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The Energy Flow Approach for Oscillation Source Location and
Damping Evaluation
Lei CHENPhD, Associate Professor
Department of Electrical EngineeringTsinghua University
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Background
• What is oscillation source? – cause of oscillation
– Disturbance source in forced oscillation
– Generator with negative damping (often caused by wrongparameters) in free/natural oscillation
• Why should we find oscillation source?
– Online location of oscillation source is the key to effectivemeasures for oscillation suppression
– Remove the disturbance source or adjust the negativelydamped generator
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Energy Based Idea• The concept of energy is widely used in oscillation or vibration
analysis
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The component producing energy is the oscillation source, which maintains or increases the oscillation
amplitude
– Oscillations are accompanied by the conversion of energy• Kinetic energy, potential energy
– The amount of energy is consistent with the oscillationamplitude• More energy, larger oscillation amplitude
– The dissipation of energy brings damping effect• Friction
Concept of Energy Flow• Energy in power system dynamics: Transient energy
– The construction of energy function is very difficult
– Not suitable for online application with measurements
• Energy flow
– Computed with measurements, independent of energyfunctions
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– The energy dissipation orproduction can be identified withthe energy flow on the network
Energy Flow Computation
• The energy flowing from bus 𝑖 to branch 𝐿𝑖𝑗 is [1]
• Computed with WAMS data and independent of energy functions
• Identical to the transient energy
• The energy flow into an element is composed of two types of terms:
conservative term (independent of integral path) - transient energy
non-conservative term (dependent of integral path) - energy dissipation
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, , , ,( d d )
( d d ) ( 2 d d (ln ) )
i j i j x i y i j y i x
i j
i j i i i j i i j i
i
W I U I U
QP U P f t Q U
U
0
* 2 2
0 0
1Im d d
2
x
G i i J m
x
T P D t
I V
[1] Lei Chen, Yong Min, Wei Hu. An energy-based method for location of power system oscillation source. IEEE Trans
Power Syst, 2013, 28(2): 828-836.
Conservative and Non-Conservative Terms
conservative term - transient energy - oscillating
non-conservative term - energy dissipation – monotonically changing (rising or descending)
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0
* 2 2
0 0
1Im d d
2
x
G i i J m
x
T P D t
I V
Energy Dissipation or Production
• The energy dissipation/production can be extracted from theenergy flow, which reflects the damping of a component inlow frequency oscillation
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Energy flow into a generator that dissipates transient energy and has positive damping
• Net Energy Flow / Dissipating Energy Flow
– Computed with deviations
– Reserve non-conservative terms but eliminate conservative terms
d d ln
2 d d ln
D
ij ij i i j i
i j i i j i
W P Q U
P f t Q U
Energy Dissipation Corresponds to Positive Damping
• Energy dissipation is consistent with damping torque of a generator– Mathematically proved: in Heffron-Phillips model, actual energy
dissipation in a period equals the energy dissipated by the damping torque
– Damping torque can be evaluated with energy dissipation
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2 2
2 20
0( ) d dd d
t td
q Dt t
d d
TE t K t
X X
Test results
Energy Dissipation in Detailed Generator Model
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0
1 1 1
1 1 1
2 2 2
J m e
fd fd fd fd
d d d
q q q
q q q
T P P D
U R I
R I
R I
R I
2
0
2
1 1 2
2
1 1
2 2
1 1 1
12
1 1
2
1 1 2 2 2
2
1 1 2 2
2 2
2 2 1 1 1 2
1 22
1 1 2 2
1
2
( 2 )1( )
2
1( )
2 2
( 2 )1( )
2
1( )
2 2
m J
a d d ffd a d
d d
ffd d a d
d fd ffd d
a d fd d
ffd d a d
a q q q a q
q q
q q a q
q q q q
a q q q
q q a q
P T
X X X XX I
X X X
X XX
X X X
X X X XX I
X X X
X XX
X X X
Conservative terms
Generator with a
field winding and 3
damper windings
2
0
2
2
1 1 1
2
1 1 1
2
2 2 2
d t
( )d
d
d
d
D
fd fd fd fd fd
d d d
q q q
q q q
W D
W U I I R t
W I R t
W I R t
W I R t
Non-conservative terms
Energy dissipations of
windings : damping [2]
Energy dissipation coefficients as Pm
changes
[2] Lei Chen, Fei Xu, Yong Min, Fang Li. Evaluation of damping of windings in a generator using oscillation energy
dissipation. 2014 IEEE Power & Energy Society General Meeting, 27-31 July 2014, National Harbor, Maryland, USA.
Energy Production of Disturbance Source in Forced Oscillation
• The disturbance source in forced oscillation produces
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s inm m d d
P P P t
0s in d
d dP t t
s infd fd d d
E E E t
1
s in dd d q
d d
E t E t
X X
Periodic disturbance on
mechanical power
Periodic disturbance on
field voltage
Energy production of
disturbance
Energy production of
disturbance
Online Oscillation Source Location
• PMU/WAMS based
– Used data: P, Q, U, f
• Steps
– When the oscillation is detected, compute the energy flowin the network using a short period (often less than 10s) ofdata with
– Compute the slope of 𝑊𝑖𝑗𝐷 using linear fitting, which
reflects the power of the energy flow
– Find the energy source using the direction and themagnitude of the energy flow power, and it is theoscillation source
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2 d d lnD
ij ij i ij iW P f t Q U
Actual Oscillation Incidents Analysis
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Pingban plant oscillation - 0.94Hz
• Caused by the trip of one sending
line Pingban-Baise
• Negatively damped free oscillation
• The generators in Pingban are
producing energy
P of line Pingban-Shapo
Energy flow from Pingban generators to the
system
Actual Oscillation Incidents Analysis
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Three gorges station oscillation - 0.82Hz
• Caused by wrong PSS parameters in
Youer plant
• Nearly zero damped free oscillation
• The Youer plant is producing energy
Energy flow from different plants to the system
Actual Oscillation Incidents Analysis
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Faer plant oscillation - 0.30Hz
• Caused by governor fault in gen #4 of
Faer plant, which induces power
oscillation of the generator
• Forced oscillation
• Gen #4 is producing energy
Energy flow from generators to the system
P of line gen #4
Online System Implementation• Based on PMU/WAMS in China Southern Grid
• Successfully locate oscillation sources in many incidents since its commissioning in 2013
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Main interface
Online System Implementation
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When oscillation detected
Online System Implementation
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When oscillation detected
Other Applications• Also implemented in Center China Grid Company
• Successfully used in China Xinjiang and Xizang Grids for oscillation incident analysis
• Through the energy flow inside the generator, the oscillation source can be further located at exciter or governor, which is helpful for cause analysis and defect correction
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Exciter
Governor
1dfd q
d d
E EX X
dmP
2
2 2( )1
( )2
q
d d q q
d d
EX I X I
X X
2
0
1
2JT
20 ( ) ddq
d d
TE t
X X
2
0 dD t
deP
deQU
U
deP
d dd q q dI U I U
d( )eP
Generator
Power GridTransient Energy Energy Dissipation
Connection with Modal/Eigen Analysis
• The energy dissipation is connected with damping ratio in modal analysis [3]
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,E D C i
i
K
σ : real-part of eigenvalue
𝐾𝐸𝐷𝐶,𝑖 : energy dissipation
coefficient of generator
The damping of the whole system of a mode comes
from the total energy dissipations of generators
[3] Lei Chen, Yong Min, Yiping Chen, et al. Evaluation of generator damping using oscillation energy dissipation and
the connection with modal analysis. IEEE Trans Power Syst, 2014, 29(3): 1393-1402.
Discussions on New Developments• Physical meaning of oscillation energy flow
– Connection with the actual electrical power
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2
1 1 1
2
1 1 1
2
2 2 2
d
d
d
d d d
q q q
q q q
W I R t
W I R t
W I R t
• Application in transient
stability– The transient energy injection
of a fault can be computedthrough the energy flow atthe fault point with thevoltages and the currents
– Energy function is not needed
– Transient stability may be studied through the energy flow on the network
Thanks!
Lei CHENPhD, Associate Professor
Department of Electrical EngineeringTsinghua University
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