An Optimal Reactive Power Dispatch Model
for Deregulated Electricity Markets
I. El-Samahy, Student Member, IEEE, C. A. Cañizares, Fellow, IEEE, K. Bhattacharya, Senior
Member, IEEE, and J. Pan, Senior Member, IEEE
 further states that a reactive power provider should not be
Abstract—This paper proposes a reactive power dispatch financially compensated when operating within a power factor
model that takes into account both the technical and economical range of 0.95 lagging and 0.95 leading, but an Independent
aspects associated with reactive power provision in the context of System Operator (ISO) may change this range at its discretion.
the new operating paradigms in deregulated electricity markets. Traditionally, reactive power dispatch has always been
The main objective of the proposed model is to minimize the total viewed by researchers as an optimization problem wherein the
amount of dollars paid by the ISO to the generators for
objective is to minimize real power transmission loss subject
providing the required reactive power support. The real power
generation is decoupled and assumed fixed during the reactive to various system constraints such as nodal active and reactive
power dispatch procedures; however, due to the effect of reactive power flow balance, bus voltage limits, and reactive power
power on real power, real power generation is allowed be re- limits -. Multi-objective optimization models have also
scheduled within given limits. The 32-bus CIGRE benchmark been proposed for the reactive power dispatch problem. In
system is used to illustrate the proposed reactive power dispatch these models, reactive power is dispatched to achieve other
technique. The developed model is generic in nature and can be objectives, in addition to the traditional loss minimization,
adopted for any electricity market structure. such as maximizing voltage stability margin , , or
minimizing voltage and transformers taps deviations .
Index Terms—Ancillary services, electricity markets, In the context of deregulated electricity markets, reactive
deregulation, reactive power dispatch, system operation.
power dispatch corresponds to short-term allocation of
reactive power required from suppliers based on current
I. INTRODUCTION operating conditions . The ISO is concerned with
O PTIMAL dispatch of reactive power services has always
been of great interest to researchers as well as system
operators, especially after the restructuring of the power
determining the optimal reactive power schedule for all
providers based on a given objective that depends on system
operating criteria. Different objective functions can be used by
industry. Reactive power is tightly related to bus voltages the ISO, besides the traditional transmission losses
throughout a power network, and hence reactive power minimization, such as minimization of reactive power cost
services have a significant effect on system security. -, minimization of deviations from contracted
Insufficient reactive power supply can result in voltage transactions , minimization of the cost of adjusting
collapse, which has been one of the reasons for some recent reactive power control devices , or maximization of
major blackouts; for example, the US-Canada Power System system loadability to minimize the risk of voltage collapse
Outage Task Force states in its report that insufficient reactive , .
power was an issue in the August 2003 blackout, and has Any of the aforementioned objectives can be adopted, but
recommended strengthening the reactive power and voltage since some of them are of a conflicting nature, the ISO needs
control practices in all North American Electric Reliability to choose a criterion that best suits a competitive market
Council (NERC) Regions . structure. In this paper, a cost-based reactive power dispatch
In deregulated electricity markets, the Independent System model is proposed that seeks to minimize the total cost of
Operator (ISO) is responsible for the provision of additional reactive power dispatch from generators, considering the costs
services that are necessary to support the transmission of associated with the supply of this reactive power, including
electrical energy while maintaining secure and reliable opportunity costs resulting from active power re-scheduling
operation of the power system; these services are referred to
when generator capability limits are reached, as well as the
as ancillary services. According to the Federal Energy
cost associated with the use of balance services to supply the
Regulatory Commission (FERC) Order No.888, reactive
required active power load levels. The proposed model
power supply and voltage control from generators is one of
six ancillary services that transmission providers must include incorporates both the economic and technical aspects of
in an open access transmission tariff . FERC Order 2003 reactive power support. The economic aspect is considered by
virtue of the objective function which minimizes the total cost
This work was supported in part by ABB US Corporate Research, and of reactive power purchase from service providers, while the
NSERC Canada. technical aspect is taken care of through the security
I. El-Samahy, K. Bhattacharya, and C. A. Cañizares are with the constraints such as the bus voltage limits, reactive power
Department of Electrical and Computer Engineering, University of Waterloo,
Waterloo, Ontario, Canada. capability limits, and transmission line power transfer limits.
Emails: email@example.com; firstname.lastname@example.org; The paper is organized as follows: In Section II, the
traditional reactive power dispatch model is discussed. The economical and technical aspects associated with reactive
proposed dispatch model is then presented in Section III, power service provision.
including general discussions regarding the overall dispatch
procedures. In Section IV, the proposed model is implemented III. PROPOSED REACTIVE POWER DISPATCH MODEL
on the CIGRE 32-bus system and two cases are tested. In practice, active power and reactive power have generally
Finally, in Section V, the main contributions of the proposed been handled separately by most power system operators.
work are summarized and highlighted. Typically, active power dispatch is carried out based a Linear
Programming (LP) model associated with an Economical
II. TRADITIONAL REACTIVE POWER DISPATCH MODEL Load Dispatch (ELD) problem that maximizes social welfare,
The main objective of optimal reactive power dispatch has while guaranteeing that system security constraints are met
always been to minimize the total transmission losses subject . Reactive power, on the other hand, is dispatched based
to system operational constraints. The following OPF model on power flow studies and operational experience. However,
represents a traditional loss minimization reactive power there are several complex issues involved in reactive power
dispatch model , : service provision in deregulated electricity market that call for
further systematic procedures to arrive at better solutions.
Min. Loss = 0.5∑ Gi , j Vi 2 + V j2 − 2ViV j cos(δ j − δ i ))) Thus, reactive power should be dispatched from generators in
an economical manner that minimizes the ISO’s payment
burden, while considering system security constraints.
(1) Figure 1 shows the proposed schematic procedure for short-
s.t. PGi − PDi = ∑ ViV jYij cos(θ ij + δ j − δ i ) (2) term dispatch of reactive power services. In this model, the
j ISO carries out the reactive power dispatch in a time frame of
QGi − QDi = −∑ ViV j Yij sin (θ ij + δ j − δ i ) (3)
one hour to half-hour ahead of real-time by solving an OPF
that minimizes the cost of reactive power provision from
generators, the cost of active power rescheduling, and the cost
Vi min ≤ Vi ≤ Vi max (4) of real power balance, subject to power flow and security
constraints. The payments to the service providers are
QGg ≤ Q max
calculated post real-time operation, based on the actual usage
QGg ≥ QGg
(6) and dispatch requested by the ISO aggregated over a period of
Pij ≤ Pijmax (7)
A. Real Power Market Clearing
where The flow chart in Fig. 1 illustrates how real and reactive
PGi: Active power generation at bus i in p.u. power markets can be decoupled from each other, so that the
QGi: Reactive power generation at bus i in p.u. ISO does not handle reactive power dispatch in the same time-
PDi: Active power demand at bus i in p.u. frame as that of real power market clearing. The decoupling of
QDi: Reactive power demand at bus i in p.u. real and reactive power , also suggested in -,
Vi: Voltage magnitude in p.u. at bus i. implies that the OPF problem can be separated into two parts:
δi: Voltage angle in radians at bus i. An active power sub-problem that provides the real power
Pij: Power flow from bus i to bus j in p.u. dispatch and prices in real-time based on a cost minimization
Yij: Element ij of admittance matrix in p.u.; (or social welfare maximization) model; and a Q- sub-
Yij = Gij + j Bij = |Yij| ∠θij problem that provides reactive power dispatch levels required
In the above model, (2) and (3) represent the nodal active and to achieve a certain objective as determined by the ISO,
reactive power flow equations, respectively. The voltage which, in this paper, is the minimization of total payments,
limits are represented by (4); the generators’ reactive power while taking into account system security constraints. It is
upper and lower limits are represented by (5) and (6), important to note that the solution obtained from a coupled
respectively; and limits in the power transfers are represented OPF, simultaneously dispatching real and reactive power, is
by (7). theoretically closer to the optimal; however, in addition to
If the ISO seeks only to minimize losses to determine the market power and price volatility issues that constrain the ISO
required reactive power support, it could end up with an from handling them simultaneously, computational burden
expensive set of service providers, which is not preferred in a also becomes an issue for practical sized power systems, since
market-based environment. Hence, a reactive power cost- it requires solving a rather complex and large-scale non-linear
based dispatch model would be more suitable, from the programming (NLP) model every few minutes (e.g. every 5
economical point of view, for a competitive market structure. minutes in Ontario). Decoupling the OPF problem provides
The main objective of the ISO should always be to provide the required flexibility for spot market applications, and
reactive power support at the least payment, while maintaining alleviates the problems associated with model complexity,
system constraints that ensure a secure operation of the power while retaining an acceptable level of accuracy.
system. In this context, a reactive power dispatch approach is Most ISOs throughout the world use DC-based OPF auction
proposed in the next section that takes into account both the models for active power market clearing and dispatch, with
iterative mechanisms to guarantee system security . In this
instructions price components
Q-capability Solve ORPD
P-market curves model minimizing
clearing the ISO payments
Determine the required
reactive power support
Fig. 1. Flow chart for the proposed reactive power dispatch model.
paper, for the purpose of numerical simulations, real power
market clearing and dispatch is obtained by means of an ac
Fig. 2. Synchronous generator capability curve.
OPF model that minimizes the cost of energy production,
subject to system security constraints and some pre-dispatch area in Fig. 2 represents the “mandatory” base reactive power
information. The interested reader is referred to  for provision range set by the system operator. Any reactive
further discussions regarding the advantages and/or power provision required by the operator beyond this area is
disadvantages of these two auctions models, which are beyond eligible for payment, due to increased costs associated with
the scope of the current paper. losses in its windings. Such mandatory and ancillary
B. Reactive Power Capability Curves classification of reactive power capability is in line with what
most system operators have in place for reactive power
The real and reactive power output from a synchronous management (e.g. the IESO of Ontario requires a mandatory
generator is usually limited by the capability of its prime provision from all generators within the power factor range of
mover. When real power and terminal voltage are fixed, the 0.9 lead and 0.95 lag).
armature and field winding heating limits determine the The generator’s reactive power capability curves impose
reactive power capability of a generator, as shown in Fig. 2 the requirement that reactive power generated should be
. The armature heating limit is a circle with a radius (VtIa) within or on the limiting curve; hence, any reactive output
and centered at the origin, and expressed by the following increase requested by the ISO beyond QGA will require a
equation: decrease in active power generation. Therefore, an
opportunity cost payment is expected for the reactive power
PG2 + QG ≤ (Vt I a ) 2
(8) service in this case to account for the lost opportunity of the
generator to sell its real power in the energy market and the
The field limit, on the other hand, is a circle with radius associated revenue loss. Thus, the following three regions for
(VtEaf/Xs) at (0, -Vt2/Xs), and expressed by the following reactive power generation can be identified in Fig. 2:
equation: • Region I (QGmin ≤ QG = QG1 ≤ 0) refers to the under-
excitation region, in which the generator is required
2 2 to absorb reactive power.
⎛ V 2 ⎞ ⎛V E ⎞ • Region II (0 ≤ QG = QG2 ≤ QGA) refers to the over-
P + ⎜ QG + t ⎟ ≤ ⎜ t af
⎜ ⎟ (9)
Xs ⎟ ⎜ Xs ⎟
excitation region, in which the generator is required
⎝ ⎠ ⎝ ⎠ to supply reactive power within its reactive power
where Vt is the voltage at the generator terminal bus, Ia is the
• Region III (QGA ≤ QG = QG3 ≤ QGB) refers to the loss
armature current, Eaf is the excitation voltage, and Xs is the
of opportunity region, in which the generator is asked
synchronous reactance, and PG and QG are the real and
to reduce its active power production in order to meet
reactive power outputs of the generator, respectively. The
the system reactive power requirements.
generator’s MVA rating is the point of intersection of the two
curves, and therefore its MW rating is given by PGR. At an
operating point A, with real power output PGA such that C. Reactive Power Dispatch Model
PGA<PGR, the limit on QG is imposed by the generator’s field It can be observed from Fig. 2, as well as from the previous
heating limit; whereas, when PGA>PGR, the limit on QG is discussions, that reactive power production capability of a
imposed by the generator’s armature heating limit. The shaded generator essentially depends on the current state of real
power generation (PG). Hence, prior knowledge of PG is where
essential in order to calculate reactive capability limits. The ρB1: Price of the upward balance services PB in $/MW.
values of PG for the generators are obtained from real power ρB2: Price of the downward balance services PB in $/MW.
market clearing information, as shown in Fig. 1 and discussed ρ0g: Availability price for generator g in $.
in Section III.A. ρ1g: Price of Losses in the under-excitation region for
A cost-based Q-dispatch model is proposed here, which generator g in $/MVar.
takes into account both economic and technical issues ρ2g: Price of losses in the over-excitation region for
associated with reactive power service provisions in a generator g in $/MVar.
competitive electricity market. The model is formulated as ρ3g: Loss of opportunity price for generator g in
⎛ ρ 0 g + ρ 2 g ⋅ QG 2 g − ρ1g ⋅ QG1g ⎞ ΔPGi Reduction in active power at bus i due to increase in
Min ∑⎜ + ρ
⎜ ⋅ QG3 g − 0.5ρ3 g ⋅ (QG3 g − QGA )
reactive power beyond heating limits.
⎝ 2g ⎠ PGoi: Pre-determined active power dispatch at bus i.
+ ∑ ρ B1 ⋅ PB1g + ∑ ρ B 2 ⋅ PB 2 g PBi1: Upward balance service at bus i.
g g PBi2: Downward balance service at bus i.
ci: Maximum allowed level of active power reduction at
s.t. PGio − ΔPGi + PBi − PDi bus i.
PGxg: New active power dispatch for generator g.
= ∑ ViV jYij cos(θ ij + δ j − δ i ) (11)
j In the above model, the objective function (10) comprises two
QGi − QDi = −∑ ViV jYij sin (θ ij + δ j − δ i ) (12) major terms: The first represents the payments associated with
reactive power provided from generators, wherein QG1, QG2
and QG3 denote the reactive power generation if the generator
Vi min ≤ Vi ≤ Vi max (13) is operating in Region I, II, and III respectively, in addition to
an availability payment to account for the capital cost of
Pij ≤ P max
reactive power production. The predetermined reactive power
ΔPGi ≤ ci PGio (15) price components associated with each region of operation
(ρ0g, ρ1g, ρ2g , and ρ3g) are input to the dispatch model as per Fig.
PBmini ≤ PB1, 2i ≤ PBmaxi
1, 2 1, 2 (16) 1. A detailed discussion on these price components and how
they can be calculated can be found in , where the authors
proposed a reactive power market model that addresses
⎛ (V I ) 2 − Q 2 several issues associated with reactive power management and
⎜ t a Gg
⎜ pricing. Determining reactive power prices in a different
if QGg ≥ QGAg & PGgo > PRg timeframe than that of active power minimizes price volatility
risks, and thus help reduce market inefficiencies.
PGxg ⎜ ⎛ Vt Eaf ⎞ − ⎛ Q + Vt ⎞
= ⎜ ⎟ ⎜ ⎟ (17)
Under certain loading conditions, some generators may be
⎜ ⎜ Xs ⎟ ⎜ G Xs ⎟ asked to supply reactive power in Region III, in which case
⎜ ⎝ ⎠ ⎝ ⎠ the generators will be required to reduce their real power
⎜ if QGg ≥ QGAg & PGgo < PRg generation in order to meet the system reactive power
⎜ requirement. Consequently, a re-schedule of their real power
⎜ PGog otherwise dispatch (ΔPG) will be called for, and a balance service (PB)
⎝ might be required to compensate for this real power deviation
from the already dispatched values (PGo). Thus, the second
term in (10) seeks to minimize the payments associated with
PGog − PGg = ΔPGg (18)
these energy balance services, from available providers, which
PGoi − ΔPGi + PBi ≤ P max
Gi (19) might be an upward or downward balance services within the
limits defined in (16). The prices for these balance services
Gg ≤ QG1g ≤ QGblead g (ρB1 and ρB2) are pre-determined from the energy balance
market. Accordingly, the nodal active power flow equation
QGblag g ≤ QG 2 g ≤ QGAg (20) (11) is modified to include both ΔPG and PB1,2. To minimize
QGAg ≤ QG 3 g ≤ QGBg the effect on real power dispatch (assumed known from a
separate auction), the reduction in real power will only be
QG1g ⋅ QG 2 g = 0 allowed up to a certain level (e.g. 5-10%) as per constraint
(15); in principle, this value could be set to zero, which reverts
QG 2 g ⋅ QG 3 g = 0 (21) the problem back to the classical reactive power dispatch.
QG1g ⋅ QG 3 g = 0 The required reduction in the real power a certain
generators (ΔPG) is determined by (17) and (18), where PGx is
QGg = QG1g + QG 2 g + QG 3 g (22) the new value of the real power after re-scheduling. Observe
that ΔPG will only have a non-zero value if the generator is
operating in Region III, i.e. if the generator hits its field limit
(PGA<PGR) or armature limit (PGA>PGR); otherwise PGx in (17)
will be equal to PGo and hence, according to (18), ΔPG will be
zero. Constraint (19) ensures that the total real power for each
generator, including the rescheduling and the balance service
if applicable, does not exceed its maximum value.
The three regions of reactive power production identified
from the generator’s capability characteristic (see Fig. 2) are
introduced through (20)-(22). It is to be noted that the two
constraints (21) and (22) guarantee that only one of the three
regions (out of QG1, QG2 and QG3) will be selected at a time,
for each generator. This is a non-convex NLP problem with
complementarity constraints, which requires special solvers
and/or solution techniques. In , the authors proposed an
iterative approach that can be used for solving this
optimization problem without the need for binary variables to
select one region out of the three operating regions.
The proposed reactive power dispatch model is supposed to
run in a 30 min to 1 h window, and the solution yields the
required reactive power support that minimizes the payment
by the ISO, while considering system security constraints Fig. 3. CIGRE 32-bus system.
represented through voltage limits (13) and transmission line for these generators is zero. The prices of the energy balance
power flow limits (14). services ρB1 and ρB2 are predetermined from the energy
balance auction, and are assumed here to be equal to 10 and
IV. IMPLEMENTATION AND TEST RESULTS 15 $/MW, respectively, for both cases. The four reactive
The results of applying the proposed reactive power dispatch power price components defined earlier in Section III.C are
model (10)-(22) to the CIGRE 32-bus test system (Fig. 3 ) also given in Table I, where they are fixed for both of the two
are presented and discussed in this section. Without loss of case studies. All power values in all tables are given in p.u. for
generality, power flow limits are assumed for all transmission a 100 MVA base.
elements simply based on their voltage ratings; thus, 2000 The solution of the model yields the required reactive
MW for 400 KV lines, 350 MW for 220 KV, and 250 MW for power support from each generator; the amount of real power
130 KV. All generators are assumed to be eligible for to be re-scheduled in order to meet the system reactive power
financial compensation in all of the three regions of requirements; the amount of energy balance services needed
operations, i.e. QGblead and QGblag in Fig. 2 are assumed to be to compensate for the losses as well as the change in real
equal to zero for all generators without any loss of generality. power resulting from this reactive power dispatch; and the
The optimization models, which are essentially NLP total payment of the ISO to the service providers.
problems, are modeled in GAMS  and solved using the
A. Case I
Two cases are considered here to examine the proposed Table II shows the solution for this low-loading level case,
reactive power dispatch model: indicating first the required reactive power generation for each
• Case I: “Low” (80%) loading condition. generator. Observe that each generator is operating in only
one of the three regions discussed earlier in Section III.B. It
• Case II: “High” (110%) loading condition.
can be seen from these results that there are no generators
In both cases, the input to the dispatch model is the list of
required to operate in Region III; hence, no real power
predetermined price components for each generator ; real
rescheduling is required and the value of ΔPG is zero for all
power obtained from the energy market clearing process that
the generators. This is expected as the system is lightly
took place prior to the reactive power dispatch procedures;
loaded, and thus reactive power requirements are not as high.
reactive power capability curves for each of the available
A small amount of balance service, from generator 4072, is
generators, which are functions of real power as per (9) and
required to compensate for the system losses. The value of the
(9); and the available energy balance services for each
objective function in this case is $2793, denoting the total
generator. Table I includes these input parameters for each of
amount to be paid by the ISO for the generators.
the 20 generators for the two case studies. The available real
power for energy balance is zero for a generator if its real B. Case II
power generation is at its maximum limit, indicating that this Table III shows the solution for this high-loading level case.
generator cannot provide any additional real power. For the Observe that now three generators (1012, 1022, and 1043) are
high loading conditions (Case II), more generators are required to operate in Region III, since the total system
working at their maximum real power capacity and hence they demand has increased; thus, these generators need to reduce
cannot participate in the energy balance service auction; PBmax their real power generation in order to meet the reactive power
TABLE I TABLE III
INPUT PARAMETERS FOR THE DISPATCH MODEL SOLUTION FOR CASE II
Case I Case II VAR Price Components Bus QG1 QG2 QG3 QG ΔPG PB1
Bus for both Cases 4072 0 2.653 0 2.653 0 0
PGo PBmax PGo PBmax ρ0 ρ1 ρ2 ρ3 4071 0 0 0 0 0 0
4072 11.75 4.11 18.9 6.63 .78 .59 .74 .35 4011 0 0 0 0 0 0.251
4071 4.7 0 4.7 0 .78 .59 .74 .35 4012 0 0 0 0 0 0
4011 3.97 1.39 6.47 2.27 .78 .59 .74 .35 4021 -0.3 0 0 -0.3 0 0
4012 5.42 1.90 7.52 0 .78 .59 .74 .35 4031 0 0 0 0 0 0
4021 2.82 0 2.82 0 .92 .91 .91 .36 4042 0 0 0 0 0 0
4031 3.29 0 3.29 0 .92 .91 .91 .36 4041 0 0 0 0 0 0
4042 2.50 0.87 6.58 0 .92 .91 .91 .36 4062 0 0 0 0 0 0
4041 2.82 0 2.82 0 .92 .91 .91 .36 4063 0 2.447 0 2.447 0 0
4062 2.99 1.05 5.64 0 .85 .53 .81 .26 4051 0 1.549 0 1.549 0 0
4063 9.68 1.60 11.3 0 .85 .53 .81 .26 4047 0 0 0 0 0 0
4051 5.83 0.75 6.58 0 .85 .53 .81 .26 2032 0 0.175 0 0.175 0 0
4047 1.20 0.42 11.3 0 .85 .53 .81 .26 1013 0 0 0 0 0 0
2032 7.99 0 7.99 0 .92 .91 .91 .36 1012 0 0 2.729 2.729 0 0
1013 4.74 0.90 4.75 0.89 .78 .59 .74 .35 1014 0 0 0 0 0 0
1012 7.52 0 7.52 0 .78 .59 .74 .35 1022 0 0 0.853 0.853 0 0
1014 3.72 1.30 4.45 1.56 .78 .59 .74 .35 1021 0 1 0 1 0 0
1022 2.35 0 2.35 0 .92 .91 .91 .36 1043 0 0 0.959 0.959 0.125 0
1021 4.71 0.93 4.80 0.84 .92 .91 .91 36 1042 0 0 0 0 0 0
1043 0.58 0.20 1.88 0 .85 .53 .81 .26
1042 3.76 0 3.76 0 .85 .53 .81 .26
TABLE II A cost-based reactive power dispatch model for competitive
SOLUTION FOR CASE I electricity markets is proposed in this paper. The model seeks
to minimize the total payments of the ISO, and hence the
Bus QG1 QG2 QG3 QG ΔPG PB1 objective function from minimization comprises three terms:
4072 0 0.299 0 0.299 0 0.064
the cost associated with reactive power service provision; the
4071 0 0 0 0 0 0
4011 0 5.095 0 5.095 0 0 cost of real power rescheduling resulting from reactive power
4012 -0.524 0 0 -0.524 0 0 dispatch; and the cost of providing additional energy balance
4021 -0.3 0 0 -0.3 0 0 services needed to compensate for the system losses and the
4031 -0.4 0 0 -0.4 0 0 change in real power generation.
4042 0 0 0 0 0 0 The results show that as the system demand increases, there
4041 -2 0 0 -2 0 0
4062 0 0 0 0 0 0
is more need for reactive power to maintain the system
4063 0 0.543 0 0.543 0 0 voltage as well as power transfer limits within the assigned
4051 0 0.236 0 0.236 0 0 limits, thus ensuring secure power system operation, as
4047 0 0 0 0 0 0 expected. The region of reactive power operation is
2032 0 1.685 0 1.685 0 0 determined by the generator capability curves, which also
1013 0 0 0 0 0 0
relate reactive power to real power; as the system reactive
1012 0 0 0 0 0 0
1014 0 0 0 0 0 0 power requirements increase, some generators will reach their
1022 0 0 0 0 0 0 capability limits (field or armature thermal limits) and thus
1021 0 1.156 0 1.156 0 0 reduce their real power output. These generators are eligible
1043 -0.2 0 0 -0.2 0 0 for additional opportunity-loss payment for not being able to
1042 -0.4 0 0 -0.4 0 0 sell their real power to the market.
requirements. For generators 1012 and 1022, no re-scheduling VI. REFERENCES
of their real power is required as both are operating on the
 US-Canada Power System Outage Task Force, Final Report on the
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Part C, Vol. 138, pp. 27-38, Jan. 1991. Engineer degree from the Escuela Politécnica Nacional (EPN), Quito-
 K. H. Abdul-Rahman, and S. M. Shahidehpour, “Reactive power Ecuador, in 1984 where he held different teaching and administrative
optimization using fuzzy load representation," IEEE Trans. Power Syst., positions from 1983 to 1993. His MSc (1988) and PhD (1991) degrees in
vol. 9, pp. 898–905, May 1994. Electrical Engineering are from University of Wisconsin-Madison. He has
 B. Venkatesh, G. Sadasivam, and M. A. Khan, “A new optimal reactive been with the E&CE Department, University of Waterloo since 1993, where
power scheduling method for loss minimization and voltage stability he has held various academic and administrative positions and is currently a
margin maximization using successive multi-objective fuzzy LP full Professor. His research activities concentrate in the study of stability,
technique,” IEEE Trans. Power Syst., vol. 15, pp. 844–851, May 2000. modeling, simulation, control and computational issues in power systems
 C. T. Su and C. T. Lin, “Fuzzy-based voltage/reactive power scheduling within the context of competitive electricity markets. Dr. Cañizares was the
for voltage security improvement and loss reduction,” IEEE Trans. recipient of IEEE-PES Working Group Recognition Award 2005 for
Power Del., vol. 16, pp. 319–323, Apr. 2001. Outstanding Technical Report, as the editor and co-author of Power Systems
 N. Grudini, "Reactive power optimization using successive quadratic Stability Subcommittee Special Publication "Voltage Stability Assessment:
programming method," IEEE Trans. Power Syst., vol. 13, pp. 1219– Concepts, Practices and Tools".
1225, Nov. 1998.
 I. El-Samahy, K. Bhattacharya, and C. A. Cañizares, “A Unified Kankar Bhattacharya (M’95, SM’01) received the Ph.D. degree in electrical
Framework for Reactive Power Management in Deregulated Electricity engineering from Indian Institute of Technology, New Delhi, in 1993. He was
Markets,” Proc. of the IEEE-PES Power Systems Conference and with the Faculty of Indira Gandhi Institute of Development Research,
Exposition (PSCE), Atlanta, Oct. 2006, 7 pages. Bombay, India, during 1993-1998, and the Department of Electric Power
 V.L. Paucar and M.J. Rider, “Reactive Power Pricing in Deregulated Engineering, Chalmers University of Technology, Gothenburg, Sweden,
Electrical Markets Using a Methodology Based on the Theory of during 1998-2004. Since January 2003, he has been with the Department of
Marginal Costs,” Proc. IEEE Large Engineering Systems Conference on Electrical and Computer Engineering, University of Waterloo, Canada, as an
Power Engineering, pp. 7-11, 2001. Associate Professor. His research interests are in power system dynamics,
 J. W. Lamont and J. Fu, “Cost analysis of reactive power support,” IEEE stability and control, economic operations planning, electricity pricing and
Trans. Power Syst., vol. 14, pp. 890-898, Aug. 1999. electric utility deregulation. Dr. Bhattacharya received the 2001 Gunnar
 S. Hao, “A reactive power management proposal for transmission Engström Foundation Prize from ABB Sweden for his work on power system
operators,” IEEE Trans. Power Syst., vol. 18, pp. 1374-1381, Nov. 2003. economics and deregulation issues.
 J. Zhong and K. Bhattacharya, “Toward a competitive market for
reactive power,” IEEE Trans. Power Syst., vol. 17, pp. 1206-1215, Nov. Jiuping Pan (M'97, SM'04) received his B.S. and M.S. in electric power
2002. engineering from Shandong University, Jinan, China and his Ph.D. in
 Y. Zhang, and Z. Ren, “Optimal reactive power dispatch considering electrical engineering from Virginia Tech, USA. He is currently a principal
costs of adjusting the control devices,” IEEE Trans. Power Syst, vol. 20, consulting R&D engineer with ABB Corporate Research in USA. His
pp. 1349– 1356, Aug. 2005. expertise includes power system analysis, generation and transmission
 V. Ajjarapu, P. L. Lau, and S. Battula, “An Optimal Reactive Power planning, power system reliability, energy market modeling and simulation
Planning Strategy Against Voltage Collapse,” IEEE Trans. Power Syst, studies.
vol. 9, pp. 906 – 917, May 1994.
 A. Berizzi, P. Bresesti, P. Marannino, G. P. Granelli, and M. Montagna,
“System-Area Operating Margin Assessment and Security Enhancement
Against Voltage Collapse,” IEEE Trans. Power Syst, vol. 11 pp. 1451 –
1462, Aug. 1996.
 C. A. Cañizares and S. K. M. Kodsi, “Power System Security in Market
Clearing and Dispatch Mechanisms,” Proc. IEEE-PES General Meeting
2006, Invited paper, Montreal, June 2006, 6 pages.
 A. D. Papalexopoulos, C. F. Imparato, and F. F. Wu, “Large-scale
optimal power flow: effects of initialization, decoupling and
discretization,” IEEE Trans. on PAS, vo1.4, pp. 748-759, 1989.
 A. El-Keib and X. Ma, “Calculating short-run marginal costs of active
and reactive power production,” IEEE Trans. Power Syst, pp. 559-565,
 V. L. Paucar and M. J. Rider, “Reactive power pricing in deregulated
electrical markets using a methodology based on the theory of marginal
costs,” Proceedings of the IEEE Large Engineering Systems Conference
on Power Engineering, pp. 7-11, 2001.
 T. J. Overbye, X. Cheng, and Y. Sun, “A comparison of the AC and DC
power flow models for LMP calculations,” Proc. 37th Annual Hawaii
Int. Conf. Syst. Sc., Jan. 2004, 9 pages.
 I. El-Samahy, K. Bhattacharya, C. A. Cañizares, M. Anjos, and J. Pan,
“A Procurement Market Model for Reactive Power Services Considering
System Security,” submitted to IEEE Trans. Power Syst, July 2006, 12
 GAMS Release 2.50, “A User’s Guide,” GAMS Development