Detection of Bad Data in Phasor Measurement Units ...

International Conference on Innovations in Power and Advanced Computing Technologies [i-PACT2017]

Detection of Bad Data in Phasor Measurement Units Using Distributed Approach 1

1

Polly Thomas

Dept of Electrical and Electronics Engineering Saintgits College of Engineering Kottayam, India [email protected]

Emil Ninan Skariah


Abstract—. The chances for presence of bad data in Phasor measurement units are increasing due to complicated power system. Thus the voltage magnitude and phase angle obtained from PMU is no longer accurate. Hence it is important to detect the presence of bad data and identify the PMU which contains the error. In order to implement bad data detection and identification, state estimation is carried out to obtain the true state variables using weighted least square method. In this paper a distributed approach is chosen for identification of bad data. The system network is divided into different areas and the technique is applied to each area separately. The area and the meter which contains error is identified through this method. The system works in MATLAB platform. Keywords—power system; state measurement units; distributed detection

estimation;

Phasor

I. INTRODUCTION A power system is a complex system that connects power generators through transmission and distribution networks across a large area. With the increasing size of power system, increase in demand and limited number of resources the power system is becoming more and more complicated in structure Thus reliability of power system becomes a major issue that has to be dealt with nowadays in power system. The reliability of the system can be maintained by providing the system operators with information regarding the control and protection of the system. State estimation (SE), one of the key functions for control and protection, has gained importance. State estimation (SE) is to find the unknown state variables or to find the best optimal state form the available redundant measurements. In traditional methods state estimation used measurements of bus voltage magnitudes, power Àows and injections which are taken through the network provided by Supervisory Control and Data Acquisition (SCADA) system [5-7]. The voltage magnitude and phase angle are estimated using analog measurements obtained from the Phasor measurement units. State estimation methods can be mainly classified into two groups. The first group is categorized as mathematical

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Sheena Thomas Varghese


methods and the second group is categorized as intelligent methods. Weighted Linear Least (WLS), Weighted least Absolute Value (WLAV) and Estimation with Non-Fixed Error (M-Estimator) are the mathematical methods Whereas Fuzzy Inference System (FIS), state estimation based on Neural Network (NT) and Adaptive Neuron Fuzzy Inference System (ANFIS) are the intelligent methods. Intelligent methods requires less time, but they have not sufficient accurate when compared with mathematical methods. The accuracy and speed of WLS and WLAV are better than the other mathematical methods [8-12].State estimation is carried out using weighted least square method. Phasor measurement unit provides the phasor information both magnitude and phase angle) in real time [13]. The presence of bad data in phasor measurement units can arise severe power system security issues like blackouts. While considering the role of metering infrastructures involving measuring devices and sensors, the indication of system to fall into blackout may or may not be done by the meters or PMU. In such cases the presence of bad data in measurement plays an essential role to make the system into blackout condition. It is considered that the bad data in PMU may arise either due to the internal PMU error or due to the wrong connection of PMU’s. The internal meter error introduces deviation in actual meter readings whereas the reverse/wrong connection of meters can produce negative readings. The presence of bad data measurements affects the accuracy of state estimation therefore influencing the effectiveness of control and protection system .One or more of the measured data can be greatly affected by improper functioning of measuring instruments or transmission system or both. Even if proper care is taken in order to ensure the accuracy of the system unavoidable noise enters the measurement process which may distort the physical states of the system. If a measurement is grossly bad, it must be detected and identified so that it can be removed from the measurements for the optimal operation of the power system.

978-1-5090-5682-8 /17/$31.00 ©2017 IEEE

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Fig.1. Base case system with normal (all line flows are within limits) line flow condition

II. SYSTEM DESCRIPTION

III. STATE ESTIMATION

Consider a 14-bus system modeled as shown in Fig 1 which consists of five generation units and ten loads. There are 19 transmission lines which indicates the power flow. The system is modeled in ETAP 1. IEEE 14 bus system data including the resistance, susceptances and shunt admittances is tabulated in table I

State estimation is the process of assigning a value to an unknown system state variable based on measurements from that system according to some criteria. In a power system, the state variables are the voltage magnitudes and relative phase angles at the system nodes. The estimator is designed to produce the “best estimate” of the system voltage and phase angles, recognizing that there are errors in measured quantities and that there may be redundant measurements [14-15]. State estimation problem can be described as

TABLE I: SYSTEM LINE DATA x

Sr. No 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

From Bus 1 1 2 2 2 3 4 4 4 5 6 12 13 14 15 16 17 18 19 20

[z i − f i(x)]

2

min J (x ) = To Bus

R(pu)

X(pu)

B/2(pu)

2 5 3 4 5 4 5 7 9 6 11 6 6 7 7 9 9 10 12 13

0.01938 0.05403 0.04699 0.05811 0.05695 0.06701 0.01335 0.0000 0.0000 0.0000 0.09498 0.12291 0.06615 0.0000 0.0000 0.03181 0.12711 0.08205 0.22092 0.17093

0.05917 0.22304 0.19797 0.17632 0.17388 0.17103 0.04211 0.20912 0.55618 0.25202 0.19890 0.25581 0.13027 0.17615 0.11001 0.08450 0.27038 0.19207 0.19988 0.34802

0.0264 0.0246 0.0219 0.0170 0.0173 0.0064 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Nm

¦

σ

i =1

(1)

2 i

We first form the gradient of J(x) as

∇ ª∂ f 1 « «∂x 1 « «∂ f 1 = −2« « ∂ x2 « « # « « ¬

ª ∂J (x ) º «∂ x 1 »» J (x ) = « « ∂J (x ) » « » «¬ ∂ x 2 »¼

x

∂

f

∂

2

∂ x1

f ∂x

∂

#

f

3

∂ x1 2 2

f ∂x

∂

#

3 2

(2)

º !» ª 1 »« 2 » «σ 1 »« !» « »« »« »« »« »¬ ¼

º »ª »« »« »« »« »« %» « »¬ ¼

[z i − f i (x)] º»

1

σ

» »

[z i − f i (x)] »»

2 2

#

(3)

» ¼

If we put the fi(x) functions in a vector form f(x) and calculate the Jacobian of f(x), we would obtain ª∂ f 1 « « ∂ x1 « ∂f ( x ) « ∂ f 1 =« ∂x « ∂ x1 « « # « ¬«

f x ∂ f ∂x

∂

∂

2

#

f x ∂ f ∂x ∂

∂

2 2 2

3 3 3

3

#

º !» » » » !» » » » » ¼»

( 4)

2

International Conference on Innovations in Power and Advanced Computing Technologies [i-PACT2017] where m is the number of measurements and n is the number of estimates obtained. The threshold value is the ultimate limit for detecting the bad data. The threshold value should be selected with standard methods. Here the threshold value is set using standard chisquare table. Degree of freedom is defined as m-n. There are 42 measurements and 27 estimates in the test case used. Therefor e the degree of freedom is m-n i.e. 42-27=15. Steps of Chi-square test is as follows 1) Compute the objective function

This matrix is expressed as [H]. Then ª∂ f 1 « « ∂ x1 « «∂ f 1 [H ] = « « ∂ x1 « « # « ¬«

f x

∂ ∂

∂ ∂

f x ∂ f ∂ x

∂

2

∂

2

f x

2 2

º ! » » » » !» » » » » ¼»

3

3

#

3 3

#

(5 )

And its transpose is

[H ]

T

To make

ª∂ f 1 « « ∂ x1 « «∂ f 1 =« «∂ x2 « « # « «¬

∂

f x ∂ f ∂ x

∂

f x ∂ f ∂ x

∂

2

∂

1

2 2

3

1

#

3 2

#

º ! » » » » !» » » » » »¼

(6 )

∇ J (x) equal zero, we apply Newton’s method, then x

ª ∂ ∇ x J (x )º [− ∇ « » ∂x ¬ ¼

x

=

The Jacobian constant matrix

Δ

x

=

[[H ] [R] T

∇

x

x

]

J (x )

−1

T

[z i − f i(x)] º»

ª « « −1 « « « « ¬

[z i − f i(x)] #

» » » » » ¼

(8)

• • • • • •

Enter the measurements that is the line data and measurement data Calculate the Jacobian matrix [H] using equations for real and reactive power flows and injections Determine the gain matrix using the Jacobian matrix and covariance matrix as Gm = [H] T[R]-1[H] Determine the ǻx that is the estimates Calculate maximum of ǻx Check convergence that is max of ǻx is less than ‫ ڙ‬if yes then stop otherwise go to step 7 Update the estimates

2

(10 )

i

2) Let the level of significance be 1%. The degree of freedom is 15. A value corresponding to the level of significance and degree of freedom is chosen from the Chi-square table. 3) Test J(x) ≥ χ

. If yes the bad data is detected. Else

the measurements are free of bad data. B. Bad Data Identification After the bad data is successfully detected using Chi square test, bad measurement is identified applying the largest normalized residual (LNR) test [16-17]. The LNR test can be considered as one of the hypothesis testing problem. This procedure is undertaken by following these steps Computation of the normalized residual vector after solving the estimation problem. 2) Whenever the largest normalized residual is found larger than a chosen identification threshold, the corresponding measurement is suspected as bad data and we proceed to step 3. Else, the procedure is concluded. 3) Elimination of the suspected measurement from the measurement set and go to step C. Steps Involved in the Algorithm • • •

IV. BAD DATA DETECTION AND IDENTIFICATION A. Bad data Detection There are various mathematical methods for bad data detection such as Chi-square test, calibration factor method optimization methods. Chi-square test is the most commonly used method. In this paper the bad data is detected using Chisquare test. The error shown by the meter follows the normal distribution [16]. It can be shown that

[zi − f i (x)]

σ

1)

A. Steps involved in the Algorithm •

i =1

m−n

(7)

J (x ) is calculated by treating [H] as a

[H ]] [H ] [R]

−1

Nm

2

−1

Δ

[z i − f i (x )] ¦

2

J (x ) =

• • • • •

Conduct the state estimation and obtain the estimated values Determine the total error by comparing the estimated values with measured values. Check whether the error is greater than the threshold value, If yes go to next step else print no error Determine the error in ndividual meter Determine the area in which error occurs Determine the areas average error Check if single meter contains error. If yes display the meter number else go to step 8 Determine the different combination of meters which contains bad data error and display the meters

2

Nm

J ( x) = ¦ i =1

σ

2

followsa χ

2 m− n

(9)

i

3


V. PROGRAM AND OUTPUT A. Program The proposed method was demonstrated using an IEEE 14 bus system. The input data required to perform the load Àow analysis included the measurement data and line data. The line data included the from and to bus, resistances, reactance and shunt susceptances.The measurement data included voltage magnitudes, voltage angles, real and reactive power flows and injections at each bus of the system. Ybus matrix was formulated using the line data. Newton raphson load Àow analysis was performed on the data. From the results of NR load flow analysis the jacobian matrix H is obtained. The H matrix includes the partial derivatives of voltage magnitude and angles, real power flows and injections, reactive power flow and injections with respect to voltage magnitude and angles. Weighted least square is implemented using 42 measurements. Weighted least square state estimation is performed as per the algorithm as shown above. Jacobian matrix was calculated. The state variables were assumed to have a Àat voltage start. In each iteration the state variables gets modi¿ed and when the objective function satis¿es the convergence criteria the iteration is stopped. The output included the voltage magnitude of all the buses and angle of buses from 2 to 14, bus 1 being considered as the slack bus. The result obtained is as follows After the state estimation, the bad data detection and identification is done in a distributed approach. The system network is divided into different area/zone and the detection is applied in each area separately.

Once the bad data is detected, the system must be divided into different areas to avoid problems such as complexity of program and program delay. Here the entire system is divide into mainly 3 zones. The division of the 14 bus system is shown in Figure 2. The 14 bus system is divided into 3 areas such that area 1 and area 3 is having 5 buses and area 2 is having 4 buses as shown in table II A distributed approach for bad data identification is implemented in [3-4]. In this approach, the system is divided into different areas and detection procedure is applied to each area with Chi square test. The zone/area of error along with the meters in which error occurs can be located. Both the individual and multiple meter errors is identified using this method. The same approach is found to be applicable for bad data identification in Measurement Units. So distributed detection method is adopted in this paper for Bad data identification in PMU. First by calculating the total error occurred in the area the region, the error is identified. If the error exceeds threshold value, it is required to identify the PMU in which errors are present. Hence thorough checking is adopted inside each area which undergoes bad data error. The meter identification involves determining individual PMU errors in each area separately for the purpose identifying the location of error in the whole system. The error value is then compared with the threshold value mentioned as per the chi-square approach. The error may occur in more than one PMU simultaneously in the system. Hence combinational meter identification is required in the case of multiple meter errors. Thus the region or area associated with reasonable meter can be located easily for further correction proceedings. The average area error is determined in order to identify the area which possesses dominant error in the system [1-4].

Fig. 2. Bus system with distributed detection approach

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International Conference on Innovations in Power and Advanced Computing Technologies [i-PACT2017] TABLE IV: ACTUAL VALUES TABLE II: DISTRIBUTION OF BUSES INTO DIFFERENT ZONES AREA 1 Bus 1

AREA 2 Bus 7

AREA 3 Bus 6

Bus 2

Bus 9

Bus 8

Bus 3

Bus 10

Bus 11

Bus 4

Bus 14

Bus 12 Bus 13

Bus 5

BUS NO

At first the error in voltage magnitude is identified and then the error in phase angle is identified. Both the error in voltage magnitude and phase angle is identified with the distributed approach method B. Output The state estimation is done with MATLAB coding on IEEE 14 bus system using weighted least square method and the voltage magnitude and phase angle is obtained as shown in Table III TABLE III: ESTIMATED VALUES

BUS NO 1

VOLTAGE MAGNITUDE 1.0230

PHASE ANGLE 0.0000

2

0.9494

-2.1210

3

1.1693

-3.7056

4

0.9510

-11.8672

5

0.8711

-7.7488

6

0.8148

-21.3445

7

0.9405

-15.1744

8

1.2235

-12.0750

9

0.8373

-12.5583

10

1.0951

-16.6273

11

1.0626

-18.4374

12

1.1737

-18.7287

13

0.8989

-16.3912

14

1.0264

-15.9072

The actual measurements with which the estimated values are compared in order to obtain the error is tabulated in Table IV

1

VOLTAGE MAGNITUDE 1.06

PHASE ANGLE 0

2

1.045

-4.98

3

1.010

-12.72

4

1.0

-10.33

5

1.0

-8.78

6

1.070

-14.22

7

1.0

-13.37

8

1.090

-13.36

9

1.0

-14.94

10

1.0

-15.10

11

1.0

-14.79

12

1.0

-18.07

13

1.0

-15.16

14

1.0

-16.04

Figure 3 shows the difference between actual measurement and estimated measurement of the voltage magnitude that is the error in meters and Figure 4 shows the difference between actual and estimated measurement of phase angle

Fig. 3. Deviation in Voltage magnitude

Fig. 4. Deviation in Phase angle

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International Conference on Innovations in Power and Advanced Computing Technologies [i-PACT2017] Fig. 6 shows the case for “No error” condition in case of phase angle. It means that the measured data that is the phase angle from all meter connected in various buses of the system network gives accurate reading

After the state estimation bad data detection and identification is done using chi square with distributed approach. Fig. 5 shows the case for “No error” condition in case of voltage magnitude. It means that the measured data that is the voltage magnitude from all meter connected in various buses of the system network gives accurate reading.

Fig. 6. Case for No error condition (Phase Angle)

Fig. 7 shows the graph of deviation in measurements of voltage magnitude and phase angle during no error condition. It is clear that all the measured reading overlaps the estimated value which indicates the accurate measurement. Hence it is not required to identify the location.

Fig. 5. Case for No error condition (Voltage Magnitude)

DEVIATION IN MEASUREMENT 1.12 Estimated Measured

VOLTAGE MAGNITUDE

1.1

1.08

1.06

1.04

1.02

1

0

2

4

6

8

10

12

14

METERS

(a) DEVIATION IN MEASUREMENT 0 Estimated Measured

-2 -4

PHASE ANGLE

-6 -8 -10 -12 -14 -16 -18 -20

0

2

4

6

8

10

12

14

METERS

(b) Fig 7: Deviation graph for No error condition (a) Voltage magnitude (b) Phase Angle

6


Consider the case where the meters 1, 6, 9, and 10 meters in area 1, area 3 and area 2 are provided with sufficient deviation in readings and given during the run time as measured data.

TABLE V: CASE FOR ERROR IN METERS 1, 6.9 AND 10

Error Detection Bad data detected

The error is identified in corresponding meters in which error occurs as tabulated in Table 5

No error detected No error detected

TABLE VI: CASE FOR ERROR IN METERS 1, 6.9 AND 10

Meter No 1

Meter Readings(V)

2 3

0.9494

4 5

0.9510

6 7

1.8148

8 9

1.2235

10 11

1.7951

12 13

1.1737 0.8989


14

1.0264

No error detected

1.9230 1.1693

Meter No 1 2 3 4 5 6 7 8 9 10 11 12 13 14


0.8711

Bad data detected No error detected

0.9405

No error detected Bad data detected

1.8373

Bad data detected No error detected

1.0626

Now it is considered that bad data error occurred in case of voltage magnitude in some meters in the system network.

Meter Readings(deg)

Error Detection No error detected Bad data detected No error detected No error detected No error detected No error detected Bad data detected No error detected No error detected No error detected Bad data detected No error detected No error detected No error detected

0.0000 -2.7210 -3.7056 -11.8672 -7.7488 -21.3445 -15.8744 -12.0750 -12.5583 -16.6273 -18.9374 -18.7287 -16.3912 -15.9072

DEVIATION IN MEASUREMENT 2 Estimated Measured

1.9

VOLTAGE MAGNITUDE

1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1

0

2

4

6

8

10

12

14

METERS

(a) DEVIATION IN MEASUREMENT 0 Estimated Measured

-2 -4

PHASE ANGLE

-6 -8 -10 -12 -14 -16 -18 -20

0

2

4

6

8

10

12

14

METERS

(b) Fig. 8. Deviation graph for Error condition (a)Voltage Magnitude (b) Phase Angle

7


Now it is considered that bad data error occurred in case of phase angle in some meters in the system network. Consider the case where the meters 2, 7, and 11 meters in area 1, area 2 and area 3 are provided with sufficient deviation in readings and given during the run time as measured data. The error is identified in corresponding meters in which error occurs as tabulated in Table 6. Fig.8 shows the graph of deviation in measurements of voltage magnitude and phase angle when during error condition. As the error occurs, the measured reading and the estimated reading no longer overlaps. VI. CONCLUSION In this paper a distributed detection approach is proposed to detect the presence of bad data in Phasor measurement units of IEEE 14 bus test system. State estimation was used to find out best estimates among the PMU values. Chi-square method was used for setting the value of threshold. The method identified the areas in which there is presence of bad data. Also it detects the respective PMU which is under the influence of bad data. The graph shows the clear variation of measured phase angle and magnitude value from the actual value under the influence of bad data. The proposed method works efficiently so that precise location of affected PMU is found out.

[10] Seyed Mahdi Mahaei, Mohammad Reza Navayi.” Power System State Estimation with Weighted Linear Least Square”. International Journal of Electrical and Computer Engineering (IJECE) Vol. 4, No. 2, April 2014, pp. 169~178 [11] D Chauhan and D Singh and J P Pandey, “Topology Identification, Bad Data Processing, and State Estimation Using Fuzzy Pattern Matching”, IEEE Transaction Power System, Vol. Pas 20, Aug 2005, pp. 15701579. [12] Khwanram J, Damrongkulkamjorn P. “Multiple Bad Data Identification in Power System State Estimation using Particle Swarm Optimization”. 6th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, Pataya. May 2009. [13] Mr. K. S. Chandragupta Mauryan et al, “Phasor measurement unit in a power system – A review” IJAICT volume-1 Issue 1 may 2014 [14] Wood.A.J, Wollenberg.B.F, and Sheble.G.B. 2013. Power generation, operation, and control. 3rd Ed. John Wiley & Sons.New York, USA.pp.481-498. [15] “Weighted Least Squares Topology Error Detection And Identication” Master Thesis of Jason Glen Lindquist, 2010, University of Minnesota [16] Gu, Yun, Ting Liu, Dai Wang, Xiaohong Guan, and Zhanbo Xu. "Bad data detection method for smart grids based on distributed state estimation." In Communications (ICC), 2013 IEEE International Conference on, pp. 4483-4487. IEEE, 2013. [17] Sahu, Abhijeet. "Bad Data Detection and Identification in Power Systems."

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