Electrical Power and Energy Systems 57 (2014) 49–63

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Congestion management with generic load model in hybrid electricitymarkets with FACTS devices

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.11.035

⇑ Corresponding author.E-mail addresses: ashwa_ks@yahoo.co.in (A. Kumar), ramkumar.mittapalli@

gmail.com (R.K. Mittapalli).

Ashwani Kumar a,⇑, Ram Kumar Mittapalli b

a Department of Electrical Engineering at NIT Kurukshetra, Indiab Power Systems Engineering at NIT Kurukshetra, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 January 2013Received in revised form 2 August 2013Accepted 19 November 2013

Keywords:Generator re-dispatchCongestion managementBlock bid functionFACTS devicesHybrid electricity market

The load variations during the entire day specially during the peak hours have substantial impact on theloading pattern of the transmission system. The voltage profile become poor during such situation of peakloading of the network and can lead to congestion during such events. This paper attempts congestionmanagement considering the impact of constant impedance, current, and power (ZIP) load model alongwith the load variation pattern in a day-a-head hybrid electricity market. The main contribution of theproposed work is: (i) Optimal rescheduling based congestion management for a hybrid market modelwith three bid offer from generators, (ii) study of the impact of ZIP load model and load variations onrescheduling and congestion cost, (iii) impact of third generation FACTS devices on congestion manage-ment, (iv) comparison of results obtained for hybrid market model without and with ZIP load model. Thegenerators offer three block bid structure to the ISO in a day-a-head market for congestion management.The base case economic load dispatch has been obtained for generators and is taken as base case gener-ation output data during the congestion management to obtain new generation schedule. The three blockbid structure submitted to the ISO has been modeled as a linear bid curve which is a function of incre-ment/decrement (inc./dec.) of generation within the upper and lower bounds offered for congestion man-agement. The results have been obtained for IEEE 24 bus test systems.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Fair and open access of transmission system is one of the keyrequirements for competitive electricity markets existence. Thecongestion that may occur in transmission system due to viola-tions of physical limits is undesirable as it can distort marketbehavior due to change in the prices and increased risk of marketmanipulations and may compromise security of the system [1].The North American Electric Reliability Council (NERC) InterchangeDistribution Calculator (IDC) which consists of a set of applications,hardware, communication infrastructure, and procedures is de-signed to manage transmission congestion and mitigate transmis-sion system security limit violations in the North American EasternInterconnection [2]. The implementation of the Transmission Load-ing Relief (TLR) procedure to manage the flow in a particular inter-faces/flowgates on a NERC Reliability Coordinators request, the IDCcalculates the adjustments to interchange transactions. A frame-work for transmission dispatch and congestion management withkey responsibilities of the ISO and its models was proposed in [3].

Congestion management as one of the key elements of trans-mission system dispatch may be relieved in many cases by cost-free means such as network reconfiguration and enhancement oftransmission system capability to alleviate congestion using net-work expansion planning [4,5]. The other methods like operationof transformer taps, voltage regulators, and operation of flexiblealternating current transmission systems (FACTS) devices can beutilized by the transmission system operators to alleviate over-loads by means of switching operations that may avoid costly gen-eration or load curtailments. In extreme cases of system operation,it may not be possible to relieve congestion by cost-free means,and the system operator can adopt some non-cost-free controlmethods, such as re-dispatch of generation, curtailment of loadsand other market based financial instruments for relieving trans-mission congestion [6–15]. Since there is a wide range of eventswhich can lead to transmission system congestion, a key functionin system operation is to manage and respond to operating condi-tions in which system voltages and or power flow limits are vio-lated adopting different congestion management basedapproaches [6].

The congestion management (CM) is one of the important tasksof the ISO and includes both congestion relief actions and the ISOcan utilize market based approaches for alleviating congestion.The market-based methods using locational marginal prices

Nomenclature

k index for an hrt index for bid block of generator bid functiontmax maximum no of bid blocks for each generator and is ta-

ken as threea(i,k), b(i,k), c(i,k) cost coefficients of generator-i at hr kap(i,k), bp(i,k), cp(i,k) coefficients for real ZIP load at each load bus

and hr kaq(i,k), bq(i,k), cq(i,k) coefficients for reactive ZIP load at each load

bus and hr kPg(i,t,k) base case real power generation at each bus-i for bid

block t and hr kQg(i,t,k) base case reactive power generation at each bus-i for

bid block t and hr kPd(i,k) base case power demand at each bus-i for hr kPgn(i,t,k), Qgn(i,t,k) new power generation schedule after conges-

tion management for bid block t and hr k consideringZIP load model

DPupg ði; t; kÞ active power increment for generator at bus-i for

each bid block and k hrsDPdown

g ði; t; kÞ active power decrement for generator bus-i foreach bid block t and hrs k

DPupgmin;DPup

gmax vector of upper and lower limit for up generation

DPdowngmin;DPdownp

gmax vector of upper and lower limit for down gener-ation

CC, CC(k) total congestion cost and congestion cost for hr kDCðPup

g ði; t; kÞÞ price offered by generator for up generation atbus-i for congestion management for each bid block tand hr k

DCðPdowng ði; t; kÞÞ price offered by generator for up generation at

bus-i for congestion management for each bid block-tand hr k

GDsecureij secure bilateral transaction matrix

GDsecureij;;max upper limit for secure bilateral transaction

Gij, Bij real and imaginary part of Ybus

Gsh, Bsh shunt conductance and succeptance of STATCOMPexchange real power exchange via DC linkPC

i ;QCi real and reactive power injection at a bus with STAT-

COMPC

ij ;QCij real and reactive power injection with SSSC and UPFC

Pbg ;P

pg vector of bilateral and pool generation

Pbd;P

pd vector of bilateral and pool demand

P(i,k) real power injection at bus-i based on the demand var-iation for hr k

Q(i,k) reactive power injection at bus-i based on the demandvariation for hr k

Pmaxg ðiÞ; Pmin

g ðiÞ;Qmaxg ðiÞ;Qmin

g ðiÞ upper and lower limits for realand reactive power generation for base case

Pmaxgn ðiÞ; P

mingn ðiÞ;Q

maxgn ðiÞ;Q

mingn ðiÞ upper and lower limits for real

and reactive power generation during congestion man-agement

k1n(i, t, k) and k2n(i, t, k) price coefficients of linear bid curve ($/MW h) offered by the generator to increase and de-crease its power schedule for congestion management

Rupg ði; t; kÞ and Rdown

g ði; t; kÞ price offered in ($/h) as constant partof linear bid curve by the generator to increase and de-crease its power schedule for congestion management

ðPt;kij Þ; ðQ

t;kij Þ real and reactive power flow calculated for each

block t and hours kVsh,STATCOM and dsh,STATCOM shunt voltage and angle for STATCOMVse,SSSC and dse,SSSC series injected voltage and angle for SSSCVsh,UPFC, dsh,UPFC shunt voltage and angle, Series injected voltage

and angle as control parameters for UPFC

Vse;UPFC ; dse;UPFCV0ði;kÞ;V ði;;kÞ voltage at any bus-i for base case and

during congestion management at hr kVmax

i ;Vmini upper and lower limit for voltage

Vmaxði;kÞ x;V

minði;kÞ upper and lower limit for voltage at bus-i at hr k

50 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

(LMPs) and other economic signals [7–11] have been proposed tomanage and relieve transmission congestion. The essence of thesemethods is to modify the injection and withdrawal patterns ofpower flows so that the transmission network can accommodatethem without violating the constraints. The market basedapproaches can be categorized based on LMPs, price area zones,financial transmission rights, and curtailment of preferred sched-ules of generation and loads. A congestion management systembased on LMPs with two new approaches for locational powermarket screening was presented in [9]. Authors presented a novelcontrol scheme for obtaining optimal power balancing and conges-tion management in electrical power systems using nodal pricesdeveloping an explicit controller that guarantees economicallyoptimal steady-state operation while respecting all line flow con-straints in steady-state [11]. Financial transmission rights as amarket solution that can hedge congestion charges when utilizedwith LMPs thereby defining zonal boundaries to manage conges-tion and efficient use of transmission system [12–14].

Re-dispatching based schemes, curtailment of preferred sched-ules along with re-dispatch, security constrained OPF, zonal basedapproach with sensitivity factors, and impact of FACTS to managetransmission congestion minimizing the congestion cost is pre-sented by many authors [15–32]. Fang and David [15,16] proposeda transmission dispatch methodology as an extension of spot pric-ing theory in a pool and bilateral as well as multilateral transac-tions model. Prioritization of electricity transactions andwillingness-to-pay for minimum curtailment strategies has been

investigated as a practical alternative to deal with the congestion.Authors in [17] proposed FACTS based curtailment strategy basedon [15] for congestion management. The phase-shifters and taptransformers play vital preventive and corrective roles in conges-tion management. These control devices can help the ISO to miti-gate congestion without re-dispatching generation away frompreferred schedules. A procedure for minimizing the number ofadjustments of preferred schedules to alleviate congestion andapply control schemes to minimize interactions between zonestaking contingency-constrained limits into consideration was pre-sented in [18]. A method for the decentralized solution of the con-gestion management problem in large interconnected powersystems is presented [19]. A transmission congestion managementprocedure has been formulated using a combination of load cur-tailment and generation re-dispatch based on the set of indicesto measure the effectiveness of the extent of load curtailmentand economic impact [20]. The multi-area congestion managementis achieved through cross-border coordinated re-dispatch by regio-nal transmission system operators. A method of congestion man-agement with generation rescheduling and load shedding basedon the sensitivities of the overloaded lines to bus injections andthe costs of generation and load shedding considered for rankingthe generation and load buses has been presented in [21]. Twoapproaches for a unified management of congestions due to volt-age instability and thermal overload in a deregulated environmentsimultaneously handling of operating and security constraints withrespect to several contingencies is proposed with an objective of

A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63 51

adjustment of generator output and possibly load consumption atthe least cost while the second one aims at curtailing power trans-actions in a transparent and non-discriminatory way [22].

A comprehensive literature survey of congestion managementmethods and their categorization based on the methods used arepresented in [23]. A congestion management approach based onreal and reactive power congestion distribution factors basedzones and generator’s rescheduling was proposed in [24]. A meth-od of overload alleviation by real power generation reschedulingbased on relative electrical distance (RED) concept has been intro-duced with enhancement in relative stability margin due to im-proved voltage profile and reduced losses [25]. Role of demandside management is investigated on congestion relief in deregu-lated electricity markets [26]. With the environmental constraintsposing restrictions for installations of new transmission lines,FACTS technology all over the world is playing a key role for foster-ing the transmission network to be utilized to its full potential.Many authors developed the methodology to incorporate FACTSdevices to manage the transmission congestion [27–34]. Authorsproposed a novel methodology for placement of SVC and TCSC torelieve congestion in the system with improvement of static secu-rity margin [28]. A method to determine the optimal location ofthyristor controlled series compensators (TCSCs) has been sug-gested based on real power performance index and reduction of to-tal system VAR power losses and the device can be utilized tocontrol congestion in the network [30]. Acharya proposed a newmethodology based on LMPs differences and congestion rent forthe location of series FACTS devices for congestion management[31]. A congestion management strategy for a pool electricity mar-ket model with combined operation of hydro and thermal genera-tion companies has been proposed in [32]. An approach isproposed for transmission lines congestion management in arestructured market environment using a combination of demandresponse (DR) and flexible alternating current transmission system(FACTS) devices with a two-step market clearing procedure in [33].Kumar and Sekhar proposed congestion management in the pres-ence of FACTS devices considering loadability limits into accountand comparison of UPFC with Sen transformer a new power flowcontroller with wide range capability of controlling power flows[34,35]. However, the authors have considered only constant P, Qload models for study and impact of realistic load model needsto be investigated for congestion management. A sensitivity basedmethod for ranking the load buses and allocating distributed gen-erators (DGs) for congestion relief and voltage security simulta-neously have been presented in [36]. Generation capacities havebeen obtained for DGs based on GA considering losses reductionand voltage profile improvement.

Under the overloading of transmission system, the voltage pro-file have tendency to sag and voltage dependent loads can havesubstantial impact on the system behavior under such circum-stances. The load variation during the entire day especially duringthe peak hours can influence the network power flow profiles andthe congestion behavior of transmission system. Therefore, theconsideration of both load models and load variations is essentialfrom security reasons to study transmission congestion. In thiscontext, along with the static security as line flow limits, ZIP loadmodel and load variation in the entire day horizon has been takenfor the study of the congestion.

In the present work, generator rescheduling based congestionmanagement approach has been implemented for a hybrid elec-tricity market model. The main contribution of the proposed workis: (i) Implementation of optimal rescheduling based congestionmanagement for a hybrid market model, (ii) study of the impactof ZIP load model and load variation on rescheduling and conges-tion cost, (iii) impact of third generation FACTS devices on conges-tion management, (iv) the comparison of results obtained for

hybrid market model with constant P, Q load and with ZIPload model. The optimal generators’ rescheduling has been ob-tained for three block bid structure submitted to the ISO in aday-a-head market. The base case economic load dispatch has beenobtained for generators and is taken as base case generation outputdata during the congestion management to obtain new generationschedule. The three block bid structure submitted to the ISO hasbeen modeled as a linear bid curve which is a function of inc./dec. generation within the upper and lower limits offered for con-gestion management from each Gencos. The results have been ob-tained for IEEE 24 bus test system. The results obtained with allFACTS devices have been compared. The optimal location of FACTSdevices have been obtained based in the congestion distributionfactors and the procedure is well explained in [35]. The optimalpower flow problem using non-linear programming approach hasbeen solved using NLP solver of GAMS [37,38]. The MATLAB andGAMS interfacing has been utilized to solve the complex non-lin-ear optimization problem [38]. The results have been obtainedfor IEEE 24 bus Reliability Test System [39].

2. Mathematical model of rescheduling based congestionmanagement

Congestion management based on generation rescheduling hasbeen formulated as an optimization problem minimizing conges-tion cost. Three bids structure is submitted to the ISO by eachGencos for regulating their units to manage congestion. To obtainthe new generation schedule, base case generation is essential toobtain, solving economic load dispatch problem. The generationrescheduling based congestion management has been studied formulti-line congestion with FACTS devices viz. Static Compensator(STATCOM), Static Synchronous Series Compensator (SSSC), andUnified Power Flow Controller (UPFC). Their impact has been incor-porated in an optimal power flow model using power injectionmodel and optimal generation rescheduling has been obtainedafter removal of congestion in the network. The detailed staticmodel of FACTS devices has been given in [40,41]. The complexnon-linear optimization problem has been solved using GAMSand MATLAB interfacing [37,38]. Optimal location of FACTS deviceshave been obtained based on the power flow sensitivity corre-sponding the power injection at any bus-i. These sensitivity factorsprovide information about the change in power flows therebyloading of transmission system corresponding to the change inpower injections at any bus in a system. These factors thus provideimportant information of loading sensitivity of lines and are alsocalled as congestion distribution factors (CDFs) [35]. The method-ology for obtaining optimal location of FACTS devices has been wellexplained in [35].

2.1. Economic load dispatch of generators under base case

In this section, the base case output of generators for three bidblock structure submitted to the ISO has been obtained by mini-mizing the fuel cost function. The economic generation scheduleis essential to obtain the new generation up/down schedule duringthe congestion management. The base case power output has beenobtained considering cost function comprising three bid blocks foreach generator. The economic load dispatch problem has beensolved using GAMS CONOPT solver [37].

Objective function is:Minimize fuel cost for each bid block

obj ¼Xng

i¼1

X24

k¼1

cði; kÞXtmax

t¼1

Pgði;t;kÞ

!2

þ bði; kÞXtmax

t¼1

Pgði;t;kÞ þ aði; kÞ

0@

1A ð1Þ

52 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

Subject to constraints as:(i) Real and reactive power balance equationsXtmax

t¼1

Pgði; t; kÞ � Pdði; kÞ ¼ Pði; kÞ ð2Þ

Xtmax

t¼1

Q gði; t; kÞ � Q dði; kÞ ¼ Qði; kÞ ð3Þ

(i) Real and reactive power generation limits

Pming ði; kÞ 6

Xtmax

t¼1

Pgði; t; kÞ 6 Pmaxg ði; kÞ ð4Þ

Q ming ði; kÞ 6

Xtmax

t¼1

Qgði; t; kÞ 6 Q maxg ði; kÞ ð5Þ

k is the number of hour in a day and t is the number of bid blockstaken as three.

The real power demand for a day has been calculated multiply-ing the demand at base case with load scaling factor. The demandcurve for a day taken for the study is shown in Fig. 1.

The economic output of the generators for 24 h can thus be ob-tained for all bid blocks submitted to the ISO. These optimal out-puts of each generator have been taken as base values for thegenerators’ scheduling during the congestion hours. Obtainingthe base case optimal outputs for all Gencos, the congestion man-agement model for hybrid market can be developed with ZIP loadmodel. The next section describes the congestion managementmodel.

2.2. Generation rescheduling based congestion management model forhybrid market

Generation rescheduling is a real time congestion managementtool with bid offers for up and down rescheduling and is marketbased solution. Each generator can participate for the congestionmanagement offering bids for regulating their outputs during24 h. The generators have offered three bid blocks to the ISO forcongestion management during a day. The congestion manage-ment problem is defined as:

Min congestion cost CC ¼X24

k¼1

CCðkÞ ð6Þ

005

1015

20250

0.5

1

1.5

2

2.5

3

3.5

Load buses

Load

(p.u

.)

Fig. 1. Demand variatio

Congestion cost (CC) is composed of two components: (i) upregulation (or inc.) cost component and (ii) down regulation (ordec.) cost component. The inc./dec. cost components of generatorshas been taken as linear bid functions submitted by each generatorto the ISO. The congestion cost function with subscripts i for num-ber of buses, t for bid blocks, and k hrs can be expressed as:

CCðkÞ ¼Xng

i¼1

Xtmax

t¼1

ðDCðPupg ði; t; kÞÞ þ DCðPdown

g ði; t; kÞÞÞ ð7Þ

The cost components for inc./dec. bids expressed as a functionof up and down regulation of generators as a linear bids are:

Inc. bid function:

DCðPupg ði; t; kÞÞ ¼ k1nði; t; kÞ � DPup

g ði; t; kÞ � bsmvaþ Rupg ði; t; kÞ ð8Þ

Dec. bid function:

DCðPdowng ði; t; kÞÞ ¼ k2nði; t; kÞ � DPdown

g ði; t; kÞ � bsmva

þ Rdowng ði; t; kÞ ð9Þ

The up and down regulation of generators offered for conges-tion management must be within the lower and upper limits de-clared well in advance by each generators to the ISO. The limitsare:

(i) Up and down regulation constraints:

DPupgminði; t; kÞ 6 DPup

g ði; t; kÞ 6 DPupgmaxði; t; kÞ ð10Þ

DPdowngminði; t; kÞ 6 DPdown

g ði; t; kÞ 6 DPdowngmaxði; t; kÞ ð11Þ

(ii) up and down regulation of each units must remain same tomeet the load.Xng

i¼1

X24

k¼1

Xtmax

t¼1

DPupg ði; t; kÞ �

Xng

i¼1

X24

k¼1

Xtmax

t¼1

DPdowng ði; t; kÞ ¼ 0 ð12Þ

(ii) Power balance equations for real and reactive power at eachbus can be expressed asXtmax

t¼1

Pgnði; t; kÞ � Pdði; kÞ ¼ Pði; kÞ ð13Þ

Xtmax

t¼1

Q gnði; t; kÞ � Qdði; kÞ ¼ Qði; kÞ ð14Þ

510

1520

25

Hrs

n for 24 h in a day.

A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63 53

The real and reactive power from bus-i to bus-j and bus-j tobus-i is:

Pij ¼ V2i Gij � ViVj½Gij cosðdi � djÞ þ Bij sinðdi � djÞ� ð15Þ

Q ij ¼ �V2i Bij þ ViVj½Bij cosðdi � djÞ � Gij sinðdi � djÞ� ð16Þ

Pji ¼ V2j Gij � ViVj½Gij cosðdi � djÞ � Bij sinðdi � djÞ� ð17Þ

Q ji ¼ �V2j Bij þ ViVj½Bij cosðdi � djÞ þ Gij sinðdi � djÞ� ð18Þ

The FACTS devices have capabilities to maintain the voltageprofile and changes power flow patterns. Therefore, these deviceshave capability to control congestion in the network. To considerthe impact of FACTS devices, the power injection model of the de-vices can be added in an optimization model. With FACTS devices,the power flow equations can be modified with all the FACTS de-vices as discussed in [40,41]. Based on the power injection model,the power injection equations for STATCOM, SSSC, and UPFC can beobtained [40,41]. The real and reactive power injection at any bus iof the STATCOM are:

Pci ¼ V2

i Gsh þ ViVsh½Gsh cosðdi � dshÞ þ Bsh sinðdi � dshÞ� ð19ÞQ c

i ¼ �V2i Bsh þ ViVsh½Gsh sinðdi � dshÞ � Bsh cosðdi � dshÞ� ð20Þ

Real power exchange via DC link as an operational constraintwith STATCOM can be written as:

Pexchange ¼ ReðVshI�shÞ ¼ 0

or V2i Gsh þ ViVsh½Gsh cosðdi � dshÞ � Bsh sin di � dshÞ� ¼ 0ð

ð21Þ

The working principle of SSSC and its mathematical model hasbeen well presented in [40,41]. If Vse is the compensating voltageinserting in the transmission line with angle dse, then injected realand reactive power at bus i connected by line i–j where SSSC isplaced, can be written as:

Pcij ¼ V2

i Gii þ ViVj½Gij cosðdijÞ þ Bij sinðdijÞ� þ ViVse½Gij cosðdi

� dseÞ þ Bij sinðdi � dseÞ� ð22Þ

Q cij ¼ �V2

i Bij þ ViVj½Gij sinðdijÞ � Bij cosðdijÞ� þ ViVse½Gij sinðdi

� dseÞ � Bij cosðdi � dseÞ� ð23Þ

The injected real and reactive power at bus j can be written as:

Pcji ¼ V2

j Gjj þ ViVj ½Gij cosðdijÞ þ Bij sinðdijÞ� þ VjVse½Gij cosðdj � dseÞ þ Bij sinðdj � dseÞ� ð24ÞQc

ij ¼ �V2j Bij þ ViVj ½Gij sinðdijÞ � Bij cosðdijÞ� þ VjVse½Gij sinðdj � dseÞ � Bij cosðdj � dseÞ� ð25Þ

where Gii, Bij are taken form Ybus.Active power exchange via DC link as an operating constraint

with SSSC is:

Pexchange ¼ ReðVseI�jiÞ ¼ 0 ð26Þ

It can also be written as:

ViVse½Gij cosðdi � dseÞ � Bij sinðdi � dseÞ� þ VjVse½Gij cosðdj

� dseÞ � Bij sinðdj � dseÞ�¼ 0 ð27Þ

The working of UPFC and its mathematical model has been wellpresented in [40,41]. The injected active and reactive power equa-tions at bus i and bus j can be written as:

Pcij ¼ V2

i ðGii þ GshÞ þ ViVj½Gij cosðdijÞ þ Bij sinðdijÞ� þ ViVse½Gij

� cosðdi � dseÞ þ Bij sinðdi � dseÞ� þ ViVsh½Gsh cosðdi

� dshÞ þ Bsh sinðdi � dshÞ� ð28Þ

Qcij ¼ �V2

i ðBij þ BshÞ þ ViVj½Gij sinðdijÞ � Bij cosðdijÞ� þ ViVse½Gij

� sinðdi � dseÞ � Bij cosðdi � dseÞ� þ ViVsh½Gsh sinðdi

� dshÞ � Bsh cosðdi � dshÞ� ð29Þ

Pcji ¼ V2

j Gjj þ ViVj½Gij cosðdijÞ þ Bij sinðdijÞ� þ VjVse½Gij

� cos dj � dseÞ þ Bij sinðdj � dseÞ��

ð30Þ

Qcji ¼ �V2

j Bij þ ViVj½Gij sinðdijÞ � Bij cosðdijÞ� þ VjVse½Gij

� sin dj � dseÞ � Bij cosðdj � dseÞ��

ð31Þ

Operating constraints is real power exchange via DC link can bewritten as

ViVse½Gij cosðdi � dseÞ � Bij sinðdi � dseÞ� þ VjVse½Gij cosðdj

� dseÞ � Bij sinðdj � dseÞ� þ V2i Gsh þ ViVsh½Gsh cosðdi � dshÞ

� Bsh sinðdi � dshÞ�¼ 0 ð32Þ

where 1/Zsh = Gsh + jBsh; Gij and Bij are taken from Ybus.The real power injections at each bus can be determined based

on the load variation for a day. The power injection equations forreal and reactive power can be written as:

Pi;k ¼XNb

j¼1

Vi;kVj;k½Gij cosðdi;k � dj;kÞ þ Bij sinðdi;k � dj;kÞ� 8 i

¼ 1;2; . . . ;Nb; k 2 hrs ð33Þ

Qi;k ¼XNb

j¼1

Vi;kVj;k½Gij sinðdi;k � dj;kÞ � Bij cosðdi;k � dj;kÞ� 8 i

¼ 1;2; . . . ;Nb; k 2 hrs ð34Þ

The net inc./dec. generation must match to meet load andpower balance equation for each Genco can be written as givenin (36):

XNg

i¼1

DPupg ði; t; kÞ �

XNg

i¼1

DPdowng ði; t; kÞ ¼ 0 ð35Þ

Pgnði; t; kÞ ¼ Pgði; t; kÞ þ DPupg ði; t; kÞ � DPdown

g ði; t; kÞ ð36Þ

The new generation schedule Pgn with ZIP load model duringcongestion management can be expressed as:

Xtmax

t¼1

Pgnði; t; kÞ � Pdnði; kÞ ¼ Pði; kÞ ð37Þ

Xtmax

t¼1

Qgnði; t; kÞ � Qdnði; kÞÞ ¼ Qði; kÞ ð38Þ

The real and reactive power demands with ZIP load coefficientsfor real and reactive loads as ap, bp, cp and aq, bq, cq can be expressedin terms of base case voltage V0

i at any as:

Pdnði; kÞ ¼ P0dði; kÞ � ðapði; kÞ �

Viði; kÞV0

i ði; kÞ

!2

bpði; kÞ �Viði; kÞV0

i ði; kÞ

!

þ cpði; kÞÞ ð39Þ

Qdnði; kÞ ¼ P0dði; kÞ

� aqði; kÞ �Viði; kÞV0

i ði; kÞ

!2

bqði; kÞ �Viði; kÞV0

i ði; kÞ

!þ cqði; kÞ

0@

1Að40Þ

54 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

The values of ZIP load coefficients for both real and reactiveloads have been taken same for each hour k in a day.

New schedule of real power generation after congestion man-agement can be expressed as:

Pgnði; t; kÞ ¼ Pgði; t; kÞ þ DPupg2Ngup ði; t; kÞ � DPdown

g2Ngdown ði; t; kÞ ð41Þ

2.3. Inequality constraints

(i) Up/down demand limits for demand management:The limits for up and down demand management are given by

DPdowngmin 6 DPg 6 DPdown

gmax ð42ÞDPup

gmin 6 DPg 6 DPupgmax ð43Þ

Pmingn 6 Pgn 6 Pmax

gn ð44Þ

Q ming 6 Q g 6 Q max

g ð45Þ

Voltage and angle limits are:

Vmini 6 Vi 6 Vmax

i ð46Þdmin

i 6 di 6 dmaxi ð47Þ

(ii) Power flow limits

ðPijÞ2 þ ðQijÞ2 6 ðSmaxij Þ

2 ð48Þ

(i) Constraints for FACTS devices parameters:

VminSH;STATCOM 6 VSH;STATCOM 6 Vmax

SH;STATCOM; dminSH;STATCOM 6 dSH;STATCOM

6 dmaxSH;STATCOM ð49Þ

VminSE;SSSC 6 VSE;SSSC 6 Vmax

SE;SSSC ; dminSE;SSSC 6 dSE;SSSC 6 dmax

SE;SSSC ð50Þ

VminSE;UPFC 6 VSE;UPFC 6 Vmax

SE;UPFC dminSE;UPFC 6 dSE;UPFC 6 dmax

SE;UPFC ð51Þ

dminSH;UPFC 6 dSH;UPFC 6 dmax

SH;UPFC ð52Þ

Fig. 2a. Base case Pg for bid block-1.

2.4. Equations for hybrid market model

Based on the bilateral demand negotiations, the ISO has to en-sure the secure bilateral transactions for any physical violationsof the transmission system [42]. For bilateral market model, thesesecure transactions have been added as additional equations inoptimization model. With the secure bilateral matrix GDsecure

ij , thepower balance equations are:

Pbd ¼

Xi

GDsecureij ð53Þ

Pbg ¼

Xj

GDsecureij ð54Þ

Pg ¼ Ppg þ Pb

g ð55Þ

Pd ¼ Ppd þ Pb

d ð56Þ

Additional inequality constraints for the bilateral matrix can beadded as:

0 6 GDsecureij 6 GDsecure

ij;;max 6 minðPmaxgi ; PdjÞ ð57Þ

The congestion management model for hybrid market can beobtained adding additional equality and inequality constraintsfor power balance equations in terms of secure bilateral demandmatrix as described from (53)–(57).

3. Results and discussions

3.1. Results for IEEE 24 bus test system

The results have been obtained for multi-line congestion casewith linear bid function submitted by the GENCOs to the ISO forcongestion management. The congestion management study hasbeen carried out with ZIP load model and load variations in a sys-tem during 24 h. The case for congestion in transmission lines havebeen considered assuming the power flow maximum rating in thecorresponding lines below their base case power flows. For creat-ing the congestion, the three lines as 23rd, 18th, and 11th lineshave been taken as the congested lines. The power flow rating of23rd line connected between buses 14 and 16 has been taken as2.60 p.u. compared to its given rating of 5.00 p.u., the rating of18th line connected between buses 11 and 13 has been taken as2.25 p.u. compared to its given rating of 5.00 p.u. and rating of11th line connected between buses 7 and 8 has been taken as1.50 p.u. compared to its given rating of 1.75 p.u. The results havebeen obtained for IEEE 24 RTS [40].

The impact of the FACTS controllers’ viz. STATCOM, SSSC, andUPFC has been studied on generation scheduling and the conges-tion cost. The congestion cost per hour and total congestion costfor a day has been obtained. The economic generation scheduleat base case and new generation schedule after removing conges-tion has been obtained without and with FACTS devices consider-ing ZIP load model. The results have also been obtained forconstant load model. The base case generation is obtained solvingeconomic load dispatch with three bid structure submitted to theISO.

3.1.1. Congestion management with generators’ rescheduling withoutFACTS controllers (WOF) and constant P, Q load model

The base case generation schedule for three bid structure hasbeen obtained solving optimal power flow problem for all threebid blocks and is shown in Figs. 2a–2c. From figures it is observedthat the base case generation schedule is different for all bid blocksdue to the different coefficients of fuel cost curves and for bid block3, the generation share is higher compared to other bid blocks dueto lower fuel cost offered during third bid block. The optimal newschedule of generators after congestion management is shown inFigs. 2d–2f. The up and down generation for all bid blocks has beenobtained and are shown for bid block 3 only in Figs. 3a and 3b.

The generator at buses 1, 2 and 7 from bid block-1 and genera-tors at buses 1, 2, 7 and 13 from bid block-2 and bid block-3 goesup generation for congestion management. The generator at buses18, 21, 22 and 23 from bid block-1, bid block-2 and bid block-3 re-duces their generation during congestion management. The newgeneration schedule is shown in Figs. 2d–2f. It is observed that dif-ferent optimal schedules are obtained after the participation ofgenerators during congestion management.

Fig. 2b. Base case Pg for bid block-2.

Fig. 2c. Base case Pg for bid block-3.

Fig. 2d. New Pg for bid block-1 without FACTS.

Fig. 2e. New Pg for bid block-2 without FACTS.

Fig. 2f. New Pg for bid block-3 without FACTS.

Fig. 3a. Up generation for bid block-3 (WOF).

Fig. 3b. Down generation for bid block-3 (WOF).

Fig. 4a. New Pg for bid block-1 with STATCOM.

A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63 55

3.1.2. Generators rescheduling with STATCOMThe optimal output of all generators for three bid structure is

shown in Figs. 4a–4c with STATCOM. The pattern of the power gen-eration obtained with STATCOM is similar to the power generationpattern obtained without STATCOM, however, the up and downgeneration schedule have slightly lower values compared to thecase without STATCOM. The up and down generation with STAT-

COM have been obtained for all bid block and is shown in Figs.5a and 5b for bid block 3 only. Comparing the up and down gener-

Fig. 4b. New Pg for bid block-2 with STATCOM.

Fig. 4c. New Pg for bid block-3 with STATCOM.

Fig. 5a. Up generation for bid block-3 with STATCOM.

Fig. 5b. Down generation for bid block-3 with STATCOM.

Fig. 6a. New Pg for bid block-1 with SSSC.

Fig. 6b. New Pg for bid block-2 with SSSC.

Fig. 6c. New Pg for bid block-3 with SSSC.

Fig. 7a. Up generation for bid block-3 with SSSC.

56 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

ation schedule without STATCOM, it is observed that generatorsare subjected to lower values of generation rescheduling with dif-ferent schedule in each hr a day. The cost of congestion reducesdue to lower rescheduling values in 24 h duration. The congestioncost obtained without and with STATCOM is shown in Fig. 10.

The generator at buses 1, 2, 7 and 13 from bid block-1 and bidblock-2, generators at buses 2 and 7 bid block-3 goes up generationfor congestion management. The generator at buses 21, 22 and 23from bid block-1, bid block-2 and generator at buses 18, 21 and 22from bid block-3 participate during congestion management.

3.1.3. Generators rescheduling with bid block with SSSC (without ZIP)The optimal output of all generators for three bid structure is

shown in Figs. 6a–6c with SSSC. The pattern of the power genera-tion obtained with SSSC is different than obtained without SSSCand STATCOM. The up and down generation with SSSC is shownin Figs. 7a and 7b for bid block 3 only. Comparing the up and downgeneration schedule without STATCOM, it is observed that genera-tors are subjected to lower values of generation reschedulingthereby the cost of congestion reduces to lower values in 24 hduration. The congestion cost variation is shown in Fig. 10.

The generator at buses 1, 2 and 7 from bid block-1 and genera-tors at buses 2 and 7 from bid block-2 and generators at buses 2, 7and 13 from bid block-3 goes up generation for congestion man-

Fig. 7b. Down generation for bid block-3 with SSSC.

Fig. 8b. New Pg for bid block-2 with UPFC.

A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63 57

agement. The generator at buses 18, 21 and 22 from bid block-1,and generators at buses 18, 21 and 22, and 23 from bid block-2and bid block-3 are participating during congestion management.The generators are subjected to lower values of rescheduling dur-ing each hr a day with SSSC. The congestion cost is observed lowerthan with STATCOM and without any FACTS device. The congestioncost for 24 h is shown in Fig. 10.

Fig. 8c. New Pg for bid block-3 with UPFC.

Fig. 9a. Up generation for bid block-3 with UPFC.

3.1.4. Generators’ rescheduling with UPFC (without ZIP)The optimal output of all generators for three bid structure is

shown in Figs. 8a–8c with UPFC. The pattern of the power genera-tion obtained with UPFCC is different than obtained with SSSC andSTATCOM. The optimal up and down generation pattern with UPFChave been obtained for all bid blocks and is shown in Figs. 9a and9b for bid block 3 only. Comparing the up and down generationpattern without any FACTS devices and with STATCOM and SSSC,it is observed that generators are subjected to lower values of upand down generation. The cost of congestion is observed lower in24 h duration. The congestion cost variation is shown in Fig. 10.

The generator at buses 2, 7 and 13 from bid block-1, bid block-2and from bid block-3 goes up generation during congestion man-agement. The generator at buses 13, 15, 16, 18 and 21 from bidblock-1, bid block-2 and generators at buses 7, 13, 16, 18 and 21from bid block-3 are participating for congestion management.The congestion cost obtained without FACTS (WOF) and with allFACTS devices is shown in Fig. 10. Comparing the congestion costfor a day, it is observed that congestion cost reduces with all FACTSdevices, however, with UPFC it is found lower compared to otherFACTS devices. With STATCOM and SSSC, the congestion cost vari-ation is marginal compared to without FACTS for a day. The totalcongestion cost reduces with all FACTS devices and is found lowerwith UPFC. The total congestion cost and its values in 24 h is alsogiven in Table 1.

Fig. 8a. New Pg for bid block-1 with UPFC.

Fig. 9b. Down generation for bid block-3 with UPFC.

3.2. Results with ZIP load model without and with FACTS Devices

The results have been obtained with ZIP load considering thevariation of ZIP load coefficients. The ZIP load coefficients variationat all the load buses have been shown in Fig. A1 in Appendix A. Thesecure bilateral transactions matrix is obtained solving non-linearoptimization problem as discussed in [41]. The secure bilateraltransaction matrix is shown in Fig. A2 in Appendix A. These secure

Fig. 10. Comparison of congestion cost without and with FACTS devices.

Table 1Congestion cost for 24 h without and with FACTS devices.

WOF STATCOM SSSC UPFC

Hour-1 1778.86 1778.499 1379.688 1725.592Hour-2 2648.432 2631.712 2418.423 2433.068Hour-3 2284.387 2284.149 2282.563 2300.955Hour-4 2429.552 2413.472 2198.316 2233.685Hour-5 1974.662 1958.425 2009.983 1561.305Hour-6 2459.652 2442.151 2227.742 2246.774Hour-7 2219.357 2199.24 2148.249 2018.485Hour-8 2256.212 2233.258 1910.485 2071.882Hour-9 2185.27 2163.275 1838.678 1972.697Hour-10 2423.296 2400.794 2194.179 2224.594Hour-11 2132.97 2115.975 1884.221 1916.977Hour-12 2369.891 2348.839 2333.775 2170.496Hour-13 2298.331 2279.584 2063.955 2123.384Hour-14 2370.317 2352.497 2280.858 2127.747Hour-15 1945.257 1934.684 1795.2 1438.16Hour-16 2389.287 2371.072 2217.498 2199.477Hour-17 2411.799 2393.761 2270.282 2204.404Hour-18 2563.048 2540.535 2340.015 2389.06Hour-19 2345.814 2326.066 2116.79 2177.159Hour-20 2198.661 2178.698 2136.029 2010.406Hour-21 2261.09 2242.181 2027.498 2059.675Hour-22 2320.379 2301.543 2153.276 2111.095Hour-23 1970.803 1955.459 1873.304 1271.741Hour-24 1933.537 1919.176 1957.907 1512.436Cost ($/h) 54170.86 53765.0460 50058.91 48501.253

Fig. 11a. New Pg for bid block-1 (WOF).

Fig. 11b. New Pg for bid block-2 (WOF).

Fig. 11c. New Pg for bid block-3 (WOF).

Fig. 12a. Up generation for bid block-1 (WOF).

Fig. 12b. Up generation for bid block-2 (WOF).

58 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

bilateral transactions have been utilized in a hybrid market modelalong with pool transactions. In this work, 50% demand has beentaken as bilateral demand. The optimal output of all generatorsafter congestion management is obtained for three bid structureand is shown in Figs. 11a–11c with ZIP load. The pattern of thepower generation obtained with ZIP load is different than obtainedwith constant P, Q load. It can be observed from Figs. 2d–2f and11a–11c obtained after the congestion management. The up anddown generation with ZIP load is shown in Figs. 12a–12f. Compar-

ing the up and down generation schedule without ZIP load, it is ob-served that generators are subjected to lower values of generationrescheduling due to voltage dependency of loads. The generatorsare subjected to lower values of up and down generation sched-ules; thereby the cost of congestion reduces to lower values in

Fig. 12c. Up generation for bid block-3(WOF).

Fig. 12d. Down generation for bid block-1 (WOF).

Fig. 12e. Down generation for bid block-2 (WOF).

Fig. 12f. Down generation for bid block-3 without FACTS.

Fig. 13a. New Pg for bid block-1 with STATCOM.

Fig. 13b. New Pg for bid block-2 with STATCOM.

Fig. 13c. New Pg for bid block-3 with STATCOM.

Fig. 14a. Up generation for bid block-3 with STATCOM.

A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63 59

24 h duration. The total congestion cost and its variation in a day isshown in Fig. 19.

The generator G1, G2, G7 and G13 from bid block-1 and bidblock-2 and bid block-3 goes up generation during congestionmanagement. The generator at buses 15, 16, 18 and 21 from bidblock-1, generators at buses 15, 16, 18 and 21 from bid block-2and from bid block-3 are participate for congestion management.The congestion cost is shown in Fig. 19.

3.2.1. Generators rescheduling with bid block with STATCOM (withZIP)

The optimal output of all generators with STATCOM for threebid structure is shown in Figs. 13a–13c with ZIP load. The patternof the power generation obtained with ZIP load is different thanobtained with constant P, Q load and also without STATCOM. The

Fig. 14b. Down generation for bid block-3 with STATCOM.Fig. 15b. New Pg for bid block-2 with SSSC.

60 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

up and down generation with ZIP load is obtained with all bidblocks and is shown in Figs. 14a and 14b for bid block 3 only. Com-paring the up and down generation schedule without ZIP, it is ob-served that generators are subjected to lower values of generationrescheduling with STATCOM as well as without STATCOM, therebythe cost of congestion reduces.

The generator G1, G2, G7, and G13 from bid block-1, bid block-2and bid block-3 goes up generation for congestion management.The generator at buses 13, 16, 18 and 21 from bid block-1, bidblock-2 and bid block-3 participates for congestion management.The congestion cost is shown in Fig. 19.

Fig. 15c. New Pg for bid block-3 with SSSC.

Fig. 16a. Up generation for bid block-3 with SSSC.

3.2.2. Generators rescheduling with bid block with SSSC (with ZIP load)The optimal output of all generators for three bid structure is

shown in Figs. 15a–15c with ZIP load. The pattern of the powergeneration obtained with ZIP load is different than obtained withconstant P, Q load. The up and down generation with ZIP loadhas been obtained for all bid block and is shown in Figs. 16a and16b for bid block 3 only. Comparing the up and down generationschedule without ZIP, it is observed that generators are subjectedto lower values of generation rescheduling with STATCOM therebythe cost of congestion reduces. The congestion cost variation isshown in Fig. 19. The generation schedule with up and down reg-ulation lowers with SSSC and thereby the congestion cost reducescompared to the case without SSSC. The congestion cost is alsofound lower with SSSC compared to the case with STATCOM asthe values of up and down generation lowers with SSSC comparedto the case with STATCOM.

The generator at buses 7 and 13 from bid block-1, bid block-2and bid block-3 goes up generation for congestion management.The generator at buses 16 and 18 from bid block-1, generators atbus at 16, 18 and 21from bid block-2 and buses 18, 21, and 23 frombid block-3 are participating for congestion management. Differentschedules are obtained with ZIP load compared to the case for con-stant P, Q loads.

Fig. 15a. New Pg for bud block-1 with SSSC.

Fig. 16b. Down generation for bid block-3 with SSSC.

3.2.3. Generators rescheduling with bid block with UPFC (with ZIP)The optimal output pattern obtained for congestion manage-

ment with UPFC for all generators for three bid structure is shownin Figs. 17a–17c with ZIP load. The pattern of the power generationobtained with ZIP load is different than obtained with constant P, Qload. The up and down generation with ZIP load has been obtainedfor all bid blocks and is shown in Figs. 18a and 18b for bid block 3only. It is observed from the pattern of generation up and downschedule during congestion management with UPFC compared to

Fig. 17a. New Pg for bid block-1 with UPFC.

Fig. 17b. New Pg for bid block-2 with UPFC.

Fig. 17c. New Pg for bid block-3 with UPFC.

Fig. 18a. Up generation for bid block-3 with UPFC.

Fig. 18b. Down generation for bid block-3 with UPFC.

Fig. 19. Comparison of congestion cost without and with FACTS devices.

Table 2Congestion cost ($/hr) for 24 h in a day without and with FACTS devices.

WOF STATCOM SSSC UPFC

Hour-1 2478.259 2446.161 1908.911 1915.02Hour-2 1546.814 1477.435 948.1891 948.9065Hour-3 2485.89 2451.337 1852.383 1921.865Hour-4 2485.89 2451.337 1914.342 1928.299Hour-5 2220.934 2219.47 2353.395 1932.227Hour-6 2302.556 2265.717 1664.131 1735.848Hour-7 2121.023 2071.054 1498.954 1538.263Hour-8 2094.751 2021.804 1438.536 1202.627Hour-9 2122.819 2051.547 1455.297 1220.579Hour-10 1987.815 1947.171 1360.273 1383.987Hour-11 2016.907 1978.051 1394.657 1420.596Hour-12 1625.922 1570.075 990.8218 986.5067Hour-13 2152.268 2106.98 1543.324 1572.745Hour-14 1664.889 1604.876 1039.787 1035.639Hour-15 2260.733 2233.229 1629.889 1704.518Hour-16 1632.008 1565.387 996.3064 983.1842Hour-17 2327.142 2277.18 1670.542 1739.301Hour-18 2209.009 2182.835 1624.878 1648.173Hour-19 2031.478 1991.654 1403.208 1441.217Hour-20 2068.688 2012.621 1437.284 1478.299Hour-21 2124.759 2075.497 1507.784 1540.703Hour-22 2206.587 2168.665 1604.98 1634.198Hour-23 2514.799 2482.865 1879.957 1950.593Hour-24 2514.799 2482.865 1941.366 1950.593Cost($/h) 51196.74 50135.81 37059.19 36813.89

A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63 61

patterns of up and down generation schedule with STATCOM andSSSC, the patterns obtained are different and generators are sub-jected to lower values of up and down schedule. Comparing the

up and down generation schedule without ZIP, it is observed thatgenerators are subjected to lower values of generation reschedul-ing with UPFC. Due to lower generation up and down regulationpattern with UPFC, the congestion cost is observed lower com-pared to without FACTS and with STATCOM and SSSC. The conges-tion cost is also observed lower compared to the case with P, Q load

05

1015

2025

05

1015

20250

0.5

1

1.5

2

BusesBuses

Rea

l pow

er (p

.u)

Fig. A2. Secure bilateral transaction matrix.

62 A. Kumar, R.K. Mittapalli / Electrical Power and Energy Systems 57 (2014) 49–63

model. The congestion cost is shown in Fig. 19 and is also given inTable 2.

The generator at bus 7, 13, and 21 from bid block-1, bid block-2and bid block-3 goes up generation for congestion management.The generator at buses 16, 18 and 21 from bid block-1, generatorsat buses 15, 16 and 18 bid block-2 and bid block-3 participates forcongestion management. The congestion cost obtained withoutFACTS (WOF) and with all FACTS devices is shown in Fig. 19. Com-paring the congestion cost for a day, it is observed that congestioncost reduces with all FACTS devices. With STATCOM, the conges-tion cost reduces marginally compared to without FACTS. WithUPFC, the congestion cost is obtained lower compared to STATCOMand SSSC. However, the congestion cost reduction with SSSC iscomparable to UPFC for hybrid market model. The congestion costfor 24 h without and with FACTS devices is given in Table 2. Com-paring congestion cost obtained for pool model with ZIP load andhybrid market model with ZIP load, it is observed that for hybridmarket model, the congestion cost is found lower. This is due tothe fact of change in the power flow patterns with the incorpora-tion of bilateral demand and counter flows that may occur in thesystem thereby reducing the impact of congestion in the network.

4. Conclusions

In this work, the generators’ rescheduling based congestionmanagement with three bid block structure offered by the Gencoshas been implemented for hybrid market model. The impact of ZIPload model and load variations have been incorporated taking loadscaling factor. The congestion cost for each hour of day has beencalculated without and with FACTS controllers and comparisonhas been provided with out and with FACTS devices consideringconstant P, Q and ZIP load model. The economic load dispatch re-sults are obtained for base case data with three bid block structurefor each Gencos. It is observed from the results that the congestioncost obtained with ZIP load model is lower compared to the con-gestion cost obtained for constant P, Q load model. The congestioncost reduces with all FACTS controllers compared to the case with-out FACTS controllers. With UPFC and SSSC the cost is lower com-pared to the case with STATCOM. The congestion cost reduces withFACTS devices as the generators are subjected to lower up anddown regulation. The ZIP load model has considerable impact onthe congestion cost and the ISO should analyze the system for con-gestion management with realistic load model.

Appendix A

See Figs. A1 and A2.

Fig. A1. ZIP load coefficients at load buses.

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