TSM Base Case Algorithms
State Estimation
-Abhimanyu Gartia, WRLDC
2-1
SE Problem Development
 What’s
A State?
– The complete “solution” of the power system is
known if all voltages and angles are identified at
each bus. These quantities are the “state
variables” of the system.
– Why Estimate?
– Meters aren’t perfect.
– Meters aren’t everywhere.
– Very few phase measurements?
– SE suppresses bad measurements and uses the
2-2
measurement set to the fullest extent.
SE Problem Development (Cont.)
 Mathematically
Speaking...
Z = [ h( x ) + e ]
where,
Z = Measurement Vector
h = System Model relating state vector to the
measurement set
x = State Vector (voltage magnitudes and
angles)
e = Error Vector associated with the
measurement set
2-3
SE Problem Development (Cont.)
 Linearizing…
Z=H
x+e
(This looks like a load flow equation )
 Classical
Approach -> Weighted Least
Squares…
Minimize: J(x) = [z - h(x)] t. W. [z - h(x)]
where,
J = Weighted least squares matrix
W = Error covariance matrix
2-4
SE Functionality
 So
What’s It Do?
– Identifies observability of the power system.
– Minimize deviations of measured vs estimated
values.
– Status and Parameter estimation.
– Detect and identify bad telemetry.
– Solve unobservable system subject to observable
solution.
– Observe inequality constraints (option).
2-5
SE Measurement Types
 What Measurements Can Be Used?
– Bus voltage magnitudes.
– Real, reactive and ampere injections.
– Real, reactive and ampere branch flows.
– Bus voltage magnitude and angle differences.
– Transformer tap/phase settings.
– Sums of real and reactive power flows.
– Real and reactive zone interchanges.
– Unpaired measurements ok
2-6
State Estimation Process
 Two
Pass Algorithm
– First pass… observable network.
– Second pass… total network (subject to first pass
solution).
– High confidence to actual measurements.
– Lower confidence to schedule values.
– Option to terminate after first pass.
2-7
Observability Analysis
 Bus
Observability
– A bus is observable if enough information is
available to determine it’s voltage magnitude and
angle.
– Observable area can be specified (“Region of
Interest”).
 Bus or station basis
2-8
Bad Data Suppression
 Bad
Data Detection
– Mulit-level process.
– “Bad data pockets” identified.
– Zoom in on “bad data pocket’ for rigorous
topological analysis.
– Status estimation in the event of topological
errors.
2-9
Final Measurement Statuses
 Used… The measurement was found to be “good”
and was used in determining the final SE solution.
 Not Used… Not enough information was
available to use this information in the SE solution.
 Suppressed… The measurement was initially
used, but found to be inconsistent (or “bad”).
 Smeared… At some point in the solution process,
the measurement was removed. Later it was
determined that the measurement was “smeared” by
another bad measurement.
2-10
Solution Algorithms
 Objective…
Weighted Least Squares:
Minimize: J(x) = .5 [Z - h(x)] t R -1 [Z - h(x)]
where,
J = Weighted least squares matrix
R = Error covariance matrix
 Choice
of Givens Rotation or Hybrid
Solution Methods
2-11
Solution Algorithms (Cont.)
 Given’s
Rotation (Orthogonalization)
– Least tendency for numerical ill-conditioning.
– Uses orthogonal transformation methods to
minimize the classical least squares equation.
– Higher computational effort.
– Stable and reliable.
2-12
SE Problem Development (Cont.)
 Hybrid
Approach
– Mixture of Normal Equations and
Orthogonalization.
– Orthogonalization uses a fast Given’s rotation for
numerical robustness.
– Normal Equations used for solution state updates
which minimizes storage requirements.
– Stable, reliable and efficient.
2-13
SE Program Constants

Please Refer To
Real-Time Program
Constants Display.
2-14
Base Case Algorithms
Power Flow
2-15
PF Problem Development
 Purpose
– Solve the general network consisting of all
voltages and branches flows.
 How
PF Differs From SE
– Unlike the SE algorithm, PF does not have to
contend with measurement inconsistencies (I.e.,
branch flows are not inputs to the algorithm).
– PF has no concept of “observability”.
2-16
PF Problem Development
(Cont.)
 Algorithm
– The PF algorithm revolves about the fact that the
total power injection at each bus is zero.
– Injections (generations, loads, and shunts) are
specified.
Pi =
Pgeni +
Ploadi +
Pbranchi(0ik,Vik) = 0
Qi =
Qgeni +
Qloadi +
Qbranchi( 0ik,Vik) = 0
(where Pload and Qload include shunt contributions.)
2-17
Fully Coupled Power Flow
 Newton’s
Method
– Objective is to minimize mismatch.
– Express in matrix form, take derivative, and set to
zero…
P
Q
=
P
0
Q
0
P
V
Q
V
0
V
2-18
Fast Decoupled Power Flow
 Basic
Assumptions
– Branch reactances are larger than resistances.
– Angular separations between adjacent buses are
near zero.
– Given the above, the following approximations
are made:
P
V = 0
Q = 0
0
2-19
Fast Decoupled Power Flow (Cont.)
 Given
Fast Decoupled Assumptions...
P / V = B’
0
Q / V = B’’
0
(We divide by the vector V for simplicity)
2-20
Power Flow Algorithm Options
 Newton
(Fully Coupled)
– Best convergence properties.
– More iterations required (does it matter
anymore?).
 XB
(Fast Decoupled)
– Resistances are ignored in the B’ matrix only so
that it is made only of branch reactances. Good
for high X/R ratios.
2-21
Power Flow Algorithm Options
 BX
(Cont.)
(Fast Decoupled)
– Resistances are ignored in the B’’ matrix only.
More effective for low X/R ratios.
 Suggestions:
– Use what works for you.
– Fast Decoupled was developed for improved
performance… may not be that much of a factor
with faster CPUs.
– “Newton algorithm is best” - an instructor’s
opinion.
2-22
GENS Implementations
Running The Applications
&
Interpreting Results
2-23
Getting Around Tabular
Displays
 Display
Index
– Provides access to “all” TSM tabular displays.
– Displays are grouped by topic: General, Base
Case, Measurements, Contingency Analysis,
Optimization, Fault Level Analysis.
 “Special”
Pull Down Menu
– Provides access to TSM tabular displays.
– Menu contents are “sensitive” to the display
currently active.
2-24
Message Displays
 Message History
– Logs all TSM program activity.
 Execution Messages
– Logs informative messages relative to a “base
case” analysis.
 Network Configuration Messages
– Summarizes network topology.
 Error/Warning Report
– Summarizes data inconsistencies.
2-25
Regional Information
System Summary
Area Summary
Area Detail
Company Summary
Company Detail
Zone Summary
District Summary
Station Summary
Station Detail
2-26
Bus Information
Breaker Detail
Bus Summary
Bus Detail
Device Details
2-27
Device Information
Generator
Summary
Generator
Detail
Load
Summary
Load
Detail
Shunt
Summary
Shunt
Detail
Line
Summary
Line
Detail
Transformer
Summary
Transformer
Detail
Load Group
Detail
Note:
All device
details link
to the attachment bus(s).
2-28
Device Information (Cont.)
DC Link
Summary
DC Link
Detail
SVC
Summary
SVC
Detail
SRD
Summary
SRD
Detail
2-29
Displaying Results On OneLines
 One-Lines Data Sources
– SCADA
– TSM Case… Attaches to the case currently
assigned (I.e., real-time or study).
– CME Points… CME point update feature must be
active in TSM real-time case.
 One-Line Display Linkages
– Linkages between one-lines.
– Linkages from tabulars to one-lines.
2-30
TSM Constraints
 Limit
–
–
–
–
–
–
Sets (1,2,3)
Devices
Reserve Groups
Net Interchange Groups
Corridor Groups
Bus Voltages
Voltage Magnitude/Angle Differences
2-31
TSM Constraints (Cont.)
 Specifying
Monitored Devices
– Each device may be specified as either
“monitored” or “not monitored”.
 Specifying
Monitored Limit Set
– A separate limit set can be monitored for each
limit type (Constraint Limit Sets display).
 Alarm!
“Constraints Violated”
– RTNA issues an alarm if any constraint (in the
specified limit monitoring set) is violated.
2-32
State Estimation...
Measurements and Estimates
 SE
Measurement Summary Display
– Standard Deviations… Indicates the relative
confidence placed on an individual measurement.
– Measurement Status… Each measurement may
be determined as “used”, “not used”, or
“suppressed”.
– Meter Bias… Accumulates residual to help
identify metering that is consistently poor. The
bias value should “hover” about zero.
2-33
State Estimation...
Measurements and Estimates (Cont.)
 Suppressed
Display
Measurement Summary
– SE will suppress measurements it feels are
inconsistent with the other system measurements.
3.7
10
9.5
15.2
NOPE!
2-34
State Estimation...
Measurements and Estimates (Cont.)
 How
Bad Is It?
– Residual value provides indication as to “how
bad” a measurement is:
Measurement Value - Estimated Value
Residual =
(Standard Deviation)2
– A measurement is “suppressed” if the calculated
residual exceeds a specified threshold.
 Alarm!
“Bad Data Detected”
2-35
State Estimation...
Measurements and Estimates (Cont.)
 Observable
System
– Portions of the system that can be completely
solved based on real-time telemetry are called
“observable”.
– Observable buses and devices are not color-coded
(white).
 Unobservable
System
– Portions of the network that cannot be solved
completely based on real-time telemetry are
called “unobservable” and are color-coded
yellow.
2-36
Penalty Factors
 Real-Time
Penalty Factors
– Calculated on successful completion of RTNA.
– Available for use by Generation Dispatch and
Control.
– Penalty Factor display.
 Penalty
Factor Grid
– Historical “smoothed” factors.
– Available for use by Generation Dispatch and
Control and Unit Commitment.
– HISR Form interface.
2-37
Study Applications
Be Free…
You can’t hurt anything
2-38
How Do Study Applications Differ?
 No
Measurements
 Schedule Data For All Devices
 Freedom To Alter Any Input Data
2-39
Study Case Control Display
 Study
Case Creation
– Real-Time Case.
– Source Database (From UFBL).
– IEEE or PTI Network Model.
 Schedule
Initialization
– Individual device types.
– Equipment Outage Scheduler (EOS).
– All schedules.
2-40
Study Case Control Display (Cont.)
 External
Subsystems Initialization
– Generation Dispatch and Control (GDC)… unit
dispatch characteristics (for optimization
purposes) including IHR, fuel cost, efficiency,
penalty factor, etc.
– Unit Commitment (UC)… Generation Schedules
and Load Forecast from any UC study case.
– Unit Commitment (UC)… Accepted Case
generations and load is used by default (if
available).
2-41
Study Case Control Display (Cont.)
 Penalty
Factors
– May be updated to penalty factor grid (demand
only).
 Solution
Dump
– Solution may be dumped to file (or printing
device) in IEEE, PTI, or GENS DPF format.
2-42
Study Case Control Display (Cont.)
 Module
Indicators
– Same as real-time with the following exceptions:
– NC… Does not retrieve real-time telemetry.
Rather uses predefined switch statuses and device
schedules.
– DPF… Replaces SE functionality. Solves the
network model and reports violations.
2-43
Study Program Sequences
Study Network Analysis (STNA)
CA
RPA
SCD
INIT
NC
DPF
VVS
STNA
FLA
2-44
Freedom To Play
 Modify:
–
–
–
–
–
–
–
–
Switch Statuses
Load
Generation
Shunts
Taps
Voltage Schedules
Constraints
Etc.
2-45
Automatic Control Simulation
 Control
–
–
–
–
–
–
–
Options:
Remote voltage control by MVAR generation.
Local/Remote voltage control by shunts.
Local/Remote voltage control by TCULs.
MVAR flow control by TCULs.
MW flow control by phase shifters.
Area MW interchange control.
Reactive generation limit enforcement.
2-46
Viewing Results
 Displays
Same As Real-Time
– Measurement displays do not apply.
 One-Line
(MDS) Functionality
– Keys off case number assignment.
2-47