Effect of Phasor Measurement Unit (PMU) on the Network Estimated Variables
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Effect of Phasor Measurement Unit (PMU) on the Network Estimated Variables

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The classical method of power measurement of a ...

The classical method of power measurement of a
system are iterative and bulky in nature. The new technique
of measurement for bus voltage, bus current and power flow is
a Phasor Measurement Unit. The classical technique and PMUs
are combined with full weighted least square state estimator
method of measurement will improves the accuracy of the
measurement. In this paper, the method of combining Full
weighted least square state estimation method and classical
method incorporation with PMU for measurement of power
will be investigated. Some cases are tested in view of accuracy
and reliability by introducing of PMUs and their effect on
variables like power flows are illustrated. The comparison of
power obtained on each bus of IEEE 9 and IEEE 14 bus system
will be discussed.

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    Effect of Phasor Measurement Unit (PMU) on the Network Estimated Variables Effect of Phasor Measurement Unit (PMU) on the Network Estimated Variables Document Transcript

    • Full Paper ACEEE Int. J. on Electrical and Power Engineering, Vol. 4, No. 1, Feb 2013 Effect of Phasor Measurement Unit (PMU) on the Network Estimated Variables Jitender Kumar*1, J.N.Rai2, Vipin3 and Ramveer S. Sengar4 1 Electrical Engineering Deptt, G L Bajaj Instt of Tech & Management, Gr. Noida, India *corresponding author: jitender3k@gmail.com 2 Electrical Engineering Department, Delhi Technological University, Delhi, India 3 Mechanical Engineering Department, Delhi Technological University, Delhi, India 4 Electrical Engineering Deptt, Accurate Instt of Management & Tech., Gr. Noida, India Email: jnrai.phd@gmail.com, vipin2867@yahoo.co.in, ramveerchiro@gmail.comAbstract - The classical method of power measurement of a and classical technique. The natural approaches of parametersystem are iterative and bulky in nature. The new technique measurement will extravagance the PMU as computationalof measurement for bus voltage, bus current and power flow is burden on measurement. The optimal placement of PMUa Phasor Measurement Unit. The classical technique and PMUs devices is a difficult task for power system state estimation isare combined with full weighted least square state estimator investigated, in the literature. This paper will reflect the effectmethod of measurement will improves the accuracy of themeasurement. In this paper, the method of combining Full of PMU on the accuracy of measurement on state estimationweighted least square state estimation method and classical parameters. In case 1, the classical state estimation methodmethod incorporation with PMU for measurement of power without using any PMU. But in case P, the measurement ofwill be investigated. Some cases are tested in view of accuracy state estimation with PMU only is discussed.and reliability by introducing of PMUs and their effect onvariables like power flows are illustrated. The comparison of II. WLS STATE ESTIMATION METHODpower obtained on each bus of IEEE 9 and IEEE 14 bus systemwill be discussed. Consider the set of measurements given by the vector z:- z  h( x)  e (1)Keywords – classical method; phasor measurement units(PMUs); state estimation; full weighted least square (WLS) Where:state. h T  [ h 1 ( x ), h 2 ( x ), h 3 ( x ),..... h m ( x )] (2) I. INTRODUCTION hi (x) is the non-linear function relating measurement i to the state vector x The nature of electrical waves on grid will reflect the xT = [ x1, x2, x3............ xn] is the state vector of systemhealth of the system. The electrical wave is consisting of a eT = [e1 e2 e3……..em ] is the error measurement in state vector.complex number that represents both the magnitude and The full weighted least square estimator [1] [3] [6] willphase angle of the sine waves. The “Synchrophasor” is a minimize the following objective function:device which measure nature of waves with respect to time[5] [10]. The PMU is a device that allows the measurement of m (zi  hi (x))2 J (x)    [z  h(x)]T R 1[z  h( x)] (3)voltage with multiple current options at each bus. The recently i 1 Riideveloped PMU [7] [8] [9] will help in deciding to stall powerimprovement devices at proper location for:- At minimum value of objective function, the first-order  Comprehensive planning optimum condition to be satisfied. It can be expressed as  More accurate follows:  Congestion tracking, J ( x )  Advanced warning systems, g ( x)    H T ( x ) R 1 [ z  h ( x )]  0 (4) x  Information sharing, The Taylor series of non-linear function g(x) can be  Enhancement of System Integrity Protection expanded for the state vector xk by neglecting the higher Schemes (SIPS), order terms [2] will be as  Quick restoration of Grids,  Effective grid operation, g ( x)  g ( x k )  G ( x k )( x  x k )  .......  0 (5)  Dynamically manage the grid. The Gauss-Newton method is used to solve the above The classical method of measurement of power flow and equation:voltage on a bus of power system are iterative and bulky in x k+1= xk – [G(xk)] -1 . g(xk) (6)nature. The full weighted least square state technique is a where, k is the iteration index, xk is the state vector at iterationnonlinear in nature, but with first order Taylor series it become k and G(x) is called the gain matrix and expressed as:a linear. Formerly conducted research will help in formulationof a relation between full weighted least square state technique© 2013 ACEEE 46DOI: 01.IJEPE.4.1. 2
    • Full Paper ACEEE Int. J. on Electrical and Power Engineering, Vol. 4, No. 1, Feb 2013 g ( x k ) IV. CLASSICAL METHOD WITH WLSG ( x)   H T ( x k ) R 1 H ( x k ) (7) x A PMU device will measure one voltage with multiple k T k 1 k (8) current phasors on a bus. Figure 1 shows a 4-bus systemg (x )  H (x ) R [ z  h ( x )] example which has single PMU at bus 1. It consist of one Normally, the gain matrix is sparse matrix and decomposed voltage with three current phasor measurements, namely asinto triangular factors. At each iteration k, the gain matrix are V1  θ1, I1  δ1, I2  δ2 and I3  δ3solved by using forward / backward substitutions, wherex k 1  x k 1  x k and[G( xk )] xk 1  H T ( xk )R1 [ z  h( xk )]  H T ( xk ). R1 zk (9)These iterations are going on till the maximum variable kdifference satisfies the condition, ‘ Max x   ‘. III. CLASSICAL METHOD The traditional/classical method of measurement is Figure 1. Single PMU Measurement Modelconsider current as a relation of power flow with respect to The transmission line normally defined as pie networkbus voltages as due to their advantages on system constraints. If y is defined 2 2 2 2 as the series admittance and yshunt as shunt admittance thenI ij  ( g ij  bij ) (V i  V j  2Vi V j Cos  ij ) the current measurements can be in rectangular coordinates 2 2 as in Fig 2. Pij  Qij (10)  ViThe power injection at bus i can be expressed as, S i  Pi  jQi (11) NPi  Vi  j 1 V j (Gij cos  ij  Bij sin ij ) (12) NQi  Vi j 1 V j (Gij sin ij  Bij cos ij ) (13) Figure 2. Transmission Line in ‘π’ Model The expressions for current in real and imaginaryThe power flow from bus i to bus j are, component are as:- S ij  Pij  jQij (14) Cij  Vi Ysi cos(i si )  Vj Yij cos( j ij )  Vi Yij cos(i ij ) (18) 2P  Vi (gsi  gij )  Vi Vj (gij cosij  bij sinij ) ij (15) Dij  Vi Ysi sin( i si )  Vj Yij sin( j ij )  Vi Yij sin( i ij ) (19)    2 where, state vector is specified as:Qij   Vi (bsi  bij )  Vi Vj (gij sinij  bij cosij ) (16) x  [ V1 0 0 , V2  2 , V3  3 ..........VN  N ] T (20)So the Jacobian H matrix will be as The Jacobian H matrix corresponding to their real and reactive parts is:   P inj  P inj     Cij  P V   Ysi cos( i   si )  Yij cos( i  ij ) (21)  flow  P flow  Vi   V    Q inj  Q inj  C ij    Yij cos(  j   ij ) (22)H    V  V j   Q flow  Q flow    V  (17) Cij   I mag  I mag    Vi Ysi sin(i  si )  Vi Yij sin(i  ij ) (23)   i   V    V mag   C ij 0   V j Yij sin(  j   ij )   V   (24) 47  j© 2013 ACEEEDOI: 01.IJEPE.4.1.2
    • Full Paper ACEEE Int. J. on Electrical and Power Engineering, Vol. 4, No. 1, Feb 2013Dij ˆ E T T  A  Ysi sin( i   si )  Yij sin( i   ij ) (25) x     ( H new R 1 H new ) 1 H new R 1   ˆ (36) Vi ˆ B F  Dij ˆ So that equation for x can be written in rectangular forms  Yij sin(  j   ij ) (26) of z vector and H matrix. They are all in real numbers. In V j respect of the system, the PMU can deliver more preciseDij information about system parameters. Some cases to be  Vi Ysi cos(i  si )  Vi Yij cos(i  ij ) (27) performed on classical measurement set with and without i PMUs. The different cases simulations and analysis are as shown in Table I with some IEEE bus systems in the next D ij section.  V j Yij cos(  j   ij ) (28)  j TABLE I. D IFFERENT CASES IN IEEE SYSTEMThe measurement vector z will be T T T T T T Tz  [ Pinj , Qinj , Pflow , Q flow , V ,  T , Cij , Dij ]T (29) Generally, measurements attain by PMUs are moreaccurate as compared to the traditional measurements. Sothat measurements performed with PMUs are projected to be VI. SIMULATION RESULTSmore precise and accurate as estimated by classical methods. Some cases are tested for analyzing the system variables V. STATE ESTIMATION WITH PMUS accuracy with or without PMU, with the help of MATLAB simulink software. The PMU locations in IEEE 9 Bus System The state vector can be expressed as in rectangular and IEEE 14 Bus System at specific Bus Number are as showncoordinates. The voltage measurement ( V  V  ) can be in Table II.state as (V = E + jF), and the current measurement can be TABLE II. PMU LOCATIONS FOR EACH IEEE SYSTEMstate as (I = C + jD). Where series admittance of the line as( gij + jbij ) and shunt admittance of the transmission line as(gsi ??+ jbsi ). The flow of line current Iij can be expressed as:-Iij  [(Vi  V j )  ( gij  jbij )]  [Vi  (gsi  jbsi )] The circuit diagram will be shown as in Figure 3 for IEEE (30) 9 bus system and Figure 4 for IEEE 14 bus system. Vi  [(gij  jbij )  ( gsi  jbsi )]  V j  ( gij  jbij )The vector z is state as z = h(x) + e, (where x is a system statevector, h(x) is a linear equations, and e is an error vector). Inrectangular coordinates:z = ( Hr + jHm )( E + jF ) + e (31)where, H = Hr + jHm , x = E + jF and z = A + jB.A and B are expressed by:A = Hr  E – Hm  F (32)B = Hm  E + Hr  F (33)In matrix form, A  H r  H m  E  B    H H r  F  e (34)   m   ˆ ˆ ˆThen, the estimated value x  E  jF can be solved as:-x  ( H T R 1H ) 1 H T R 1z  G 1H T R 1z ˆ (35)If we define the linear matrix Hnew as  H  Hm  Figure 3. IEEE 9 Bus SystemH new   r  H m H r  , then the eq. (35) can be written  In this segment, IEEE bus systems as IEEE 9 bus system [4] and IEEE 14 bus system [11] are tested with their respectiveas: cases to find out the consequences of the PMUs to the precision of the estimated variables.© 2013 ACEEE 48DOI: 01.IJEPE.4.1. 2
    • Full Paper ACEEE Int. J. on Electrical and Power Engineering, Vol. 4, No. 1, Feb 2013 The graph to be designed on the basis of Standard Deviation (S D) variation in each parameter’s on each Bus which is planned for 20 cycle of operation of each IEEE system, it has standard deviation categorized in two categories i.e. Minimum & Maximum variation on actual parameters received at each Bus. The figure 5 & figure 7 will illustrate the variation in Standard Deviation at Minimum & Maximum of Real Power (P) with respect to Each Bus on Figure 6. Graph P (SD) vs Bus Number Figure 4. IEEE 14 Bus System Assume n as the number of variables, m as the number ofmeasurements and ε as the ratio of the number ofmeasurements per the number of variables. During the tests,maintained ε as 1.6. Table III has more detailed informationabout the measurement numbers for the tests [12]. TABLE III. VARIABLE T YPE AND MEASUREMENTS Figure 7. Graph P (SD) vs Bus Number A PMU has much smaller error deviations than classicalmeasurements as 0.0000001.The parameters measured are realpower (flow & injected) and reactive power (flow & injected)measurements. The variation of parameters with or withoutPMU easily reflected in the Figure 5 – 12 as given below: Figure 8. Graph P (SD) vs Bus Number Figure 5. Graph P (SD) vs Bus Number Figure 9. Graph Q (SD) vs Bus Number© 2013 ACEEE 49DOI: 01.IJEPE.4.1.2
    • Full Paper ACEEE Int. J. on Electrical and Power Engineering, Vol. 4, No. 1, Feb 2013 The table IV illustrates that how the Standard Deviation (S D) enhanced at each stage as PMU increase from No PMU to Only PMUs. In IEEE 14 bus system, the S.D. of the estimated Power is approximately 1.88E-05 when there is no PMUs, but at Only PMUs it become 1.16E-01. It means that the S.D. of ‘No PMUs’ is increased by adding PMUs in system. The interesting thing is that the standard deviation increasing as increasing PMU. Therefore, this result demonstrates that the effectively installing of PMUs will reduce the chances of error in measurement of estimated variables. Figure 10. Graph Q (SD) vs Bus Number CONCLUSION Now, the classical measurement method with the PMU is able to measure the voltage and current with their magnitude and phasors. The current measurement is implemented but the measurement set as in the rectangular form. The Jacobian matrixes are illustrated in detail for the measurements which include the elements of Equations. The state estimation in the linear formulation is investigated with PMU. All the variables and their respective measurements are improved as all in rectangular form, and then treated separately during the Figure 11. Graph Q (SD) vs Bus Number estimation process. Such linear formulation of the PMU data can produce the estimation result by a single calculation without performing the any bulky iteration as in classical methods. If only PMU data measurement set is exist in the real measurement world, and then there will be improvement in the computation time and accuracy estimation as compare to the linear formulation of the state estimation. The advantages of using PMU will advances the accuracy of the estimated variables. Some cases are tested while gradually increasing the number of PMUs which are added to the measurement set. With the help of advanced accuracy of PMU, it was seen that the estimated accuracy is also Figure 12. Graph Q (SD) vs Bus Number increases. One of the motivating thing is that the accuracyvarying the number of PMU accretion from ‘No PMU (Case improves most effectively when the number of implemented1)’ to ‘Only PMU (Case P)’ for IEEE 9 bus system. Similarly PMUs are around ‘14 %’ of the system buses. It is provedFigure 6 & Figure 8 will illustrate the variation in Standard that the quality of the estimation is enhanced by adoptingDeviation at Minimum & Maximum of Real Power (P) with PMU data to the set of measurement. The PMUrespect to Each Bus on varying the number of PMU accretion measurements will provide us improved accuracy andfrom ‘No PMU (Case 1)’ to ‘Only PMU (Case P)’ for IEEE 14 redundancy for the system.bus system. The Standard Deviation in Reactive Power (Q) The study is carried out to establish a relationship amongwill be illustrated in Figure 9 – 12 from ‘No PMU (Case 1)’ to classical method, full weighted least square state estimation‘Only PMU (Case P)’ for IEEE 9 bus system and IEEE 14 bus method and Phasor Measurement Units. Further it is visualizedsystem. that the information of power variation on each bus of system TABLE IV. AVERAGE S.D. IN ESTIMATED VARIABLES are more precise and accurate as compared to the classical method. The linear formulation will suggest us a more specific and accurate information of power variation without doing any bulky iteration as performed in the classical methods. The use of PMUs will lead us to enhanced accuracy in results. REFERENCES [1] Abur and Exposito A. G., Power System State Estimation, Theory and Implementation, MAECEL DEKKER, 2005, pp. 9-27. [2] Chakrabarti S. and Kyriakides E., “Optimal Placement of Phasor Measurement Units for Power System© 2013 ACEEE 50DOI: 01.IJEPE.4.1.2
    • Full Paper ACEEE Int. J. on Electrical and Power Engineering, Vol. 4, No. 1, Feb 2013 Observability”, IEEE TRANSACTIONS ON POWER [7] Phadke A. G., “SYNCHRONIZED PHASOR SYSTEMS, VOL. 23, NO. 3, AUGUST 2008, 0885-8950 © MEASUREMENTS – A HISTORICAL OVERVIEW”, 0- 2008 IEEE, pp.1433–1440 7803-7525-4/02 © 2002 IEEE, pp.476–479[3] Cheng Y., Hu X., and Gou B., “A New State Estimation using [8] Phadke A.G, Thorp J.S., Nuqui R.F. and Zhou M., “Recent Synchronized Phasor Measurements”, 978-1-4244-1684-4/08 Developments in State Estimation with Phasor ©2008 IEEE, pp.2817–2820 Measurements”, 978-1-4244-3811-2/09 ©2009 IEEE, pp.1-7[4] Ebrahimpour R., Abharian E. K., Moussavi S. Z. and Birjandi [9] Rahman K. A., Mili L., Phadke A., Ree J. D. L. & Liu Y., A. A. M., “Transient Stability Assessment of a Power System “Internet Based Wide Area Information Sharing and Its Roles by Mixture of Experts”, INTERNATIONAL JOURNAL OF in Power System State Estimation”, 0-7803-6672-7/01 © 2001 ENGINEERING, (IJE) Vol. 4, March 2011 pp.93–104. IEEE, pp.470–475[5] Klump R., Wilson R.E. and Martin K.E., “Visualizing Real- [10] Real time dynamics monitoring system [Online]. Available: Time Security Threats Using Hybrid SCADA / PMU http://www.phasor rtdms.com Measurement Displays”, Proceedings of the 38th Hawaii [11] Tanti D.K., Singh B., Verma M.K., Mehrotra O. N., “An International Conference on System Sciences – 2005, 0-7695- ANN based approach for optimal placement of DSTATCOM 2268-8/05 ©2005 IEEE, pp.1–9 for voltage sag mitigation”, INTERNATIONAL JOURNAL[6] Madtharad C., Premrudeepreechacham S., Watson N. R. and OF ENGINEERING SCIENCE AND TECHNOLOGY Saenrak D., “Measurement Placement Method for Power (IJEST), ISSN : 0975-5462 Vol. 3 No. 2 Feb 2011 pp.827– System State Estimation: Part I”, 0-7803-7989-6/03 ©2003 835 IEEE, pp.1629–1632 [12] Xu B. and Abur A., “Observability Analysis and Measurement Placement for Systems with PMUs”, 0-7803-8718-X/04 © 2004 IEEE, pp.1–4© 2013 ACEEE 51DOI: 01.IJEPE.4.1.2