IEEE-Power&Energy-Jan2004[Overbye Power System Simulation]

20 IEEE power & energy magazine january/february 2004

TTHIS ARTICLE IS THE FOURTH INa series based on the IEEE PES PowerSystem Basics for Business Profession-als tutorial. The article provides a sum-mary of the presentation given in thecourse on power system operations,building on the foundation provided bythe “Electricity Basics” portion of thecourse (see the IEEE Power & EnergyMagazine May/June 2003 article byPeter Sauer). The intended audience forthis article is the same as the course:business professionals working in theelectricity industry who do not havetechnical training in the area of electricpower systems. Simulation software isused throughout the article to explainmany of the concepts associated withpower system operations. Readers candownload a free, 12-bus version of thesimulation software by visitinghttp://www.powerworld.com/FREE_DOWNLOADS/Simulator_EVAL.asp.This download is licensed for personaleducational use and includes the small-er power system cases referenced inthis article.

OverviewThe primary purpose of an ac electricpower system is to move electric powerfrom the sources of the electric power,the generators, to the consumers of theelectric power, the loads, through thewires joining the two, the transmissionand distribution system. Power systemscome in a variety of sizes, ranging insize from those with a single small gen-erator and perhaps a handful of loads tothe gigantic. For example, except for a

few islands and some small isolatedsystems, the entire electric grid in NorthAmerica is really just one big electriccircuit. The humble wall outlet is actu-ally a gateway to one of the largest andmost complex objects ever built. Thisgrid encompasses billions of individualelectric loads, tens of millions of milesof wires, and thousands of generators.The focus of this article is on the opera-tion of these large, interconnected grids.

This high degree of interconnectionhas two primary benefits. The first isreliability: with thousands of generatorsinterconnected through tens of thousandsof transmission lines, the loss of even thelargest generator or transmission lineusually has but a minuscule impact on

the reliable operation of the system.When one device fails others are able tomake up for the loss. The second benefitis economic, providing the key to thedevelopment of power markets.Although the system was not builtexplicitly for bulk power transmission(the movement of electric power fromone region of the system to another) par-ticipants can buy and sell electric energywith each other, taking advantage of dif-ferentials in the cost of electric service.

However, this connectivity hassome detrimental side effects as well.Since an interconnected system is real-ly just one large electric circuit, prob-lems in one portion of the system canrapidly propagate to the remainder of

Thomas J. Overbye

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power system simulationunderstanding small- and large-system operations

1540-7977/04/$20.00©2004 IEEE

figure 1. A three-bus power system.

Authorized licensed use limited to: University of Illinois. Downloaded on November 19, 2009 at 16:07 from IEEE Xplore. Restrictions apply.

the system, possibly resulting in a cas-cading blackout. To explain the opera-tion of such interconnected systems,this tutorial starts with the simulationof a small electric power system andthen gradually moves up in size until

ending with a large system.

Interconnecyed PowerSystem Operations To begin the exploration of intercon-nected power system operations, start

the simulation software, and open theB3Novar case. The computer displayshould be similar to Figure 1, whichshows a one-line diagram (so namedbecause the actual three conductors ofthe underlying three-phase electric sys-tem are represented using a singleequivalent line on the display; one-linesare used extensively to represent theactual three-phase system) for a three-bus power system. On the one-line thethree thick lines represent nodes atwhich a number of electric devices areconnected (i.e., buses), the circles repre-sent generators, the large arrows repre-sent aggregate electric loads, and thethinner black lines correspond to high-voltage transmission lines. On eachdevice the red squares model circuitbreakers, which are used to open orclose a device, while the circular piecharts on each transmission line are anindication of the power flow on that linerelative to the capacity of the line; whenthe pie is full the line is at its limit.

figure 2. Example load variation over a week.

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Lines can be operated over their limits,but doing so in a real system couldcause the line conductors to heat exces-sively, sag, and perhaps eventually shortout, causing a dramatic explosion in theprocess; definitely to be avoided.

Numeric fields are also used on theone-line to show the amount of powerbeing supplied by the generators, con-sumed by the loads, and flowingthrough the transmission lines. Thesmall green arrows superimposed toeach device are used to visualize theflow of power through the system, withthe size and animation speed of thearrows corresponding to the amount ofreal power flowing through the device.Notice the power is “flowing” from thegenerators, through the transmissionsystem to the load.

As power flows from the generatorsto the loads, it must, of course, obey thelaws of physics. One of these laws is“conservation of power,” which statesthat the net power into any bus in thesystem must be zero. Hence the 200

MW of load consumed at bus 2 must besupplied from a combination of the localgeneration and any transmission linesincident to the bus. This power balance iseasily verified in the figure, with 150MW coming from the local generator, 17MW coming from the line joining bus 2with bus 1, and 33 MW coming from theline joining it with bus 3. Throughout thesimulation the software will insure thatthis law is always satisfied.

A consequence of this law is therequirement that at each instant in timethe total power produced by all thegenerators must be equal to the totalpower consumed by all the loads plusany losses due to the flow of electricitythrough the wires. Such line losses arealways present anytime power is flow-ing because of the resistance of the lineconductors. Since electricity cannot beeasily stored, one of the key challengesin power system operations is insuringthere is always sufficient generationavailable to meet this changing electricload. With the customer is in ultimate

control of the electric switch, andhence the total electric load, the loadcan be quite variable. However, sincepeople are creatures of habit, it doesusually follow a somewhat predictablepattern, with a strong daily variation, aswell as significant dependence on theweather conditions. Figure 2 shows thevariation in a small utility’s load overthe course of one week.

As a disclaimer it must be mentionedthat in actual power system operationsthe total mechanical power supplied tothe generators is seldom exactly equal tothe total electric power consumed by theload plus the losses. When they are notequal the system either “accelerates” ifthere is too much power in to the gener-ators, causing the generators to spinfaster and hence to increase the systemelectrical frequency, or “decelerates” ifthere is not enough power into the gen-erators causing the electrical frequencyto decrease. Luckily, power engineershave been quite successful in developingcontrol schemes that usually keep the


january/february 2004 IEEE power & energy magazine

system frequency very constant. In largeinterconnected systems such as the East-ern or Western North America grids, thechanges in electrical frequency are usu-ally quite small, with the system fre-quency seldom deviating by more than0.05% from the specified value (60 Hzin North America and 50 Hz in Europe).

In order to discuss the main issuesassociated with power system opera-tions, without undue complications, inthis article the system frequency will beassumed to remain constant. In the sim-ulation software this is done by requir-ing that the total generation always beequal to the total load plus losses. In thethree-bus example this is accomplishedby the generation at bus 1 automaticallychanging to match any changes in theloads, any changes in the other genera-tors, and any changes in system losses.Hence, the generator at bus 1 can bethought of as picking up the “slack”between the generation supplied by theother generators and the total systemload plus losses. In power engineeringterminology this bus is called the slackbus. The engineering problem of deter-mining how power flows in the trans-mission network is known as the powerflow (sometimes called the load flow).The power flow is the tool most widelyused by power engineers, and everypower flow model always has a desig-nated slack bus. The simulator uses asequential power flow approach to sim-ulate power system operations.

To begin a time-domain simulationof the three bus system in the softwarepackage select Simulation, Play. Thesimulation model starts at 6:00 a.m. ona Monday, a time when the load on theelectric system is rapidly increasing.The simulation itself runs at a rate equalto 30 times real-time, so a minute of“simulation time” will go by in two sec-onds. So events can happen quickly, butat any time the simulation can bepaused by selecting Simulation, Pause,or restarted by selecting Simulation,Restart and then Simulation, Play.

Notice that at every instant in timethe power balance constraints are satis-fied for each bus in the system. This istrue even if a line is removed from serv-

ice, which is done by clicking on one ofthe red circuit-breaker symbols on theline, or if the generation is varied, whichis done by clicking on the up/downarrows next to the generator’s megawattfield. Aside from the use of the circuitbreakers to open or close a transmissionline, there is no way to directly controlthe flow on the line. Rather, the lineflows are determined based upon theimpedances of all the lines in the sys-tem, where the power is generated, andwhere the power is consumed. The flowcan, however, be controlled indirectly bychanging the generation dispatch.

Figure 3 shows the system after sev-eral minutes of simulation, with theline from bus 1 to 2 removed and thegeneration varied. Notice that the loss-es on the line from bus 2 to bus 3 arenow apparent, with 126 MW flowinginto the line and 124 MW flowing outof the line; the “missing” 2 MWs areconsumed by the resistance in the line’sconductors. The total system genera-tion is 608 MW compared to a totalload of 605 MW with the 3-MW differ-ence due to the total system losses.

Control Areas,ACE, and AGCWhile an interconnected system is reallyjust one big electric circuit, it has histori-

cally been divided into groupingsknown as operating areas (areas). Typi-cally, each operating area correspondedto the portion of the grid owned by asingle utility. Lines joining differentoperating areas are known as tie-lines.The net flow of power out of an area isthen defined as its interchange. Since itcosts money to generate electric power,a key aspect of power system operationsis concerned with insuring that eacharea’s net interchange is equal to itsspecified “scheduled” value. This sched-uled value is simply the sum of all thepower transfers for the area, with a signconvention that power exported from thearea (i.e., sold) is considered positive. Aslong as the system frequency is equal toits specified value (the assumption here),the difference between an area’s actualinterchange and its scheduled inter-change is known as the area controlerror (ACE) (the area control error alsoincludes a term dependent on the devia-tion in the system frequency from thespecified value; this frequency-depend-ent term is not discussed here). TheACE is the single most important num-ber associated with control operations; itis continuously monitored. Anytime theACE is negative the area is undergener-ating and needs to increase its total gen-eration. Conversely, if the ACE is

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figure 3. A three-bus system with the line from bus 1 to 2 removed.



positive, the area is overgenerating andneeds to decrease its generation.

The three-bus example is dividedinto two operating areas, “Left” withbuses 2 and 3, and “Right” with justbus 1. The tie-lines are then the linefrom bus one to two, and the line frombus one to three. Hence, for the Figure3 case, which has no scheduled powertransactions, the ACE is –43 MW forarea Left and +43 MW for area Right.To correct its ACE, Left shouldincrease its generation by 43 MWs andRight should decrease its generation bythe same amount. To view a strip-chartdisplay of the ACE for area Left selectOptions/Tools, Charts, ACE Chart.

Since the ACE depends on the load,and the load is constantly changing, thetotal area generation needs to be con-tinually adjusted to keep the ACE closeto zero. Historically, this process wasfigure 4. ACE chart.


done manually, with the control areaoperator or the operators in individualgenerating plants monitoring an ACEstrip chart and then adjusting the gener-ation accordingly. Figure 4 shows anexample of how this process can beduplicated in the software.

Over the last several decades, prac-tically all control areas have switchedto an automatic process known as auto-matic generation control (AGC). AGCautomatically adjusts the generation inan area to keep the ACE close to zero,which in turn keeps the net area powerinterchange at its specified value. Sincethe ACE has a small amount of almostrandom “ripple” in its value due to therelentlessly changing system load, theusual goal of AGC is not to keep theACE exactly at zero but rather to keepits magnitude close to zero, with anaverage value of zero.

In the software, to place area Left onAGC control, first click on the “OFFAGC” fields next to the generators atbuses 2 and 3 to toggle their individualAGC statuses. Then click twice on the“OFF AGC” field in the lower left-handportion of the display to place the entireLeft area on AGC control. Once on AGCthe outputs of the generators at buses 2 and3 will be automatically adjusted to keepthe area ACE close to zero. By default,area Right is initially on AGC control.

Unless an operating area has but asingle generator, a crucial AGC sub-problem is determining how the totalgeneration requirements for the areashould be allocated to the individualgenerators within the area. Optimallydetermining this allocation can, howev-er, be quite complicated, requiring thesolution of at least two problems withtwo different time horizons. First, oneneeds to determine which generatorsshould be turned on and hence avail-able for AGC control. Because of theneed to have sufficient generationcapacity to meet the peak electric load,for most hours of the year there is morethan sufficient generation capacity.Since generators are costly to run evenwhen not producing any power,unneeded generators should be turnedoff. But turning on and off generators,

particularly large coal and nuclearplants, can be quite time-consuming,often requiring many hours or evendays. Hence planning is required a day

or two in advance to determine whichgenerators should be on and whichshould be off. This is known as the unitcommitment (UC) problem. The UC

figure 5. Marginal costs for the generators at buses 2 and 3.


problem gets even more complex whenhydro generators need to be consideredwith reservoir constraints. Because UCmust be done well in advance of real-time it is not part of AGC.

The second problem is to determinehow to allocate the total area generationrequirement among the online genera-tors. Generators can have widely differ-ent short-time marginal costs; that is,

how much it costs to get one moreMWh out of the generator. Nuclear andcoal plants can have quite low costs,sometimes below $10/MWh for nuclearand $15/MWh for coal, while oil plantsmight have costs above $100/MWh.Ideally, one would like to dispatch thegeneration as optimally as possible, tak-ing into account both the limits associ-ated with the individual generators such

as staying within their minimum andmaximum power limits and the limitsimposed by the transmission network,such as avoiding overloading any trans-mission lines. However, computationaland data limitations usually dictate amore simplistic but robust approach beimplemented within AGC itself.

Some AGC implementations use aparticipation factor approach, in whicha required change in area-wide genera-tion is allocated to individual generatorsaccording to prespecified, generator-spe-cific participation factors that dictate thepercentage of the total change in thearea generation that is assigned to a par-ticular generator. Participation factorcontrol has had the advantage of requir-ing relatively little computation. Howev-er, as computational costs have dropped,some AGC implementations havemoved to doing an economic dispatch(ED) approach in which the generatorsare always dispatched to minimize thetotal area short-term operating costs.Combination algorithms are also used inwhich ED is run periodically to deter-mine each generator’s setpoint dispatch.Participation factor control is then run ata faster rate to determine each genera-tor’s deviation from this setpoint valuedue to changes in the area ACE.

A necessary condition for an opti-mal economic dispatch solution is thatthe marginal costs for each generator,expressed in $/MWh, are equal unless agenerator is constrained at a limit. Thisvalue is often called the area lambda.The marginal costs of generators oper-ating at their limits will be less than thearea lambda if the generator is operat-ing at its maximum limit and greaterthan the area lambda it the generator isat its minimum limit. Historically, themarginal cost curve information usedin the economic dispatch had beenderived from the actual cost curves forthe generators. However, with deregu-lation and the development of competi-tive electricity markets this is changing.Now, in some markets the generationowners are allowed to submit price-based bids, which allows them to keeptheir actual costs hidden.

The three-bus example allows either


figure 7. B7Flat seven-bus, three-area case.

figure 6. Area Left selling 50 MW to area Right.


january/february 2004 IEEE power & energy magazine

participation factor or economic dis-patch AGC; simply click on the AGCfield in the lower left-hand portion ofthe display to toggle between these twocontrol modes or no AGC control. Thegenerator at bus 2 has a minimummegawatt limit of 150 MW and a maxi-mum limit of 600 MW, while the gen-erator at bus 3 has limits of 100 MWand 700 MW (right-clicking on thegenerator symbol will display a dialogshowing additional information abouteach generator). The generator partici-pation factors for the two generatorsare identical, so when AGC is modeledusing participation factor control,changes in area generation are allocat-ed equally to the two units. Figure 5shows the marginal cost curves for thetwo generators when dispatched eco-nomically, with the red dots indicatingthe current output for each unit (currentunit output). Note the identical margin-al costs at the economic dispatch.

With the ACE/AGC approach,power transactions between differentareas are easily implemented just byeach area entering the algebraic sum ofall their power transfers in the sched-uled transaction term used in their ACEcalculation. Modifying this value caus-es a change in the ACE, which in turncauses AGC to automatically adjust thegeneration in the area to the actualinterchange with other areas matchesthe scheduled value. For example, ifarea A has contracts to sell 200 MW toarea B, and to buy 50 MW from area C,then their net schedule transactionswould be 200 – 50 = 150 MW. Area A’sAGC would then adjust its generationto be 150 MW more than what isrequired for its own load plus losses.Of course, for this system to work theother areas would need to adjust theirscheduled transactions as well—eachtransaction must have a buyer and aseller. It is important to note that froman AGC perspective the details on theindividual transactions are not required.AGC only needs to know the total sumof all the transactions.

Figure 6 shows an example with thethree-bus case in which Left is selling50 MW to Right. In the software, once

area Left is on AGC control the amountof scheduled transactions for Left canbe modified by clicking on the arrowsnext to the field immediately below the“Scheduled Transactions” text. Notethat a net of 50 MWs is being trans-ferred from Left to Right, with 128MW flowing out of Left on the linefrom bus 3 to bus 2 and 78 MW flowinginto Left on the line from bus 1 to 2.

Loop Flow and PowerTransfer Distribution Factors (PTDFs)To illustrate some of the complicationsthat can arise in systems with more thantwo areas, open the B7Flat case, sonamed because the case models a seven-bus power system but with no load vari-ation. The system one-line is shown inFigure 7. Notice the system has three

27

figure 9. PTDFs for a power transfer from area A to area I.

figure 8. B7Flat case with 100 MW transaction from area Left to Right.


areas, with the top five buses composingarea Top, the bottom left bus composingarea Left, and the bottom right bus com-posing area Right. Initially, all the areasare on AGC control with no scheduledtransactions and no line violations. Notethat the sum of the tie line flows foreach area are close to zero. Select Simu-lation, Play to begin the animation.

Next, to supplement the initial one-line display, select File, Open Oneline

and then select the b7area.pwd file.This opens an alternative, higher-levelview of the system, showing just thethree control areas rather than all theindividual buses, the sum of the tie-lineflows between each area, and the sched-uled transactions between the areas.Enter a 100-MW transaction betweenarea Left and Right by using the greenfield shown below the line joining thefield as shown in Figure 8. Following

the initiation of this transactions two sig-nificant changes occur in the network.First, 100 MW is being transferred fromLeft to Right, with the generation in Leftincreased by 100 MW and the genera-tion in Right decreased by a similaramount. Second, the line from bus 2 to 5in area Top has become overloaded as aresult of this transaction.

The second change illustrates animportant characteristic of interconnect-ed electricity networks: changes in onepart of the network can have impacts inother parts of the network, includingoverloading lines in other areas. Con-ceptually, part of the transactionbetween Left and Right goes from Leftto Top and then on into Right, loopingthrough the lines in Top. The powertransfers through the system accordingto the impedances of the lines, irrespec-tive of ownership. Such third-partyimpacts are referred to as loop flow. Inactual practice, how loop flow is man-aged depends upon the degree of sys-tem coordination and market rules. Anuncoordinated approach would be toallow the transaction, forcing Top tointernally redispatch its generation tocorrect the problem. Alternatively, acoordinated approach would be toeither prevent the transaction from eventaking place through a mechanism suchas the available transfer capacity (ATC)calculation (see the IEEE Power &Energy Magazine May/June 2003 arti-cle by Peter Sauer) or curtail the trans-actions if it has already been initiated.

In order to prevent or curtail transac-tions one needs to know the impact aparticular power transfer will have onthe individual lines. In North Americathe North American Electric ReliabilityCouncil (NERC) uses a calculationknown as the power transfer distributionfactor (PTDF). In short, a PTDF showsthe incremental impact a power transfer,from a specified source of the power to aspecified sink for the power, would haveupon each power system element. Forexample, if for a particular power trans-fer a line has a PTDF value of 10%, then10% of the power transfer would flowon that line; if the power transfer is 300MW, the line’s megawatt loading would


figure 11. One-line diagram of electric grid in Northern Illinois.

figure 10. PTDFs for a power transfer from area G to area F.


change by 30 MW. Then, through aprocess known as transmission lineloading relief (TLR), any time a line isoverloaded, transactions with PTDF val-ues greater than 5% on the overloadedelement can be curtailed.

To illustrate PTDFs on a slightly larg-er system, open the B9 case, which con-tains nine buses with each bus modeledas its own operating area. Figure 9 showsthe one-line for this system, but ratherthan showing the actual power flows, itdisplays the PTDFs for a power transferfrom bus A to bus I. Notice that 100% ofthe transfer leaves bus A, and 100%arrives at bus I. However, rather than fol-lowing a single path, the transfer loopsthroughout much of the system, with allbut one line having PTDFs above 5%.PTDFs for any other transfer can be cal-culated in the software by selectingOptions/Tools, Power Transfer Distri-bution Factors (PTDFs) to display thePTDF dialog. Figure 10, which showsthe PTDFs for a transaction between theadjacent G and F buses, illustrates that

even when the buses are directly con-nected, a high percentage of the powermay loop through other lines.

Large System Operation Conceptually, the operation of a largeinterconnected grid, such as the NorthAmerican Eastern Interconnect, is quite

similar to what has been presented here,albeit utilizing much larger models. Forexample, Figure 11 shows a one-line ofthe Northern Illinois portion of the East-ern Interconnect with the display con-taining about 1,000 buses. The operationof such a large network is more complex,but it still follows the principles intro-

figure 12. PTDFs for a power transfer from Wisconsin to Tennessee.


duced for the small systems: the powerbalance equations at each bus in the net-work need to be satisfied, the flow ofpower through the network can be visu-alized by the use of animated arrows andpie charts, power almost instantaneouslyredispatches through the system follow-ing the loss of any elements, AGC con-trol is used to control area interchange,and PTDFs are used to track the impact

of various power transactions.Of course, the large system size does

present some challenges. Current modelsfor the Eastern Interconnect contain over42,000 buses, 57,000 transmission linesand transformers, 6,800 generators, and142 control areas. Understanding andinterrupting the behavior of such a largesystem continues to challenge engineersrequiring the use of advanced visualiza-

tion techniques. At any given time hun-dreds or even thousands of power transac-tions may be taking place simultaneously,often with hundreds of miles between thebuyers and sellers and substantial loopflow. Figure 12 shows the PTDFs for apower transaction from Wisconsin to Ten-nessee, with a color contour used to shadeeach line based upon its PTDF value.While the figure shows data for thousandsof lines, with the color contour the loopflow is readily apparent. Overall, about600 different lines carry at least 2% of thetransaction, with 5% (the NERC thresh-old for TLR) flowing on more than 150lines. Hence, this transaction might besubject to curtailment if any one of these150 lines experienced an overload.

Going ForwardWhile the operation of the grid is com-plex, the hope is that this brief techtorialhas helped to explain at least someaspects of grid operations. Of course, ofnecessity, much has also been leftunsaid, with topics such as optimalpower flow (OPF), security-constrainedOPF, locational marginal prices (LMPs),reactive power flow, and voltage controlleft for another day. If you haven’talready done, so please download thesoftware and experiment with the exam-ples for yourself. Hands-on experiencewith a user-friendly simulation packagecan be a wonderful learning tool. Also,please check the IEEE PES Web site forthe next offering of the IEEE PESPower System Basics for Business Pro-fessionals course.

BiographyThomas J. Overbye is a professor ofelectrical and computer engineering atthe University of Illinois at Urbana-Champaign. He received his B.S., M.S.,and Ph.D. degrees in electrical engineer-ing from the University of Wisconsin-Madison in 1983, 1988, and 1991,respectively. He was employed withMadison Gas and Electric Companyfrom 1983 to 1991, where he worked tohelp develop their energy managementsystem. His research interests includepower system analysis, restructuring,and visualization. p&e


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