Improved Marginal Loss Calculations During Hours of Transmission Congestion

Transcription

1 Improved Margnal Loss Calculatons Durng Hours of Transmsson Congeston Judth B. Cardell Smth College Abstract Shortcomngs of the current polcy focus and accepted mplementatons for calculatng and settlng transmsson losses strctly as margnal losses are presented. One modfed margnal loss calculaton approach for hours of transmsson congeston s proposed and demonstrated usng a 5-bus model from the PJM system. The objectve of the suggested change n the use and determnaton of margnal losses s both to mprove market transparency through an ncreased understandng of margnal loss calculatons, and to mprove the accuracy of the margnal loss calculaton durng hours wth bndng transmsson constrants. Along wth an ablty to hedge rsks assocated wth losses, these changes wll lead to better defned market rules and property rghts n electrcty markets. 1. Introducton Ths paper dscusses some shortcomngs of the current polcy emphass on prcng transmsson losses strctly on an ncremental bass, and presents a modfcaton applcable durng hours of regonal transmsson congeston. To provde context for the polcy debate, some standard methods for calculatng margnal losses n a power system are revewed brefly below. Ths revew serves to emphasze that there s no sngle, correct method for calculatng margnal losses, as s suggested by recent FERC orders. In contrast, margnal loss mplementatons often rely upon specfc smplfyng assumptons and system modelng decsons relatng to the selecton of the reference bus. These dfferent methods, well defned n engneerng lterature [1-7, 14, 16], wll typcally lead to dfferent though equally correct results. The sgnfcance of ths revew s to hghlght the fact that though the varous calculaton methodologes are accepted by ndustry, they are n fact dfferent and typcally wll result n dfferent economc mpacts for dfferent market partcpants. Followng the revew of margnal loss calculatons, the next secton dentfes an exstng flaw n many margnal loss methodologes. Specfcally, durng hours of system congeston, when by defnton generators can only serve a porton of the regonal load (beng ether export or mport-constraned from other areas) margnal losses must be calculated and charged to each generator or load bus n terms of the margnal losses that occur n the sub-regon that contans the gven bus. Sample calculatons of margnal losses n a constraned and un-constraned system, usng a 5-bus model from the PJM system are presented as part of the dscusson. 2. Margnal Loss Calculaton Methodologes Margnal losses represent the ncremental change n system losses due to an ncremental change n ether generator output or load consumpton. The ntended purpose of calculatng margnal losses and ncludng them n energy prces s to provde both short run and long run economc sgnals to market partcpants and nvestors. The short run sgnals are ntended to ensure effcent unt commtment and economc dspatch, whle the long run sgnals are ntended to be used n decdng the most effcent locatons to ste new generaton and load. As regons mplement full locatonal margnal prcng ( LMP ), each LMP value has margnal losses as one component of the prce (along wth energy and congeston). However, n order for ths economc sgnal to acheve ts ntended purpose the conveyng of dspatch and nvestment or stng ncentves market partcpants must have accurate knowledge of each component of the prce. If the nformaton s unavalable, not relable, or naccurate then the value of the ntended economc sgnal s degraded. In addton, market desgn must be perceved as far a test whch strct ncremental loss prcng does not pass as a result of the over-collecton of revenues through ncremental loss prcng Standard LMP Components Electrcty markets are gradually adoptng nodal prcng, or LMP, whch s composed of three prce components: energy, margnal losses and congeston. These components can be represented accordng to γ λ + γ + γ = ref L C where γ s the LMP or nodal prce at bus, λ ref s equal to the energy prce at the reference bus, γ L s the margnal loss component of the nodal prce, and γ C s the congeston component of the nodal prce. [11] (1) 1

2 Calculaton of the LMP Components. Two general methods exst for calculatng each LMP. One s to determne the three components from (1) separately and to sum them to obtan the LMP. A second method, adopted for example n New England, s to frst calculate each LMP value and then back out the ndvdual components. To ths end, the energy component of each LMP s smply the margnal cost of energy for the system, λ ref, at the reference bus. Any dfference between the prce of energy at the reference bus and the LMP at other buses represents the cost for transmsson, ncludng both losses and congeston (when transmsson congeston s present). When there s congeston ths method frst uses the loss penalty factor to determne the porton of the LMP that represents losses. Followng ths loss calculaton, any remanng amount from LMP - λ ref s assumed to represent transmsson congeston between the bus of nterest, bus, and the reference bus. Though clear theoretcally, n actual mplementaton, ths determnaton of the loss component s not transparent to market partcpants and s naccurate durng hours of congeston. These shortcomngs of the margnal loss calculaton and LMP settlement, present for example n New England, result n a falure to convey the ntended prce sgnal for stng and nvestment decsons, and are lkely to send the ncorrect dspatch sgnal durng tmes of congeston.. 3. Standard Methods For Calculatng Margnal Losses 3.1. Proposed Prcng Polcy Standard methods for calculatng the effect of margnal losses on locatonal margnal prces focuses on determnng the loss factor, or penalty factor, Pf, for each bus. Ths factor s defned as Pf 1 = P 1 P loss In determnng the optmal system operatng pont, the penalty factor s multpled by the margnal cost at each node, λ, such that Pf 1 λ 1 = Pf 2 λ 2 = Pf n λ n. In the absence of transmsson congeston, the penalty factors account for any dfference between the ndvdual LMPs and the reference energy prce, λ ref. The wdespread use of penalty factors n the lterature supports recent FERC decsons requrng the use of these factors. Unfortunately, recognton that there are multple methods for determnng penalty factors, and that these methods wll typcally result n dfferent, yet all vald, values for the penalty factors, s mssng from the FERC dscussons and rulngs. [11]. The mplcaton of ths (2) current polcy trend s that there s only one way to calculate penalty factors, and therefore, f market partcpants know that penalty factors are used, then they should know how the entre calculaton s performed. Ths assumpton s ncorrect and results n lack of market transparency and ll-defned market rules. In New England for example, the ISO recently mplemented the use penalty factors for margnal loss calculatons. As stated above, the use of a penalty factor for determnng the nodal prce component of losses s standard and accepted by the ndustry, yet there s no sngle, best method for calculatng and mplementng these factors. Therefore, complete nformaton must be provded to all market partcpants, suffcent to allow partcpants to understand the method used to calculate the factors, and to understand the effect of the selected method relatve to other possble methods Optons For Calculatng Margnal Losses The explanaton for the exstence of multple methods for calculatng the penalty factor can be seen from the expresson for the penalty factors, n equaton (2). As there s more than one accepted method for calculatng the margnal loss quantty P loss / P, there s also more than one accepted method for calculatng the penalty factors From the engneerng lterature, the dfferent methods are known to have dfferent tradeoffs n terms of accuracy and ease of mplementaton, and no one method has been recognzed as clearly superor to others by all authors. Wthn the varety of optons for calculatng margnal losses, there are two man methods. The drect method s the most accurate, but can be computatonally ntensve to mplement and tme consumng to use for real tme markets. Ths method uses data on voltage angles throughout the transmsson system and sgnfcantly makes no approxmatons n the calculaton of margnal losses. On study has shown that ths method, usng the transposed Jacoban matrx, can be computatonally superor to the second group of methods that nvolve some system smplfcatons. [1] The second method calculates what s called the B matrx or B coeffcents, and reles upon smplfyng assumptons to facltate mplementaton, resultng n a method conceptually accessble to a wder audence. Subsequently, a varety of methods have been developed to calculate the B matrx. An mportant pont to note here, whch wll be dscussed further below, s that the standard representaton for P loss, that P loss = ΣB*P 2, s a smplfcaton of the actual system loss equaton. Workng from ths smplfcaton, varous accepted methods for calculatng the B coeffcents for ths expresson have been developed, wth no one method beng adopted as the ndustry standard. One drawback of the common use of ths representaton, known to be a useful smplfcaton n the engneerng communty, s 2

3 that t tends to be represented as beng fully accurate n most polcy debates, whch thus do not nclude dscussons of the tradeoffs between dfferent methods for calculatng penalty factors and margnal losses Drect Method For Calculatng Margnal Losses. The calculaton of margnal losses begns wth an expresson for total system losses, from whch the ncremental, or margnal, value can be calculated. The total system real power loss s readly accounted for va the overall energy balance for any power system P loss ( PG P ) = P = L where P s the net power at bus, P G s the generaton at bus, and P L s the load at bus. The power flow equaton for bus represents the power flowng nto the transmsson network at bus, and s of the form P = n k= 1 V V k ( g cosθ + b snθ ) k where the subscrpts and k represent dfferent buses, P agan represents net power at bus, V the voltage magntude, θ the phase angle, and g and b the lne admttance values. Note that the quantty P s postve for net generaton at bus and negatve for net demand at bus. Realzng that the expresson for power at each bus on the transmsson network takes the form of equaton (4), and that the equatons for each bus are summed for the system energy balance of equaton (3), t s easy to see that the equaton (3) becomes very complex. It s possble to make a number of observatons from the expresson for system loss, equaton (3) combned wth (4). Frst, total system loss s clearly dependent upon the power generated or consumed at every bus and the admttance on every lne. Second, total system loss s also dependent upon the voltage magntude, V phase angle, θ, at every bus. A power flow model uses ths set of equatons to fnd P for every bus. A basc step before solvng the equatons though s to select a reference bus, for whch P s determned after the power flow s run and the generaton for every other bus has been determned. Wth the reference bus specfed, a soluton can be found followng procedures presented n [1, 2], resultng n an exact calculaton of the net power at each bus, P, and the total system loss, P loss. At ths pont, the margnal loss can be obtaned from (3) by frst dfferentatng load flow equaton (4) for each bus, wth respect to the state varables n (4), and then multplyng these values by the partal dervatves of V and θ wth respect to P. As t s easy to see that the energy balance equaton becomes very complex, t s also apparent that the partal dervatve of equaton (3) for every bus, P loss / P, (requred for fndng the penalty factors) can become qute complex. k k k (3) (4) An mportant property of these loss calculatons s ther dependency upon the selecton of the reference bus. As dscussed more below, numerous researchers have developed methods for usng a dstrbuted slack bus n calculatng margnal losses, wth the objectve of reducng or elmnatng ths senstvty n the values calculated for penalty factors. [4, 9, 10, 15] The B Matrx For Calculatng Margnal Losses. A second, wdely used method for calculatng margnal losses reles on an approxmaton for transmsson lne losses. Ths method captures the fact that losses are proportonal to the square of the power flow on a lne, and ntroduces the concept of the B coeffcents, for whch a number of calculaton methods have been developed over the years. The basc equaton [7, 14] s P loss T [ B] B0 P + B00 = P T P + where the matrx P contans each P, the power at each bus, B 0 and B 00 are constants and [B] represents the matrx of coeffcents that are the focus of many calculaton methodologes. A number of approaches for determnng the B coeffcents make a further smplfcaton by focusng exclusvely on the frst term of ths equaton [4] P = P T loss [ B]P wth the result that the margnal loss calculaton reduces smply to P loss P = 2 n j= 1 B j P j From ths expresson, t s apparent that gven a load flow soluton wth all P solved, the only unknown quanttes for calculatng margnal losses are the B coeffcents whch orgnated from an approxmaton of the actual system loss. From ths pont, varous methods can be used to calculate the B coeffcents. The general accuracy of ths approxmaton, and relatve accessblty of the dervaton has resulted n wdespread use of B coeffcents and the assocated equaton for approxmatng lne losses (6) Determnng the B Coeffcents. There are a number of accepted methods for calculatng the B coeffcents. Some methods may rely on a dstrbuted load bus, others may use a sngle reference bus [14] whle others may dspense wth the slack bus altogether [2]. Regardless of the methodology selected, the approaches dscussed above are all dependent upon the operatng pont of the power system at the tme the B coeffcents are calculated. Ths s to say that dfferent B coeffcent values are requred for dfferent load levels, dfferent patterns of generator output, and dfferent lne flows. In (6) (7) 3

4 New England, for example, a weghted average of the load buses s used for calculatng margnal loss [8]. For ths and all smlar markets, to provde transparency and better understandng of the market mechansms, the specfc nformaton and methodology for determnng these coeffcents should be made avalable to market partcpants for 3.4. Margnal Losses Summary Methods for calculatng margnal losses ncorporate the use of the loss penalty factor n order to determne the effect of loss on prces. The calculaton of the penalty factor, n turn, reles upon calculatng the quantty P loss / P whch can be acheved ether through drect calculaton or through a varety of acceptable methods for determnng B coeffcents. Each of these methods wll typcally result n dfferent values beng calculated for margnal loss at each bus. In addton to the dfferent loss calculaton methods, the selecton of the reference bus also mpacts loss calculatons for each bus. If the selected the reference bus s close to a gven bus, then bus would appear to ncur relatvely low margnal losses. In contrast the selecton of a more dstant bus as the reference bus would lead to the calculaton of hgher margnal losses at bus (snce the power must now apparently travel further to the reference bus and so ncur greater losses along the way). The drect calculaton procedures from [1, 2] calculate loss accurately, makng no smplfyng assumptons n fndng margnal loss. Nonetheless, these procedures share the property wth methods relyng on B coeffcents that the margnal loss value attrbuted to each bus wll change dependng upon the selecton of the slack, or reference bus. Alternatve calculaton methods rely upon the use of a dstrbuted reference bus for solvng the power flow equatons (drawng on the analogous role played by AGC unts) [15, 16], or the use of a dstrbuted slack bus comprsed of load buses that proportonally ncrease ther demand n response to an ncremental ncrease n generaton at bus. [9, 10, 16] In spte of these efforts, the results of these studes tend to show that reference bus, whether tradtonal (sngle) or dstrbuted, consstently has some affect on the calculaton of margnal losses. Thus the defnton of the reference bus s seen to drectly affect the resultng margnal loss and penalty factor calculatons, and subsequently the nodal prce, or LMP, calculatons. Ths hghlghts the need for all ths nformaton to be made publcly avalable. A smple statement that the standard penalty factors are beng calculated, as has been accepted by FERC [11] s nsuffcent snce there s no standard or unversally accepted method. 4. Margnal Loss Calculatons and Congeston In standard mplementatons, margnal losses are calculated n the same manner durng hours wth congeston as durng hours wthout congeston. For a gven load level, margnal losses from each bus are calculated to be the same whether or not buses are constraned from the rest of the system. Ths s to say that margnal losses are calculated to be the same regardless of whether or not the margnal power generaton can actually flow on the entre transmsson system, and so ncur regonal losses. Though t does make sense to use the same method for hours wth and wthout congeston, the actual calculaton for margnal losses should be adjusted for the presence of congeston n large, regonal electrcty markets encompassng geographcally and electrcally dspersed transmsson systems. By defnton, transmsson congeston between two buses or two regons n a power system means that there s a bndng transmsson constrant between these two ponts. In turn, a bndng transmsson constrant means that no addtonal net ncremental power can flow between the two regons. Therefore, addtonal, or ncremental, load n one regon can be met only by ncremental generaton n that same regon ncremental supply from the regon on the other sde of the constrant cannot be used to serve ncremental load n the frst regon. The fact that ncremental generaton s thus constraned to flow wthn the smaller sub-regons has drect consequences for the calculaton of ncremental or margnal loss. Specfcally, snce ncremental power flows are constraned to a sub-regon, these flows can only cause ncremental (or margnal) loss n ths same sub-regon. A couple of studes have developed methods for loss calculatons between dstnct regons, for uncongested hours. [4b, 15] A dfferent study also modeled only uncongested hours and found that the proposed dstrbuted slack bus methodology dd not reduce the slack bus dependency of loss calculatons for buses dstant from the dstrbuted slack bus (comprsed of load buses n ths case). [9, 10] Ths result ndcates that even wthout transmsson constrants, the assumpton of slack bus ndependent loss calculatons does not hold for all buses n a large regon, but nstead s true only for the buses electrcally close to the area contanng the buses n the dstrbuted slack bus (whch s to say, buses that are close to the regonal load centers). A specfc market mplementaton wth a dstrbuted load slack bus has been proposed for New England. [8] Ths method develops the use of a weghted average of the load bus as the dstrbuted slack for calculatng margnal loss. Though questons exst about the selecton of the weghts selected, the coeffcents developed to 4

5 apporton loss responsblty across load buses, and an offset value to facltate a soluton to the lnear program model, these assumptons are accepted as beng areas for further research. Ths paper addresses an ssue not rased n [8] the accuracy of loss calculatons durng hour of transmsson congeston Margnal Losses Calculatons Durng Hours of Congeston The result of the observaton that transmsson constrants essentally dvde a system nto two or more sub-regons, wth respect to ncremental power flows and ncremental loss, s that durng hours wth congeston all margnal loss must be calculated n terms of power flows n the smaller sub-regons, and not n terms of power flows throughout the entre regon of the gven electrcty market. Durng hours when transmsson constrants prevent some buses from supplyng ncremental power to the load centers defnng a dstrbuted slack bus, margnal losses at those constraned-off buses, or more specfcally the penalty factors for those buses, need to be determned n terms of the smaller, constraned porton of the regonal transmsson network. In terms of the development of the dfferent calculaton methods, the presence of congeston can be seen to mpact drectly the system energy balance equaton (3). In hours wthout congeston, ths equaton wll nclude terms for every bus n the system. For hours wth transmsson congeston though, ndvdual P terms should be ncluded only for those buses that are wthn a gven export-constraned or mport-constraned subregon, snce each sub-regon must now mantan the ncremental supply-demand balance ndependently of the other sub-regon(s). The result of changng the number of terms n equaton (3) s that the margnal losses,.e., the partal dervatve of equaton (3), P loss / P, wll also change. The energy balance equaton changes because the number of terms n the equaton decreases. The subsequent change to the partal dervatve, P loss / P, whch s smply the margnal loss, hghlghts the fact that the margnal loss calculaton wll be dfferent wth and wthout congeston present. It s sgnfcant to note that calculatons wth the loss formulae, as defned for example n [14] are relevant when constrants on power flows are gnored. These loss formulae are not defned for a system wth bndng transmsson lmts. Ths dscusson hghlghts the mportance of defnng a dfferent reference bus for constraned sub-regons durng hours of transmsson congeston. In terms of the mplementaton of margnal loss calculatons n regons usng a dstrbuted load bus, a new reference bus e.g., a new dstrbuted, weghted-average, load bus n New England must be defned for each constraned regon durng hours of congeston Results of Margnal Loss Calculatons Durng Hours Wth and Wthout Congeston To llustrate how margnal losses and nodal penalty factors are lkely to vary n a power system between perods wth and wthout congeston, a 5 bus example, based on an example from PJM [12], s presented below. In ths example, the margnal losses and penalty factors were modeled accordng to the procedure defned n [5]. To begn, the margnal losses and penalty factors are calculated assumng there s no congeston on the system, so that ncremental power generated at any node s avalable to supply ncremental demand at any node. In ths stuaton, the penalty factors are as shown n Table 1. Because margnal loss s dependent upon the net power output at each node, the margnal losses and assocated penalty factors wll be dfferent at dfferent load and generaton levels. Table 1 shows a possble startng pont for the example. Bus 1 s used as the slack bus, wth the result that margnal losses at ths bus are zero,.e., the penalty factor s defned to be In the system wthout congeston, all dfferences n LMP values are attrbuted to losses there s no congeston prce component, γ C from equaton (1), at any bus. Table 1: Penalty factors for 5-bus system wthout congeston Bus Pgen Pload Reference Prce Penalty Factor Bus Prce: LMP Loss Prce Component Congeston Prce Component If there s congeston n ths system, the penalty factors, as well as the reasons behnd dfferences n LMPs, all change. An example wth congeston n the 5 bus system s shown n Table 2. In ths case buses 1, 2 and 3 are export-constraned from buses 4 and 5, whch are mport-constraned. It s assumed that an ncremental ncrease n load, wth the subsequent ncremental ncrease n lne flows caused the transmsson lne constrants to become bndng. In ths way, the startng pont for the system n Table 2 s the same as shown n Table 1, except for a 1MW ncrease n load at bus 5. In ths example, bus 1 s used as the reference bus for the subsystem wth buses 1, 2 and 3. Bus 5 s the 5

6 reference bus n the second subsystem, composed of buses 4 and 5. Table 2: Penalty factors for 5-bus system wth congeston Bus Pgen Pload Reference Prce Penalty Factor Bus Prce: LMP Loss Prce Component Congeston Prce Component Note that n order to make comparsons between prces and penalty factors easer, an ncremental ncrease s assumed n the demand at bus 5, and the LMP at bus 5 ncreased. Note also that n the system wth congeston there are two reference buses, one for each subsystem. In lookng at Table 2, there are four dfferences between the results shown n Table 1 and those n Table 2. Frst s the fact that the penalty factors have changed, wth a drect mpact on the LMP values. Note that these changes wll affect dfferent partcpants dfferently, as dscussed above. Second, whle bus 1 s stll used as the reference bus and thus s the reference prce for buses 2 and 3, the prce at bus 5 s now used as the reference prce for bus 4. The mportant pont to observe here s that the prces between these reference buses are dfferent, but ths dfference s attrbutable to congeston, and not to losses. Ths s the thrd mportant observaton, and s demonstrated n the row Congeston prce component. Ths row represents the prce component for congeston between the export mport constraned portons of the full system (buses 4 and 5 beng mport-constraned) and the orgnal reference bus, bus 1. The fnal mportant observaton s the changes to the loss prce component, n row 7. The values n ths row show that, n ths smple example, buses 2 and 3 now see ncrementally hgher LMPs compared to the uncongested system such that load would pay more for energy at these nodes whle generators would receve the hgher prce Summary of Examples These results demonstrate that usng a dfferent reference bus for each subsystem durng tmes of congeston does lead to dfferent loss penalty factors and so dfferent LMP values. The specfc values n Tables 1 and 2 are not ntended to represent results for buses n an actual power system, but nstead are a smplfed example for comparson between cases wth and wthout congeston. A second mportant concept from ths example s the nterpretaton of the dfferences n LMPs between buses n the system. Durng perods wth no congeston, all LMP dfferences are attrbutable to loss. Durng a perod wth congeston, the dfference n LMP from the reference n the mport-constraned subsystem to the orgnal reference bus (assumed to be the major porton of the power system) s attrbutable entrely to congeston. Ths reflects the fact that no ncremental power can flow between the subsystems when there s congeston, wth the result that there s no margnal loss between the subsystems. Wthn each subsystem however, the dfferences n LMP values s attrbutable to loss. In ths manner, the prce sgnals representng transmsson congeston and transmsson losses reman separate and clearly understood. A mechansm for hedgng transmsson congeston already exsts through FTR auctons. A mechansm for hedgng transmsson losses, once losses are more rgorously dentfed, s watng to be developed, allowng for a more complete market structure. The results of ths example demonstrate two mportant ponts applcable to the New England electrcty markets. The frst s that durng hours of congeston, margnal losses n each sub-regon are lkely to be less f calculated correctly than f they are calculated accordng to the exstng methodology n New England. Specfcally, snce each generator s restrcted to supplyng ncremental power to load n the gven sub-regon a regon that s smaller than the full New England system the overall margnal losses wll be lower (because all ncremental power s flowng wthn smaller sub-regons, and, therefore, flowng over shorter dstances, thus ncurrng lower losses). Ths wll reduce the over-collecton of loss revenues and partally address the farness ssue. The second sgnfcant result s that margnal loss s zero between the mport constraned regon from the basecase export constraned system reference bus. Ths s because ncremental power s not flowng from the mport constraned regon to the orgnal system reference bus, and so cannot be ncurrng losses on power lnes over whch t s not flowng. The entre LMP prce dfference between the reference bus and the mport constraned subregon LMP λ = ref γ C s attrbutable to congeston. Because no ncremental power can flow between the regons, there s no ncremental or margnal loss between these regons. Any dfference n LMP values s due to the congeston between the regons. (8) 6

7 4.3.1 Effcency Concerns In Calculatng the LMP Components Accurately. As ntroduced above, the ntended purpose of calculatng margnal losses and transmsson congeston, and ncludng them n energy prces, s to provde both short run and long run economc sgnals to market partcpants. If, however, the components of the LMP are calculated ncorrectly, such that part of the congeston cost s attrbuted to margnal losses, then the wrong economc sgnal s beng sent both to potental nvestors n the transmsson system and for potental stng decsons for generaton and load. Ths wll lead to neffcent decsons beng made by market partcpants wth respect to nvestment n power system facltes. In addton, durng tmes of congeston, a less effcent unt s lkely to be dspatched The Self-Supply Of Margnal Losses The second shortcomng of the mplementaton of margnal losses n most electrcty markets arses from the fact that these markets do not offer an opton for ether the self-supply of losses or the hedgng of loss costs. Ths s n stark contrast to the fact that generators and loads are allowed to self-supply or purchase from thrd partes, system servces such as regulaton and are also able to hedge congeston costs. Ths mssng mechansm leaves the market defnton ncomplete, hnderng the development of a complete market for electrcty. Ths s the mssng pece of selfsupply and loss hedgng, when combned wth forward markets for energy and transmsson rghts, would allow supplers and customers to drectly account for all three components of LMP, energy, margnal losses and congeston. 5. Conclusons The ntended purpose of calculatng margnal losses and ncludng them n energy prces s to provde both short run and long run economc sgnals to market partcpants and nvestors. If the nformaton assocated wth the calculatons s unavalable, not trusted, or naccurate then the value of the ntended economc sgnal s degraded. For these reasons market partcpants must have accurate knowledge of the determnaton of each component of the LMP. Because the dfferent methods for calculatng margnal losses wll have varous economc mplcatons for dfferent market partcpants, t s partcularly mportant that the specfc calculaton method be made publc as part of the actual market mplementaton. Margnal losses tend to be calculated usng the same penalty factors for hours wth and wthout congeston even though the margnal power generaton cannot actually flow on the entre transmsson system. Though t does make sense to use the same method for hours wth and wthout congeston, the actual calculaton for margnal losses should be adjusted for the presence of congeston n large, regonal electrcty markets. An example demonstratng the dependence of penalty factors on the extent of the power system over whch ncremental power can flow (.e., f some regons are export or mportconstraned) s shown n Tables 1 and 2. Fnally, t s mportant to provde a means for market partcpants to hedge the rsks assocated wth losses. Ths mssng mechansm leaves the market defnton ncomplete, hnderng the development of a complete market for electrcty. A mechansm for hedgng transmsson congeston already exsts through FTR auctons. A mechansm for hedgng transmsson losses, once losses are more rgorously dentfed, must also be developed, allowng for a more complete market structure. One provson that partally addresses ths shortcomng s the ablty to self-supply losses. Ths s the mssng pece whch, when combned wth forward markets for energy and transmsson rghts, would allow supplers and customers to drectly account for all three components of LMP, energy, margnal losses and congeston. The solutons and calculaton approaches proposed n ths paper, along wth a well defned mechansm for selfsupply of losses, wll lead to mproved transparency as a result of an ncreased understandng n the determnaton of margnal losses, and an mproved margnal loss calculaton methodology for hours wth transmsson congeston. These changes wll lead to better defned property rghts and better defned regonal electrcty markets. 6. References [1] Alvarado, F.L., Penalty Factors from Newton s Method, IEEE Transactons on Power Apparatus and Systems, Vol. PAS-97, No. 6, Nov/Dec 1976, pp [2] Bergen, Arthur, Power Systems Analyss, Prentce- Hall, Englewood Clffs, NJ, 1986, pages [3] Conejo, A.J., Arroyo, J.M., Alguacl, N., Gujarro, A.L., Transmsson loss allocaton: a comparson of dfferent practcal algorthms, IEEE Transactons on Power Systems, Vol. 17, No. 3, August 2002, pp [4] da Slva, A.M.L., de Carvalho Costa, J.G., Transmsson loss allocaton I Sngle energy market, IEEE Transactons on Power Systems, Vol. 18, No. 4, Nov. 2003, pp [4b] da Slva, A.M.L., de Carvalho Costa, J.G., Transmsson loss allocaton II Multple 7

8 Interconnected Energy Markets, IEEE Transactons on Power Systems, Vol. 18, No. 4, Nov. 2003, pp [5] El-Abad, H, Power System Analyss and Plannng, McGraw Hll, 1983, Chapter 11. [6] Granger, John J., Wllam D. Stevenson, Jr., Power System Analyss, McGraw Hll Inc., New York, [7] Krchmayer, L.K., G.W. Stagg Evaluaton of Methods of Co-ordnatng Incremental Fuel Costs and Incremental Transmsson Losses, Transactons of the Amercan Insttute of Electrcal Engneers, part 3, [8] Ltvnov, Eugene, Tongxn Zheng, Gary Rosenwald and Payman Shamsollah, Margnal Loss Modelng n LMP Calculaton, IEEE Transactons on Power Systems (forthcomng 2004). [9] Moon, Young-Hyun, Byoung-Kon Cho, Heon-Su Ryu, Jae-Suk Jung, Ho-Mn Park, Slack-bus ndependent penalty factor for spot prcng under deregulaton, IEEE Power Engneerng Socety Wnter Meetng, Volume 2, January 2000, pp [10] Moon, Young-Hyun, Hyo-Sk Hong, Heon-Su Ryu, Byoung-Kon Cho, Jung-Do Park, Slack-bus ndependent penalty factor for regonal spot prcng under deregulaton, IEEE Power Engneerng Socety Wnter Meetng, Volume 2, January 2000, pp [11] New England Power Pool, et al., 101 FERC 61,287 (2002); see Northeast Utltes Servce Co., et al. v. ISO New England Inc., et al., 105 FERC 61,122 at P 21 (2003). [12] PJM Interconnecton LLC, Locatonal Margnal Prcng, presentaton at [13] Schweppe, Fred C., Mchael Caramans, Rchard Tabors, Roger Bohn, et. al., Spot Prcng of Electrcty, Kluwer Academc Publshers, Boston, [14] Wood, Allen, Bruce Wollenberg, Power Generaton Operaton and Control, 2 nd ed., Wley-Interscence, New York, [15] Yan, Png, Modfed dstrbuted slack bus load flow algorthm for determnng economc dspatch n deregulated power systems, IEEE Power Engneerng Socety Wnter Meetng, Vol. 3, 28 Jan.-1 Feb. 2001, pp [16] Zoban, A., Ilc, M.D., Unbundlng of transmsson and ancllary servces. I. Techncal ssues, IEEE Transactons on Power Systems, Vol. 12, No. 2, May 1997, pp