State Estimation in Power Systems with FACTS Devices and PMU Measurements

Valeriu Iulian PRESADA, Cristian Virgil CRISTEA, Mircea EREMIA, Lucian TOMA Department of Electrical Power Systems

University Politehnica of Bucharest Bucharest, Romania

Email: presadaval@yahoo.com

Abstract This paper presents an algorithm for state estimation in power systems that include FACTS devices and PMUs. The FACTS devices are equipments of special purpose capable of changing the natural behavior of transmission systems. They may be able to influence the voltage, the active power or the reactive power flows based on predefined targets so that the classical power flow and steady state calculations must be adapted. Furthermore, PMU measurements are increasing in number so that the accuracy in steady state calculations can be improved. A state estimation algorithm was developed by considering the behavior of TCSC and SVC devices, while including some improvements due to the integration of synchronized measurements. A Matlab application was developed and simulations were performed on various test networks. In this paper, results obtained on the IEEE 30 bus test system only will be presented.

Index Terms-- Flexible AC Transmission Systems (FACTS), Phasor Measurement Units, State Estimation, Static VAr Compensator (SVC), Thyristor Controlled Series Capacitor (TCSC)

I. INTRODUCTION The electrical power systems are sometimes operating

close to their stability limits due also to the expansion of interconnections between neighbor power systems and implementation of the power market. Although technology is progressing, the power system become more complex. At the same time, powerful tools are implemented, e.g the Energy Management System (EMS) which is of great importance for the system operators because of the increasing need for reliable and consistent data in the operation process [1]. State estimation [2], a key function of EMS, provides the best possible approximation for the state of a power system by processing the available information [3], [4]. The state estimator is the algorithm that, based on available SCADA measurements [5], network model and other data (pseudo-measurements), provides reliable information about the steady state of a power system, i.e. voltage magnitudes, angles, active and reactive power flows, circuit breakers status, etc.

The classical state estimator uses measurements from the already classical SCADA system as follows [6]: active and

reactive power flows through branches; real and reactive powers injections at buses; bus voltage magnitudes; current magnitude flowing through the transmission lines. However, PMU devices provide two types of measurements, namely voltage phasors and current phasors [7].

In the actual context of the power markets and the increased concerns for the power grid safety, the power system state estimation has become a critical tool for the power system operator. Figure 1 indicates the purpose of the state estimation in power system operation.

Figure 1. The purpose of state estimation in power system operation.

Various state estimation methods proposed in literature are based on synchronized measurements from PMUs. However, even if PMU devices have been widely implemented, SCADA measurements are the only data used in many power systems. Examples can be found in [6], [8] or [14].

The FACTS devices are increasingly employed in many power systems due to their major benefits that they provide in improving the reliability and stability of the power systems. This paper proposes an improved algorithm for state estimation by considering the characteristics and behavior of FACTS devices and measurements from PMUs.

The classical two step state estimator algorithm implemented in MATLAB as presented in [8], was upgraded to incorporate additional SVC and TCSC devices state

variables. The algorithm was improved also by integrating PMU measurements. In order to test the application, simulations were performed on the IEEE 30 bus system and the results were compared with valid power flow results.

II. INTEGRATING SVC AND TCSC INTO TWO STEP STATE ESTIMATION ALGORITHM

The two step state estimation algorithm uses conventional SCADA measurements in the first step. PMU measurements are added in the second step.

Operational equations of the FACTS devices are included in the first step of the state estimation algorithm. This leads to an increased size of the Jacobian matrix, and its structure can be outlined as follows [9],[10]:

Conventional

FACTS devices

x x r r1 1 ... ... nC nF f1

fnCg1

gnF

Figure 2. Integrating FACTS devices equations into the Jacobian matrix.

The algorithm is improved by integrating synchronized PMU measurements as input data in the second step.

In Figure 2, xnC stands for the classical state variables, namely, nodal voltage magnitudes and phase angles, and rnF stands for the additional FACTS devices state variables. Measurements of classical quantities and FACTS devices quantities are denoted by fnC and gnF, respectively.

The model of the TCSC device (Fig. 3) is based on the simple concept of a variable series reactance, the value of which is adjusted automatically in order to keep the power flowing through the branch i-j to a specified value.

Vi VjIi Ij

XL

XC

XTCSC

Figure 3. Thyristor-controlled series capacitor (TCSC) equivalent circuit.

The fundamental frequency equivalent reactance XTCSC of the TCSC is calculated with expression [11]:

1

22

( )1 2 sin 2

( )

cos tan tan

TCSC

CTCSC

X

X CB

C

where

2

1 24 ( )

( )( ) ( )

; ; C LC LC C LLCL C L

X X X X XC C XX X X

In order to consider the TCSC in the state estimator, additional measurements should be included to the set of equations, namely the active and reactive power flows through the TCSC branch, given by the susceptance BTCSC, i.e.

( ) sinij i j TCSC i jP V V B

2 ( )ij i TCSC i j TCSC i jQ V B V V B cos These new elements helps determining the susceptance

BTCSC in the iterative calculation process.

The Jacobian matrix is therefore expanded by addition of new elements attached to the TCSC branch, representing power flow measurements. Thus, the new terms to be added in the Jacobian matrix associated with the known and unknown variables, attached to the TCSC device, are as follows:

i j i i j j TCSC

ij ij ij ij iji ji

i j j j TCSC

ji ji ji ji jii jj

i j i j TCSC

ij ij ij ij iji ji

i j i j TCSC

ji jij

i

ij

ji

ij

ji

V V V V B

P P P P PV VP V V B

P P P P PV VP V V B

Q Q Q Q QV VQ

V V BQ Q

Q

P

P

Q

Q

ji ji jii j

j i j TCSC

ij ij ij ij iji j

i j i j TCSC

ji ji ji ji jii j

i j i j TCSC

ij ij ij ij iji j

i j i j TCSC

ji ji ji ji jii j

i j i j TCSC

Q Q QV V

V V BP P P P P

V VV V B

P P P P PV V

V V BQ Q Q Q Q

V VV V B

Q Q Q Q QV V

V V B

i j i i j j TCSC

ij ij ij ij iji ji

i j j j TCSC

ji ji ji ji jii jj

i j i j TCSC

ij ij ij ij iji ji

i j i j TCSC

ji jij

i

ij

ji

ij

ji

V V V V B

P P P P PV VP V V B

P P P P PV VP V V B

Q Q Q Q QV VQ

V V BQ Q

Q

P

P

Q

Q

ji ji jii j

j i j TCSC

ij ij ij ij iji j

i j i j TCSC

ji ji ji ji jii j

i j i j TCSC

ij ij ij ij iji j

i j i j TCSC

ji ji ji ji jii j

i j i j TCSC

Q Q QV V

V V BP P P P P

V VV V B

P P P P PV V

V V BQ Q Q Q Q

V VV V B

Q Q Q Q QV V

V V B

Although the TCSC controls the active power flow ( ijP ) from bus i to bus j only, the power flow equations ijQ , jiP and

jiQ can be also used to increase the estimation redundancy, as shown in equation (4).

The elements in (4) represent the sensitivities of the power flows through the transmission branch in both directions. The highlighted elements which have to their left side the + sign are not total values. As the sign indicates, these quantities are the TCSC contributions by power injections to the terminal buses. In the Jacobian matrix these elements correspond to the measurements of the bus injections of the active and reactive powers. They represent the sum of the power flow contribution of each electrical component connected to these buses.

In the case of SVC we assume that the slope of the device is zero; this assumption may be acceptable as long as the SVC operates within its design limits [9]. This assumption may lead to gross errors if the SVC is operating close to its limits. In practice, the SVC device can be represented as an adjustable reactance with either firing-angle limits or reactance limits [12].

In order to determine the appropriate value of the SVC susceptance, BSVC, introduced as an additional variable, measurement of the reactive power injection by the SVC should be included in the Jacobian.

BSVC

Vi

ISVC

Figure 4. SVC variable shunt susceptance model.

The SVC current is

SVC SVC iI jB V The equation of the reactive power measurement

introduced in the Jacobian matrix is:

2SVC i SVCQ V B

The elements of the new Jacobian matrix that are adjusted or added accordingly to SVC reactive power injection measurement are shown in the following equation:

0

SVC SVC ii SVC

i SVC i

i SVCi

i SVC

Q Q VV B

V B VV BVV B

where 2i

SVC SVC i SVCSVC

QB B V QB

The first step of the state estimation algorithm (Fig. 5), where classical notations are used [13], is modified to incorporate SVC and TCSC by changing the Jacobian matrix accordingly. The output of this step comprises the classical state vector (bus voltages and angles) with additional state variables of the FACTS devices.

Set initial conditionsx = x0 Compute

(z-h(x))Create modified Jacobian matrix

Calculate the gain matrix G(x)

G=JTR-1J

Calculate state mismatch vector X=G-1JTR-1(z-h(x))Convergence

test max(X)<

Update Xk+1=Xk+x

FIRST STEPClassical State Estimation

OUTPUT:X vector + FACTS variables

Set initial conditionsx = x0 Compute

(z-h(x))Create modified Jacobian matrix

Calculate the gain matrix G(x)

G=JTR-1J

Calculate state mismatch vector X=G-1JTR-1(z-h(x))Convergence

test max(X)<

Update Xk+1=Xk+x

FIRST STEPClassical State Estimation

OUTPUT:X vector + FACTS variables

Figure 5. First step of state estimation algorithm.

The state vector obtained in the first step of the algorithm is used in the second step where the solution is improved by integrating phasor measurements. The state estimation second step algorithm is based on a linear measurement model of the following form:

Z J V e where J is the measurement Jacobian coefficient matrix;

; TV V V Re Im is the state vector expressed in rectangular form;

e - the vector of measurement errors.

The measurement vector Z is composed of:

- the output of the classical state estimator, calculated in the first step, 1; TRe Im StepV V ;

- PMU synchronized voltage measurements ; TRe Im PMUV V ; - PMU synchronized current measurements ; TRe Im PMUI I . The expanded measurement model is shown below with

all voltages expressed in rectangular coordinates [14]:

11 12

1 21 22

31 32

41 42

51 52

61 62

Re

Im

Re

Im

Re

Im

SEVReSE

Im VStepPMUVRe Re

aug PMUIm Im VPMU

PMURe I

PMUIm PMU I

eV J JV eJ J

eV J J VZ

V J J V eJ JI eJ JI e

where J11 and J22 are unit matrices; J12 , J21 , J32 and J41 are zero matrices; J31 and J42 have only one nonzero element that is 1 in

every row, depending on the PMU placement;

The elements of J51 and J62 are made up of real parts of the branch admittance, and the elements of J52 and J61 are made up of imaginary parts of the branch admittance.

, ,51

, ,

, ,52

, ,

,61

,

;

;

;

PMU PMUPMUik Re ik ReRe

ioRe i Re k Re

PMU PMUPMUik Re ik ReRe

ioIm i Im k Im

PMUPMUik Im iIm

ioRe i Re

I IIJ G G GV V V

I IIJ B B B

V V V

I IIJ B B

V V

,

,

, ,62

, ,

;

PMUk Im

k Re

PMU PMUPMUik Im ik ImIm

ioIm i Im k Im

BV

I IIJ G G G

V V V

The linear state estimation is solved using the following equation [14]:

11 1 T TV J R J J R Z The measurements of the additional state variables

introduced by the FACTS devices obtained in the first step of the algorithm presents less accuracy than those provided from synchronized measurements with PMUs. Thereby, the above algorithm was modified accordingly to integrate those measurements before running the first step of the algorithm.

This additional step can also help improving the observability analysis of the system. Thus, the improved algorithm follows the flow chart presented in Figure 6.

SECOND STEPEnhance State Estimation with PMU Measurements

FIRST STEPClassical State Estimation

STARTSTART

Read entry data

Read weighting data ( R )

IntegrateSynchrophasor Measurements

Figure 6. Improved two-step state estimator algorithm flow chart.

III. STUDY CASE The classical two-step state estimator algorithm modified

to incorporate SVC and TCSC devices and improved by inserting an additional step to integrate PMU measurements from the beginning of the algorithm was implemented under Matlab environment.

Simulations were performed on the IEEE 30 bus system [15], with some changes. The starting point is the load flow base case. The measurement set of data was chosen from the load flow solution using minimum spanning tree logic. The

measurement set of data presented to the classical state estimator is shown in Table 1.

TABLE I. MEASUREMENT SET OF DATA

Nr. Type Value From To Nr. Type Value From To 1 Vi 1.06 1 0 44 Pij 0 12 13 2 Vi 1.0426 15 0 45 Pij 0.18101 12 15 3 Pi 2.5906 1 0 46 Pij 0.07528 12 16 4 Pi 0.183 2 0 47 Pij 0.01627 14 15 5 Pi 0 6 0 48 Pij 0.06176 15 18 6 Pi 0 9 0 49 Pij 0.05127 15 23 7 Pi -0.058 10 0 50 Pij 0.02936 18 19 8 Pi -0.112 12 0 51 Pij 0.05477 22 24 9 Pi -0.062 14 0 52 Pij 0.01897 23 24 10 Pi -0.082 15 0 53 Pij 0.03544 25 26 11 Pi -0.032 18 0 54 Pij -0.04921 25 27 12 Pi 0 22 0 55 Pij -0.1821 27 28 13 Pi -0.032 23 0 56 Pij 0.0618 27 29 14 Pi 0 25 0 57 Pij 0.07083 27 30 15 Pi 0 27 0 58 Qij -0.26083 1 2 16 Qi -0.2641 1 0 59 Qij -0.00326 1 3 17 Qi 0.68477 2 0 60 Qij 0.27614 2 4 18 Qi 0 6 0 61 Qij 0.03134 2 5 19 Qi 0 9 0 62 Qij 0.00772 2 6 20 Qi 0.18928 10 0 63 Qij -0.01679 6 7 21 Qi -0.075 12 0 64 Qij 0.03767 6 8 22 Qi -0.016 14 0 65 Qij -0.07451 6 9 23 Qi -0.025 15 0 66 Qij 0.00266 6 10 24 Qi -0.009 18 0 67 Qij 0.00718 6 28 25 Qi 0 22 0 68 Qij -0.14013 9 11 26 Qi -0.016 23 0 69 Qij 0.04447 10 17 27 Qi 0 25 0 70 Qij 0.03692 10 20 28 Qi 0 27 0 71 Qij 0.09691 10 21 29 Pij 1.7929 1 2 72 Qij 0.04393 10 22 30 Pij 0.79766 1 3 73 Qij -0.06962 12 13 31 Pij 0.62207 2 4 74 Qij 0.06595 12 15 32 Pij 0.78204 2 5 75 Qij 0.03339 12 16 33 Pij 0.51593 2 6 76 Qij 0.00587 14 15 34 Pij 0.42132 6 7 77 Qij 0.01608 15 18 35 Pij 0.2953 6 8 78 Qij 0.0264 15 23 36 Pij 0.27257 6 9 79 Qij 0.00626 18 19 37 Pij 0.15592 6 10 80 Qij 0.02549 22 24 38 Pij 0.18842 6 28 81 Qij 0.00978 23 24 39 Pij 0 9 11 82 Qij 0.02366 25 26 40 Pij 0.05051 10 17 83 Qij -0.01081 25 27 41 Pij 0.08864 10 20 84 Qij -0.02322 27 28 42 Pij 0.15624 10 21 85 Qij 0.00791 27 29 43 Pij 0.07511 10 22 86 Qij 0.00399 27 30

Measurement noise (Gaussian random variable, zero mean

unit variance) has been added to the perfect measurement to produce more realistic noisy measurements.

In the starting point, the SVC device was assumed to operate at bus 30 with a reference voltage of 1.01 p.u., for which a reactive power injection QSVC=0,02105 p.u and susceptance BSVC=-0,02064 p.u. are required. The TCSC device was set to compensate 50% of the line 4-2 reactance (Xl=0.17370p.u.) with XTCSC=0,08685 p.u.

The one-line diagram of the IEEE 30 test system, with PMUs placement according to an integer programming algorithm for minimum cost [16], implemented also in Matlab, is illustrated in Figure 7. The IEEE 30 bus test system can be summarized as follows:

- number of buses: N = 30 - number of state variables: n = 2N 1 = 59 - number of measurements: m = 86 - redundancy ratio = m/n = 1.46

Figure 7. IEEE 30 bus system with PMU placement.

When performing the first step of the two step algorithm, one assumes that the state estimator is applied on a set of measurement data that was accordingly selected to assure full observability of the system. After the first step, the state estimator solution contains a power system state vector formed by voltage magnitudes at all buses and voltage phase angles at n-1 buses as well as the additional state variables introduced by FACTS devices.

For the SVC device, the estimated state variable was BSVC = -0.02187 p.u., whereas for TCSC the estimated reactance was XTCSC = 0.08094 p.u. After modifying the algorithm to take into account PMU measurements before running the first step, the estimated variable for SVC was improved to BSVC = -0.02109 p.u., whereas for TCSC the reactance was XTCSC = 0.08454 p.u. As shown in Table 2 both estimated FACTS variables were more accurate.

TABLE II. SET OF MEASUREMENT DATA

FACTS state

variables

Power Flow solution

SE solution without PMU measurements

SE solution with PMU

measurements

Improved SE solution

with PMU XTCSC 0.08685 u.r. 0.09501 u.r. 0.08094 u.r. 0.08454 u.r. BSVC -0.02064 u.r. -0.02196 u.r. -0.02187 u.r. -0.02109 u.r.

IV. CONCLUSIONS

Comparing the state estimation results we can draw up some conclusions. Integrating PMU measurements in state estimation using two step method does not have a major impact on additional state estimation variables introduced by FACTS devices. Some improvements are obtained when PMU measurements are considered before running the first step of the algorithm.

It has been shown that when synchronized phasor measurements are added to the other SCADA measurements in sufficient numbers, the efficiency/precision of the state estimate is improved.

The improved algorithm with additional step that includes PMU measurements, have significant contributions to increase

the accuracy of the additional FACTS variables. The additional step does not require major changes in traditional way of providing the measurements set to the state estimator algorithm.

This additional step can be used to handle some deficiencies in the traditional measurement set, for example to improve network observability, to aid in bad data processing and in determining network topology, etc.

REFERENCES [1] M.T. Hagh, M. A. Jirdehi, A Robust Method for State Estimation of

Power System with UPFC, Turk J Elec Eng & Comp Sci, Vol.18, No.4, 2010.

[2] A. Monticelli, State Estimation In Electric Power System , Kluwer Academic Publishers, Boston, 1999, p. 7-33.

[3] A. Mutahen, Distribution Network State Estimation, Tampere University of Technology, Lecture Notes, 2012.

[4] O. Ivanov, M. Gavrila, B. Vicol, New models for power systems state estimation U.P.B. Sci. Bull., series C, vol. 74, no. 1, 2012.

[5] N. Arghira, D. Hossu, I. Fgran, S.S. Iliescu, D.R. Costianu, Modern SCADA philosophy in power system operation a survey, U.P.B. Sci. Bull., series C, vol. 73, iss. 2, 2011.

[6] F. Chen, X. Han, Z. Pan, L. Han, State Estimation Model and Algorithm Including PMU, 3rd Int. Conf. on Electric Utility Deregulation and Restructuring and Power Technology, China, Nanjing, 6-9 April 2008.

[7] A. Abur, A. Gomez Exposito, Power System State Estimation: Theory and Implementation, New York, Marcel Dekker, 2004.

[8] V.I. Presada, L. Toma, M. Eremia, An Algorithm for Improving the Power System State Estimation Using PMU Measurements, Proceedings of 2013 IEEE Grenoble PowerTech, Grenoble, France, 16-20 June 2013.

[9] E. Acha, C.R. Fuerte-Esquivel, H. Ambriz-Perez, C. Angeles-Camacho, FACTS Modeling and simulation in power networks, John Wiley & Sons , England 2004.

[10] X.P. Zhang, C. Rehtanz, B. Pal, Flexible AC Transmission System: Modelling and Control, Springer-Verlag Berlin Heidelberg, 2006.

[11] C.R. Fuerte-Esquivel, E. Acha, H. Ambriz-Perez, A Thyristor Controlled Series Compensator Model for the Power Flow Solution of Practical Power Networks, IEEE Trans. Power Systems, vol. 15, no. 1, pp. 58-64, Febr. 2000.

[12] H. Ambriz-Perez, E. Acha, C.R. Fuerte-Esquivel, Advanced SVC Models for NewtonRaphson Load Flow and Newton Optimal Power Flow Studies, IEEE Trans. Power Systems, vol. 15, no. 1, pp. 129-136, Feb. 2000.

[13] M. Asprou, E. Kyriakides, M. Albu, The effect of parameter and measurement uncertainties on hybrid state estimation, Proceedings of 2012 IEEE Power and Energy Society General Meeting, Vancouver, Canada, 22-26 July 2012.

[14] R. F. Nuqui, A. G. Phadke, Hybrid Linear State Estimation Utilizing Synchronized Phasor Measurements, Proceedings of IEEE 2007 Lausanne PowerTech, Lausanne, Switzerland, pp. 16651669, July 2007.

[15] Power Systems Test Case Archive, Available: http://www.ee.washington.edu /research/

[16] B. Xu, Y. J. Yoon, A. Abur, Optimal placement and utilization of phasor measurements for state estimation PSERC Pub. 05-20, October, 2005.

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