intermediate wholesale electricity markets: unit commitment

Upload: lalit-negi

Post on 02-Jun-2018

220 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    1/42

    J U N E 3 5 , 2 0 1 4 | N O R T H A M P T O N , M A

    Unit Commitment & Dis atch

    Intermediate Wholesale Electricity Markets (WEM 201)

    Ron CoutuS T R A T E G I C M A R K E T A D V I S O R ,

    B U S I N E S S A R C H I T E C T U R E & T E C H N O L O G Y

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    2/42

    Intr cti n

    Name

    Company

    How long have you been in your job and the electric industry?

    2

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    3/42

    ctiv

    Provide an understandin of how Unit Commitment UC and

    Economic Dispatch works Objectives

    Process

    Factors impacting Unit Commitment How Unit Commitment impacts Economic Dispatch

    I am always ready to learn, although I do not always like being taught.~Winston Churchill

    3

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    4/42

    T ic C v r

    Three rimar res onsibilities of ISO New En land ISO

    What is Unit Commitment?

    Fullday actual market example

    Commitment?

    4

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    5/42

    THREE PRIMARY RESPONSIBILITIES OFISO NEW ENGLAND

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    6/42

    Thr Primar R n i iliti f IS

    O erate Mana e New En lands Develo and mana e New England's

    Bulk Electric

    Power System

    Wholesale Electricity Marketplace

    Ensure a fair and

    long term planning process in

    New England Dispatch New Englands resources as a single system to:

    Maintain reliability throughoutthe region

    Minimize cost of electricity

    reasonable marketplace

    production in New England Adhere to national, regional, and local operating procedures and policies

    6

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    7/42

    A licati n f IS R n i iliti Minimize cost of electricit roduction in New En land

    ISO shall determine the least cost security constrained unit commitment and dispatch Least cost means of serving load at different locations in the

    New England Control Area based on: Scheduled or actual conditions existing on the power grid

    energy in the New England Markets (Market Rule 1)

    7

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    8/42

    WHAT IS UNIT COMMITMENT?

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    9/42

    What i nit C mmitm nt? Decision makin rocess

    On/Off scheduling for a defined period

    England well before markets (part of the implementation of

    NEPOOL in the 70s) Techniques and tools for Unit Commitment have changed and

    been updated over the years This trainin is not focused on the techni ues for solvin the Unit

    Commitment problem, complex mathematical techniques are used to quickly solve these large problems

    9

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    10/42

    WHAT IS THE OBJECTIVE?

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    11/42

    What i th ctiv f nit C mmitm nt? With demand biddin the ob ective is to maximize

    social welfare

    Without any demand bidding, the objective is to minimizethe overall committed cost of the resources needed to meet the load and reserve requirements

    n o cases, a es n o accoun a o e cos s o producing the energy, including no load costs and startup costs At the same time, UC respects each Resources characterist ics

    such as minimum up time, minimum down time

    11

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    12/42

    Param t r in nit C mmitm nt Incremental ener offer curves

    Startup costs $ (hot, cold, and intermediate) Costs incurred per startup of the resource ype o s ar s ase upon num er o ours own s nce prev ous run

    No load costs $ Fixed cost that is incurred ever hour the resource is runnin

    Minimum Run Time (in hours or fractions of hours)

    Economic Minimum and Economic Maximum

    12

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    13/42

    Basic Terms and ConceptsUnit Commitment & Dispatch

    Pool Schedule (ISO Committed)

    Action b the ISO to schedule a resource

    Self Schedule (Self Committed)

    Action of a Partici ant in committin for which the Participant submitted supply offers to sell energy

    ISO can schedule these resources in the DA Market as well as commit them to provide

    and/or scheduling its resource, to provide service in an hour, whether or not in the

    absence of

    that

    action

    the

    resource

    would

    have been scheduled or dis atched b the

    energy in the RT dispatch ISO to provide the service

    13

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    14/42

    H w D llar Val Im act nit C mmitm nt Total production cost ($)

    Fixed costs (not dependent on loading level), if unit is on cost is incurred

    Startup costs are included in the cost calculation for ever start based on hot cold and intermediate) of the unit

    No load costs are included in the cost

    calculation for

    every

    hour

    the

    unit

    is

    on

    line

    Based on the hourly economic dispatched MWh needed from each resource to meet the demand

    Minimizing the total of the fixed and incremental costs is the basic objective

    14

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    15/42

    Im act f Tim Data n nit C mmitm nt Generall classified as intertem oral arameters

    When a unit

    is

    committed,

    it must run for at least this

    When a unit

    is

    decommitted,

    it must sta down for at least

    many hours before beingshut down

    this many hours before starting up again

    15

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    16/42

    Gra hical R r ntati n f nit C mmitm nt Notification Time

    Minimum Run

    Time

    Minimum Down Time

    What do these terms mean?

    Minimum Minimum

    Release for Dispatch at

    EcoMin

    Release for shutdown at

    EcoMin

    Release for Dispatch at

    EcoMin

    Run Time Down TimeEcoMinoutput (MW)

    Start upTime (C,I,H)

    Notification Time (C,I,H)

    Generator Generator Generator

    16

    start up order issued by ISO

    connects to grid at 0MW

    ramps to EcoMin

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    17/42

    Im rtant Fact r W Hav L arn S Far Ob ective function of minimizin costs

    Factors that impact the objective function

    Self Scheduled (Self Committed) Pool Scheduled (Pool Committed)

    nter tempora m ts w on y ma e t e na so ut on more expensive

    , any one hour may have a higher cost than its minimum

    17

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    18/42

    FULLDAY ACTUAL MARKET EXAMPLE

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    19/42

    F llDa Act al Mark t Exam l Actual roblem that must be solved b ISO New En land is

    usually around

    10

    50

    resources

    needing

    to

    be

    committed

    per hour for all 24 hours of a day

    Obviously trying every possible combination is not possible given the time limits (it would take a day to run a day)

    er ma ema ca ec n ques are use o e erm nea solution

    19

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    20/42

    Ma r Cla ificati n f G n rat r

    Peaking

    Intermediate

    Base-load

    Mid

    20

    ternoon

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    21/42

    C mmitm nt Sch l ratin Plan Commitment software determines which enerators are

    scheduled to

    run

    for

    which

    hours

    Only an on/off schedule, the MW levels are not used In the DayAhead Market, we run the commitment schedule

    through a dispatch

    algorithm

    to

    determine

    loading

    levels

    and

    eman c ear ng as we as na cos s an s

    In the RealTime, the commitment schedule (also known as

    times for resources; actual dispatch of those resources is done on a fiveminute basis

    21

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    22/42

    F ll Da Exam l Da Ah a Mark t 25000

    Virtual Su l

    20000

    (Between 500 2200 MW each hour)

    15000r ua

    Supply

    Economic

    Cleared MW

    Economically Committed Resources (Between 1432 each hour)

    5000

    10000 SS ClearedMW

    Self Scheduled Resources (About 120)

    0 1 3 5 7 9 1 3 5 7 9 1 3

    22

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    23/42

    Ec n micall C mmitt R rc 9000

    Top Line Represents the Why is this gap

    7000

    8000 um o t e conom c Maximums of the

    Economically Committed Resources

    needed?

    4000

    5000

    EconomicNonDispatch MW

    EconomicDispatched MW

    2000

    3000Economic Min

    0

    1000

    23

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    24/42

    Actual Commitment ScheduleEconomically Committed Resources (32 Resources)Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0

    N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0O 8 11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1V 15 7 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1CC 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    24

    A 24 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    25/42

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    26/42

    F c n Ba l a C mmitt R rc

    Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0X 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0

    S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1

    H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    These Resources have a

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    27/42

    Ec n micall C mmitt R rc

    Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0

    N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0O 8 11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    These Resources have not run for Hour 24, which means that if they will need to meet

    Minimum Down Time next Day before running again

    V 15 7 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1CC 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    27

    A 24 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    28/42

    Long Minimum Run Times / Minimum own mes

    A sin le da unit commitment can onl take into account that days needs, but from a next day reliability perspective can we turn every unit off at hour 23?

    What if

    we

    cannot

    meet

    the

    next

    morning

    load?

    28

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    29/42

    N xt Da C mmitt R rcU n itN a m e M in R u n

    M in

    D o w n 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4

    P 1 0 .2 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0X 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0

    Z 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0A A 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0U 8 4 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0N 8 9 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0O 8 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0S 1 2 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1T 1 2 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0D D 1 2 1 2 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 1 3 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0I 1 4 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0H 1 6 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

    F 6 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0R 1 3 6 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1G 1 6 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1F F 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 1 2 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1E 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1B B 1 4 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1C C 1 4 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    Units R and G met their Minimum Down Time. What about Unit V?

    L 2 4 2 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1E E 2 4 2 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    290 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    30/42

    Startin Stat f r H r 1 f nit C mmitm nt

    Each dail Unit Commitment must start with a status for each resource from the previous day On or Off How man hours in that state?

    This status is based on two values: The previous days DayAhead Market Unit Commitment ny c anges ma e o e urren pera ng an urren

    Commitment Schedule) by the RAA process or by the Participant Self Scheduling additional or decommiting additional hours by the

    30

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    31/42

    Dail C clin C mmitt R rc

    Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0X 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0

    S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1

    H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1FF 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    These Resources have 8 to 12 hour minimum runsand total min. run + min. down < 24 these

    resources generally have the ability to come onC 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1CC 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    or one per o a ay pea

    31

    L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    32/42

    C mmitt P akin R rc

    Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0X 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0

    S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1

    H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    ea ng esources our or ess Min. run and Min. Down

    F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1FF 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1CC 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    32

    L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    33/42

    Ec n micall C mmitt R rc

    8000

    A B C D E F G H I J K L M N O P Q R S T U V W X Y Z AA BB CC DD EE FF

    6000

    7000

    Same Approximate Load; Different Commitments

    4000

    5000

    3000

    1000

    33

    0

    01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    34/42

    Comparison of Committed ResourcesHours 12 and 22Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0

    N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0O 8 11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1V 15 7 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1LMP in 22 ~ $3 less than LMP in 12C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1CC 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    34

    A 24 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    35/42

    Limit En r R rc an C mmitm nt

    Resources with limited amount of ener as ex ressed b the quantity submitted by the resource owner, are used by the Commitment to optimize the overall cost of the daily dispatch

    These Resources may or may not be used in the most expensive hours of the day (or those with the highest LMPs)

    since the commitment is usin this resource in con unction with other resources towards the overall objective

    Will not optimize the profit of that generator but will optimize

    the impact on the objective function

    35

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    36/42

    Comparison of Committed ResourcesHours 12 and 22Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0

    N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0O 8 11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1H 16 64 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1V 15 7 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

    J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    What if this Resource had only 6 hours of full output available?

    C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1CC 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    36

    A 24 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    37/42

    ECONOMIC DISPATCHHow is Dis atch Im acted b Unit Commitment?

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    38/42

    C mmitm nt Im act n Ec n mic Di atch

    Economic Dis atch is the least cost usa e of the committed generators to meet the demand

    Economic Dispatch does not have to adhere to inter temporal parameters, since commitment has adheredto them

    o n e ay ea an ea me ar e s, e se o resources are committed to maximize the social welfare

    (not the commitment)

    38

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    39/42

    Actual Commitment ScheduleDispatchable Resources (32 Resources)Unit

    Name

    Min

    Run

    Min

    Down 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

    P 1 0.2 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0W 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    Y 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0Z 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0

    AA 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0U 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0B 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0N 8 9 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0O 8 11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1S 12 8 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0T 12 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0DD 12 12 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0Q 13 7 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

    I 14 8 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1

    V 15 7 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0F 6 8 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1R 13 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0G 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0J 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1K 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1FF 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    C 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1D 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M 12 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1E 12 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1BB 14 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    ac o t e comm tte resources w nee to e economically dispatched between the resources

    minimum and maximum every hour

    39

    A 24 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1EE 24 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

    0 = Off for this Hour 1 = On for this Hour

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    40/42

    Di atch G n rati n25000

    20000

    Gap

    15000

    M

    W h Total

    Capability

    Dispatched

    Dispatched Generation

    5000

    Generation

    CommittedGen. Min

    Minimum of Committed Generators(SS and Economic)

    0

    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

    40

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    41/42

    Wra

    C r ctiv

    Provide an understandin of how Unit Commitment and Dispatch works Objectives

    Process

    Factors impacting Unit Commitment

    How Unit Commitment impacts Dispatch

    41

  • 8/10/2019 Intermediate Wholesale Electricity Markets: Unit Commitment

    42/42

    42