Techniques for Conditioning Hard-to-Solve Cases · Area Generation Control (AGC) • Before you try to enable the AGC, ensure that the case was truly solved while on AGC control •

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Techniques for Conditioning Hard-to-Solve Cases

James WeberDirector of Operations

PowerWorld [email protected]

Phone: 217 384 6330 ext 13

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Overview

• Starting with public text-file data– Low impedance mismatches– Controller Settings, Area Control

• Overview of Simulator’s “Single Solution”• Make use of the “Check Immediately” option for

Generator MVar Limits• Loss of reactive support, Voltage Collapse, and Low-

Voltage Solutions• Use of the Robust Solution Process• Achieving an initial OPF Solution

– How to handle unenforceable constraints

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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 Mismatches from low impedance lines– Voltage Controllers

• Transformers• Switched Shunts

– Area Interchange Control• These are not errors with the case or with

Simulator, but should be understood.

4

Very Large Initial Mismatches

• 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

» Minimum R = 0.0000001 = (1/1,000,000) » Minimum X = 0.00001 = (1/100,000)» Simulator will not let you set the values lower than this

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Example Case: nerc04S_f.raw

• Read in the case nerc04s_f.raw– 2003 SERIES,

NERC/MMWG BASE CASE LIBRARY

– 2004 SUMMER CASE, FINAL

• Notice mismatches come in oppositely signed “pairs”– -1567 MW, – +1566 MW

• BOWMANVL is more complicated

6

BOWMANVL - DARLNG

MW MismatchMVar Mismatch

Very Small Impedances

MVar Mismatches sum nearly to zeroMW Mismatches sum to nearly zero

BOWMANVL

-3373.97 MW-620.15 Mvar

80011

DARLNGH1

843.51 MW159.79 Mvar

80023DARLNGH2

843.58 MW159.77 Mvar

80016DARLNGH3

843.51 MW148.47 Mvar

80017DARLNGH4

843.76 MW151.06 Mvar

80018

0.000080 pu0.000000 pu

0.000080 pu0.000000 pu

0.000080 pu0.000000 pu0.000080 pu

0.000000 pu

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CLAIRVIL

MW MismatchMW Mismatch

MW Mismatches sum to nearly zeroMVar Mismatches sum nearly to zero

Very Small Impedances

804762509.05 MW

CLAIRVIL

344.55 Mvar

80481-525.38 MW

CLAIRV71

-167.97 Mvar

80482-364.13 MW

CLAIRV72

-61.35 Mvar

80483-428.04 MW

CLAIRV73

-41.35 Mvar

80484-414.53 MW

CLAIRV74

38.80 Mvar

80485-393.11 MW

CLAIRV75

-115.69 Mvar

80486-390.19 MW

CLAIRV76

-7.01 Mvar

0.000100 pu0.000000 pu

0.000100 pu0.000000 pu

0.000100 pu0.000000 pu

0.000100 pu0.000000 pu 0.000100 pu

0.000000 pu0.000100 pu0.000000 pu

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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 AGC

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If Initial Case was truly solved, Solution Will Converge Quickly

• Solution Results:

• What are flows on low-impedance branches?– They’re the same as the original mismatches

Max P: 3373.966 at bus 80011 Max Q: 728.978 at bus 80041Max P: 26.028 at bus 70509 Max Q: 38.214 at bus 70708Max P: 0.562 at bus 70693 Max Q: 0.386 at bus 70509

BOWMANVL80011

DARLNGH180023

DARLNGH280016

DARLNGH380017

DARLNGH480018

-843.51 MW-159.19 Mvar

843.51 MW158.93 Mvar

-843.57 MW-159.18 Mvar

843.58 MW158.92 Mvar

-843.51 MW-147.94 Mvar

843.51 MW147.67 Mvar

-843.76 MW-150.50 Mvar

843.76 MW150.25 Mvar

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Now start to turn on theVoltage 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

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Area Generation Control (AGC)

• Before you try to enable the AGC, ensure that the case was truly solved while on AGC control

• The best way to check this is to do following– Choose Case Information, Area Records– Look at the ACE MW column– If values are very large, then the original case was

not solved using area control– They look OK for the nerc04S_f case

12

When Case is Not Solved with AGC

• Example: SS03sum1r.raw– SS03SUM1 - 2003 SUMMER ON-PEAK BASE CASE - ERCOT ROS SSWG – FINAL - 07/01/2002 - ERCOT

• Solve this case with all controls enabled, but the AGC disabled and it solves fine.

• However, go to the Area Records and look at the ACE values

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Area ACE MW, Unspecified MW Transactions

• Large ACE Values• Unspecified MW Interchange does not sum to zero

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Area Unspecified MW 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 Area with the slack bus will

be turned off AGC and all unspecified interchange will be sent to the island slack bus

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What Does It Mean 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

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Overview of Single Solution Routine

• Pre-processing– Angle Smoothing (for newly closed lines)– Generator remote regulation viability– Estimate MW change needed

• Three Nested Loops Solution Process– MW Control Loop

• Voltage Controller Loop– Inner Power Flow loop Traditionally called the

Power Flow SolutionVoltage Control Loop

MW Control Loop (Note: The LP OPF occurs here also)

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Pre-processing

• Angle 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

18

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 BREAKER

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Pre-processing

• Estimate MW Change– Stores the initial output of the generators for referencing

during participation factor control– Modifies generator outputs in each area, super area, or

island (depending on what control is being used) to meet approximate ACE requirements

– Attempting to prevent slack bus from changing by drastic amounts during the first Newton-Raphson power flow calculation in the inner loop

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MW Control Loop

• MW Control (Outer Loop)– Repeat

• Voltage Controller Loop– Inner Power Flow Loop

• Change generation/load to meet ACE requirements– Redispatches generation and/or load using the selected AGC

control method for each area (superarea, or island)

– Until no more generation/load changes are required

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Power Flow and Control Loop

• Voltage control switching and Inner Power Flow Loop– Repeat

• 1: Inner Power Flow loop• 2: Generator MVAR Limit Checking• 3: DC Line Solution• 4: Switched Shunt Control Switching• 5: Transformer switching

– Until no more control switching is required

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Step 1: Inner Power Flow Loop

• Step 1: Repeat (Inner Power Flow loop)– Evaluation Mismatch– Generator MVAR output automatically calculated for PV

buses– Optionally (enforce Generator

MVAR limits at each step)– Perform power flow step

» Newton’s Method (this is in rectangular form)» Decoupled Power Flow» Polar Form Newton’s Method

• Until no more mismatch

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Step 2: Generator MVAR LimitsStep 3: Solve DC line equations• Step 2: Generator MVAR Limit Check

– Backs off or enforces MVAR 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

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Step 4: Switched Shunt Control

• Step 4: Switched shunt control– Checks regulated buses for voltage limit violations and adjusts

switched shunt control appropriately» Also can control the total VAR output for generators

controlling the voltage at a particular bus (good for modelling a shunt which maintains VAR 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

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Step 5: Transforming Switching

• Step 5: Transformer switching– Checks regulated Voltages, MVAR flows, and MW 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 cross-

sensitivity 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.

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• Pre-processing – Angle Smoothing, Remote Viability Check, Area Generator Estimation

• Repeat (MW Control Loop)– Repeat (Controller Loop)

• 1: Repeat (InnerPower Flow loop)– Evaluation Mismatch– Optionally (enforce Generator MVAR

limits at each step)– Perform power flow step

» Newton’s Method» Decoupled Power Flow» Polar Newton

• Until no more mismatch (or max iteration)• 2: Generator MVAR 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 ACE requirements

• Redispatches generation/load using the AGC control method for area (island)• Until no more generation changes are required

Complete Process

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Generator MVar Modeling

• Example Case from Bill Smith, Powersmiths International

• 4 generators • 2 branches

6JASPER

1JASPGT1 1JASPGT2 1JASPGT3 1JASPST1

Jasper 2

162.10 MW

0.00 Mvar

162.10 MW

0.00 Mvar

162.10 MW

0.00 Mvar

388.40 MW

0.00 Mvar

1.0204 pu 1.0203 pu

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Generator MVar Modeling:A branch outage occurs

• Take one of the branches out of service• Results in an unsolved power flow

– See depressed per unit voltage = Voltage Collapse

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What about the Generator MVarvoltage support?

• This voltage collapse occurred, but notice that the generators are all still operating at 0 MVaroutput

• If they were operating with more MVars they could prevent the collapse

• Use the “Check Immediately” option on the Solution Options

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Message Log Comparisons

Starting Single Solution using Rectangular Newton-RaphsonWarning - Total of case transactions do not sum to zero -

Case has 332.00 MW more imports than exportsNumber: 0 Max P: 424.428 at bus 6JASPER (12429)

Max Q: 144.033 at bus 6PURRYSB (13236)Number: 1 Max P: 93.225 at bus 6JASPER (12429)

Max Q: 99.736 at bus 6JASPER (12429)Gen(s) at bus 1JASPGT1 (12831) has backed off var limitGen(s) at bus 1JASPGT2 (12832) has backed off var limitGen(s) at bus 1JASPGT3 (12833) has backed off var limitGen(s) at bus 1JASPST1 (12834) has backed off var limitOther Gen Var ChangesNumber: 2 Max P: 1.860 at bus 6JASPER (12429)

Max Q: 3.816 at bus 12JEFFH6 (13028)Other Gen Var ChangesNumber: 3 Max P: 0.163 at bus 6JASPER (12429)

Max Q: 2.064 at bus 12JEFFH6 (13028)Number: 4 Max P: 0.002 at bus 6JASPER (12429)

Max Q: 0.015 at bus 12JEFFH6 (13028)Other Gen MW ChangesGeneration Adjustment Completed.Number: 0 Max P: 3.056 at bus 1AMW (12800)

Max Q: 0.015 at bus 12JEFFH6 (13028)Number: 1 Max P: 0.017 at bus 1VOGTLE2 (15102)

Max Q: 0.026 at bus 1AMW (12800)Number: 0 Max P: 0.017 at bus 1VOGTLE2 (15102)

Max Q: 0.026 at bus 1AMW (12800)Simulation: Successful Power Flow SolutionSingle Solution Finished in 2.516 Seconds

Starting Single Solution using Rectangular Newton-RaphsonWarning - Total of case transactions do not sum to zero -

Case has 332.00 MW more imports than exportsNumber: 0 Max P: 424.429 at bus 6JASPER (12429)

Max Q: 144.033 at bus 6PURRYSB (13236)Number: 1 Max P: 93.170 at bus 6JASPER (12429)

Max Q: 99.728 at bus 6JASPER (12429)Number: 2 Max P: 4.865 at bus 6PURRYSB (13236)

Max Q: 11.950 at bus 6JASPER (12429)Number: 3 Max P: 0.532 at bus 6PURRYSB (13236)

Max Q: 4.336 at bus 1JASPST1 (12834)Number: 4 Max P: 0.337 at bus 6PURRYSB (13236)

Max Q: 3.565 at bus 1JASPST1 (12834)Number: 5 Max P: 0.337 at bus 6PURRYSB (13236)

Max Q: 3.565 at bus 1JASPST1 (12834)NR PowerFlow - Power flow unable to convergeSimulation: 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

Solution sees the voltages begin to fall and backs off the minimum MVar limits to provide voltage support

Voltage Collapse Check Immediately Enabled

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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

32

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

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Result after:Robust Solution Process

• Solution is achieved!• However there seems to

be new spot of low voltages

M ARFA 2

MARAIR 2

VALTN TP2

ALAM ITO 4

ALAMI TO 2

BRYAN T2

CI EN EGA2

ATKI N SN 2

SH AFTER2

PRSID I O

PRSID I O 2

PAI SAN O 2

RGECAPT2

ALPI N E 2 ALPI N ER2

130%A

M V A

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What does the “Robust Solution Process” do

• Starts by disabling all controls– Disable LTC, Phases, Switched Shunts, AGC, Gen MVar

Limit Enforment• Solve using a Decoupled Power Flow• Solve using the Rectangular Newton• Enable Gen MVar Limits • Enable Shunts, Solve Newton• Enable LTCs, Solve Newton• Enable AGC, Solve Newton• Enabled phase shifters one at a time and solve

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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=X=

X=R=

X=R=

X=R=

X=R=

X=R=

A LA MIT O4

ALAMITO2

BRYANT2

CIENEGA2

ATKINSN2

SHAFTER2

PRSIDIO

PRSIDIO2

A

M VA

A

M VA

A

M VA

A

M VA

0 MW 0 Mvar

0.93 pu

6678

0.63 pu

6689

0.63 pu

6682

0.55 pu

6690

0.42 pu

6683

0.15 pu

6684

0.15 pu

6685

0.19597 pu0.11222 pu

0.00513 pu0.00294 pu

0.75773 pu0.44493 pu

0.34303 pu0.19643 pu

0.70851 pu0.40626 pu

0.00000 pu0.92000 pu

89%

A

MVA

87%

A

MVA

130%A

MVA

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Other Problems with Decoupled

• The Robust Solution Method 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

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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 Monitoring 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.

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Unenforceable Constraints

• If you look at the MW and MVar flows on these lines you’ll find that many have VERY large MVar flows– Add Columns for Max MW and Max MVar on LP

OPF, Lines and Transformers• If you look through the case, you’ll find many

very strange LTC tap ratio settings• Also some are due to phase-shifters being in

series with an overloaded branch

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Reset the Tap Settings

• We will set all transformers on tap control to have a ratio of 1.00– AUX File: case2-OPF Change Transformers.aux

• Also 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 – Allow the power flow solution to

dispatch according to the setpoints of the controller• OPF – Allow the OPF’s linear program to “dispatch”

the transformer for a more global optimization

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Unenforceable Constraints Left

• This results in a reduced list of 17 unenforceable constraints

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A 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• A handful of elements require greater study

– Breakdown and just start drawing a onelinediagram to represent this part of the system

– You will start to see what the problem is• Changes required are described in

– AUX File: case2-OPF Monitor Changes.aux

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Example: Internal Shawvill

Rest of the System

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

0.97 pu

SHAWVILL434

15.51 $/MWh

0.96 pu

SHAWVILL435

15.51 $/MWh

0.94 pu

SHAWVILL431

15.51 $/MWh

0.98 pu

SHAWVILL436

15.50 $/MWh 0.98 pu

SHAWVILL423

15.50 $/MWh

1.04 pu

SHAWVILL368

15.49 $/MWh

0.97 pu

PHILIPSB425

-0.11 $/MWh

0.99 pu

SHAWVILL257

15.49 $/MWh

1.05 pu

SHAWVILL373

15.52 $/MWh 1.01 pu

SHAWVILL419

15.51 $/MWh

0.96 pu

SHAWVILL424

15.51 $/MWh

1.00 pu

SHAWVILL428

15.51 $/MWh

0.98 pu ROCKTONM422 19.32 $/MWh

0.98 pu MADERA426 29.77 $/MWh

1.08 pu

SHAWVILL372

15.52 $/MWh

A

MVA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA

119.7 MW -9.0 Mvar

126.0 MW 20.3 Mvar

4.2 MW 5.5 Mvar

58.8 MW 17.7 Mvar

29.5 MW 20.7 Mvar

0.3 MW 0.0 Mvar

15.6 MW 8.5 Mvar

0.0 MW 0.0 Mvar

17.5 MW 0.0 Mvar

15.1 MW 8.3 Mvar

15.1 MW -13.0 Mvar

18.7 MW 7.5 Mvar

0.96 pu TYRONEN228 78.16 $/MWh

0.95 pu

P-BURG 1265

-0.11 $/MWh

0.99 pu

P-BURG 2360

-0.12 $/MWhA

M VA

A

M VA

0.0 MW 0.0 Mvar

0.0 MW 0.0 Mvar

0.0 MW 0.0 Mvar 13.30 Mvar

67.23 $/MWh 0.96 pu

229WESTFALL

72.05 $/MWh 1.00 pu

246TYRNE #1

30.10 $/MWh 0.97 pu

235MADERA

40.14 $/MWh 1.00 pu

465WESTOVER

19.35 $/MWh 0.97 pu

300ROCK MT

24.55 $/MWh 0.97 pu

421DUBOIS

A

MVA

A

MVA

A

MVA

A

M VA

A

M VA

A

M VA

A

M VA

A

M VA 98%

A

MVA

96%

A

MVA

82%

A

MVA

99%

A

MVA

152%

A

MVA

105%

A

MVA

143%

A

MVA

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Example: Internal MERCK

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

This means that 4216-4217 will NEVER have any flow on it. Thus the line 4214-4217 is essentially radial.

NWALES4212 59.29 $/MWh

59.63 $/MWh

NWALES4214

59.63 $/MWh

NWALES4216

59.63 $/MWhNWALES4215

59.64 $/MWhN WALES44217

59.63 $/MWh L 107004153

59.63 $/MWh L 160004154

59.64 $/MWhMERCK4195

59.64 $/MWhMERCK4196

59.62 $/MWhMERCK 34544

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

A

MVA

0.0 MW 0.0 Mvar

1.4 MW -1.5 Mvar

3.9 MW 1.6 Mvar

23.2 MW 9.0 Mvar

82.2 MW 14.1 Mvar 82.2 MW

25.2 Mvar

82.2 MW 25.2 Mvar

20.9 Mvar 90.5 MvarA

MVA

1.0131 pu

1.0186 pu

1.0186 pu

1.0186 pu

1.0185 pu

1.0184 pu 1.0184 pu

1.0181 pu

1.0283 pu 1.0149 pu

99%

A

MVA

113%

A

MVA

44

After these changes we remove all unenforceable Constraints

• Still some very high cost constraints remain• BIRDBORO – Pine LNE = 772.8 $/MVAhr

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Birdboro – Pine LNE

• Yellow Region forms a “load pocket” for two large loads – 85.3 MW – 193.7 MW

• The 69 kV lines feeding this region have high loadings

1562BIRDBORO

1553ARMORCST

1563BIRDFERO

1582LORANE

1593PINE LNE

1600SREADING

1611W.BOYTWN

1590NBOYERTO

1596RNGROCKS

1567CONTY LN

1575K.B.I.

1156NBOYERTO

1556BARTO

1566CLOUSER

1570E.TOPTON

1569E PENN

1573FRIEDNBG

1576KUTZTOWN

1584LYONS

1565CARSONIA

1555BALDY

1154LYONS

1588MOSELEM

1564CAR TECH

1585MC-KN GP

1583LYNNVILE

1568DANA

1592OUTR STA

1574GLENSIDE

1595RIVRVIEW

1571EXIDE

1598

S.HAMBRG

1612W.RDG

1589MUHLENBG

1591NTEMPLE

1554AT&T

1561BERNVILL

1577LEESPORT

1599S.HAMBRG

1605ST PETRS

1715HILL RD

1579LINC 821

1580LINC 822

1609CORSTK T

1587MG IND T

1597ROSEDALE

1560BERN CH

1557BERK 24

1578LEESPORT

1552ALTN CMT

1716HILL RD

1551ADAMSTWN

1581LINCOLN

1610U.CORSTK

1586MG IND

1604SPG VAL

1558

BERK 835

1603SIMON TP

1717PANTHER

1572FLYING H

1559BERKLEY

1602SIMON

1704PANTHER

1159NTEMPLE

1164SREADING

1606TITUS

1607TITUS

1608TITUS

1729SREADING

1730TITUS

1731TITUS

1732TITUS

A

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0.0 MW 0.0 Mvar

0.0 MW 0.0 Mvar

63.4 MW 0.0 Mvar

4.0 MW 0.0 Mvar

4.2 MW 0.0 Mvar

32.3 MW 0.0 Mvar

35.9 MW 0.0 Mvar

32.3 MW 0.0 Mvar

1 8 .8 0 M v a r

1.02 pu-88.98 $/MWh

1.02 pu-88.98 $/MWh

1.02 pu-81.03 $/MWh

1.02 pu-37.53 $/MWh

1.02 pu441.99 $/MWh

1.02 pu 17.20 $/MWh

1.02 pu280.51 $/MWh

1.02 pu207.74 $/MWh

1.02 pu252.69 $/MWh

1.02 pu216.53 $/MWh

1.02 pu216.11 $/MWh

1.02 pu 64.53 $/MWh

1.02 pu187.23 $/MWh

1.01 pu119.00 $/MWh

1.00 pu129.35 $/MWh

1.00 pu106.35 $/MWh

1.01 pu 95.95 $/MWh

1.00 pu115.29 $/MWh

1.00 pu105.97 $/MWh

1.02 pu 29.00 $/MWh

1.00 pu109.34 $/MWh

1.02 pu 62.13 $/MWh

1.01 pu 75.00 $/MWh

1.02 pu

29.18 $/MWh

1.02 pu 31.69 $/MWh

1.01 pu 88.89 $/MWh

1.02 pu 27.80 $/MWh

1.02 pu 33.11 $/MWh

1.02 pu 25.52 $/MWh

1.02 pu 43.11 $/MWh

1.02 pu 33.73 $/MWh

1.02 pu

64.80 $/MWh

1.02 pu 25.18 $/MWh

1.02 pu 36.13 $/MWh

1.02 pu 49.44 $/MWh 1.02 pu

34.11 $/MWh

1.02 pu 58.09 $/MWh

1.02 pu 57.18 $/MWh 1.02 pu

64.80 $/MWh

1.01 pu 69.42 $/MWh

1.02 pu 64.63 $/MWh

1.01 pu 24.05 $/MWh

1.01 pu 25.34 $/MWh

1.02 pu 24.51 $/MWh

1.02 pu 34.94 $/MWh

1.02 pu 41.58 $/MWh

1.02 pu 53.35 $/MWh

1.02 pu 54.67 $/MWh

1.02 pu 57.18 $/MWh

1.01 pu 63.23 $/MWh

0.96 pu 64.17 $/MWh

1.01 pu 21.65 $/MWh

1.02 pu 25.73 $/MWh

1.02 pu 24.51 $/MWh

1.02 pu 34.94 $/MWh

1.02 pu 34.75 $/MWh

1.02 pu 50.00 $/MWh

1.02 pu 54.04 $/MWh

0.96 pu 62.25 $/MWh

1.02 pu 18.43 $/MWh

1.06 pu 50.00 $/MWh

1.02 pu 54.04 $/MWh

0.96 pu 61.10 $/MWh

1.01 pu 57.67 $/MWh

1.01 pu 46.69 $/MWh

1.02 pu 16.33 $/MWh

1.02 pu 16.24 $/MWh

1.02 pu 16.33 $/MWh

1.02 pu 16.89 $/MWh

1.06 pu 15.59 $/MWh

1.06 pu 15.47 $/MWh

1.06 pu 15.59 $/MWh

85.3 MW -25.6 Mvar

16.4 MW -3.3 Mvar

12.6 MW 5.0 Mvar

268.5 MW -35.7 Mvar

193.7 MW -16.4 Mvar

83%

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100%

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95%

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94%

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97%A

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46

Contour of Prices aroundBirdboro – Pine Lne

• Load Pocket• These prices could be

reasonable.1562BIRDBORO

1553ARMORCST

1563BIRDFERO

1582LORANE

1593PINE LNE

1600SREADING

1611W.BOYTWN

1590NBOYERTO

1596RNGROCKS

1567CONTY LN

1575K.B.I.

1156NBOYERTO

1556BARTO

1566CLOUSER

1570E.TOPTON

1569E PENN

1573FRIEDNBG

1576KUTZTOWN

1584LYONS

1565CARSONIA

1555BALDY

1154LYONS

1588MOSELEM

1564CAR TECH

1585MC-KN GP

1583LYNNVILE

1568DANA

1592OUTR STA

1574GLENSIDE

1595RIVRVIEW

1571EXIDE

1598S.HAMBRG

1612W.RDG

1589MUHLENBG

1591NTEMPLE

1554AT&T

1561BERNVILL

1577LEESPORT

1599S.HAMBRG

1605ST PETRS

1715HILL RD

1579LINC 821

1580LINC 822

1609CORSTK T

1587MG IND T

1597ROSEDALE

1560BERN CH

1557BERK 24

1578LEESPORT

1552ALTN CMT

1716HILL RD

1551ADAMSTWN

1581LINCOLN

1610U.CORSTK

1586MG IND

1604SPG VAL

1558BERK 835

1603SIMON TP

1717PANTHER

1572FLYING H

1559BERKLEY

1602SIMON

1704PANTHER

1159NTEMPLE

1164SREADING

1606TITUS

1607TITUS

1608TITUS

1729SREADING

1730TITUS

1731TITUS

1732TITUS

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0.0 MW 0.0 Mvar

0.0 MW 0.0 Mvar

63.4 MW 0.0 Mvar

4.0 MW 0.0 Mvar

4.2 MW 0.0 Mvar

32.3 MW 0.0 Mvar

35.9 MW 0.0 Mvar

32.3 MW 0.0 Mvar

1 8 .8 0 M v a r

1.02 pu-88.98 $/MWh

1.02 pu-88.98 $/MWh

1.02 pu-81.03 $/MWh

1.02 pu-37.53 $/MWh

1.02 pu441.99 $/MWh

1.02 pu 17.20 $/MWh

1.02 pu280.51 $/MWh

1.02 pu207.74 $/MWh

1.02 pu252.69 $/MWh

1.02 pu216.53 $/MWh

1.02 pu216.11 $/MWh

1.02 pu 64.53 $/MWh

1.02 pu187.23 $/MWh

1.01 pu119.00 $/MWh

1.00 pu129.35 $/MWh

1.00 pu106.35 $/MWh

1.01 pu 95.95 $/MWh

1.00 pu115.29 $/MWh

1.00 pu105.97 $/MWh

1.02 pu 29.00 $/MWh

1.00 pu109.34 $/MWh

1.02 pu 62.13 $/MWh

1.01 pu 75.00 $/MWh

1.02 pu 29.18 $/MWh

1.02 pu 31.69 $/MWh

1.01 pu 88.89 $/MWh

1.02 pu 27.80 $/MWh

1.02 pu 33.11 $/MWh

1.02 pu 25.52 $/MWh

1.02 pu 43.11 $/MWh

1.02 pu 33.73 $/MWh

1.02 pu 64.80 $/MWh

1.02 pu 25.18 $/MWh

1.02 pu 36.13 $/MWh

1.02 pu 49.44 $/MWh 1.02 pu

34.11 $/MWh

1.02 pu 58.09 $/MWh

1.02 pu 57.18 $/MWh 1.02 pu

64.80 $/MWh

1.01 pu 69.42 $/MWh

1.02 pu 64.63 $/MWh

1.01 pu 24.05 $/MWh

1.01 pu 25.34 $/MWh

1.02 pu 24.51 $/MWh

1.02 pu 34.94 $/MWh

1.02 pu 41.58 $/MWh

1.02 pu 53.35 $/MWh

1.02 pu 54.67 $/MWh

1.02 pu 57.18 $/MWh

1.01 pu 63.23 $/MWh

0.96 pu 64.17 $/MWh

1.01 pu 21.65 $/MWh

1.02 pu 25.73 $/MWh

1.02 pu 24.51 $/MWh

1.02 pu 34.94 $/MWh

1.02 pu 34.75 $/MWh

1.02 pu 50.00 $/MWh

1.02 pu 54.04 $/MWh

0.96 pu 62.25 $/MWh

1.02 pu 18.43 $/MWh

1.06 pu 50.00 $/MWh

1.02 pu 54.04 $/MWh

0.96 pu 61.10 $/MWh

1.01 pu 57.67 $/MWh

1.01 pu 46.69 $/MWh

1.02 pu 16.33 $/MWh

1.02 pu 16.24 $/MWh

1.02 pu 16.33 $/MWh

1.02 pu 16.89 $/MWh

1.06 pu 15.59 $/MWh

1.06 pu 15.47 $/MWh

1.06 pu 15.59 $/MWh

85.3 MW -25.6 Mvar

16.4 MW -3.3 Mvar

12.6 MW 5.0 Mvar

268.5 MW -35.7 Mvar

193.7 MW -16.4 Mvar

83%A

M VA

100%A

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95%A

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94%A

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97%A

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100%A

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Page 24

24

47

SIEGFRIE – NAZARETH Limits

Taking out the negative loads at NAZARETH and then an equivalent amount of positive load at SIEGRIE results in relieving the very difficult to remove overloads on these branches.

0.99 pu KEY CM 13390-86.64 $/MWh

0.99 pu KEY CM 23391 47.17 $/MWh

0.97 puSIEGFRIE3408 78.20 $/MWh

1.02 pu NAZARETH

3399 14.73 $/MWh

1.01 pu SIEGFRIE3081 59.99 $/MWh

1.01 pu PALM T13403 65.58 $/MWh

1.01 puPALM T23404

65.67 $/MWh

1.04 pu MARTINSC3174 27.90 $/MWh

1.03 pu CH HL T13375 15.59 $/MWh

1.03 pu LSTAR T13392 32.02 $/MWh

1 03 pu LSTAR T23393 32.02 $/MWh

1.03 pu CH HL T23415 20.88 $/MWh

EPALMERT3376

EPALMERT3061MWh

1.03 pu M3 55.67 $/MWh

1.04 p 27.96 $

1.04 pu M 28.22 $/MWh 1.03 pu MT BETHE

3396 21.04 $/MWh

pu ARROWHEA3195$/MWh

1.01 pu MECKESVI3394 63.46 $/MWh

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131.2 MW0 0 Mva

7.31 Mvar

19.65 Mvar

2.35 Mvar

28.27 Mvar

10.47 Mvar

10.33 Mvar

0.00 Mvar

0.0 MW 0.0 Mvar

64.0 MW 24.3 Mvar

64.0 MW 24.3 Mvar

64.0 MW 24.3 Mvar

71.3 MW 10.8 Mvar

59.7 MW -0.1 Mvar

59.7 MW -0.1 Mvar

94%

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94%

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MVA

94%

A

MVA

100%

A

MVA

48

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