Congestion management with FACTS devices in deregulated electricity markets ensuring loadability limit

Electrical Power and Energy Systems 46 (2013) 258–273

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Congestion management with FACTS devices in deregulated electricity markets ensuring loadability limit Ashwani Kumar a,⇑, Charan Sekhar b a b

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

a r t i c l e

i n f o

Article history: Received 4 October 2011 Received in revised form 30 September 2012 Accepted 9 October 2012 Available online 23 November 2012 Keywords: Generator re-dispatch Congestion management Congestion distribution factors Block bid function FACTS devices Loadability limit

a b s t r a c t This paper addresses an important issue of transmission system congestion management in a pool electricity market environment with the consideration of voltage stability as loadability limit. The optimal generators’ rescheduling has been obtained for three block bid structure submitted to the ISO in a day-a-head market. The base case economic load dispatch has been obtained for generators ensuring the loadability limits and is taken as base case generation output data during the congestion management to obtain new generation scheduling. The generation pattern has been obtained for three bid blocks taking load variation for 24 h considering load scaling factor. The three block bid structure offered to the ISO has been modeled as a linear curve, function of up and down rescheduling within the upper and lower limits offered for congestion management. The impact of third generation FACTS devices has also been studied on the optimal rescheduling of generators’ outputs and thereby the congestion cost. The results have been obtained for IEEE 24 bus and IEEE 57 bus test systems. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Electricity supply industries all over the world are shifting their electricity busyness to a competitive environment with technical innovations expecting the reduction in the electricity price and better customer focus. With fair and open access of transmission system as one of the key factors for open competition, the bulk power transactions has resulted the problem of transmission congestion [1]. NERC standards used transmission loading relief (TLR) procedures when the transmission network is overloaded with a level of classifications from Level 0 to Level 6. Transaction curtailment is allowed if Level 3 congestion is reached. With non-utility generators (NUGs) and wind energy integration, the transmission system may not be able to accommodate the transactions thereby the transmission congestion can cause market inefficiency as well may threaten the overall security of the system [1]. The congestion management (CM) is one of the important tasks of the ISO and utilizes market based approaches in competitive markets for alleviating congestion [1]. The market based approaches can be categorized based on locational marginal prices, price area zones, and financial transmission rights, generation rescheduling. A decomposition of spot prices to reveal congestion was presented by Finney et al. [2]. The differences in the locational ⇑ Corresponding author. E-mail addresses: [email protected] (A. Kumar), [email protected] (C. Sekhar). 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2012.10.010

marginal prices reflect the presence of congestion in a transmission system and the customers charges are based on these locational differences [3]. The relationship between real and reactive nodal prices and evaluation of the impact of congestion to develop appropriate price signals in the pool paradigm for congestion management was investigated in [4]. A method to manage transmission congestion based on ex ante congestion prices was presented in [5]. Gan and Bourcier presented a congestion management system based on locational pricing with two new approaches for locational power market screening [6]. Alomoush and Shahidehpour proposed fixed transmission rights that can hedge congestion charges when utilized with locational marginal prices thereby defining zonal boundaries to managing congestion and efficient use of transmission system [7,8]. An algorithm for long-term values of transmission rights (TRs) to manage congestion was proposed in [9]. The basic concepts of transmission management, dispatch model, and role of the ISO for congestion management are proposed in [10]. Re-dispatching based schemes, curtailment of preferred schedules along with re-dispatch, security constrained OPF, zonal based approach with sensitivity factors, and impact of FACTS to manage transmission congestion minimizing the congestion cost is presented by many authors [11–32]. Fang and David [11,12] proposed a transmission dispatch methodology as an extension of spot pricing theory in a pool and bilateral as well as multilateral transactions model. Prioritization of electricity transactions and willingness-to-pay for minimum curtailment strategies has been

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investigated as a practical alternative to deal with the congestion. Authors in [13] proposed FACTS based curtailment strategy based on [12] for congestion management. An optimal power flow based approach using nodal congestion price signals for computing the optimal power output of generators has been proposed in [14]. An OPF approach based on DC load flow as well as AC load flow has been formulated to minimize the net cost of re-dispatch to manage inter-zonal and intra-zonal congestion [15]. A novel Lagrangian Relaxation based algorithm for area decomposition OPF, minimizing the congestion cost of re-dispatch in order to deal with the multi-zone congestion management, has been proposed in [16]. Both inter-zonal and intra-zonal congestion management problem has been formulated. A similar method with augmented Lagrangian Relaxation based algorithm has been proposed in [17]. Bompard et al. [19] developed a unified framework for mathematical representation of the market dispatch and re-dispatch problems, which is based on Congestion Management (CM) schemes and the associated pricing mechanisms. A unified framework has been used to develop and compare the various CM approaches so as to assess their efficiency and effectiveness of the market signals provided to the market participants. A comprehensive literature survey of congestion management methods and their categorization based on the methods used are presented in [21]. A congestion management approach based on real and reactive power congestion distribution factors based zones and generator’s rescheduling was proposed in [20]. Kumar et al. proposed distribution factors based generators’ rescheduling for CM [23,24]. With the environmental constraints posing restrictions for installations of new transmission lines, FACTS technology all over the world is playing a key role for fostering the transmission network to be utilized to its full potential. Many authors developed the methodology to incorporate FACTS devices to manage the transmission congestion [25–32]. Authors proposed a novel methodology for placement of SVC and TCSC to relieve congestion in the system with improvement of static security margin [31]. With the environmental concerns, right-of-way problems, and necessity for optimal use of transmission system, power system is forced to operate near to their limits in the deregulated environment. Therefore, the security and the stability issues are also important to be considered during the study of transmission congestion. In this context, along with the static security as line flow limits, voltage stability limits should also be considered. In the present work, generator rescheduling based congestion management approach has been proposed with voltage stability constraint taken as loadability parameter into consideration along with the line security limits. Three bid block structure with linear bid function submitted by each GENCOs to the ISO for congestion management has been considered. The impact of Static Compensators (STATCOMs) and Static Synchronous Series Compensator (SSSC), and Unified Power Flow Controller (UPFC) has also been studied for congestion management. The results obtained with all FACTS devices have been compared. The optimal power flow problem using non-linear programming approach has been solved using CONOPT solver of GAMS [33]. The results have been obtained for IEEE 24 bus Reliability Test System [34] and IEEE 57 bus test systems.

sensitivity of lines and are also called as congestion distribution factors (CDFs) [37]. These factors have been obtained as:

CDFijn ¼

@Pij @Pn

ð1Þ

The real power flow from bus-i to bus-j can be written as:

Pij ¼ V i V j Y ij cosðhij þ dj  di Þ  V 2i Y ij cos hij

ð2Þ

Using Taylor series approximation, change in line flows can be written, (ignoring second and higher order terms) as:

@P ij @Pij @Pij @Pij Ddi þ Ddj þ DV i þ DV j @di @dj @V i @V j

DPij ¼

ð3Þ

The partial derivative coefficients in (3) can be obtained using the partial derivatives of real power flow with respect to variables d and V as:

8 > <

9 for k–i; j > = @P ij V i V j Y ij sinðhij þ dj  di Þ for k ¼ i ¼ > @dk > : ; V i V j Y ij sinðhij þ dj  di Þ for k ¼ j 0

8 0 > @Pij < ¼ V j Y ij cosðhij þ dj  di Þ  2V i Y ij cos hij @V k > : V i Y ij cosðhij þ dj  di Þ

ð4Þ 9 for k–i; j > = for k ¼ i

for k ¼ j

> ;

ð5Þ

The Eq. (19) can be arranged in matrix form as:

 ½DPij  ¼

@Pij @Pij @d @V



Dd DV

 ð6Þ

From N–R load flow, the change in angle and voltage can be obtained as:



Dd DV



¼ ½J1



DP DQ

"

 ¼

@P @d @Q @d

@P @V @Q @V

#1 

DP DQ



ð7Þ

From the above equation, the sensitivity factors defined in (1) can be determined as follows.Considering coupling between DP  DV and DQ  Dd, assuming that the reactive power injections at all the buses are constant, (DQ = 0), the change in power injections can be written as:

DP ¼ J11 Dd þ J12 DV

ð8Þ

0 ¼ J 21 Dd þ J 22 DV

ð9Þ

From (8) and (9), the following equation can be obtained:

DP ¼ J 11 Dd  J 12 J 1 22 J 21 Dd ¼ J red Dd

ð10Þ

where Jred is the reduced Jacobian matrix. From (10), the value of change in voltage angle can be written as:

Dd ¼ ½Jred 1 DP

ð11Þ

From (9), the change in voltage in terms of change in power can be written as: 1 1 DV ¼ J1 22 J21 Dd ¼ J22 J21 ½Jred  DP

ð12Þ

Eqs. (11) and (12) can be written in the following form: 2. Optimal location of FACTS devices

Ddi ¼ Optimal location of FACTS devices have been obtained based on the power flow sensitivity corresponding the power injection at any bus-i. These sensitivity factors provide information about the change in power flows thereby loading of transmission system corresponding to the change in power injections at any bus in a system. These factors thus provide important information of loading

NB X m0il DP l

i ¼ 1; 2; . . . ; nb ;

i–s

ð13Þ

l¼1

DV i ¼

NB X m0ilv DPl

i ¼ 1; 2; . . . ; nb ;

i–s

l¼1

The change in real power flow is given as:

ð14Þ

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power injection model and optimal generation rescheduling has been obtained after removal of congestion in the network. The detailed static model of FACTS devices has been given in [35,36]. The complex non-linear optimization problem has been solved using GAMS and MATLAB interfacing [33,38]. 3.1. Economic load dispatch of generators under base case with loadability limit

Fig. 1. Congestion distribution factors.

DPij ¼ aij

nB X

nB X

l¼1

l¼1

m0il DPl þ bij

m0jl DPl þ cij

nB X m0jlv DPl l¼1

nB X þ dij m0jlv DPl

ð15Þ

l¼1

Eq. (15) can be rewritten as:

  DPij ¼ aij m0i1 þ bij m0j1 þ cij m0i1v þ dij m0j1v DP1   þ . . . aij m0in þ bij m0jn þ cij m0inv þ dij m0jnv DPn

In this section, the base case real output of generators for three bid block structure submitted to the ISO has been obtained by minimizing the fuel cost function. This economic generation schedule is essential to obtain the new generation up/down schedule during the congestion in a day. The base case real power for a day has been obtained considering cost function for three bid blocks for each generator. The loadability factor has also been maximized to take the impact of voltage stability limit on economic dispatch. The economic load dispatch problem has been solved using GAMS CONOPT solver [33]. Two objectives functions have been solved using multisolver facility available in GAMS [33]. Objective function is: Minimize fuel cost for each bid block

obj ¼

DPij ¼ CDFij1 DP 1 þ CDFij2 DP2 þ    þ CDFijn DPn

ð17Þ

CDFijn ¼ aij m0in þ bij m0jn þ cij m0inv þ dij m0jnv

ð18Þ

0 @cðiÞ

tX max

!2

Pgði;t;kÞ

þ bðiÞ

t¼1

i¼1 k¼1

ð16Þ

Therefore, the change in the power flow in the line-ij, connecting buses i and j, can be rewritten as:

ng X 24 X

tX max

1

Pgði;t;kÞ þ aðiÞA

ð19Þ

t¼1

Max. loadability parameter qSubject to constraints as: (i) Power balancing equation tX max

P g ði; t; kÞ  q  P d ði; kÞ ¼

X

Pði; kÞ

ð20Þ

t¼1

(i) Power generation limits

The congestion distribution factors have been obtained and are shown in Fig. 1. These CDFs are found higher corresponding to the congested lines. These lines have been considered as a potential candidate for the optimal location of FACTS devices. For the lines, where CDFs are higher, means that the lines are more sensitive to power injection and any change in the line parameters for these lines, they will be more effective to control the power flow patterns. These parameters have been calculated and plotted. The STATCOM has been placed at bus 14 with higher congestion distribution factor at bus 14. The value of CDF at bus 14 is 0.488 and at bus 16 is 0.488. The SSSC and UPFC has been placed on line 14–16 based on the higher CDFs at buses 14 and 16. Similarly, the FACTS device location has been obtained for IEEE 57 bus test system. STATCOM is located at bus 15. The SSSC and UPFC are located at line 15–3. 3. Generator rescheduling based congestion management with loadability limit Congestion management based on generation rescheduling has been formulated as an optimization problem minimizing congestion cost based on the three bids structure submitted to the ISO by each GENCOs for regulating their units to manage congestion. The lodability limit has also been maximized to ensure voltage stability during congestion management. To obtain the new generation schedule, base case generation is essential to obtain solving economic load dispatch problem respecting loadability limits. The generation rescheduling based congestion management has been studied for multi-line congestion with FACTS devices viz. Static Compensator (STATCOM), Static Synchronous Series Compensator (SSSC), and Unified Power Flow Controller (UPFC). Their impact has been incorporated in an optimal power flow model using

Pmin g ði; kÞ 6

tX max

Pg ði; t; kÞ 6 Pmax ði; kÞ g

ð21Þ

t¼1

Q min g ði; kÞ 6

tX max

Q g ði; t; kÞ 6 Q max ði; kÞ g

ð22Þ

t¼1

k is the hour and t is the number of bid blocks. The real power demand for 24 h has been calculated multiplying the demand at base case with load scaling factor. The demand curve for 24 h is shown in Fig. 2. The economic output of the generators for 24 h can thus be obtained for three bid blocks submitted to the ISO. These optimal outputs of each generator have been taken as base values for the generators scheduling during the congestion hours. 3.2. Generation rescheduling based congestion management model with loadability limit The congestion management model for 24 h with submitted bids to the ISO for congestion management is described as follows:

Min CC ¼

24 X CCðkÞ

ð23Þ

k¼1

and Max loadability limit (q) Congestion cost is composed of two components of up and down regulation of generators taken as linear bid function submitted by each generator with three bid blocks as:

CCðkÞ ¼

ng tX max     X down DC Pup ði; t; kÞ g ði; t; kÞ þ DC P g

ð24Þ

i¼1 t¼1 up up DCðPup g ði; t; kÞÞ ¼ k1n ði; t; kÞ  DP g ði; t; kÞ  bsmv a þ Rg ði; t; kÞ

ð25Þ

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Fig. 2. Demand curve for 24 h.

Pexchange ¼ ReðV sh Ish Þ

DCðP down ði; t; kÞÞ ¼ k2n ði; t; kÞ  DPdown ði; t; kÞ  bsmv a g g þ Rdown ði; t; kÞ g

¼ 0orV 2i Gsh þ V i V sh ½Gsh cosðdi  dsh Þ  Bsh sinðdi

ð26Þ

 dsh Þ

Subjected to operating constraints as: (i) Inequality constraints

¼0

up up DPup g min ði; t; kÞ 6 DP g ði; t; kÞ 6 DP g max ði; t; kÞ

ð27Þ

DPdown g min ði; t; kÞ

ð28Þ

6

DPdown ði; t; kÞ g

6

DPdown g max ði; t; kÞ

(i) Equality constraints ng X ng X 24 tX max 24 tX max X X DPup DPdown ði; t; kÞ ¼ 0 g ði; t; kÞ  g i¼1 k¼1 t¼1

Pcij ¼ V 2i Gii þ V i V j ½Gij cosðdij Þ þ Bij sinðdij Þ þ V i V se ½Gij cosðdi

Power balance equation becomes

Pgn ði; t; kÞ  q  Pd ði; kÞ ¼ Pði; kÞ

The working of SSSC and its mathematical model has been well presented in [35,36]. If Vse is the compensating voltage inserting in the transmission line with angle dse, then injected real and reactive power at bus i connected by line i–j where SSSC is placed, can be written as [35,36]:

ð29Þ

i¼1 k¼1 t¼1

tX max

 dse Þ þ Bij sinðdi  dse Þ ð30Þ

t¼1

Q gn ði; t; kÞ  Q d ði; kÞ ¼ Q ði; kÞ

ð31Þ

t¼1

Pij ¼ V 2i Gij  V i V j ½Gij cosðdi  dj Þ þ Bij sinðdi  dj Þ

ð32Þ

Q ij ¼ V 2i Bij þ V i V j ½Bij cosðdi  dj Þ  Gij sinðdi  dj Þ

ð33Þ

Pji ¼ V 2j Gij  V i V j ½Gij cosðdi  dj Þ  Bij sinðdi  dj Þ

ð34Þ

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

Q ji ¼ V 2j Bij þ V i V j ½Bij cosðdi  dj Þ þ Gij sinðdi  dj Þ

ð35Þ

 dse Þ þ Bij sinðdj  dse Þ

With FACTS devices, the power flow equations can be modified with the power injection equations for the FACTS devices [35,36]. Based on the power injection model, the power injection equations for STATCOM, SSSC, and UPFC can be obtained [35,36]. The real and reactive power injection at any bus i of the STATCOM are [35,36]:

¼

þ V i V sh ½Gsh cosðdi  dsh Þ þ Bsh sinðdi  dsh Þ

Q ci ¼ V 2i Bsh þ V i V sh ½Gsh sinðdi  dsh Þ  Bsh cosðdi  dsh Þ

ð36Þ ð37Þ

Operational constraint of the STATCOM (real power exchange via DC link) can be written as:

ð41Þ

Q cij ¼ V 2j Bij þ V i V j ½Gij sinðdij Þ  Bij cosðdij Þ þ V j V se ½Gij sinðdj  dse Þ  Bij cosðdj  dse Þ

V 2i Gsh

ð40Þ

Pcji ¼ V 2j Gjj þ V i V j ½Gij cosðdij Þ þ Bij sinðdij Þ þ V j V se ½Gij cosðdj

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

Pci

ð39Þ

Q cij ¼ V 2i Bij þ V i V j ½Gij sinðdij Þ  Bij cosðdij Þ þ V i V se ½Gij sinðdi  dse Þ  Bij cosðdi  dse Þ

tX max

ð38Þ

ð42Þ

where Gii, Bij are taken form Ybus. Operating constraint of the SSSC, (active power exchange via DC link) is:

  Pexchange ¼ Re V se Iji ¼ 0

ð43Þ

It can also be written as:

V i V se ½Gij cosðdi  dse Þ  Bij sinðdi  dse Þ þ V j V se ½Gij cosðdj  dse Þ  Bij sinðdj  dse Þ ¼0

ð44Þ

The working of UPFC and its mathematical model has been well presented in [35,36].The injected active and reactive power equations at bus i and bus j can be written as [35,36]:

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Pcij ¼ V 2i ðGii þ Gsh Þ þ V i V j ½Gij cosðdij Þ þ Bij sinðdij Þ þ V i V se ½Gij

(i) Constraints for FACTS devices parameters: max V min SH;STATCOM 6 f  V SH;STATCOM 6 V SH;STATCOM ;

 cosðdi  dse Þ þ Bij sinðdi  dse Þ þ V i V sh ½Gsh cosðdi  dsh Þ þ Bsh sinðdi  dsh Þ

max V min SE;SSSC 6 f  V SE;SSSC 6 V SE;SSSC ;

Q cij ¼ V 2i ðBij þ Bsh Þ þ V i V j ½Gij sinðdij Þ  Bij cosðdij Þ þ V i V se ½Gij  sinðdi  dse Þ  Bij cosðdi  dse Þ þ V i V sh ½Gsh sinðdi  dsh Þ  Bsh cosðdi  dsh Þ

ð46Þ

Pcji ¼ V 2j Gjj þ V i V j ½Gij cosðdij Þ þ Bij sinðdij Þ þ V j V se ½Gij cosðdj  dse Þ þ Bij sinðdj  dse Þ

ð47Þ

Q cji ¼ V 2j Bij þ V i V j ½Gij sinðdij Þ  Bij cosðdij Þ þ V j V se ½Gij sinðdj  dse Þ  Bij cosðdj  dse Þ

6 f  dSH;STATCOM 6

ð45Þ

ð48Þ

Operating constraints is real power exchange via DC link can be written as:

¼0

ð49Þ

where 1/Zsh = Gsh + jBsh; Gij and Bij are taken from Ybus. The real power injections at each bus can be determined for 24 h based on the load variation for a day. The power injection equations for real and reactive power are:

ð64Þ

k t tmax

a,

b, c

Qi ¼

Nb X

ð50Þ

V i V j ½Gij sinðdi  dj Þ  Bij cosðdi  dj Þ

j¼1

8 i ¼ 1; 2; . . . Nb Ng Ng X X DPup DPdown ¼0 g  g g¼1

base case power generation at each bus-i for bid block t and hour k,

Pd(i, k)

Base case power demand at each bus-i for hour k, new power generation schedule after congestion management for bid block t and hour k, active power increment for generator at bus-i for each bid block and k hours, active power decrement for generator bus-i for each bid block t and hours k,

Pgn(i, t, k)

down ði; t; kÞ Pgn ði; t; kÞ ¼ Pg ði; t; kÞ þ DPup g ði; t; kÞ  DP g

DPdown ði; t; kÞ g

DCðP up g ði; t; kÞÞ

price offered by generator for up generation at bus-i for congestion management for each bid block and hour k,

DCðP down ði; t; kÞÞ g

price offered by generator for up generation at bus-i for congestion management for each bid block and hour k, real power injection at bus-i for hour k based on the demand variation for hour k, reactive power injection at bus-i for hour kbased on the demand variation for hour k,

ð51Þ

ð52Þ

g¼1

ð53Þ

3.3. (b)Inequality constraints

P(i, k)

(i) Up/down demand limits for demand management: The limits for up and down demand management are given by down DPdown g min 6 DP g 6 DP g max

ð54Þ

up DPup g min 6 DP g 6 DP g max

ð55Þ

max Pmin gn 6 Pgn 6 Pgn

ð56Þ

Q min 6 Q g 6 Q max g g

ð57Þ

refers an hour, refers block of generator bid function, is maximum no of bid blocks for each generator and is taken as 3, are cost coefficients of generator, is the loadability factor,

Pg(i, t, k)

j¼1

8 i ¼ 1; 2; . . . Nb

Q(i, k)

max Pmax ðiÞ; Pmin ðiÞ; Q min g g g ðiÞ; Q g (i)

Voltage and angle limits are:

V min 6 V i 6 V max i i

ð58Þ

6 di 6 dmax dmin i i

ð59Þ

(i) Power flow limits

 2  2  2 Pt;k þ Q t;k  Smax ij ij ij

ð60Þ

ð62Þ

max dmin SH;UPFC 6 f  dSH;UPFC 6 dSH;UPFC

DPup g ði; t; kÞ

Nb X Pi ¼ V i V j ½Gij cosðdi  dj Þ þ Bij sinðdi  dj Þ

max dmin SE;SSSC 6 f  dSE;SSSC 6 dSE;SSSC

ð63Þ

q

 Bsh sinðdi  dsh Þ

ð61Þ

max min max V min SE;UPFC 6 f  V SE;UPFC 6 V SE;UPFC dSE;UPFC 6 f  dSE;UPFC 6 dSE;UPFC

V i V se ½Gij cosðdi  dse Þ  Bij sinðdi  dse Þ þ V j V se ½Gij cosðdj  dse Þ  Bij sinðdj  dse Þ þ V 2i Gsh þ V i V sh ½Gsh cosðdi  dsh Þ

dmin SH;STATCOM

dmax SH;STATCOM

k1n ði; t; kÞ; k2n ði; t; kÞ

price coefficient of linear bid curve ($/MW h) by the generator to increase and decrease its power schedule for congestion management

are upper and lower limits for real and reactive power generation

A. Kumar, C. Sekhar / Electrical Power and Energy Systems 46 (2013) 258–273 down Rup (i, g ði; t; kÞ; Rg

t, k)

ðPt;k Þ; ðQ t;k Þ ij ij Vsh,STATCOM and dsh,STATCOM Vse,SSSC and dse,SSSC Vsh,UPFC, dsh,UPFC, Vse,UPFC, dse,UPFC

price offered ($/h) as constant part of linear bid curve by the generator to increase and decrease its power schedule for congestion management real and reactive power flow calculated for each block t and hours k, Shunt voltage and angle for STATCOM, Series injected voltage and angle for SSSC, Shunt voltage and angle, Series injected voltage and angle for UPFC.

4. Results and discussion

2.25 p.u. compared to its given rating of 5.00 p.u. and rating of 11th line connected between buses 7 and 8 has been taken as 1.50 p.u. compared to its given rating of 1.75 p.u. The results have been obtained for IEEE 24 RTS [33]. The impact of the FACTS controllers’ viz. STATCOM, SSSC and UPFC has been studied on generation scheduling and the congestion cost. The congestion cost per hour and total congestion cost of day has been obtained. The economic generation schedule at base case and new generation schedule after removing congestion has been obtained without and with FACTS devices. The base case generation is obtained solving economic load dispatch with three bid structure submitted to the ISO. 4.1.1. Congestion management with generators’ rescheduling without FACTS controllers (WOF) The base case generation for three bid blocks taking stability limit into account is obtained solving ELD problem described in Section 2. The base case economic load dispatch is shown in Figs. 3a–c. It is observed that the base case generation share for bid

4.1. Results for IEEE 24 bus test system The results have been obtained for multi-line congestion case with three bid function submitted by the GENCOs to the ISO for congestion management. The congestion management study has been carried out with voltage stability limit taken as loadability increase in a system. The case for congestion in transmission lines have been considered assuming the power flow maximum rating in the corresponding lines below their base case power flows. For creating the congestion, the three lines as 23rd, 18th, and 11th lines have been taken as the congested lines. The power flow rating of 23rd line connected between buses 14 and 16 has been taken as 2.60 p.u. compared to its given rating of 5.00 p.u., the rating of 18th line connected between buses 11 and 13 has been taken as

Fig. 3c. Base case Pg for bid block-3 without FACTS controllers.

Fig. 3a. Base case Pg for bid block-1 without FACTS controllers. Fig. 4a. Up generation for bid block-1 without FACTS controllers.

Fig. 3b. Base case Pg for bid block-2 without FACTS controllers.

263

Fig. 4b. Up generation for bid block-2 without FACTS controllers.

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A. Kumar, C. Sekhar / Electrical Power and Energy Systems 46 (2013) 258–273

Fig. 5a. New Pg for bid block-1 without FACTS controllers. Fig. 4c. Up generation for bid block-3 without FACTS controllers.

Fig. 5b. New Pg for bid block-2 without FACTS controllers. Fig. 4d. Down generation for bid block-1 without FACTS Controllers.

Fig. 5c. New Pg for bid block-3 without FACTS controllers. Fig. 4e. Down generation for bid block-2 without FACTS Controllers.

Fig. 4f. Down generation for bid block-3 without FACTS Controllers.

block 1 is higher compared to the generation share for bid blocks 2 and 3. This is due to the fact that the cost of bid blocks 2 and 3 are

comparatively higher compared to the bid block1. For bid block 2 the generators G1, G2, G15, and G23 share and for bid block 3, the generators G1, G2, G7, and G22 share as shown in figures. The up and down generation and new generation reschedule are shown in Figs. 4a–f. It is observed from the figures that the generators G7 and G13 participate for up generation for bid block 1 and G2, G7 and G13 participate for up regulation for bid blocks 2 and 3 for congestion management. The generators G13, G16, and G18 decrease their generation for bid blocks 1 and 2 and G7, G13, G16, and G18 reduce their generation for bid block 3. The patterns of the participation of generators are different for each bid block due to their qualifying bid blocks. The new generation schedule obtained for each bid block after removal of congestion is shown in Figs. 5a–c. The new generation schedule patterns are different for each bid blocks for a day. Comparing the patterns of generation before and after the congestion, the optimal outputs of each generator are different corresponding to each bid block for a day.

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Fig. 6a. Up generation for bid block-1 with STATCOM.

Fig. 6e. Down generation for bid block-2 with STATCOM.

Fig. 6f. Down generation for bid block-3 with STATCOM. Fig. 6b. Up generation for bid block-2 with STATCOM.

Fig. 7a. New Pg for bid block-1 with STATCOM. Fig. 6c. Up generation for bid block-3 with STATCOM.

Fig. 6d. Down generation for bid block-1 with STATCOM.

Fig. 7b. New Pg for bid block-2 with STATCOM.

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Fig. 7c. New Pg for bid block-3 with STATCOM.

4.1.2. Congestion management with generators’ rescheduling and STATCOM The up and down generation for each bid block are shown in Figs. 6a–f. It is observed from the figures that the generators G2, G7 and G13 participate for up generation for bid block 1 and G2, G7 and G13 participate for up regulation for bid blocks 2 and 3 for congestion management. The generators G13, G16, and G18 decrease their generation for bid blocks 1 and 2 and G13, G16, G18 and G21 reduce their generation for bid block 3 during congestion management. The pattern of the participation of generators is different for each bid block and hour. The new generation schedule obtained for each bid block after congestion management is shown in Figs. 7a–c. The new generation schedule patterns are different for each bid blocks after the removal of the congestion. Comparing the patterns of generation before and after the congestion, the optimal outputs of each generator are different corresponding to each bid block. From the comparison of graphs for up and down rescheduling of generators without and with FACTS controllers, it is observed that the participation of generators decreases with STATCOM compared to without FACTS controllers. Thus, with STATCOM, the congestion cost has been found to reduce due to reduction in the up and down regulation of generator for congestion management. 4.1.3. Congestion management with generators’ rescheduling with SSSC The up and down generation for each bid block for each hour a day are shown in Figs. 8a–f. It is observed from the figures that the generators G7 and G16 participate for up generation for bid block 1 and G7 participate for up regulation for bid block 2 and G7 and G13 bid block-3 for congestion management. The generators G13, G16, and G18 decrease their generation for bid blocks 1 and 2 and 3 during congestion management. The pattern of the participation of generators is different for each bid block and hour. The new gener-

Fig. 8a. Up generation for bid block-1 with SSSC.

Fig. 8b. Up generation for bid block-2 with SSSC.

Fig. 8c. Up generation for bid block-3 with SSSC.

Fig. 8d. Down generation for bid block-1 with SSSC.

Fig. 8e. Down generation for bid block-2 with SSSC.

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Fig. 8f. Down generation for bid block-3 with SSSC.

Fig. 9a. New Pg for bid block-1 with SSSC.

Fig. 10a. Up generation for bid block-1 with UPFC.

Fig. 9b. New Pg for bid block-2 with SSSC.

Fig. 10b. Up generation for bid block-2 with UPFC.

Fig. 9c. New Pg for bid block-3 with SSSC.

Fig. 10c. Up generation for bid block-3 with UPFC.

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Fig. 10d. Down generation for bid block-1 with UPFC.

Fig. 11a. New Pg for bid block-1 with UPFC.

Fig. 10e. Down generation for bid block-2 with UPFC. Fig. 11b. New Pg for bid block-2 with UPFC.

Fig. 10f. Down generation for bid block-3 with UPFC.

ation schedule obtained for each bid block after congestion management is shown in Figs. 9a–c. The new generation schedule patterns are different for each bid blocks after the removal of the congestion. Comparing the patterns of generation before and after the congestion, the optimal outputs of each generator are different corresponding to each bid block and hour due to different up and down regulation of generator at each bus and hour. The generators at bus 7 and 16 from bid block-1, at bus7 from bid block-2 and at buses 7 and 13 from bid block-3 goes up generation for congestion management. The generator at buses 13, 16 and 18 from every bid block goes down generation to manage the congestion. With implementation of SSSC total amount of up/ down generation reduces considerably compared to without SSSC as well as STATCOM as observed from figures. Thus, the congestion cost reduces compared to STATCOM and without any FACTS.

4.1.4. Congestion management with generators’ rescheduling with UPFC The up and down generation for each bid block are shown in Figs. 10a–f. It is observed from the figures that the generators

Fig. 11c. New Pg for bid block-3 with UPFC.

G2, G7 and G13 participate for up generation for bid block 1 and G2 and G13 participate for bid block 2. G2, G7 and G13 participate for up generation for bid block-3 for congestion management. The generators G2, G7, G13, G18, and G21 decrease their generation for bid blocks 1 and G2, G7, G13, G16 decrease their generation for bid blocks 2 and 3 during congestion management. The pattern of the participation of generators is different for each bid block during a day. The new generation schedule obtained for each bid block after congestion management is shown in Figs. 11a–c. The new generation schedule patterns are different for each bid blocks after the removal of the congestion. Comparing the patterns of generation before and after the congestion, the optimal outputs of each generator are different corresponding to each bid block due to different up and down regulation of generator at each bus and hour. With UPFC, the pattern of generator participation for congestion management is different compared to STATCOM and SSSC. If the total area of up/down generation is considered as deviation, the deviation is observed less compared to without FACTS controllers.

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Fig. 12. Comparison of congestion cost without and with FACTS controllers.

Table 1 Congestion cost ($/h) without and with FACTS controllers. Hour

CC WOF

CC with STATCOM

CC with SSSC

CC with UPFC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1423.883 2469.416 2467.761 2469.312 1629.876 2290.747 1533.183 2017.799 1954.529 1937.01 1996.582 1640.745 2129.508 1320.633 2226.414 1617.94 1281.845 2186.182 1876.734 2046.983 1931.084 2183.008 2486.312 1311.894

1419.016 2453.723 2452.622 2453.619 1621.797 2274.724 1521.927 2010.111 1946.816 1928.832 1981.933 1629.621 2114.009 1313.057 2210.751 1606.322 1272.399 2170.831 1868.948 2031.743 1922.941 2167.94 2470.577 1306.162

905.1434 1832.932 1844.231 1834.881 1229.231 1686.369 1114.982 1433.091 1375.261 1346.322 1403.584 1115.914 1515.825 858.0169 1593.575 1172.855 859.3217 1571.635 1311.55 1442.095 1357.156 1590.654 1867.34 862.9572

948.5374 1387.875 1384.421 1387.779 1328.204 1254.264 916.6688 1034.346 1029.419 1016.501 1048.505 936.5463 1147.861 827.45 1419.365 1096.734 841.7865 1181.58 1055.65 1086.991 1212.764 1177.666 1402.682 954.9964

The overall generation rescheduling is observed lower compared to STATCOM and SSSC and without FACTS. Due to lower values of generation rescheduling, the congestion cost is also observed lower with UPFC compared to other cases. From the results obtained, the comparison of congestion cost for 24 h without and with FACTS devices has been shown in Fig 12 and the congestion cost is also given in Table 1 for a day. The comparison of total congestion cost is also presented in Table 2. It is observed that with the presence of STATCOM, the congestion cost reduces compared to the case without STATCOM although the reduction in the cost is marginal. The congestion cost reduces considerably with SSSC and UPFC. The overall congestion cost is found minimum with UPFC compared to other FACTS devices and without FACTS devices. The loadability is found higher with UPFC

Fig. 13a. Base case Pg for bid block-1.

Fig. 13b. Base case Pg for bid block-2.

compared to other devices thus have more voltage stability margin compared to other devices. 5. Results for IEEE 57 bus system The results have been also been obtained for multi-line congestion case with three bid function. For creating the congestion, the

Table 2 Comparison of congestion cost, losses and loadability factor. Congestion cost of day

WOF

STATCOM

SSSC

UPFC

Cost ($)/day Total real power loss (p.u.) Total reactive power loss (p.u.) Loadability factor

46429.38 0.4775 1.2838 1.042765

46150.42 0.4816 1.2863 1.052606

33124.92 0.610 0.57285 1.137438

27078.6 0.5181 1.4445 1.178804

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Fig. 14d. Down generation for bid block-1.

Fig. 13c. Base case Pg for bid block-3.

Fig. 14e. Down generation for bid block-2.

Fig. 14a. Up generation for bid block-1.

Fig. 14f. Down generation for bid block-3.

Fig. 14b. Up generation for bid block-2.

Fig. 14c. Up generation for bid block-3. Fig. 15a. New Pg for bid block-2.

power flow ratings of the two lines 15th and 18th have been taken 0.5 p.u. compared to its given rating of 1.00 p.u. The results have been obtained with FACTS devices. However, the results obtained without FACTS and with UPFC have been provided in this section. The optimal location of STATCOM has been obtained at bus 15. The optimal location of SSSC and UPFC has been obtained at line 15–3.

5.1. Results without FACTS devices The base case generation for three bid blocks taking stability limit into account is obtained solving ELD problem described in Section 2. The base case economic load dispatch is shown in Figs.

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Fig. 16c. Up generation for bid block-3. Fig. 15b. New Pg for bid block-2.

Fig. 16d. Down generation for bid block-1.

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

Fig. 16e. Down generation for bid block-2.

Fig. 16a. Up generation for bid block-1.

Fig. 16f. Down generation for bid block-3.

Fig. 16b. Up generation for bid block-2.

13a–c. It is observed that the base case generation share for bid block 1 is higher compared to the generation share for bid blocks 2 and 3. This is due to the fact that the cost of bid blocks 2 and 3

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

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

agement by decreasing their generation are: G2 and G3 for bid block 1, G2, G7 for bid block 2, and G3 and G7 for bid block 3. The pattern of the participation of generators is different for each bid block during a day. The new generation schedule patterns are different for each bid blocks after the removal of the congestion is shown in Figs. 17a–c. Comparing the patterns of generation before and after the congestion, the optimal outputs of each generator are different corresponding to each bid block due to different up and down regulation of generator at each bus and hour. With UPFC, the generators are subjected to lower rescheduling compared to the case with STATCOM and SSSC and without FACTS devices. The congestion cost obtained without and with FACTS devices is shown in Fig. 18. The congestion cost obtained with UPFC is found lower compared to the congestion cost obtained with other FACTS devices and without FACTS device. The total congestion cost for 24 h without FACTs devices is 41428.7697$/h. The congestion cost with STATCOM is 38420.9410$/h, with SSSC is 36095.9971$/h, and with UPFC is 15621.4467$/h. With FATS devices there is considerable reduction in the congestion cost as generators are subjected to lower values of up and down rescheduling with FACTS devices. 6. Conclusions

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

Fig. 18. Comparison of congestion cost without and with FACTS controllers.

are comparatively higher compared to the bid block1. The up and down generation and new generation reschedule are shown in Figs. 14a–f. G3, G5 and G11 participate for up generation for bid block 1. In bid block 2, the generators G1, G2, G3, G5, G7, G8, and G11 participate for down generation, however, the participation of G1, G2, and G3 is lower compared to other generators. For bid block-3, the G1, G2, G3, G5, G7, G8, and G11 participate for down generation; however, the participation of G1, G2, G3 is lower compared to other generators. Similarly, the down generation for all bid blocks is shown in Fig. 14d–f. The generators participate for up and down rescheduling at different hours. The new optimal generation schedule after congestion management is shown in Figs. 15a–c. 5.2. Results with UPFC The up and down generation for each bid block are shown in Figs. 16a–f. It is observed from the figures that the generators which participate for congestion management regulating their generation up for different bid blocks are: G3, G5 and G11 for bid block 1 and G5 and G11 for bid block 2, G5, G8 and G11 for bid block-3. The generators which participate for congestion man-

In this work, the congestion management based on generators’ rescheduling with three bid block structure has been carried out ensuring static security and voltage stability limits. The 24 h variation of load has been incorporated taking load scaling factor into account. The congestion cost for each hour of day has been calculated without and with FACTS controllers and comparison has been made. The economic load dispatch results are obtained as base data during congestion management. The results shows the congestion cost reduces with FACTS controllers compared to the case without FACTS controllers. The congestion cost reduction is found lowest with UPFC compared to other FACTS devices. The comparison has been made on total congestion cost of day, real power loss, and reactive power loss and loadability factor. With UPFC, the loadability margin of the system is higher compared to other devices. The three bid blocks offered by Gencos for congestion management will be helpful to the ISO with renewable energy sources integration in the system. The authors are working in this direction with more renewable energy sources in the system and offering themselves for congestion control during congestions hours. References [1] Shahidehpour Mohammed, Alomoush Muwaffaq. Restructured electrical power systems, operation, trading, and volatility. New York: Marcel Dekker, Inc.; 2001. [2] Finney JD, Othman HA, Rutz WL. Evaluating transmission congestion constraints in system planning. IEEE Trans Power Syst 1997;12(3):1143–9. [3] Singh H, Hao S, Papalexopoulos A. Transmission congestion management in competitive markets. IEEE Trans Power Syst 1998;13(2):672–80. [4] Bompard E, Carpenato E, Chicco G, Gross G. The role of load demand elasticity in congestion management and pricing. In: Proc IEEE PES, summer meeting, vol. 4; 16–20 July 2000. p. 2229–34. [5] Hao S, Shirmohammadi D. Congestion management with Ex Ante pricing for decentralized markets. IEEE Trans Power Syst 2002;17(4):1030–6. [6] Gan D, Bourcier DV. Locational market power screening and congestion management: experience and suggestions. IEEE Trans Power Syst 2002;17(1):180–5. [7] Alomoush MI, Shahidehpour SM. Fixed transmission rights for zonal congestion management. IEE Proc Gener Transm Distrib 1999;146(5):471–6. [8] Alomoush MI, Shahidehpour SM. Generalized model for fixed transmission rights auction. Electr Power Syst Res 2000;54(June):207–20. [9] Yu CN, Ilic M. An Algorithm for implementing transmission rights in a competitive power industry. In: Proc IEEE PES, winter meeting; February 2000. p. 1708–14. [10] Shirmohammadi D, Wollenberg B, Vojdani A, Sandrin P, Pereira M, Rahimi F, et al. Transmission dispatch and congestion management in the emerging energy market structures. IEEE Trans Power Syst 1998;13(4):1466–76.

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