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RTO Scale Unit Commitment Test Cases

Test case data set status and preliminary results

Eric Krall (FERC)Richard O’Neill (FERC)

Disclaimer: The content of this presentation does not necessarily represent the views of the Commission, its members, or other FERC staff

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Overview

Origin:

June 2010 FERC conference, discussion of large scale test problem creation

Purpose:

Create a data set that can be used to model RTO-scale unit commitment and economic dispatch. Intended to be used to produce representative unit commitment models.

Not intended to simulate the exact operation of an actual RTO.

To enable benchmarking of methods among researchers and engineers to test improvements optimization methods and demonstrate formulations

Similar to IEEE test sets (14 bus, 73 bus, etc), but larger (> 10,000 bus) and contains more day ahead market characteristics (e.g. demand bidding, virtual bidding).

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The Data Set

Contains information to construct an approximation of an RTO day ahead unit commitment.

To test scheduling, dispatch and pricing optimization algorithms. Not to replicate reliability functions, mitigation functions, or other analysis.

RTO scale system

Network – over 10,000 buses, over 15,000 transmission elements

Generators - over 1,000 generating units, including wind following a profile

Loads – including fixed demand, price sensitive demand, demand response

Inc and dec bids

Data Set

Generator data – from EIA 411, EIA 860, EPA, NREL, RTO website

Generators offer curves estimated, created using data from publicly available sources

Demand data – RTO website

Network data – Obtained from an RTO

Generator and Demand data was assembled from public information, CEII restrictions on the network model

Ramp Rates

Ramp rate inputs were developed from statistical analysis of EPA data on units in the RTO. Ramp rates predicted as a function of the unit nameplate capacity.

0.0%

0.5%

1.0%

1.5%

2.0%

0 200 400 600 800 1000 1200 1400 1600

Nameplate Capicity

Perc

ent R

amp

(per

Min

ute)

Actual Pct Down Ramp

Pred Pct Down Ramp

Similar analysis undertaken to predict min run level as a function of max capacity

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Day Ahead Unit Commitment

This talk discusses a model that was created to verify that the data set produces reasonable solutions

Scenarios in the data set

The data set contains information for two days: Summer (Day A), Winter (Day B) both were solved

Each day has different demand information; variation in network and generator information

Day ahead unit commitment (UC) - Mixed Integer Programming problem. Modeled in GAMS and solved using a leading solver.

Model is a “first order approximation” of an RTO Day Ahead UC

Includes: Commitment and dispatch constraints, transmission constraints, flowgates, reserves, inc/dec bids, price responsive demand, DR, wind

Does not include: AC feasibility iteration, contingencies, self-schedules, losses

Day Ahead Unit Commitment – Sets and Indices

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Sets and Indices t ϵ T Time periods (hours) g ϵ G Generators dr ϵ DR Demand Response Resources pd ϵ PD Price Responsive Demand Bids inc ϵ INC Inc Bids dec ϵ DEC Dec Bids r ϵ R Market Entities/Resources R = G∪DR∪PD∪INC∪DEC

n ϵ N Network Buses nb

r Market Entity to Bus Mapping k ϵ K Transmission Elements (XFMRs, Branches) int ϵ INT Interfaces kint Subset of branches belonging to interface int nf

k Transmission Element From Bus nt

k Transmission Element To Bus s ϵ S Bid/Offer curve Steps

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Day Ahead Unit Commitment – Variables

Variables Qrst MW cleared for market entity r, step s, hour t Qrt

tot Total cleared MW for market entity r, hour t

NetInjnt Net Injection (if positive) Withdrawal (if negative) at bus n in hour t

Qr+gt Ramp up variable

Qr-gt Ramp down variable

Resgt Reserves provided by generator g, hour t Vgt Startup variable for generator g, hour t Wgt Shutdown variable for generator g, hour t Ugt Commitment variable for generator g, hour t, Ugt ϵ

{0,1} fkt Transmission element k flow in hour t f+/-

kt Monitored transmission element limit relaxation F+/-

kt Flowgate limit relaxation s+/-

kt Global power balance violation

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Day Ahead Unit Commitment – Model Parameters

Parameters Fk

Max Transmission Element Long Term Thermal Rating

LIMtint Interface Limit in period t

PrMax

Resource Maximum Cleared Quantity Pr

Min Resource Minimum Cleared Quantity

NLg No-Load Cost for generators UTg Min Run Time for generators DTg Min Down Time for generators Rg

Max,up Max ramp-up rate for generators

RgMax,dn

Max ramp-down rate for generators MWrs MW quantity Bid/Offer for resource r step s Crs Cost Bid/Offer for resource r step s

Day Ahead Unit Commitment – Model Parameters

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INJntLoop

Uncompensated Loop flow injections at bus n (negative if withdrawal), hour t

INJntTie

Tie Schedule Injections at bus n (negative if withdrawal), hour t

INJntWind

Wind power day ahead forecast at bus n, hour t DEMnt

Fix Day ahead fixed demand at bus n, hour t

DEMntForecast

Day ahead forecast demand at bus n, hour t SFnk Shift factor for injection at bus n on element k relative to a

withdrawal at the slack bus dr Indicates whether a market entity cleared MW is an injection

or withdrawal: 1 for injection, -1 for withdrawal Penbranch Limit relaxation penalty for transmission elements Penflowgate Limit relaxation penalty for interface

Penbalance Constraint violation penalty for system power balance 

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Day Ahead Unit Commitment - Formulation

The Objective Function

Minimize:(Start Up Costs) +(No Load Costs) + (Generator Energy Dispatch Costs) +

(Demand Response Costs) + (Virtual Supply Costs) + (Constraint Violation Penalty Costs) -(Price Sensitive Demand Value) - (Virtual Demand Value)

Minimize z =

r s t CrsQrstdr +

g t(VgtSUg + UgtNLg)

+ k t

Penbranch ( ktf + kt

f )+i t

Penflowgate ( ktF + kt

F )

+t

Penbalance ( ttSS

)

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Day Ahead Unit Commitment - Formulation

Power Balance and Network Constraints

Note that this formulation is lossless

Dual variable (system power balance) ∑r Qrt

tot dr = ∑n DEMntfix - ∑n (INJnt

Tie+INJntLoop) +(st

++st-) ∀t λt

(net injection/withdrawal at bus)

}|{ nrbnr

Qrttot dr - NetInjnt = DEMnt

fix - (INJntTie+INJnt

Loop) ∀n,t

(thermal transmission constraints) fkt - ∑n NetInjnt SFnk = 0

- Fkmax

fkt –fkt++fkt

- Fkmax

∀k,t μ-kt, μ+

kt

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Commitment Constraints

Day Ahead Unit Commitment - Formulation

(startup and shutdown constraints)

1, tggtgtgt UUWV ∀ g,t

(minimum run time for generators)

01

'

'

gUTt

ttgt

g

gt VUTU

∀t

(minimum down time for generators)

01

'

'

gDTt

ttgt

g

gt WDTU

∀t

= 0

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(offer curve constraints) Qrt

tot - s

Qrst = 0 ∀ r,t

Qrst ≤ MWrs ∀ r,s,t

(generator max capability and minimum run level) Qrt

tot + Resgt - Pgmax

*Ugt ≤ 0 ∀g,t

Qrttot - Pg

min *Ugt ≥ 0 ∀g,t

(ramp rate constraints) Qgt

tot – Qgt-1tot

- Qr+gt ≤ 0 ∀g,t

Qr+gt – 60*Ugt-1*

gupmax,R -

gmaxP Vgt≤ 0 ∀ g,t

Qgt-1tot

- Qgttot

- Qr-gt ≤ 0 ∀g,t

Qr-gt - 60*Ugt-1*

gdnmax,R -

gmaxP Wgt 0 ∀ g,t

Day Ahead Unit Commitment - Formulation

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Day Ahead Unit Commitment - Formulation

(reserve constraints) ∑g Resgt +

}{ SuppOfflinegPg

max*(1- Ugt) ≥ SysRest ∀ t

∑g Resgt ≥ 0.5*SysRest ∀ t

(non-negativity, binary constraints) Qgt

tot, Qrst , Qr-

gt , Qr+gt , Resgt ≥ 0

Ugt Vgt Wgt ϵ {0,1}

Solution Time

Solution Time Summary (minutes) Summer Winter

Presolve 13.3 11.4

Root Node Linear Program 11.4 11.4

Branch and Bound 13.4 7.6

Nodes Explored 0 (root) 0 (root)

Final Solve (presolve + LP) 20.3 20.8

Things that could speed this up?•Better formulation of the problem; experiment with solvers and settings•Starting point

Machine: Virtual machine with 4x 2.40 GHz CPUs and 64 GB RAM

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Solution Time

MIP - After the root node LP is solved, the branch and bound search for an integer solution

Previously slide shows time to solution within 5% of best possible

Allowing the algorithm to continue, charts show solution improvement with time (for Day A)

After about 20 minutes, a solution with around 1% optimality gap was found, not proven optimal after 100 minutes (1% ~$150,000 gap)

MIP Gap vs Branch and Bound Search Time

0

0.01

0.02

0.03

0.04

0.05

0.06

0 20 40 60 80 100

Search Time (min)

MIP

Gap

Best Bound, Best Solution vs Time

1.50E+07

1.55E+07

1.60E+07

1.65E+07

0 20 40 60 80 100

Search Time (min)

Obj

ectiv

e Va

lue

Best Bound Best Solution

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Day Ahead LMPs

Max, Min and Average Day Ahead LMP

across all buses by Hour

Day A:

Max LMP $804.20 at Bus 1648

Min LMP $(171.40) at Bus 1506

Day B:

Max LMP $301.82 at Bus 1021

Min LMP $(64.59) at Bus 1051

Avg, Max, Min LMP By Hour

$(100.00)

$(50.00)

$-

$50.00

$100.00

$150.00

$200.00

$250.00

$300.00

$350.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

$/M

Wh Min

AvgMax

$(200.00)

$-

$200.00

$400.00

$600.00

$800.00

$1,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

$/M

Wh

Hour

Avg, Max, Min LMP by Hour

Min

Avg

Max

Day Ahead LMPs by Zone

Demand Weighted LMP by Zone Day B

$-

$10.00

$20.00

$30.00

$40.00

$50.00

$60.00

$70.00

ZONE70ZONE28ZONE33ZONE46ZONE59

ZONE2ZONE32

ZONE4ZONE72ZONE18ZONE55ZONE54ZONE51ZONE71

ZONE3ZONE8ZONE19

Demand Weighted LMP by Zone Day A

$-

$10.00

$20.00

$30.00

$40.00

$50.00

$60.00

$70.00

ZONE44ZONE2ZONE5ZONE23ZONE63

ZONE4ZONE32ZONE11

ZONE3ZONE67ZONE54ZONE71ZONE50ZONE27ZONE15ZONE72ZONE19

Day Ahead LMPs By Zone

Demand Weighted LMP Both Days

$-

$10.00

$20.00

$30.00

$40.00

$50.00

$60.00

$70.00

ZONE44ZONE2ZONE5ZONE23ZONE63

ZONE4ZONE32ZONE11

ZONE3ZONE67ZONE54ZONE71ZONE50ZONE27ZONE15ZONE72ZONE19

Day ADay B

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Congestion in the Day Ahead solution

The data set contains 5 flowgates (interfaces). In the model, these were monitored in addition to over 4,000 individual transmission elements, for congestion.

Day A: Day ahead congestion on flowgate 3.

No flowgates were congested in Day B, at day ahead demand levels.

Congestion on Flowgate 3 by Hour

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

$/M

Wh

Congestion in the Day Ahead solution

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Branch and Transformer Congestion - Day A

$-

$200

$400

$600

$800

$1,000

$1,200

1 6 11 16 21

Hr

$/M

Wh

Branch1259

Branch146

Branch2506

Branch447

Branch920

Branch1420

Branch1923

Branch2608

XFMR1121

XFMR1208

Branch1287

In each scenario, significantly high congestion on multiple transmission elements

Congestion in the Day Ahead solution

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Branch and Transformer Congestion - Day B

$-

$100

$200

$300

$400

$500

$600

$700

$800

1 6 11 16 21Hr

$/M

Wh

Branch906

Branch1394

Branch3135

Branch3136

Branch6513

Branch12805

Branch12808

XFMR371

XFMR691

Branch1311

Branch2424

Branch2458

Branch2965

XFMR1095

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Day Ahead Generation – by Fuel TypeGeneration by Fuel Type and Hour - Day A

0

20000

40000

60000

80000

100000

120000

HR1

HR3

HR5

HR7

HR9HR11HR13HR15HR17HR19HR21HR23

Hour

MW

h

Natural GasOilOtherWindCoalNuclear

Generation by Fuel Type and Hour - Day B

0

1000020000

3000040000

50000

6000070000

8000090000

100000

HE1

HE3

HE5

HE7

HE9HE11HE13HE15HE17HE19HE21HE23

Hour

MW

h

Natural GasOilOtherWindCoalNuclear

Generation Quantities clearing in the representative day ahead market scenarios

Other formulations of the problem

“B-Theta” linear approximation of power flow

Whereas the previous formulation in this presentation used shift factors to compute flow on monitored transmission constraints, the B-theta formulation treats voltage angle at each end of the line as decision variables:

fkt = -Bk (θnt – θmt)

Nodal power balance constraints

∑Qrttotdr - DEMnt

fix +(INJntloop+INJnt

tie) - fk(n,.)t + fk(.,n)t = 0

With this formulation, the single period (hour) formulation of the model solves in less than two minutes.

Multiple period optimizations with this formulation can grow rapidly in solution time.

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Next Steps

Determine limits on access to the data set

Evaluating possibility of additional data sets

Evaluate the need to add additional detail to the data set and model (or a follow on data set)

Self Schedules

AC parameters

Acknowledgements

Michael Higgins (FERC)

Joann Staron (P3 Consulting)

Questions?