MIT International Journal of Electrical and Instrumentation Engineering Vol. 4, No. 2, August 2014, pp. 100-103 100

Effect of Bad measurements on IEEE-14 Bus System in Power System State Estimation

Ankhi GulatiAssistant Professor

Electrical Engg. DepartmentIFTM University, Moradabad

Anil KumarAssistant Professor

Electrical Engg. DepartmentIFTM University, Moradabad

Niyati GulatiAssistant Professor

Electrical Engg. DepartmentMIT, Moradabad

INTRODUCTION

algorithm for converting redundant meter readings and other available information’s into an estimate of the state vector, while measured data are taken to be time invariant and static model of

the objective is to provide a reliable and consistent data base for security monitoring, contingency analysis and system control. To meet the above objectives, SE is required to [1].

and angles.

A major factor in the success of producing a good estimate of the system state is the ability to handle errors that exist in the

BAD DATA PROCESSING CYCLE

The ability of power system state estimator to detect and identify noise in the measurement data enables it to provide a dependable data base for power system operation and control. If one or more of the telemetered measurements are contaminated with gross errors (bad data), the estimated system state and the correspond-ing data base will be biased. Bad data may occur as a single bad measurement or multiple bad measurements; therefore, the main

objective of the power system state estimation is to minimize the bias in the data base [2].

Bad data processing in conventionally performed in three steps:

i. A detection procedure to determine whether bad data present.

-ments in the measurement set and their location in the system.

on the state estimate.

Fig. 1: Conventional bad data processing cycle

ERROR ESTIMATION

answers, but in reality never know the absolutely true state of a physically operating system. Even when great care is taken to ensure accuracy, unavoidable random noise enters into the measurements process to distort more or less the physical results. However, repeated measurements of the same quantity under carefully controlled conditions reveal certain statistical properties from which the true value can be estimated [3].

usually present in the telemetered measurements acquired through the data acquisition system and which determines the system

Key Words:

ABSTRACT

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MIT International Journal of Electrical and Instrumentation Engineering Vol. 4, No. 2, August 2014, pp. 100-103 101

The measured values are plotted as a function of their relative frequency of occurrence, a histogram is obtained to which a

curve most commonly encountered is the bell–shaped function

or normal probability density function, has the formula

p(z) =

21 z

21p(z)

2€

…(1)

And the variable representing the values of the measured quantity along the horizontal axis is known as the Gaussian or normal random variable z. Areas under the curve give the probabilities associated with the corresponding intervals of the horizontal axis. In the probability that z takes on values between the points a and b in the shaded area given by

p(a < z < b) =

Fig. 2: The Gaussian Probability Function

PROBLEM FORMULATION AND SOLUTION

Measurement equations can be written as:

Zmeas = Ztrue + …(3)

where Zmeas = value of a measurement from measurement device

Ztrue

random measurement error

For state estimation the weighted least-squares (WLS) criterion is applied [4], where the objective is to minimize the sum of the squares of the weighted deviations of the estimated measure-

ments, Æ , from the actual measurements, z. So if a single pa-rameter x is estimated, using Nm measurements, the expression as per WLS criterion will be

…(4)

where

ith measurement ,

12 = variance for the ith measurement ,

J(x) = measurement residual (error),

Nm = number of independent measurements,

Zmeas = ith measured quantity

Thus, meters with smaller error variances have narrower curves and provide more accurate measurements. In formulating the objective function f of Eq. (4), preferential weighting is given to the more accurate measurements by choosing the weight wi as the reciprocal of the corresponding variance

12 . Errors of

smaller variance thus have greater weight. Henceforth,

W = R–1 =

21

211

21

21

1. . .

1. . .

W R1

. . .

1. . .

€

€

€

€

…(5)

And the gain matrix G then becomes

G = HT R–1 H …(6)

CIRCUIT MODEL OF THE SYSTEM

System has 5 generation buses and 11 loads. Simulated test data has 41 number of measurements i.e. (Nm), and there are 27 state variables i.e. (Ns = 2N-1), where N is the number of nodes. Redundancy or degree of freedom in the measurement is 14 i.e. (Nm-Ns) There are 13 i.e. (N – 1) angles and14 voltages V to be determined in the test case.

Fig. 3:

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MIT International Journal of Electrical and Instrumentation Engineering Vol. 4, No. 2, August 2014, pp. 100-103 102

Table 1 presents the actual voltages and angles and estimated voltages and angles also their relative % error in voltage is pre-

magnitude (p.u) by without error is shown. [5]

Table 1: Estmated states without noise and their % errors

Fig. 4: Plot Between Buses No. Vs Voltage Magnitude (p.u)

WITHOUT BAD DATA BUT WITH NOISE

In this case 5% noise measurement noise has been added in measurement number 2, 10, 18 and 30. And also 5% noise in each measurement has been added and thereby estimation of the states is carried out. Table 2 presents the actual voltages and angles and estimated voltages and angles also their relative % errors. Figure 5 gives plot between buses no. Vs voltage magnitude (p.u).

Table 2 Estimated states with noise

Fig. 5: Plot Between Buses No. Vs Voltage Magnitude (p.u)

CONCLUSION

Test results of IEEE-14 bus system have been presented. These test systems are categorized in two parts. First part discusses the results of without bad data containing without noise in the measurements. Results of estimated voltages in (p.u) and angles in (degrees) as well as the % error in voltages are given. In part 2 the state estimate without bad data containing but with 5% noise in the measurement vector are presented. After compar-ing between result between without and by adding noise in the measurements we see the whole state of the system will affected.

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MIT International Journal of Electrical and Instrumentation Engineering Vol. 4, No. 2, August 2014, pp. 100-103 103

REFERENCES

1. R.L. Lugtu, D.F. Hackett, K.C. Liu and D.D. Might, “Power System State Estimation: Detection of Topological Errors”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99, No. 6 Nov/Dec 1980.

2. E. Handschin, F.C. Schweppe, J. Kohlas and A. Fiechter, “Bad Data Analysis for Power system State Estimation”, IEEE Trans. On Power Apparatus and Systems, Vol. PAS-94, No.2, pp. 329-337, March/April 1975.

3. John J. Grainger, W.D. Stevenson J.R., Power System Analysis, McGraw Hill International,USA, 1984.

4. A. Monticelli, “Electric Power System State Estimation,” in the Proceeding of the IEEE, vol. 88, no. 2, pp. 262-282, February 2000.

5. M.A. Pai, Computer Technique in Power System Analysis, Second

Edition, Tata McGraw-Hill Edition, 2006.

6. Felix F.Wu, Wen-Hsiung, “Observability Analysis and Bad Data

Processing for State Estimation with Equality Constraints”, IEEE

Trans. on Power System, Vol. 3, No. 5, pp. 541-548, May 1988.

7. Felix F. Wu, Wen-Hsiung, E. Liu and Shau-Ming lun, “Observability

Analysis and Bad Data Processing for State Estimation with

Equality constraints”, IEEE Trans. on Power Systems, Vol. 3, No.2,

pp. 541-548, May 1988.

8. Roberto Mínguez and Antonio J. Conejo, Fellow, IEEE, State

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Systems, Vol. 22, No. 3, August 2007.

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