dynamic phasors for small signal stability analysisinteractions between nearby hvdc converters a...
TRANSCRIPT
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.
Transient Simulation
Time(s) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 3.8 4.71.2 f
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
Gen
erat
or S
peed
Cha
nge
(Rad
/s)
-0.084 0.181 0.265
Min -1.998 Max 1.754 Diff 3.752
W2
25
50
75
100
125
150
175
200
225
250
Bus
Volta
ge (k
V)
227.277 230.320 3.043
Min 195.244 Max 230.363 Diff 35.120
V4
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 Small Signal Analysis
Structural Information
Oscillation modes (frequencies and correspondingdamping).
Mode Shapes of oscillation frequencies.
Participation of state variables in oscillation modes.
Observability of oscillation modes.
Controllability of oscillation modes.
Residues for input-output pairs.
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 Small Signal Analysis:
Participation Factors
Participation Factors show the relative participation of statevariables when a mode is excited.
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
110
State Variables
Perc
enta
ge P
artic
ipat
ion
HVDC1 Z1
Z2 F1 and F2 HVDC2 Z3
Z4 F3 and F4Tie
Generator
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 Small Signal Analysis: Mode
Shape
Mode Shape shows whether the state variables are oscillatingtogether or not.
Mode 6 Mode 7
Mode 8 Mode 9
30
210
240
270
300
150
330
180 0
60
90
120
Idcr1
Vcap1Idcr2
Idci2
Vcap2
30
210
240
270
300
150
330
180 0
60
90
120
Idcr1
Idci1
Vcap1
Idcr2
Idci2
Vcap2
X r2 X r1Idci1
30
210
60
240
90
270
120
300
150
330
180 0
Idcr1
X r1
Vcap1Idcr2
V
X r2
cap2
30
210
60
240
90
270
120
300
150
330
180 0Idcr1
X r1
Idci2
Idcr2
Idci1
X r2
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Simulation and Analysis TechniquesTypical OutputsModelling of Components
Machine Models
Transient Stability and Small Signal Stability
Rotor fluxes are modelled as state variables.Stator fluxes are NOT modelled as state variables.
Electromagnetic Transient Simulation
Rotor fluxes and stator fluxes are modelled as statevariables.
Common to both
Dynamics of the rotor and that of auxiliary controllers aremodelled using differential equations.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Simulation and Analysis TechniquesTypical OutputsModelling of Components
Transmission Line Models
Transient Stability and Small Signal Stability
Series inductance and shunt capacitance are modelled asconstant impedances (admittances) calculated at thenominal frequency ω0.
Electromagnetic Transient Simulation
Transmission line is modelled using differential equations(telegraphic equations).
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Simulation and Analysis TechniquesTypical OutputsModelling of Components
Small Signal Stability: Frequency domain technique
Only accurate in the vicinity of nominal frequency.
Structural Information relevant to the system is available.
Transient Stability: Time domain technique
Only accurate in the vicinity of nominal frequency.
Large integration time step is used ⇒ simulation is fast.
Electromagnetic Transient Simulation: Time domain technique
Accurate over a wide frequency range.
Integration time step is small ⇒ simulation is slow.
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Dynamic Phasors
Instantaneous Current Waveform
iac = Amejφe jω0t = [Am cos(φ) + jAm sin(φ)]e jω0t
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
Comparison of EMT, SS-traditional, and
SS-Dynamic Phasor Approach.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
0
0.02
0.04
0.06
0.08
time(s)
curre
nt (k
A)
(a) Change in Idcr of HVDC1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
−0.01
0
0.01
0.02
time(s)
curre
nt (k
A)
(b) Change in Idcr of HVDC2
PSCAD/EMTDCModel−1Model−2
PSCAD/EMTDCModel−1Model−2
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Rotor Oscillations: SS-traditional and SS-Dynamic
Phasors give same results
0 0.5 1 1.5 2 2.5 3 3.5 4
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1x 10−3
time(s)
spee
d (p
u)
Change in Generator Speed
PSCAD/EMTDCModel−1Model−2
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Frequency Response of the Model – EMT Vs
SS-Dynamic Phasor
0 20 40 60 80 100 120 140 160 180 2000
0.5
1
1.5
2
2.5
frequency (Hz)
% c
hang
e
Magnitude (input: , output: Vcap)
PSCAD/EMTDCSSS model
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
200
frequency (Hz)
phas
e an
gle
(Deg
.)
Phase (input: , output: Vcap)
PSCAD/EMTDCSSS model
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Response to a 200 Hz signal
Changes in Rectifier side DC currents for a 5 %, 200Hzsinusoidal change of the HVDC1 rectifier side AC sourcevoltage (VS1).
0 0.01 0.02 0.03 0.04 0.05 0.06 0.070.04
0.02
0
0.02
0.04
time(s)
curre
nt (k
A)
(a) Change in Idcr of HVDC1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
0.01
0.005
0
0.005
0.01
time(s)
curre
nt (k
A)
(b) Change in Idcr of HVDC2
PSCAD/EMTDC Model 2 Model 1
PSCAD/EMTDC Model 2 Model 1
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Participation Factors ⇒ presence of an interaction
between the two HVDC converters
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
110
State Variables
Perc
enta
ge P
artic
ipat
ion
HVDC1 Z1
Z2 F1 and F2 HVDC2 Z3
Z4 F3 and F4Tie
Generator
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Mode Shape ⇒ state variables of the two
converters oscillate against each other
Mode 6 Mode 7
Mode 8 Mode 9
30
210
240
270
300
150
330
180 0
60
90
120
Idcr1
Vcap1Idcr2
Idci2
Vcap2
30
210
240
270
300
150
330
180 0
60
90
120
Idcr1
Idci1
Vcap1
Idcr2
Idci2
Vcap2
X r2 X r1Idci1
30
210
60
240
90
270
120
300
150
330
180 0
Idcr1
X r1
Vcap1Idcr2
V
X r2
cap2
30
210
60
240
90
270
120
300
150
330
180 0Idcr1
X r1
Idci2
Idcr2
Idci1
X r2
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Torsional Interactions
The CIGRE benchmark HVDC test system with somemodifications.
A synchronous generator is connected at rectifier side ACbus to supply half of the P-Q requirement of rectifier.
S2Rectifier InverterS1 DC Line
Idcr IdciVcap
F1
F2
Z1 Z2
G
Generator with a multi-mass turbine
Udaya Annakkage (University of Manitoba) Dynamic Phasors for Small Signal Stability Analysis
IntroductionDynamic Phasors
ApplicationsCurrent Research Work
Interactions Between Nearby HVDC ConvertersTorsional Interactions
Comparison of EMT and SS-Dynamic Phasor
SS-Dynamic-Phasor provides accurate results in the frequencyrange of interest
10 % change in rectifier current reference for 10 ms
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
time(s)
curre
nt (k
A)
Change in Rectifier side DC current
PSCAD/EMTDCSSS model
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