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

1. 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)

2. PAPERS
 PAPER 1.
Power System State Estimation and Bad Data Analysis Using
Weighted Least Square Method
1.T P Vishnu
2.Vidya Vishwan
3.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]
2

3. PAPER 1.
Power System State Estimation(PSSE) and Bad Data
Analysis Using Weighted Least Square Method
 OUTLINE :-
1. Abstract
2. Introduction
3. State Estimation
4. Component Modelling
5. Newton Raphsons Load Flow Analysis
6. Weighted Least Square State Estimatios
7. Bad Data Detection And Identification
8. Bad Data Detection
9. Bad Data Identification
10.Program And Output
11.References
3

4. 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.
4

5. 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.
5

6. 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.
6

7. 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.
7

8. INTRODUCTION
 Based on the operating condition power system can remain in any of the
five operating states :
8
Preventive
control
Emergency
control
Resynchronization
Load pick up
Fig .1 operating state

9. STATE ESTIMATION
 The state estimators typically include the following functions:
9
Topology processor
Observability analysis
State estimation solution
Bad data processing
Error processing

10. 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
10

11.  The effect of a tap changing transformer on a Ybus is shown in Fig 3.
11
Ybus can be obtained by writing the nodal equations at each node.

12. NEWTON RAPHSONS LOAD FLOW
ANALYSIS
 The true measurements for the PSSE is found out using
Newton Raphsons Load flow analysis .
 NR load flow analysis
12
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.

13. 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.
13

14. 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:
14

15. 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.
15

16. 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∼
16

17. 17
X
ChisquareB. 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

18. 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.
18

19. PROGRAM AND OUTPUT
19

20. PAPER 2.
Power System State Estimation Using Weighted Least
Trimmed Sum of Absolute Deviation
 OUTLINE :-
1. Abstract
2. Introduction
3. 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
20

21. 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
21

22. 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.
22

23. 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) + e
where,
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.
23

24.  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.
24

25. 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:
25

26. B. ORTHOGONAL CROSSOVER BASED DIFFERENTIAL EVOLUTION
 the convergence characteristics of the conventional DE depend mainly on
two important parameters:
1. The tuning of control parameters
2. 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) .
26

27. IMPLEMENTATION OF PSSE USING OXDE
27
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

28. RESULTS AND DISCUSSION
 the power system are estimated using the conventional and PMU
measurements placed optimally across the power system network.
28
Table .1 The problem statistics are summarized
Table .2 Control parameter settings for both the test systems

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

30. B. BAD DATA CONDITION
30
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

31. 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
31

32. 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.
32

33. 33
Thank you