OPTIMUM OPERATION OF HYDROPOWER SYSTEMSIN GHANA WHEN AKOSOMBO DAM ELEVATION IS BELOW MINIMUM DESIGN VALUE

8/14/2019 OPTIMUM OPERATION OF HYDROPOWER SYSTEMSIN GHANA WHEN AKOSOMBO DAM ELEVATION IS BELOW MINIMU

1/10

Optimum operation ofhydropower system n ghana Fiagbe and Obeng

OPTIMUM OPERATIONOF HYDROPOWERSYSTEMS NGHANA WHEN AKOSOMBO DAM ELEVATION IS BELOWMINIMUM DESIGNVALUEY.A.K. Fiagbe. and D.M. ObengD epartm ent of M echanical Engineering

Kwame Nkrumah University of Science and TechnologtKumasi. Ghana

ABSTRACTHydropower plants in Ghanu have suffered several low level operations within the past two dec-ades. This paper looks at optimum operations of the plants during these low level conditions. Thetwo hydropower plants arc located along the Volta River at Akosombo and Kpong. The Akosomboplant is at the apstream such that its discharge createsuvuilable headfor the Kpong plant which isdownstream. The Akosombo plant is designed to operate between the levels of 75.59m minimumand 84.12m maximum wkile the Kpong pd,antoperatesbetween14.5m and 17.7m. The mode of unitcombinations or optimum p oh'erg eneration i s d etermined i n t his p aper. This c oald s erve a s aguideinoperatingthetwo Hydropowerplants.Themethodpresentedcouldalsofanctionasapower prediction tool during the low level conditions at Akosombo (i.e. below 75.59m).Keywords: Hydropower, Optimum, Low level, The Akosombo plant with six units of turbine-Head, Unit combinqtions. Cenerators peratesunder normal condition be-INTRODUCTION tween 84.12m (276ft) maximurn and 75.59mrhe orta iveruthorityvRA)peratesnd f:rjfl ff#'llff:j:"*Tffi1nit#l;ffiimanages the two hydroelectric power plants in units;ith 40MW capacity per unit making aGhana' The plants at Akosombo and Kpong totul output of 160Mw. The normal water levelwere commissioned in 1965 and 1982, respec- for operation of the plant is between l7.1,0mtively and they provide the bulk of Ghana'selec- -a"imum and 14.50m minimum. The availabletricity. The two stations account for I,072 mega- head for the running of Kpong plant is built upwatts (MW) out of a total national power- from the discharge rom thi Akoiombo plant.generating capacity of 1,652 MW, withetosombo providing 912 MW while Kpong Since the installation of thelJydropower plantsprovides 160MW. The plants are located on th! at Akosombo and Kpong, there have been re-Volta River with Akosombo at the upstream of cords of low water level periods at theKpong. Akosombo danl which were below the mini-74 journal ofscienceand technologt,volume26 no. 2, Augast,2006


2/10

Optimum operatiotr of ltydropower system n ghana Fiagbe and Obengmum design condition. Those periods includethe unprecedented drought of 1982-83 with arecord of 71.86m on 12th June 1984 (VRA,1996), which compelled the rationing of electric-ityuntil 1986.InAugust1994,the evelof VoltaLake was 72.99m.The year 1998also ecordedalow water level of 72.21m. These levels werewell below the 7 5.59rn which is the minimumlevel for generating power without risk of dam-aging the turbines.The objective of the paper s to develop a systemfor estimating an optimal power output from thehydropower system n Ghana at the low headwa-ter elevation conditions of the Akosombo hydro-power plant.REVIEW AND OPTIMISATIONTECHNIQUESOptimisation is the processof finding the con-ditions that give maximum or minimum value ofa function (Stoecker,1971). Optimisation s oftwo levels, namely, Comparison of alternateconceptsand Optimisation within a concept.Comparison of alternate concepts is a problemmostly encountered during the designing stage.It involves deciding on an optimum designamong other alternatives. Optimisation within aconcept most often has to do with operationalmethods of a system where the most optimumoutput is sought. It applies to existing or alreadydesigned systems.This is the kind of problem tobe dealt with in this paper.In hydropower systems there are two relatedshort-term optimisation p roblems, namely, 'unitcommitment' and 'economic dispatch' (Power,2002).Unit commitment is the processof decid-ing when and which generating units at eachpower station are to be started and shut down.The unit commitment problem tends to answerthe question: Given that there are a number ofsubsets of the complete set of 'N' generatingunits that would satisfy the expected demand,which of these subsetsshouldbe used n order toprovide the minimum operating cost (Wood,

1984).Economic dispatch s the processof de-ciding what the individual power outputs shouldbe at eachpoint in time given the scheduledgen-erating units. It assumes hat there are 'N' unitsalready connected o the system(Power, 2002).There is a number of hydropower optimisationsoftware developed and are available for use.Examples of such available hydro system soft-ware are:(i) MICROHYP software is an optimisationmodule, which uses a dynamic programmingtechnique to choose a design, which meets thepower requirements at the least possible cost(Swansea, 002).(iD MaxHydro is HydropowerOptimisation Software designed to optimizehydroelectric generation in the new de-regulating market environment. MaxHydro takesinto account changes n market conditions thatwill maximize profits from power sales whileoptimizing the operation and planning of theentire hydropower system (Z&M Numerics,2002). (iii) VALORAGUA is software whosemain objective is to determine the optimal gen-erating strategy of a mixed hydro-thermal elec-tric power systems.The optimal operating strat-egy is obtained for the system as a whole, withemphasison the detailed simulation and optimi-sation of the hydro subsystem operation. (iv)VANSIMTAP is an integratedsoftwarepackagefor the simulation of one or more river systems(Sintef 2002). It is primarily aimed at hydro-power production. (v) VRASIM (Volta RiverAuthority Simulation Model) is a generationexpansion model capable of representing bothhydro and thermal plants. It can model reservoiroperations, power generation and dispatch(includingVRA's contract with VALCO), loadgrowth, system additions capital and operatingcosts. tariffs and revenues and much more(Acres, 1992). (vi) SISOPT is an optimizationmodel developed or the managementand opera-tions of the Brazilian hydropower system(Barros et al. 2003). This system employs, first,linearzedtechniques for the b asic model whichwas non-liner and then solved by linear pro-

journal ofscience and technologlt, volume 26 no. 2, Augast, 2006 75


3/10

Optimum operation of hydropower system in ghana Fiagbe and Obenggrarnrning. The problem was formulated for thenonnal operatingconditions.Most of the hydropower optimisation softwaresand rrpdels appearo have airrredat regulatingunitsoperating at a time to satisfy power demandandin normal operating condition. The scenario tobe dealt with in this paper, however, involvesoperation of the Akosombo and Kpong turbineunits as limited by the available head at up-stream reservoir when it is below the designwater evel.There are several techniques or solving optimi-sation problems. These include mainly LinearProgramming, Calculus Method, Dynamic pro-gramming, Geometric Programming and SearchMethod. Technique of optimisation are consid-ered and chosen based on the problem at hand(Denardo,1982;Stoecker, 97l).P : gnfiuqu + ankqk b(rrqr)t (l)

WhereT: P$l'lula = 2E- ! , - v [n ( r i , L , ' , ) * t n "q " ] and

An - P E 7 1 ^ tu - At'1 total efficiency, q : discharge n m3/s, H :head in metre, p: density of water (kg/m3) g :acceleration ue o gravity (equal9,81 m/s2), :number of turbines, t: time in secondL1 : headwater level in metres, L2 : tail water level inmetres, A : area covered by water body in m2.Subscript 'a' refer to Akosombo plant and sub-script 'k' refers to Kpong plant.The model equation was derived from the firstprinciple with following assumptions: Inflowinto the pond of Kpong plant is solely dependenton discharge rom Akosombo plant (it would notbe possible o spillwater fromAkosornbo damwhen the level is below the design level and that

inflow due to rainfall ta.ken to be negligible);Out flow from the Kpong pond is only throughthe turbine (pond water level is not expectedtorise to causea spill of water); Power outputs andflows through the turbines at each plant are thesame for each unit; and tail water levels remainconstant within the period of estimate. Themodel is limited to low level conditions, i.e.head water level below 75.59m, with plant effi-ciency of 84.5% and 93.5%oat Aksombo andKpong plants respectively (Obeng and Fiagbe,2005).The model as given is non-linear and involvesinteger variables nu and n1. The linear program-ming is inapplicable due to non-linearity of theequation.Dynamic programming cannot be em-ployed since the energy demand, which couldhave been a target, cannotbe considered.Calcu-lus method is inapplicable due to the integervariable that makes he equationnot continuous.In considerationof geometric programming, thedegree of difficulty is six, making the methodnot a good one. The search method of optimisa-tion is the best applicable method. The Searchtechnique s therefore employed in the optimisa-tion of the system.HYDROELECTRIC POWER PL.ANTSINGHANAThe Hydroelectric power plants in Ghanaconsistof two p lants ocatedat Akosornboand Kpongon the Volta River in a cascadedmanner. TheAkosombo plant is at the upstream.Figure I isthe schematic epresentationof the plants.The available head for the Kpong plant is cre-ated mainly out of the discharge at theAkosomboplant making the numberof operat-ing units subject to amount of dischargeor num-ber of units rururing at the Akosombo plant.The operation of the hydroelectric plants is in-fluenced by two malr, factors; namely energydemand and the water level at Akosombo head-work. The water level limits the production ca-pacity of the generating system. In normal op-

76 journal ofscience and technologt, volume 26 no, 2, August, 2006


4/10

Optimum operation ofhydropower system n ghana Fiagbe and ObengAkosombo Plant

P : P a + P kFig.2: Schematictates f thesystem

KpongPlant

eration, the energy demand is the main criterionfor operating hydropower plants. Optimisationof hydroelectric plants is mostly basedon energydemandresulting in the problem of unit commit-ment and./oreconomic discharge.The operation of the integral hydrothermal sys-tem currently is such that the thermal componentof the system is operated in full capacity andsupplementedwith the hydro plants.When the head water level is below 75.59m, theAkosombo p lant may be operateduntil a mini-

mum value of 71.93m. At this level there is thepossibility of formation of vortex with air en-trainment at the intake. The 71.93m level may beconsideredas a critical level.THE HYDROPOWER PLANT MODELThe mathematical model of the hydropowerplants in Ghana consisting of the two plants,under the low conditions as stated in equation(1) holds for averageefficiencies of 84.5%o nd93.5Yoat Akosombo and Kpong plant respec-tively under the low level conditions of theAkosombo dam (Obeng and Fiagbe, 2005).

Fig I : Schematic epresentationof the V'RA Hydropower plants

journal ofscienceand technologt,volume26 no.2, Aagust,2006 77


5/10

Optimum operation of hydropower system in ghana Fiagbe and ObengSYSTEM OPTIMISATIONThe Problem: It is required to find the unitcombinationsof the two plants that will give theoptimumpower.Input:. Initial Lake Volta (Akosombo Dam) level,. Initial Kpong pond level,. Tail water level at Akosombo and Kpongplants, and. Estimated nflow into the Lake Volta.Objective Function:P : gnuHuq" anrgr - b(.tuqr)' (1)

/ ^ \^Ha=lg+"!"1,


6/10

Optimum operation of hydropower system in ghana Fiagbe and ObengALGORITHMThe algorithm for solution involves the follow-ing steps:1. Input data(headand tail water levels).2. For stage , set allowabledecreasenheadwater evel for AkosomboPlant,AHiu.3. For numberof units, n'u: 6 to Ifind for a day duration the number of unitsto satisfy step 2

LHL =with n'" determine the maximum possibledischarge hat satisfy step 2.

4. Find net head : Head water level - Tailwater evel i.e.Hi: Liur Liuz)5. Determine new head water level. L"l'*' :Liul - DHi"6. Set minimum head water level for KpongPlant.Li117. For nurnberof units, n'r:4 to Ifind for an hour duration (as t is within designcondition), number of units to satisfy step6.

En=Lni t , @LQo-nLqr)t4,.with n'pdetermine he maximum possibledischarge hat satisfy step 6

9. If Akosombo headwater level > 236ft or day< 7 then go to next stage i + l) a step 2.The programme s coded n Visual Basic.

SAMPLE RUN RESULTSThe number of turbine units to run is influencedby the head water level as well as the inflow intothe Akosornbo dam. Sample runs were consid-ered^ or expected inflow values of 0m3/s and62m'ls (average nflow during low level period)with water levels of 75.29n1 14.68n, 73.76n"73.15mand12.24m(levels ower than minimumdesign value) at Akosombo head works and15.0mat Kpong headworks. The headof 15.0mwas chosen or the Kpong plant because t is theaverage evel during the low level periods. Theresults ofthe test are presented n Figures 3 and4.ExpectedReservoir Inflow of 0.0m3/sWith zero or no inflow (Qi": 0), at the headwa-ter level of 75.29m at Akosombo Dam there are614 (the first figure represents units at Ako-sombo plant and the second units at Kpongplant) units available for operation upto 75.24mwhere we then have 5/4 and 5/3 units available.The units reduce to 4/3 and 4/2 at 74.58m; 3/3and 3/2 at 73.92m. This is shown in Figure 3together with 74.68n, 73.76rt, 73.15m and72.24m initial water levels.Expected Reservoir Inflow of 62.0m3/sWith inflow of 62.0m3/s.at the head water levelof 75.29m at Akosombo Dam there are 6/4 unitsavailable for operationupto 75.06m then5/4 and5/3 units. The units reduce to 413 and 412 at74.42m;3/3and3/2 at73.77m.This s shown nFigure 4 togetherwith 74.68m, 73.76m, 73.15mand 72.24m initial elevations. From the figure,we have 6/4 units at 75.29m, 514 and 513 at75.06rn,4/3 and 412 at7 4.42m: 313 and 312at73.76m;2/2 and2/l at73.l2m: ll l and /0 at72.41m.

(Qn - nLq) tA a

8. Evaluatea) c: PBrub)d=ffluo{tt,c)B:ry: - Lr,z)*Lq, l

and Pi- gniuHiuq"* anirQa b(nid")t

journal ofscienceand technologt,volume26 no. 2, August,2006 79


7/10

Optimuntoperation of hydropower system n ghana Fiagbe and ObengINFLOW = O.Om3/s

1000.0900.0800.0700.o600.0500.0400.0300.02o0.o100.0

o. o

gI4t3 (74.54m1

3|/3(73.92m)

22 (73.24m\

OI O 71.97m,I 108 215 322 429 536 643 750 857 4 107' t ' t17ApA5 1392 t4991606' ,17131A2019272034214122442355

limc (Hour)

Fig. 3: Unit combinations at zero inflow

INFLOW= 62.0m3/s

5/4 (75.06m)

-Level = 75.29m-Levet = 74.68m

Level = 73.76m ----- Level =73.1 5m-Leve t=72 .24m -

- Level =75.29m-Level = 74.68m -

Levet=/J./bm-- - Level =73.15m -

- Level = 72.24m

1000.0900.0800.0700.0600.0500.0400.0300.0200.0100.0

3gq

413 74.42m)

212 73.12m\

th (72.47m)

1 10A 215 322 429 5?6 643 750 857 964 10711't7812A51352499160617131A2019272034214122442355Time(Hour)

Fig.4: Unit combinations at inflow of 62.0m3/s

80 journal ofscience ndtechnologt,volume6no' 2, August,2006


8/10

Optimum operation ofhydropower system n ghana Fiagbe and Obeng

Gonerated nd SimulatedPower

3='

1000.0009 0 0 .0 0 08 0 0 .0 0 0700.000600.000500.0004 0 0 .0 0 0300.000200.000

1 0 0 .0 0 00 .0 0 0

1s i June,'t995 lSth June, 19th July, 4th May, 25th Ma y1 9 9 5 1995 . t9 9 S 1 9 9 9 l s tJu n e , 2 5 th Ju n e , 3 0 th 4 th 2 n d Ma r ch , 2 n d Ma r ch ,1399 '1999 January, Febtuary, 2OO2 2002 (95%l2002 2002Dat

Power resultig . 5: Operation and Simulation

sD

c

PercentageDifferenceBetweenGeneration nd Simulation

l s tJune,'t999

Fig. 6: Percentageof Simulation over Actual Operation

+Total PowerGenerated MW )+Total PowerSimulated MW )

3othJanuary,20024thFebruary,2002

journal ofscienceand technologt,volume26 no, 2, August,2006 81


9/10

Optimum operation of hydropower system n ghana Fiagbe and ObengDISCUSSIONPower output data from operationof the plantsare compared with the simulated power resultsand these are as presented n Figure 5. The re-sults indicated a higher power estimate rom thehydropower plants.A decrease in headwater elevation aI theAkosombo dam is assumed o vary linearly be-tween 0.0254m (at 15.59m elevation) and0.0038m atTl.93melevation). The Kpongplantpond level is limited to a minimum of 14.7mwhich is about the normal design headwaterlevel. The minimum operating evel is, however,14.25m.The operational and simulated power outputresults are compared in Figure 6 for the stateddates.The operation data for 1" June 1995 whenthe inflow was 358m'/s, head water levels were74.65mat Akosombo dam and 15.1lm at Kpongpond, the total outputs was 665.208MW. Thesimulated result corresponding to these condi-tions is 905.925MW. This result ndicatesavaii-able higher power of36% over the actual opera-tion as shown in Figure 6. The subsequentdatafor the given dates also show available higherpower as to what was generatedwith exceptionof 25* June1999and2noMarch2002.For 2 5ft June I 999 t he g eneratedp ower o utputwas 489.250MW whilst the simulatedvaluewas470.2llMW with a difference of 19.039MWlower i.e. 3.8%. The 2ndMarch 2002 result nd!cates an actual generated power output of655.417MW and the simulationas 602.865MW.This is about 8% lower. The difference may beattributedto a testing program that was carriedout on the retrofitted units at the Akosomboplant during the period. It was, however, foundthat the retrofitted units operate with better effi-ciency of about 95o/oeven at the low levels at theAkosornbo plant. The simulation was however atefficiency of 84.5%. The simulation at efficiencyof 95%ogave 665MW as compared with the655.417MW.

CONCLUSION AND RECOMMENDA-TIONOptimal operation of the hydropower plants atAkosombo and Kpong, when headwater evelatAkosombo dam is belowminimum designlevel, has been carried out with application ofsearch technique. The mode of operating thetwo plants by means of number of units to runat various plants has been determined for optimal power generation. Optimisation of thesystem s programmedwith coding in VisualBasic:The results include the number of units thatcan be run on hourly bases o obtain the opti-mum power output within given constrains.The Power output indicated is that availablefor the period by remaining within the statedconstraints. It is advised that Kpong plantunits are always maintained at peak efficiency.Figure 5 comparers given operation data tothose obtainedfrom the simulation.The result of this paper is recommended foruse as a guide in the operation of Akosomboand Kpong Hydropower plants by VRA. Itmay also be used to predict the availablepower for some period ahead.The program isdevelopedmainly for the headsof water levelsat Akosombo dam less han the normal recom-mended minimum of 75.59m. It is expectedthat by the use of this program, optimal poweroutput shall be obtained at the low water levelat Akosombo dam.

REF'ERENCESAcres Intemational Limited, (August 1983).Akosombo and Kpong Generating StationsSpecial Studies 1982/1983, (Report #3),Optimized Joint Operations of Akosomboand Kpong, Volta River Authority, Ghana.Acres International Limited, (1992). Combus-tion turbine Feasibility study main report,Volta River Authoritv. Ghana.

82 journal ofscienceand technolog), olume26 no. 2, Augast,2006


10/10

Optimum operation of h1td7ep6yt",system in ghana Fiagbe and ObengBarros, M.T.L., Tsai, F.T-C., Yang, S., Lopes,J.E.G., and Yeh, W.W-G., (2003)."Optimization of Large-Scale HydropowerSystem Operations". Journal of Water Re-sources Planning and Management, 128(3):17 8 188 .Denardo, E.V. (1982). Dynamic ProgrammingModels and Applications, Prentice-Hall, Inc.Englewood Cliffs, USA.Hoffman, L.D., Gerald L.B. (1995). FiniteMathematics with Calculus. McGraw-Hill.Inc., USA. pp 153 209Obeng D.M. and Fiagbe Y.A.K., (2005)."Modelling of hydropower systemsof Ghanaat low level conditions at Akosombo dam".

.,Journal of Science and Technologt, 25(2):t3t-136.Power Optimisation, (2002). Unit Cornmitmentand Economic Dispatch software opitimisethe short-term scheduling of Electric Powergeneration,Power Optimisation Ltd., Wood-side Avenue, Beaconsfield, Buckingham-sh i r e , HP9 I JJ , Eng land , U K.www.powerop.co.uk (Accessed: February,2002).

Sintef, 2002. VASIMTAP Software, SINTEF,NO-7465 Trondheirrl Norway. www.sinte .no/units/civil/water/rs s/interact/vansbas.htm accessed: ebruary,2002).

Stoecker,W.F. (1971). Design of Thermal Sys-tems, McGraw-Hill, Inc. New York.VRA (1996). Information Brochure on the VoltaRiver Authority, The Information & Public-ity Section,Organizational ServicesDepart-ment, VRA, Accra.SwanseaUniversity, (2002). Micro-Hydro Opti-misation, Swansea University, SingletonPack,Swansea,SA2 8PPWales,UK. www.swan.ac.uk/civeng/research/h]rdro/optimi-satiom.htm (accessed:February, 2002).Wood, A.J., Wollenberg, B.F. (1984). PowerGeneration Operation and Control, JohnWiley and Sons, nc., USA.Z & M Numerics, (2002). MaxHydro Software,Z &M Numerics Ltd., P.O. Bo x 3 00-102,Albany, Auckland l3l, New Zealand.www.zmnumerics.co.nzlmaxHvdro-L.htm(accessed: ebruary, 2002).

journal ofscienceandtechnologt,volume26 no. 2,August,2006 83

Documents

OPTIMUM OPERATION OF HYDROPOWER SYSTEMSIN GHANA WHEN AKOSOMBO DAM ELEVATION IS BELOW MINIMUM DESIGN VALUE