2-1

TSM Base Case Algorithms

State Estimation

-Abhimanyu Gartia, WRLDC

2-2

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 measurement set to the fullest extent.

2-3

SE Problem Development (Cont.)

�Mathematically Speaking...Z = [ h( x ) + e ]

where,Z = Measurement Vectorh = System Model relating state vector to the

measurement setx = State Vector (voltage magnitudes and

angles)e = Error Vector associated with the

measurement set

2-4

SE Problem Development (Cont.)

�Linearizing…

�Classical Approach -> Weighted Least Squares…

Z = H x + e

(This looks like a load flow equation )

Minimize: J(x) = [z - h(x)] t. W. [z - h(x)]where,

J = Weighted least squares matrixW = Error covariance matrix

2-5

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).

2-6

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

2-7

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.

2-8

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

2-9

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.

2-10

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.

2-11

Solution Algorithms

�Objective… Weighted Least Squares:

�Choice of Givens Rotation or Hybrid Solution Methods

Minimize: J(x) = .5 [Z - h(x)] t R -1 [Z - h(x)]where,

J = Weighted least squares matrixR = Error covariance matrix

2-12

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.

2-13

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.

2-14

SE Program Constants

� Please Refer To Real-Time Program Constants Display.

2-15

Base Case Algorithms

Power Flow

2-16

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”.

2-17

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( ik,Vik) = 00

Qi = Qgeni+ Qloadi

+ Qbranchi( ik,Vik) = 00

(where Pload and Qload include shunt contributions.)

2-18

V

Fully Coupled Power Flow

�Newton’s Method– Objective is to minimize mismatch.

– Express in matrix form, take derivative, and set to zero…

PQ

∂ P∂ 0

∂ P∂

V∂ Q∂ 0

∂ Q∂

V0=

2-19

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:

V∂ P∂∂ Q∂ 0

= 0

= 0

2-20

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)

2-21

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.

2-22

Power Flow Algorithm Options (Cont.)

�BX (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.

2-23

GENS Implementations

Running The Applications &

Interpreting Results

2-24

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.

2-25

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.

2-26

Regional Information

System Summary

Area Summary

Company Summary

Zone Summary

District Summary

Station Summary

Area Detail

Company Detail

Station Detail

2-27

Bus Information

Bus Summary Bus DetailBreaker Detail

Device Details

2-28

Device Information

Generator Summary

LoadSummary

ShuntSummary

LineSummary

TransformerSummary

GeneratorDetail

LoadDetail

ShuntDetail

LineDetail

TransformerDetail

Load GroupDetail

Note:All devicedetails linkto the attach-ment bus(s).

2-29

Device Information (Cont.)

DC Link Summary

SVCSummary

SRDSummary

DC LinkDetail

SVCDetail

SRDDetail

2-30

Displaying Results On One-Lines

�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.

2-31

TSM Constraints

�Limit Sets (1,2,3)– Devices

– Reserve Groups

– Net Interchange Groups

– Corridor Groups

– Bus Voltages

– Voltage Magnitude/Angle Differences

2-32

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.

2-33

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.

2-34

State Estimation...Measurements and Estimates (Cont.)

� Suppressed Measurement Summary Display– SE will suppress measurements it feels are

inconsistent with the other system measurements.

10 9.5

3.7

15.2NOPE!

2-35

State Estimation...Measurements and Estimates (Cont.)

�How Bad Is It?– Residual value provides indication as to “how

bad” a measurement is:

– A measurement is “suppressed” if the calculated residual exceeds a specified threshold.

�Alarm! “Bad Data Detected”

Residual = Measurement Value - Estimated Value

(Standard Deviation)2

2-36

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.

2-37

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.

2-38

Study Applications

Be Free…

You can’t hurt anything

2-39

How Do Study Applications Differ?

�No Measurements

� Schedule Data For All Devices

� Freedom To Alter Any Input Data

2-40

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.

2-41

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).

2-42

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.

2-43

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.

2-44

Study Program SequencesStudy Network Analysis (STNA)

INIT NC DPF

CA RPA

SCD

VVS

STNAFLA

2-45

Freedom To Play

�Modify:– Switch Statuses

– Load

– Generation

– Shunts

– Taps

– Voltage Schedules

– Constraints

– Etc.

2-46

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.

2-47

Viewing Results

�Displays Same As Real-Time– Measurement displays do not apply.

�One-Line (MDS) Functionality– Keys off case number assignment.