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)

PAPERS PAPER 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 1. B. Vedik 2.Ashwani Kumar Chandel [IEEE INDICON 2015]

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

OUTLINE :-1. Abstract2. Introduction3. State Estimation4. Component Modelling5. Newton Raphsons Load Flow Analysis6. Weighted Least Square State Estimatios7. Bad Data Detection And Identification8. Bad Data Detection9. Bad Data Identification10.Program And Output11.References

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ABSTRACT

This 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 flow analysis.

Power flow, power injections and voltage magnitudes are the various measurements taken from load flow 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.

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ABSTRACT

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 identification is performed using largest normalized residual method.

Weighted least square algorithm is applied on an IEEE 14 bus.

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INTRODUCTION

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, 1. Transformer Tap Position, 2. Circuit Breaker Position 3. Network Topology Transmission of these information to the SCADA center is not always

reliable. Errors can be caused by improper connection of transducer loss 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.

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INTRODUCTION PSSE 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 define a power system are

voltage magnitude and voltage angle. Hence they are referred as the static state of the system.

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INTRODUCTION

Based on the operating condition power system can remain in any of the five operating states :

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Preventive control

Emergency control

Resynchronization

Load pick up

Fig .1 operating state

STATE ESTIMATION The state estimators typically include the following functions:

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Topology processor

Observability analysis

State estimation solution

Bad data processing

Error processing

COMPONENT MODELLING For running the state estimation algorithm power system network topology

has to be known. Transmission lines are represented by a two-port π 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

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

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

NEWTON RAPHSONS LOAD FLOW ANALYSIS

The true measurements for the PSSE is found out using Newton Raphsons Load flow analysis .

NR load flow analysis

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Calculate Ybus

Take voltage magnitude and voltage angle using bus deta

Caculate P and Q injections

Select Specified value of (Pi,Qi) which is usually the power injection at each bus

Calculated Change in power injection ΔPi,Δqi &Jacobian matrix is calculated

Using the Jacobian matrix the change in state variable is calculated

process is repeated.

WEIGHTED LEAST SQUARE STATE ESTIMATION

1. 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 flows are given by Eqn 4 – 7.

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2. Gain Matrix G(x):

WLS State Estimation involves an iterative solution of the objective function which is given by :

WLS equations are given by:

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BAD DATA DETECTION AND IDENTIFICATION

Functions of a state estimator is :-1. Detect measurement errors.2. Identify and eliminate them if possible . Errors in measurements are due to various reasons:-1. Accuracy of meters.2. Telecommunication networks lead to random errors.3. The meters have biases, drifts or wrong connections. 4. Telecommunication system failures. Negative voltage measurements or large difference in current entering and

leaving the bus are possible large bad data.

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BAD DATA DETECTION

A. Chi 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 defined as :

will have chi squared distribution with N degrees of freedom i.e. Y χ2 N ∼

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X

Chi

squ

are

B. Use of χ2 distribution for bad data detection

Probability of finding x is given by the area under the curve in the χ2 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. χ2 Test for Detecting Bad Data

Solve the WLS estimation problem

and compute the objective function:

From the χ2 distribution table find the value corresponding to probability p and degrees of freedom (m−n).

If there is a bad data

then

BAD DATA IDENTIFICATION Identification 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:1. Calculate the residual covariance matrix Ω using following steps. 2. Hat Matrix K = H ×G^1 ×HT ×R^1 .3. Residual Sensitivity Matrix S = I −K.4. Residual Covariance Matrix Ω=S ×R.

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PROGRAM AND OUTPUT

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

OUTLINE :-1. Abstract2. Introduction3. State Estimation Problem Formulation 4. Orthogonal Crossover Based Differential Evolution Algorithm 5. Implementation Of Psse Using Oxde 6. Results And Discussion 7. Conclusions 8. References

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ABSTRACT 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 υ.

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

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INTRODUCTION 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.

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STATE ESTIMATION PROBLEM FORMULATION

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 σ.) In the present work, the above SE problem is solved using:- the weighted least trimmed sum of absolute deviation estimator.

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The WLTA estimator minimizes the sum of the υ 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 υ can be increased to increase the accuracy and efficiency of the SE.

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ORTHOGONAL CROSSOVER BASED DIFFERENTIAL EVOLUTION ALGORITHM A. CLASSICAL DIFFERENTIAL EVOLUTION ALGORITHM After initialization, Differential evolution (DE) performs difference

vector mutation and crossover operation to generate new vectors. 1. Mutation operation :

2.Crossover operation:

3. Selection:

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B. ORTHOGONAL CROSSOVER BASED DIFFERENTIAL EVOLUTION the convergence characteristics of the conventional DE depend mainly on

two important parameters:1. The tuning of control parameters2. The selection of donor and trial vectors generation strategies Selected randomly by generating a number uniformly in between 0 and 1

for mutant vector that undergoes quantization orthogonal crossover operation :

where, (0,1) rand indicates the uniformly distributed random number generated

in-between (0,1) .

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IMPLEMENTATION OF PSSE USING OXDE

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Obtain true measurement by performing load flow analysis

Read system data and initialize the control parameter

Perform offline synchronization of measurement

Perform PSSE using orthogonal crossover differential evolution

final report

RESULTS AND DISCUSSION the power system are estimated using the conventional and PMU

measurements placed optimally across the power system network.

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Table .1 The problem statistics are summarized

Table .2 Control parameter settings for both the test systems

The comparison of the proposed method with WLS method is performed using the performance indices such as ,

1. Average absolute voltage error (AAVE)

2. Average absolute angle error (AAAE)

of the estimated state variables of the estimated measurements.A. NORMAL OPERATING CONDITION

29Table .3 Performance indices of different systems under normal condition

B. BAD DATA CONDITION

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Table .4 Performance indices of different systems by considering single bad data measurement

Table .5 Performance indices of different systems by considering two bad data measurement

Table .6 Performance indices of different systems by considering three bad data measurement

Table .7 Performance indices of different systems by considering four bad data measurement

CONCLUSIONS

A new robust weighted least trimmed sum of absolute deviation estimator is introduced to PSSE.

The robustness of the proposed method in comparison with WLS algorithm has been validated by applying it to IEEE 14-bus and IEEE 30-bus test systems under normal and bad data conditions.

The PSSE problem has been solved as an optimization problem using OXDE technique

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REFERENCES

[A] Hui Xue, Quing-quan Jia ‘A Dynamic state estimation method with PMU and SCADA Measurement for Power System’, The 8th International Power Engineering Conference, pp. 848-853, Dec 2007.

[B] F.C.Schweppe, and J.Wildes,‘Power system static-state estimation, part 1: exact model’, IEEE trans. Power app. Syst., vol. 3, no. 4, pp. 120–135 Jan. 1970.

[1] A. K. Al-Othman and M. R. Irving, “Robust state estimator based on maximum constraints satisfaction of uncertain measurements,” Measurement, Vol. 40, No. 3, pp. 347–359, Apr. 2007.

[2] D. M. Hawkins and D. Olive, “Applications and algorithms for least trimmed sum of absolute deviations regression,” Computational Statistics & Data Analysis, Vol. 32, No. 2, pp. 119-134, Dec. 1999.

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Thank you