ECEN 615 Lect1

ECEN 615Methods of Electric PowerSystems AnalysisLecture 11 SensitivityProf. Tom OverbyeDept. of Electrical and Computer EngineeringTexas A&M Universityoverbye@tamu.edu

Announcements Homework 3 should be done before the first exambut need not be turned in Start reading Chapter 7 (the term reliability is nowoften used instead of security) First exam is in class on Thursday Oct 1 Distance learning students do not need to take the examduring the class periodClosed book, notes. One 8.5 by 11 inch notesheet andcalculators allowedLast’s years exam is available in Canvas with answersLecture 12 will be on the August 14, 2003 Blackout1

Power Flow Topology Processing Anytime a status change occurs the power flow mustperform topology processing to determine whetherthere are either 1) new islands or 2) islands havemerged Determination is needed to determine whether theisland is “viable.” That is, could it truly function as anindependent system, or should the buses just bemarked as dead–A quite common occurrence is when a single load orgenerator is isolated; in the case of a load it can beimmediately killed; generators are more tricky2

Topology Processing Algorithm Since topology processing is performed often, it mustbe quick (order n ln(n))! Simple, yet quick topology processing algoritm–––Set all buses as being in their own island (equal to busnumber)Set ChangeInIslandStatus trueWhile ChangeInIslandStatus Do –Go through all the in-service lines, setting the islands for each of thebuses to be the smaller island number; if the island numbers aredifferent set ChangeInIslandStatus trueDetermine which islands are viable, assigning a slack bus asnecessaryThis algorithm does depend on the depth of the system3

Example of Island Formation44 MW42 MWA1.05 puBus 131 MW0.99 puMVA31 MWAMVABus 3106 MWAGC ON62 MWBus 437 MWAAMVAMVA80 MW30 Mvar110 MW40 Mvar1.00 pu32 MWAACase Hourly Cost16919 /hMVA38 MWMVAA61 MW1.04 pu80 MWBus 214 MW80%33 MWTop Area Cost94 MWAGC ON1.01 pu78 MWBus 5MVA8078 /h40 MW20 MvarAA41 MWMVA171 MWAGC ON20 MWA21 MW1.04 pu39 MW21 MW200 MW0 MvarAGC ONLeft Area Cost4189 /hMVA1.04 puMVABus 6200 MW130 MW40 Mvar38 MW42 MWAMVA20 MWBus 7This option allows some islandsRight Area Costto not have a power flow solutionslack4652 /h198 MW200 MW0 MvarAGC ONSplitting large systems requires a careful consideration of theflow on the island tie-lines as they are opened4

Bus Branch versus Node Breaker Due to a variety of issues during the 1970’s and 1980’sthe real-time operations and planning stages of powersystems adopted different modeling approachesReal-Time OperationsPlanningUse detailed node/breaker modelEMS system as a set of integratedapplications and processesReal-time operating systemReal-time databasesUse simplified bus/branch modelPC approachUse of filesStand-alone applicationsEntire data sets and software tools developed aroundthese two distinct power system models5

Google View of a 345 kV Substation6

Example of Using a Disconnect toBreak Load Current7

Substation Configurations Several different substation breaker/disconnectconfigurations are common: Single bus: simple but a faultany where requires taking out theentire substation; also doing breakeror disconnect maintenance requirestaking out the associated lineSource: schemes.html8

Substation Configurations, cont. Main and Transfer Bus:Now the breakers can be takenout for maintenance withouttaking out a line, but protectionis more difficult, and a faulton one line will take out at least two Double Bus Breaker:Now each line is fully protectedwhen a breaker is out, so highreliability, but more costlySource: schemes.html9

Ring Bus, Breaker and Half As the name implies with a ringbus the breakers form a ring;number of breakers is same asnumber of devices; any breaker canbe removed for maintenance The breaker and half has two busesand uses three breakers for twodevices; both breakers and busescan be removed for maintenanceSource: schemes.html10

EMS and Planning Models EMS Model––– Planning ModelUsed for real-time operationsCalled full topology modelHas node-breaker detail50 MW20 Mvar–––-30 MW-18 MvarUsed for off-line analysisCalled consolidated model byPowerWorldHas bus/branch detail-30 MW-18 Mvar10 MW3 Mvar10 MW3 Mvar-40 MW-10 Mvar10 MW5 Mvar-40 MW-10 Mvar10 MW5 Mvar11

Node-Breaker Consolidation One approach to modeling systems with large numbersof ZBRs (zero branch reactances, such as from circuitbreakers) is to just assume a small reactance and solve––This results in lots of buses and branches, resulting in a muchlarger problemThis can cause numerical problems in the solution The alterative is to consolidate the nodes that areconnected by ZBRs into a smaller number of buses–After solution all nodes have the same voltage; use logic todetermine the device flows12

Node-Breaker ExampleCase name is FT 11Node. PowerWorld consolidates nodes(buses) into super buses; available in the Model Explorer:Solution, Details, Superbuses.13

Node-Breaker ExampleNote there is ambiguity on how much power is flowing in eachdevice in the ring bus (assuming each device really has essentiallyno impedance)14

Contingency Analysis Contingency analysis is the process of checking theimpact of statistically likely contingencies––Example contingencies include the loss of a generator, the lossof a transmission line or the loss of all transmission lines in acommon corridorStatistically likely contingencies can be quite involved, andmight include automatic or operator actions, such as switchingload Reliable power system operation requires that thesystem be able to operate with no unacceptableviolations even when these contingencies occur–N-1 reliable operation considers the loss of any single element15

Contingency Analysis Of course this process can be automated with the usualapproach of first defining a contingency set, and thensequentially applying the contingencies and checkingfor violations––This process can naturally be done in parallelContingency sets can get quite large, especially if oneconsiders N-2 (outages of two elements) or N-1-1 (initialoutage, followed by adjustment, then second outage The assumption is usually most contingencies will notcause problems, so screening methods can be used toquickly eliminate many contingencies–We’ll cover these later16

Contingency Analysis in PowerWorld Automated using the Contingency Analysis tool17

Power System Control andSensitivities A major issue with power system operation is thelimited capacity of the transmission system–––lines/transformers have limits (usually thermal)no direct way of controlling flow down a transmission line(e.g., there are no valves to close to limit flow)open transmission system access associated with industryrestructuring is stressing the system in new ways We need to indirectly control transmission line flow bychanging the generator outputs Similar control issues with voltage18

Indirect Transmission Line Control What we would like to determine is how a changein generation at bus k affects the power flow on aline from bus i to bus j.The assumption isthat the changein generation isabsorbed by theslack bus19

Power Flow Simulation - Before One way to determine the impact of a generatorchange is to compare a before/after power flow. For example below is a three bus case with anoverload131.9 MW124%One200.0 MW71.0 MVRTwo68.1 MW68.1 MW200 MW100 MVRZ for all lines j0.1Three1.000 pu0 MW64 MVR20

Power Flow Simulation - After Increasing the generation at bus 3 by 95 MW (andhence decreasing it at bus 1 by a correspondingamount), results in a 30.3 MW drop in the MW flow onthe line from bus 1 to 2, and a 64.7 MW dropon the flow from 1 to 3.101.6 MW100%One105.0 MW64.3 MVRTwo3.4 MWZ for all lines j0.1Limit for all lines 150 MVAThree98.4 MW92%200 MW100 MVRExpressed as apercent,30.3/95 32% and64.7/95 68%1.000 pu95 MW64 MVR21

Analytic Calculation of Sensitivities Calculating control sensitivities by repeat power flowsolutions is tedious and would require many powerflow solutions. An alternative approach is toanalytically calculate these valuesThe power flow from bus i to bus j isPij Vi V jSo Pij X ijsin( i j ) i jX ij i jX ijWe just need to get ij PGk22

Analytic SensitivitiesFrom the fast decoupled power flow we know θ B 1 P (x)So to get the change in θ due to a change ofgeneration at bus k, just set P( x) equal toall zeros except a minus one at position k. P 0 1 Bus k 0 23

Three Bus Sensitivity ExampleFor a three bus, three line case with Zline j 0.1 20 10 10 20 10 Ybus j 10 20 10 B 10 20 10 10 20 Hence for a change of generation at bus 3 2 3 1 20 10 0 0.0333 10 20 10.0667 0.0667 0Then P3 to 1 0.667 pu0.1 P3 to 2 0.333 pu P 2 to 1 0.333 pu24

More General Sensitivity Analysis:Notation We consider a system with n buses and L lines givenby the set given by the set L @{ 1, 2, , L}–Some authors designate the slack as bus zero; an alternativeapproach, that is easier to implement in cases with multipleislands and hence slacks, is to allow any bus to be the slack,and just set its associated equations to trivial equations juststating that the slack bus voltage is constant We may denote the kth transmission line or transformerin the system, k , askfrom node@( ik , jk ),to node25

Notation, cont. We’ll denote the real power flowing on k from bus ito bus j as ƒk The vector of real power flows on the L lines is:, f L]Tf @[ f 1, f 2,which we simplify to f [ f1 , f 2 , , f L ] The bus real and reactive power injection vectors areT1212p @ [p , p ,q @ [q , q ,NTNT,p ],q ]26

Notation, cont. The series admittance of line is g jb and wedefineB @ diag b1 , b 2 , , b L We define the L N incidence matrix a T1 T a 2 A @ a TL The component j of ai isnonzero whenever line i iscoincident with node j. HenceA is quite sparse, with twononzeros per row27

Analysis Example: Available TransferCapability The power system available transfer capability or ATCis defined as the maximum additional MW that can betransferred between two specific areas, while meetingall the specified pre- and post-contingency systemconditions ATC impacts measurably the market outcomes andsystem reliability and, therefore, the ATC valuesimpact the system and market behavior A useful reference on ATC is Available TransferCapability Definitions and Determination fromNERC, June 1996 (available online)28

ATC and Its Key Components Total transfer capability (TTC )–Amount of real power that can be transmitted across aninterconnected transmission network in a reliable manner,including considering contingencies Transmission reliability margin (TRM)–Amount of TTC needed to deal with uncertainties in systemconditions; typically expressed as a percent of TTC Capacity benefit margin (CBM)–Amount of TTC needed by load serving entities to ensureaccess to generation; typically expressed as a percent of TTC29

ATC and Its Key Components Uncommitted transfer capability (UTC)UTC TTC – existing transmission commitment Formal definition of ATC isATC UTC – CBM – TRM We focus on determining Um,n, the UTC from node mto node n Um,n is defined as the maximum additional MW thatcan be transferred from node m to node n withoutviolating any limit in either the base case or in any postcontingency conditions30

UTC (or TTC) Evaluation tm tfi(0 ) ffnjmaxU m ,n max tGoal isto loadthe linesup toa limitis hits .t .f( j) f fmax Lfor the base case j 0 and each contingency casej 1,2 , J31

Conceptual Solution Algorithm1. Solve the initial power flow, corresponding to theinitial system dispatch (i.e., existing commitments); setthe change in transfer t(0) 0, k 0; set step size d; j isused to indicate either the base case (j 0) or acontingency, j 1,2,3 J2. Compute t(k 1) t(k) d3. Solve the power flow for the new t(k 1)4. Check for limit violations: if violation is foundset Ujm,n t(k) and stop; else set k k 1, and goto 232