Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency...
Transcript of Low Inertia for Power System Frequency Control · Embracing Low Inertia for Power System Frequency...
Embracing Low Inertia for Power System Frequency ControlA Dynamic Droop Approach
Enrique Mallada
4th Grid Science Winter School and ConferenceJanuary 14, 2021
Acknowledgements
Yan Jiang Richard Pates Fernando PaganiniHancheng Min Petr VorobevEliza Cohn
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Dynamic Degradation
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In the United States:
[FERC, Nov. 16]
Dynamic Degradation
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In the United States:
[FERC, Nov. 16]
Inverter‐based Control
Challenges• Measurements with noise and delays• Stability + robustness (plug & play)• Lack of incentives
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Virtual Synchronous Generator
Controller
Telecom Analogy
Current approach: Use inverter‐based control to mimic generators response
Inverter‐based Control
Challenges• Measurements with noise and delays• Stability + robustness (plug & play)• Lack of incentives
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Virtual Synchronous Generator
Controller
Telecom Analogy
Current approach: Use inverter‐based control to mimic generators response
It works, but perhaps there is
something better…
Inverter‐based Control
Challenges• Measurements with noise and delays• Stability + robustness (plug & play)• Lack of incentives
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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
Merits and Trade‐offs of Inertia
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Merits and Trade‐offs of Inertia
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Merits and Trade‐offs of Inertia
Pros: Provides natural disturbance rejection Cons: Hard to regain steady‐state
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Merits and Trade‐offs of Low Inertia
Cons: Susceptible to disturbances Pros: Regains steady‐sate faster
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• Performance Specification
•Limits of Virtual Inertia and Droop Control
•Dynamic Droop Control: iDroop
Roadmap to Low Inertia Frequency Control
IEEE Transactions on Automatic Control, October 2020
arXiv preprint arXiv:1910.04954 (2019)
IEEE Transactions on Automatic Control, July 2020
• Performance Specification
•Limits of Virtual Inertia and Droop Control
•Dynamic Droop Control: iDroop
Roadmap to Low Inertia Frequency Control
Power System Performance
Depends on several factors: generators, network, disturbancegood performance metric must identify the source of the degradation!
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Frequency Response Control Effort
Performance Specification
Decomposition of Step Response
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Synchronization Error
Center of Inertia: Kundur ‘94
System Frequency
Center of Inertia: Kundur ‘94
System Frequency
Step Disturbance Performance
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RoCoF
Nadir
Nadir RoCoF
Deviation from Mean
Synchronization Cost
Steady‐state
Steady‐state
Frequency Response Control Effort
Performance Specification
RoCoF
Nadir
Steady‐state
Sync. Cost
System Freq. :
Sync. Error :
Control Effort
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Inverter Power
Power Rating
Power Rating Max Energy
Injected Energy
Steady‐State Effort
Steady‐State Effort
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
• Performance Specification
• Limits of Virtual Inertia and Droop Control
• Controller Design: iDroop
Roadmap to Low Inertia Frequency Control
Power Network Model
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Laplacian Matrix
Step:
[Bergen Hill ‘81]
Bus DynamicsGenerator:
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Model: Swing Equations Turbine
inverter
generator
ci
+ ! i
power imbalance
frequency
gi
piBus Dynamics
+
+
xiinverter
power injection
ui − pe,i
Bus DynamicsGenerator:
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Model: Swing Equations Turbine
inverter
generator
ci
+ ! i
power imbalance
frequency
gi
piBus Dynamics
+
+
xiinverter
power injection
ui − pe,i
Bus DynamicsInverter:
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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:
Control of Low Inertia Pendulum
Cons: Susceptible to disturbances Pros: Regains steady‐sate faster
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Control of Low Inertia Pendulum
Pros:Provides disturbance rejection
Cons: Hard to regain steady‐state + excessive control effort
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Virtual Mass Control:
Control of Low Inertia Pendulum
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Pros: Provides disturbance rejection, quickly restore steady‐state, with reasonable control effort.
Virtual Friction Control:
Cons?None, at least for pendulum
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
Modal Decomposition for Multi‐Rated Machines
Assumption: Let be the machine relative inertia ( ), and assume
Swing Equations + Turbine Virtual Inertia
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Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia ( ), and assume
Swing Equations + Turbine Virtual Inertia
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.
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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:
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F -12 V Tu u
Change of Vars.
F -12V
w w
Change of Vars.
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
System Frequency w/ Virtual Inertia
Nadir Overshoot Elimination:
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requires 𝝂 𝟎 in low inertia systems (low 𝒎)
Virtual Inertia Droop ControlNo Control
System
Freq.
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
Control Effort
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System
Freq.
Control Effo
rt
Virtual InertiaNo Control Droop Control
• Performance Specification
•Limits of Virtual Inertia and Droop Control
•Dynamic Droop Control: iDroop
Roadmap to Low Inertia Frequency Control
Pros: Provides disturbance rejection, quickly restore steady‐state, with reasonable control effort.
Control of Low Inertia Pendulum
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Virtual Friction Control:
Cons? Large steady‐state effort in power systems
iDroop: Dynamic Droop Control
Instead of Virtual Inertia:
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Virtual Inertia
iDroop: Dynamic Droop Control
Instead of Virtual Inertia:
We use
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iDroop – Lead iDroop – Lag
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
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Control of Low Inertia Pendulum
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Dynamic Friction Control:
Control of Low Inertia Pendulum
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Dynamic Friction ControlNo Control
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
Overshoot Elimination w/ iDroop
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Whenever and
System
Freq.
Control Effo
rt
Virtual Inertia Droop Control iDroop
Overshoot Elimination w/ iDroop
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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
-
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
-
Step Disturbance
Base Case: No Inverter Control
Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)
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Icelandic Grid
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
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Icelandic Grid
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
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
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
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
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Richard Pates Fernando PaganiniPetr VorobevYan Jiang
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
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Swing Equations + Turbine Virtual Inertia
Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia ( ), and
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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’]
Modal Decomposition for Multi‐Rated Machines
Assumption: Let the machine relative inertia (. ), and
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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:
Step Disturbance
Base Case: No Inverter Control
Example: Icelandic Power Grid• Iceland power network: 189 buses, 35 generators, load 1.3GW (PSAT)
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Icelandic Grid
Step Disturbance ‐ Frequency
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iDroop Tuning
• Droop equally shared between gens. and inverters.• Virtual inertia tuned for critically damped response 𝝂 𝝂𝒎𝒊𝒏• iDroop tuned for Nadir elimination
Step Disturbance – Control EffortInertia parameters of iDroop and VI are set to achieve zero overshoot.
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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
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.
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Zero Nadir Tuning
0 50 100-0.5
-0.4
-0.3
-0.2
-0.1
0
SW DC VI iDroop0
0.5
1
Step DisturbanceInertia parameters of iDroop and VI are set to achieve zero overshoot.
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System Frequency Synchronization Cost