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  • Power System State Estimation And Bad Data Analysis Using WLS Method And Weighted Least Trimmed Sum Of Absolute Deviation

    -:Prepared by:- Divyangkumar R Soni.(160410707008)

  • PAPERSPAPER 1. Power System State Estimation and Bad Data Analysis Using Weighted Least Square Method1.T P Vishnu 2.Vidya Vishwan3.Vipian A M[2015 IEEE International Conference on Power, Instrumentation, Control and Computing (PICC) ]PAPER 2.Power System State Estimation Using Weighted Least Trimmed Sum of Absolute Deviation B. Vedik 2.Ashwani Kumar Chandel [IEEE INDICON 2015]*

  • PAPER 1. Power System State Estimation(PSSE) and Bad Data Analysis Using Weighted Least Square Method

    OUTLINE :-AbstractIntroductionState EstimationComponent ModellingNewton Raphsons Load Flow AnalysisWeighted Least Square State EstimatiosBad Data Detection And Identification Bad Data DetectionBad Data IdentificationProgram And OutputReferences*

  • ABSTRACTThis paper explains the concept of Weighted Least Square static state estimation. Static state estimation is performed on the data made available through the SCADA system. In this paper this data is obtained through Newton Raphson Load ow analysis. Power ow, power injections and voltage magnitudes are the various measurements taken from load ow analysis as the measurements for state estimation. Weighted least square method estimates the state of the power system based on the weight given to each measurement.A state estimator should have the ability to detect and identify the presence of a bad data.



    If a bad data is present among the measurements, then the estimated state variables will vary from the actual state variables.In this paper bad data detection is performed using Chi Squared test and bad data identication is performed using largest normalized residual method. Weighted least square algorithm is applied on an IEEE 14 bus.*


    State estimation is an important part of power system security analysis. Power system operations can be controlled from the load dispatch center on obtaining various informations about the current state of the power system. These information include various meter readings, Transformer Tap Position, Circuit Breaker Position Network TopologyTransmission of these information to the SCADA center is not always reliable. Errors can be caused by improper connection of transducerloss of data while transmitting or due to the presence of faulty meters. So,if these wrong data is used for Contingency Analysis in power system it will give false alarm signal and can even cause unnecessary tripping of power system elements. *


  • INTRODUCTIONPSSE is simply do using SCADA system.Using Phasor Measurement Units (PMU) increase the accuracy of the state estimation technique. PMU based state estimation algorithm to obtain a more robust result . Recent techniques of SE using Multi Sensor data fusion theory can give a better result.the network topology and voltage phasor, all the measurements can be estimated. So the least number of variables that can dene a power system are voltage magnitude and voltage angle. Hence they are referred as the static state of the system.*

  • INTRODUCTIONBased on the operating condition power system can remain in any of the ve operating states :*Preventive controlEmergency controlResynchronization Load pick up Fig .1 operating state

  • STATE ESTIMATIONThe state estimators typically include the following functions:*Topology processor

    Observability analysisState estimation solutionBad data processingError processing

  • COMPONENT MODELLINGFor running the state estimation algorithm power system network topology has to be known. Transmission lines are represented by a two-port network whose impedance and shunt reactances are the positive sequence component impedances . A transmission line with a positive sequence series impedance of R+jX and total line charging susceptance of j2B, will be modelled by the equivalent circuit shown in Fig 2 *

  • The effect of a tap changing transformer on a Ybus is shown in Fig 3.

    *Ybus can be obtained by writing the nodal equations at each node.


    The true measurements for the PSSE is found out using Newton Raphsons Load ow analysis . NR load ow analysis*Calculate Ybus Take voltage magnitude and voltage angle using bus deta Caculate P and Q injectionsSelect Specied value of (Pi,Qi) which is usually the power injection at each busCalculated Change in power injection Pi,qi &Jacobian matrix is calculated Using the Jacobian matrix the change in state variable is calculated

    process is repeated.

  • WEIGHTED LEAST SQUARE STATE ESTIMATION Measurement Function :The state vector is given by following equation :Each equation corresponding to the measured variable can be represented. Equations of active and reactive power injection and power ows are given by Eqn 4 7.


  • Gain Matrix G(x):WLS State Estimation involves an iterative solution of the objective function which is given by :

    WLS equations are given by:



  • BAD DATA DETECTION AND IDENTIFICATIONFunctions of a state estimator is :- Detect measurement errors.Identify and eliminate them if possible . Errors in measurements are due to various reasons:-Accuracy of meters.Telecommunication networks lead to random errors.The meters have biases, drifts or wrong connections. Telecommunication system failures. Negative voltage measurements or large difference in current entering and leaving the bus are possible large bad data.*

  • BAD DATA DETECTIONChi Squared Test Consider a set of n independent random variables X1,X2,X3...Xn where each Xp is distributed according to the Standard Normal distribution :Xp N(0,1) A new random variable Y can be dened as :will have chi squared distribution with N degrees of freedom i.e. Y 2 N


  • *XChi squareB. Use of 2 distribution for bad data detectionProbability of nding x is given by the area under the curve in the 2 probability density function(pdf).

    Once we set the probability as say 0.1 then we can calculate the threshold x as in eqn 18.

    C. 2 Test for Detecting Bad Data Solve the WLS estimation problem and compute the objective function: From the 2 distribution table nd the value corresponding to probability p and degrees of freedom (mn). If there is a bad data then

  • BAD DATA IDENTIFICATIONIdentication can be accomplished by further processing of the residuals. Largest Normalized Residual Test can identify the presence of a bad data and has following steps: Calculate the residual covariance matrix using following steps. Hat Matrix K = H G^1 HT R^1 . Residual Sensitivity Matrix S = I K. Residual Covariance Matrix =S R.*


  • PAPER 2.Power System State Estimation Using Weighted Least Trimmed Sum of Absolute Deviation

    OUTLINE :-Abstract IntroductionState Estimation Problem Formulation Orthogonal Crossover Based Differential Evolution Algorithm Implementation Of Psse Using Oxde Results And Discussion Conclusions References *



    This paper suggests the application of one such robust estimator known as weighted least trimmed sum of absolute (WLTA) deviation estimator to PSSE. The main principle of WLTA estimator is to optimize the weighted sum of the absolute residuals of rank . In the present work, the PSSE problem is solved as an optimization problem using orthogonal crossover based differential evolution algorithm. The proposed method has been demonstrated on IEEE 14-bus and IEEE 30-bus systems under normal and bad data conditions *


    SE problem is generally solved iteratively using Gauss-Newton based weighted least squares (WLS) estimator due to its high efficiency . In order to make WLS estimator robust it is generally followed by largest normalized residual test to recognize and remove the bad measurements.The main contribution of the paper is to introduce a new statistical robust estimator known as weighted least trimmed sum of absolute deviation estimator to PSSE. The state estimation problem has been solved as an optimization problem using orthogonal crossover based differential evolution (OXDE) algorithm. The efficacy and robustness of the proposed approach is tested on :-IEEE 14-bus and IEEE 30-bus systems under both normal and bad data conditions.*


    The mathematical model for SE that relates measurements to the state variables is expressed by the following equation : Z=h(x) + ewhere, Z= signifies the measurement vector of order (m*1)x =indicates the state vector of order ( n*1) e= represents measurements errors of order (m*1), (these errors are normally assumed as Gaussian distributed with zero mean and standard deviation .)In the present work, the above SE problem is solved using:- the weighted least trimmed sum of absolute deviation estimator. *

  • The WLTA estimator minimizes the sum of the th order residuals that is given as follows :-

    Where, ri is indicate the i th residual . wi is indicate i th measurement error .

    Depending upon the number of bad data measurements the value of can be increased to increase the accuracy and efficiency of the SE.



    CLASSICAL DIFFERENTIAL EVOLUTION ALGORITHM After initialization, Differential evolution (DE) performs difference vector mutation and crossover operation to generate new vectors.1. Mutation operation :