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2-1 TSM Base Case Algorithms State Estimation - Abhimanyu Gartia, WRLDC

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2-2 SE Problem Development v 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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2-3 SE Problem Development (Cont.) v 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

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2-4 SE Problem Development (Cont.) v Linearizing… v Classical Approach -> Weighted Least Squares… Z = Hx + e (This looks like a load flow equation ) Minimize: J(x) = [z - h(x)] t. W. [z - h(x)] where, J = Weighted least squares matrix W = Error covariance matrix

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2-5 SE Functionality v 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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2-6 SE Measurement Types v 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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2-7 State Estimation Process v 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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2-8 Observability Analysis v 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”). u Bus or station basis

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2-9 Bad Data Suppression v 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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2-10 Final Measurement Statuses v Used… The measurement was found to be “good” and was used in determining the final SE solution. v Not Used… Not enough information was available to use this information in the SE solution. v Suppressed… The measurement was initially used, but found to be inconsistent (or “bad”). v 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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2-11 Solution Algorithms v Objective… Weighted Least Squares: v 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 matrix R = Error covariance matrix

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2-12 Solution Algorithms (Cont.) v 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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2-13 SE Problem Development (Cont.) v 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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2-14 SE Program Constants v Please Refer To Real-Time Program Constants Display.

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2-15 Base Case Algorithms Power Flow

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2-16 PF Problem Development v Purpose –Solve the general network consisting of all voltages and branches flows. v 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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2-17 PF Problem Development (Cont.) v 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. P i = P gen i + P load i + P branch i ( ik,V ik ) = 0 0 Q i = Q gen i + Q load i + Q branch i ( ik,V ik ) = 0 0 (where P load and Q load include shunt contributions.)

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2-18 V Fully Coupled Power Flow v Newton’s Method –Objective is to minimize mismatch. –Express in matrix form, take derivative, and set to zero… P Q P 0 P V Q 0 Q V 0 =

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2-19 Fast Decoupled Power Flow v 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

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2-20 Fast Decoupled Power Flow (Cont.) v Given Fast Decoupled Assumptions... P / V = B’ 0 Q / V = B’’ 0 (We divide by the vector V for simplicity)

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2-21 Power Flow Algorithm Options v Newton (Fully Coupled) –Best convergence properties. –More iterations required (does it matter anymore?). v 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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2-22 Power Flow Algorithm Options (Cont.) v BX (Fast Decoupled) –Resistances are ignored in the B’’ matrix only. More effective for low X/R ratios. v 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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2-23 GENS Implementations Running The Applications & Interpreting Results

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2-24 Getting Around Tabular Displays v Display Index –Provides access to “all” TSM tabular displays. –Displays are grouped by topic: General, Base Case, Measurements, Contingency Analysis, Optimization, Fault Level Analysis. v “Special” Pull Down Menu –Provides access to TSM tabular displays. –Menu contents are “sensitive” to the display currently active.

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2-25 Message Displays v Message History –Logs all TSM program activity. v Execution Messages –Logs informative messages relative to a “base case” analysis. v Network Configuration Messages –Summarizes network topology. v Error/Warning Report –Summarizes data inconsistencies.

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2-26 Regional Information System Summary Area Summary Company Summary Zone Summary District Summary Station Summary Area Detail Company Detail Station Detail

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2-27 Bus Information Bus SummaryBus Detail Breaker Detail Device Details

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2-28 Device Information Generator Summary Load Summary Shunt Summary Line Summary Transformer Summary Generator Detail Load Detail Shunt Detail Line Detail Transformer Detail Load Group Detail Note: All device details link to the attach- ment bus(s).

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2-29 Device Information (Cont.) DC Link Summary SVC Summary SRD Summary DC Link Detail SVC Detail SRD Detail

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2-30 Displaying Results On One- Lines v 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. v One-Line Display Linkages –Linkages between one-lines. –Linkages from tabulars to one-lines.

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2-31 TSM Constraints v Limit Sets (1,2,3) –Devices –Reserve Groups –Net Interchange Groups –Corridor Groups –Bus Voltages –Voltage Magnitude/Angle Differences

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2-32 TSM Constraints (Cont.) v Specifying Monitored Devices –Each device may be specified as either “monitored” or “not monitored”. v Specifying Monitored Limit Set –A separate limit set can be monitored for each limit type (Constraint Limit Sets display). v Alarm! “Constraints Violated” –RTNA issues an alarm if any constraint (in the specified limit monitoring set) is violated.

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2-33 State Estimation... Measurements and Estimates v 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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2-34 State Estimation... Measurements and Estimates (Cont.) v Suppressed Measurement Summary Display –SE will suppress measurements it feels are inconsistent with the other system measurements NOPE!

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2-35 State Estimation... Measurements and Estimates (Cont.) v 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. v Alarm! “Bad Data Detected” Residual = Measurement Value - Estimated Value (Standard Deviation) 2

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2-36 State Estimation... Measurements and Estimates (Cont.) v 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). v 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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2-37 Penalty Factors v Real-Time Penalty Factors –Calculated on successful completion of RTNA. –Available for use by Generation Dispatch and Control. –Penalty Factor display. v Penalty Factor Grid –Historical “smoothed” factors. –Available for use by Generation Dispatch and Control and Unit Commitment. –HISR Form interface.

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2-38 Study Applications Be Free… You can’t hurt anything

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2-39 How Do Study Applications Differ? v No Measurements v Schedule Data For All Devices v Freedom To Alter Any Input Data

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2-40 Study Case Control Display v Study Case Creation –Real-Time Case. –Source Database (From UFBL). –IEEE or PTI Network Model. v Schedule Initialization –Individual device types. –Equipment Outage Scheduler (EOS). –All schedules.

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2-41 Study Case Control Display (Cont.) v 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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2-42 Study Case Control Display (Cont.) v Penalty Factors –May be updated to penalty factor grid (demand only). v Solution Dump –Solution may be dumped to file (or printing device) in IEEE, PTI, or GENS DPF format.

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2-43 Study Case Control Display (Cont.) v 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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2-44 Study Program Sequences Study Network Analysis (STNA) INITNCDPF CARPA SCD VVS STNA FLA

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2-45 Freedom To Play v Modify: –Switch Statuses –Load –Generation –Shunts –Taps –Voltage Schedules –Constraints –Etc.

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2-46 Automatic Control Simulation v 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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2-47 Viewing Results v Displays Same As Real-Time –Measurement displays do not apply. v One-Line (MDS) Functionality –Keys off case number assignment.

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