Pumped Storage Hydro Modeling

Thes heduling andpre-dispat hin ludingPSH unitsinpowersystemshasbeena topi

ofresear hfor alongtime. In 1965,KennedyandMabu e analyzedin[85℄thedispat h

ofPSHonaninter onne tedhydrothermalsystem,des ribingpra ti alappli ationte h-

niques. Lateron,Aoki etal. presenteda newmethod forsolvinge iently a large-s ale

optimal UCPin luding PSHunits using Lagrangian relaxation[86℄.

Morere ently,Borghettietal. [87℄presentedaMILPmodelto solvetheUCPwithboth

thermalandhydrounitswithpumpedstorage apa ities,inamarket-basedenvironment.

Theauthors onsideredhydropowerplantswithmoremultipleturbines,allofthembeing

supplied bya single upper reservoir. The head-ee t istaken into a ount by means of

an enhan ed linearisation te hnique. Ramp transition onstraints and pumped-storage

areother important te hni al issues in luded in theproposedMILP model. Interesting

results were found for small instan es, for a planning horizon of one week. However,

solutiona ura yand omputationaltimesverifyarelevantde reaseforbiggerinstan es,

asa onsequen e of theadvan edlinearisations introdu ed to themodel.

Khatod, Pant and Sharma [84℄ presented a new approa h for optimising a day-ahead

s heduling onsidering wind and PSH units owned by an independent GENCO that

aims at maximising prots in an ele tri ity market. Hydro generation and pumping

imply operating osts and a penalty is applied for unutilized wind energy, in order to

avoid waste of this energy. In this approa h, the amount of dispat hed power during

low pri e periods seeks to be as minimum as possible, while during high pri e periods

windandhydroenergyissuppliedatthemaximumallowed level. Themodelappearsto

besimple and helpful for GENCOsusing renewable sour es andoperatinginele tri ity

markets. However, due to the several simpli ations andrelaxations, thenalsolutions

might be far fromtheoptimal.

Hinojosaand Leyton [88℄ take advantage ofevolutionaryalgorithms to solve theshort-

without pumping apa ities. The proposed methodology proved to be interesting for

small andmedium sizeinstan es.

Asto hasti approa hisintrodu ed byVespu ietal. [83℄for thes heduling ofagener-

ationsystemin luding PSHunits and windpower plantsina ompetitive environment.

The proposedmodel assumes a hydro systemwith a setof inter onne ted hydro plants

and onsiders water ows between hydro units and possibility of water spillage. The

wind un ertainty is integrated by using a s enario tree to represent the wind hourly

produ tion. Thesystemismathemati ally representedbyadire tedmulti-graph,where

nodes represent reservoirs and ar s represent water ows. After testing in an Italien

ele tri ityprodu er,theauthorsfound thesto hasti modelpreferable totheequivalent

deterministi model.

Duqueetal. [89℄andGonzalezetal. [90℄developeds enario-basedsto hasti approa hes

to optimiseajointoperationbetween awind power plant and aPSH farminele tri ity

markets. They on luded that hydro plants an be useful to minimise the imbalan e

osts aused byerrorsintheWPF.

As a on lusion on the literature review, sto hasti approa hes proved to be more ad-

equate to solve s heduling problems with PSH units and large wind penetration. The

wind variability an be balan ed by the PSH units, that provide additional exibility

of operation. The obje tive fun tion varies from the maximisation of prot (based on

market energy pri es) to the minimisation of osts. Hydro produ tion is mainly on-

sidered as free of osts. The PSH units are mostly isolated (not onne ted to a river)

and are provided with an upper reservoir. Evolutionary algorithms have proved to be

ableto ndgoodsolutions inreasonabletimes onsidering therealnon-linear fun tions,

but the nal solution is not optimal. However, when exa t methods are used to solve

A Multiple Criteria Utility-based

Approa h for the WHTUCP

Notation

Constants

• η_hp

 e ien y of the pumping y le ofhydrounit

h

.

• η_hg

 e ien y of the generating y leof hydro unit

h

.

• dl

h, duh

lower andupperpumping powerlimits ofhydrounit

h

[MW℄.

• gl

h, guh

lower anduppergeneration limitsofhydrounit

h

[MW℄.

• capl

h, capuh

lower andupper apa itylimitsof reservoirof hydro unit

h

[MWh℄.

• volinitial_h

, vol_hfinal

initial and nallevels inthereservoir [MWh℄.

Variables



vhts

 energy stored inthereservoir of hydro unit

h

,inperiod

t

,for s enario

s

[MWh℄.



qhts

 waterdis harge rateofhydro unit

h

,inperiod

t

,for s enario

s

[MW℄.



pphts

pumpinginputpowerofhydrounit

h

,inperiod

t

,fors enario

s

[MW℄.



whts

water spillage ofhydrounit

h

,inperiod

t

,for s enario

s

[MWh℄.

•

Auxiliary variables:



z

p

hts

 1 if hydro unit

h

is in pumping mode, in period

t

, for s enario

s

,

0

otherwise℄.



z

g

hts

 1 if hydro unit

h

is in generating mode, in period

t

, for s enario

s

,

0

otherwise℄.

This hapter presents the assumptions and a formulation for the integration of PSH

fa ility in the proposed WTUCP, in order to evaluate the inuen e of those units on

dealing withwind power variability. The work hereby presented in an extension of the

approa hdevelopedin hapters 3and5. We present the onstraintsrelatedtothehydro

omponent,aswellasthene essarymodi ationsintrodu edinthemodel. Theobje tive

is to investigate ifthe new WHTUCP model isable to ree t theDM risk proles and

nd out the ontribution of PSH fa ilities to improve the nal solutions. In order to

a hievethat goal, we onsider isolatedPSH units thatoperate at no osts. Then,water

ows from rivers or spillage of water arenot onsidered. On this way, theoperation of

ea h PSH unit boilsdown ex lusively to the onsumption of energy to pumpand store

wateror theusageofstored watertogenerate ele tri ityusedto servetheloaddemand.

7.1 Assumptions

Sin e we ontinue the proposedWTUCP model dis ussed before, theprevious assump-

•

Thehydrosystem onsistsofasetofhydrounits. Ea hhydrounitisprovidedwith a turbine and a single upstream reservoir. Ea h hydro unit may either generate

ele tri energy using stored water from the reservoir or onsume energy to pump

water into thereservoir;

•

Headee tisnot onsidered-Ele tri poweroutputofhydrounitsdoesnotdepend onthewaterlevelinthereservoir. Thedis hargeoutputpowerisdenedbyalinear

onversion using a pre-dened oe ient (

η

g

h

) that represents the ratio of energy inje ted into the power system to the (equivalent) energy onsumed from stored

water.

•

Water isalways availableto bepumped into thereservoir;

•

Thevolume ofwater storedinthereservoir isrepresentedbyanequivalentenergy level(MWh). Theinitialandnalenergylevelsofthereservoirareknownapriori;

•

Only energy generated by wind turbines, in ea h period, an be used to pump water tothe reservoir;

•

Generation of ele tri power and waterpumping byhydrounits are onsideredat no osts;

•

Hydro units annot provide reserve;

•

Thepossibilityofwater spillage isnot allowed;

In document A Multiple Criteria Utility-based Approa h for the Unit Commitment with Wind Power and Pumped Storage Hydro (Page 92-97)