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J. Inst. Eng. India Ser. B DOI 10.1007/s40031-015-0211-7
ORIGINAL CONTRIBUTION
FACTS Devices Cost Recovery During Congestion Management in Deregulated Electricity Markets Ashwani Kumar Sharma1 • Ram Kumar Mittapalli1 • Yash Pal1
Received: 1 August 2014 / Accepted: 4 June 2015 Ó The Institution of Engineers (India) 2015
Abstract In future electricity markets, flexible alternating current transmission system (FACTS) devices will play key role for providing ancillary services. Since huge cost is involved for the FACTS devices placement in the power system, the cost invested has to be recovered in their life time for the replacement of these devices. The FACTS devices in future electricity markets can act as an ancillary services provider and have to be remunerated. The main contributions of the paper are: (1) investment recovery of FACTS devices during congestion management such as static VAR compensator and unified power flow controller along with thyristor controlled series compensator using non-linear bid curves, (2) the impact of ZIP load model on the FACTS cost recovery of the devices, (3) the comparison of results obtained without ZIP load model for both pool and hybrid market model, (4) secure bilateral transactions incorporation in hybrid market model. An optimal power flow based approach has been developed for maximizing social welfare including FACTS devices cost. The optimal placement of the FACTS devices have been obtained based on maximum social welfare. The results have been obtained for both pool and hybrid electricity market for IEEE 24-bus RTS. Keywords Congestion management Ancillary services FACTS devices cost recovery Hybrid electricity market ZIP load
& Ashwani Kumar Sharma [email protected] 1
Department of Electrical Engineering, National Institute of Technology Kurukshetra, Kurukshetra 136119, Haryana, India
List of symbols bij Bi ðPDi Þ ¼ b1di P2Di þb2di PDi þ b0i BSVC Ci ðPGi Þ ¼ ai P2Gi þbi PGi þ ci CS (CS)without FACTS (CS)with
FACTS
CSVC CTCSC CUPFC CFACTS annual CFACTS DF FACTS r Gij;eff ¼ r2 þðx ijx Þ2 ; ij x c Þ ij ðx Bij;eff ¼ r2 þðxij xc Þ2 ij c ij GD, GDij
GDmax ij ISO Nb Ng PS (PS)without (PS)with
FACTS
FACTS
Weighing factor indicating the importance of a particular transaction Bid function for the loads Susceptance of SVC Bid function for the generators Consumer surplus Consumer surplus without FACTS devices Consumer surplus with FACTS devices Cost function of SVC Cost function of TCSC Cost function of UPFC Cost with FACTS devices Annual cost with FACTS devices ac distribution factors Flexible ac transmission systems Effective conductance and susceptance with TCSC Represents a bilateral contract between a supplier (Pgi) of row i with a consumer (Pdj) of column j Maximum transaction amount Independent system operator Number of buses in the system Set of generators Producer surplus Producer surplus without FACTS devices Producer surplus with FACTS devices
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J. Inst. Eng. India Ser. B
Pdp, Pdb Pfp, Pfb Pgp, Pgb Pgi Pi max Pmin gi ; Pgi Pgi, Qgi Pdi, Qdi Qi max Qmin gi ; Qgi QSVC Rannual FACTS Sij, Sij Smax ij SVC TCSC UPFC Vi Vsh,, dsh, Vse, dse Vimin ; Vimax Yij ¼ Gij þ Bij di max dmin i ; di gen k , kload kgen;FACTS , kload;FACTS
Vector of pool and bilateral demand Vector of line flows due to the pool and bilateral transactions Vector of pool and bilateral generation Active power pool generator-i Real power injection at bus-i Minimum and maximum generation limit Real and reactive power generation at bus-i Real and reactive power demand at bus-i Reactive power injection at bus-i Minimum and maximum generation limit Reactive support provided by SVC Annual revenue earned with FACTS devices Line flow limit Static VAR compensator Thyristor controlled series compensator Unified power flow controller Voltage magnitude at bus-i Shunt voltage and angle, series injected voltage and angle for UPFC Upper and lower voltage magnitude limit i-j th element of Y-bus matrix Load angle at bus-i Upper and lower angle limit Nodal price at generator and load buses without FACTS devices Nodal prices at the generator and load buses with FACTS devices
Introduction With the emerging competitive electricity markets, new technical challenges have emerged with many market players negotiating power purchase from market at competitive prices in a pool or bilateral coordinated electricity markets. The independent system operator (ISO) has to provide fair and transparent access to all market participants with more and bilateral negotiations of power purchase that may lead to congestion in the transmission system and may threaten system security. The congestion management has become a challenging issue for the ISO for better market operation as it may lead market inefficiency due to rise in the nodal prices with the change in
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generation schedule [1, 2]. The electricity price will not be able to operate at its competitive equilibrium in congested systems in economic terms and may lead to ‘dead weight’ loss to the society. In order to alleviate congestion, some inexpensive generators in congested zone have to reduce their dispatch and some expensive generators in congested zone have to increase their dispatch. This can further lead to creation of local ‘market power’ and hinders the development of competitive environment in electricity trade [3]. When the system operator sets the electricity price and decides the dispatch amount in order to alleviate congestion, the operation of transmission directly affects the profit of the market participants. Thus, in recent years, congestion management has been a subject of great concern in deregulated electricity market. The market based approaches can be categorized based on locational marginal prices, price area zones, financial transmission rights, generation rescheduling, and load curtailment which are well explained [4–18]. A decomposition of spot prices to reveal congestion and the differences in the locational marginal prices reflect the presence of congestion in a transmission system and the customers charges are based on these locational differences in [4], assessment of impact of congestion to develop appropriate price signals in the pool paradigm for congestion management by Bompard et al. in [5], transmission congestion based on ex ante congestion prices are explained in [6]. A 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 are presented in [7, 8]. Re-dispatching based schemes and application of FACTS to manage transmission congestion minimizing the congestion cost is presented by many authors [9–19]. Fang and David [9, 10] proposed a transmission dispatch methodology as an extension of spot pricing theory in a pool and bilateral as well as multilateral transactions model with willingness-to-pay for minimum curtailment to deal with the congestion, Ref. [11] presented optimal power dispatch in the presence of congestion, basic concepts using three approaches to mange congestion are proposed [12] and Bompard et al. [13] developed a unified framework and compared the various CM approaches so as to assess their efficiency and effectiveness of the market signals provided to the market participants. Tuan et al. proposed an interruptible load services during congestion management [14]. A comprehensive literature survey of congestion management methods and their categorization are presented [15]. A congestion management approach based on real and reactive power congestion distribution factors based zones and generator’s rescheduling was proposed [16, 17]. Many authors developed the methodology to incorporate FACTS devices to manage the transmission
J. Inst. Eng. India Ser. B
congestion [18–27]. Recently demand side management (DSM) has been considered as a tool for congestion management in deregulated electricity markets [28–31]. For better utilization of existing power system, the role of FACTS devices has become imperative with benefits of increasing power transfer capability, security and stability of the transmission network [32–36]. The modeling of FACTS devices and their impact for loadability enhancement, real and reactive nodal prices determination in deregulated electricity markets are presented [37–41]. The ISO has to ensure secure bilateral transactions for dispatch of generators and these transactions have been determined [42–44]. These transactions have been incorporated along with pool transactions for the study of hybrid system. The ISO may procure the services of FACTS devices as an ancillary service and since, the capital as well as running cost is involved in the installation of FACTS devices and therefore, have to remunerate their services. Several studies, based on OPF calculations, have been carried out to determine the optimal placement of such devices in the system in order to get the maximum benefits out of their capabilities [45–52]. Some of the previous studies took into account the cost of FACTS devices and these can provide cost effective solution [53]. Generally, there are still very few studies of economic benefits arising from installation of FACTS devices. Most of the authors have concentrated on constant P-Q load models; however, the generic load model consideration is essential. The composite constant impedance-currentpower (ZIP) [54, 55] model has widely accepted as a default model among utility industries. The FACTS devices cost model has also been included in an optimization model and the methodology for FACTS cost remuneration was tested for five bus test system with TCSC only in [56]. The study was conducted with P,Q load considering the linear bid curves. However, generic load model incorporation is essential to incorporate as during congestion the voltage profile in the network become poor and bid curves are also non-linear in nature. In this study, a FACTS cost remuneration based approach described in [56] has been extended with three types of FACTS devices (static VAR compensator (SVC), thyristor controlled series capacitor (TCSC), and unified power flow controller (UPFC). The OPF based approach is employed to solve the non-linear optimization problem of maximizing social welfare. Optimal location of the devices has been obtained based on the procedure developed in [56] considering non-linear bid curves. The impact of ZIP load model has also been incorporated. The results have been obtained for pool market along with the secure bilateral transactions with constant P-Q and ZIP load model. The GAMS and MATLAB interfacing has been utilized to obtain optimal values calling CONOPT solver
[57, 58]. The results have been obtained on IEEE RTS-24 test system [59].
Mathematical Model of FACTS Devices and Cost Function In this section, the model of the FACTS devices for congestion management has been presented. For such applications, FACTS devices can be modeled as Power Injection Model (PIM) [37, 38]. The injection model describes the FACTS as a device that injects a certain amount of active and reactive power to a particular selected node, so that the FACTS device is represented as PQ element. The advantage of PIM is that it does not destroy the symmetrical structure of the admittance matrix and allows easy integration of FACTS devices into existing power system software tools [37, 38]. In this paper three FACTS devices namely SVC, TCSC, UPFC, is used to demonstrate the effectiveness of the proposal for investment recovery of these devices. Static VAR Compensator (SVC) The static VAR compensator (SVC) is a shunt compensation device comprising of fixed capacitor and variable inductor controlled through firing angle. It is originally designed for voltage maintenance in power systems. Operation of SVC is controlled by the adjusting by the selection of the firing angle of GTOs (Gate turn off transistors) or thyristors to change the reactance of inductor. During operation SVC behaves like shunt variable susceptance. SVC can work in inductive or capacitive region. For the steady state operation, constant susceptance model is considered. SVC is connected on any bus i shown in Fig. 1 [37]. The reactive power injection at bus i is given by QSVC ¼ Vi2 BSVC
ð1Þ
The cost function of SVC is given by an expression [47] CSVC ¼ 0:0003 s2 0:3051 s þ 127:38 $=kVAR
ð2Þ
Thyristor Controlled Series Compensator (TCSC) The model of a transmission line with TCSC connected between buses i and j is shown in Fig. 2. TCSC behaves as variable capacitive reactance. It reduces the line reactance during the operation which improves the power transfer capability. It works on the principle of series compensation. Reactance of TCSC is the function of firing angle of the thyristors. But the steady-state impedance of the TCSC is that of parallel LC circuit consisting of fixed capacitive
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J. Inst. Eng. India Ser. B
Vi
Vi
Pijc + jQ cij
Iij
Vs
Bus i
Zse
e
Pjic + jQ cji
Iji
Bus j
Ish Vi
XC
BSVC XL
Vj
Fig. 3 Model of UPFC
-jXc
Pji+jQji
Zij=Rij+jX Bus i
Re(V I∗ − V I* ) = 0 sh sh se ji
Vsh
Fig. 1 SVC and SVC variable susceptance
Pij+jQij
Zsh
jBc
Bus j
connected with the line with two coupling transformers. In the steady state operation, the main objective of an UPFC is to control voltage and power flow. The power injected model of UPFC is as shown Fig. 3 [37, 38]. The active power and reactive power equations at bus i and bus j can be written as: Pcij ¼ Vi2 ðGii þ Gsh Þ þ Vi Vj ½Gij cosðdij Þ þ Bij sinðdij Þ þVi Vse ½Gij cosðdi dse Þ þ Bij sinðdi dse Þ þVi Vsh ½Gsh cosðdi dsh Þ þ Bsh sinðdi dsh Þ
ð8Þ
Qcij ¼ Vi2 ðBij þ Bsh Þ þ Vi Vj ½Gij sinðdij Þ Bij cosðdij Þ
Fig. 2 Model of TCSC
þVi Vse ½Gij sinðdi dse Þ Bij cosðdi dse Þ þVi Vsh ½Gsh sinðdi dsh Þ Bsh cosðdi dsh Þ impedance. The static model of TCSC is as shown in Fig. 2 [37, 38]. The power injection equations are Pcij ¼ Vi2 Gij;eff þ Vi Vj ðGij;eff cos dij þ Bij;eff sin dij Þ
ð3Þ
Qcij ¼ Vi2 ðBij;eff þ Bc Þ þ Vi Vj ðGij;eff sin dij Bij;eff cos dij Þ ð4Þ Pcji ¼ Vj2 Gij;eff þ Vi Vj ðGij;eff cos dji þ Bij;eff sin dji Þ
ð5Þ
Qcji ¼ Vj2 ðBij;eff þ Bc Þ þ Vi Vj ðGij;eff sin dji Bij;eff cos dji Þ ð6Þ where effective conductance and susceptance is given as rij Gij;eff ¼ 2 rij þ ðxij xc Þ2 Bij;eff ¼
ðxij xc Þ rij2
The cost function of TCSC is given by [47] ð7Þ
Unified Power Flow Controller (UPFC) An UPFC consists of two converters based on GTO (gate turn off), one is series connected and another is shunt
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Pcji ¼ Vj2 Gjj þ Vi Vj ½Gij cosðdij Þ þ Bij sinðdij Þ þ Vj Vse ½Gij cosðdj dse Þ þ Bij sinðdj dse Þ
ð10Þ
Qcji ¼ Vj2 Bij þ Vi Vj ½Gij sinðdij Þ Bij cosðdij Þ þ Vj Vse ½Gij sinðdj dse Þ Bij cosðdj dse Þ
ð11Þ
The operating constraint for UPFC Vi Vse ½Gij cosðdi dse Þ Bij sinðdi dse Þ þ Vj Vse ½Gij cosðdj dse Þ Bij sinðdj dse Þ þ Vi2 Gsh þ Vi Vsh ½Gsh cosðdi dsh Þ Bsh sinðdi dsh Þ ¼ 0 ð12Þ The cost function of UPFC is given by [47] CUPFC ¼ 0:0003 s2 0:2691 s þ 189:22 $ /kVAR ð13Þ
þ ðxij xc Þ2
CTCSC ¼ 0:0015 s2 0:7130 s þ 153:75 $=kVAR
ð9Þ
The cost function of the FACTS devices as presented in [47] is shown in Fig. 4 and has been utilized for FACTS cost calculation along with the social welfare maximization in pool and hybrid market model. The impact of FACTs devices on producer and consumer surplus during the congestion management has been obtained so that FACTS devices can be remunerated according to their services in the electricity markets.
J. Inst. Eng. India Ser. B
constant P, Q as well as generic load model (ZIP load). The formulation has been discussed for pool and bilateral market model. Problem Formulation Constant P-Q Load Model Pool Market Model
Fig. 4 Cost functions of the FACTS devices: SVC, TCSC and UPFC. Red curve upper limit: total investment costs; blue curve lower limit: equipment costs: UPFC:TCSC:SVC. (Color figure online)
The operating range of FACTS devices has been obtained based on maximum social welfare solving nonlinear program as discussed earlier. Once the optimum compensation level is found, the corresponding cost of FACTS is calculated from above equations. The cost can be compared with revenue (or benefit) that can be derived from FACTS. In this paper, the comparison is made by converting the cost, as well as the benefit (or revenue) into annual cost (annuity) (US$/year). To compute the annual capital cost and benefit (revenue) of FACTS, the following assumptions have been made: Project lifetime (n): 5 years Discount rate(r): 10 % Average utilization (u): 40 %
i2Ng
Operational cost of FACTS device is neglected. Annual capital cost of FACTS in US$/year can be found as: r ð1 þ r Þn Annual CFACTS ¼ CFACTS s 1000 ð14Þ ð1 þ r Þn 1 The revenue from the use of FACTS is based on additional surplus and have the unit of ‘‘US$/h’’. Annual revenue from use of FACTS in US $/year can be determined as: RAnnual FACTS
¼ CFACTS 8760 u
In a pool market, the ISO dispatches optimally all the generators such that the social welfare is maximized respecting power injection equations as equality constraints and voltage, angle, power flow limits as inequality constraints. The impact of FACTS devices on the social welfare can be accounted taking the cost function of FACTS devices together with the social welfare function. The social welfare function comprises bids offered to the ISO by the Gencos and Discos. These bid functions have been taken as the quadratic bid functions. The objective of the OPF program is to minimize the total cost which is equivalent the maximization of the social welfare. The OPF program calculates the spot prices and the amount of optimal power the Gencos produce and Discos consume. The consumers can be billed based on the spot prices at respective buses. The formulation of social welfare maximization together with the FACTS devices cost function can be expressed as follows: min Ctotal ¼ CFACTS ðsÞ þ Csurplus Pgi ; Pdi ð16Þ ! X X Ci Pgi Bi ðPdi Þ ð17Þ Csurplus ¼ i2Nd
Cost of FACTS devices are represented as quadratic cost functions. The bid offers from the producers and consumers can be expressed as quadratic functions with their cost coefficients. Ci ðPGi Þ ¼ ai P2Gi þ bi PGi þ ci Bi ðPDi Þ ¼ b1di
P2Di
In this section, an optimization based approach of maximizing social welfare with FACTS devices cost function has been formulated. The loads have been modeled as
þ b2di PDi þ b0i
ð19Þ
Subject to: Equality constraints: Pi ¼ Pgi Pdi ¼
Nb X
Vi Vj ½Gij cosðdi dj Þ
ð20Þ
j¼1
ð15Þ
An Optimal Power Flow Based Approach for FACTS Devices Remuneration for Congestion Management
ð18Þ
þ Bij sinðdi dj Þ Qi ¼ Qgi Qdi ¼
Nb X
8 i ¼ 1; 2; . . .Nb
Vi Vj ½Gij sinðdi dj Þ
ð21Þ
j¼1
þ Bij cosðdi dj Þ 8 i ¼ 1; 2; . . .Nb Pij ¼ Vi2 Gij Vi Vj Gij cos di dj þ Bij sin di dj ð22Þ
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J. Inst. Eng. India Ser. B
Qij ¼ Vi2 Bij þ Vi Vj Bij cos di dj Gij sin di dj ð23Þ
Pji ¼ Vj2 Gij Vi Vj Gij cos di dj Bij sin di dj
ð24Þ
Inequality constrains: Real and reactive power generation for generators is given as follows max Pmin g Pg Pg
ð25Þ
max Qmin g Qg Qg
ð26Þ
Transaction limit between seller bus-i and buyer bus j can be written as max GDmin ij GDij GDij
ð27Þ
Limits on voltage magnitude and angle can be expressed as Vimin Vi Vimax
ð28Þ
di dmax dmin i i
ð29Þ
MVA power flow limit is given by P2ij
þ Q2ij Smax2 ij
ð30Þ
Hybrid Market The problem formulation in pool plus bilateral market consists of the above equations along with some additional constraints as power balance equations for demand and generation for hybrid market model using bilateral demand matrix GD. In addition to power balance equations, the bilateral matrix follows limits to be respected and can be added as a range rule. The methodology for the computation of secure bilateral transactions in a hybrid market model is well explained in [43]. The bilateral transactions can be represented as the bilateral negotiations between Gencos (G) and Discos (D). ½GD ¼ DGT ð31Þ Each element of GD, namely GDij, represents a bilateral contract between a supplier (Pgi) of row i with a consumer (Pdj) of column j. Furthermore, the sum of row i represents the total power produced by generator i and the sum of column j represents the total power consumed at load j. GD can be expressed as 2 3 GD1;1 . . .GD1;nd 6 7 GD 4 GD2;1 . . .GD2;nd 5 ð32Þ GDng;1 . . .GDng;nd where, ng is the number of generators; and nd is the number of loads.
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In general, the conventional load flow variables generation (Pbg) and load (Pbd) vectors are now expanded into two dimensional transaction matrix as given in (33). "
Pbd Pbg
#
GDT ¼ 0
0 GD
"
ug ud
# ð33Þ
Vector ug and ud are column vectors of ones with the dimensions of ng and nd respectively. There are some intrinsic properties associated with this transaction matrix GD (32). These are column rule, row rule, range rule, and flow rule. These properties have been explained in [42]. Each contract has to range from zero to a maximum allowable value, GDmax ij . This maximum value is bounded by the value of corresponding Pmax or Pdj whichever is gi smaller. The range rule satisfies:
max 0 GDij GDmax ð34Þ ij min Pgi ; Pdj It is also possible for some contracts to be firm so that GD0ij is equal to GDmax [20]. According to flow rule the line ij flows of the network can be expressed as follows: h i Pline ¼ DFAC Pbg Pbd ð35Þ The matrix DFAC is the distribution factors matrix [43]. If the representations of the Pbg and Pbd are substituted by using the definition of GD, the line flows can be expressed in an alternative as follows:
Pline
2 3 1 6 .7 7 ¼ DF GD GDT 6 4 .. 5
ð36Þ
1 With secure bilateral transaction matrix, the power injection equations can be modified with bilateral demand along with the pool demand. Problem Formulation with ZIP Load The general formulation of the problem is same as that without ZIP load. However, the loads are represented as a function of ZIP load coefficients and the voltages at each buses corresponding to the base case voltages. The real and reactive power injection equations are modified for ZIP load model as [54, 55]: Pi ¼ Pgni Pdni
ð37Þ
Qi ¼ Qgni Qdni
ð38Þ
where the real and reactive ZIP loads are represented as [55]:
J. Inst. Eng. India Ser. B
"
# Vi Pdni ¼ Pd0 ap þ bp þ c p V0i " # Vi 2 Vi aq þ b q þ cq Qdni ¼ Qd0 V0i V0i Vi V0i
2
ð39Þ
$/MWh C A
ð40Þ
Consumer surplus
*
D B
Producer surplus
The ZIP load coefficients with real and reactive power demand are ap ? bp ? cp = 1 and aq ? bq ? cq = 1. The different combinations of ZIP load coefficients have been taken for the Pdni and Qdni calculation in the power injection equations considering their impact on the investment recovery of FACTS devices.
Aggregate supply curve
Aggregate demand curve
Production cost O
P*
MW
Fig. 5 Surplus under unconstrained case
Investment Recovery of FACTS Devices for Congestion Management In the electricity market, Gencos and Discoms are the entities to generate and consume power. The generation companies sell power at a marginal price to recover the cost of capital investment and operating costs with a marginal profit to execute the new plant after the life of the plant is over. In a competitive electricity markets, both the Gencos as well as consumer must get benefits in terms of producer’s profit and the consumer’s benefit. The sum of Gencos and consumer surplus represents the social profit or social welfare (SW). Both the parties obtain the surplus for the economic and efficient electricity market operation. Thus, the objective of maximizing the social welfare recovers the price the electricity and makes the market operation economically efficient and viable. With both bid based market mechanism in a competitive electricity markets, the market clearing (MCP) is obtained at the point of cross section of aggregate marginal cost of production of Gencos and the aggregate willingness to pay curve of loads at point D as shown in Fig. 5. The MCP is denoted as k* at the cross section of aggregate curves corresponding to a power P* under unconstrained transmission case. The market equilibrium is disturbed due to the physical limits violation of the transmission system and other reasons like voltage limits, generation capacity constraints etc. Due to the transmission constraints called as transmission system congestion, the social surplus reduces as congestion rent. With a transmission physical limits violations, the power transfer will reduce from P* to Plimit as shown in Fig. 6. There will be two different prices at the two buses due to congestion in the network. At generator surplus bus the price reduces and at consumer bus the price goes up. This causes decrease in both consumer and producer surplus as shown in Fig. 6. An area representing a surplus loss with an arrow is shown in the Fig. 6. The congestion results an overall loss to society called as ‘dead-weight’
loss [56]. The congestion cost collected by the ISO is used either to compensate for the losses or to reinforce the transmission grid or transfer to the participants based on market rules. The price and quantity can be solved by solving the optimization problem with the objective of social welfare maximization subject to equations for power balance, line limits, voltage limits, and capacity limits constraints. The Lagrange multiplier of the real power balance equation as equality constraint gives the nodal price of energy. The producer’s surplus (PS) and consumer’s surplus (CS) can be calculated using equations based on the bid curves for both demand and supply submitted to the ISO and market clearing price. Form Fig. 5, PS and CS surplus can be defined. Producer surplus (PS) can be calculated as: Z Pdi PS ¼ ðki CðPgi ÞÞoPgi ; i 2 Ng ð41Þ Pmin di
Consumer surplus (CS) can be calculated as: Z Pdi ðC ðPdi Þ ki ÞoPdi ; i 2 Nd CS ¼
ð42Þ
Pmin di
C
Consumer surplus
surplus loss A
load
D Congestion cost
B Aggregate demand curve
gen
Producer surplus O
Aggregate supply curve
Production cost Plimit
P*
MW
Fig. 6 Surplus under constrained case
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J. Inst. Eng. India Ser. B
The congestion rent is given as: X X ðki Pdi Þ ki Pgi CC ¼ i2Nd
ð43Þ
i2Ng
A
E load
where ki is the price of energy (that is, LMP) at bus i, the cost functions taken as quadratic equations for both producer and consumer is given as the quadratic generator bid curve and quadratic demand bid curve. Remuneration Cost Calculation for FACTS Devices During Congestion Management The FACTS devices have the capability of changing power flow patterns and voltage profile improvement in the network. With their incorporation in the network, these devices control transmission congestion due to change in the power flow patterns. These devices help the ISO for security enhancement and in future can play a role of ancillary service providers. Since huge capital cost is involved for their installation and these devices needs to be remunerated to recover capital as well as operating cost during their life time as an ancillary service providers. With the incorporation of FACTS devices, the resulting situation for the simple two-bus system as an example is shown in Fig. 6 also explained well in [57]. In the case of transmission congestion, the decrease in producer and consumer surplus as a congestion cost is shown in Fig. 7 with area EGHFE. The nodal price at generator and load buses is kgen and kload respectively. The congestion rent collected by the ISO shown by area EGHFE can be calculated as the product of the price differences and the area maximum flow through the link, that is, Plimit(kload - kgen). With FACTS devices installed in the system for congestion control, the Plimit increase to PFACTS and the nodal prices at the generator and load buses changes and are kgen;FACTS and kload;FACTS respectively. Therefore, the congestion cost now is represented by an area IMNJI. The congestion rent collected by the ISO shown by an area IMNJI can be calculated as the product of the price difference and the area maximum flow through the link, that is, PFACTS(kload,FACTS - kgen,FACTS) as shown in Fig. 7. Comparing areas with and without FACTS devices, the congestion cost reduces with FACTS devices with improvement in both consumer and producer surplus. The congestion rent that the ISO collect from the market participants, due to LMP difference at source and sink decreases due to the decrease in nodal prices difference. There is considerable increase in the surplus of consumer as shown by area IMCI as well as producer surplus shown by area JNOJ as shown in Fig. 7. Comparing the areas in the Fig. 7 with FACTS, the corresponding increase in the producer surplus is EGMIE and producer surplus is JNHFJ. The surplus areas are also shown in Figs. 8, 9 and the surplus loss as dead weight also decreases.
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surplus lossnew
Consumer surplus
$/MWh C
G
load,FACTS
Congestion K L cost
J gen,FACTS
B
N
Aggregate demand curve
F
gen
Aggregate supply curve
M D
I
H
Production cost
Producer surplus O
Plimit
P*
MW
PFACTS
Fig. 7 Surplus under constrained case with FACTS
The corresponding increase in both producer and consumer surplus is due to the impact of FACTS devices and it can be considered as a benefit to FACTS devices installation. This increase in surplus can be transferred to investment on FACTS devices and recovery of operational cost of FACTS devices. The increase in the consumer surplus is shown in Fig. 8 as an area EMIE. This increase in the producer can be calculated knowing the CS without and with FACTS devices. The CS without and with FACTS devices can be expressed as: Z Pdi ;limit ðCSÞwithout FACTS ¼ C ðPdi Þ kload oPdi ; i 2 Nd i Pmin di
ð44Þ ðCSÞwith FACTS ¼
Z
Pdi ;FACTS
Pmin di
CðPdi Þ kload;FACTS oPdi ; i
i 2 Nd ð45Þ
$/MWh
C E
load load,FACTS
G I
M
K
B Aggregate demand curve
O
Plimit
PFACTS
MW
Fig. 8 Transfer of consumer surplus to FACTS investment at load bus
J. Inst. Eng. India Ser. B
$/MWh A
gen,FACTS
L
J
gen
Aggregate supply curve
N
H F
O
Plimit
PFACTS
MW
Fig. 10 ZIP load coefficients taken at each load bus in the system Fig. 9 Transfer of producer surplus to FACTS investment at generator bus
The consumer surplus enhancement with FACTS can thus be calculated as area EMIE and can be expressed as difference of CS with and without FACTS devices as: ðCSÞenhancement ¼ ðCSÞwith FACTS ðCSÞwithout FACTS ð46Þ Z Pdi ;FACTS
C ðPdi Þ kload;FACTS ðCSÞenhancement ¼ oPdi i Pmin di Z Pdi ;limit oPdi ; C ðPdi Þ kload i Pmin di
i 2 Nd ð47Þ The producer surplus enhancement with incorporation of FACTS devices is shown in Fig. 9 as an area JNHFJ. The enhanced area can be calculated knowing the PS without and with FACTS devices. PS without FACTS is given as: Z Plimit gi gen ðPSÞwithout FACTS ¼ ki C Pgi oPgi ; i 2 Ng Pmin gi
ð48Þ PS with FACTS is given as: Z PFACTS
gi kgen;FACTS C Pgi oPgi ; ðPSÞwith FACTS ¼ i Pmin gi
load bus decreases with FACTS, then the contribution to FACTS investment comes from increase in consumer surplus as given by the shaded area. This increment in surplus can be given to the investor of FACTS devices. In a similar manner, the marginal prices at generator bus without and with FACTS are shown in Fig. 7 and with contribution of FACTS, the additional producer surplus can be obtained with different marginal prices obtained at the generator buses without and with FACTS. This additional surplus can be transferred to FACTS devices during congestion management. With the installation of FACTS devices, there can also be a situation where the marginal price at the load bus increases or marginal prices decrease at generator bus. In such case, the methodology proposed in [56] can be adopted for remuneration of FACTS devices. A portion of revenue that is a part of congestion rent can be utilized to investment recovery of FACTS devices, as FACTS devices help to relieve the network congestion. The methodology was tested for five bus test system with TCSC only [56]. In the present work, the methodology has been extended taking into consideration the cost of FACTS devices in an objective function along with social welfare maximization for IEEE 24 bus test system with three FACTS devices viz. SVC, TCSC, and UPFC for both pool and bilateral market environment.
ð49Þ
i 2 Ng
Results and Discussion
The enhancement in PS is given as: ðPSÞenhancement ¼ ðPSÞwith FACTS ðPSÞwithout FACTS Z PFACTS
gi kgen;FACTS C Pgi oPgi ðPSÞenhancement ¼ i
ð50Þ
Pmin gi
Z
Plimit gi Pmin gi
kgen C Pgi oPgi ; i
ð51Þ
i 2 Ng The marginal prices with and without FACTS installation at load bus are shown in Fig. 7. It shows that if the price at
The results have been obtained for the IEEE RTS-24 test system [59]. The system consists of 38 lines and 24 buses including 17 load buses and 10 generation buses. The total numbers of generating units are 32 with the installed capacity of 3405 MW. The annual peal load is 2850 MW. The results have been obtained considering three lines congestion cases as: 1.
The rating of 23rd line which is connected between buses 14 and 16 is taken as 2.60 p.u while the actual rating is 5.00 p.u
123
J. Inst. Eng. India Ser. B Table 1 Different parameters without ZIP load WOF
SVC
TCSC
UPFC
Producer surplus ($/h)
67.5500
67.57188
67.66357
67.66966
Customer surplus ($/h)
108.4865
108.498
108.606
108.646
Revenue (US $ million)
–
0.6278
0.791
0.903
Capital cost (US $ million)
–
0.266
0.768
0.937
Facts cost ($/kVAR)
–
126.7395
153.7043
187.5455
Size (kVAR)
1015.0
475.2692
890.7336
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
Table 2 Different parameters with ZIP load WOF
SVC
TCSC
UPFC
Producer surplus
66.8834
66.90118
66.92453
68.0812
Customer surplus
105.0145
105.139
105.089
105.347
Revenue (US $ million)
–
0.892
0.639
0.762
Capital (US $ million)
–
0.1742
0.7684
0.9405
FACTS cost ($/kVAR)
–
126.9618
153.695
188.1114
Size (kVAR)
1015.6
475.2628
890.098
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
Table 3 Various parameters without ZIP load WOF
SVC
TCSC
UPFC
Social welfare ($/h)
14,581.2240
14,581.25
14,581.22
14,580.73
Producer surplus ($/h)
67.5467
67.57114
67.6526
68.80726
Customer surplus ($/h)
108.4683
108.479
108.582
108.855
Revenue (US $ million)
–
0.624
0.786
0.721
Capital (US $ million)
–
0.6337
0.7684
1.046918
FACTS cost ($/kVAR)
–
126.7405
153.6939
187.9527
Size (kVAR)
1014.9
475.2613
890.5106
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
2.
3.
The rating of 18th line which is connected between buses 11 and 13 is taken as 2.25 p.u while the actual rating is 5.00 p.u The rating of 11th line which is connected between buses 7 and 8 is taken as 1.50 p.u while the actual rating is 1.75 p.u. The different combinations for ZIP load model taken for the study are shown in Fig. 10.
The location for the FACTS devices has been obtained based on the social welfare maximization as described. Each FACTS device is placed at a time at respective buses and social welfare is calculated. The location where maximum social welfare has been obtained, it is taken as the optimal location for the FACTS devices. Optimal location of the devices has been described well in [56]. The location and the sizes obtained for the maximum social welfare is
123
shown in the red color in the Tables 1, 2 for pool model with constant P-Q load and ZIP load model and in Tables 3, 4 for hybrid market model with constant P-Q load and ZIP load model. Results for Pool Market with Constant P-Q Load Model and ZIP Load Model The proposed methodology for FACTS cost benefit evaluation is implemented on IEEE 24 bus RTS with FACTS devices, such as, SVC, TCSC, and UPFC. The results have been obtained with pool market model and hybrid market model considering secure bilateral transaction matrix. The determination of secure bilateral transactions is well explained in [43, 44]. The results obtained without and
J. Inst. Eng. India Ser. B Table 4 Various parameters with ZIP load WOF
SVC
TCSC
UPFC
Social welfare ($/h)
14,571.9894
14,571.99
14,571.99
14,571.64
Producer surplus ($/h)
66.862
66.87985
66.91184
68.14574
Customer surplus ($/h)
104.9217
105.045
104.994
105.286
Revenue (US $ million)
–
0.88
0.625
0.898
Capital (US $ million)
–
0.6348
0.7684
0.9401
FACTS cost ($/kVAR)
–
126.9618
153.6946
188.0199
Size (kVAR)
1015.6
475.2643
898.7595
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
Table 5 LMP with and without FACTS devices and without and with ZIP load model Bus no
Without ZIP load
With ZIP load
WOF
SVC
TCSC
UPFC
WOF
SVC
TCSC
UPFC
1
25.45112
25.46602
25.48389
25.49263
25.73018
25.7017
25.74706
26.51303
2
25.45143
25.46263
25.48735
25.49683
25.71593
25.75055
25.73484
26.41233
3
25.93828
25.94925
25.97232
25.98701
30.92398
30.90214
30.86925
31.19723
4
26.33459
26.36552
26.37907
26.39572
27.1202
28.26886
27.16584
27.45158
5
26.12985
26.14889
26.17999
26.19465
26.38816
26.37611
26.41352
27.70024
6
26.35448
26.35188
26.46488
26.48326
26.60554
26.6366
26.63923
26.65765
7 8
20.1373 26.32156
20.13728 26.32365
20.13726 26.37977
20.13722 26.40104
20.1357 26.98817
20.1357 26.98791
20.1357 27.00794
20.13583 26.84638
9
25.9475
25.95197
25.99383
26.01158
27.09526
27.09606
27.14739
27.1191
10
26.00658
26.00872
26.06985
26.08854
26.36131
26.36522
26.39366
26.20044
11
25.90783
25.90359
25.96227
25.97122
26.14497
26.14549
26.16966
26.10281
12
25.83835
25.83591
25.87927
25.88138
26.13129
26.13197
26.15719
26.08649
13
25.32762
25.32904
25.36485
25.36744
25.34472
25.34543
25.36463
25.30988
14
25.79388
25.78618
25.86532
25.87647
25.74246
25.7423
25.75947
25.72315
15
25.04023
25.03984
25.03788
25.03776
25.05308
25.05297
25.05082
25.05806
16
25.07704
25.07702
25.07161
25.06923
25.05367
25.05374
25.05122
25.05303
17
24.60374
24.60342
24.593
24.58927
24.41226
24.41364
24.403
24.40978
18
24.46281
24.46192
24.45157
24.44942
24.21188
24.21359
24.2032
24.20957
19
25.29748
25.29617
25.28774
25.29874
25.24822
25.24806
25.24286
25.24709
20
25.25984
25.25903
25.2365
25.26338
25.2281
25.22807
25.2096
25.22474
21
24.38409
24.38248
24.37323
24.37251
24.15905
24.16095
24.15057
24.15698
22 23
23.76215 25.152
23.76099 25.15249
23.75012 25.15978
23.74823 25.15754
23.50218 25.14361
23.50542 25.14365
23.48757 25.14847
23.49566 25.13888
24
25.62903
25.62921
25.63964
25.64726
27.002
26.9956
26.98784
27.09376
with FACTS devices considering constant P,Q loads as well as ZIP load model. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost with the location of FACTs devices and their sizes for providing reactive support are given in Table 1. As observed from table that there is increase in producer surplus of 67.57188 $/h with SVC, 67.6657 $/h with TCSC and 67.669661 $/h with UPFC. The FACTS devices cost obtained for UPFC is more
compared to the cost of other devices due to higher reactive support obtained from UPFC compared to other FACTS devices as well as its cost curve. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost with the location of FACTs devices and their sizes for providing reactive support with ZIP load are given in Table 2. With ZIP load it is observed that social welfare reduces. The produce and consumer surplus also reduces compared to the case with
123
J. Inst. Eng. India Ser. B WOF (P,Q)
SVC(P,Q)
TCSC(P,Q)
UPFC(P,Q)
WOF(ZIP)
SVC(ZIP)
TCSC(ZIP)
Marginal prices ($/MWh)
35 30 25 20 15 10 5
21
23
r
17
umbe
WOF(ZIP)
19
13
Bus n
15
9
Fig. 14 Customer surplus 11
5
7
1
3
0
WOF (P,Q)
Fig. 11 Comparison of LMPs without and with FACTS devices and ZIP load model
Fig. 15 Annual revenue Fig. 12 FACTS cost comparison Table 6 Coefficients for ZIP load Bus no
Fig. 13 Producer surplus
P,Q load model. This is due to the slight reduction in the loads due to the voltage dependency as voltage decrease during congestion in a system. The FACTS devices cost obtained for UPFC is more compared to the cost of other devices due to more reactive support obtained from UPFC compared to other FACTS devices. The cost is also found slightly higher with ZIP load compared to constant P,Q load due to higher reactive support requirements with ZIP load. The nodal prices obtained without and with FACTS devices are also given in Table 5. It is found that LMPs at each bus with FACTS devices are found different than without FACTS devices. With UPFC, LMPs are observed lower compared to the other FACTS devices. With ZIP
123
Real power
Reactive power
ap
bp
cp
aq
bq
cq
1
0.1
0.2
0.7
0.1
0.2
0.7
2
0.2
0.3
0.5
0.2
0.3
0.5
3
0.3
0.2
0.5
0.3
0.2
0.5
4
0.2
0.1
0.7
0.2
0.1
0.7
5
0.1
0.1
0.8
0.1
0.1
0.8
6
0.2
0.2
0.6
0.2
0.2
0.6
7 8
0.3 0.2
0.2 0.1
0.5 0.7
0.3 0.2
0.2 0.1
0.5 0.7
9
0.1
0.2
0.7
0.1
0.2
0.7
10
0.1
0.1
0.8
0.1
0.1
0.8
13
0.2
0.3
0.5
0.2
0.3
0.5
14
0.3
0.2
0.5
0.3
0.2
0.5
15
0.2
0.1
0.7
0.2
0.1
0.7
16
0.1
0.1
0.8
0.1
0.1
0.8
18
0.3
0.2
0.5
0.3
0.2
0.5
19
0.2
0.1
0.7
0.2
0.1
0.7
20
0.1
0.2
0.7
0.1
0.2
0.7
load, the marginal prices are obtained different and LMPs at some buses reduces with FACTS devices. The comparison of marginal prices obtained without and with ZIP load is shown in Fig. 11.
J. Inst. Eng. India Ser. B Table 7 LMP with and without ZIP load Bus no
Without ZIP load
With ZIP load
WOF
SVC
TCSC
UPFC
WOF
SVC
TCSC
1
25.45403
25.47113
25.4861
26.25056
25.72554
25.69728
25.74203
26.55775
2
25.45308
25.46611
25.48813
26.15286
25.71138
25.74584
25.73
26.45304
3
25.93651
25.94814
25.96898
26.15674
30.94599
30.9242
30.87754
31.21111
4
26.33134
26.36337
26.37471
26.7007
27.13883
28.28044
27.18543
27.45363
5
26.12544
26.14546
26.17408
27.65623
26.36878
26.35683
26.394
28.00983
6
26.32881
26.32192
26.43468
26.04916
26.56813
26.59901
26.6019
26.71749
7 8
20.1375 26.29321
20.1375 26.29377
20.1375 26.34727
20.1375 26.23523
20.13538 26.72894
20.13538 26.72869
20.13538 26.74734
20.13535 26.65078
9
25.94284
25.94722
25.98795
26.02741
27.11963
27.12042
27.17302
27.09416
10
25.99637
25.99749
26.0576
25.80542
26.33132
26.33522
26.36378
26.22583
11
25.90639
25.90187
25.96007
25.88376
26.14301
26.14353
26.16785
26.09779
12
25.83737
25.83475
25.87759
25.79854
26.12895
26.12963
26.15516
26.08059
13
25.32455
25.32567
25.36101
25.30126
25.34336
25.34407
25.36345
25.30583
14
25.79304
25.78496
25.86393
25.81232
25.74187
25.74171
25.75864
25.72072
15
25.0404
25.04002
25.03669
25.04664
25.05333
25.05322
25.05104
25.05855
16
25.07717
25.07717
25.07128
25.0741
25.05363
25.0537
25.05124
25.05291
17
24.60358
24.60323
24.59235
24.60318
24.41117
24.41254
24.40305
24.40997
18
24.46288
24.46195
24.45122
24.4637
24.21051
24.21222
24.20329
24.20988
19
25.29842
25.29716
25.28833
25.29449
25.24827
25.24811
25.2428
25.24669
20
25.26029
25.25949
25.23655
25.25601
25.228
25.22797
25.20946
25.22414
21
24.38448
24.38285
24.37274
24.38634
24.15748
24.15938
24.15061
24.15737
22 23
23.76233 25.15146
23.76114 25.1519
23.7496 25.15909
23.76319 25.14732
23.49939 25.14343
23.50262 25.14347
23.4875 25.14827
23.49595 25.13825
24
25.62955
25.62995
25.63887
25.71701
27.00879
27.0024
26.99063
27.0996
The FACTS cost comparison is shown in Fig. 12. It is observed from the figure that FACTS cost per kVAR is higher for UPFC compared to other FACTS devices. This is due to the higher reactive support and correspondingly higher cost component for UPFC. With ZIP load, the FACTS cost component is found slightly higher due to more reactive support demanded by the ZIP load due to its voltage dependency. The producer surplus, customer surplus, and annual revenue obtained with FACTS devices without and with ZIP load is shown in Figs. 13, 14 and 15. With ZIP load, the customer surplus slightly reduces compared to constant P,Q load. However, the surplus improves with all FACTS devices for P,Q as well as ZIP load model. The producer surplus with ZIP load model improves with all FACTS devices and with UPFC in case of ZIP load model, PS is observed slightly higher due to increase in marginal prices at respective nodes with UPFC. Annual revenue earned with UPFC is higher compared to other FACTS devices due to the higher support of reactive power obtained from UPFC. In case of SVC, the annual revenue earned is more for ZIP load compared to constant P,Q load due to its higher reactive power support in case of ZIP load.
UPFC
Results for Hybrid Market For hybrid market model, 30 % bilateral and 70 % have been taken as Pool demand. The results are obtained with ZIP load as well as constant P-Q load. The date for the ZIP load coefficients is given in Table 6. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost with the location of FACTs devices and their sizes for providing reactive support are given in Table 3. As observed from table producer surplus of 67.57144 $/h with SVC, 67.6526 $/h with TCSC and 68.80726 $/h with UPFC are obtained and it increases with FACTS devices. The FACTS cost obtained for UPFC is more compared to the cost of other devices due to more reactive support obtained from UPFC compared to other devices as well as higher cost component. For ZIP load model, the FACTS devices cost slightly increases compared to constant P-Q load due to higher reactive support in the system. The producer’s and customers’ surplus increase with FACTS devices for both load models. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost
123
J. Inst. Eng. India Ser. B
Marginal prices ($/MWh)
WOF (P,Q)
SVC(P,Q)
TCSC(P,Q)
UPFC(P,Q)
WOF(ZIP)
SVC(ZIP)
TCSC(ZIP)
UPFC(ZIP)
35 30 25 20 15 10 5
21
23
er
17
SVC(ZIP)
19
13
nu mb
15
9
Bus
11
5
7
1
3
0
Fig. 18 Producer surplus
WOF (P,Q)
Fig. 16 Comparison of LMPs without and with FACTS devices and ZIP load model
Fig. 19 Customer surplus
Fig. 17 Comparison of FACTS cost
with the location of FACTs devices and their sizes for providing reactive support with ZIP load are given in Table 4. With ZIP load it is observed that the producer and consumer surplus reduces slightly compared to the case with P-Q load model. This is due to the reduction in the loads due to the voltage dependency as voltage profile becomes poor during congestion in the system. During congestion, the reactive power consumption and loss pattern increases due to higher current in the system that results in voltage profile to become poor and thereby reducing loads at some buses. The nodal prices obtained without and with FACTS devices are also given in Table 7. It is found that LMPs changes at each bus for both load models. With FACTS devices LMPs at some buses increases and at some other buses these decreases. The comparison of LMPs obtained at each bus without and with FACTS devices without and with ZIP load is also shown in Fig. 16. With ZIP load model, LMPs are found different with and without FACTS devices. The FACTs cost comparison is shown in Fig. 17. It is observed from the figure that FACTS cost per kVAR is higher for UPFC compared to other FACTs devices. This is due to the higher reactive support and correspondingly higher cost component for UPFC. With ZIP load, the FACTS cost component is found slightly higher due to more reactive support demanded by the ZIP load due to its
123
Fig. 20 Annual revenue
voltage dependency. The producer surplus, customer surplus, and annual revenue obtained without and with FACTS devices and constant P,Q load and ZIP load is shown in Figs. 18, 19 and 20. Both PS and CS increases with FACTS devices for constant P,Q load as well as ZIP load model. With UPFC, the PS and CS are higher compared to other FACTS devices both for P,Q and ZIP load models. Annual revenue with SVC and UPFC with ZIP load is found higher due to the higher reactive support from SVC and UPFC with ZIP load.
Conclusions In this paper, the investment recovery of FACTS devices for congestion management has been implemented for both pool and hybrid electricity market models considering both
J. Inst. Eng. India Ser. B
constant power loads and generic load model. In hybrid market model, the secure bilateral transactions have been obtained and incorporated in the model. The impact of ZIP load model has also been studied for both the market model and the producers and consumers surplus has been obtained. The annual revenue with the FACTS devices has been also obtained. The PS and CS increases with all FACTS devices considering both P,Q and ZIP load models. With ZIP load, PS as well as CS reduces slightly due to the changes in marginal prices at both load and generator buses. Annual revenue earned with UPFC is more compared to other FACTS devices. It is important to consider realistic load model for FACTS cost remuneration as FACTS devices provide reactive support services along with change in marginal prices. In future electricity markets, FACTS devices will sell their support services as ancillary services provider and need to be remunerated for their services.
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ORIGINAL CONTRIBUTION
FACTS Devices Cost Recovery During Congestion Management in Deregulated Electricity Markets Ashwani Kumar Sharma1 • Ram Kumar Mittapalli1 • Yash Pal1
Received: 1 August 2014 / Accepted: 4 June 2015 Ó The Institution of Engineers (India) 2015
Abstract In future electricity markets, flexible alternating current transmission system (FACTS) devices will play key role for providing ancillary services. Since huge cost is involved for the FACTS devices placement in the power system, the cost invested has to be recovered in their life time for the replacement of these devices. The FACTS devices in future electricity markets can act as an ancillary services provider and have to be remunerated. The main contributions of the paper are: (1) investment recovery of FACTS devices during congestion management such as static VAR compensator and unified power flow controller along with thyristor controlled series compensator using non-linear bid curves, (2) the impact of ZIP load model on the FACTS cost recovery of the devices, (3) the comparison of results obtained without ZIP load model for both pool and hybrid market model, (4) secure bilateral transactions incorporation in hybrid market model. An optimal power flow based approach has been developed for maximizing social welfare including FACTS devices cost. The optimal placement of the FACTS devices have been obtained based on maximum social welfare. The results have been obtained for both pool and hybrid electricity market for IEEE 24-bus RTS. Keywords Congestion management Ancillary services FACTS devices cost recovery Hybrid electricity market ZIP load
& Ashwani Kumar Sharma [email protected] 1
Department of Electrical Engineering, National Institute of Technology Kurukshetra, Kurukshetra 136119, Haryana, India
List of symbols bij Bi ðPDi Þ ¼ b1di P2Di þb2di PDi þ b0i BSVC Ci ðPGi Þ ¼ ai P2Gi þbi PGi þ ci CS (CS)without FACTS (CS)with
FACTS
CSVC CTCSC CUPFC CFACTS annual CFACTS DF FACTS r Gij;eff ¼ r2 þðx ijx Þ2 ; ij x c Þ ij ðx Bij;eff ¼ r2 þðxij xc Þ2 ij c ij GD, GDij
GDmax ij ISO Nb Ng PS (PS)without (PS)with
FACTS
FACTS
Weighing factor indicating the importance of a particular transaction Bid function for the loads Susceptance of SVC Bid function for the generators Consumer surplus Consumer surplus without FACTS devices Consumer surplus with FACTS devices Cost function of SVC Cost function of TCSC Cost function of UPFC Cost with FACTS devices Annual cost with FACTS devices ac distribution factors Flexible ac transmission systems Effective conductance and susceptance with TCSC Represents a bilateral contract between a supplier (Pgi) of row i with a consumer (Pdj) of column j Maximum transaction amount Independent system operator Number of buses in the system Set of generators Producer surplus Producer surplus without FACTS devices Producer surplus with FACTS devices
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J. Inst. Eng. India Ser. B
Pdp, Pdb Pfp, Pfb Pgp, Pgb Pgi Pi max Pmin gi ; Pgi Pgi, Qgi Pdi, Qdi Qi max Qmin gi ; Qgi QSVC Rannual FACTS Sij, Sij Smax ij SVC TCSC UPFC Vi Vsh,, dsh, Vse, dse Vimin ; Vimax Yij ¼ Gij þ Bij di max dmin i ; di gen k , kload kgen;FACTS , kload;FACTS
Vector of pool and bilateral demand Vector of line flows due to the pool and bilateral transactions Vector of pool and bilateral generation Active power pool generator-i Real power injection at bus-i Minimum and maximum generation limit Real and reactive power generation at bus-i Real and reactive power demand at bus-i Reactive power injection at bus-i Minimum and maximum generation limit Reactive support provided by SVC Annual revenue earned with FACTS devices Line flow limit Static VAR compensator Thyristor controlled series compensator Unified power flow controller Voltage magnitude at bus-i Shunt voltage and angle, series injected voltage and angle for UPFC Upper and lower voltage magnitude limit i-j th element of Y-bus matrix Load angle at bus-i Upper and lower angle limit Nodal price at generator and load buses without FACTS devices Nodal prices at the generator and load buses with FACTS devices
Introduction With the emerging competitive electricity markets, new technical challenges have emerged with many market players negotiating power purchase from market at competitive prices in a pool or bilateral coordinated electricity markets. The independent system operator (ISO) has to provide fair and transparent access to all market participants with more and bilateral negotiations of power purchase that may lead to congestion in the transmission system and may threaten system security. The congestion management has become a challenging issue for the ISO for better market operation as it may lead market inefficiency due to rise in the nodal prices with the change in
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generation schedule [1, 2]. The electricity price will not be able to operate at its competitive equilibrium in congested systems in economic terms and may lead to ‘dead weight’ loss to the society. In order to alleviate congestion, some inexpensive generators in congested zone have to reduce their dispatch and some expensive generators in congested zone have to increase their dispatch. This can further lead to creation of local ‘market power’ and hinders the development of competitive environment in electricity trade [3]. When the system operator sets the electricity price and decides the dispatch amount in order to alleviate congestion, the operation of transmission directly affects the profit of the market participants. Thus, in recent years, congestion management has been a subject of great concern in deregulated electricity market. The market based approaches can be categorized based on locational marginal prices, price area zones, financial transmission rights, generation rescheduling, and load curtailment which are well explained [4–18]. A decomposition of spot prices to reveal congestion and the differences in the locational marginal prices reflect the presence of congestion in a transmission system and the customers charges are based on these locational differences in [4], assessment of impact of congestion to develop appropriate price signals in the pool paradigm for congestion management by Bompard et al. in [5], transmission congestion based on ex ante congestion prices are explained in [6]. A 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 are presented in [7, 8]. Re-dispatching based schemes and application of FACTS to manage transmission congestion minimizing the congestion cost is presented by many authors [9–19]. Fang and David [9, 10] proposed a transmission dispatch methodology as an extension of spot pricing theory in a pool and bilateral as well as multilateral transactions model with willingness-to-pay for minimum curtailment to deal with the congestion, Ref. [11] presented optimal power dispatch in the presence of congestion, basic concepts using three approaches to mange congestion are proposed [12] and Bompard et al. [13] developed a unified framework and compared the various CM approaches so as to assess their efficiency and effectiveness of the market signals provided to the market participants. Tuan et al. proposed an interruptible load services during congestion management [14]. A comprehensive literature survey of congestion management methods and their categorization are presented [15]. A congestion management approach based on real and reactive power congestion distribution factors based zones and generator’s rescheduling was proposed [16, 17]. Many authors developed the methodology to incorporate FACTS devices to manage the transmission
J. Inst. Eng. India Ser. B
congestion [18–27]. Recently demand side management (DSM) has been considered as a tool for congestion management in deregulated electricity markets [28–31]. For better utilization of existing power system, the role of FACTS devices has become imperative with benefits of increasing power transfer capability, security and stability of the transmission network [32–36]. The modeling of FACTS devices and their impact for loadability enhancement, real and reactive nodal prices determination in deregulated electricity markets are presented [37–41]. The ISO has to ensure secure bilateral transactions for dispatch of generators and these transactions have been determined [42–44]. These transactions have been incorporated along with pool transactions for the study of hybrid system. The ISO may procure the services of FACTS devices as an ancillary service and since, the capital as well as running cost is involved in the installation of FACTS devices and therefore, have to remunerate their services. Several studies, based on OPF calculations, have been carried out to determine the optimal placement of such devices in the system in order to get the maximum benefits out of their capabilities [45–52]. Some of the previous studies took into account the cost of FACTS devices and these can provide cost effective solution [53]. Generally, there are still very few studies of economic benefits arising from installation of FACTS devices. Most of the authors have concentrated on constant P-Q load models; however, the generic load model consideration is essential. The composite constant impedance-currentpower (ZIP) [54, 55] model has widely accepted as a default model among utility industries. The FACTS devices cost model has also been included in an optimization model and the methodology for FACTS cost remuneration was tested for five bus test system with TCSC only in [56]. The study was conducted with P,Q load considering the linear bid curves. However, generic load model incorporation is essential to incorporate as during congestion the voltage profile in the network become poor and bid curves are also non-linear in nature. In this study, a FACTS cost remuneration based approach described in [56] has been extended with three types of FACTS devices (static VAR compensator (SVC), thyristor controlled series capacitor (TCSC), and unified power flow controller (UPFC). The OPF based approach is employed to solve the non-linear optimization problem of maximizing social welfare. Optimal location of the devices has been obtained based on the procedure developed in [56] considering non-linear bid curves. The impact of ZIP load model has also been incorporated. The results have been obtained for pool market along with the secure bilateral transactions with constant P-Q and ZIP load model. The GAMS and MATLAB interfacing has been utilized to obtain optimal values calling CONOPT solver
[57, 58]. The results have been obtained on IEEE RTS-24 test system [59].
Mathematical Model of FACTS Devices and Cost Function In this section, the model of the FACTS devices for congestion management has been presented. For such applications, FACTS devices can be modeled as Power Injection Model (PIM) [37, 38]. The injection model describes the FACTS as a device that injects a certain amount of active and reactive power to a particular selected node, so that the FACTS device is represented as PQ element. The advantage of PIM is that it does not destroy the symmetrical structure of the admittance matrix and allows easy integration of FACTS devices into existing power system software tools [37, 38]. In this paper three FACTS devices namely SVC, TCSC, UPFC, is used to demonstrate the effectiveness of the proposal for investment recovery of these devices. Static VAR Compensator (SVC) The static VAR compensator (SVC) is a shunt compensation device comprising of fixed capacitor and variable inductor controlled through firing angle. It is originally designed for voltage maintenance in power systems. Operation of SVC is controlled by the adjusting by the selection of the firing angle of GTOs (Gate turn off transistors) or thyristors to change the reactance of inductor. During operation SVC behaves like shunt variable susceptance. SVC can work in inductive or capacitive region. For the steady state operation, constant susceptance model is considered. SVC is connected on any bus i shown in Fig. 1 [37]. The reactive power injection at bus i is given by QSVC ¼ Vi2 BSVC
ð1Þ
The cost function of SVC is given by an expression [47] CSVC ¼ 0:0003 s2 0:3051 s þ 127:38 $=kVAR
ð2Þ
Thyristor Controlled Series Compensator (TCSC) The model of a transmission line with TCSC connected between buses i and j is shown in Fig. 2. TCSC behaves as variable capacitive reactance. It reduces the line reactance during the operation which improves the power transfer capability. It works on the principle of series compensation. Reactance of TCSC is the function of firing angle of the thyristors. But the steady-state impedance of the TCSC is that of parallel LC circuit consisting of fixed capacitive
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Vi
Vi
Pijc + jQ cij
Iij
Vs
Bus i
Zse
e
Pjic + jQ cji
Iji
Bus j
Ish Vi
XC
BSVC XL
Vj
Fig. 3 Model of UPFC
-jXc
Pji+jQji
Zij=Rij+jX Bus i
Re(V I∗ − V I* ) = 0 sh sh se ji
Vsh
Fig. 1 SVC and SVC variable susceptance
Pij+jQij
Zsh
jBc
Bus j
connected with the line with two coupling transformers. In the steady state operation, the main objective of an UPFC is to control voltage and power flow. The power injected model of UPFC is as shown Fig. 3 [37, 38]. The active power and reactive power equations at bus i and bus j can be written as: Pcij ¼ Vi2 ðGii þ Gsh Þ þ Vi Vj ½Gij cosðdij Þ þ Bij sinðdij Þ þVi Vse ½Gij cosðdi dse Þ þ Bij sinðdi dse Þ þVi Vsh ½Gsh cosðdi dsh Þ þ Bsh sinðdi dsh Þ
ð8Þ
Qcij ¼ Vi2 ðBij þ Bsh Þ þ Vi Vj ½Gij sinðdij Þ Bij cosðdij Þ
Fig. 2 Model of TCSC
þVi Vse ½Gij sinðdi dse Þ Bij cosðdi dse Þ þVi Vsh ½Gsh sinðdi dsh Þ Bsh cosðdi dsh Þ impedance. The static model of TCSC is as shown in Fig. 2 [37, 38]. The power injection equations are Pcij ¼ Vi2 Gij;eff þ Vi Vj ðGij;eff cos dij þ Bij;eff sin dij Þ
ð3Þ
Qcij ¼ Vi2 ðBij;eff þ Bc Þ þ Vi Vj ðGij;eff sin dij Bij;eff cos dij Þ ð4Þ Pcji ¼ Vj2 Gij;eff þ Vi Vj ðGij;eff cos dji þ Bij;eff sin dji Þ
ð5Þ
Qcji ¼ Vj2 ðBij;eff þ Bc Þ þ Vi Vj ðGij;eff sin dji Bij;eff cos dji Þ ð6Þ where effective conductance and susceptance is given as rij Gij;eff ¼ 2 rij þ ðxij xc Þ2 Bij;eff ¼
ðxij xc Þ rij2
The cost function of TCSC is given by [47] ð7Þ
Unified Power Flow Controller (UPFC) An UPFC consists of two converters based on GTO (gate turn off), one is series connected and another is shunt
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Pcji ¼ Vj2 Gjj þ Vi Vj ½Gij cosðdij Þ þ Bij sinðdij Þ þ Vj Vse ½Gij cosðdj dse Þ þ Bij sinðdj dse Þ
ð10Þ
Qcji ¼ Vj2 Bij þ Vi Vj ½Gij sinðdij Þ Bij cosðdij Þ þ Vj Vse ½Gij sinðdj dse Þ Bij cosðdj dse Þ
ð11Þ
The operating constraint for UPFC Vi Vse ½Gij cosðdi dse Þ Bij sinðdi dse Þ þ Vj Vse ½Gij cosðdj dse Þ Bij sinðdj dse Þ þ Vi2 Gsh þ Vi Vsh ½Gsh cosðdi dsh Þ Bsh sinðdi dsh Þ ¼ 0 ð12Þ The cost function of UPFC is given by [47] CUPFC ¼ 0:0003 s2 0:2691 s þ 189:22 $ /kVAR ð13Þ
þ ðxij xc Þ2
CTCSC ¼ 0:0015 s2 0:7130 s þ 153:75 $=kVAR
ð9Þ
The cost function of the FACTS devices as presented in [47] is shown in Fig. 4 and has been utilized for FACTS cost calculation along with the social welfare maximization in pool and hybrid market model. The impact of FACTs devices on producer and consumer surplus during the congestion management has been obtained so that FACTS devices can be remunerated according to their services in the electricity markets.
J. Inst. Eng. India Ser. B
constant P, Q as well as generic load model (ZIP load). The formulation has been discussed for pool and bilateral market model. Problem Formulation Constant P-Q Load Model Pool Market Model
Fig. 4 Cost functions of the FACTS devices: SVC, TCSC and UPFC. Red curve upper limit: total investment costs; blue curve lower limit: equipment costs: UPFC:TCSC:SVC. (Color figure online)
The operating range of FACTS devices has been obtained based on maximum social welfare solving nonlinear program as discussed earlier. Once the optimum compensation level is found, the corresponding cost of FACTS is calculated from above equations. The cost can be compared with revenue (or benefit) that can be derived from FACTS. In this paper, the comparison is made by converting the cost, as well as the benefit (or revenue) into annual cost (annuity) (US$/year). To compute the annual capital cost and benefit (revenue) of FACTS, the following assumptions have been made: Project lifetime (n): 5 years Discount rate(r): 10 % Average utilization (u): 40 %
i2Ng
Operational cost of FACTS device is neglected. Annual capital cost of FACTS in US$/year can be found as: r ð1 þ r Þn Annual CFACTS ¼ CFACTS s 1000 ð14Þ ð1 þ r Þn 1 The revenue from the use of FACTS is based on additional surplus and have the unit of ‘‘US$/h’’. Annual revenue from use of FACTS in US $/year can be determined as: RAnnual FACTS
¼ CFACTS 8760 u
In a pool market, the ISO dispatches optimally all the generators such that the social welfare is maximized respecting power injection equations as equality constraints and voltage, angle, power flow limits as inequality constraints. The impact of FACTS devices on the social welfare can be accounted taking the cost function of FACTS devices together with the social welfare function. The social welfare function comprises bids offered to the ISO by the Gencos and Discos. These bid functions have been taken as the quadratic bid functions. The objective of the OPF program is to minimize the total cost which is equivalent the maximization of the social welfare. The OPF program calculates the spot prices and the amount of optimal power the Gencos produce and Discos consume. The consumers can be billed based on the spot prices at respective buses. The formulation of social welfare maximization together with the FACTS devices cost function can be expressed as follows: min Ctotal ¼ CFACTS ðsÞ þ Csurplus Pgi ; Pdi ð16Þ ! X X Ci Pgi Bi ðPdi Þ ð17Þ Csurplus ¼ i2Nd
Cost of FACTS devices are represented as quadratic cost functions. The bid offers from the producers and consumers can be expressed as quadratic functions with their cost coefficients. Ci ðPGi Þ ¼ ai P2Gi þ bi PGi þ ci Bi ðPDi Þ ¼ b1di
P2Di
In this section, an optimization based approach of maximizing social welfare with FACTS devices cost function has been formulated. The loads have been modeled as
þ b2di PDi þ b0i
ð19Þ
Subject to: Equality constraints: Pi ¼ Pgi Pdi ¼
Nb X
Vi Vj ½Gij cosðdi dj Þ
ð20Þ
j¼1
ð15Þ
An Optimal Power Flow Based Approach for FACTS Devices Remuneration for Congestion Management
ð18Þ
þ Bij sinðdi dj Þ Qi ¼ Qgi Qdi ¼
Nb X
8 i ¼ 1; 2; . . .Nb
Vi Vj ½Gij sinðdi dj Þ
ð21Þ
j¼1
þ Bij cosðdi dj Þ 8 i ¼ 1; 2; . . .Nb Pij ¼ Vi2 Gij Vi Vj Gij cos di dj þ Bij sin di dj ð22Þ
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J. Inst. Eng. India Ser. B
Qij ¼ Vi2 Bij þ Vi Vj Bij cos di dj Gij sin di dj ð23Þ
Pji ¼ Vj2 Gij Vi Vj Gij cos di dj Bij sin di dj
ð24Þ
Inequality constrains: Real and reactive power generation for generators is given as follows max Pmin g Pg Pg
ð25Þ
max Qmin g Qg Qg
ð26Þ
Transaction limit between seller bus-i and buyer bus j can be written as max GDmin ij GDij GDij
ð27Þ
Limits on voltage magnitude and angle can be expressed as Vimin Vi Vimax
ð28Þ
di dmax dmin i i
ð29Þ
MVA power flow limit is given by P2ij
þ Q2ij Smax2 ij
ð30Þ
Hybrid Market The problem formulation in pool plus bilateral market consists of the above equations along with some additional constraints as power balance equations for demand and generation for hybrid market model using bilateral demand matrix GD. In addition to power balance equations, the bilateral matrix follows limits to be respected and can be added as a range rule. The methodology for the computation of secure bilateral transactions in a hybrid market model is well explained in [43]. The bilateral transactions can be represented as the bilateral negotiations between Gencos (G) and Discos (D). ½GD ¼ DGT ð31Þ Each element of GD, namely GDij, represents a bilateral contract between a supplier (Pgi) of row i with a consumer (Pdj) of column j. Furthermore, the sum of row i represents the total power produced by generator i and the sum of column j represents the total power consumed at load j. GD can be expressed as 2 3 GD1;1 . . .GD1;nd 6 7 GD 4 GD2;1 . . .GD2;nd 5 ð32Þ GDng;1 . . .GDng;nd where, ng is the number of generators; and nd is the number of loads.
123
In general, the conventional load flow variables generation (Pbg) and load (Pbd) vectors are now expanded into two dimensional transaction matrix as given in (33). "
Pbd Pbg
#
GDT ¼ 0
0 GD
"
ug ud
# ð33Þ
Vector ug and ud are column vectors of ones with the dimensions of ng and nd respectively. There are some intrinsic properties associated with this transaction matrix GD (32). These are column rule, row rule, range rule, and flow rule. These properties have been explained in [42]. Each contract has to range from zero to a maximum allowable value, GDmax ij . This maximum value is bounded by the value of corresponding Pmax or Pdj whichever is gi smaller. The range rule satisfies:
max 0 GDij GDmax ð34Þ ij min Pgi ; Pdj It is also possible for some contracts to be firm so that GD0ij is equal to GDmax [20]. According to flow rule the line ij flows of the network can be expressed as follows: h i Pline ¼ DFAC Pbg Pbd ð35Þ The matrix DFAC is the distribution factors matrix [43]. If the representations of the Pbg and Pbd are substituted by using the definition of GD, the line flows can be expressed in an alternative as follows:
Pline
2 3 1 6 .7 7 ¼ DF GD GDT 6 4 .. 5
ð36Þ
1 With secure bilateral transaction matrix, the power injection equations can be modified with bilateral demand along with the pool demand. Problem Formulation with ZIP Load The general formulation of the problem is same as that without ZIP load. However, the loads are represented as a function of ZIP load coefficients and the voltages at each buses corresponding to the base case voltages. The real and reactive power injection equations are modified for ZIP load model as [54, 55]: Pi ¼ Pgni Pdni
ð37Þ
Qi ¼ Qgni Qdni
ð38Þ
where the real and reactive ZIP loads are represented as [55]:
J. Inst. Eng. India Ser. B
"
# Vi Pdni ¼ Pd0 ap þ bp þ c p V0i " # Vi 2 Vi aq þ b q þ cq Qdni ¼ Qd0 V0i V0i Vi V0i
2
ð39Þ
$/MWh C A
ð40Þ
Consumer surplus
*
D B
Producer surplus
The ZIP load coefficients with real and reactive power demand are ap ? bp ? cp = 1 and aq ? bq ? cq = 1. The different combinations of ZIP load coefficients have been taken for the Pdni and Qdni calculation in the power injection equations considering their impact on the investment recovery of FACTS devices.
Aggregate supply curve
Aggregate demand curve
Production cost O
P*
MW
Fig. 5 Surplus under unconstrained case
Investment Recovery of FACTS Devices for Congestion Management In the electricity market, Gencos and Discoms are the entities to generate and consume power. The generation companies sell power at a marginal price to recover the cost of capital investment and operating costs with a marginal profit to execute the new plant after the life of the plant is over. In a competitive electricity markets, both the Gencos as well as consumer must get benefits in terms of producer’s profit and the consumer’s benefit. The sum of Gencos and consumer surplus represents the social profit or social welfare (SW). Both the parties obtain the surplus for the economic and efficient electricity market operation. Thus, the objective of maximizing the social welfare recovers the price the electricity and makes the market operation economically efficient and viable. With both bid based market mechanism in a competitive electricity markets, the market clearing (MCP) is obtained at the point of cross section of aggregate marginal cost of production of Gencos and the aggregate willingness to pay curve of loads at point D as shown in Fig. 5. The MCP is denoted as k* at the cross section of aggregate curves corresponding to a power P* under unconstrained transmission case. The market equilibrium is disturbed due to the physical limits violation of the transmission system and other reasons like voltage limits, generation capacity constraints etc. Due to the transmission constraints called as transmission system congestion, the social surplus reduces as congestion rent. With a transmission physical limits violations, the power transfer will reduce from P* to Plimit as shown in Fig. 6. There will be two different prices at the two buses due to congestion in the network. At generator surplus bus the price reduces and at consumer bus the price goes up. This causes decrease in both consumer and producer surplus as shown in Fig. 6. An area representing a surplus loss with an arrow is shown in the Fig. 6. The congestion results an overall loss to society called as ‘dead-weight’
loss [56]. The congestion cost collected by the ISO is used either to compensate for the losses or to reinforce the transmission grid or transfer to the participants based on market rules. The price and quantity can be solved by solving the optimization problem with the objective of social welfare maximization subject to equations for power balance, line limits, voltage limits, and capacity limits constraints. The Lagrange multiplier of the real power balance equation as equality constraint gives the nodal price of energy. The producer’s surplus (PS) and consumer’s surplus (CS) can be calculated using equations based on the bid curves for both demand and supply submitted to the ISO and market clearing price. Form Fig. 5, PS and CS surplus can be defined. Producer surplus (PS) can be calculated as: Z Pdi PS ¼ ðki CðPgi ÞÞoPgi ; i 2 Ng ð41Þ Pmin di
Consumer surplus (CS) can be calculated as: Z Pdi ðC ðPdi Þ ki ÞoPdi ; i 2 Nd CS ¼
ð42Þ
Pmin di
C
Consumer surplus
surplus loss A
load
D Congestion cost
B Aggregate demand curve
gen
Producer surplus O
Aggregate supply curve
Production cost Plimit
P*
MW
Fig. 6 Surplus under constrained case
123
J. Inst. Eng. India Ser. B
The congestion rent is given as: X X ðki Pdi Þ ki Pgi CC ¼ i2Nd
ð43Þ
i2Ng
A
E load
where ki is the price of energy (that is, LMP) at bus i, the cost functions taken as quadratic equations for both producer and consumer is given as the quadratic generator bid curve and quadratic demand bid curve. Remuneration Cost Calculation for FACTS Devices During Congestion Management The FACTS devices have the capability of changing power flow patterns and voltage profile improvement in the network. With their incorporation in the network, these devices control transmission congestion due to change in the power flow patterns. These devices help the ISO for security enhancement and in future can play a role of ancillary service providers. Since huge capital cost is involved for their installation and these devices needs to be remunerated to recover capital as well as operating cost during their life time as an ancillary service providers. With the incorporation of FACTS devices, the resulting situation for the simple two-bus system as an example is shown in Fig. 6 also explained well in [57]. In the case of transmission congestion, the decrease in producer and consumer surplus as a congestion cost is shown in Fig. 7 with area EGHFE. The nodal price at generator and load buses is kgen and kload respectively. The congestion rent collected by the ISO shown by area EGHFE can be calculated as the product of the price differences and the area maximum flow through the link, that is, Plimit(kload - kgen). With FACTS devices installed in the system for congestion control, the Plimit increase to PFACTS and the nodal prices at the generator and load buses changes and are kgen;FACTS and kload;FACTS respectively. Therefore, the congestion cost now is represented by an area IMNJI. The congestion rent collected by the ISO shown by an area IMNJI can be calculated as the product of the price difference and the area maximum flow through the link, that is, PFACTS(kload,FACTS - kgen,FACTS) as shown in Fig. 7. Comparing areas with and without FACTS devices, the congestion cost reduces with FACTS devices with improvement in both consumer and producer surplus. The congestion rent that the ISO collect from the market participants, due to LMP difference at source and sink decreases due to the decrease in nodal prices difference. There is considerable increase in the surplus of consumer as shown by area IMCI as well as producer surplus shown by area JNOJ as shown in Fig. 7. Comparing the areas in the Fig. 7 with FACTS, the corresponding increase in the producer surplus is EGMIE and producer surplus is JNHFJ. The surplus areas are also shown in Figs. 8, 9 and the surplus loss as dead weight also decreases.
123
surplus lossnew
Consumer surplus
$/MWh C
G
load,FACTS
Congestion K L cost
J gen,FACTS
B
N
Aggregate demand curve
F
gen
Aggregate supply curve
M D
I
H
Production cost
Producer surplus O
Plimit
P*
MW
PFACTS
Fig. 7 Surplus under constrained case with FACTS
The corresponding increase in both producer and consumer surplus is due to the impact of FACTS devices and it can be considered as a benefit to FACTS devices installation. This increase in surplus can be transferred to investment on FACTS devices and recovery of operational cost of FACTS devices. The increase in the consumer surplus is shown in Fig. 8 as an area EMIE. This increase in the producer can be calculated knowing the CS without and with FACTS devices. The CS without and with FACTS devices can be expressed as: Z Pdi ;limit ðCSÞwithout FACTS ¼ C ðPdi Þ kload oPdi ; i 2 Nd i Pmin di
ð44Þ ðCSÞwith FACTS ¼
Z
Pdi ;FACTS
Pmin di
CðPdi Þ kload;FACTS oPdi ; i
i 2 Nd ð45Þ
$/MWh
C E
load load,FACTS
G I
M
K
B Aggregate demand curve
O
Plimit
PFACTS
MW
Fig. 8 Transfer of consumer surplus to FACTS investment at load bus
J. Inst. Eng. India Ser. B
$/MWh A
gen,FACTS
L
J
gen
Aggregate supply curve
N
H F
O
Plimit
PFACTS
MW
Fig. 10 ZIP load coefficients taken at each load bus in the system Fig. 9 Transfer of producer surplus to FACTS investment at generator bus
The consumer surplus enhancement with FACTS can thus be calculated as area EMIE and can be expressed as difference of CS with and without FACTS devices as: ðCSÞenhancement ¼ ðCSÞwith FACTS ðCSÞwithout FACTS ð46Þ Z Pdi ;FACTS
C ðPdi Þ kload;FACTS ðCSÞenhancement ¼ oPdi i Pmin di Z Pdi ;limit oPdi ; C ðPdi Þ kload i Pmin di
i 2 Nd ð47Þ The producer surplus enhancement with incorporation of FACTS devices is shown in Fig. 9 as an area JNHFJ. The enhanced area can be calculated knowing the PS without and with FACTS devices. PS without FACTS is given as: Z Plimit gi gen ðPSÞwithout FACTS ¼ ki C Pgi oPgi ; i 2 Ng Pmin gi
ð48Þ PS with FACTS is given as: Z PFACTS
gi kgen;FACTS C Pgi oPgi ; ðPSÞwith FACTS ¼ i Pmin gi
load bus decreases with FACTS, then the contribution to FACTS investment comes from increase in consumer surplus as given by the shaded area. This increment in surplus can be given to the investor of FACTS devices. In a similar manner, the marginal prices at generator bus without and with FACTS are shown in Fig. 7 and with contribution of FACTS, the additional producer surplus can be obtained with different marginal prices obtained at the generator buses without and with FACTS. This additional surplus can be transferred to FACTS devices during congestion management. With the installation of FACTS devices, there can also be a situation where the marginal price at the load bus increases or marginal prices decrease at generator bus. In such case, the methodology proposed in [56] can be adopted for remuneration of FACTS devices. A portion of revenue that is a part of congestion rent can be utilized to investment recovery of FACTS devices, as FACTS devices help to relieve the network congestion. The methodology was tested for five bus test system with TCSC only [56]. In the present work, the methodology has been extended taking into consideration the cost of FACTS devices in an objective function along with social welfare maximization for IEEE 24 bus test system with three FACTS devices viz. SVC, TCSC, and UPFC for both pool and bilateral market environment.
ð49Þ
i 2 Ng
Results and Discussion
The enhancement in PS is given as: ðPSÞenhancement ¼ ðPSÞwith FACTS ðPSÞwithout FACTS Z PFACTS
gi kgen;FACTS C Pgi oPgi ðPSÞenhancement ¼ i
ð50Þ
Pmin gi
Z
Plimit gi Pmin gi
kgen C Pgi oPgi ; i
ð51Þ
i 2 Ng The marginal prices with and without FACTS installation at load bus are shown in Fig. 7. It shows that if the price at
The results have been obtained for the IEEE RTS-24 test system [59]. The system consists of 38 lines and 24 buses including 17 load buses and 10 generation buses. The total numbers of generating units are 32 with the installed capacity of 3405 MW. The annual peal load is 2850 MW. The results have been obtained considering three lines congestion cases as: 1.
The rating of 23rd line which is connected between buses 14 and 16 is taken as 2.60 p.u while the actual rating is 5.00 p.u
123
J. Inst. Eng. India Ser. B Table 1 Different parameters without ZIP load WOF
SVC
TCSC
UPFC
Producer surplus ($/h)
67.5500
67.57188
67.66357
67.66966
Customer surplus ($/h)
108.4865
108.498
108.606
108.646
Revenue (US $ million)
–
0.6278
0.791
0.903
Capital cost (US $ million)
–
0.266
0.768
0.937
Facts cost ($/kVAR)
–
126.7395
153.7043
187.5455
Size (kVAR)
1015.0
475.2692
890.7336
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
Table 2 Different parameters with ZIP load WOF
SVC
TCSC
UPFC
Producer surplus
66.8834
66.90118
66.92453
68.0812
Customer surplus
105.0145
105.139
105.089
105.347
Revenue (US $ million)
–
0.892
0.639
0.762
Capital (US $ million)
–
0.1742
0.7684
0.9405
FACTS cost ($/kVAR)
–
126.9618
153.695
188.1114
Size (kVAR)
1015.6
475.2628
890.098
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
Table 3 Various parameters without ZIP load WOF
SVC
TCSC
UPFC
Social welfare ($/h)
14,581.2240
14,581.25
14,581.22
14,580.73
Producer surplus ($/h)
67.5467
67.57114
67.6526
68.80726
Customer surplus ($/h)
108.4683
108.479
108.582
108.855
Revenue (US $ million)
–
0.624
0.786
0.721
Capital (US $ million)
–
0.6337
0.7684
1.046918
FACTS cost ($/kVAR)
–
126.7405
153.6939
187.9527
Size (kVAR)
1014.9
475.2613
890.5106
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
2.
3.
The rating of 18th line which is connected between buses 11 and 13 is taken as 2.25 p.u while the actual rating is 5.00 p.u The rating of 11th line which is connected between buses 7 and 8 is taken as 1.50 p.u while the actual rating is 1.75 p.u. The different combinations for ZIP load model taken for the study are shown in Fig. 10.
The location for the FACTS devices has been obtained based on the social welfare maximization as described. Each FACTS device is placed at a time at respective buses and social welfare is calculated. The location where maximum social welfare has been obtained, it is taken as the optimal location for the FACTS devices. Optimal location of the devices has been described well in [56]. The location and the sizes obtained for the maximum social welfare is
123
shown in the red color in the Tables 1, 2 for pool model with constant P-Q load and ZIP load model and in Tables 3, 4 for hybrid market model with constant P-Q load and ZIP load model. Results for Pool Market with Constant P-Q Load Model and ZIP Load Model The proposed methodology for FACTS cost benefit evaluation is implemented on IEEE 24 bus RTS with FACTS devices, such as, SVC, TCSC, and UPFC. The results have been obtained with pool market model and hybrid market model considering secure bilateral transaction matrix. The determination of secure bilateral transactions is well explained in [43, 44]. The results obtained without and
J. Inst. Eng. India Ser. B Table 4 Various parameters with ZIP load WOF
SVC
TCSC
UPFC
Social welfare ($/h)
14,571.9894
14,571.99
14,571.99
14,571.64
Producer surplus ($/h)
66.862
66.87985
66.91184
68.14574
Customer surplus ($/h)
104.9217
105.045
104.994
105.286
Revenue (US $ million)
–
0.88
0.625
0.898
Capital (US $ million)
–
0.6348
0.7684
0.9401
FACTS cost ($/kVAR)
–
126.9618
153.6946
188.0199
Size (kVAR)
1015.6
475.2643
898.7595
Location
Bus 6
Line 6–10
Bus 6, Line 6–10
Table 5 LMP with and without FACTS devices and without and with ZIP load model Bus no
Without ZIP load
With ZIP load
WOF
SVC
TCSC
UPFC
WOF
SVC
TCSC
UPFC
1
25.45112
25.46602
25.48389
25.49263
25.73018
25.7017
25.74706
26.51303
2
25.45143
25.46263
25.48735
25.49683
25.71593
25.75055
25.73484
26.41233
3
25.93828
25.94925
25.97232
25.98701
30.92398
30.90214
30.86925
31.19723
4
26.33459
26.36552
26.37907
26.39572
27.1202
28.26886
27.16584
27.45158
5
26.12985
26.14889
26.17999
26.19465
26.38816
26.37611
26.41352
27.70024
6
26.35448
26.35188
26.46488
26.48326
26.60554
26.6366
26.63923
26.65765
7 8
20.1373 26.32156
20.13728 26.32365
20.13726 26.37977
20.13722 26.40104
20.1357 26.98817
20.1357 26.98791
20.1357 27.00794
20.13583 26.84638
9
25.9475
25.95197
25.99383
26.01158
27.09526
27.09606
27.14739
27.1191
10
26.00658
26.00872
26.06985
26.08854
26.36131
26.36522
26.39366
26.20044
11
25.90783
25.90359
25.96227
25.97122
26.14497
26.14549
26.16966
26.10281
12
25.83835
25.83591
25.87927
25.88138
26.13129
26.13197
26.15719
26.08649
13
25.32762
25.32904
25.36485
25.36744
25.34472
25.34543
25.36463
25.30988
14
25.79388
25.78618
25.86532
25.87647
25.74246
25.7423
25.75947
25.72315
15
25.04023
25.03984
25.03788
25.03776
25.05308
25.05297
25.05082
25.05806
16
25.07704
25.07702
25.07161
25.06923
25.05367
25.05374
25.05122
25.05303
17
24.60374
24.60342
24.593
24.58927
24.41226
24.41364
24.403
24.40978
18
24.46281
24.46192
24.45157
24.44942
24.21188
24.21359
24.2032
24.20957
19
25.29748
25.29617
25.28774
25.29874
25.24822
25.24806
25.24286
25.24709
20
25.25984
25.25903
25.2365
25.26338
25.2281
25.22807
25.2096
25.22474
21
24.38409
24.38248
24.37323
24.37251
24.15905
24.16095
24.15057
24.15698
22 23
23.76215 25.152
23.76099 25.15249
23.75012 25.15978
23.74823 25.15754
23.50218 25.14361
23.50542 25.14365
23.48757 25.14847
23.49566 25.13888
24
25.62903
25.62921
25.63964
25.64726
27.002
26.9956
26.98784
27.09376
with FACTS devices considering constant P,Q loads as well as ZIP load model. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost with the location of FACTs devices and their sizes for providing reactive support are given in Table 1. As observed from table that there is increase in producer surplus of 67.57188 $/h with SVC, 67.6657 $/h with TCSC and 67.669661 $/h with UPFC. The FACTS devices cost obtained for UPFC is more
compared to the cost of other devices due to higher reactive support obtained from UPFC compared to other FACTS devices as well as its cost curve. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost with the location of FACTs devices and their sizes for providing reactive support with ZIP load are given in Table 2. With ZIP load it is observed that social welfare reduces. The produce and consumer surplus also reduces compared to the case with
123
J. Inst. Eng. India Ser. B WOF (P,Q)
SVC(P,Q)
TCSC(P,Q)
UPFC(P,Q)
WOF(ZIP)
SVC(ZIP)
TCSC(ZIP)
Marginal prices ($/MWh)
35 30 25 20 15 10 5
21
23
r
17
umbe
WOF(ZIP)
19
13
Bus n
15
9
Fig. 14 Customer surplus 11
5
7
1
3
0
WOF (P,Q)
Fig. 11 Comparison of LMPs without and with FACTS devices and ZIP load model
Fig. 15 Annual revenue Fig. 12 FACTS cost comparison Table 6 Coefficients for ZIP load Bus no
Fig. 13 Producer surplus
P,Q load model. This is due to the slight reduction in the loads due to the voltage dependency as voltage decrease during congestion in a system. The FACTS devices cost obtained for UPFC is more compared to the cost of other devices due to more reactive support obtained from UPFC compared to other FACTS devices. The cost is also found slightly higher with ZIP load compared to constant P,Q load due to higher reactive support requirements with ZIP load. The nodal prices obtained without and with FACTS devices are also given in Table 5. It is found that LMPs at each bus with FACTS devices are found different than without FACTS devices. With UPFC, LMPs are observed lower compared to the other FACTS devices. With ZIP
123
Real power
Reactive power
ap
bp
cp
aq
bq
cq
1
0.1
0.2
0.7
0.1
0.2
0.7
2
0.2
0.3
0.5
0.2
0.3
0.5
3
0.3
0.2
0.5
0.3
0.2
0.5
4
0.2
0.1
0.7
0.2
0.1
0.7
5
0.1
0.1
0.8
0.1
0.1
0.8
6
0.2
0.2
0.6
0.2
0.2
0.6
7 8
0.3 0.2
0.2 0.1
0.5 0.7
0.3 0.2
0.2 0.1
0.5 0.7
9
0.1
0.2
0.7
0.1
0.2
0.7
10
0.1
0.1
0.8
0.1
0.1
0.8
13
0.2
0.3
0.5
0.2
0.3
0.5
14
0.3
0.2
0.5
0.3
0.2
0.5
15
0.2
0.1
0.7
0.2
0.1
0.7
16
0.1
0.1
0.8
0.1
0.1
0.8
18
0.3
0.2
0.5
0.3
0.2
0.5
19
0.2
0.1
0.7
0.2
0.1
0.7
20
0.1
0.2
0.7
0.1
0.2
0.7
load, the marginal prices are obtained different and LMPs at some buses reduces with FACTS devices. The comparison of marginal prices obtained without and with ZIP load is shown in Fig. 11.
J. Inst. Eng. India Ser. B Table 7 LMP with and without ZIP load Bus no
Without ZIP load
With ZIP load
WOF
SVC
TCSC
UPFC
WOF
SVC
TCSC
1
25.45403
25.47113
25.4861
26.25056
25.72554
25.69728
25.74203
26.55775
2
25.45308
25.46611
25.48813
26.15286
25.71138
25.74584
25.73
26.45304
3
25.93651
25.94814
25.96898
26.15674
30.94599
30.9242
30.87754
31.21111
4
26.33134
26.36337
26.37471
26.7007
27.13883
28.28044
27.18543
27.45363
5
26.12544
26.14546
26.17408
27.65623
26.36878
26.35683
26.394
28.00983
6
26.32881
26.32192
26.43468
26.04916
26.56813
26.59901
26.6019
26.71749
7 8
20.1375 26.29321
20.1375 26.29377
20.1375 26.34727
20.1375 26.23523
20.13538 26.72894
20.13538 26.72869
20.13538 26.74734
20.13535 26.65078
9
25.94284
25.94722
25.98795
26.02741
27.11963
27.12042
27.17302
27.09416
10
25.99637
25.99749
26.0576
25.80542
26.33132
26.33522
26.36378
26.22583
11
25.90639
25.90187
25.96007
25.88376
26.14301
26.14353
26.16785
26.09779
12
25.83737
25.83475
25.87759
25.79854
26.12895
26.12963
26.15516
26.08059
13
25.32455
25.32567
25.36101
25.30126
25.34336
25.34407
25.36345
25.30583
14
25.79304
25.78496
25.86393
25.81232
25.74187
25.74171
25.75864
25.72072
15
25.0404
25.04002
25.03669
25.04664
25.05333
25.05322
25.05104
25.05855
16
25.07717
25.07717
25.07128
25.0741
25.05363
25.0537
25.05124
25.05291
17
24.60358
24.60323
24.59235
24.60318
24.41117
24.41254
24.40305
24.40997
18
24.46288
24.46195
24.45122
24.4637
24.21051
24.21222
24.20329
24.20988
19
25.29842
25.29716
25.28833
25.29449
25.24827
25.24811
25.2428
25.24669
20
25.26029
25.25949
25.23655
25.25601
25.228
25.22797
25.20946
25.22414
21
24.38448
24.38285
24.37274
24.38634
24.15748
24.15938
24.15061
24.15737
22 23
23.76233 25.15146
23.76114 25.1519
23.7496 25.15909
23.76319 25.14732
23.49939 25.14343
23.50262 25.14347
23.4875 25.14827
23.49595 25.13825
24
25.62955
25.62995
25.63887
25.71701
27.00879
27.0024
26.99063
27.0996
The FACTS cost comparison is shown in Fig. 12. It is observed from the figure that FACTS cost per kVAR is higher for UPFC compared to other FACTS devices. This is due to the higher reactive support and correspondingly higher cost component for UPFC. With ZIP load, the FACTS cost component is found slightly higher due to more reactive support demanded by the ZIP load due to its voltage dependency. The producer surplus, customer surplus, and annual revenue obtained with FACTS devices without and with ZIP load is shown in Figs. 13, 14 and 15. With ZIP load, the customer surplus slightly reduces compared to constant P,Q load. However, the surplus improves with all FACTS devices for P,Q as well as ZIP load model. The producer surplus with ZIP load model improves with all FACTS devices and with UPFC in case of ZIP load model, PS is observed slightly higher due to increase in marginal prices at respective nodes with UPFC. Annual revenue earned with UPFC is higher compared to other FACTS devices due to the higher support of reactive power obtained from UPFC. In case of SVC, the annual revenue earned is more for ZIP load compared to constant P,Q load due to its higher reactive power support in case of ZIP load.
UPFC
Results for Hybrid Market For hybrid market model, 30 % bilateral and 70 % have been taken as Pool demand. The results are obtained with ZIP load as well as constant P-Q load. The date for the ZIP load coefficients is given in Table 6. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost with the location of FACTs devices and their sizes for providing reactive support are given in Table 3. As observed from table producer surplus of 67.57144 $/h with SVC, 67.6526 $/h with TCSC and 68.80726 $/h with UPFC are obtained and it increases with FACTS devices. The FACTS cost obtained for UPFC is more compared to the cost of other devices due to more reactive support obtained from UPFC compared to other devices as well as higher cost component. For ZIP load model, the FACTS devices cost slightly increases compared to constant P-Q load due to higher reactive support in the system. The producer’s and customers’ surplus increase with FACTS devices for both load models. The producer surplus, consumer surplus, annual revenue with FACTS devices, capital cost, and FACTS devices cost
123
J. Inst. Eng. India Ser. B
Marginal prices ($/MWh)
WOF (P,Q)
SVC(P,Q)
TCSC(P,Q)
UPFC(P,Q)
WOF(ZIP)
SVC(ZIP)
TCSC(ZIP)
UPFC(ZIP)
35 30 25 20 15 10 5
21
23
er
17
SVC(ZIP)
19
13
nu mb
15
9
Bus
11
5
7
1
3
0
Fig. 18 Producer surplus
WOF (P,Q)
Fig. 16 Comparison of LMPs without and with FACTS devices and ZIP load model
Fig. 19 Customer surplus
Fig. 17 Comparison of FACTS cost
with the location of FACTs devices and their sizes for providing reactive support with ZIP load are given in Table 4. With ZIP load it is observed that the producer and consumer surplus reduces slightly compared to the case with P-Q load model. This is due to the reduction in the loads due to the voltage dependency as voltage profile becomes poor during congestion in the system. During congestion, the reactive power consumption and loss pattern increases due to higher current in the system that results in voltage profile to become poor and thereby reducing loads at some buses. The nodal prices obtained without and with FACTS devices are also given in Table 7. It is found that LMPs changes at each bus for both load models. With FACTS devices LMPs at some buses increases and at some other buses these decreases. The comparison of LMPs obtained at each bus without and with FACTS devices without and with ZIP load is also shown in Fig. 16. With ZIP load model, LMPs are found different with and without FACTS devices. The FACTs cost comparison is shown in Fig. 17. It is observed from the figure that FACTS cost per kVAR is higher for UPFC compared to other FACTs devices. This is due to the higher reactive support and correspondingly higher cost component for UPFC. With ZIP load, the FACTS cost component is found slightly higher due to more reactive support demanded by the ZIP load due to its
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Fig. 20 Annual revenue
voltage dependency. The producer surplus, customer surplus, and annual revenue obtained without and with FACTS devices and constant P,Q load and ZIP load is shown in Figs. 18, 19 and 20. Both PS and CS increases with FACTS devices for constant P,Q load as well as ZIP load model. With UPFC, the PS and CS are higher compared to other FACTS devices both for P,Q and ZIP load models. Annual revenue with SVC and UPFC with ZIP load is found higher due to the higher reactive support from SVC and UPFC with ZIP load.
Conclusions In this paper, the investment recovery of FACTS devices for congestion management has been implemented for both pool and hybrid electricity market models considering both
J. Inst. Eng. India Ser. B
constant power loads and generic load model. In hybrid market model, the secure bilateral transactions have been obtained and incorporated in the model. The impact of ZIP load model has also been studied for both the market model and the producers and consumers surplus has been obtained. The annual revenue with the FACTS devices has been also obtained. The PS and CS increases with all FACTS devices considering both P,Q and ZIP load models. With ZIP load, PS as well as CS reduces slightly due to the changes in marginal prices at both load and generator buses. Annual revenue earned with UPFC is more compared to other FACTS devices. It is important to consider realistic load model for FACTS cost remuneration as FACTS devices provide reactive support services along with change in marginal prices. In future electricity markets, FACTS devices will sell their support services as ancillary services provider and need to be remunerated for their services.
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