Introduction Dynamic Phasors Applications Current Research Work Dynamic Phasors for Small Signal Stability Analysis Udaya Annakkage (University of Manitoba) Chandana Karawita (Transgrid Solutions) Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
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Dynamic Phasors for Small Signal Stability AnalysisInteractions Between Nearby HVDC Converters A simple Network for model Validation Two HVDC lines, ac lters, ac transmission line,
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IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Dynamic Phasors for Small Signal Stability
Analysis
Udaya Annakkage (University of Manitoba)
Chandana Karawita (Transgrid Solutions)
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Outline
1 IntroductionSimulation and Analysis TechniquesTypical OutputsModelling of Components
2 Dynamic Phasors
3 ApplicationsInteractions Between Nearby HVDC ConvertersTorsional Interactions
4 Current Research Work
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Simulation and Analysis TechniquesTypical OutputsModelling of Components
Power System Simulation and Analysis
Electromagnetic Transient Simulation - Time DomainTechnique
Transient Stability Simulation - Time Domain Technique
Small Signal Stability Analysis - Frequency DomainTechnique
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Simulation and Analysis TechniquesTypical OutputsModelling of Components
Typical Output of an EMT Simulation
Sample responses of a four-generator power system after athree phase fault
The amplitude of the 60 Hz voltage waveform is modulated bythe low frequency of oscillations of the rotor.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Simulation and Analysis TechniquesTypical OutputsModelling of Components
Typical Output of a TS Simulation
Sample responses of a four-generator power system after athree phase fault
Rotor angle of generator 2 and the rms voltage of Bus 2 showlow frequency oscillations around 1 Hz.
Am is the magnitude of the current , φ is the phase of thecurrent, and ω0 is the nominal system frequency.
In Rectangular Coordinates
iac = (IR + jII )ejω0t
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Modelling a Transmission Line using Dynamic
Phasors
Series Branch
Series R-L circuit connected between nodes 1 and 2.
v12 = Ldi12dt
+ Ri12
Using the Complex rotating phasor relationships
(VR + jVI )ejω0t = L
d(IR + jII )ejω0t
dt+ R(IR + jII )e
jω0t
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Assuming that the nominal system frequency (ω0) is constant
VR + jVI = Ld(IR + jII )
dt+ (R + jω0L)(IR + jII )
Since L is in pu, (ω0/L) terms appear instead of (1/L)
[∆IR∆II
]=
[ −Rω0
Lω0
−ω0−Rω0
L
] [∆IR∆II
]+
ω0
L0 −ω0
L0
0 ω0
L0 −ω0
L
∆V 1R
∆V 1I
∆V 2R
∆V 2I
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Modelling a Transmission Line using Dynamic
Phasors
Parallel Branch
[∆V1R
∆V1I
]=
[ −ω0
RCω0
−ω0−ω0
RC
] [∆V1R
∆V1I
]+
ω0
C0
0 ω0
C
[∆IR∆II
]
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Other Interpretations of Dynamic Phasors
d-q Components of Network Voltages and Currents
Network voltages and currents are represented by their d-qcomponents which are modelled as state variables.
Fourier Components of Network Voltages and Currents
Network voltages and currents are represented by their Fouriercomponents which are modelled as state variables.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Power System Signals as Amplitude Modulated
Signals
If R and I components are constants
The instantaneous waveforms are sinusoidal.
If R and I components are oscillating at frequency ω
The instantaneous waveforms are amplitude modulatedwaveforms with carrier frequency ω0. This results in twosidebands of ω0 − ω and ωo + ω
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Power System Signals as Amplitude Modulated
Signals
Example
If f0 = 60 Hz and f = 5 Hz, the two sideband frequencies aref1 = 55 Hz and f2 = 65 Hz. Both are close to 60 Hz and theconstant admittance representation of transmission network isacceptable.
Example
If f0 = 60 Hz and f = 25 Hz, the two sideband frequencies aref1 = 35 Hz and f2 = 85 Hz . Both are significantly different to60 Hz and the constant admittance representation oftransmission network is NOT acceptable.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Interactions Between Nearby HVDC Converters
A simple Network for model Validation
Two HVDC lines, ac filters, ac transmission line, and agenerator.
A pulse of magnitude of 5 % and duration 0.3s wasapplied to the rectifier current controller input.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Torsional Interaction Modes
Mode Freq. D Major Participants(Hz) (%)
A 16.24 -0.03 HVDC-Generator-TurbineB 16.36 1.05 HVDC-Generator-Turbine
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Participating states are identified using
Participation Factors
0
20
40
60
80
100
0
20
40
60
80
100
Gen−Turbine HVDC
Mode−B
Mode−A
!LPB!LPA !IP !HP!gen XCCC XCEA Idcr Idci Vcap
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Publications
1 C. Karawita, U.D. Annakkage, A Hybrid Network Model forSmall Signal Stability Analysis of Power Systems, IEEETransactions on Power Systems, Vol 25, 2010, Page(s):443–451.
2 C. Karawita, U.D. Annakkage, Multi-Infeed HVDC InteractionStudies Using Small-Signal Stability Assessment, IEEETransactions on Power Delivery, Vol 24, 2009, Page(s):910–918.
3 C. Karawita, U.D. Annakkage, HVDC-Generator-TurbineTorsional Interaction Studies Using A Linearized Model WithDynamic Network Representation, International Conference onPower System Transients (IPST), Kyoto, Japan, June 2009.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Current Research Work
SSR between DFIG based Wind Power Plant and seriescompensated transmission lines (Hiranya).
SSI between nearby LCC-HVDC and VSC-HVDCterminals (Kevin – MH).
SSR mitigation using FACTS controllers (TGS).
Transient Stability Simulation using Dynamic Phasors(Rae – MH).
Chandana has developed an SSR–Small Signal AnalysisProgram
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Acknowledgements
Research Funding – HVDC Interactions – NSERC,University of Manitoba, and Province of Manitoba.
Research Funding – Wind Power Plant SSR Studies –NSERC and Manitoba Hydro.
Valuable Feedback – Bret Davis, Ioni Fernando, Ani Gole,Shaahin Filizadeh, and Garth Irwin.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis