+ All Categories
Home > Documents > Effect of UPFC on Voltage Stability Margin

Effect of UPFC on Voltage Stability Margin

Date post: 30-Mar-2015
Category:
Upload: sithansakthi
View: 113 times
Download: 0 times
Share this document with a friend
4
Effect of UPFC on Voltage Stability Margin J. Raju, and P.S. Venkataramu Abstract: This paper investigates the effect of Unified Power Flow controller (UPFC) on Voltage stability Margin in a real power system. The original load flow Jacobian is modified incorporating the static model of an UPFC and the minimum singular values (MSV) of this Jacobian matrix are computed and compared with that of MSVs of a non-UPFC system. The results of the case study carried out on a 22 bus, 400kV South Indian real system is presented. Index Terms -- MSV, Voltage Collapse, UPFC. I. INTRODUCTION R ECENT power systems are being operated very close to their stability limits due to the ever-increasing demand for electrical power and reduced investments by the utilities in transmission line expansion. These stressed power systems are experiencing a new threat of voltage instability in addition to conventional angle instability. Several incidents of system collapse for the past one decade are mainly caused by the voltage instability leading to voltage collapse. Many researchers all over the world have studied this phenomenon and have come out with very useful conclusions on the causes, effects and possible control actions etc. Basically voltage instability is described as the monotonic decrease in bus voltages due to insufficient and fast reactive power support. This decrease in bus voltages results in an insufficient synchronsing power causing the synchronous machines to pull out of synchronism (traditional angle instability problem) [1]. Though voltage instability is a dynamic phenomenon, it is being studied from static methods also mainly due to the fact that the static methods can provide very vital information regarding the loadability margin of a bus. Apart from this, static methods are very fast in computation and hence suitable for on-line applications in evaluating the static security of the system. Many static indicators are reported in literature and few of them are very effective [2-5]. Minimum singular value (MSV) of a load flow Jacobian is one of the accurate static indicator, which provides voltage stability margin (VSM) of the system for a selected operating condition with less computational effort [6-8]. With the advent of high power electronics devices, it is possible to design power electronics equipments of high rating for high voltage system. This has enabled the power system engineers to realize the concept of flexible A.C transmission systems (FACTS). Unified power flow controller (UPFC) is one such FACTS device which can be used to control the active power and reactive power flow through a transmission J. Raju is with VIT University, Vellore, Tamilnadu, India (e-mail: jraju(!avit.ac.in) P.S. Venkataramu is with VIT University, Vellore, Tamilnadu, India 978-1-4244-1762-9/08/$25.00 C2008 IEEE line. Presence of UPFC in the system also contributes in altering the VSM of the system. Hence, it is very important to study and quantify the effect of UPFC on VSM of the system. Few researchers have worked in the area of development of UPFC model, control aspects of UPFC etc. Noroozian et.al [9] proposed optimal power flow control in electric power system by the use of UPFC, where it has been shown that UPFC has the capability of regulating power flow and minimizing power losses. Fuerte Esquivel and E.Acha [10] presented a load flow model of UPFC, which can be incorporated into an existing FACTS Newton Raphson load flow algorithm. Padiyar.K.R and Kulkarni.A.M [11] proposed a control strategy for UPFC in which real power flow through the line is controlled while regulating magnitudes of the voltages at its two ports. O.Z.Fang et.al [12] proposed an improved injection modeling approach for power flow analysis of UPFC embedded power system. Padiyar.K.R et.al [13] presented the development of a control scheme for series injected voltage of the UPFC to damp the power oscillations and improve transient stability in a power system. Fang.W.L et.al [14] have developed an effective and reliable method to perform load flow control and calculation for multiple UPFC-embedded systems. Chen.H et.al [15] discussed co-ordinated excitation and UPFC control to improve power system transient stability and voltage stability where a robust approach is used to deal with the uncertainties caused by parameter variations and the inclusion of UPFC controller. Huayuan Chen et.al [16] discussed coordinated excitation and UPFC control to improve power system transient stability where the power system is linearised through direct feedback linearisation technique. Cazzol.M.V et.al [17] introduced a model of UPFC in the framework of an interior point based OPF procedure and the good performance of the solver is demonstrated. However there is no much work reported in quantifying the effect of UPFC on VSM of a bus in a system. Essentially this has to be investigated through various case studies on real systems which provides better insight in to the effect of UPFC. In this paper the static model proposed at [9] is used and the case study is carried out on a real 22-bus, 400kV system for three different UPFC locations. II. COMPUTATION OF VSM USING MSV Minimum singular value (MSV) of the load flow Jacobian is one of the effective Static Voltage Collapse Proximity Indicator (VCPI), which accurately indicates the nearness of the system to voltage instability. The MSV is computed through Singular Value Decomposition (SVD) of load flow Jacobian matrix. The application of the SVD method to power system voltage stability analysis has been reported widely in the past. The use of MSV of the load flow Jacobian was first proposed as a measure of static voltage stability by Thomas et.al [6-8]. The SVD is an important and practically useful
Transcript
Page 1: Effect of UPFC on Voltage Stability Margin

Effect ofUPFC on Voltage Stability MarginJ. Raju, and P.S. Venkataramu

Abstract: This paper investigates the effect of Unified PowerFlow controller (UPFC) on Voltage stability Margin in a realpower system. The original load flow Jacobian is modifiedincorporating the static model of an UPFC and the minimumsingular values (MSV) of this Jacobian matrix are computed andcompared with that of MSVs of a non-UPFC system. The resultsof the case study carried out on a 22 bus, 400kV South Indianreal system is presented.

Index Terms -- MSV, Voltage Collapse, UPFC.

I. INTRODUCTION

R ECENT power systems are being operated very close totheir stability limits due to the ever-increasing demand forelectrical power and reduced investments by the utilities

in transmission line expansion. These stressed power systemsare experiencing a new threat of voltage instability in additionto conventional angle instability. Several incidents of systemcollapse for the past one decade are mainly caused by thevoltage instability leading to voltage collapse. Manyresearchers all over the world have studied this phenomenonand have come out with very useful conclusions on the causes,effects and possible control actions etc. Basically voltageinstability is described as the monotonic decrease in busvoltages due to insufficient and fast reactive power support.This decrease in bus voltages results in an insufficientsynchronsing power causing the synchronous machines to pullout of synchronism (traditional angle instability problem) [1].

Though voltage instability is a dynamic phenomenon, it isbeing studied from static methods also mainly due to the factthat the static methods can provide very vital informationregarding the loadability margin of a bus. Apart from this,static methods are very fast in computation and hence suitablefor on-line applications in evaluating the static security of thesystem. Many static indicators are reported in literature andfew of them are very effective [2-5]. Minimum singular value(MSV) of a load flow Jacobian is one of the accurate staticindicator, which provides voltage stability margin (VSM) ofthe system for a selected operating condition with lesscomputational effort [6-8].

With the advent of high power electronics devices, it ispossible to design power electronics equipments of high ratingfor high voltage system. This has enabled the power systemengineers to realize the concept of flexible A.C transmissionsystems (FACTS). Unified power flow controller (UPFC) isone such FACTS device which can be used to control theactive power and reactive power flow through a transmission

J. Raju is with VIT University, Vellore, Tamilnadu, India(e-mail: jraju(!avit.ac.in)P.S. Venkataramu is with VIT University, Vellore, Tamilnadu, India

978-1-4244-1762-9/08/$25.00 C2008 IEEE

line. Presence of UPFC in the system also contributes inaltering the VSM of the system. Hence, it is very important tostudy and quantify the effect ofUPFC on VSM of the system.Few researchers have worked in the area of development ofUPFC model, control aspects ofUPFC etc. Noroozian et.al [9]proposed optimal power flow control in electric power systemby the use of UPFC, where it has been shown that UPFC hasthe capability of regulating power flow and minimizing powerlosses. Fuerte Esquivel and E.Acha [10] presented a load flowmodel of UPFC, which can be incorporated into an existingFACTS Newton Raphson load flow algorithm. Padiyar.K.Rand Kulkarni.A.M [11] proposed a control strategy for UPFCin which real power flow through the line is controlled whileregulating magnitudes of the voltages at its two ports.O.Z.Fang et.al [12] proposed an improved injection modelingapproach for power flow analysis of UPFC embedded powersystem. Padiyar.K.R et.al [13] presented the development of acontrol scheme for series injected voltage of the UPFC todamp the power oscillations and improve transient stability ina power system. Fang.W.L et.al [14] have developed aneffective and reliable method to perform load flow control andcalculation for multiple UPFC-embedded systems. Chen.Het.al [15] discussed co-ordinated excitation and UPFC controlto improve power system transient stability and voltagestability where a robust approach is used to deal with theuncertainties caused by parameter variations and the inclusionof UPFC controller. Huayuan Chen et.al [16] discussedcoordinated excitation and UPFC control to improve powersystem transient stability where the power system is linearisedthrough direct feedback linearisation technique. Cazzol.M.Vet.al [17] introduced a model ofUPFC in the framework of aninterior point based OPF procedure and the good performanceof the solver is demonstrated. However there is no much workreported in quantifying the effect ofUPFC on VSM of a bus ina system. Essentially this has to be investigated throughvarious case studies on real systems which provides betterinsight in to the effect ofUPFC.

In this paper the static model proposed at [9] is used andthe case study is carried out on a real 22-bus, 400kV systemfor three different UPFC locations.

II. COMPUTATION OF VSM USING MSV

Minimum singular value (MSV) of the load flow Jacobianis one of the effective Static Voltage Collapse ProximityIndicator (VCPI), which accurately indicates the nearness ofthe system to voltage instability. The MSV is computedthrough Singular Value Decomposition (SVD) of load flowJacobian matrix. The application of the SVD method to powersystem voltage stability analysis has been reported widely inthe past. The use of MSV of the load flow Jacobian was firstproposed as a measure of static voltage stability by Thomaset.al [6-8]. The SVD is an important and practically useful

Page 2: Effect of UPFC on Voltage Stability Margin

orthogonal decomposition method used for matrixcomputation. If the matrix A (nxn) is a real quadratic then theSVD is given by

A =U VT ---- (3.1)Where U and V are the orthonormal matrices whose

columns contains the singular vectors. L is the diagonalmatrix with singular values.

To use the theory of SVD on power systems, a linearisedrelation between the active and reactive powers at nodesversus voltage magnitudes and node angles has to be foundwhich is established by the power flow Jacobian matrix. If theSVD is applied to the power flow Jacobian matrix then, such a

matrix decomposition is written as

J = U E V ----- (3.2)E is the diagonal matrix of real singular values where the

minimum singular value is given by 62(n-1)If J is non-singular, the effect on [AOAV]T for a small changein active and reactive power injection is given by

LAO] FAP1

-AVj LAQj =ZSiAViUiT (3.3)

Close to voltage collapse point, where the singular value is

almost zero, system response is entirely determined byminimum singular value 62(n-1), its singular vector V2(n-1) andU2(n-1),

Hence

0Z52(n-I)V2(n-I)U2(n-1) /Q

Assuming

LQ =U2(n-1)

ThenAO]

AV] -:::: V2(nl1) 1'52(n-1).......(3.4)

Hence the following observations are madei.) The smallest singular value of a Load flow Jacobianis an indicator of proximity to static stability limit.

ii.The right singular vector indicates the sensitivevoltages and angles.

iii.) The left singular vector indicates the most sensitivedirection for change of the active and reactive powerinjections.

III. STATIC MODEL OF UPFC

The static UPFC model proposed in [9] is incorporated in

this paper. This UPFC injection method can easily beincorporated in to the steady state power flow model.

The UPFC injection model is shown in Fig. 1.

Psi, Ps,Qsi Qsj

Fig. 1. UPFC model.

The active and reactive powers at the ends are as givenbelow

Psi= r bs Vi Vj sin (Oij + y)Psj =-rbs Vi Vj sin(Oij+y)Qsi = r bs Vi2 cos YQsj =- r bs Vi Vj cos (Oij + y)

---(4.1)---(4.2)---(4.3)---(4.4)

The UPFC is located between node i and node j in a power

system. The admittance matrix is modified by adding a

reactance equivalent to Xs between node i and node j. TheJacobian matrix is modified by addition of appropriateinjection powers. If the linearized load flow model isconsidered as below:

0AP -H N-j AO...(4.5)

The Jacobian matrix is modified as given below (where thesuperscript 'o' denotes the Jacobian elements without UPFC).

This modified Jacobian matrix is incorporated in to the loadflow algorithm and the MSVs are computed. In this study theparameters of UPFC (r, y) are arbitrarily chosen, as this workis mainly to investigate the effect of UPFC connected indifferent lines on VSM.

IV. CASE STUDY AND RESULTS

To investigate the effect of UPFC on VSM a real 22-bus,400kV, 27 lines south Indian system is selected. The peak loadon the system is 3715.61 MW and 1042.66 MVAR.VSMs indicated by MSVs are computed for base load

condition (without UPFC) for the following cases of change inbusloads:

i. Increase of only active power load keeping reactivepower load constant.

o oH(i,j) H (i,j) - Qsj N(i,j) = N (i,j) - Psj

o oH(i,j) H (i,j) ± Qsj N(i,j) = N (i,j) - Psj

o oH(j,i) H (j,i) ± Qsj N(,i) = (j,i) + Psj

o oH(j,j) H (,j) - Qsj N(,j) = (N,j) ± Psj

o oJ(i,i) J (,i) L(,i) = L (,i) + 2Qsi

o oJ(i,j J (i,j) L(i,j) = L (i,j)

o oJjo,i) J (j,i) - Psj L(j,i) = L (j,i) ± Qsj

o oJ(j,j J(j,) ± sj L(jj) = L(j,j) ± Qsj

Page 3: Effect of UPFC on Voltage Stability Margin

ii. Increase of only reactive power load keeping activepower load constant.

One UPFC with r=0.03 and y=60' is connected in thefollowing three locations individually:

i. Line connecting a load bus and generator bus (bust 1-busl 7)

ii. Heavily loaded line connecting two load buses(busl3-busl4)

iii. Relatively lightly loaded line connecting two loadbuses (bus2-bus8)

VSMs indicated by MSVs of the modified Jocabian matrixare computed for all the locations of UPFC and for twodifferent cases of busload increase.

The results are tabulated in Table I and Table II. Followingobservations are made based on the results:

i. In general VSMs of all the buses varies considerablywith incorporation ofUPFC in the system.

ii. VSMs of most of the buses (9 out of 13) increasesubstantially with UPFC connected between agenerator bus and load bus for real power increasecase. But in case of reactive increase it is noticed thatVSMs increases in four buses out of which increaseis very marginal in two buses.

iii. VSMs of the neighboring two buses (bus 10 & bus19) increases very sharply both in active powerincrease and reactive power increase case.

iv. VSMs of most of the buses (including the bus towhich UPFC is connected) are found to be decreasedwith the incorporation of UPFC between two loadbuses (13 & 14, heavily loaded line) for both thecases of load increase

v. Increase VSM is very marginal whereas decrease inVSM is very sharp with the UPFC connected in aheavily loaded line for both cases of load increases.

vi. Similar observations (no. 4 & no.5) are found withthe UPFC located in a relatively lightly loaded line (2& 8).

Based on the system selected and for the selected UPFCparameters it may be concluded that if UPFC is locatedbetween the generator bus and load bus considerableenhancement in VSM could be achieved for both the cases ofload increase.

TABLE IVSMs LOAD BUSES WITHOUT AND WITH UPFC

(LOAD INCREASE BY VARYING ACTIVE POWER ONLY)

MSV MSVMSV with UPFC with UPFC

with UPFC between between

Bus MSV between two load two loadwithout Generator bus bus

no UPFC and load (3-14) (2-8)

bus (Heavily (Lightly(11-17) loaded loaded

line) line)2 0.0559 0.1963 0.0559 0.07635 0.0524 0.2252 0.0423 0.00057 0.0297 0.1805 0.0418 0.00368 0.0713 0.1143 0.1067 0.261510 0.0236 0.2056 0.0627 0.0657

1 1 0.0345 0.2081 0.0199 0.0285 l12 0.1948 0.0888 0.1887 0.147013 0.1495 0.0493 0.1333 0.129714 0.2461 0.1201 0.3494 0.165819 0.0519 0.2102 0.0451 0.053220 0.0456 0.4404 0.0349 0.044321 0.0377 0.1967 0.0208 0.0359

TABLE IIVSMs LOAD BUSES WITHOUT AND WITH UPFC

(LOAD INCREASE BY VARYING REACTIVE POWER ONLY)

MSV MSVMSV with UPFC with UPFC

with UPFC between between

Bus MSV between two load two loadwithout Generator bus busno UPFC and load (13-14) (2-8)

bus (Heavily (Lightly(11-17) loaded loaded

line) line)2 0.1276 0.1846 0.0277 0.07625 0.3408 0.1801 0.1974 0.12637 0.2671 0.2614 0.2673 0.26778 0.3886 0.0846 0.0571 0.067010 0.0872 0.1826 0.0376 0.092811 0.0406 0.2406 0.0072 0.047912 0.3065 0.0059 0.2241 0.205113 0.3475 0.1553 0.2399 0.222214 0.5186 0.0203 0.2914 0.476819 0.1033 0.1403 0.0881 0.108520 0.6033 0.2596 0.6083 0.572121 0.3934 0.2358 894.53 0.1618

To draw further inferences on the effect of UPFC, theanalysis is carried out based on the changes in the overallsystem active power losses. System losses are initiallycomputed with the load of a bus maintaining at its voltagecollapse point without UPFC. Losses are computedincorporating the UPFC in above mentioned three location andresults are tabulated in Table III and I Table V. Followingobservations are made based on the results:

i. Losses are reduced in most of the cases when theUPFC is located between generator bus and a loadbus (11 & 17). Losses are increased marginally whenthe loads of the following buses are kept at theircollapse point: bus 2, 5,7,12 & 20.

ii. When bus 11 is at its collapse point losses arereduced considerably with the UPFC located betweena generator bus and load bus.

iii. System looses are reduced marginally for most of thecases with the UPFC located in a heavily loaded linefor varying real power case whereas it increases forvarying reactive power case.

iv. Losses are increased and decreased in equal numberof cases with the UPFC connected in a lightly loadedline.

It may be concluded from the above observations that theconnection ofUPFC in the system has a considerable effect onaltering the system losses when the system load is at collapsepoint.

Page 4: Effect of UPFC on Voltage Stability Margin

TABLE IIISYSTEM LOSSES WHEN EACH BUS LOAD IS AT THE COLLAPSE

POINT WITHOUT AND WITH UPFC(LOAD INCREASE BY VARYING ACTIVE POWER ONLY)

ActiveActive Power Active Power Active PowerActive loss in MW loss in MW loss in MWPower with UPFC with UPFC

Bus loss in between two between twono MW between load bus load bus

without Generator and (13-14) (2-8)UPFC load bus (Heavily (Lightly

loaded line) loaded line)2 621.204 640.360 619.531 622.8025 498.565 544.103 499.780 383.0377 597.747 631.156 593.131 624.8448 354.670 348.102 351.630 347.69010 364.250 296.000 353.950 354.62411 375.159 301.255 377.410 376.39912 285.230 285.393 284.803 287.60213 263.863 263.709 263.682 265.30914 187.166 185.600 184.630 187.82719 367.289 297.309 367.283 366.77820 395.843 443.020 392.309 395.43521 391.340 307.065 386.815 390.869

TABLE IVSYSTEM LOSSES WHEN EACH BUS LOAD IS AT THE COLLAPSE

POINT WITHOUT AND WITH UPFC(LOAD INCREASE BY VARYING REACTIVE POWER ONLY)

eActive Power Active Power Active PowerActver loss in MW loss in MW loss in MWPower wtUPC with UPFC with UPFC

Bus loss in between two between twono MW

between load bus load buswithout

Generator and (13-14) (2-8)withou load bus (Heavily (Lightlyloaded line) loaded line)

2 419.492 440.036 433.020 425.2075 359.928 359.239 364.881 368.0597 244.431 241.262 242.890 243.6638 242.416 246.823 250.544 247.18410 275.384 247.942 279.650 273.87511 429.823 457.711 421.640 428.36812 217.052 196.389 218.063 218.47413 201.959 201.861 202.440 202.42814 170.403 171.482 170.899 169.64919 582.898 549.515 584.243 581.17620 450.536 474.377 448.344 453.93221 384.280 385.625 396.070 390.641

V. CONCLUSION

A case study carried out on real power system to

demonstrate the effect of UPFC on VSM of the system. Theresults reveal that it is possible to quantify the effect of UPFCon VSM and the system losses, which may intern help indeciding the location of the UPFC. Though the case studylimited only for an arbitrarily selected UPFC parameters, theconcept and model presented in this paper can be used forvarious studies involving different locations and parameters ofUPFC.

VI. ACKNOWLEDGEMENT

The authors are grateful to the managements of VelloreInstitute of Technology, Vellore, National Institute ofEngineering, Mysore and Govt. of Bhutan for theencouragement and support.

VII. REFERENCES

[1] Khoi T Vu and Chen-ching Liu, "Shrinking stability regions and voltagecollapse in power systems", IEEE transactions on circuit and systems-Ifundamental theory and applications.Vol.39, No.4, April, 1992, pp.271-289

[2] Lof, P.A., Smed, T., Anderson G.and Hill, D.J, "Fast calculation of avoltage stability index", IEEE Transactions on power systems, vol.7,No. 1. Feb. 1992, pp. 54-63.

[3] Lof, P.A., Anderson, G. and Hill D.J., "Voltage stability indices forstressed power systems", IEE Transactions on power systems. Vol.8,No.1, Feb.1992, pp 326-335.

[4] Gao, B., G.K and Kundor, P., "Voltage stability evaluation usint modelanalysis", IEEE Transactions on power systems, vol.7, No.4, Nov. 1992,pp 1529-1542.

[5] Kessel P. and Galvitisch, H. "Estimating the voltage stability of powersystems", IEEE Transactions on power delivery, vol. PWRD-1, No.3,July-1996, pp. 346-352.

[6] R.J.Thomas, A.Tiranuchit, 'Voltage instabilities in Electric PowerNetworks", proceedings of the 18th southeastern symposium on systemtheory, Knoxville, Tennessee, April 1996.

[7] A.Tiranuchit, R.J.Thomas, "A posturing strategy against voltageinstability in Electric Power Systems", IEEE transactions on powersystems, vol.PWRS-3, No.1, Feb. 1998

[8] A.Tiranuchit, L.M.Ewarbring, R.A.Durgea, R.J.Thomas, F.K.Luk,"Toward the computationally feasible on-line voltage stability index",IEE transactions on power system, vol. PWRS-3, No.2, May 1998.

[9] Noroozian. M, Angquist. L,Ghandhari. M,Andersson.G, "Use of UPFCfor optimal power flow control", IEEE Trans on Power Delivery,Vol.12, Oct. 1997, pp 1629-1633.

[10] Fuerte-Esquivel.C.R, Acha.E, "Unified power flow controller: a criticalcomparison of Newton-Raphson UPFC algorithms in power flowstudies", IEE Proc. On Generation, Transmission, Distribution, Vol.144,No.5, Sept. 1997, 437-444.

[11] Padiyar.K.R, Kulkarni.A.M, "Control Design and Simulation of UnifiedPower Flow Controller", IEEE Trans. On Power Delivery, Dec. 1997, pp1-7.

[12] Fang.D.Z, Fang.Z, Wang.H.F, "Application of the injection modelingapproach to power flow analysis for systems with unified power flowcontroller" International Journal On Electric Power and Energy Systems,Vol. 23, 2001, pp 421-425.

[13] Padiyar.K.R, Uma Rao.K, "Modeling and control of unified power flowcontroller for transient stability", International Journal On ElectricPower and Energy Systems, Vol.21, 1999, pp 1-1 1

[14] Fang.W.L Ngan.H.W "Control setting of unified power flowcontrollers through a robust load flow calculation" ,IEE Proc. OnGeneration, Transmission, Distribution, Vol. 146, No.4, July l999,pp365-369.

[15] Chen.H, Wang.Y, Zhou.R "Transient and voltage stability enhancementvia co-ordinated excitation and UPFC control", IEE Proc. OnGeneration, Transmission, Distribution, Vol.148, No.3, May 2001, pp20 1-208.

[16] Huayuan Chen, Youyi Wang, Rujing Zhou "Transient stabilityenhancement via coordinated excitation and UPFC control",International Journal On Electric Power and Energy Systems, Vol.24,2002, pp 19-29.

[17] M.V.Cazzol, Garzillo.A, Innorta.M, Libardi.M.G, Ricci.M, "Unifiedpower flow controller model in the framework of interior point basedactive and reactive OPF procedure", International Journal On ElectricPower and Energy Systems, Vol.24, 2002, pp 431-437


Recommended