Techniques for Conditioning Hard-to-Solve Cases. Overview

Techniques for Conditioning Hard-to-Solve Cases James Weber Director of Operations PowerWorld Corporation weber@powerworld.com Phone: 217 384 6330 ext 13 1 Overview Starting with public text-file data Low impedance mismatches Controller Settings, rea Control Overview of Simulator s Single Solution ake use of the Check Immediately option for Generator Var Limits Loss of reactive support, Voltage Collapse, and Low- Voltage Solutions Use of the Robust Solution Process chieving an initial OPF Solution How to handle unenforceable constraints 2 1

Reading in a Solved Text-File Public Power Flow Formats You receive a case from someone which is supposed to be solved, but it won t solve Issues with initial case Large ismatches from low impedance lines Voltage Controllers Transformers Switched Shunts rea Interchange Control These are not errors with the case or with Simulator, but should be understood. 3 Very Large Initial ismatches Very large initial mismatches Primarily caused by low-impedance branches Other software treats branches below a threshold impedance as exactly zero. The buses at either end of the branch are then merged and the transmission line is ignored PowerWorld never merges buses this way We do have minimum R and X of values however» inimum R = 0.0000001 = (1/1,000,000)» inimum X = 0.00001 = (1/100,000)» Simulator will not let you set the values lower than this 4 2

Example Case: nerc04s_f.raw Read in the case nerc04s_f.raw 2003 SERIES, NERC/WG BSE CSE LIBRRY 2004 SUER CSE, FINL Notice mismatches come in oppositely signed pairs -1567 W, +1566 W BOWNVL is more complicated 5 BOWNVL - DRLNG W ismatch Var ismatch BOWNVL 80011-3373.97 W -620.15 var Very Small Impedances 0.000000 pu 0.000080 pu 0.000000 pu 0.000080 pu 0.000000 pu 0.000080 pu 0.000000 pu 0.000080 pu DRLNGH1 80023 843.51 W 159.79 var DRLNGH2 80016 843.58 W 159.77 var DRLNGH3 80017 843.51 W 148.47 var DRLNGH4 80018 843.76 W 151.06 var W ismatches sum to nearly zero Var ismatches sum nearly to zero 6 3

CLIRVIL W ismatch W ismatch CLIRVIL 80476 2509.05 W 344.55 var 0.000000 pu 0.000100 pu 0.000000 pu 0.000100 pu Very Small Impedances 0.000000 pu 0.000100 pu 0.000000 pu 0.000000 pu 0.000100 pu 0.000100 pu 0.000000 pu 0.000100 pu CLIRV71 80481-525.38 W -167.97 var CLIRV72 80482-364.13 W -61.35 var CLIRV73 80483-428.04 W -41.35 var CLIRV74 80484-414.53 W 38.80 var CLIRV75 80485-393.11 W -115.69 var W ismatches sum to nearly zero Var ismatches sum nearly to zero CLIRV76 80486-390.19 W -7.01 var 7 Solve Initial Case First remove mismatches due to the low-impedance branches without moving any controllers Disable LTCs Disable Switched Shunts Disable Phase Shifters Disable GC 8 4

If Initial Case was truly solved, Solution Will Converge Quickly Solution Results: ax P: 3373.966 at bus 80011 ax Q: 728.978 at bus 80041 ax P: 26.028 at bus 70509 ax Q: 38.214 at bus 70708 ax P: 0.562 at bus 70693 ax Q: 0.386 at bus 70509 What are flows on low-impedance branches? They re the same as the original mismatches BOWNVL 80011-843.51 W -159.19 var -843.57 W -159.18 var -843.51 W -147.94 var -843.76 W -150.50 var 843.51 W 158.93 var DRLNGH1 80023 843.58 W 158.92 var DRLNGH2 80016 843.51 W 147.67 var DRLNGH3 80017 843.76 W 150.25 var DRLNGH4 80018 9 Now start to turn on the Voltage Controllers Turn on the Switched Shunt Controllers First Solve Power Flow Then the LTCs Solve Power Flow Then the Phase Shifters Solve Power Flow Normally these will perform fine Depends on how the controllers settings were defined in the other software package. Controller settings are not included in the file formats 10 5

rea Generation Control (GC) Before you try to enable the GC, ensure that the case was truly solved while on GC control The best way to check this is to do following Choose Case Information, rea Records Look at the CE W column If values are very large, then the original case was not solved using area control They look OK for the nerc04s_f case 11 When Case is Not Solved with GC Example: SS03sum1r.raw SS03SU1-2003 SUER ON-PEK BSE CSE - ERCOT ROS SSWG FINL - 07/01/2002 - ERCOT Solve this case with all controls enabled, but the GC disabled and it solves fine. However, go to the rea Records and look at the CE values 12 6

rea CE W, Unspecified W Transactions Large CE Values Unspecified W Interchange does not sum to zero 13 rea Unspecified W Interchange Each area can have an export specified which does not have a receiving end specified This is called Unspecified It is very important that these unspecified values sum to zero. If they do not sum to zero, then you have an export to nowhere When this occurs, the rea with the slack bus will be turned off GC and all unspecified interchange will be sent to the island slack bus 14 7

What Does It ean to do a Single Solution in Simulator? Single solution should not be confused with a single Newton-Raphson (or other technique) power flow Simulator s Single Solution encompasses three nested loops that iterates between a power flow routine, logic for control device switching, and generation control until the power flow is solved and no more device switching is detected 15 Overview of Single Solution Routine Pre-processing ngle Smoothing (for newly closed lines) Generator remote regulation viability Estimate W change needed Three Nested Loops Solution Process W Control Loop Voltage Controller Loop Inner Power Flow loop Traditionally called the Power Flow Solution Voltage Control Loop W Control Loop (Note: The LP OPF occurs here also) 16 8

Pre-processing ngle Smoothing Reduces large angle differences across transmission elements that have recently been closed in (or added to the case) to reduce initial power flow mismatches Previously if you closed in a line with a large angle difference, the power flow would diverge 17 Pre-processing Generator Remote Regulation Viability Checks for a viable transmission path between a generator bus and it s remotely regulated bus If a generator has no transmission path, or if all possible transmission routes to the regulated bus are intercepted by other voltage controlled buses, then the generator is internally turned off of voltage regulation If a generator on left are set to control voltage at the bus on the right, then this would cause convergence difficulty OPEN BREKER 18 9

Pre-processing Estimate W Change Stores the initial output of the generators for referencing during participation factor control odifies generator outputs in each area, super area, or island (depending on what control is being used) to meet approximate CE requirements ttempting to prevent slack bus from changing by drastic amounts during the first Newton-Raphson power flow calculation in the inner loop 19 W Control Loop W Control (Outer Loop) Repeat Voltage Controller Loop Inner Power Flow Loop Change generation/load to meet CE requirements Redispatches generation and/or load using the selected GC control method for each area (superarea, or island) Until no more generation/load changes are required 20 10

Power Flow and Control Loop Voltage control switching and Inner Power Flow Loop Repeat 1: Inner Power Flow loop 2: Generator VR Limit Checking 3: DC Line Solution 4: Switched Shunt Control Switching 5: Transformer switching Until no more control switching is required 21 Step 1: Inner Power Flow Loop Step 1: Repeat (Inner Power Flow loop) Evaluation ismatch Generator VR output automatically calculated for PV buses Optionally (enforce Generator VR limits at each step) Perform power flow step» Newton s ethod (this is in rectangular form)» Decoupled Power Flow» Polar Form Newton s ethod Until no more mismatch 22 11

Step 2: Generator VR Limits Step 3: Solve DC line equations Step 2: Generator VR Limit Check Backs off or enforces VR limits Checks for controller oscillation» Generators that appear to be oscillating between control settings are internally set off of control Updates mismatch and voltage vectors» Incorporates voltage vector changes by processing generators in series Step 3: Solve DC line equations 23 Step 4: Switched Shunt Control Step 4: Switched shunt control Checks regulated buses for voltage limit violations and adjusts switched shunt control appropriately» lso can control the total VR output for generators controlling the voltage at a particular bus (good for modelling a shunt which maintains VR reserves) Checks for controller oscillations» Switched shunts that appear to be oscillating between control settings are internally set off of control Updates mismatch and voltage vectors» Incorporates voltage vector changes by processing switched shunts in series 24 12

Step 5: Transforming Switching Step 5: Transformer switching Checks regulated Voltages, VR flows, and W flows for limit violations and adjusts transformer controls Checks for controller oscillations» Transformers that appear to be oscillating between control settings are internally set off of control Updates mismatch and voltage vectors» Incorporates vector changes by building a crosssensitivity matrix for all transformers being switched, and processes all switching transformers in parallel» This requires the construction and factorization of a full matrix dimensioned by the number of transformers which need to be switched. Normally a small number are switched each time. 25 Complete Process Pre-processing ngle Smoothing, Remote Viability Check, rea Generator Estimation Repeat (W Control Loop) Repeat (Controller Loop) 1: Repeat (InnerPower Flow loop) Evaluation ismatch Optionally (enforce Generator VR limits at each step) Perform power flow step» Newton s ethod» Decoupled Power Flow» Polar Newton Until no more mismatch (or max iteration) 2: Generator VR Limit Checking 3: DC Line Solution 4: Switched Shunt Control Switching 5: Transformer switching Until no more control switching is required (or at max iteration) Change generation/load to meet CE requirements Redispatches generation/load using the GC control method for area (island) Until no more generation changes are required 26 13

Generator Var odeling Example Case from Bill Smith, Powersmiths International 4 generators 162.10 W 0.00 var 162.10 W 0.00 var 162.10 W 0.00 var 2 branches 388.40 W 0.00 var 1JSPGT1 1JSPGT2 1JSPGT3 1JSPST1 6JSPER Jasper 2 1.0204 pu 1.0203 pu 27 Generator Var odeling: branch outage occurs Take one of the branches out of service Results in an unsolved power flow See depressed per unit voltage = Voltage Collapse 28 14

What about the Generator Var voltage support? This voltage collapse occurred, but notice that the generators are all still operating at 0 Var output If they were operating with more Vars they could prevent the collapse Use the Check Immediately option on the Solution Options 29 essage Log Comparisons Voltage Collapse Starting Single Solution using Rectangular Newton-Raphson Warning - Total of case transactions do not sum to zero - Case has 332.00 W more imports than exports Number: 0 ax P: 424.429 at bus 6JSPER (12429) ax Q: 144.033 at bus 6PURRYSB (13236) Number: 1 ax P: 93.170 at bus 6JSPER (12429) ax Q: 99.728 at bus 6JSPER (12429) Number: 2 ax P: 4.865 at bus 6PURRYSB (13236) ax Q: 11.950 at bus 6JSPER (12429) Number: 3 ax P: 0.532 at bus 6PURRYSB (13236) ax Q: 4.336 at bus 1JSPST1 (12834) Number: 4 ax P: 0.337 at bus 6PURRYSB (13236) ax Q: 3.565 at bus 1JSPST1 (12834) Number: 5 ax P: 0.337 at bus 6PURRYSB (13236) ax Q: 3.565 at bus 1JSPST1 (12834) NR PowerFlow - Power flow unable to converge Simulation: Power Flow did not Converge! Single Solution Finished in 3.047 Seconds Voltage Collapse Occurs This is seen by the fact that the Reactive Power Equations can not converge Check Immediately Enabled Starting Single Solution using Rectangular Newton-Raphson Warning - Total of case transactions do not sum to zero - Case has 332.00 W more imports than exports Number: 0 ax P: 424.428 at bus 6JSPER (12429) ax Q: 144.033 at bus 6PURRYSB (13236) Number: 1 ax P: 93.225 at bus 6JSPER (12429) ax Q: 99.736 at bus 6JSPER (12429) Gen(s) at bus 1JSPGT1 (12831) has backed off var limit Gen(s) at bus 1JSPGT2 (12832) has backed off var limit Gen(s) at bus 1JSPGT3 (12833) has backed off var limit Gen(s) at bus 1JSPST1 (12834) has backed off var limit Other Gen Var Changes Number: 2 ax P: 1.860 at bus 6JSPER (12429) ax Q: 3.816 at bus 12JEFFH6 (13028) Other Gen Var Changes Number: 3 ax P: 0.163 at bus 6JSPER (12429) ax Q: 2.064 at bus 12JEFFH6 (13028) Number: 4 ax P: 0.002 at bus 6JSPER (12429) ax Q: 0.015 at bus 12JEFFH6 (13028) Other Gen W Changes Generation djustment Completed. Number: 0 ax P: 3.056 at bus 1W (12800) ax Q: 0.015 at bus 12JEFFH6 (13028) Number: 1 ax P: 0.017 at bus 1VOGTLE2 (15102) ax Q: 0.026 at bus 1W (12800) Number: 0 ax P: 0.017 at bus 1VOGTLE2 (15102) ax Q: 0.026 at bus 1W (12800) Simulation: Successful Power Flow Solution Single Solution Finished in 2.516 Seconds Solution sees the voltages begin to fall and backs off the minimum Var limits to provide voltage support 30 15

Voltage Collapse If Voltage Support Devices are missing from an area it can result in Voltage Collapse Once this situation occurs, even closing in the capacitors will not bring the voltages back up You often get a low voltage solution. Unsolved Voltage Collapse Cap at 8290 closed, but voltage still low 31 Recovering From a Low Voltage Solution First Choice: Go back to an original good case and recreate your case Second Choice: Isolate the area with low voltage and resolve Then bring back in the area that collapse slowly. Third Choice: Try the flat start solution with the Robust Solution Process 32 16

VLTN TP2 RIR 2 RF 2 LITO 2 130% V L ITO 4 BRYN T2 CI EN EG2 TKIN SN 2 SH FTER2 PRSID I O 2 PRSID I O PI SN O 2 LPIN E 2 RGECPT2 LPIN ER2 Result after: Robust Solution Process Solution is achieved! However there seems to be new spot of low voltages 33 What does the Robust Solution Process do Starts by disabling all controls Disable LTC, Phases, Switched Shunts, GC, Gen Var Limit Enforment Solve using a Decoupled Power Flow Solve using the Rectangular Newton Enable Gen Var Limits Enable Shunts, Solve Newton Enable LTCs, Solve Newton Enable GC, Solve Newton Enabled phase shifters one at a time and solve 34 17

V V 89% V 87% V V V V Problems with Decoupled Power Flow Solution Decoupled Solution has a lot of trouble with transmission lines with high R/X ratios The Right is a close-up of the region from the previous solution which resulted in low voltages Notice that R/X values are very large! Normal Value about 0.2 These are 1.5 and higher. This can be fixed by opening the series of lines, solving, closing the line back in, and resolving. R= 0.75773 pu X= 0.44493 pu R= 0.00513 pu X= 0.00294 pu R= 0.19597 pu X= 0.11222 pu R= 0.34303 pu X= 0.19643 pu R= 0.70851 pu X= 0.40626 pu R= 0.00000 pu X= 0.92000 pu 0 W 0 var 130% LITO4 6689 BRYNT2 0.63 pu 6682 CIENEG2 0.63 pu 6690 TKINSN2 0.55 pu 6683 SHFTER2 0.42 pu 6684 PRSIDIO2 0.15 pu 6685 PRSIDIO 0.15 pu 6678 LITO2 0.93 pu 35 Other Problems with Decoupled The Robust Solution ethod often works great in the WECC and the ERCOT cases, so do not hesitate to use it there. However, we have not had great success on extremely large cases of the Eastern Interconnect This is a topic we will be researching more this summer 36 18

Setting up an Initial OPF Case The first step in setting up an Initial OPF Case is to obtain Cost Information for your generators Example: Load Case2-OPF.pwb (has cost info) Choose LP OPF, Primal LP We end up with 45 unenforceable constraints Of these many seem to be caused by radial Change Limit onitoring Settings to Ignore Radial Lines and Buses Radial Bus is connected to the system by only one transmission line Radial Line is a line connected to a radial bus. Choosing this reduces the unenforceable list to 29 constraints. 37 Unenforceable Constraints If you look at the W and Var flows on these lines you ll find that many have VERY large Var flows dd Columns for ax W and ax Var on LP OPF, Lines and Transformers If you look through the case, you ll find many very strange LTC tap ratio settings lso some are due to phase-shifters being in series with an overloaded branch 38 19

Reset the Tap Settings We will set all transformers on tap control to have a ratio of 1.00 UX File: case2-opf Change Transformers.aux lso will change all phase-shifters to be controlled by the OPF solution Phase Shifters have three control options None leave at a fixed angle Power Flow llow the power flow solution to dispatch according to the setpoints of the controller OPF llow the OPF s linear program to dispatch the transformer for a more global optimization 39 Unenforceable Constraints Left This results in a reduced list of 17 unenforceable constraints 40 20

V V V V V V V V V V V V V V V V V V V V V Closer Look Look more closely at the majority of the remaining unenforceable constraints Continues to show a large number of under radial elements which should probably just be ignored handful of elements require greater study Breakdown and just start drawing a oneline diagram to represent this part of the system You will start to see what the problem is Changes required are described in UX File: case2-opf onitor Changes.aux 41 Example: Internal Shawvill 360 P-BURG 2 13.30 var -0.12 $/Wh 0.99 pu 0.0 W 0.0 var 265 P-BURG 1-0.11 $/W h 0.95 pu 0.0 W 0.0 var 0.0 W 0.0 var 72.05 $/Wh 0.0 W 0.0 var 78.16 $/W h 228 0.96 pu TYRONEN 99% V 246 TYRNE #1 67.23 $/Wh 0.96 pu 17.5 W 0.0 var 29.77 $/Wh 426 0.98 pu DER 229 WESTFLL 30.10 $/W h 0.97 pu 235 DER 40.14 $/Wh 0.3 W 0.0 var 465 WESTOVER 24.55 $/W h 0.97 pu Rest of the System 421 DUBOIS 373 425 PHILIPSB -0.11 $/Wh 0.97 pu SHW VILL 15.52 $/Wh 1.05 pu 423 436 SHWVILL SHW VILL 15.50 $/Wh 15.50 $/Wh 0.98 pu 0.98 pu 15.51 $/Wh 0.97 pu V 434 SHW VILL 435 SHWVILL 15.51 $/Wh V 0.96 pu 4.2 W 5.5 var 18.7 W 7.5 var 126.0 W 20.3 var 15.1 W -13.0 var 368 SHWVILL 15.49 $/W h 1.04 pu 143% 105% 29.5 W 20.7 var 15.1 W 8.3 var 257 SHW VILL 15.49 $/W h 0.99 pu 15.6 W V 8.5 var 431 SHW VILL 15.51 $/W hv 0.94 pu 119.7 W -9.0 var 98% 82% 152% 96% 419 V SHWVILL 15.51 $/W h 372 SHWVILL 15.52 $/Wh 1.08 pu V 428 SHW VILL 15.51 $/W h 19.32 $/Wh 422 0.98 pu ROCKTON 58.8 W 17.7 var 424 SHWVILL 15.51 $/Wh 0.96 pu 19.35 $/Wh 0.97 pu 300 ROCK T Four of the stepup transformers experience high loadings. I choose to just ignore these limits. The lines from 426-228 and 423-426 also experience high loadings because the generators are all at their low limits and can not back down far enought to remove these problems. To fix this, I have turned off generators at buses 431 and 424 42 21

V V V V V V V V V V V V V V Example: Internal ERCK 59.29 $/Wh 1.0131 pu 4212 NWLES 82.2 W 25.2 var 82.2 W 14.1 var 23.2 W 99% 9.0 var 90.5 var 4217 N WLES4 59.64 $/Wh 1.0185 pu 4216 NWLES 59.63 $/Wh 1.0186 pu 82.2 W 25.2 var 20.9 var 4214 NWLES 59.63 $/Wh 1.0186 pu 113% 4215 NWLES 59.63 $/Wh 1.0186 pu 4217-4216 line has a large impedance of 0.15 compared to the lines 4214-4217, 4214-4215, 4216-4215 which have impedances of 0.0002 4153 59.63 $/Wh L 10700 1.0184 pu 59.64 $/Wh 1.0181 pu 3.9 W 1.6 var 59.63 $/Wh 1.0184 pu 4195 ERCK 4154 L 16000 This means that 4216-4217 will NEVER have any flow on it. Thus the line 4214-4217 is essentially radial. 4196 4544 ERCK ERCK 3 59.64 $/Wh 59.62 $/Wh 1.0283 pu 1.0149 pu 0.0 W 1.4 W 0.0 var -1.5 var 43 fter these changes we remove all unenforceable Constraints Still some very high cost constraints remain BIRDBORO Pine LNE = 772.8 $/Vhr 44 22

64.53 $/Wh 64.53 $/Wh V V 1156 NBOYERTO V 15.59 $/Wh 1730 1164 4.0 W 4.2 W 1.06 pu TITUS SREDING 0.0 var 0.0 var 46.69 $/Wh V V 16.33 $/Wh 1606 TITUS 1729 16.89 $/Wh SREDING 15.47 $/Wh 1731 32.3 W V V 1.06 pu TITUS 0.0 var 16.24 $/Wh 1607 18.43 $/Wh 1572 V V TITUS V FLYING H V V V V 1600 21.65 $/Wh 1551 35.9 W SREDING 24.51 $/Wh 1610 DSTWN 16.33 $/Wh 1608 V 0.0 var 17.20 $/Wh U.CORSTK TITUS 15.59 $/Wh 1732 V V V V V 1.06 pu TITUS 24.51 $/Wh 1609 24.05 $/Wh 1579 CORSTK T LINC 821 V V V V -81.03 $/Wh 1563 25.52 $/Wh 1574-37.53 $/Wh 1582 V V BIRDFERO GLENSIDE 32.3 W LORNE 0.0 var 25.18 $/Wh 1612 W.RDG 1553 V RORCST V V V V -88.98 $/Wh V V V 1562 27.80 $/Wh 1568 BIRDBORO DN -88.98 $/Wh V 1156 NBOYERTO V 1590 NBOYERTO 1590 NBOYERTO 207.74 $/Wh 441.99 $/Wh 18.80 var V 1611 W.BOYTWN 280.51 $/Wh V 1611 W.BOYTWN 1593 PINE VLNE 0.0 W 0.0 var V V 187.23 $/Wh 1593 PINE LNE 0.0 W 0.0 var V V V 1575 K.B.I. 1556 BRTO 1596 RNGROCKS 1567 CONTY LN 216.53 $/Wh V 1575 K.B.I. 216.11 $/Wh 1556 BRTO V 1596 RNGROCKS 252.69 $/Wh V 252.69 $/Wh V 1567 CONTY LN 129.35 $/Wh 1566 CLOUSER 119.00 $/Wh V 1566 CLOUSER 119.00 $/Wh V 0.0 W 0.0 var 106.35 $/Wh 1570 E.TOPTON 115.29 $/Wh 1570 E.TOPTON V 1573 FRIEDNBG 1569 E PENN 29.00 $/Wh V 1573 FRIEDNBG 95.95 $/Wh 1576 KUTZTOWN 1569 E PENN 1576 KUTZTOWN V 1565 CRSONI V 1565 CRSONI V 1585 C-KN GP 1585 C-KN GP 31.69 $/Wh V 109.34 $/Wh V 88.89 $/Wh V 1571 EXIDE 33.73 $/Wh V V 1555 BLDY V 1571 EXIDE 33.73 $/Wh V V V 1555 BLDY V 1554 T&T 34.11 $/Wh 1599 S.HBRG V 1583 LYNNVILE 64.63 $/Wh 105.97 $/Wh 29.18 $/Wh V 1583 LYNNVILE 64.63 $/Wh 1584 LYONS 62.13 $/Wh V 1554 T&T 1599 S.HBRG 64.80 $/Wh 1584 LY ONS V V 64.80 $/Wh 64.80 $/Wh 64.17 $/Wh 0.96 pu 62.25 $/Wh 0.96 pu 61.10 $/Wh 0.96 pu V 34.75 $/Wh 15.59 $/Wh 1730 1164 1.06 pu TITUS SREDING 4.0 W 4.2 W 46.69 $/Wh 0.0 var 0.0 var V V 16.33 $/Wh 1606 TITUS 1729 16.89 $/Wh SREDING 15.47 $/Wh 1731 32.3 W V V 1.06 pu TITUS 0.0 var 16.24 $/Wh 1607 18.43 $/Wh 1572 V V V TITUS FLY ING H V V V V 1600 21.65 $/Wh 1551 35.9 W SREDING 24.51 $/Wh 1610 DSTWN 16.33 $/Wh 1608 V 0.0 var 17.20 $/Wh U.CORSTK TITUS 15.59 $/Wh 1732 V V V V V 1.06 pu TITUS 24.51 $/Wh 1609 24.05 $/Wh 1579 CORSTK T LINC 821 V V V V -81.03 $/Wh 1563 25.52 $/Wh 1574-37.53 $/Wh 1582 V V BIRDFERO GLENSIDE 32.3 W LORNE 0.0 var 25.18 $/Wh 1612 W.RDG 1553 V RORCST V V V V -88.98 $/Wh V V V 1562 27.80 $/Wh 1568 BIRDBORO DN -88.98 $/Wh 207.74 $/Wh 441.99 $/Wh 18.80 var 100% V V 100% V 280.51 $/Wh V 187.23 $/Wh V V V V 216.11 $/Wh 216.53 $/Wh 94% V 129.35 $/Wh V 0.0 W 0.0 var 106.35 $/Wh 115.29 $/Wh V 29.00 $/Wh 95% V 95.95 $/Wh V 31.69 $/Wh V 109.34 $/Wh V 88.89 $/Wh V V 105.97 $/Wh 29.18 $/Wh 62.13 $/Wh 34.11 $/Wh 64.80 $/Wh 64.17 $/Wh 0.96 pu 62.25 $/Wh 0.96 pu 0.96 pu 61.10 $/Wh 83% V V 34.75 $/Wh V V V V 1564 CR TECH 1154 LYONS V V V V V 1564 CR TECH 1598 S.HBRG 1715 HILL RD 1154 LY ONS 1598 S.HBRG 1715 HILL RD 1580 LINC 822 25.34 $/Wh 1577 V LEESPORT 57.18 $/Wh 1592 OUTR ST V 34.94 $/Wh 1587 V 1604 G IND T V SPG VL 1578 LEESPORT 57.18 $/Wh 1716 HILL RD 1717 PNTHER 1704 PNTHER V V V 63.4 W 0.0 var V V V 1577 V LEE SPORT V 33.11 $/Wh 34.94 $/Wh 75.00 $/Wh 1580 LINC 822 25.34 $/Wh 25.73 $/Wh V 1592 OUTR ST V 34.94 $/Wh 1587 V 1604 G IND T V SPG VL 1578 LEESPORT 1716 HILL RD 1717 PNTHER 1704 PNTHER V V V V 63.4 W 0.0 var 57.18 $/Wh 97% V V V 33.11 $/Wh 34.94 $/Wh 57.18 $/Wh 75.00 $/Wh 25.73 $/Wh V V 1586 G IND 1561 BERNVILL V 58.09 $/Wh V 1588 OSELE V 1557 V BERK 24 54.67 $/Wh V 1586 G IND 1557 V BERK 24 1561 BERNVILL V 58.09 $/Wh V V 1588 OS ELE V 54.67 $/Wh 1581 LINCOLN V V V 1560 BERN CH 53.35 $/Wh 69.42 $/Wh 1581 LINCOLN V 1603 SION TP 54.04 $/Wh 1602 SION V 1560 BERN CH 53.35 $/Wh 69.42 $/Wh 1589 UHLENBG 36.13 $/Wh 1603 SION TP 54.04 $/Wh 1602 SION 54.04 $/Wh V 41.58 $/Wh 1605 ST PETRS 1589 UHLENBG 36.13 $/Wh V 41.58 $/Wh 54.04 $/Wh 1605 ST PETRS 43.11 $/Wh 1558 BERK 835 50.00 $/Wh V V 43.11 $/Wh 1558 BERK 835 50.00 $/Wh V V 1597 ROSEDLE V V V 1597 ROSEDLE V V 1595 RIVRVIEW 1559 BERKLEY 50.00 $/Wh 1.06 pu V 49.44 $/Wh 63.23 $/Wh V 1595 RIVRVIEW 1559 BERKLEY 50.00 $/Wh 1.06 pu V 49.44 $/Wh V 63.23 $/Wh 1591 NTEPLE 1552 LTN CT V 1591 NTEPLE 1552 LTN CT V V 57.67 $/Wh V V 57.67 $/Wh V 1159 NTEPLE V 1159 NTEPLE Birdboro Pine LNE Yellow Region forms a load pocket for two large loads 85.3 W 193.7 W The 69 kv lines feeding this region have high loadings 100% 100% 85.3 W -25.6 var 94% 95% 193.7 W -16.4 var 83% 97% 16.4 W -3.3 var 12.6 W 5.0 var 268.5 W -35.7 var 45 Contour of Prices around Birdboro Pine Lne Load Pocket These prices could be reasonable. 16.4 W -3.3 var 12.6 W 5.0 var 268.5 W -35.7 var 85.3 W -25.6 var 193.7 W -16.4 var 46 23

V V V V V V V V V V V V V V V V V V V V V V V V V V SIEGFRIE NZRETH Limits 59.99 $/Wh 3081 SIEGFRIE 55.67 $/Wh 3 Wh 3061 1.03 pu EPLERT V V V $/Wh pu 19.65 var 3376 EPLERT 59.7 59.7 W W -0.1-0.1 var var 63.46 $/Wh 3394 7.31 var ECKESVI 3195 RROWHE 47.17 $/Wh 3391 0.99 pu KEY C 2 0.00 var 94% 94% 28.27 var 3408 V 27.96 $ 78.20 $/Wh V 3399 20.88 $/Wh 3415 10.47 var SIEGFRIE 1.04 p 0.97 pu 14.73 $/Wh 1.03 pu CH HL T2 NZRETH 65.58 $/Wh 3403 27.90 $/Wh 3174 PL T1 10.33 var 100% 94% 1.04 pu RTINSC 0.0 W -86.64 $/Wh 3390 3404 0.0 var 64.0 W 71.3 W V 24.3 var 0.99 pu KEY C 1 V 10.8 var PL T2 65.67 $/Wh 64.0 W 64.0 W 24.3 var 24.3 var 15.59 $/Wh 3375 2.35 var Taking out the negative loads at NZRETH and then an equivalent amount of positive load at SIEGRIE results in relieving the very difficult to remove overloads on these branches. 32.02 $/Wh 103pu 1.03 pu CH HL T1 32.02 $/Wh 3392 1.03 pu LSTR T1 3393 LSTR T2 21.04 $/Wh 3396 1.03 pu 28.22 T BETHE $/Wh 1.04 pu 131.2 W 00va 47 Difficult OPF Solutions Summary Look for radial systems and load pockets Look for generators or phase-shifters which can relieve problems Give the OPF more controls to FIX the problems Look for constraints which don t make sense Radial lines serving load Radial transformers/lines leaving generators Use your judgement to setup a reasonable case Realize that some unenforceable constraints are inevitable at first 48 24