electrothermal coordination part ii: case studies

1738 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 4, NOVEMBER 2005

Electrothermal Coordination Part II: Case StudiesNatalia Alguacil, Member, IEEE, M. Hadi Banakar, Member, IEEE, and Francisco D. Galiana, Fellow, IEEE

Abstract—The concept of electrothermal coordination (ETC) inpower system operation introduced in Part I proposes to exploitthermal inertia to coordinate line temperature dynamics withexisting power system controls, thus increasing power transfercapability and enhancing system security and economic perfor-mance. In this Part II, the characteristics of ETC and its benefitsin operational functions such as augmenting power transfer ca-pability, emergency control, congestion management, and systemloadability are numerically analyzed through a number of casestudies. This paper also examines some practical issues concerningthe deployment of ETC.

Index Terms—Congestion management, emergency control,heat balance equation, line thermal rating, load shedding, powertransfer capability, temperature dynamics.

I. INTRODUCTION

THIS PAPER complements the ideas presented in Part I [1]by analyzing the potential benefits of electrothermal co-

ordination (ETC) through a number of case studies in trans-mission congestion management, line maintenance scheduling,emergency load shedding, and system loadability. In addition,some practical considerations regarding the online deploymentof ETC in existing power systems are discussed.

First, we briefly recall the fundamental differences betweenthe conventional optimal power flow (OPF) and ETC.

1) ETC explicitly models the thermal inertia of the conduc-tors of thermally limited lines through the so-called dy-namic heat balance differential equation that includes thethermoelectric coupling provided by the heating effect oftransmission losses.

2) With ETC, the operational limits of thermally limitedlines are imposed by a maximum conductor temperatureand not by the conventional static or dynamic power flowratings.

3) The benefits of these ETC characteristics are that duringtemperature transients (possibly lasting up to half anhour), one can operate beyond the conventional powerflow limits without necessarily violating the more funda-mental maximum line temperature criterion. Therefore,

Manuscript received June 28, 2004; revised October 20, 2004. This work wassupported in part by the Natural Sciences and Engineering Research Council(NSERC), Canada, by the Fonds québécois de la recherche sur la nature et lestechnologies, Québec. The work of the first author was supported in part by theMinistry of Science and Technology of Spain under Grant CICYT DPI2003-01362, in part by the Junta de Comunidades de Castilla-La Mancha, Spain,under Grant GC-02-006, and in part by the University of Castilla-La Mancha,Spain, under Project 011.100616. Paper no. TPWRS-00342-2004.

N. Alguacil is with the Department of Electrical Engineering, University ofCastilla-La Mancha, Ciudad Real, Spain (e-mail: [email protected]).

M. H. Banakar and F. D. Galiana are with the Department of Electrical andComputer Engineering, McGill University, Montreal, QC H3A 2A7, Canada(e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRS.2005.857836

TABLE ICHARACTERISTICS OF TEST CASES (FOR NOMENCLATURE, SEE PART I)

in power system operation, especially under emergencyconditions following an outage, ETC affords additionaltime and room to maneuver.

This paper demonstrates how to exploit this additional flexi-bility through five case studies.

II. CASE STUDIES

The five cases are analyzed under both “conventional”and “ETC” approaches, where the former is an OPF thatdoes not characterize line temperature effects, enforcing onlysteady-state power flow limits.

Table I summarizes the defining characteristics of the fivecase studies. Cases A, B, and C analyze a two-bus network withtwo generators and one or two lines, case D examines a five-bus,six-line, three-generator system, while case E is a case studybased on the 24-bus IEEE RTS model [2].

In all cases, both ETC and OPF use a nonlinear power flowmodel with the simplification that sufficient var resources areavailable to maintain all bus voltage magnitudes constant at1 p.u. In both OPF and ETC, the simplifying constant voltageassumption is not necessary and can be relaxed by addingvoltage-reactive power constraints. The constraints consideredare generator capacity and ramp rate limits as well as linethermal limits, which for ETC take the form of line temperaturelimits. This choice of constraints is helpful to show the impactof thermal inertia on line power transfer capability when com-pared to those given by static and dynamic rating approaches.Note that if ETC were considered as the primary online oper-ational tool, power system security should be addressed in amuch broader sense by including a host of other engineeringand operational constraints in ETC formulation. In particular,when line switching is considered by ETC, it should accountfor post switching voltage levels and voltage angles acrossswitched lines to ensure realistic voltage profiles and breakerclosure.

0885-8950/$20.00 © 2005 IEEE

ALGUACIL et al.: ELECTROTHERMAL COORDINATION PART II: CASE STUDIES 1739

TABLE IIGENERATOR DATA—CASES A–C

TABLE IIILINE DATA—CASES A–D

TABLE IVLINE THERMAL COEFFICIENTS—CASES A–E

The objective function minimized in the ETC formulationcan take different forms depending on the operational aims, ofwhich the more standard is the total cost of generation over thecoordination interval. However, as summarized in Table I, insome case studies (D and E), the objective function can also in-clude the total load shed during an emergency.

The line thermal data used for all simulations are based onIEEE standards [3]. Additional generator and line data are pre-sented in Tables II and III, respectively.

In all case studies, the coordination period can last up to 4 hwith 5-min time-discretization intervals.

It is assumed that the weather conditions remain constantduring the coordination period, which implies that the radiationcoefficient , the solar heating radiation rate , and theconvection coefficient , all of which are weather depen-dent, also remain constant. Note that although coefficientdepends on conductor temperature, which may vary with time,this is a second-order effect that has been neglected. In the cal-culation of the effect of convection on the heat balance, we alsoassume that the angle between the wind speed direction and theconductor axis is 90 . The line thermal coefficients are given inTable IV.

From a mathematical perspective, cases A–C and E are non-linear programming problems with continuous variables only,while case D is a mixed-integer nonlinear program with bi-nary variables. All are solved using the optimization packagesMINOS 5.51 and SBB under GAMS [4] on a 240-GHz PC Pen-tium IV with 480 MB of RAM.

In cases A and B, the power system comprises two identicalparallel short lines transferring power from bus 1 to bus 2 (seeFig. 1). The maximum allowed line temperature of 100 C ineach line is reached with a steady-state power flow of 216.6 MW.

The generators are assumed to have linear cost functions, inother words, and , withgenerator 2 being incrementally four times more expensive thangenerator 1 (see Table II).

Fig. 1. Two-bus system. Cases A and B.

A. Temporary Line Outage

Here, in the pre-fault state, the system of Fig. 1 is transmittingpower from generator 1 through lines 1 and 2 to the load at bus 2,which is constant at 221 MW over the 4-h coordination horizon.Initially, the demand is fully supplied by the cheaper generator1 that produces about 235 MW, with transmission losses of ap-proximately 7 MW per line. Generator 2 is on but is dispatchedat zero output since it is incrementally more expensive.

Line 2 is now subject to a temporary outage, forcing line 1 tooperate above its steady-state power flow limit. Thus, under theconventional approach, either the expensive generator 2 must beredispatched to supply part of the load or, if generator 2 is notfast enough to pick up the imbalance, then some load shedding isneeded. In what follows, we have assumed that the up-rampingcapability of generator 2 is sufficiently high.

What we demonstrate below is that under ETC, we can sys-tematically take advantage of thermal time delay to operate theremaining line 1 above its steady-state power flow limit as longas its temperature remains below 100 C. Then, if line 2 can berestored before line 1 reaches its maximum allowed tempera-ture, redispatching the expensive generator becomes unneces-sary. This is a new form of emergency control only possiblethrough ETC with temperature-sensor-based relays.

The proposed ETC approach is compared with two variationsof the conventional optimal dispatch: one with static and theother with dynamic power flow ratings. The static rating as-sumes a standard ambient temperature of 40 C, while the dy-namic rating and ETC models are both based on the actual am-bient temperature, in this case 25 C.

Note that both static and dynamic power flow ratings are ob-tained at the maximum allowed conductor temperature. How-ever, in the static approach, the line resistance is calculated atthe reference temperature. This is consistent with present prac-tice, which neglects transient temperature effects.

The line resistance under the dynamic rating approach is up-dated periodically as a function of the most recent measured linetemperature. The fundamental difference between the dynamicrating approach and ETC is that ETC not only models the tem-perature dependence of the line resistance but it also explicitlyaccounts for the dynamic heat balance equation as part of thecoordination process.

The temporary outage of line 2 begins at min and endswith the line being restored at min. The immediateeffect of the outage is to more than double the sending flow onthe remaining line 1 to 261.7 MW, thus violating the static limitof 216.6 MW by about 17% and the dynamic limit of 243.7 MWby 7%.

Fig. 2 shows the evolution of the temperature of lines 1 and 2under ETC. When line 2 is disconnected at min, it begins


Fig. 2. Line temperatures under ETC. Case A.

TABLE VGENERATION AND INCREMENTAL COSTS UNDER CONVENTIONAL

AND ETC APPROACHES—CASE A

to cool down, while line 1 heats up. When line 2 is restored, bothlines are loaded identically and their temperatures converge tothe same steady-state value. Therefore, by restoring line 2 at

min, the temperature of line 1 remains below 100 Cso that the redispatch of generator 2 or load shedding becomesunnecessary.

Tables V and VI summarize some numerical results forthis case study. Table V shows that under the static and dy-namic-based rating methods and ETC, generator 2 produceszero output just before the line outage. Just after the outage,however, under static rating, generator 2 is redispatched toproduce 26.0 MW throughout the outage, while, under dynamicrating, generator 2 is redispatched to generate power rangingfrom 7.1 to 11.8 MW. Table V also shows that under both staticand dynamic ratings the marginal cost of generating powerat bus 2 during the outage is 100 $/MWh. In comparison,under ETC, the expensive generator 2 does not produce anypower after the outage so that the marginal cost at bus 2 variesonly slightly due to varying line losses but never exceeds$38.72/MWh.

The discrepancies observed in Table V between the static anddynamic rating cases in the generation levels and the marginalprices before and after the fault are due to differences in lineresistance. This is due to the fact that under static rating, the line

TABLE VIPOWER FLOW, LOSS, AND TEMPERATURE UNDER CONVENTIONAL

AND ETC APPROACHES—CASE A

resistance is based on the reference temperature, while underdynamic rating, it is based on a measured or estimated actualconductor temperature.

Table VI shows additional details about case study A, specif-ically the time evolution of line loss, power flow, and line tem-perature. Observe that under ETC, the line temperature alwaysremains below the specified limit of 100 C even though duringthe outage, the flow in line 1 is above the conventional static anddynamic ratings. Note also that under dynamic rating, the linecapacity is higher than under the static rating due to the lowerambient temperature of 25 C.

Another point distinguishing ETC from the conventional ap-proaches is that under ETC, the results are affected by the ini-tial line temperature. Thus, a line that is initially “cool” offersthe operator more room to maneuver than one that is initially“warm.”

What this case shows is that by exploiting thermal transients,ETC squeezes out a higher power transfer than the conventionalapproaches, even with dynamic line rating, and that this canbring significant security and economic benefits.

B. Line Maintenance Planning

This case highlights the ability of ETC to plan line main-tenance outages by exploiting the time delays between lineloading changes and temperature limit violations. Consideringthe system of Fig. 1 once more, this case study shows thatthe maximum disconnection time of one of its lines is directlyrelated to the line loading and can be calculated for purposesof line maintenance.

The solution shown in Fig. 3 is based on a series of ETC runswith steadily increasing net demand. For each simulation, wecalculate the time that it takes the healthy line to reach 100 C.For example, when the net demand is below 220 MW at an am-bient temperature of 40 C, the allowed time for maintenance ofthe line is at least 15 min. Observe also that the weather condi-tions have an impact on the available maintenance time. In thiscase, if the ambient temperature were 25 instead of 40 C, theavailable maintenance time would be 30 instead of 15 min.

C. Line Congestion Management

This case study illustrates the ability of ETC to manage linecongestion during peak demand periods. Consider the systemin Fig. 4. From the data in Table II, recall that generator 1 isincrementally four times cheaper than generator 2 and has ten


Fig. 3. Relation between net demand and maintenance time. Case B.

Fig. 4. Two-bus system for line congestion management. Case C.

Fig. 5. Load profile. Case C.

times more capacity. The load located at bus 2 varies in time asdepicted in Fig. 5. The ambient line temperature is 40 C so thatthe dynamic and static line ratings are the same at 216.6 MW.

Under conventional dispatch, the maximum power that gen-erator 1 can produce so as not to exceed the sending end powerrating of the line is 216.6 MW. Since this level of generationresults in 27.7 MW of transmission losses, only 188.9 MW arereceived at bus 2, which is insufficient to meet the peak demandof 242 MW, even if generator 2 were dispatched at its maximumof 50 MW. Therefore, under conventional line rating, some loadshedding becomes necessary during the peak demand interval.

Under ETC, however, no load shedding is necessary. TheETC results, presented in Figs. 6 and 7, show that the cheapergenerator 1 is dispatched from =15 to =40 at levels signifi-cantly above the line power rating, reaching a peak generationof 246 MW. During this interval, the temperature rises rapidlyuntil it hits its limit of 100 C, at which point the expensive gen-erator 2 is dispatched, eventually reaching its limit of 50 MW.This ensures that the line cools down enough to provide suffi-cient transfer capability to get over the peak demand withoutexceeding the temperature limit.

ETC is therefore able to solve this difficult congestion man-agement problem without load shedding. This is a consequenceof ETC’s line thermal inertia model and its coordination withthe system electrical variables.

Fig. 6. Generation output power under ETC. Case C.

Fig. 7. Line temperature profile under ETC. Case C.

Fig. 8. Loads, maximum generations, and initial line temperatures. Case D.

D. Emergency Load Shedding

This case shows how ETC can minimize the amount of loadshed when the system is in an emergency state.

Initially, the system depicted in Fig. 8 is operating in anormal state, that is, the demands located at buses 2 (280 MW),4 (300 MW), and 5 (290 MW) are fully met and the tempera-tures of all the lines are below their limits. Following the tripof the generator at bus 5, all remaining generators increasetheir outputs to make up for the lost generation. However,because of the limited transfer capacities of lines 1 (1–2),


Fig. 9. Temperature evolution in lines 1, 2, and 6. Case D.

TABLE VIILINE TEMPERATURES AND LOAD SHED—CASE D

2 (1–4), and 6 (3–4), generators 1 and 3 cannot supply thedemands and some load shedding becomes necessary. In thissimulation with a coordination period of 1 h, we restrict loadshedding to blocks of 30, 50, and 40 MW at buses 2, 4, and5, respectively. The load at bus during the 5-min interval isdefined as MW, where is aninteger 0/1 variable indicating whether or not the blockis to be shed. The maximum allowed temperature of all linesis fixed at 100 C, with a corresponding steady-state thermallimit of 216.6 MW. The ambient temperature is again assumedto be 40 C.

Under the conventional optimal dispatch, the maximum loadsupplied occurs when blocks of 30 and 50 MW are shed at buses2 and 4 over the entire 1-h time horizon for a total of 80 MWh.

Under ETC, Fig. 9 shows that during the first 25 min, allline temperatures remain below 100 C and no load sheddingis required. Thereafter, in order for the temperature of line 6not to exceed 100 C, the load shedding process summarized inTable VII is set in motion. We observe from this table that themaximum load supplied over the 1-h horizon occurs by shed-ding certain combinations of blocks of load at buses 2, 4, and5 at specific time steps. The total energy shed under ETC is

Fig. 10. 24-bus IEEE system. Case E.

42.5 MWh compared to the 80 MWh lost under the conven-tional approach.

E. IEEE 24-Bus System Loadability Study

This case study compares the maximum system load that canbe supplied (system loadability) under OPF and ETC followingthe loss of a strategic line on the IEEE 24-bus reliability testsystem [2] (see Fig. 10). The coordination period in this studyis taken to be 30 min with 5-min discretization intervals. Theweather conditions are assumed constant throughout the simu-lation with an ambient temperature of 40 C.

All generating units except the nuclear and hydro are subjectto the ramp limits specified in [2]. The outputs of the nuclearunits in buses 18 and 21 are assumed to remain constant at theirmaximum of 400 MW throughout the coordination period. Alllines are subject to the power flow limits specified in [2] (notnecessarily imposed by thermal considerations), with the excep-tion of line 15–21, which we assume is thermally limited witha maximum allowed temperature of 100 C. Under OPF, line15–21 is subject to the static thermal rating of about 676 MW(note that in this case, the dynamic and static thermal ratings areidentical). This thermal limit is calculated assuming a diameterof 35 mm, as well as the data from Tables IV and VIII and [3].Other input data such as generator costs and limits, line param-eters, and load levels have been taken from [2].

Line 15–21 is critical since it carries a large fraction of thepower being directed toward the southern part of the RTS net-work where most of the load is located.


TABLE VIIILINE DATA—CASE E

TABLE IXPOWER FLOW, LOSS, AND TEMPERATURE UNDER OPF AND ETC

FOR LINE 15–21. BASE LOADING—CASE E

We now consider the outage of line 16–17, since this lossforces much of the power being generated in the north to flowthrough the thermally limited line 15–21.

Under OPF, the amount of power that can be generated in thenorthern buses 18, 21, and 22 is limited to the 676-MW thermalrating of line 15–21. The result is two-fold: One is that the hydrounits in bus 22 decrease their output, and the second is the gen-erators in the southern part of the network attempt to match thisdeficit by increasing their outputs subject to their ramp limits.This optimum corrective action on the part of the generators isfeasible for the base load defined in [2]; however, as the totaldemand increases, at some point, the southern generators areincapable of picking up the generation deficit because of theirlimited ramps and some load shedding becomes necessary. Inthis case study, under OPF, we were able to increase the loadat all buses uniformly by up to a factor of 14% (except at bus18, where the load is kept constant at 333 MW). In contrast,under ETC, we could increase the load by 17% without any loadshedding.

The increased loadability under ETC is possible because thethermally limited line 15–21 can temporarily transmit morepower than the thermal rating of 676 MW. As seen in Table IX,for the case with demand at its base level, the sending flow frombus 21 through line 15–21 exceeds the thermal rating, reachinga maximum of about 761 MW during the first 5-min intervalfollowing the outage. This flow decreases gradually over thenext 25 min as the line temperature approaches its maximum of100 C. Under ETC, the extra power sent through line 15–21during the first 20 min provides the generators closer to the loadsufficient time to increase their output subject to their ramplimits, thus averting any load shedding even with a loading of117%.

The generation for 117% loading under ETC and 114%loading under OPF are shown in Tables X and XI, respectively,where the symbol “+” denotes binding up ramp limits.

TABLE XGENERATION UNDER ETC. 117% LOADING—CASE E

TABLE XIGENERATION UNDER OPF. 114% LOADING—CASE E

III. PRACTICAL CONSIDERATIONS

ETC Online Deployment: Ideally, the online deployment ofETC should support three functions: 1) dispatch; 2) operation-planning; and 3) remedial control, the details of which are nowdiscussed for both traditional and market-driven utilities.

A. Traditional Power Utility Operation

In its dispatch mode, ETC will run every 5 min, providingpredictive dispatch capability that would replace the traditional


economic, transmission-constrained, and security-constraineddispatch functions. For a typical power system, this applicationof ETC would be time critical and CPU intensive. In addition,ETC requires an up-to-date starting point provided by the stateestimator.

For “real-time” control purposes, the generation set pointsand participation factors can be obtained from the ETC solutionfor the first two time steps and passed onto the AGC function.The information in the remaining time steps provides systemoperators with a look-ahead operational capability.

ETC in its operation-planning mode could run in conjunctionwith the unit commitment (UC) function to identify those ther-mally limited lines that need to be directly enforced by the UClogic. In this way, ETC allows forecasts of weather parametersto be introduced into the UC problem.

In its remedial mode, ETC would run following the securityanalysis (SA) function. It would determine control strategiesthat are needed to relieve the power system from existing and/oranticipated line temperature and flow limit violations due to thecredible contingency cases identified by the SA.1 Here, ETC cantake advantage of its flexibility to find solutions to cases thatwould be infeasible under conventional approaches.

B. Market-Driven Operation

Here, ETC runs every 5 min to clear the balancing energymarket with a horizon of few hours during which the weatherforecasts are relatively accurate. Again, in this mode, ETC notonly clears the market but also allows the ISO to look aheadand evaluate the impending system conditions. In particular, bychoosing the coordination period to be 4 h, ETC would permitthe ISO to assess the need for starting up units to serve as ca-pacity reserve on a timely basis.

As in the case of traditional utility operation, the first twosteps of the ETC can be used for “real-time” system control.In this case, however, the control decisions are conveyed to thegenerators for implementation.

The operation-planning mode of the ETC in this case is theday-ahead energy market. Additionally, when the ISO performsUC on behalf of generators, as described in the case of tra-ditional utility operations, ETC can identify transmission con-straints that must be enforced by UC.

Since the ISO and the traditional power utilities perform es-sentially the same type of SA, they would use ETC in a similarmanner to calculate remedial controls.

Line Longevity: As demonstrated by the case studies, theadvantages of ETC are obtained by exploiting thermal inertiaand, on the average, by operating critical lines at higher tem-peratures than under conventional dispatching methods. Thetendency of ETC to operate the lines at higher average tem-peratures is the result of formulating the ETC problem withinan optimization framework. Since typical objective functionsdo not contain costs for temperature changes, whenever anopportunity to reduce the objective function via temperaturechanges is detected, the ETC algorithm pursues it to the fullestextent.

Although many utilities are now sanctioning high-tempera-ture operation of equipment [5], still the fact remains that both

1See the discussion on SA in [1].

high-temperature operation and heating and cooling cycles canhave negative implications for equipment longevity [6]. How-ever, since the line temperatures are explicit variables, underETC, one has the opportunity to minimize the impact of tem-perature cycles by introducing into the ETC formulation a va-riety of constraints and costs to limit the size and duration ofthe heating/cooling cycles, to restrict the rate of line tempera-ture change, and to penalize high temperatures.

Stochasticity of Weather Parameters: Some HBE termsstrongly depend on local ambient temperature and wind ve-locity [3]. These quantities are stochastic in nature and theirvery short–term forecasts may contain errors.

As ambient temperature changes are normally gradual, adap-tive very short-term prediction algorithms are proposed to catchand correct errors in ambient temperature predictions. Similarly,line temperatures do not respond to sudden, brief wind gusts butrather to the average wind velocity [7], which, to be consequen-tial, must be both consistent (have the same sign) and persistent(stay longer than 5 min). Adaptive wind prediction algorithmswould be able to detect and respond to errors by adjusting theexisting wind forecast accordingly.

IV. CONCLUSION

This paper has demonstrated that the essential notions pre-sented in Part I on electrothermal coordination of power systemsare feasible and bring benefits in terms of system security andeconomics that are beyond the capabilities of today’s models.

The key difference between ETC and existing approaches tosystem operation is the ability of ETC to model and coordi-nate the thermal dynamic behavior of transmission lines withthe electrical characteristics of the system.

This proposed coordination approach has been applied to casestudies in emergency generation redispatch, line maintenanceplanning, congestion management during peak demand periods,emergency load shedding, and system loadability. Some of thespecific benefits identified by using ETC are as follows.

1) Additional time is gained to avoid redispatching genera-tion or shedding load following line or generator outages.

2) Components of the transmission network can be discon-nected for maintenance over intervals of time longer thanwhat is currently possible without exceeding the operationlimits of the remaining network. Moreover, ETC allows usto calculate the available maintenance time as a functionof system loading and weather conditions.

3) When predicting system congestion due to expectedpeaking demand or structural changes, ETC extendsthe current preventive control capabilities. For example,before the anticipated congestion, ETC can redispatchpower to lower the temperature in critical lines (whileincreasing the temperature of noncritical paths). Thisprepositions the system state so that at the time of con-gestion, the system provides optimum power transfercapability.

4) If load shedding is required after an outage, ETC calcu-lates a load shedding pattern over time among the network


buses to minimize the unserved system load. ETC accom-plishes this by alternatively cooling and heating differenttransmission paths.

We have also presented arguments to support the contentionthat ETC can be implemented in practice on top of existing dy-namic line rating systems. As discussed in Part I, ETC can alsobe deployed into utility energy management systems but withcertain modifications, of which the most essential is the data-base. Modifications to other online functions such as the stateestimator, dispatcher power flow, and security analysis are alsodesirable.

From these results, it can be concluded that irrespective of thetechniques and technologies used, conventional thermal-rating-based approaches cannot provide the same power transfer capa-bilities as ETC, since ETC is the only approach that models andexploits line thermal inertia. To achieve these power transfer ca-pability gains and their associated economic and security ben-efits, traditional power flow constraints should be replaced bytemperature limits in thermally limited lines.

We recognize that line temperature manipulation may have anegative impact on the longevity of lines; however, this impactcan be systematically contained by imposing additional con-straints on line temperature variations within the ETC formula-tion. In addition, to reduce the negative impact of weather pre-diction errors, we propose that very short-term adaptive weatherforecast functions be incorporated in ETC.

Numerous other applications of ETC in system operation andoperation planning can be envisioned. For example, the deicingof transmission lines through the coordination of their temper-atures is an appealing possibility. The additional transfer capa-bility offered by ETC could be exploited in security-constrainedUC to avoid having to commit fast reserve generators in areaswhere the potential loss of some lines can lead to generation de-ficiency. ETC could increase the time available to deploy slowerreserve following such outages, thus reducing the level of fastreserve that must be pre-scheduled.

REFERENCES

[1] H. Banakar, N. Alguacil, and F. D. Galiana, “Electrothermal coordina-tion Part I: Theory and implementation scheme,” IEEE Trans. PowerSyst., vol. 20, no. 2, pp. 798–805, May 2005.

[2] IEEE RTS Task Force of APM Subcommittee, “IEEE reliability testsystem-1996,” IEEE Trans. Power App. Syst., vol. 98, no. 6, pp.2047–2054, Nov./Dec. 1979.

[3] “IEEE standard 738–1993,” IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors, Nov. 1993.

[4] A. Brooke, D. Kendrick, A. Meeraus, and R. Raman. (2003) GAMS: Auser’s guide [Online]. Available: http://www.gams.com/.

[5] S. L. Chen, W. Z. Black, and M. L. Fancher, “High temperature sagmodel for overhead conductors,” IEEE Trans. Power Del., vol. 18, no.1, pp. 183–1188, Jan. 2003.

[6] G. D. Troia, “Effects of high temperature operation on overhead trans-mission full-tension joints and conductors,” WG 12, Aug. 2000.

[7] W. Z. Black and R. A. Bush, “Conductor Temperature Research,”,El 5707, EPRI Final Project Report-2546-1, May 1988.

Natalia Alguacil (M’01) received the Ingeniero en Informática degree from theUniversidad de Málaga, Málaga, Spain, in 1995, and the Ph.D. degree in powersystem operations and planning from the Universidad de Castilla-La Mancha,Ciudad Real, Spain, in 2001.

Her research interests include operations, planning, and economics of electricenergy systems, as well as optimization and parallel computation.

M. Hadi Banakar (M’81) received the M.Eng. and Ph.D. degrees in electricalengineering from McGill University, Montreal, QC, Canada, in 1977 and 1981,respectively.

Since 1981, he has held key positions at CAE Electronics and ALSTOMESCA, with direct responsibilities for development of EMS and ElectricityMarket applications. Presently, he is a Consultant to power utilities and aResearch Associate at McGill University. His current research interests arepower system operation, operations planning, integrated electricity markets,risk analysis and management, and integration of wind energy into power grids.

Francisco D. Galiana (F’92) received the B.Eng. (Hons.) degree from McGillUniversity, Montreal, QC, Canada, in 1966 and the S.M. and Ph.D. degrees fromthe Massachusetts Institute of Technology, Cambridge, in 1968 and 1971, re-spectively.

He spent several years at the Brown Boveri Research Center, Baden, Switzer-land, and the University of Michigan, Ann Arbor. Currently, he is Professor ofelectrical and computer engineering at McGill University. His research interestsare in problems related to the operation and planning of power systems.

electrothermal coordination part ii: case studies

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