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1 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 [3] 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 [4]-[9]. 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 [10], [11], or minimizing voltage and transformers taps deviations [12]. 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 [13]. 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. [14]-[16], minimization of deviations from contracted Insufficient reactive power supply can result in voltage transactions [17], minimization of the cost of adjusting collapse, which has been one of the reasons for some recent reactive power control devices [18], 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 [19], [20]. 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 [1]. 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 [2]. 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: ieselsam@engmail.uwaterloo.ca; kankar@ece.uwaterloo.ca; The paper is organized as follows: In Section II, the ccanizar@uwaterloo.ca. 2 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 [21]. 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 [5], [6]: 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 i, j 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 j 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 Gg (5) calculated post real-time operation, based on the actual usage QGg ≥ QGg min (6) and dispatch requested by the ISO aggregated over a period of time. 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 [13], also suggested in [22]-[24], 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 [21]. In this 3 P-dispatch Predetermined instructions price components Q-capability Solve ORPD P-market curves model minimizing clearing the ISO payments Determine the required reactive power support Q-settlements and payments 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 [25] 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 [13]. 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 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 2 ⎜ ⎟ (9) Xs ⎟ ⎜ Xs ⎟ G excitation region, in which the generator is required ⎝ ⎠ ⎝ ⎠ to supply reactive power within its reactive power capability limits. 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 4 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 follows: $/MVAr/MVar. ⎛ 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 ) 2 ⎟ ⎟ (10) reactive power beyond heating limits. g ⎝ 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 j 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 ij (14) 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 [25], 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 ⎜ ⎜ 2 risks, and thus help reduce market inefficiencies. 2 2 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 Q min 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 5 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 [25], 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 [25]) 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 [27] and solved using the A. Case I MINOS solver. 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 [25]; 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 6 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 V. CONCLUSIONS 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 [1] US-Canada Power System Outage Task Force, Final Report on the limit of their reactive power capability curves, i.e. at point A August 14, 2003 Blackout in the United States and Canada: Causes and in Fig. 2. 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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 [11] 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 [12] 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. [13] 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 [14] 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, [15] 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 [16] 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. [17] 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 [18] 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 [19] 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. [20] 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. [21] 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. [22] 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. [23] A. El-Keib and X. Ma, “Calculating short-run marginal costs of active and reactive power production,” IEEE Trans. Power Syst, pp. 559-565, May 1997. [24] 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. [25] 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. [26] 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 pages. [27] GAMS Release 2.50, “A User’s Guide,” GAMS Development Corporation, 1999.

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