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• Introduction. • Power System State Estimation. • Solution Methodologies. • Weighted Least Square State Estimator. • Bad Data Processing. • Conclusion. • References.
POWER SYSTEM STATE ESTIMATION Presentation by Ashwani Kumar Chandel Associate Professor NIT-Hamirpur Presentation Outline • Introduction • Power System State Estimation • Solution Methodologies • Weighted Least Square State Estimator • Bad Data Processing • Conclusion • References Introduction • Transmission system is under stress. Generation and loading are constantly increasing. Capacity of transmission lines has not increased proportionally. Therefore the transmission system must operate with ever decreasing margin from its maximum capacity. • Operators need reliable information to operate. Need to have more confidence in the values of certain variables of interest than direct measurement can typically provide. Information delivery needs to be sufficiently robust so that it is available even if key measurements are missing. • Interconnected power networks have become more complex. • The task of securely operating the system has become more difficult. Difficulties mitigated through use of state estimation • Variables of interest are indicative of: Margins to operating limits Health of equipment Required operator action • State estimators allow the calculation of these variables of interest with high confidence despite: measurements that are corrupted by noise measurements that may be missing or grossly inaccurate Objectives of State Estimation • Objectives: To provide a view of real-time power system conditions Real-time data primarily come from SCADA SE supplements SCADA data: filter, fill, smooth. To provide a consistent representation for power system security analysis • On-line dispatcher power flow • Contingency Analysis • Load Frequency Control To provide diagnostics for modeling & maintenance Power System State Estimation • To obtain the best estimate of the state of the system based on a set of measurements of the model of the system. • The state estimator uses Set of measurements available from PMUs System configuration supplied by the topological processor, Network parameters such as line impedances as input. Execution parameters (dynamic weight- adjustments…) Power System State Estimation (Cont.,) • The state estimator provides Bus voltages, branch flows, …(state variables) Measurement error processing results Provide an estimate for all metered and unmetered quantities. Filter out small errors due to model approximations and measurement inaccuracies; Detect and identify discordant measurements, the so- called bad data. State Estimation Analog Measurements P i , Q i , P f , Q f , V, I, θ km Circuit Breaker Status State Estimator Bad Data Processor Network Observability Check Topology Processor V, θ Power System State Estimation (Cont.,) • The state (x) is defined as the voltage magnitude and angle at each bus • All variables of interest can be calculated from the state and the measurement mode. z = h(x) i j i i V Ve 1 2 n 1 b x [V ,V , ,V , , , ] Measurement Model: h(x) I 12 P 12 V 1 Power System State Estimation (Cont.,) • We generally cannot directly observe the state But we can infer it from measurements The measurements are noisy (gross measurement errors, communication channels outage) Ideal measurement: H(x) Noisy Measurements z=h(x)+e Measurement: z [...]... angles as the state variables for the threebus system since knowing them allows all other quantities to be calculated • If we can use measurements to estimate the “states” of the power system, then we can go on to calculate any power flows, generation, loads, and so forth that we desire State Estimation: determining our best guess at the state • We need to generate the best guess for the state given... assumed to equal zero ) This results in the system flows as shown in Figure Note that the predicted flows match at M13, and M32 but the flow on line 1-2 does not match the reading of 62 MW from M12 Power System State Estimation (Cont.,) • The only thing we know about the power system comes to us from the measurements so we must use the measurements to estimate system conditions • Measurements were used... Actual distribution x 0 3 Weighted least Squares -State Estimator • The problem of state estimation is to determine the estimate that best fits the measurement model • The static -state of an M bus electric power network is denoted by x, a vector of dimension n=2M-1, comprised of M bus voltages and M-1 bus voltage angles (slack bus is taken as reference) • The state estimation problem can be formulated as... measurements in the entire system will have a large error • Multiple bad data: More than one measurement will be in error (Cont.,) • Critical measurement: A critical measurement is the one whose elimination from the measurement set will result in an unobservable system The measurement residual of a critical measurement will always be zero • A system is said to be observable if all the state variables can... measurements actually contain bad data Detection and identification of bad data depends on the configuration of the overall measurement set in a given power system Bad data can be detected if removal of the corresponding measurement does not render the system unobservable A single measurement containing bad data can be identified if and only if: it is not critical and it does not belong to a critical... J( x) x H T R 1 (e H x) 0 H T R 1H x G x H T R 1e H T R 1e Weighted Least Squares-Example • x est est 1 est 2 (Cont.,) • To derive the [H] matrix, we need to write the measurements as a function of the state variables are written in per unit as M12 f12 M13 f13 M 32 f32 1 ( 1 0.2 1 ( 1 0.4 1 ( 0.25 1 2 3 3 ) 5 ) 2 and 2 5 2 1 2.5 ) 1 4 2 These functions (Cont.,) • 5 [H] 2 M12 R 5 2.5 0 0 4 2 M12 2 M13... each bus (0.62 (5 1 5 2 )) 2 J( 1 , 2 ) 0.0001 2.14 (0.06 (2.5 1 )) 2 0.0001 (0.37 (4 2 )) 2 0.0001 Solution of the weighted least square example Bad Data Processing • One of the essential functions of a state estimator is to detect measurement errors, and to identify and eliminate them if possible • Measurements may contain errors due to Random errors usually exist in measurements due to the finite... constraint zi= hi(x) + ei Where, σ2 = variance of the measurement W=weight of the measurement (reciprocal of variance of the measurement) ei = zi-hi(x), i=1, 2, 3 ….m h(x) = Measurement function, x = state variables and Z= Measured Value m=number of measurements (Cont.,) • The measurements are assumed to be in error: that is, the value obtained from the measurement device is close to the true value... not critical Only redundant measurements may have nonzero measurement residuals • Critical pair: Two redundant measurements whose simultaneous removal from unobservable the measurement set will make the system (Cont.,) • When using the WLS estimation method, detection and identification of bad data are done only after the estimation process by processing the measurement residuals J x (z h( x))' W z h(x)...Consider a Simple DC Load Flow Example Three-bus DC Load Flow The only information we have about this system is provided by three MW power flow meters (Cont.,) Only two of these meter readings are required to calculate the bus phase angles and all load and generation values fully M13 5MW 0.05pu M32 40MW . POWER SYSTEM STATE ESTIMATION Presentation by Ashwani Kumar Chandel Associate Professor NIT-Hamirpur Presentation Outline • Introduction • Power System State Estimation • Solution. for power system security analysis • On-line dispatcher power flow • Contingency Analysis • Load Frequency Control To provide diagnostics for modeling & maintenance Power System State Estimation •. 0.06pu M 37MW 0.37pu Power System State Estimation (Cont.,) • The only thing we know about the power system comes to us from the measurements so we must use the measurements to estimate system conditions. •