System Frequency Response –
Linearization Analysis
JSIS Meeting
March 04, 2015
Felipe Wilches-Bernal and Joe H. Chow
Rensselaer Polytechnic Institute
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Presentation Outline
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Introduction
US interconnects Typical Frequency Responses
System Identification
Test system – frequency control
Frequency control and linearization
Results
Conclusions and Future Work
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Introduction
• Frequency is a key variable visible throughout the entire
power system that depends on the balance of generation and
load.
• Frequency need to be kept constant  actions to control
frequency are applied in different stages (primary frequency
control, action for first 60 seconds).
• Frequency control in the US interconnects is deteriorating due
to high increase of power electronics interfaced generation
(wind, solar, storage…).
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US interconnects Typical
Frequency Responses
• US interconnects typical frequency response data.
Focused on WECC and ERCOT.
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US interconnects Typical
Frequency Responses
• US interconnects typical frequency response data.
Focused on WECC and ERCOT.
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System Identification
• Using MATLAB system ID toolbox, reduced system with similar
step responses can be found.
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System Identification
• The responses have a dominant mode at a very low frequency
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Frequency Response
Test System Tuning
Using Linearization Analysis
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Test System- Frequency Control
• Test system: Modified version of the two-area, four-machine
system.
G5
13
7
G1
PSS
1
9
8
5
11
6
10
4
2
17
G2
3
L17
G3
PSS
Swing
Bus
19
L19
G4
• Loss of generation simulated by tripping generator 5 in the middle
of the transfer path.
• First task, study effects of system parameters in the frequency
response of the test system.
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Frequency Control Small Signal Analysis
Test System Frequency Response Parameter Study
• Frequency response variations with changes in machine
parameters
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Frequency Control Small Signal Analysis
Test System Frequency Response Parameter Study
• Frequency response variations with changes in load
modeling
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Frequency Control Small Signal Analysis
Test System Frequency Response
• Eigenvalue most affected is a complex pair close to zero.
• Referred to as frequency regulation mode.
• Participation factor calculation shows that all generators
participate in this mode.
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KRK Test System -Results
• By adjusting the 5 parameters of the machines a
close match was obtained for the WECC and ERCOT
data
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KRK Test System -Results
Frequency regulation mode:
• ERCOT: -0.2089 + 0.5385j  f = 0.0857Hz
• WECC: -0.2528 + 0.6093j  f = 0.0970Hz
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Conclusions and Future Work
Conclusions
• Frequency regulation for the test system is mainly determined
by a system mode (frequency regulation mode).
• Adjusting parameters such as: inertia, speed of governor,
governor droop and load modeling affects the frequency
response and the frequency regulation mode.
• WECC and ERCOT typical frequency responses were matched
for the KRK test system.
Future Work
• Develop a method to change systematically the parameters
depending on the desired frequency response to match.
• Adjust larger system (16 machine, 48 buses).
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Acknowledgment
This research is supported in part by the Global Climate and
Energy Project (GCEP) from Stanford University and in part by
the Engineering Research Center Program of the National
Science Foundation and the Department of Energy under NSF
Award Number EEC-1041877 and the CURENT Industry
Partnership Program.
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Questions?
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Thank you!
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