YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014 A Novel Approach of Unified Power flow Controller in a distributed Power Systems YASWANTH KUMA , V.SINGARAIA and Dr.I.PRABHAKAR REDD PG Student [EPS], Dept. of EEE, NEC, Nellore (D), Andhra Pradesh, India1 Assistant Professor, Dept. of EEE,NEC, Nellore (D), Andhra Pradesh, India2 Professor & Head of Dept. of EEE, NEC, Nellore (D), Andhra Pradesh, India3 Abstract— Flexible Alternating Current Transmission Systems (FACTS) devices have been proposed to be effective for controlling power flow and regulating bus voltage in electrical power systems, resulting in an increased transfer capability, low system losses and improved stability. This paper deals with an alternative proposition for the steady state modeling of unified power flow controller (UPFC). Since current limitations are determinant to FACTS apparatus de-sign, the proposed current based model (CBM) assumes the cur-rent as variable, allowing easy manipulation of current restric- tions in optimal power flow evaluations. The performance of the proposed model, optimal location and size of the UPFC’s and of the power injection model (PIM) is com- pared through a Quasi-Newton optimization approach. Two operating situations of a medium size network with 39 bus bars were studied from the point of view of optimization and current limits, observing the performance of the UPFC modeling. Index Terms—FACTS, optimal power flow, Quasi- Newton method, cost, size, UPFC. I. INTRODUCTION POWER flow studies and optimization techniques are essential tools for the safe and economic operation of large electrical systems. The FACTS equipment appeared in the 1980s and, in the early 1990s, voltage source inverters (VSI) were developed. The UPFC is one of the most complete equipment of this new technological family, allowing the regulation of active and reactive powers, substantially enlarging the operative flexibility of the system [1]–[7]. Steady state models of UPFC described in the literature em-ploy the power balance equation, resulting in the equality of the series and shunt active power of converters assuring no internal active power consumption or generation. One of the first proposed models [8] uses this condition, but only in particular cases, when power and voltage are admittedly known, is the implementation of the model in traditional power flow program viable. The employed models in [9] and [10] represent the active elements through equivalent passive circuits, including the power balance equation. In [11], the passive model consists of a sus-ceptance and an ideal voltage transformer and the fundamental power balance equation is intrinsically included. Voltage source models employed in [12]–[15] consist of series and shunt volt-ages presented in the equations as control variables. The model described in [16], known as power injection model (PIM), is quite spread in the literature, representing the effect of active elements by equivalent injected powers. II. CURRENT BASED MODEL The developed model represents the UPFC in steady state, introducing the current in the series converter as variable (see Fig. 1). Series voltage: Series transformer impedance: Transmission line impedance: Let us consider bus bar and existent in the transmission line where the UPFC will be located, with impedance . Fictitious bus bars and are created in order to include the UPFC in the system. The series impedance of UPFC coupling transformer and the transmission line are added, resulting in the equivalent impedance connected to the internal node and node is eliminated. This association is quite simple, even in case of two port lines represented by circuits. The equivalent network is presented in Fig. 2, with the series voltage inserted between bus bars and . The invented model represents the UPFC in steady state, introducing the current in the series converter as variable (seeFig12).
Transcript
YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY
International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014
A Novel Approach of Unified Power flowController in a distributed Power Systems
YASWANTH KUMA , V.SINGARAIA and Dr.I.PRABHAKAR REDDPG Student [EPS], Dept. of EEE, NEC, Nellore (D), Andhra Pradesh, India1Assistant Professor, Dept. of EEE,NEC, Nellore (D), Andhra Pradesh, India2
Professor & Head of Dept. of EEE, NEC, Nellore (D), Andhra Pradesh, India3
Abstract— Flexible Alternating Current TransmissionSystems (FACTS) devices have been proposed to beeffective for controlling power flow and regulating busvoltage in electrical power systems, resulting in anincreased transfer capability, low system losses andimproved stability. This paper deals with an alternativeproposition for the steady state modeling of unified powerflow controller (UPFC). Since current limitations aredeterminant to FACTS apparatus de-sign, the proposedcurrent based model (CBM) assumes the cur-rent asvariable, allowing easy manipulation of current restric-tions in optimal power flow evaluations. The performanceof the proposed model, optimal location and size of theUPFC’s and of the power injection model (PIM) is com-pared through a Quasi-Newton optimization approach.Two operating situations of a medium size network with39 bus bars were studied from the point of view ofoptimization and current limits, observing theperformance of the UPFC modeling.
Index Terms—FACTS, optimal power flow, Quasi-Newton method, cost, size, UPFC.
I. INTRODUCTION
POWER flow studies and optimizationtechniques are essential tools for the safe andeconomic operation of large electrical systems. TheFACTS equipment appeared in the 1980s and, in theearly 1990s, voltage source inverters (VSI) weredeveloped. The UPFC is one of the most completeequipment of this new technological family, allowingthe regulation of active and reactive powers,substantially enlarging the operative flexibility of thesystem [1]–[7].
Steady state models of UPFC described in theliterature em-ploy the power balance equation,resulting in the equality of the series and shunt activepower of converters assuring no internalactive power consumption or generation. One of thefirst proposed models [8] uses this condition, but onlyin particular cases, when power and voltage areadmittedly known, is the implementation of themodel in traditional power flow program viable.
The employed models in [9] and [10] represent theactive elements through equivalent passive circuits,including the power balance equation. In [11], thepassive model consists of a sus-ceptance and an idealvoltage transformer and the fundamental powerbalance equation is intrinsically included. Voltagesource models employed in [12]–[15] consist ofseries and shunt volt-ages presented in the equationsas control variables.
The model described in [16], known as powerinjection model (PIM), is quite spread in theliterature, representing the effect of active elementsby equivalent injected powers.
II. CURRENT BASED MODEL
The developed model represents the UPFC insteady state, introducing the current in the seriesconverter as variable (see Fig. 1).
Series voltage:Series transformer impedance: Transmission line
impedance:
Let us consider bus bar and existent in thetransmission line where the UPFC will be located,with impedance . Fictitious bus bars and arecreated in order to include the UPFC in the system.The series impedance of UPFC coupling transformer
and the transmission line are added, resulting inthe equivalent impedance connected tothe internal node and node is eliminated. Thisassociation is quite simple, even in case of two portlines represented by circuits.
The equivalent network is presented in Fig. 2, withthe series voltage inserted between bus bars and .The invented model represents the UPFC in steadystate, introducing the current in the series converteras variable (seeFig12).
YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY
International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014
Fig: 1 UPFC and network
Series voltage: VsSeries transformer impedance: ZsTransmission line impedance: Z/
eLet us consider bus bar i and k existent in thetransmission line where the UPFC will be located,with impedance Z/
e. fictitious bus bars j and j/arecreated in order to include the UPFC in the system.The series impedance of UPFC coupling transformerZs and the transmission line are added, resulting inthe equivalent impedance = / + connected tothe internal node j and j/node is eliminated. Thisassociation is quite simple, even in case of two portlines represented by circuits. The equivalentnetwork is presented in Fig. 13, with the seriesvoltage inserted between bus bars i and j.
Fig: 2 Equivalent model of UPFC in the electricnetworkA. Injected Power Due to Current:
The power consumption of the system load at bus bari is called
Fig: 3 Injected power due to current in bus bars I andj
Additional powers and , due to current ,̅ areeasily calculated according to fig14 .current ̅introduces two variables I, , related to module andphase of the current.We can write the new power terms due to current:= ∗̅
= − ∗̅= ( − )= ( − )= − −= − −And we have = +== +=Putting the new variable and I at n and 2n positionrespectively the new vector of variable can bewritten:[ ] = [ , , … … , , , , … . . ] …. (1)
B. Series Voltage Equations:
The following treatment of the seriesvoltages for the UPFC is general for FACTS devicesthat can employ this feature. The main example is theSSSC and, as a consequence, other equipment suchas IPFC and GIPFC that use series voltage can bemodeled as well.
Writing the voltage equation between nodes i andj, we obtain− = …….. (2)The series voltage will be treated similarly to the PIMmodel of steady state performance comparison ofmulticonverter VSC-based FACTS controllers= ……….(3)
Where r is the factor for series voltage and is theseries voltage angle. That equation substituted in(2) results − 1 + = 0……….(4)
If r and are constants, in a regular power flowcase, calling the complex variable∠ ∝= −(1 + ∠ ) ……. (5)
We can write + ∠ = 0 …… (6)
We obtain the equation, relative to the real andimaginary parts, = 0 = 0 respectively:= ( + ) + ……. (7)
YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY
International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014
= ( + ) + …….. (8)
These equations will be put at the end of the equationsystem. If r and are variables in an optimizationcase, we have [ ] =[ , , … … , , , , , … . . , , ](9)= − [ ( ) + ( + )](10)= − [ ( ) + ( + )](11)
C. Power Balance
In order to complete the UPFC model, it is necessaryto introduce the power balance equation betweenseries and shunt converters. The series power will beadded to the shunt power of bus bar, similarly toVSC-based FACTS controllers.
Fig: 4UPFC series voltage power
Fig: 5Injected powers in the bus bars with theinclusion of UPFC
Let us calculate the power in the series converter:= ( + − )(12)= ( + − )(13)
Active power is included in node i. show in fig(5)
III. FORMATION OF JACOBIANMATRIX:
Calling the Jacobian matrix, without UPFC poweraddition
= (14)
Let us add the injected power due to current in busbars i and j and also the voltage equations
and the additional correction of theJacobian matrix, due to the power balance equation,is also included, complementing the formulation[ ] = [ ] + [ ] + [ ](15)
The elements of the Jacobian matrix are presentedbelow
A. Optimization Approach:The behavior of the proposed model was studied
with an optimization power flow code based on theQuasi-Newton method. The Quasi-Newton methodwas used in order to compare time answers of PIMand CBM models, adopting the same initialconditions and trying to obtain similar results aspossible, although some differences in the equationsof both cases can lead to small discrepancies in somevariables of the system. The approximation formulaused in the Quasi-Newton method is given byConditioning of Quasi-Newton methods for functionminimization,”
The formula is given below= − − +(16)
WhereInverse of approximation of Taylor series
Expansion of the gradients of in= Secant relationship or Quasi-Newton;Taylor series expansion (∇ ( + 1) − ∇ ( ))Identity matrix.
Current restrictions are introduced in theformulation. In the CBM, current module and angleare the variables of the problem, while for PIMcurrent equation is introduced according to̅ = ∠ + ∠( + ) − ∠ ( )
(17)Equation would be a little more complex if theseries = admittance was not simplified to =
disregardingseries impedance losses.
IV. Simulation ResultsMany comparative tests performed with CBM andPIM models presented identical results in powerflow analysis using a Mat lab code. An additionalrelationship with the model of Steady-state anddynamic models of unified power flow controller(UPFC) for power system Studies were made,using the Power World program. Some changes in
YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY
International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014
the New England System of 39 bus bars wereintroduced with the purpose of highlighting theoptimization results. The customized New Englandsystem is represented in Appendix A. Generator 2is the swing bus bar, and the other generators areconsidered power variable generators angeneration costs are also presented. In the modifiednetwork, the base case does not converge andconvergence can only be attained if the powergeneration cost is optimized. If current restrictionsare used in some lines, convergence is onlyattained with UPFCs in the network. The values ofvoltages in results it will be in the ranges of 0.92to1.05pu for network bus bar
Fig (6) New England 39 bus system with 8UPFC’s
In order to make comparison between two modelsit have same initial conditions will be given thenetwork was analyzed with 6 and 8 UPFCs.A. Network with 6 UPFCsThe lines with UPFC and their particular minimumand maximum current limits are presented in Table 3and Table 4 shows that by increasing the number ofUPFCs to6, the lower convergence time of CBM isstill more evident. The results of the values of the twomodels are not similar but generation costs are almostthe same for these limits. If the limits are increased,different generation costs can be yielded for themodels. In several cases, it was observed that for allthe set of current limits that allow convergence forthe PIM models also leads the CBM model toconvergence. On the other hand, the inverse is nottrue, with CBM presenting a better performance incases of difficult convergence due to currentlimitations, mainly cases with narrower currentlimits.
TABLE 1CURRENT LIMITS FOR 6 UPFCS
LINE UPFC Current limits
32-31 1 0-5pu
39-38 2 0-6pu
13-14 3 0-2pu
25-24 4 0-1.5pu
16-21 5 0-1pu
11-10 6 0-0.4pu
Fig (7) Voltage profile in pu with and withoutUPFC’s
YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY
International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014
Fig (8) Real &Reactive power loss with andwithout upfc’s
B. Network with 8 UPFC:The line with UPFC and their respective minimumand maximum current limits are presented in table 5Here the additional UPFCs are taken randomly byobserving of 3 UPFC systems. The table 6 showscomparison between the 6UPFC and 8UPFC ofnetwork for current base model in this analysis wecan find the 8 UPFC have same results withcomparison to 6 UPFC the lose reduction in 8 UPFCis more higher than 6 UPFC the cost is all so littlehigher the time taken was same. In this analysis theboth two systems was worked effectively. Theoptimization approach of two systems was dependson the requirements of the given system for currentbased model
TABLE 2CURRENTS LIMITS FOR 8 UPFCSLINE UPFCS Currents
limits32-31 1 0-5pu
39-38 2 0-6pu
13-14 3 0-2pu
25-24 4 0-1.5pu
16-21 5 0-1pu
11-10 6 0-0.4pu
27-28 7 0-3.2pu17-18 8 0-3pu
Fig (9) Voltage profile in pu with and withoutUPFC’s
Fig (8) Real &Reactive power loss with andwithout upfc’s
YASWANTH KUMAR, V.SINGARAIAH and Dr.I.PRABHAKAR REDDY
International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 9, Oct. 2014
CONCLUSIONS
The paper presents the treatment of series voltageconverters in power systems and the formulation canbe useful to other equipment of the FACTS family.The proposition of an alternative formulation for themodeling of UPFC was presented, considering thecurrent in the series converter as a variable. Theproposed CBM model was compared with thetraditional power injection model PIM, showingcoincident results in power flow evaluations. In anoptimization approach, despite working with twoadditional equations for each UPFC, the CBM modelreduces the computational time, when currentlimitations are introduced in the series converters,mainly when dealing with several UPFC in thesystem, which is a very important issue in FACTSdesign.
REFERENCES
[1] Marcos Pereira and Luiz Cera Zanetta, A CurrentBased Model for Load Flow StudiesWithUPFCSenior Member, IEEE,MAY 2013.[2] N. G. Hingorani and L. Gyugyi, Understanding
FACTS: Concepts andTechnology of Flexible ACTransmission Systems. NewYork:IEEEPress, 2000.[3] Y. H. Song and A. T. Johns, Flexible ACTransmission Systems—FACTS. London, U.K.: IEEPress, 1999.[4] J. Bian, D. G. Ramey, R. J. Nelson, and A. Edris,“A study of equipmentsizes and constraints for aunified power flow controller (UPFC),” IEEETrans.Power Del., vol. 12, no. 3, pp. 1385–1391, Jul. 1997.[5] C. Schauder et al., “Installation, commissioningand operation of theMVA STATCOM (Phase I);AEP UPFC Project,” IEEE Trans.Power Del., vol.13, no. 4, pp. 1530–1535, Oct. 1998.[6] K. K. Sen and E. J. Stacey, “UPFC-unified powerflow controller:Theory, modeling and applications,”IEEE Trans. Power Del., vol. 13,no. 4, pp. 1953–1960, Oct. 1998.[7] A. F. Keri et al., “Unified power flow controller(UPFC):Modeling andanalysis,” IEEE Trans. PowerDel., vol. 14, no. 2, pp. 648–654, Apr.1999.[8] L. Gyugyi, C. Schauder, and K. K. Sen, “Staticsynchronous seriescompensator: A solid state
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THUMMALA YASWANTH KUMAR (B-Tech) In ElectricalAnd Electronics Engineering (E.E.E) At GeethanjaliInstitute Of Science And Technology In NELLORE Year Of(2008-12)M Tech In ELECTRICAL POWER SYSTEMS(E.P.S) At NARAYANA ENGINEERING COLLEGE AtNELLORE(2012-14) Email: [email protected]
V.SINGARAIAH (M.Tech) InELECTRICAL ENGINEERING From JNTU And CurrentlyHe Is Working As Associate Professor Of Electrical AndElectronics Engineering Department , In NARAYANAENGINEERING COLLEGE At NELLORE , A.P, India.
Dr.I.PRABHAKAR REDDY (M Tech,Ph.D)Degrees In Electrical Engineering From Jawaharlal NehruTechnological University, Currently He Is Working AsProfessor & Head Of Department Of Electrical AndElectronics Engineering, In NARAYANA ENGINEERINGCOLLEGE At NELLORE, A.P, India
