Jiang, Cohn, Vorobev, M “Dynamic Droop Approach for Storage‐based Frequency Control,” IEEE TPS,conditionally accepted (arXiv)
• Min, Paganini, M, “Accurate Reduced Order Models for Coherent Synchronous Generators,” L‐CSS 2020• Y. Jiang, E. Cohn, P. Vorobev, and E. M, ”Storage‐Based Frequency Shaping Control,” L‐CSS 2020
Enrique [email protected]
http://mallada.ece.jhu.eduHancheng Min Eliza Cohn
Enrique Mallada JHUJan 14 2021 26
Richard Pates Fernando PaganiniPetr VorobevYan Jiang
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Backup Slides
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Power Engineering Metrics
Step Response Nadir, RoCoF, Steady‐State
60.0 Hz
59.3 Hz UFLSSetting
RoCoF
Point C: Nadir
Point B
Point A
based on classical control theory…
Eigenvalue Analysis [Verghese ‘89]Dom. Eig, Damping Ratios, Part. Fact.
Domain specific, capture system degradationRelation with cause? Eigenvalue sensitivity? More than one ”dominant” eig.?+-
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System Theoretic Metrics
‐norm: ‐norm:
Close form solutions, qualitative analysis, computational methodsRestrictive assumptions, not direct connection with RoCoF, Nadir, step disturbances+-
[Tegling… ’15, Poolla… ’15, Grunberg… ’16, Simpson‐Porco…‘16,Wu et al ’16, Adreasson ’17, Coletta ‘17… ]
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia ( ), and assume
Jan 14 2021 Enrique Mallada JHU 30
Swing Equations + Turbine Virtual Inertia
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia ( ), and
Jan 14 2021 Enrique Mallada JHU 30
F -12 V T
F -12 V Tu u
wPwP
V TF12
w! w!
Change of Vars.
F -12V
w w
Change of Vars.
[Paganini M ‘17 , Guo Low 18’]
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia (. ), and
Jan 14 2021 Enrique Mallada JHU 30
pe,1
-u1
wP,1 w1
w! ,1
c0
p0
wP,k
uk
wk
w! ,k
-
pe,k
c0
p0
1s λk
wn
w! ,n
un
wP,n
-
pe,k
c0
p0
1s λn
1s 0
System Frequency
F -12 V T
F -12 V Tu u
wPwP
V TF12
w! w!
Change of Vars.
F -12V
w w
Change of Vars.
Sync Error
[Paganini M ‘17 , Guo Low 18’]
Eigenvalues of:
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Step Disturbance
Base Case: No Inverter Control
Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)
Jan 14 2021 Enrique Mallada JHU 31
Icelandic Grid
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Step Disturbance ‐ Frequency
Jan 14 2021 Enrique Mallada JHU 32
iDroop Tuning
• Droop equally shared between gens. and inverters.• Virtual inertia tuned for critically damped response 𝝂 𝝂𝒎𝒊𝒏• iDroop tuned for Nadir elimination
![Page 67: Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency Control A Dynamic Droop Approach Enrique Mallada 4th Grid Science Winter School](https://reader035.vdocuments.net/reader035/viewer/2022071500/611ee2e23694d946c90876b2/html5/thumbnails/67.jpg)
Step Disturbance – Control EffortInertia parameters of iDroop and VI are set to achieve zero overshoot.
Jan 14 2021 Enrique Mallada JHU 33
Zero Nadir Tuning
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100-0.02
-0.01
0
0.01
0.02
0 50 100-0.2
-0.1
0
0.1
0.2
0 50 100 0 50 100
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Parameter Uncertainty
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2-224
-222
-220
-218
-216
-214
-212
-210
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Step DisturbanceInertia parameters of iDroop and VI are set to achieve zero overshoot.
Jan 14 2021 Enrique Mallada JHU 35
Zero Nadir Tuning
0 50 100-0.5
-0.4
-0.3
-0.2
-0.1
0
SW DC VI iDroop0
0.5
1
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Step DisturbanceInertia parameters of iDroop and VI are set to achieve zero overshoot.
Jan 14 2021 Enrique Mallada JHU 35
System Frequency Synchronization Cost