On-Line Transient Stability and Damping
Analysis of Large Scale Power Systems
EPCC, May 18 2015
A joint work with
PJM Interconnection, PA, USA
Tokyo Electric Power Company, Tokyo, Japan
Dr. Hsiao-Dong ChiangProf. of Cornell University, NY, USA, Tianjin University, Tianjin, PRCPresident of Bigwood Systems Inc., Ithaca, NY, USA
Contingencies cause limits on power systems
Hard Limits
Transient (angle) instability
Small-singal stability
Voltage instability
Voltage-limit violation
Thermal-limit violation
Soft Limits
Challenges at PJM Control
centerOn-Line Transient Stability Assessment (TSA)
Requires solving
• Need to perform TSA on 3,000 contingencies in
5 minutes
• One contingency involves a set of 15,000
differential equations + 40,000 nonlinear
algebraic equations
• Traditional time-domain-based approach can
not meet this requirements
Each Contingency
Time-Domain Approach:
Numerical Integration method
• At present, numerical integration method
routinely used in utilities around the world.
• This traditional time-domain approach is
accurate in predicting dynamic behaviors to its
model accuracy.
• It however suffers several disadvantages.
Time-Domain Approach:
Numerical Integration method
• Speed: too slow for on-line applications
• Degree of Stability: no knowledge of
degree of stability (critical contingencies vs
highly stable contingencies)
• Control : do not provide information
regarding how to derive effective control
Post-Fault System
x = f(x,y)
tcl< t < t
.
Time-Domain Approach Direct Methods (Energy Function)
Pre-Fault System
Numerical integration
x(t)
t = tcl t
post-fault trajectory
initial point of post-fault
trajectory1. The post-fault trajectory x(t)
is not required
2. If v(x(tcl))< vcr, x(t) is stable.
Otherwise, x(t) may be unstable.
• (Pre-fault s.e.p.) • (Pre-fault s.e.p.)
Fault-On System
x = fF(x,y)
t0< t < tcl
.
Direct stability assessment is based on
an energy function and the associated
critical energy
x(t) end point of fault-on
trajectory
t = t0 t = tclt
Numerical integration
fault-on trajectory
x(t) end point of fault-on
trajectory
t = t0 t = tclt
Numerical integration
fault-on trajectory
History of Direct Methods
• MOD (mode of disturbance) method
(1970-1980s)
• PEBS method (by Kakimoto etc.)
• Acceleration machine method (Pavella
etc.)
• Extended Equal Area Criteria (EEAC)
• Single-Machine-Equivalent-Bus (SIME)
• BCU method (since 1989)
• TEPCO-BCU method (Since 1997)
Real - Time Data
TopologicalAnalysis Contingency
A List of StateMonitor
State
Estimation
Dynamic Contingency Screening
Marginal
Stable
Cases
Unstable and/or Undecided Cases
Detailed Time-Domain Stability Analysis
On - Line Time - Domain Stability Analysis
Ranked Stable Contingencies
Ranked UnstableContingencies
Control Actions Decision
Enhancement Actions Preventive Actions
Predictive Data
Highly
Stable
Cases
Dynamic Contingency Screening
Dynamic
Contingency
Classifiers
Time- Domain Energy Index (optional)
BCU Method and TEPCO-BCU
• TEPCO-BCU is developed under this
direction by integrating BCU method,
improved BCU classifiers, and BCU-guide
time domain method. The evaluation
results indicate that TEPCO-BCU works
well on several study power systems
including a 15,000-bus test system.
Key developments
• Theoretical Foundation
• Design of Solution Algorithm
• Numerical Methods
• Implementations (Computer Programs)
• Industrial User Interactions
• Practical system installations
Key developments
1. Theoretical Foundation (gain insights and
build belief)
• Theory of stability boundary (Chiang,
Hirsch and Wu1987, - Present)
• Theory of Relevant Stability Boundary
(Chiang, 1988 – present)
• Energy Function Theory (extension of
Lyapunov function function) (Chiang, Wu
and Varaiya 1988, to present)
• Energy Functions for Transient Stability
Models (non-existence of analytical
Key developments
1. Theoretical Foundation (gain
insights and build belief)
• Theoretical Foundations of Direct
Methods (1988)
• CUEP method and Theoretical
foundation (1988)
• Theoretical Foundation of BCU
method(1995)
Post-Fault System
x = f(x,y)
tcl< t < t
.
Time-Domain Approach Direct Methods (Energy Function)
Pre-Fault System
Numerical integration
x(t)
t = tcl t
post-fault trajectory
initial point of post-fault
trajectory1. The post-fault trajectory x(t)
is not required
2. If v(x(tcl))< vcr, x(t) is stable.
Otherwise, x(t) may be unstable.
• (Pre-fault s.e.p.) • (Pre-fault s.e.p.)
Fault-On System
x = fF(x,y)
t0< t < tcl
.
Direct stability assessment is based on
an energy function and the associated
critical energy
x(t) end point of fault-on
trajectory
t = t0 t = tclt
Numerical integration
fault-on trajectory
x(t) end point of fault-on
trajectory
t = t0 t = tclt
Numerical integration
fault-on trajectory
sustained fault-on trajectory moves toward the stability boundaryintersects it at the exit point. The exit point lies on the stablemanifold of the controlling UEP of the fault-on trajectory .
If the fault is cleared before the fault-on trajectory reaches the
exit point, then the fault-clearing point must lie inside the
stability region. Hence, the post-fault trajectory starting from
the fault-clearing point must converge to the post-fault SEP .
The controlling UEP method approximates the relevant stability
boundary, which in this case is the stable manifold of the
controlling UEP, by the constant energy surface, which passes
through the controlling UEP.
The only scenario in which the controlling UEP method gives
conservative stability assessments is the situation where the fault is
cleared when the fault-on trajectory lies between the connected
constant energy surface and the relevant stability boundary which
is highlighted in the figure.
Key developments
2. Design of Solution algorithms
• BCU method for computing
CUEP (1993)
• BCU Classifiers (1997)
• High-yield BCU classifiers
(1999)
Important Implications
• CUEP method is the “must”; I do not believe other method can provide reliable results.
• To directly compute CUEP of the original power system model is impossible.
• Analytical results serve to explain why previous direct methods developed in the 1970s and 1980s did not work.
Important Implications
• Analytical results provide directions for developing BCU method.
• Do not pursue analytical energy functions; instead we should use semi-analytical energy functions.
Fundamentals of BCU Method
What: a boundary of stability region based
controlling unstable equilibrium point
method to compute the critical energy
Basic Ideas: Given a power system stability
model (which admits an energy function), the
BCU method computes the controlling u.e.p. of
the original model via the controlling u.e.p. of a
dimension-reduction system whose controlling
u.e.p. can be easily, reliabily computed.
1uÝ
u------U u w x y – g1 u w x y +=
2wÝ
w-------U u w x y – g2 u w x y +=
TxÝ
x------U u w x y – g3 u w x y +=
MzÝ Dz
y------U u w x y –– g4 u w x y +=
yÝ z=
1uÝ
u------U u w x y –=
2 wÝ
w-------U u w x y –=
TxÝ
x------U u w x y –=
yÝ z=
MzÝ Dz
y------U u w x y ––=
1 uÝ
u------U u w x y –=
2wÝ
w-------U u w x y –=
T xÝ
x------U u w x y –=
yÝ 1 – z
y------U u w x y –=
MzÝ Dz 1 – z
y------U u w x y –––=
0
u------U u w x y – g1 u w x y +=
0
w-------U u w x y – g2 u w x y +=
TxÝ
x------U u w x y – g3 u w x y +=
yÝ
y------U u w x y – g
4u w x y +=
(Step 7)
(Step 6)
(Step 5)
(Step 4)
(Step 3)
(Step 2)
(Step 1)
Static and Dynamic Relationships
?
1 uÝ
u------U u w x y – g1 u w x y +=
2wÝ
w-------U u w x y – g2 u w x y +=
TxÝ
x------U u w x y – g3 u w x y +=
yÝ
y------U u w x y – g4 u w x y +=
1uÝ
u------U u w x y –=
2 wÝ
w-------U u w x y –=
TxÝ
x------U u w x y –=
yÝ
y------U u w x y –=
1uÝ
u------U u w x y –=
2 wÝ
w-------U u w x y –=
TxÝ
x------U u w x y –=
yÝ
y------U u w x y –=
MzÝ Dz–=
4/22/96 HDC
Challenges for Practical Applications of Direct
MethodsChallenges Descriptions Possible Solutions
Modeling (I) Models admitting energy functions Development of a systematic way to
construct energy functions
Modeling (II) Post-fault system needs to be an autonomous system The fault-sequence must be specified
Condition (I) Existence of post-fault s.e.p. Computation and verification
Condition (II) The pre-fault s.e.p. lies inside the stability region of the post-fault
s.e.p.
Computation and verification
Scenario Requires the initial condition of the post-fault system Inherent problem (numerical integration of
fault-on system)
Accuracy (I) Non-existence of analytical energy functions for general transient
stability models
Numerical energy function
Accuracy (II) Direct methods, except the controlling u.e.p. method, give either
conservative or over-estimate stability assessments
Controlling u.e.p. method
Accuracy (III) Controlling u.e.p.method always gives conservative stability
assessments
Further development
Controlling
u.e.p. (I)
1. Various definitions of controlling u.e.p.
2. The controlling u.e.p. is the first u.e.p. whose stable manifold is
hit by the fault-on trajectory (at the exit point)
BCU method uses the precise definition of
controlling u.e.p.
Controlling
u.e.p. (II)
1. The computation of the exit point usually requires the bruce force
time-domain approach
2. The existing methods proposed to compute the controlling u.e.p.
based on the original power system models usually fail
BCU method and its improvements
Function Applicable for only first-swing stability analysis 1. Use transient stability model valid for
multi-swing stability analysis
2. Controlling u.e.p. method
Patents (I)
• U.S. Patent 5,483,462; "On-line Method for Determining Power System Transient Stability" Date of Patent, Jan. 9, 1996 (Inventor: Hsiao-Dong Chiang)
• U.S. Patent 5,642,000; "Method for Preventing Power Collapse in Electric Power Systems" Date of Patent, June 24, 1997 (Inventors: Rene Jean-Jumeau and Hsiao-Dong Chiang)
• U.S. Patent 5,719,787; "Method for On-Line Dynamic Contingency Screening of Electric Power Systems" Date of Patent, Feb. 17, 1998 (Inventors: Hsiao-Dong Chiang and Cheng-Shan Wang)
Patents (II)
• U.S. Patent 5,796,628; Taiwan Patent 083962; "Dynamic Method for Preventing Voltage Collapse in Power Systems" Date of patent, August 18, 1998 (Inventors: Hsiao-Dong Chiang and Cheng-Shan Wang)
• U.S. Patent 6,868,311; "Method and System for On-line Dynamical Screening of Electric Power System" Date of Patent, Mar. 15, 2005 (Inventors: Hsiao-Dong Chiang, Atsushi Kurita, Hiroshi Okamoto, Ryuya Tanabe, Yasuyuki Tada, Kaoru Koyanagi, and Yicheng Zhou)
• U.S. patent 7,483,826, "Group-Based BCU Methods for On-Line Dynamical Security Assessments and Energy Margin Calculations of Practical Power Systems" Date of Patent, Jan. 27, 2009 (Inventors: Hsiao-Dong Chiang, Hua Li, Yasuyuki Tada, Tsuyoshi Takazawa, Takeshi Yamada, Atsushi Kurit, and Kaoru Koyanagi)
Each Contingency
T = 0
min.
T = 3
min.
T = 8
min.
BSI Online TSA (TEPCO-BCU)
FunctionData
Input
(i) TEPCO-BCU Method
(ii) TEPCO-BCU
Classifiers
(iii) BCU Control
(i) Time-Domain Simulation(ii) BCU-Guided Time-Domain Simulation
S.E. Snapshot
(CIM, PSSE,
PSLF)
Contingency
List
Dynamic Data
BCU
(optimal)
Enhancement
Control
Critical
Contingencies
(with estimated
CCTs)
Base-case
Simulation
Insecure
Contingencie
s
Critically
Stable
Contingenci
esSwing
Curves
Detaile
d
Output
Report
(optional service)
Base-case
Time
Domain
Simulation
Base-case
Dynamic
Screening
(a) Reliability
(b) Efficiency
(c) On-line
Computation
BCU
(optimal)
Preventative
Control
RankingContingenc
y
Assessm
ent
Normalize
d Energy
Margin
Estimate
d CCTs
1 1288 Insecure -1.2 3 cycles
2 1758Critically
Stable0.05 10 cycles
3 1122 Stable 1.2 16 cycles
… … … … …
Base-case TSA Summary
Table
Transfer Limit for Each
InterfaceTransfe
r Limit
Binding
Contingenc
y
1 400 MW 1168
2 525 MW 1288
3 600 MW 1122
… … …
T = 8
min.
T = 15
min.
BSI Online Transfer Limit Determination
Data
Input
(i) TEPCO-BCU Method
(ii) TEPCO-BCU Classifiers
(iii) Continuation Power Flow
(iv) BCU Limiters
(i) Time-Domain Simulation(ii) BCU-Guided Time-Domain
Simulation
BCU Control
for Increasing
Transfer
Limits for
Each Interface
Time Domain
Simulation to
Determine
Exact
Transfer
Limits for
Each
Interface
Detailed
Output
Report
(optional
service)
Critical Contingencies
with Estimated
Transfer Limit for # 1
Critical Contingencies
with Estimated
Transfer Limit for # 2
Critical Contingencies
with Estimated
Transfer Limit for # n
…
Power
Transfer
Limits
Correlating
with Top 5
Binding
Constraints for
Interface # 1
Power
Transfer
Limits
Correlating
with Top 5
Binding
Constraints for
Interface # n
…
Dynamic
Screening for
Power
Transfers
(a) Reliability
(b) Efficiency
(c) On-line
Computation
Contingency List
for Each Interface
Definition of Interface
#1
Definition of Interface
#n
S.E. Snapshot
(CIM, PSSE,
PSLF)
Dynamic Data
…
Input Data
Powerflow: is prepared using the real-time
system snapshot and passed from EMS
system.
Dynamics: Dynamic data matches the
real-time powerflow and passed from EMS
system.
High-level Overview
Solution for PJM on-line Transient
Stability Assessments
EMS
Data Bridge
To Provide
Real Time Data
(BSI)
TEPCO-BCU
(BSI)
DSA Manager
& TSAT (PLI)
Result
Depository
and
Visualization
(BSI & PLI)
Data Bridge contains common fixed
data for both TEPCO-BCU/TSAT
and local data required only by
TEPCO-BCU or TSAT
Info
rma
tio
n e
xch
an
ge
PJM Evaluation Results
• The goal was to evaluate TEPCO-BCU
package in a real time environment as a
transient stability screening tool. This
evaluation study is the largest in terms of
system size, 14,500-bus, 3000 generators,
for a practical application of direct methods.
The total number of contingencies involved
in this evaluation is about 5.3 million.
PJM Data Requirements
• The “raw” contingency information (including only
cir-cuit/generator losses) is obtained from
EMS/Contingency Analysis. A contingency
processing function expands the information for
transient stability analysis. This involves:.
PJM Date Requirements
• (i) adding fault. Both three-phase and single-line-to-
ground faults are considered,
• (ii) both primary and backup fault clearance times
are provided
• (iii) for single-line-to-ground faults, additional circuits
will be lost as a result of backup clearance. This is
specified for each contingency.
PJM Evaluation Results
• Dynamic model and data : this refers to
dynamic models and data matching the real time
powerflow, including
(i) generator model (classical to two-axis 6th order
models,
(ii) excitation system (all IEEE standard exciter/AVR
and PSS models and com-mon extended models, (iii)
load: ZIP model, voltage dependent model, discharge
lighting model, (iv) SVC, and (v) User-defined
modeling (transfer function).
PJM Evaluation Results
(1) Reliability measure: TEPCO-BCU
consistently gave conservative stability
assessments for each contingency
during the three-month evaluation time.
TEPCO-BCU did not give over-estimated
stability assessment for any contingency.
PJM Evaluation Results
For a total of 5.29 million contingencies,
TEPCO-BCU captures all the unstable
contingencies.
Total No. of
contingency
Percentage of capturing
unstable contingencies
5293691 100%
Table 1.Reliability Measure
TEPCO-BCU consumes a total of 717575
CPU seconds. Hence, on average, TEPCO-
BCU consumes about 1.3556 second for
each contingency.
Speed:
Total No. of
contingency
Computation Time Time/per
contingency
5293691 717575 seconds 1.3556
second
Table 2. Speed Assessment
Screening measure:
Depending on the loading conditions and
network topologies, the screening rate
ranges from 92% to 99.5%
Total No. of contingency Percentage Range
5293691 92% to 99.5 %
Table 3. Screening Percentage Assessment
A summary
The overall performance indicates that
TEPCO-BCU is an excellent screening tool
These unstable contingencies exhibit first-
swing instability as well as multi-swing
instability.
Reliability
measure
Screening
measurement
Computation
speed
on-line
computation
100% 92% to 99.5% 1.3 second Yes
Table 4. Overall performance of TEPCO-BCU for on-line
dynamic contingency screening
Remarks
• A comprehensive evaluation study of the
TEPCO-BCU package in a real time
environment as a screening tool for on-line
transient stability assessment has been
presented.
• TEPCO-BCU package is an excellent
dynamic contingency screening tool for
on-line transient stability analysis of large-
scale power systems.
Concluding Remarks
This evaluation study represents the largest
practical application of the stability region
theory and its estimation of relevant
stability region behind the BCU
methodology in terms of the size of the
study system which is a 14,000-bus power
system dynamic model with a total of 5.3
million contingencies.
Concluding Remarks
This confirms our belief that theory-based
solution methods can lead to practical
applications in large-scale nonlinear
systems.
Bigwood Systems, Inc.
Cornell Technology Park
35 Thornwood Drive, Suite 400,
Ithaca, NY 14850, USA
Innovation prevails!
PJM Low Damping Study
Simulation Result
Big
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s, I
nc.
Case study 3: Ctg 1:3300 L500.Conastone-PeachBottom.5012 )
-45
-40
-35
-30
-25
-20
-15
-10
-5 0 5 10 15 20 25 30 35
ANGL 17[BAYONNE 13.800]1
Screening Result Time domain verification
SEP DampingNormalized
Energy
Screening
Assessment3-5” 5_30”
Verification
Assessment
-0.003 2.34 Low Damping 0.00069 0.0111 Low Damping
Big
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1. Test System
Test system: PJM online case TB2014_06_16_09_43_10_XDT
System Size
Devices Quantity
Bus 15270
Load 11735
Generator 2867
Exciter 1907
Governor 1517
PSS 438
Compensators 178
Data Preprocess
• Modify Gbase and other dynamic
parameters based on information
provided by TSAT log file and PSSE
recommendation.
Big
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Classifier VIII
Integration near post-fault SEP”
Remove DC. Conduct PRONY. Computenormalized system signal energy
SecureDamping<0.03?
Signal energy>
threshold?
4. Revised TPECO-BCU-D architecture
yes
Low damping
no
BCU Classifiers for Dynamic Contingency Screeningwith Damping Assessment
Big
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TEPCO-BCU-D screening results
Number of total
contingencies
946 PSSE verification
Unstable contingencies 0 All stable
Critical contingencies 9 Can not verify their
criticality. But they are all
stable
Low damping contingencies 60 All stable
Stable contingencies 877 All stable
Yield rate 93%
