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1
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
2
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).
3
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
6
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
7
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
8
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
9
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
10
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
11
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
)
12
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
13
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
14
(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
15
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
17
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
18
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
21
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
22
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
23
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
24
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.
26
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?