FromDeterministicEconomicDispatchtoSecureStochasticUnitCommitment/OptimalPowerFlowwith

MOST,thenewMATPOWEROptimalSchedulingTool

RayZimmerman1,CarlosMurillo-Sánchez3,DanielMuñoz-Álvarez1,AlbertoLamadrid2

1CornellUniversity(Ithaca,NY)2LehighUniversity(Bethlehem,PA)

3NationalUniversityofColombia(Manizales, Caldas, Colombia)

FERCTechnicalConferenceonIncreasingMarketandPlanningEfficiencythroughImprovedSoftware

June27-29, 2015

Acknowledgements

• AlbertoLamadrid• DanielMuñoz-Álvarez• CarlosMurillo-Sánchez• BobThomas• C.LindsayAnderson• WooyoungJeon• TimMount

2

Outline

• MATPOWER Background• MOSTOverview

– WhatisMOST?– ProblemFormulation

• MOSTExamples– Single-periodcontinuousvariableproblems– Multi-intervalproblemswithUC

3

http://www.pserc.cornell.edu/matpower/– implemented inMatlab language,

compatiblewithfreeGNUOctave– interfacestostate-of-the-artsolvers– usedworldwide inteaching,research,

industry– researchenabling tool,whosemomentum&

impactcontinues togrow,asevidencedby• 1325citationsof2011MATPOWER paper*

• roughly20,000downloads peryear

MATPOWERFree,open-sourcepowersystemsimulationenvironmentwithpowerflow(PF),ContinuationPF,extensibleOPF,nowwithMOST,stochasticunitcommitmentandmulti-intervalOPF.

4

R.D.Zimmerman,C.E.Murillo-Sánchez, andR.J.Thomas, MATPOWER Steady-StateOperations, PlanningandAnalysis ToolsforPowerSystemsResearchandEducation, PowerSystems,IEEETransactions on,vol. 26,no. 1,pp. 12-19, Feb. 2011.* GoogleScholar,6/20/16

BriefMATPOWER History• MATPOWER beganin1996asanACOPFtoolusedtoclearmarketsfor

PowerWeb,apowermarkettestingplatform.• Publiclyreleasedin1997(v1andv2)• Developmentfocusedoninternaluseuntilreleaseofv3in2005• Someofthemajorfeaturesaddedovertime:

– DCpowerflowandDCOPF– additional powerflowalgorithms– extensibleOPFarchitecture– improvedOPFsolvers, includingnativeMatlab primal-dualinteriorpoint– continuation powerflow– explicitopensourcelicense(BSD)– realistictestcases(Polish, French, Europeancasesupto13kbuses)

• Combinationofhighqualitysolversandready-to-usecasescreatedadefactobenchmarkplatform(foroptimization&powersystemsresearch)

• MATPOWER 6.0b1* includesMOST (MATPOWER OptimalSchedulingTool)

5*releasedJune1,2016– asofJune18,morethan1,000downloads

Outline

• MATPOWER Background• MOSTOverview

– WhatisMOST?– ProblemFormulation

• MOSTExamples– Single-periodcontinuousvariableproblems– Multi-intervalproblemswithUC

6

WhatisMOST?

• MATPOWER OptimalSchedulingTool*

• Optimizationtoolforsolvingageneralizedschedulingproblem,whichcaninclude:– priceresponsivedemand– transmissionnetworkmodel(ornot)– securedispatchviaco-optimizedreserves(zonalorendogenously

determinedfromcontingencies)– stochasticinputs(e.g.renewables,load)– integercommitmentdecisions,startup&shutdowncosts– multi-intervaldispatchwithrampingconstraints&costs– fullunitcommitmentwithminimumup-&down-timeconstraints– energystorageanddeferrabledemandresources

7* Previously referred to as MOPS –MATPOWER Optimal Power Scheduler

OurFormulation

• GeneralizedextensionofcombinedUC/OPFproblem,toinclude…– intertemporalenergyconstraintsforstorage,flexible/deferrable

demand– endogenous,priceresponsivecontingencyandrampingreserves– multi-stagestochasticapproachw/scenariorecombination

• Formulationpresentedherein2013andpublishedin[1]andsomepreliminarytestingresultspresentedherein2015.

[1]CarlosE.Murillo-Sánchez,RayD.Zimmerman,C.LindsayAnderson andRobertJ.Thomas,“SecurePlanningandOperationsofSystemswithStochasticSources,EnergyStorageandActiveDemand”,SmartGrid,IEEETransactionson,vol.4,no.4,pp.2220-2229,Dec.2013.Available:http://dx.doi.org/10.1109/TSG.2013.2281001

8

MOSTContinuousSinglePeriodProblems

23

single deterministicsystem state

multiple probabilisticsystem states

secureED

secureDC OPF

secureAC OPF

stochastic secure

ED

stochasticsecureDC OPF

stochasticsecureAC OPF

stochasticED

stochasticDC OPF

stochasticAC OPF

EDw/reserves

DC OPFw/reserves

AC OPFw/reserves AC OPF

DC OPF

economicdispatch

EDw/reserves

DC OPFw/reserves

AC OPFw/reserves AC OPF

DC OPF

economicdispatch

MATPOWER

secureED

secureDC OPF

stochastic secure

ED

stochasticsecureDC OPF

stochasticED

stochasticDC OPF

EDw/reserves

DC OPFw/reserves DC OPF

economicdispatch

MOST

multi-period+ ramping

multi-period+ storage

multi-period+ ramping+ storage

with integer commitment+ transition costs

+ min up/down times

multi-period

with integercommitment + transition

costs

with integercommitment

continuousdispatch

singleperiod

MOPSMixedIntegerandMulti-PeriodProblems

37

Outline

• MATPOWER Background• MOSTOverview

– WhatisMOST?– ProblemFormulation

• MOSTExamples– Single-periodcontinuousvariableproblems– Multi-intervalproblemswithUC

38

minx

f(x) where

f(x) = fp

(p, p+, p�)

+ fz

(rz

)

+ fr

(r+, r�)

+ f�

(p)

+ flf(�+, ��)

+ fs

(s0, psc, psd)

+ fuc(u, v, w)

ObjectiveFunction

39

expectedactivepower(re)dispatchcosts

contingency reservecosts

expectedrampingwear&tearcosts

loadfollowing rampreservecosts

expectedvalueofleftover storedenergy

startup,shutdown&noloadcosts

zonalreservecosts

Constraints

40

(1) standardOPFconstraints• powerbalanceequations• transmission flowlimits,otherOPFinequalities

(3)intertemporal constraints• loadfollowing ramping limitsandreserves• energystorageconstraints

(4)unit commitmentconstraints• injection limitsvs.commitmentvariables• startup/shutdownevents• minimum up/downtimes

(2)securityconstraints• fixedzonalreserverequirements,or• contingencyconstraints

• reserve,redispatch andcontractvariables• rampinglimitsontransitions frombasetocontingencycases

Outline

• MATPOWER Background• MOSTOverview

– WhatisMOST?– ProblemFormulation

• MOSTExamples– Single-periodcontinuousvariableproblems– Multi-intervalproblemswithUC

41

TutorialExampleSystem• 3-bustrianglenetwork• generators

– 2identical200MWgensatbus1,diffreserve cost– 500MWgenatbus2– all3haveidenticalquadraticgenerationcosts

• load450MWatbus3,curtailable@$1000• branches

– 300MWlimit,line1–2– 240MWlimit,line1–3– 300MWlimit,line2–3

• adequacy requirement– reserve requirement

• 150MWlimit– contingencies

• generator 2atbus1• line1–3

42

240 MW

bus 1 bus 2

bus 3

200 MW 200 MW 500 MW

450 MW

300 MW

300 MW

100 MW

gen 1 gen 2 gen 3

±80 MW

200 MWh

TutorialExampleSystem• 3-bustrianglenetwork• generators

– 2identical200MWgensatbus1,diffreserve cost– 500MWgenatbus2– all3haveidenticalquadraticgenerationcosts

• load450MWatbus3,curtailable@$1000• branches

– 300MWlimit,line1–2– 240MWlimit,line1–3– 300MWlimit,line2–3

• adequacy requirement– reserve requirement

• 150MWlimit– contingencies

• generator 2atbus1• line1–3

• wind– 100MWunitatbus2– 3samplesofnormaldistributionaround50MW

43

240 MW

bus 1 bus 2

bus 3

200 MW 200 MW 500 MW

450 MW

300 MW

300 MW

100 MW

gen 1 gen 2 gen 3

±80 MW

200 MWh

SinglePeriodContinuousExamples

44

Economic Dispatch

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

SinglePeriodContinuousExamples

45

Economic Dispatch w/reserves

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

SinglePeriodContinuousExamples

46

DC OPF

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

SinglePeriodContinuousExamples

47

DC OPF w/reserves

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

SinglePeriodContinuousExamples

48

secure DC OPF

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

SinglePeriodContinuousExamples

49

stochastic DC OPF

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

SinglePeriodContinuousExamples

50

secure stochastic DC OPF

Gen1 2 3 4

MW

0

50

100

150

200

250

300Generation & Reserves

Bus1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Nodal Prices

Line1 2 3

$/MW

0

10

20

30

40

50

60

70

80

90

100Flow Constraint Shadow Prices

InputData

loadmd()

mpcMATPOWER case

data

xgdadditional

generator data(xGenData)

sdadditional

storage unit data (StorageData)

profilestime varying parameters

contabcontingency

data

transmattransition probability matrices

most()

MATPOWEROptimal

Scheduling Tool

solveroptions

mpopt mpc.busmpc.branch

mpc.gen

mpc.gencost

offer(t).PositiveActiveReservePrice

offer(t).PositiveActiveReserveQuantity

offer(t).PositiveLoadFollowReservePrice

offer(t).PositiveLoadFollowReserveQuantity

RampWearCostCoeff

Storage.MinStorageLevel

Storage.MaxStorageLevel

Storage.InitialStorage

Storage.InitialStorageLowerBound

Storage.InitialStorageUpperBound

Storage.OutEff

Storage.InEff

Storage.TerminalStoragePrice

offer(t).NegativeActiveReservePrice

offer(t).NegativeActiveReserveQuantity

offer(t).NegativeLoadFollowReservePrice

offer(t).NegativeLoadFollowReserveQuantity

Storage.LossFactor

cont(t,j).contab

tstep(t).OpCondSched(j).tab

tstep(t).TransMat

md – MOST Data struct

InitialState, MinUp, MinDown

CommitKey, CommitSched, InitialPg

51

ExampleCode

• DCOPFmdi = loadmd('ex_case3a');mdo = most(mdi);

• EconomicDispatchmpopt = mpoption('most.dc_model', 0);mdo = most(mdi, mpopt);

• Withzonalreservesreserves.zones = [1 1 1 0];reserves.req = 150;

reserves.cost = [1; 3; 5];reserves.qty = [100; 100; 200];mdi.FixedReserves = reserves;mpopt = mpoption('most.dc_model', 1);mdo = most(mdi, mpopt);

52

SecureDCOPF

• Definingcontingencies:examplecontabfunction contab = ex_contab

define_constants;% label probty type row column chgtype newvaluecontab = [

1 0.06 CT_TGEN 2 GEN_STATUS CT_REP 0; %% gen 2 at bus 12 0.04 CT_TBRCH 2 BR_STATUS CT_REP 0; %% line 1-3

];

• Samemechanismusedtomodifyabasecaseforeachperiodinmulti-intervaloptimization

53

“Extra”GeneratorData- xGenData

• Generatorparametersnotincludedinbasecasedata,e.g.unitcommitmentdata,reserveoffers,rampingcosts,andmore

function xgd_table = ex_xgd_res(mpc)xgd_table.colnames = {

'PositiveActiveReservePrice', ...'PositiveActiveReserveQuantity', ...

};xgd_table.data = [

5 250;0 100;1.5 600;0 800;

];

• RuntheSecureDCOPFmpc = loadcase('ex_case3a');xgd = loadxgendata('ex_xgd_res', mpc);

mdi = loadmd('ex_case3a', [], xgd, [], 'ex_contab');mdo = most(mdi, mpopt); 54

Outline

• MATPOWER Background• MOSTOverview

– WhatisMOST?– ProblemFormulation

• MOSTExamples– Single-periodcontinuousvariableproblems– Multi-intervalproblemswithUC

55

TutorialExampleSystem• 3-bustrianglenetwork• generators

– 2identical200MWgensatbus1,diffreserve cost– 500MWgenatbus2– gencosts marginal startup shutdown

1 $25 $0 $02 $30 $200 $2003 $40 $3000 $600

• load300-540MW atbus3,curtailable@$1000• branches

– 300MWlimit,line1–2– 240MWlimit,line1–3– 300MWlimit,line2–3

• adequacy requirement– reserve requirement

• 150MWlimit– contingencies

• generator 2atbus1• line1–3

• wind– 0-166MWunitatbus2– 3samplesofnormaldistributionaroundvaryingmean

56

240 MW

bus 1 bus 2

bus 3

200 MW 200 MW 500 MW

450 MW

300 MW

300 MW

100 MW

gen 1 gen 2 gen 3

±80 MW

200 MWh

TutorialExampleSystem• 3-bustrianglenetwork• generators

– 2identical200MWgensatbus1,diffreserve cost– 500MWgenatbus2– gencosts marginal startup shutdown

1 $25 $0 $02 $30 $200 $2003 $40 $3000 $600

• load300-540MW atbus3,curtailable@$1000• branches

– 300MWlimit,line1–2– 240MWlimit,line1–3– 300MWlimit,line2–3

• adequacy requirement– reserve requirement

• 150MWlimit– contingencies

• generator 2atbus1• line1–3

• wind– 0-166MWunitatbus2– 3samplesofnormaldistributionaroundvaryingmean

• storageatbus3– 200MWhenergycapacity, 80MWpowercapacity

57

240 MW

bus 1 bus 2

bus 3

200 MW 200 MW 500 MW

450 MW

300 MW

300 MW

100 MW

gen 1 gen 2 gen 3

±80 MW

200 MWh

Mult-Interval(UC)Examples

1 2 3 4 5 6 7 8 9 10 11 12Period

0

100

200

300

400

500

600

MW

Load and Wind Profiles

LoadDeterministic WindStochastic Wind

58

DeterministicUCExamples

59

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent Base : No Network

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW

0100200300400500

Net

Loa

d, M

WGen 1Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

DeterministicUCExamples

60

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + DC Network

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

DeterministicUCExamples

61

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Startup/Shutdown Costs

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

DeterministicUCExamples

62

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Min Up/Down Time Constraints

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

DeterministicUCExamples

63

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Ramping Constraints/Ramp Reserve Costs

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

DeterministicUCExamples

64

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Storage

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW

Gen 1Gen 2Gen 3Storage ChargeStorage Discharge

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

StochasticWind

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

150

200

MW

Wind Profile, Individual Trajectories

Wind ScenariosPossible Transitions

65

StochasticWind

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

150

200

MW

Wind Profile, Full Transition Probabilities

Wind ScenariosPossible Transitions

66

DeterministicUCw/oStorage

67

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Ramping Constraints/Ramp Reserve Costs

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

StochasticUCExamples

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent Individual Trajectories

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

150

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

68

StochasticUCExamples

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent Full Transition Probabilities

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

150

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

69

StochasticUCExamples

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Contingencies

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW Gen 1

Gen 2Gen 3

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

150

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

70

StochasticUCExamples

1 2 3 4 5 6 7 8 9 10 11 12Period

Gen 3 @ Bus 2

Gen 2 @ Bus 1

Gen 1 @ Bus 1

Uni

t Com

mitm

ent + Storage

1 2 3 4 5 6 7 8 9 10 11 12Period

0100200300400500

Gen

erat

ion,

MW

Gen 1Gen 2Gen 3Storage ChargeStorage Discharge

1 2 3 4 5 6 7 8 9 10 11 12Period

0

50

100

150

Nod

al P

rice,

$/M

Wh

Bus 1Bus 2Bus 3

0100200300400500

Net

Loa

d, M

W

71

StorageDatafunction storage = ex_storage(mpc)

ecap = 200; %% energy capacity

pcap = 80; %% power capacityscost = 45.17; %% cost/value of initial/residual stored energy

% bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin ...storage.gen = [

3 0 0 0 0 1 100 1 pcap -pcap ...];

storage.xgd_table.colnames = {'CommitKey', 'CommitSched', 'PositiveActiveReservePrice', ... };

storage.xgd_table.data = [2 1 0 2*pcap 0 2*pcap 0 0 0 2*pcap 0 2*pcap;

];

72

StorageData(continued)function storage = ex_storage(mpc)...storage.sd_table.OutEff = 1;

storage.sd_table.InEff = 1;storage.sd_table.LossFactor = 0;storage.sd_table.rho = 0;storage.sd_table.colnames = {

'InitialStorageLowerBound', ...'InitialStorageUpperBound', ...

'InitialStorageCost', ...

'TerminalStoragePrice', ...'MinStorageLevel', ...

'MaxStorageLevel' };storage.sd_table.data = [

0 ecap scost scost 0 ecap;];

73

LoadProfileInputfunction loadprofile = ex_load_profile

loadprofile = struct( ...

'type', 'mpcData', ...'table', CT_TLOAD, ...'rows', 0, ...

'col', CT_LOAD_ALL_PQ, ...'chgtype', CT_REP, ...

'values', [] );

loadprofile.values(:, 1, 1) = [

440;480;

540525;500;

450;400;

350;300;325;

375;425;

];

loaddataforallloadsshouldbereplacedwithspecifiedvalues

74

number of periods in planning horizon

WindProfileInputfunction windprofile = ex_wind_profile

windprofile = struct( ...

'type', 'mpcData', ...'table', CT_TGEN, ...'rows', 1, ...

'col', PMAX, ...'chgtype', CT_REL, ...

'values', [] );

windprofile.values(:, :, 1) = [

0.72 0.80 0.88;0.49 0.65 0.81;

0.36 0.60 0.84;0.50 0.82 1.14;0.60 1.00 1.40;

0.22 0.70 1.18;0.00 0.50 1.00;

0.33 0.85 1.37;0.46 1.00 1.54;0.54 1.10 1.66;

0.48 1.06 1.64;0.35 0.95 1.55;

];

generatorparameterPMAX(maxgeneration)ofwindgenerator1shouldbescaledbyspecifiedvalues

75

number of periods in planning horizon

number of wind scenarios

TransitionProbabilitiesfunction transmat = ex_transmat(nt)

transmat = cell(1, nt);

transmat{1} = [ 0.16;0.68;0.16 ];

transmat{2} = [ 0.16 0.16 0.16;0.68 0.68 0.68;0.16 0.16 0.16 ];

.

.

.transmat{nt} = [ 0.16 0.16 0.16;

0.68 0.68 0.68;0.16 0.16 0.16 ];

76

scenarios in period 2

scenarios in period 1

ExampleCodempc = loadcase('ex_case3b');xgd = loadxgendata('ex_xgd_uc', mpc);[iwind, mpc, xgd] = addwind('ex_wind_uc', mpc, xgd);

[iess, mpc, xgd, sd] = addstorage('ex_storage', mpc, xgd);profiles = getprofiles('ex_wind_profile', iwind);profiles = getprofiles('ex_load_profile', profiles);nt = size(profiles(1).values, 1);transmat = ex_transmat(nt);

mdi = loadmd(mpc, transmat, xgd, sd, 'ex_contab', profiles);

mpopt = mpoption(mpopt, 'most.storage.cyclic', 1);

mdo = most(mdi, mpopt);

ms = most_summary(mdo);

plot_uc(mdo)plot_storage(mdo)

77

StorageProfileSolution

0 2 4 6 8 10 12 14Period

-50

0

50

100

150

200

250En

ergy

, MW

hStored Energy for Storage Unit 1 (Gen 6) @ Bus 3

78

MOSTv1.0b1

• MOSTv1.0b1isavailableaspartofMATPOWER6.0b1fromtheMATPOWER website:– http://www.pserc.cornell.edu/matpower/

• FulldescriptionofMOSTproblemformulation,softwarereference,andtutorialexamplesfoundin:– R.D.ZimmermanandC.E.Murillo-Sánchez,MATPOWER OptimalSchedulingTool(MOST)User’sManual,2016.

http://www.pserc.cornell.edu/matpower/MOST-manual.pdf79

Questions?

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