Power System Economics and Market Modeling
M8: Developing an LMP Analysis for a Large Case
2001 South First Street
Champaign, Illinois 61820
+1 (217) 384.6330
[email protected]
http://www.powerworld.com
LMP Analysis: Outline
• Sample PJM study: process overview
– One possible “step by step” approach for developing LMP Analysis on a large case
– Use of Super Area to model ISO control
– Unenforceable constraints
• More on unenforceable constraints and other OPF challenges
M8: LMP Large System
© 2014 PowerWorld Corporation
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Sample PJM Study
M8: LMP Large System
© 2014 PowerWorld Corporation
3
Process Overview
• Case Development
– Select area(s) of interest for study
– Establish the set of OPF controls: OPF, unit commitment, and AGC settings
– Establish the set of OPF constraints: Limit Monitoring settings
• Load cost curves for thermal generators
• Solve unconstrained OPF for area lambdas
• Set hydro dispatch to historical levels and hydro cost curves to unconstrained area lambdas
• Solve OPF
• Review results, analyze unenforceable constraints, and iterate process as necessary
M8: LMP Large System
© 2014 PowerWorld Corporation
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Case Development Suggestions
• Full OPF analysis on a large case may be time consuming
• For extremely congested cases, there may be no solution that satisfies all constraints
• For meaningful results, it is recommended that the scope of analysis be limited to a region of interest such as a few control areas or a single RTO territory
M8: LMP Large System
© 2014 PowerWorld Corporation
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Case Development Suggestions
• Align the part of the system to be optimized with the generator controls to remove the constraints
• Do not monitor elements in the part of the system not on OPF control
• Only place the part of the system to be studied on OPF control
M8: LMP Large System
© 2014 PowerWorld Corporation
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Eastern.pwb
Eastern Interconnect Case
• Load the Eastern.pwb case
– 3964 total generating units
– 143 branch thermal violations in base case
• Suppose we wish to model an LMP market for the Eastern portion of the PJM Interconnect
– 11 separate control areas
– 593 total generating units, 407 committed generating units
– 37 branch thermal violations in base case
M8: LMP Large System
© 2014 PowerWorld Corporation
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Starting Case with Overloads on High‐
Voltage Grid
Note use of Emphasis, Dynamic Formatting, and dynamically‐
sized pie charts on one‐line diagram
M8: LMP Large System
© 2014 PowerWorld Corporation
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Case Development
• Area/Zone Filters: show areas 25‐35 only
• OPF Controls
– Set areas 25‐35 on OPF control
– Set AGC to YES for all generators in areas 25‐35 except hydro (settings stored in cost curve aux file)
• Limit Monitoring Settings
– Report limits for areas 25‐35 only, 100 kV and above
– Do not monitor radial lines
M8: LMP Large System
© 2014 PowerWorld Corporation
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Limit Monitoring
M8: LMP Large System
© 2014 PowerWorld Corporation
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Cost Curves
• Load cost curves for thermal units: stored in aux file M08_LMP Large System\EasternCostCurvePJM.aux
M8: LMP Large System
© 2014 PowerWorld Corporation
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Solve Unconstrained OPF
• Do not enforce branch or interface constraints
M8: LMP Large System
© 2014 PowerWorld Corporation
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Set Cost Curves for Hydro Units
• For each Hydro Unit (advanced filter Hydro PJM)
– Set offer price (MWh Price 1) equal to MW Marginal Cost of its bus
– Set AGC = YES
M8: LMP Large System
© 2014 PowerWorld Corporation
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Solve Constrained OPF
• Enable constraint enforcement (on Constraint Options)
• Solve OPF, note several unenforceable constraints
M8: LMP Large System
© 2014 PowerWorld Corporation
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LMP Contour
• Note high LMPs on receiving end of constrained lines and areas with low reserve margin
M8: LMP Large System
© 2014 PowerWorld Corporation
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Effect of Line Constraints
ROXBURY
0.0 MW
0.0 Mvar
Bus: ROXBURY (221)
Nom kV: 115.00
Area: PENELEC (26)
Zone: PN 115KV (5)
0.99 pu
114.17 KV
22.42 Deg
329.56 $/MWh
0.00 MW
0.00 Mvar
ID 1
A
15.9 MW
10.1 Mvar
18.8 MVA
109.3 MW
-26.9 Mvar
112.6 MVA
87%
0.9780 tap
MVA
A
CKT 1
ROXBURY
A
99%
233
01GRANDP
20187
0.98 pu
135.84 KV
AP
0.00 $/MWh
Note difference in LMP on each end of constrained line
A
Amps
etc…
Amps
CKT 1
CARLISLE
205
0.99 pu
113.87 KV
275.59 $/MWh
CKT 1
SHADE GP
223
1.01 pu
116.61 KV
-448.11 $/MWh
86%
0.9790 tap
MVA
CKT 1
ROXB SUB
256
CARL PKE
260
CARLISLE
205
0.99 pu
113.87 KV
275.59 $/MWh
LMP
M8: LMP Large System
18.6 MW
-1.9 Mvar
18.7 MVA
112.0 MW
18.7 Mvar
113.6 MVA
© 2014 PowerWorld Corporation
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Options for Further Analysis
• Increase available units (and reserve margin) in areas with limited supply
– Many generators at their max output
– Only 4.4% operating reserves
– A competitive market would likely have more units committed – more controls
• Place PJM Areas on Super Area Control
M8: LMP Large System
© 2014 PowerWorld Corporation
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Unit Commitment and Reserves
• Most generators in high‐LMP area DP&L on Delmarva Peninsula are at max
M8: LMP Large System
© 2014 PowerWorld Corporation
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PJM Super Area
Hydro Price
= $57
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© 2014 PowerWorld Corporation
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Options for Further Analysis
• Check sensitivities on unenforceable constraints
– Optionally ignore or raise limits, change unit commitment, or include demand response (curtailable
load)
– Some unenforceable constraints may be unavoidable due to load pockets
• Incorporate contingencies with Contingent Interfaces (flowgates)
• Change cost curves (e.g. model a 10% increase in fuel cost)
M8: LMP Large System
© 2014 PowerWorld Corporation
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Unenforceable Constraints
• Examine LP Basis Matrix
• Run multiple element TLR on overloaded lines to understand relationship between flows and generator and load values
M8: LMP Large System
© 2014 PowerWorld Corporation
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LP Basis Matrix
• Marginal controller sensitivities have very low absolute value – suggests presence of load pockets
• The sensitivity vector of each control has a mix of signs – adjusting the control to relieve one constraint makes another worse
M8: LMP Large System
© 2014 PowerWorld Corporation
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Multiple Element TLR
• TLR on overloaded lines with Super Area as buyer
• Negative values on de‐
committed generators indicate units that may relieve congestion if committed
• Positive values on committed generators (especially those at Min MW) indicate that de‐committing may help
M8: LMP Large System
© 2014 PowerWorld Corporation
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Multiple Element TLR
• Add ETLR field to generator display and sort
• Note how committed units with most negative ETLR are generally maxed out
• Try committing more units with negative ETLR or those with highest product of ETLR and Max MW (custom expression “TLR Potential”) • Solve power flow, then Re‐
solve OPF
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© 2014 PowerWorld Corporation
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Demand Response
• Loads may have benefit functions, allowing them to respond to price signals in the OPF
• Load the aux file EasternLoadBenefitModels.aux: includes benefit functions for 156 loads that impact unenforceable constraints
• Enable load controls in OPF Options and Results
and re‐solve OPF
M8: LMP Large System
© 2014 PowerWorld Corporation
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Demand Response
• OPF Load Records display or Difference Flows may be used to identify curtailed loads and marginal benefit
• Unenforceable constraints due to load pockets are relieved
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© 2014 PowerWorld Corporation
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Price Contour with Demand Response
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Incorporate Contingencies with Flowgates
• Load EasternContingentInterfaces.aux
• Each flowgate interface includes a monitored element and a contingent element
• Make sure Contingent Interface Elements are Enforced in OPF (Simulator Options ‐> General tab or OPF ‐> Interfaces Display)
• Re‐solve OPF
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© 2014 PowerWorld Corporation
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More on OPF Challenges
M8: LMP Large System
© 2014 PowerWorld Corporation
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OPF Formulation and Solution
• More on Unenforceable Constraints
– Radial Elements
– Mvar loops in AC power flow
– Unusual modeling parameters
• Insufficient Reserves: not enough controls to satisfy area ACE constraint
• Too Much Power Transfer
M8: LMP Large System
© 2014 PowerWorld Corporation
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Eastern2.pwb
Analysis of Unenforceable Constraints
• Example: Load Eastern2.pwb (has cost info)
• Choose Add Ons ribbon tab  Primal LP
– We end up with 46 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 30 constraints.
M8: LMP Large System
© 2014 PowerWorld Corporation
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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 Add Ons ribbon tab  OPF Case Info  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
M8: LMP Large System
© 2014 PowerWorld Corporation
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Reset LTC Taps
• Set all transformers on LTC control to a tap ratio of 1.00
– AUX File: M08_LMP Large System\Eastern2ChangeTransformers.aux
• Re‐solve power flow, then OPF
• May also examine Circulating Mvar Flows
– Tools ‐> Connections ‐> Find Circulating MW or Mvar Flows
– Check relative tap ratios in Flow Cycles with high Loss Mvar Reduction
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© 2014 PowerWorld Corporation
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Unenforceable Constraints
• This results in a reduced list of 20 unenforceable constraints
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© 2014 PowerWorld Corporation
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Phase‐Shifting Transformers
• Phase Shifters have three control options
– None – leave at a fixed angle
– Power Flow – Allow the power flow solution to dispatch according to the MW setpoints of the controller
– OPF – Allow the OPF’s linear program to “dispatch” the transformer for a more global optimization
• OPF phase‐shifter control is often necessary if load is varied with the time‐step simulation, unless appropriate phase‐shifter control settings are known for each load level
M8: LMP Large System
© 2014 PowerWorld Corporation
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Use Caution with Phase‐Shifter OPF Control
• Phase‐shifter setpoints are often important for stability
• The setpoints may vary with load or seasonal generation pattern
• Options to consider:
– ignore MVA/Amp limit enforcement where obvious conflicts occur between limit and phase‐shifter setpoints (e.g. overloaded line in series with phase‐shifter)
– allow only a few phase shifters to operate on OPF control where it is known that stability margins are sufficient
– choose to Enforce MW Regulation Limits in OPF (branch field for phase‐shifters)
– tighten the angle limits of phase shifters to limit range of OPF dispatch
M8: LMP Large System
© 2014 PowerWorld Corporation
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Conflict between Phase‐Shifter Setpoint and Line Limits
WP PH.S1
Bus: WP PH.S1 (6372)
Nom kV: 34.50
Area: BGE (32)
Zone: 32 (32)
0.00 MW
0.00 Mvar
1.01 pu
34.80 KV
-43.78 Deg
-2293.83 $/MWh
64.8 MW
-11.9 Mvar
65.9 MVA
45.00 MVA
64.8 MW
11.9 Mvar
65.9 MVA
41.00 MVA
A
161%
1.0000 tap
MVA
A
Phase‐shifter setpoint is 60.3 –
72.9 MW, but line limits are <=45 MVA; ignore these lines
Limts
M8: LMP Large System
CKT 1
GOULDST
6361
1.00 pu
33.94 KV
NEWGT871
6287
NEWGT872
6288
WP PH.S2
6373
GOULDST
5906
GOULDST
6596
GOULDST
6599
146%
1.0000 tap
MVA
CKT 1
WESTPORT
6362
1.01 pu
13.96 KV
WSPT521
6045
WSPT525
6177
WESTPORT
6367
© 2014 PowerWorld Corporation
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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
– Draw a oneline diagram to represent this part of the system
– You will start to see what the problem is
• Changes described in following slides may be automatically loaded with M08_LMP Large System\Eastern2Monitor Changes.aux
M8: LMP Large System
© 2014 PowerWorld Corporation
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Example: Internal Shawville
0.0 Mvar
13.10 Mvar
178.42 $/MWh
0.96 pu
MVA
228
TYRONEN
-32.64 $/MWh
0.97 pu
17.5 MW
0.0 Mvar
265
0.0 MW P-BURG 1
0.0 Mvar -146.43 $/MWh
0.95 pu
235
MADERA
15.43 $/MWh
1.00 pu
A A
0.0 MW
0.0 Mvar
360
P-BURG 2
-142.60 $/MWh
0.99 pu
A
99%
MVA
MVA
MVA
A
-26.95 $/MWh
0.98 pu
426
MADERA
465
WESTOVER
A
MVA
0.3 MW
0.0 Mvar
-33.74 $/MWh
0.98 pu
MVA
421
DUBOIS
A
A
MVA
425
PHILIPSB
-146.43 $/MWh
0.97 pu
15.1 MW
-13.0 Mvar
15.1 MW
8.3 Mvar
368
SHAWVILL
-71.26 $/MWh
1.04 pu
A
98%
A
MVA
MVA
7.5 Mvar
A
A
152%
431
SHAWVILL MVA
-5002.14 $/MWh
0.94 pu
101%
435
SHAWVILL MVA
-17008.59 $/MWh
0.96 pu
50.2 MW
21.0 Mvar
A
373
M8: LMP Large System
A
A
424
SHAWVILL
-5032.14 $/MWh
0.96 pu
MVA
428
SHAWVILL
-7263.56 $/MWh
1.00 pu
MVA
A
4.2 MW
5.5 Mvar
MVA
100%
MVA
MVA
Four of the stepup transformers
experience high loadings. We could
choose to ignore these limits.
A
A
MVA
A
-7285.82 $/MMVA
Wh
0.97 pu
MVA
434
A SHAWVILL
300
ROCK MT
MVA
423
SHAWVILL
-61.44 $/MWh
0.98 pu
151%
SHAWVILL
-17075.95 $/MWh
1.05 pu
-53.10 $/MWh
0.97 pu
A
MVA
A
A
MVA
A
MVA
422
ROCKTONM
A
A
257
SHAWVILL
-65.73 $/M
Wh
MVA
0.99 pu 15.6 MW
8.5 Mvar
18.7 MW
436
SHAWVILL
-61.14 $/MWh
0.98 pu
-50.38 $/MWh
0.98 pu
MVA
Rest of
the
System
419
SHAWVILL
-17055.17 $/MWh
1.01 pu
50.1 MW
17.1 Mvar
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.
We could turn off generators at buses
431 and 424 to fix this.
MVA
372
SHAWVILL
-16997.95 $/MWh
1.08 pu
126.0 MW
20.3 Mvar
119.7 MW
-9.1 Mvar
© 2014 PowerWorld Corporation
39
Example: Internal Merck
59.29 $/MWh
1.0131 pu
4212
NWALES
82.2 MW
14.1 Mvar
82.2 MW
25.2 Mvar
A
MVA
4217
N WALES4
59.64 $/MWh
A
23.2 MW 99%
9.0 Mvar
90.5 Mvar
MVA
4216
NWALES
1.0185 pu
MVA
20.9 Mvar
A
113%
4214
NWALES
82.2 MW
25.2 Mvar
59.63 $/MWh
1.0186 pu
A
A
A
MVA
MVA
4215
NWALES
59.63 $/MWh
1.0186 pu
MVA
59.63 $/MWh
1.0186 pu
A
MVA
A
A
MVA
MVA
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.
3.9 MW
1.6 Mvar
4153
59.63 $/MWh
L 10700
1.0184 pu
59.63 $/MWh
1.0184 pu
A
A
MVA
MVA
59.64 $/MWh
1.0181 pu
4195
MERCK
A
A
MVA
MVA
A
MVA
4544
MERCK 3
59.62 $/MWh
1.0149 pu
4196
MERCK
59.64 $/MWh
1.0283 pu
0.0 MW
0.0 Mvar
M8: LMP Large System
4154
L 16000
1.4 MW
-1.5 Mvar
© 2014 PowerWorld Corporation
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Siegfried – Nazareth Limits
463.58 $/MWh
A
MWh
A A
3081
1.01 pu
42.2
SIEGFRIE
1.03
3061
EPALMERT
MVA
MVA
MVA
A
A
MVA
A
A
MVA
MVA
81%
A
MVA
3151.26 $/MWh
M VA
3391
0.98 pu
KEY CM 2
A
28.96 Mvar
18.37 Mvar
1202.26 $/MWh
3376
EPALMERT
2858.32 $/MWh
11.02 Mvar
3403
0.96 pu
1.01 pu
A
A
A
MVA
MVA
3404
MVA
-32 MW
-32 MW
21.61 Mvar
3399
A
106%
-2645.85
$/MWh
MV A
64.0 MW
71.3 MW
0.98 pu
24.3 Mvar 10.8 Mvar
64.0 MW
64.0 MW
24.3 Mvar
24.3 Mv ar
64.0 MW
24.3 Mvar
PALM T2
1211.81 $/MWh
1.01 pu
59.7
59.7
MW
MW
-0.1
-0.1
Mvar
Mvar
MVA
3408
SIEGFRIE
MVA
-5347.63 $/MWh
1.02 pu
A
A
PALM T1 11.02 Mvar
MVA
99%
MVA
MVA
A
99%
A
-4437.97 $/MWh
MVA
A
A
3390
A
1.70 Mvar
7.33 Mvar
$/MWh
3195
729.78 $/MWh
1.01 pu
3394
MECKESVI
A
MVA
pu
ARROWHEA
A
MVA
1.04 p
M VA
A
KEY CM 1
Removing the negative loads at
NAZARETH and an equivalent
amount of positive load at
SIEGFRIE relieves the otherwise
difficult overloads on the
branches between them.
9.63 Mvar
567 33 $/MWh
M8: LMP Large System
3412
-3403.1
MVA
99%
MVA
-5219.33 $/MWh
1.03 pu
MVA
CH HL
A
A
MVA
3415
NAZARETH1.03 pu
3375
CH HL T1
A
MVA
A
A
MVA
MVA
-4410.75 $/MW
1.03 pu
-3157.48 $/MWh
1.03 pu
-3157.48 $/MWh
3393
3392
LSTAR T1
A
MVA
1.03 pu
LSTAR T2
-3067.50 $/M
1.03 pu
© 2014 PowerWorld Corporation
41
After these changes we remove all unenforceable Constraints
• Still some very high cost constraints remain
• BIRDBORO – PINE LANE = $753/MVAhr
M8: LMP Large System
© 2014 PowerWorld Corporation
42
Birdboro – Pine Lane
• Yellow Region forms a “load pocket” for two large loads 15.59 $/MWh
1730
1.06 pu
TITUS
1164
M
16.33 $/MWh
1606
1.02 pu
TITUS
0.0 Mvar
TITUS
1607
16.24 $/MWh
M
1729
16.89 $/MWh
A
M
V A
SREADING
1.02 pu
A
M
V A
V A M
1572
18.43 $/MWh
A
A
V A
TITUS
1.02 pu
V A
4.2 MW
0.0 Mvar
V A
32.3 MW
1731
1.06 pu
A
M
46.69 $/MWh
1.01 pu
A
V A M
15.47 $/MWh
A
4.0 MW
0.0 Mvar
SREADING
A
M
M
FLYING H
1.02 pu
A
V A
A
V A
M
A
V A
A
M
V A
M
1600
35.9 MW 16.33 $/MWh
0.0 Mvar 1.02 pu
15.59 $/MWh
1732
1.06 pu
TITUS
A
1608
A
M
24.51 $/MWh
1610
17.20 $/MWh
1.02 pu
U.CORSTK
V A
TITUS
V A
ADAMSTWN
1.01 pu
A
M
A
V A
M
M
V A
M
16.4 MW
-3.3 Mvar
A
1.02 pu
A
24.51 $/MWh
V A
A
M
V A
V A
M
M
V A
1.02 pu
A
A
M
V A
1609
24.05 $/MWh
1579
CORSTK T
1.01 pu
LINC 821
V A
A
M
A
V A
M
-81.03 $/MWh
1582
1.02 pu
LORANE
-37.53 $/MWh
32.3 MW
0.0 Mvar
1.02 pu
1563
25.52 $/MWh
1574
BIRDFERO
1.02 pu
GLENSIDE
A
A
M
A
M
ARMORCST
V A
M
M
1.02 pu
W.RDG
A
M
A
V A
12.6 MW
5.0 Mvar
1580
A
M
V A
V A
LINC 822
-88.98 $/MWh
A
1.02 pu
A
LINCOLN
1.02 pu
V A
M
1581
25.73 $/MWh
V A
1612
A
V A M
V A
A
V A
25.18 $/MWh
1553
A
M
– 85.3 MW – 193.7 MW
1551
21.65 $/MWh
SREADING
A
V A
M
M
25.34 $/MWh
V A
1.01 pu
V A
1562
27.80 $/MWh
1568
BIRDBORO
1.02 pu
DANA
-88.98 $/MWh
A
100%
1.02 pu
M
V A
29.18 $/MWh
1564
1.02 pu
CAR TECH
A
1593
441.99 $/MWh
MVA
PINE LNE 0.0 MW
1.02 pu
43.11 $/MWh
1595
1.02 pu
RIVRVIEW
V A
A
0.0 Mvar
A
M
A
M
V A
M
1596
1592
33.11 $/MWh
CARSONIA
1.02 pu
100%
V A
1565
29.00 $/MWh
OUTR STA
1.02 pu
A
A
M
RNGROCKS
V A
MVA
1611
64.53 $/MWh
1156
1.02 pu
NBOYERTO
M
V A
1585
252.69 $/MWh
1.02 pu
A
W.BOYTWN
M
A
M
MC-KN GP
31.69 $/MWh
V A
1589
M
A
95%
216.53 $/MWh
A
A
M
M
V A
1.02 pu
A
V A
M
1587
V A
SPG VAL
A
M
M
V A
M
41.58 $/MWh
1597
1.02 pu
ROSEDALE
V A
A
M
1.02 pu
49.44 $/MWh
1591
1.02 pu
NTEMPLE
A
1578
95.95 $/MWh
1.01 pu
94%0.0 MW
V A
BERK 24
A
1.02 pu
A
V A
M
V A
S.HAMBRG
1577
64.80 $/MWh
1.02 pu
LEESPORT
57.18 $/MWh
M
A
54.67 $/MWh
1.02 pu
1599
0.0 Mvar
1566
A
M
V A
M
1602
A
M
V A
V A
268.5 MW
-35.7 Mvar
SIMON
54.04 $/MWh
1.02 pu
V A
1.02 pu
CLOUSER
V A
SIMON TP
54.04 $/MWh
A
M
M
A
119.00 $/MWh
1.01 pu
M
A
V A
M
V A
1598
64.80 $/MWh
1558
S.HAMBRG
1.02 pu
BERK 835
50.00 $/MWh
A
A
A
M
88.89 $/MWh
1583
1.01 pu
LYNNVILE
M
1.02 pu
A
V A
A
M
V A
M
1561
V A
M
V A
A
1715
1.02 pu
HILL RD
V A
1560
BERNVILL
64.63 $/MWh
M
A
BERN CH
V A
M
58.09 $/MWh
V A
53.35 $/MWh
1.02 pu
1.02 pu
A
106.35 $/MWh
1569
64.17 $/MWh
E PENN
1.00 pu
M
M
1716
V A
0.96 pu
A
1559
BERKLEY
HILL RD
V A
50.00 $/MWh
A
187.23 $/MWh
1.02 pu
62.25 $/MWh
1556
M
BARTO
109.34 $/MWh
1555
61.10 $/MWh
M
0.96 pu
A
M
1.06 pu
V A
V A
1704
PANTHER
63.4 MW
0.0 Mvar
A
M
1717
A
BALDY
1.00 pu
V A
PANTHER
0.96 pu
M
63.23 $/MWh
1552
1.01 pu
ALTN CMT
A
A
A
V A
M
V A
M
V A
V A
A
M
V A
115.29 $/MWh
1576
A
M
69.42 $/MWh
1605
1.01 pu
ST PETRS
V A
KUTZTOWN
1.00 pu
A
A
A
M
129.35 $/MWh
1.00 pu
75.00 $/MWh
1588
1.01 pu
MOSELEM
M
V A
V A
1570
E.TOPTON
M
1584
105.97 $/MWh
A
V A
© 2014 PowerWorld Corporation
97%
LYONS
1.00 pu
A
193.7 MW83%
-16.4 Mvar
M8: LMP Large System
1557
1.02 pu
A
V A
1603
57.18 $/MWh
MVA
M
M
LEESPORT
A
A
V A
V A
1573
FRIEDNBG
• The 69 kV lines feeding this region have high loadings
M
A
34.11 $/MWh
1.02 pu
V A
V A
AT&T
1.02 pu
A
A
V A
1554
33.73 $/MWh
1.02 pu
M
NTEMPLE
A
V A
M
85.3 MW
-25.6 Mvar
1159
1.01 pu
V A
1.02 pu
V A
MG IND T
1.02 pu
A
A
M
EXIDE
A
V A
1.02 pu
1571
216.11 $/MWh
A
M
NBOYERTO
207.74 $/MWh
1604
M
MVA
K.B.I.
1590
34.75 $/MWh
V A
V A
1575
1 8 .8 0 M v a r
M
57.67 $/MWh
A
34.94 $/MWh
M
CONTY LN
MUHLENBG
36.13 $/MWh
A
A
1567
MG IND
1.02 pu
1.02 pu
V A
280.51 $/MWh
1.02 pu
1586
34.94 $/MWh
MVA
62.13 $/MWh
1154
1.02 pu
LYONS
MVA
43
Contour of Prices around
Birdboro – Pine Lane
• Load Pocket
• These prices could be reasonable.
15.59 $/MWh
1730
1.06 pu
TITUS
1164
4.0 MW
0.0 Mvar
SREADING
46.69 $/MWh
A
M
V A M
V A
1606
TITUS
16.33 $/MWh
1.02 pu
15.47 $/MWh
1731
1.06 pu
TITUS
32.3 MW
0.0 Mvar
A
M
A
M
V A
V A
M
A
M
1607
TITUS
16.24 $/MWh
1.02 pu
A
V A
4.2 MW
0.0 Mvar
1.01 pu
A
V A
1729
SREADING
16.89 $/MWh
1.02 pu
A
M
V A
M
V A
A
M
1572
FLYING H
18.43 $/MWh
1.02 pu
A
V A
A
M
A
V A
A
M
V A
M
1600
35.9 MW 16.33 $/MWh
0.0 Mvar 1.02 pu
15.59 $/MWh
1732
A
M
V A M
TITUS
1.06 pu
1608
17.20 $/MWh
1.02 pu
V A
A
V A
1551
21.65 $/MWh
SREADING
A
M
TITUS
24.51 $/MWh
1610
1.02 pu
U.CORSTK
ADAMSTWN
1.01 pu
A
A
M
V A
A
M
V A
24.51 $/MWh
A
A
M
M
V A
M
M
V A
1609
24.05 $/MWh
1579
1.01 pu
LINC 821
CORSTK T
1.02 pu
A
V A
16.4 MW
-3.3 Mvar
V A
V A
A
M
V A
A
M
-81.03 $/MWh
1582
1.02 pu
LORANE
-37.53 $/MWh
32.3 MW
0.0 Mvar
1.02 pu
1563
25.52 $/MWh
1574
BIRDFERO
1.02 pu
GLENSIDE
1553
ARMORCST
A
M
V A
M
M
V A
V A
M
V A
A
M
A
M
M
V A
V A
1580
A
V A
V A
LINC 822
-88.98 $/MWh
A
LINCOLN
1.02 pu
1612
W.RDG
V A
M
1581
25.73 $/MWh
A
25.18 $/MWh
1.02 pu
A
A
M
A
A
M
A
1.02 pu
V A
M
25.34 $/MWh
1.01 pu
V A
V A
1562
27.80 $/MWh
1568
1.02 pu
DANA
BIRDBORO
-88.98 $/MWh
1.02 pu
12.6 MW
5.0 Mvar
A
M
A
100%
V A
1564
29.18 $/MWh
M VA
A
PINE LNE 0.0 MW
1.02 pu
CAR TECH
1.02 pu
1593
441.99 $/MWh
M
43.11 $/MWh
1595
1.02 pu
RIVRVIEW
V A
A
A
0.0 Mvar
M
V A
M
29.00 $/MWh
1565
1.02 pu
CARSONIA
V A
1592
33.11 $/MWh
OUTR STA
1.02 pu
A
100%
M VA
1596
A
A
M
64.53 $/MWh
1156
1.02 pu
NBOYERTO
RNGROCKS
V A
M
V A
1585
252.69 $/MWh
1.02 pu
1611
W.BOYTWN
A
M
A
M
MC-KN GP
31.69 $/MWh
1.02 pu
V A
MG IND
1.02 pu
280.51 $/MWh
1567
34.94 $/MWh
M
M
V A
A
V A
M
34.75 $/MWh
1604
1.02 pu
SPG VAL
A
MUHLENBG
36.13 $/MWh
A
M
V A
57.67 $/MWh
1159
1.01 pu
NTEMPLE
1.02 pu
V A
MG IND T
1.02 pu
V A
A
V A
M VA
V A
1571
A
M
EXIDE
K.B.I.
33.73 $/MWh
1.02 pu
M
41.58 $/MWh
1597
1.02 pu
ROSEDALE
V A
A
V A
1554
A
V A
M
M
216.11 $/MWh
1.02 pu
A
M
A
V A
A
95%
1575
1 8 .8 0 M v a r
1590
NBOYERTO
1587
V A
M
A
CONTY LN
216.53 $/MWh
1.02 pu
A
A
M
1589
A
1.02 pu
M
V A
1586
34.94 $/MWh
M
A
34.11 $/MWh
1.02 pu
1.02 pu
M
A
V A M
V A
268.5 MW
-35.7 Mv ar
AT&T
207.74 $/MWh
V A
49.44 $/MWh
1591
1.02 pu
NTEMPLE
1573
FRIEDNBG
A
1578
95.95 $/MWh
1.01 pu
85.3 MW
-25.6 Mv ar
LEESPORT
V A
1557
M
V A
1577
S.HAMBRG
64.80 $/MWh
1.02 pu
M
A
V A
M
M
1602
M
M
SIMON
54.04 $/MWh
V A
1.02 pu
A
V A
M
V A
1598
64.80 $/MWh
1558
S.HAMBRG
1.02 pu
BERK 835
50.00 $/MWh
1.02 pu
A
A
A
M
88.89 $/MWh
1583
1.01 pu
LYNNVILE
M
A
V A
M
A
V A
M
V A
A
M
HILL RD
1.02 pu
A
BERN CH
53.35 $/MWh
BERNVILL
58.09 $/MWh
1715
64.63 $/MWh
V A
1560
1561
V A
M
V A
V A
A
57.18 $/MWh
1.02 pu
A
1.01 pu
A
54.67 $/MWh
1.02 pu
LEESPORT
1.02 pu
CLOUSER
119.00 $/MWh
V A
V A M
1599
0.0 MW
0.0 Mvar
1566
A
V A
BERK 24
A
A
A
94%
M VA
M
SIMON TP
54.04 $/MWh
A
M
A
V A
1603
57.18 $/MWh
1.02 pu
A
M
M
V A
1.02 pu
M
V A
1.02 pu
A
106.35 $/MWh
1569
64.17 $/MWh
E PENN
1.00 pu
1716
V A
1559
BERKLEY
HILL RD
0.96 pu
A
M
M
V A
50.00 $/MWh
A
187.23 $/MWh
1.02 pu
62.25 $/MWh
1556
M
V A
109.34 $/MWh
1555
A
M
1.06 pu
V A
A
61.10 $/MWh
0.96 pu
BALDY
1.00 pu
1717
PANTHER
0.96 pu
BARTO
M
V A
1704
PANTHER
63.23 $/MWh
1552
1.01 pu
ALTN CMT
63.4 MW
0.0 Mvar
A
A
A
M
V A
A
M
M
V A
M
V A
V A
A
M
V A
115.29 $/MWh
1576
A
M
193.7 MW
-16.4 Mvar
V A
KUTZTOWN
1.00 pu
A
M
129.35 $/MWh
1.00 pu
69.42 $/MWh
1605
1.01 pu
ST PETRS
A
75.00 $/MWh
1588
1.01 pu
MOSELEM
M
V A
V A
A
1570
97%
E.TOPTON
A
M
V A
1584
105.97 $/MWh
M VA
LYONS
1.00 pu
A
83%
M VA
M8: LMP Large System
© 2014 PowerWorld Corporation
62.13 $/MWh
1154
1.02 pu
LYONS
44
Unenforceable Constraints 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 judgment to setup a reasonable case
• Realize that some unenforceable constraints are inevitable at first
M8: LMP Large System
© 2014 PowerWorld Corporation
45
Eastern.pwb
Insufficient Reserves
• Load Eastern.pwb and M08 LMP Large System\aux1000Master.aux, then solve LP OPF
• In this example, Area 28 (JCP&L) does not have enough AGCable
generation
• Message Log: “Insufficient controls to enforce area … constraint”
M8: LMP Large System
© 2014 PowerWorld Corporation
46
Insufficient Reserves: Tips
• Examine Generator records or Area field “Gen MW AGC Range Up”
• To resolve
– Commit more generation
– Make more generation AGCable, or designate some units as OPF Fast Start
– Increase imports, or make Area part of a Super Area
– Decrease load, or make load dispatchable
M8: LMP Large System
© 2014 PowerWorld Corporation
47
M08EasternWideAreaMarket.pwb
Too Much Power Transfer
• In the OPF solution, a linear program (LP) iterates with the non‐linear power flow to achieve convergence of the entire solution
• If an AC OPF is performed over a very large Area (or Super Area), the LP may dispatch generators in a manner that exceeds voltage stability margins
• WECC cases may be especially susceptible
M8: LMP Large System
© 2014 PowerWorld Corporation
48
Too Much Power Transfer
• Example: A Northern and a Southern section of the eastern interconnection are modeled as one ISO market (Super Area)
– North: includes eastern PJM, AEP, First Energy
– South: includes TVA, Southern Company, Entergy
• Assume generation much less expensive in the south, so LP OPF will initially try to increase the transfer from south to north
• OPF may exceed stability margin of power flow
• Load M08EasternWideAreaMarket.pwb, then solve LP OPF
M8: LMP Large System
© 2014 PowerWorld Corporation
49
Too Much Power Transfer
• Excerpt from Message Log
LP attempts massive power transfer
Game Over!
M8: LMP Large System
© 2014 PowerWorld Corporation
50
Too Much Power Transfer: Tips
• Tighten MW Limits on generators with unrealistic limits (e.g. Max MW = 9999): in this example, AGC is set to NO for such units
• Place less of the system on OPF control
• Use interface limits
• Break a large area (or super area) into two or more smaller areas; use OPF dispatchable transactions between the smaller areas
• Manually move generation in the direction of the LP transfer, resolve power flow, restart OPF
• Use DC Power Flow
M8: LMP Large System
© 2014 PowerWorld Corporation
51
OPF Dispatchable Transactions
• Example: Break MMWG super area into Northern and Southern super areas
• Reopen M08EasternWideAreaMarket.pwb and load M08_LMP Large System\EasternNorthSouthSuperAreas.aux
• Add a new transaction between a Northern area (e.g. AEP) and a Southern area (e.g. TVA)
• Set MW limits on the new transaction and make it “Dispatchable in OPF”
• If OPF and power flow solve, try increasing the limits of the new transaction – stop when the power flow will not converge
M8: LMP Large System
© 2014 PowerWorld Corporation
52
OPF Dispatchable Transactions
South‐North transaction limited to 500 MW beyond base case transfer
OPF determines optimal transaction. If transaction is non‐binding at the solution, then areas are acting as a single super area.
M8: LMP Large System
© 2014 PowerWorld Corporation
53
Manually Move Generation
Reopen M08EasternWideAreaMarket.pwb
Solve a “Single Outer Loop” of the OPF
Look at OPF controls following the failure
Move generation in direction of transfer (e.g. 10% of the transfer)
• Attempt to resolve the OPF
•
•
•
•
– Often additional transmission constraints will become binding before the full transfer is made
– OPF will know to move in a different direction
M8: LMP Large System
© 2014 PowerWorld Corporation
54
Manually Move Generation:
OPF Controls
M8: LMP Large System
© 2014 PowerWorld Corporation
55
Manually Move Generation:
Spreadsheet
• Use a spreadsheet to step the transfer (GeneratorAdjust.xls)
• Set GenMW = Orig. Value + Delta Value * Percent Move
1. Copy OPF controls to the spreadsheet
2. Paste Gen Records back into Simulator, solve power flow, and restart LP OPF
M8: LMP Large System
© 2014 PowerWorld Corporation
56