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Power System Economics and Market Modeling M8: Developing an LMP Analysis for a Large Case

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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



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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



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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


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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



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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


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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


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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


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Limit Monitoring



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Cost Curves • Load cost curves for thermal units: stored in aux file M08_LMP Large System\EasternCostCurvePJM.aux



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Solve Unconstrained OPF • Do not enforce branch or interface constraints



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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



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Solve Constrained OPF • Enable constraint enforcement (on Constraint Options) • Solve OPF, note several unenforceable constraints



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LMP Contour • Note high LMPs on receiving end of constrained lines and areas with low reserve margin



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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


18.6 MW -1.9 Mvar 18.7 MVA

112.0 MW 18.7 Mvar 113.6 MVA


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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



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Unit Commitment and Reserves • Most generators in high‐LMP area DP&L on Delmarva Peninsula are at max



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PJM Super Area Hydro Price = $57



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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


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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



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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



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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


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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 M8: LMP Large System


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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


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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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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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More on OPF Challenges



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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



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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


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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


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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 M8: LMP Large System


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Unenforceable Constraints • This results in a reduced list of 20 unenforceable constraints



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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


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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


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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