TSM Base Case Algorithms

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TSM Base Case Algorithms

State Estimation-Abhimanyu Gartia, WRLDC

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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.

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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

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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

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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).

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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

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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.

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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

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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.

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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.

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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

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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.

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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.

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SE Program Constants

Please Refer To Real-Time Program Constants Display.

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Base Case Algorithms

Power Flow

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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”.

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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.)

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V

Fully Coupled Power Flow

Newton’s Method– Objective is to minimize mismatch.– Express in matrix form, take derivative, and

set to zero…

PQ

P0

P

VQ0

Q

V0=

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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:

VP

Q0

= 0

= 0

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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)

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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.

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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.

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GENS Implementations

Running The Applications &

Interpreting Results

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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.

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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.

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Regional InformationSystem Summary

Area Summary

Company Summary

Zone Summary

District Summary

Station Summary

Area Detail

Company Detail

Station Detail

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Bus Information

Bus Summary Bus DetailBreaker Detail

Device Details

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Device InformationGenerator Summary

LoadSummary

ShuntSummary

LineSummary

TransformerSummary

GeneratorDetail

LoadDetail

ShuntDetail

LineDetail

TransformerDetail

Load GroupDetail

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

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Device Information (Cont.)DC Link Summary

SVCSummary

SRDSummary

DC LinkDetail

SVCDetail

SRDDetail

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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.

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TSM Constraints

Limit Sets (1,2,3)– Devices– Reserve Groups– Net Interchange Groups– Corridor Groups– Bus Voltages– Voltage Magnitude/Angle Differences

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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.

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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.

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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!

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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

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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.

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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.

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Study Applications

Be Free…You can’t hurt

anything

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How Do Study Applications Differ?

No Measurements Schedule Data For All Devices Freedom To Alter Any Input Data

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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.

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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).

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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.

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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.

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Study Program SequencesStudy Network Analysis (STNA)

INIT NC DPF

CA RPA

SCD

VVS

STNAFLA

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Freedom To Play

Modify:– Switch Statuses– Load– Generation– Shunts– Taps– Voltage Schedules– Constraints– Etc.

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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.

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Viewing Results

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

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

TSM Base Case Algorithms

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