i

Tamar jiqia

,,hidrosadgurTa kaskadis muSaobis

grZelvadiani reJimebis optimizacia’’

წარმოდგენილია დოქტორის აკადემიური ხარისხის

მოსაპოვებლად

საქართველოს ტექნიკური უნივერსიტეტი

თბილისი, 0175, საქართველო

2011 წელი

საავტორო უფლება © წელი, “jiqia Tamar”2011 weli

ii

საქართველოს ტექნიკური უნივერსიტეტი

,,ენერგეტიკისა და ტელეკომუნიკაციის ფაკულტეტი’’

ჩვენ, ქვემორე ხელისმომწერნი ვადასტურებთ, რომ გავეცანით

ჯიქია თამარის მიერ შესრულებულ სადისერტაციო ნაშრომს

დასახელებით: ,,ჰიდროსადგურთა კასკადის მუშაობის გრძელვადიანი

რეჟიმების ოპტიმიზაცია” და ვაძლევთ რეკომენდაციას საქართველოს

ტექნიკური უნივერსიტეტის ,,ენერგეტიკისა და ტელეკომუნიკაციის

ფაკულტეტის” სადისერტაციო საბჭოში მის განხილვას დოქტორის

აკადემიური ხარისხის მოსაპოვებლად.

ხელმძღვანელი: g. maxaraZe

რეცენზენტი:

რეცენზენტი:

რეცენზენტი:

iii

საქართველოს ტექნიკური უნივერსიტეტი

2011 წელი

ავტორი: ჯიქია თამარი

დასახელება: ,,ჰიდროსადგურთა კასკადის მუშაობის გრძელვადიანი

რეჟიმების ოპტიმიზაცია”

ფაკულტეტი: ენერგეტიკის და ტელეკომუნიკაციის ფაკულტეტი

ხარისხი: დოქტორი

სხდომა ჩატარდა:

ინდივიდუალური პიროვნებების ან ინსტიტუტების მიერ

ზემომოყვანილი დასახელების დისერტაციის გაცნობის მიზნით

მოთხოვნის შემთხვევაში მისი არაკომერციული მიზნებით კოპირებისა

და გავრცელების უფლება მინიჭებული აქვს საქართველოს ტექნიკურ

უნივერსიტეტს.

ავტორის ხელმოწერა

ავტორი ინარჩუნებს დანარჩენ საგამომცემლო უფლებებს და არც

მთლიანი ნაშრომის და არც მისი ცალკეული კომპონენტების გადაბეჭდვა ან

სხვა რაიმე მეთოდით რეპროდუქცია დაუშვებელია ავტორის წერილობითი

ნებართვის გარეშე.

ავტორი ირწმუნება, რომ ნაშრომში გამოყენებული საავტორო

უფლებებით დაცული მასალებზე მიღებულია შესაბამისი ნებართვა (გარდა

იმ მცირე ზომის ციტატებისა, რომლებიც მოითხოვენ მხოლოდ სპეციფიურ

მიმართებას ლიტერატურის ციტირებაში, როგორც ეს მიღებულია

სამეცნიერო ნაშრომების შესრულებისას) და ყველა მათგანზე იღებს

პასუხისმგებლობას.

iv

naSroms vuZRvni baton guram maxaraZes. batoni gurami aris

pirovneba, romelic Tavisi SromiTa da pasuxixmgeblobis

grZnobiT aris gamorCeuli adamiani. batoni guramis miTiTebebiT

da rCevebiT profesiul saqmianobaSi Zalian bevri ram viswavle.

minda avRniSno, rom batoni gurami Tavisi TvisebebiT misabaZi

pirovnebaa momavali Taobis karg specialistebad Camoyali-

bebisTvis.

v

reziume

TbohidroenergosistemaSi umniSvnelovanesia maregulirebel

hesebze wyalsacavSi arsebuli wylis maragis optimaluri

gamoyeneba.

mdinareSi wylis bunebrivi Camonadenis da dagrovebuli

wylis xarjvis limitis erToblivi gaTvaliswinebiT wyalsa-

caviani hesebis muSaobis grafiki ZiriTadSi uzrunvelyofs

eleqtruli sistemis pikuri datvirTvebis dafarvas.

wyalsacaviani hesebis muSaobis dReRamuri datvirTvis

grafikis dagegmvisas, romelTa kaskadSi (dinebis mimarTulebiT)

agebulia sezonuri (Camodinebaze momuSave) hesi, wylis arsebuli

maragis (bunebrivi Camonadeni da wyalsacavidan wylis xarjis

limiti) racionalurad gamoyenebis sakiTxis damuSavebisas

gaTvaliswinebuli unda iqnes, rogorc maregulirebeli hesis,

aseve sezonuri hesis muSaobis efeqturobis moTxovnebi.

mdinareSi bunebrivad Camonadenisa da wyalsacavebSi

dagrovili wylis efeqturi gamoyeneba Tbosadgurebze mogvcems

ZviradRirebuli saTbobis ekonomiisa da mTeli sistemis

maStabiT eleqtrosadgurebs Soris aqtiuri datvirTvis

optimaluri ganawilebis saSualebas.

energosistemis muSaobis reJimebis optimizaciis amocanaTa

Soris yvelaze aqtualurs warmoadgens eleqtorsadgurebs Soris

aqtiuri datvirTvis optimaluri ganawileba da, imavdroulad,

calkeuli sadguris agregatTa Sigasasadguro optimizacia.

dasmuli amocanis srulyofili amoxsnisaTvis naSromSi

dadgenili iqna, rogorc energoblokebis saxarjo maxasiaTebeli,

aseve, calkeuli eleqtrosadguris ekvivalenturi saxarjo

maxasiaTebeli, romelic saSualebas iZleva SevafasoT

eleqtrosadguris muSaobis energetikuli maCveneblebi sadguris

datvirTvis reJimisagan damokidebulebaSi.

vi

sadguris ekvivalenturi energetikuli maxasiaTebeli

dadginda calkeuli agregatis energetikuli maxasiaTeblis

safuZvelze.

sadguris ekvivalenturi energetikuli maxasiaTeblis agebis

amocana moiTxovs sadguris agregatTa mdgomareobis analizs. Aam

agregatebidan nawili agregati SeiZleba iyos gaCerebuli, xolo

nawili muSa mdgomareobaSi.

agregatTa yoveli SemadgenlobisaTvis agebuli ekvi-

valenturi saxarjo maxasiaTeblebis safuZvelze SesaZloa

dadgindes muSaobaSi CarTuli agregatTa optimaluri ricxvi da

ganxorcieldes sadgurebs Soris aqtiuri datvirTvis

optimaluri ganawileba.

kaskadSi momuSave sezonuri hesis muSaobis specifiurobidan

gamomdinare, misi datvirTvis reJimis marTva masTan kaskadSi

(dinebis mixedviT zemoT) momuSave wyalsacaviani hesis

wyalsacavis Sevseba_damuSavebis grafikis SedgenasTan erTad,

unda uzrunvelyofdes Tbosadguris muSaobis ekonomikuri

maCveneblis gaumjobesebas, rac eleqtrosistemis sadgurebs

Soris aqtiuri datvirTvis optimaluri ganawilebis amocanis

Semadgenel nawils warmoadgens. swored am problebis

gadawyvetas eZRvneba aRniSnuli naSromi.

naSromi Sedgeba Sesavlisagan da ZiriTadi teqstis oTxi

Tavisagan, romelic moicavs eqsperimentul nawils, mis analizs,

dasmuli amocanis algoriTmizacias, gaangariSebis programas da

daskvnebs. gaangariSebis programa warmodgenilia danarTis saxiT.

pirvel TavSi saubaria maregulirebeli hesis kaskadSi

momuSave sezonuri hesis muSaobis specifiurobaze. mare-

gulirebeli hesis wyalsacavis Sevseba-damuSavebis grafikis

Sesabamisi SerCeviT miiRweva sezonuri hesis datvirTvis

reJimis marTva, riTac SesaZlebelia kidev ufro gaumjobesdes

Tbosadgurebis muSaobis ekonomokuri maCveneblebi da kidev

ufro efeqturi gaxdes eleqtrosadgurebs Soris aqtiuri

datvirTvis optimaluri ganawileba.

vii

meore TavSi energoblokebis qarxnuli da naturaluri

gazomvebis statistikuri informaciis safuZvelze, umciresi

kvadratebis meTodis gamoyenebiT, dadginda rogorc

energoblokebis saxarjo maxasiaTeblebi, aseve calkeuli

eleqtrosadguris ekvivalenturi saxarjo maxasiaTebeli meore

rigis polinomis saxiT.

aseve dadgenili iqna sadguris datvirTvis ekonomikuri

intervalebi muSaobaSi CarTuli agregatebis optimaluri

raodenobis gaTvaliswinebiT.

mesame TavSi Catarebulia eleqtrosistemaSi

eleqtrosadgurebs Soris aqtiuri datvirTvis ganawilebis

optimizaciis amocanis gantolebaTa sistemis analizi.

ganxilulia aseTi saxis amocanaTa amoxsnis meTodebi da

Sefasebulia am meTodebis gamoyenebis sferoebi.

eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis maTematikuri modeli Cawerilia konkretulad

saqarTvelos energosistemis magaliTze.

amave TavSi naCvenebia, rom dasmuli amocanis amoxsna,

Dromelic damyarebulia yvela eleqtrosadgurisaTvis

pirveladi energoresursis fardobiTi nazrdis tolobis

pirobaze ufro moxerxebulia gamoyenebuli iqnes amocanis

amoxsnis grafikuli meTodi, rac gulisxmobs pirveladi

enrgoresursis fardobiTi nazrdis grafikuli gamosaxulebis

gamoyenebas.

meoTxe TavSi TavSi ganxilulia dasmuli amocanis amoxsnis

algoriTmizacia_programireba. programireba Gganxilulia

saqarTvelos energosistemis magaliTze da ricxviT magaliTad

aRebulia eleqtrosistemis 17.12.2008w reJimi.

rogorc analizma gviCvena, programiT ganxorcielebuli

optimizaciis amocanis amoxsniT miRebuli Sedegebis mixedviT

engurhesis mier, im dRes wylis arsebuli limitis dacviT

gamomuSavebuli iqna ufro meti energia _ 8168 mgvtsT, vidre

faqtiurai reJimiT _ 7052 mgvtsT. sistemaSi aqtiuri datvirTvis

viii

optimaluri ganawilebisas, me-9 enrgoblokze saTbobis xvedriT

xarjma Seadgina 356 gr/kvtsT. nacvlad faqtiuri 359 gr/kvtsT-isa.

gaizarda am energoblokis dReRamuri gamomuSaveba (6333 mgvtsT,

nacvlad faqtiuri 4988 mgvtsT-isa).

Sedegad dReRamis intervalSi mniSvnelovnad Semcirda

eletroenergiis importi (577 mgvtsT, nacvlad faqtiuri 2125

mgvtsT-isa). 

ix

Aabstract

In heat-hydroelectric scheme the most important is optimal use of existing

water reserve in water storage of hydroelectric power stations.

Considering natural water sink into the river and limits of stored water

consumption, working schedule of water storage hydroelectric power stations mainly

provides covering maximum load of electric system.

At planning 24 hour load working schedule of water storage hydroelectric power

stations, in cascade of which (in direction of flow) seasonal hydroelectric power

station is built (working on sink) , during working out the issue of rational use of

existing water storage (natural sink and the limit of water consumption from water

storage) demands of working effectiveness of either regulating hydroelectric power

station or the seasonal one must be considered.

Effective use of natural sink into the river and the stored water in the water

storages on heat stations will let us save expensive fuel and optimally distribute active

load between power plants throughout the whole system.

Among optimization problems of energy system working regimens the most actual

is optimal distribution of active load between power plants and in the same time

internal optimization of separate station machines.

For perfect solving of the existing problem either service pattern equivalent for

energy plant or service pattern equivalent for separate energy plant, which let us

estimate energetic indices of energy plant performance in relation with regimen of

station load, were ascertained in the work. Energetic pattern equivalent to the station

was ascertained on the base of energetic patterns of separate machines.

The problem of making energetic pattern equivalent to the station requires

analysis of condition of station machines. The part of these machines can be stopped

and another part can be left in operating state.

On the base of equivalent service indices made for each makeup of machines it is

possible to ascertain optimal number of operating machines and to execute optimal

distribution of active load between stations.

Coming out of operation specificity of seasonal hydroelectric power station

working in cascade, control of its loading regimen together with making filling-

processing chart of water storage of hydroelectric power station working in cascade

x

(according the flow) should provide improving economical indices of heat station,

which represents the part of the problem of optimal distribution of workload between

energy systems. This work is devoted to the solving of this problem.

The work consists of introduction and four chapters of the main text, which

contains experimental part, its analysis, algorithmisation of given problem,

calculation program and conclusions. Calculation program is represented as an

appendix.

In the first chapter it is spoken about working specificity of seasonal hydroelectric

power station operating in the cascade of regulating hydroelectric power station. By

choosing correspondent filling-processing chart of water storage of regulating

hydroelectric power station control of loading regimen of seasonal hydroelectric

power station is reached, which can improve economical indices of heat station

operation and make more effective optimal distribution of active load between energy

plants.

In the second chapter on the base of statistical data of shop and natural

measurements of power units, by using method of least squares, either service

patterns of power plants, or equivalent service patterns of separate power plants as a

secondary polynomials, were ascertained.

Also economic intervals of station load were determined considering optimal

number of operating machines.

In the third chapter analysis of coupled equation of optimization problem of

active load distribution between power plants in electric system is done. The methods

of challenging such problems are discussed and using these methods is estimated.

Mathematical model of active load optimal distribution between power plants is

recorded after the example of concrete Georgian energy system.

In the same chapter it is shown that during solving the problem in purpose of

computerization, more comfortable is to use graphical method of challenge, which

means use of graphic pattern of relative accretion of primary power resources and is

based on equality condition of relative accretion of primary power resources for all

power plants..

In the fourth chapter algorithmization-programming of challenge of given problem

is discussed. Programming is discussed after the example of Georgian power system

and as a numerical example is given regimen of power system (17.12.2008).

xi

As analysis has shown by challenging the problem of optimization, according

the received results, that day by keeping existing water limit more energy was

produced _ 8168 MWh, than in fact _ 7052 MWh. During optimal distribution of

active load in the system, on the 9th block fuel specific consumption was 356 gr/

kWh, instead of actual 359 gr/kWh. It increased power unit 24 hour production (6333

MWh, instead of actual 4988 MWh).

In the result the import of electricity significantly decreased (577 MWh, instead

of actual 2125 MWh).

xii

sarCevi

Sesavali ---------------------------------------------------------------------------- 16

literaturis mimoxilva --------------------------------------------------------

20

Tavi 1 amocanis dasma ------------------------------------------------------------------------ 23 $ 1.1 amocanis arsi 23 $ 1.2 Camodinebaze momuSave kaskaduri hesis muSaobis

reJimis gansakuTrebuloba ----------------------------------------------------- 30

I Tavis daskvna ------------------------------------------------------------------------- 35 Tavi 2 eleqtrosadgurebis energetikuli

maxasiaTebeli ------------------------------------------------------------------------- 36

$ 2.1. samanevro maxasiaTeblebi--------------------------------------------------------- 36 $ 2.2 agregatTa energetikuli maxasiaTeblebi-------------------------------- 38 $ 2.3. eleqtrosadgurebis energetikuli maxasiaTeblebis

dagenis gzebi ---------------------------------------------------------------------------- 40

$ 2.4. eleqtrosadgurebis ekvivalenturi energetikuli maxasiaTeblebi ----------------------------------------------------------------------

53

II Tavis daskvna ---------------------------------------------------------------------- 62 Sedegebi da maTi gansja Tavi 3 optimizaciis amocanis gantolebaTa sistema-------------------------

63

$ 3.1. gantolebaTa sistemis struqtura------------------------------------------ 63 $ 3.2 optimizaciis gantolebaTa sist. amoxsnis meTodika----------- 66 $ 3.2.1. optimizaciis amocanis amoxsnis pirdapiri meTodi------------ 66 $ 3.2.2. optimizaciis amoxsnis lagranJis ganusazRvrel

mamravlTa meTodi--------------------------------------------------------------------- 68

$ 3.3. amocanis maTematikuri modeli------------------------------------------------ 69 $ 3.4. maTematikuri modeli saqarTvelos eleqtrosistemis

magaliTze----------------------------------------------------------------------------------- 76

$ 3.5. optimizaciis amocanis amoxsnis meTodis SerCeva---------------- 82 III Tavis daskvna------------------------------------------------------------------------ 84 Tavi 4 amocanis amoxsnis algoriTmizacia-programireba----------------- 86

$ 4.1. sawyisi informaciis momzadeba----------------------------------------------- 86 $ 4.2. amocanis algoriTmi---------------------------------------------------------------- 89 $ 4.3. aqtiuri datvirTvis optimaluri ganawileba saqarTvelos

eleqtrosistemaSi kompiuteruli programis meSveobiT

98 IV Tavis daskvna----------------------------------------------------------------------- 107 eqsperimentaluri nawili--------------------------------------------------------- 109 daskvna ------------------------------------------------------------------------------------- 110 danarTi ----------------------------------------------------------------------------------- 114 gamoyenebuli literatura ------------------------------------------------------ 125

xiii

cxrilebis nusxa cxrili 1 hidrsadgurebis saxarjo maxasiaTebeli saangariSo

gamosaxuleba -----------------------------------------------------------------

44 cxrili 2 Tbosadgurebis saxarjo maxasiaTebeli saangariSo

gamosaxuleba -----------------------------------------------------------------

45 cxrili 3 ekonomikuri mizanSewonilobis _ koeficienti

saqarTvelos hidrosadgurebisTvis ----------------------

60

cxrili 4 ekvivalenturi saxarjo maxasiaTebali da ekonomikuri datvirTvis zRvrebi -------------------------------

61

cxrili 5 sitemis yovelsaaTuri DdatvirTva ------------------------------- 98 cxrili 6 maregulirebelihidrosadgurebis wylis dReRamuri

limiti ----------------------------------------------------------------------------- 98 cxrili 7 sadgurebis , , sidideebi --------------------------------------- 99 cxrili 8 λ _ mamravlis mniSvneloba, saqarTvelos

maregulirebeli hidrosadgurebisTvis -----------------------

100

cxrili 9 saqarTvelos eleqtrosistemis 2008 wlis 17 dekembris realuri datvirTvebi ------------------------------

102

cxrili 10 saqarTvelos eleqtrosistemis 2008 wlis 17 dekembris programis saSualebiT ganxorcielebuli gamoTvliT miRebuli Sedegebi -------------------------------------

104

xiv

naxazebis nusxa

naxazi 1 engurhesis da masTan kaskadSi momuSave vardnilhesis sqema --------------------------------------------- 26

naxazi 2 Saorhesis da masTan kaskadSi momuSave aseve wyalsacavian tyibulhesis sqema -------------------------- 27

naxazi 3 Jinvalhesis da masTan kaskadSi momuSave zahesis da orTaWalhesis sqema -------------------------------- 28

naxazi 4 xramhesi I da masTan kaskadSi momuSave xramhesi II-is sqema ---------------------------------------------- 29

naxazi 5 kaskadSi momuSave hesebis sqema ------------------------------ 30

naxazi 6 kaskadSi momuSave hesebis datvirTvis grafiki------- 34

naxazi 7(a) saxarjo maxasiaTebeli ---------------------------------------- 40

naxazi 7(b) xvedriTi maxasiaTebeli -------------------------------------- 40

naxazi 7(g) diferencialuri maxasiaTebeli ------------------------ 40

naxazi 821 saqarTvelos eleqtro sadgurebis saxarjo maxasiaTeblebi ------------------------------------------------

4652 naxazi 22 k -1Semadgenlobidan k Semadgenlobaze gadasvlis

ekonomikuri datvirTvis gansazRvra ---------------------

56

naxazi 23 agregatTa Semadgenlobis ekonomikuri datvirTvis intervalebi m.q.k.-is SefasebiT ------------

58

naxazi 24 agregatTa Semadgenlobis ekonomikuri datvirTvis intervalebi saxarjo maxasiaTebliT --

60

naxazi 25 fardobiTi nazrdis grafiki -------------------------- 83

naxazi 26 saqarTvelos eleqtrosistemis 2008 wlis 17 dekembris datvirTvis grafiki faqtiuri ---------

103

naxazi 27 saqarTvelos eleqtrosistemis 2008 wlis 17 dekembris datvirTvis grafiki faqtiuri-----------

105

xv

მადლიერება

madloba minda gadavuxado baton miSa ruxvaZes , romelmac

didi pasuxismgebloba gamoiCina da daxmareba gamiwia dasmuli

amocanis algoriTmis programirebaSi.

16

შესავალი

saqarTveloSi mkvidrdeba politikuri da sameurneo

urTierTobaTa axali sistema, romelmic ganapirobebs qveynis

damoukidebeli arsebobisa da mdgradi ganviTarebis axal

pirobebs. Aam procesSi didi mniSvneloba eniWeba energetikuli

seqtoris gardaqmnisa da ganviTarebis pirobebis Seqmnas.

Eenergetikulma seqtorma unda Seqmnas qveynis ekonomikis

stabiluri funqcionirebisa da myari ganviTarebis safuZveli.

msoflioSi mimdinare politikuri da ekonomikuri procesebis

fonze saqarTvelos energetikul seqtors SeuZlia CaerTos

kavkasiis regionSi eleqtroenergiis warmoebis, transportirebisa

da moxmarebis procesSi, monawileoba miiRos ekonomikuri

integraciis da politikuri stabilurobis pirobebis

CamoyalibebaSi. A

axal pirobebSi saWiro gaxda qveynis mTeli energetikuli

seqtoris sistemuri gardaqmna, misi funqcionirebis sruliad

axali wesisa da menejmentis axali formebis damkvidreba,

ekonomikur sivrceSi energetikis rolisa da funqciis formaTa

Camoyalibeba.

amJamad saqarTveloSi mimdinareobs dargis struqturuli

gardaqmna da teqnikuri reabilitacia.

E energetikis udidesi mniSvneloba da masTan dakavSirebuli

xarjebis masStabebi gnapirobebs am dargis dagegmvis mimarT

gansakuTrebul yuradRebas da misi amocanebis gadawyvetaSi

mniSvneloavani resursebis CarTvas. Ddagegmvisas optimizaciis

meTodebis gamoyenebis Sedegad minimumamde mcirdeba eqspertTa da

specialistTa subieqturi SexedulebebiT gamowveuli

cdomilebebi. miRebuli gadawyvetilebebi eyrdnoba maTematikuri

gamoTvlebis obieqtur Sedegebs. sizustesTan erTad aseTi

meTodi moqnilia da farTod gamoiyeneba.

saqarTvelos gaaCnia gansakuTrebulad xelsayreli bunebrivi

pirobebi hidroenergetikis Semdgomi ganviTarebisTvis.

17

saqarTvelos energosistemis TaviseburebaTa gamoyenebiT kargi

SesaZleblobebi iqmneba pikuri eleqtroenergiis eqsportis

ganviTarebisTvis.

Tanamedrove socialur-ekonomikur viTarebaSi arsebiTad

Seicvleba energoresursebis moxmarebis struqtura. saWiroa

Camoyalibdes energomoxmarebis perspeqtiuli xedva, rogorc

komunaluri, aseve samrewvelo sferoebSi. yuradRebas imsaxurebs

saqarTvelos msxvil energomomxmarebel sawarmoTa ganviTarebis

perspeqtiva.

didi energetikuli sistemis Seqmna aris mniSvnelovani

mimarTuleba ara marto energetikisTvis, aramed mecnierul-

teqnikuri progresisTvis. amitom aucilebelia SemuSavebuli

iqnas am sistemis optimaluri marTvis srulyofili meTodebi da

saSualebebi, romelic uzrunvelyofs meurneobis mzardi

moTxovnilebis efeqtur dakmayofilebas. xazsgasmiT unda

aRiniSnos, rom didi sistemis ganviTarebis Sesaxeb optimaluri

gadawyvetilebebi miiReba arasruli informaciis pirobebSi.

amitom praqtikulad SeuZlebelia zustad ganisazRvros sistemis

mdgradi ganviTarebis strategia. rac ufro Soreuli perspeqtiva

ganixileba, miT naklebia sistemis ganviTarebis Sesaxeb miRebuli

gadawyvetilebis sizuste 6,7.

D didi energetikuli sistemebis optimaluri marTvis Teoriis

Seqmna warmoadgens rTul process. sistemis ganviTarebaze

optimaluri gadawyvetileba ZiriTadad moicavs:

sistemis struqturis arCeva;

sainformacio bazis Seqmna;

meTodebis, saSualebebis da sistemis marTvis organizebuli

formis arCeva;

sistemis ganviTarebis dagegmva drois sxvadasxva

intervalisaTvis da drois am TiToeul intervalSi

sistemis SesaZlo ganviTarebis analizi;

18

analizis safuZvelze sistemis Semdgomi ganviTarebis gegmis

koreqtireba;

optimizaciis amocanaTa gadasawyvetad sawyisi informaciis

Sesabamisi meTodebis moyvana.

optimizaciis Teoria da meTodebi da gadawyvetis realizacia

xSirad arsebiTad gansxvavebulia.

qveynis saerToenergetikuli sistemis amocanis formirebisTvis

saWiroa ganisazRvros:

qveynis sawvavis ZiriTadi bazis maragi da misi aTvisebis,

ganviTarebisa da gamoyenebis SesaZlebloba;

sawvavgadamamuSavebeli sawarmoebis profilizacia, maTi

ganlageba da mwarmoebloba;

ZiriTad energetikul raionebs Soris sxvadasxva saxis

sawvavis transportirebis saSualebaTa ganviTareba;

eleqtroenergiis nakadis sidide da mimarTuleba.

eqspluataciaSi myofi sistemis mimdinare dagegmva warmoadgens

reJimebis amocanis amoxsnis pirvel stadias. Mmimdinare dagegmvis

mTavar amocanas warmoadgens erTi Tvidan erT wlamde periodSi

miviRoT ZiriTadi rekomendacia sistemis simZlavris da

energoresursis gamoyenebaze. Aamocanas aqvs grZelvadiani

optimizaciis xasiaTi, romlisTvisac mTavaria:

hidroresursis maragis gansazRvra da maTi gamoyenebis

reJimis optimizacia;

Tboresursebis gamoyenebis optimizacia;

energiisa da simZlavris balansis Sedgena;

energetikuli mowyobilobebis kapitaluri remontebis

dagegmva;

sistemisa da misi calkeuli eleqtrosadgurebis teqniko-

ekonomikuri maCveneblis gansazRvra.

CamoTvlilTagan TiToeuli warmoadgens optimizaciis

amocanasa da misi gadawyveta mniSvnelovan wilad gansazRvravs

sistemis ekonomikur maCvenebels. realuri sistemisTvis

19

Catarebuli mravalricxovani gamoTvlebi gviCvenebs, rom

grZelvadiani optimazacia xSir SemTxvevaSi gvaZlevs SesamCnevad

did efeqts.

kerZod, hidrosadgurebis wyalsacavis Sevseba-damuSavebis

optimaluri reJimi saSualebas gvaZlevs 5-10 -iT avamaRloT

hesis mier eleqtroenergiis gamomuSaveba. aseve, kapitaluri

remontebis optimazacia ramdenime procentiT amcirebs xarjebs

remontze da saSualebas iZleva gazardos eleqtrosadguris

dadgmuli simZlavre an misi mwarmoebloba.

amJamad arsebobs algoriTmebi, romlebic gamoiyeneba

grZelvadiani optimizaciis amocanis amosaxsnelad, romlis

Taviseburebas warmoadgens is, rom maTSi gamoyenebulia

statikuri informacia – sistemis gasuli periodis datvirTvis

monacemebi, monacemebi hidrologiis Sesaxeb da sxva.

20

literaturis mimoxilva

eleqtrosadgurebisa da, mTlianad energosistemis, reJimebis

dagegmvis amocanebi moicavs maTi optimaluri marTvis amocanaTa did

jgufs, romelTa ZiriTadi mizania eleqtroenergiis warmoeba,

gadacema da ganawilebis teqnologiuri procesebis marTvisas

miRweuli iqnes maqsimaluri teqnikuri da ekonomikuri efeqti.

energosistemis reJimebis optimizaciis Teoriisa da praqtikis

ganviTarebaSi didi wvlili Seitanes mTelma rigma mecnierebma:

Веников В.А. 2,3; Горштеина В.М 4; Иделчик В.И 10;  Крумм Л.А.    16;  

Маркович И.М. 17; Мельников Н.А 10;  Мелентьев Л.А 8;   Филипова Т.А.  18;  

Цветков Е.В.  19; Холмский В.Г 9;   da sxva.

mecnieruli kvlevebis sawyis etapze dasmuli amocanebis

gadawyveta xorcieldeboda im droisTvis cnobili maTematikuri

meTodebis gamoyenebiT. kerZod, lagranJis meTodis gamoyenebiT,

romelic saSualebas gvaZlevs moiZebnos uwyveti funqciis eqstremumi

tolobis an utolobis saxis damatebiTi pirobebis gaTvaliswinebiT.

Tumca didi energetikuli sistemebisTvis damaxasiaTebeli

mravalganzomilebiani amocanis amoxsna im periodisTvis praqti-

kulad SeuZlebeli iyo.

energosistemis reJimebis marTvis amocanebis saxiT ganixileba:

eleqtrosadgurebs Soris aqtiuri da reaqtiuli datvirTvebis

optimaluri ganawileba; reaqtiuli datvirTvis optimaluri

kompensacia; pirveladi energoresursebisa da eleqtroenergiis

trnsportirebis saukeTeso marSrutebis SerCeva; hidro-

energoresursis optimaluri gamoyeneba da a.S 1,2,3,4,8,9,10,16,17,18,19,20.

energosistemebis damyarebuli reJimebis optimizaciis amocanebi

ganixileba droiTi da sivrciTi ierarqiis pirobebSi 1,2,10.

TbohidroenergosistemebisTvis damaxasiaTebelia is, rom hidro-

sadgurebs gaaCniaT SezRudvebi hidroenergoresursis maragis

gamoyenebis TvalsazrisiT drois mocemul intervalSi (dReRame,

kvira, Tve, weli). amocanas arTulebs is garemoebac, rom

eleqtrosadguris optimaluri datvirTvis gansazRvris procesSi

21

dadgenili unda iqnas am sadguris agregatTa optimaluri

Semadgenlobac 1,2, da sxv..

hidrosadguris wyalsacavis Sevseba damuSavebis reJimis

optimizacia energosistemaSi energoresursis optimaluri gamoyenebis

erTerTi ZiriTadi amocanaa. wyalsacavis racionaluri marTvis

pirobebSi hesze SeiZleba miviRoT (15)% damatebiTi eleqtroenergia,

rac saTbobis mniSvnelovan ekonomias mogvcems 2.

praqtikaSi xSirad gvxvdeba mdinaris hidroenergoresursis

gamoyenebis SemTxvevebi kaskaduri hesebis agebis gziT da amitom

saTbobis zemoT aRniSnuli ekonomia kidev ufro gaizrdeba, Tu ki

optimizaciis amocanis amoxsnisas gaTvaliswinebuli iqneba

wyalsacavian hesTan kaskadSi momuSave sezonuri hesebis muSaobis

reJimebis optimaluri marTvis sakiTxebic.

kaskaduri hesebis reJimebis optimizacia tipiuri xasiaTis

amocanaa, romelic yoveli energosistemisTvis individualur

midgomas moiTxovs. roca kaskadSi muSaobs wyalsacaviani hesebi, maSin

maTi hidroenergetikuli kavSirebi mniSvnelovnad sustia, radganac

TiToeul hess SeuZlia misi wylis maragis regulireba erTmaneTisgan

damoukideblad. rac ufro mcirea wyalsacavebis moculobebi, miT

ufro maRali xarisxisaa maT Soris hidroenergetikuli kavSirebi 2.

aRniSnulidan gamomdinare kaskadSi momuSave sezonuri hesis muSaobis

reJimi mWidro hidroenergetikul kavSirSia wyalsacaviani hesis

muSaobis reJimTan.

saqarTvelos sinamdvileSi sakmarisad didi raodenobis

mdinarezea agebuli kaskaduri hesebi: engurhesi_vardnilhesi;

Saorhesi_tyibulhesi_varcixehesebi; xramhesebis kaskadi; Jinvalhesi_

avWalahesi_orTaWalahesi; momavalSi namaxvanhesis agebis Semdeg

Seiqmneba namaxvanhesi_JoneTihesi_gumaTihesi_rionihesi_varcixehesebis

kaskadi da a.S.

aRniSnuli garemoebidan gamomdinare saqarTvelos energosi-

stemisTvis metad aqtualuria kaskaduri hesebis muSaobis reJimebis

optimizaciis amocana wyalsacavian hesebTan hidroenergetikuli

kavSirebis gaTvaliswinebiT.

22

gamoTvliTi teqnikis farTo ganviTarebam SesaZlebloba mogvca

minimaluri daSvebebis pirobebSi, drois mcire danaxarjebiT, maRali

sizustiT amovxsniT enrgosistemis reJimebis marTvis ama Tu im saxis

sakmarisad rTuli da Sromatevadi xasiaTis amocana.

warmodgenil disertaciaSi eleqtrosadgurebs Soris aqtiuri

datvirTvis optimaluri ganawilebis amocanis amoxsna xorcieldeba

grafikuli meTodiT da emyareba eleqtrosadgurebis pirveladi

energoresursis fardobiTi nazrdebis tolobis pirobas.

eleqtrosadgurebze agregatTa optimaluri Semadgenlobis

dadgena mimdinareobs procesis tempSi sadguris ekvivalenturi

energetikuli maxasiaTeblebis mixedviT, romelic gaTvaliswinebulia

da gamoyenebulia amocanis amoxsnis algoriTmSi.

23

Tavi 1. amocanis dasma

$ 1.1. amocanis arsi

TbohidroenergosistemaSi uaRresad mniSvnelovania

maregulirebel hesebze wyalsacavSi arsebuli wylis maragis

racionaluri (optimaluri) gamoyeneba. maregulirebeli hesebis

wyalsacavis damuSavebis wliuri grafiki, rogorc wesi proeqtiT

gaTvlilia da am grafikiT muSaobisas dagrovebuli wylis

gamoyeneba metnaklebad optimalurad xorcieldeba.

eleqtrosistemis eleqtruli datvirTvis dReRamuri

grafikebidan gamomdinare, wyalmcirobis periodis ama Tu im

dReRamisTvis calsaxad prognozirebulia (gansazRvrulia)

dagrovebuli wylis wliuri maragidan wylis dReRamuri

xarjvis limiti.

mdinareSi wylis bunebrivi Camonadenis da dagrovebuli

wylis xarjvis (wyalsacaviani hesis muSaobis dReRamuri grafiki)

limitis erToblivi gaTvaliswinebiT wyalsacaviani hesebis

muSaobis grafiki (sadguris datvirTvis dReRamuri grafiki)

Sedgeba ise, rom maT mier metwilad dafaruli iqnes eleqtruli

sistemis pikuri datvirTvebi.

im wyalsacaviani hesebis muSaobis dReRamuri datvirTvis

grafikis dagegmvisas, romelTa kaskadSi (qvemoT dinebis

mimarTulebiT) agebulia sezonuri (wylis Camodinebaze momuSave)

hesi, wylis arsebuli maragis (bunebrivi Camonadeni da

wyalsacavidan wylis xarjis limiti) racionalurad gamoyenebis

sakiTxis damuSavebisas gaTvaliswinebuli unda iqnes, rogorc

maregulirebeli hesis, aseve kaskadSi momuSave sezonuri hesis

muSaobis efeqturobis moTxovnebi.

eWvs gareSea, rom mdinareSi bunebrivad Camonadeni da

wyalsacavebSi dagrovebuli wylis maRalefeqturad gamoyeneba,

Tbosadgurebze gamoiwvevs ZviradRirebuli saTbobis ekonomias.

maSasadame aSkaraa, rom energosistemis maregulirebeli

hesebis wyalsacavebidan wylis xarjis SecvliT Seicvleba,

rogorc am hesis, aseve masTan kaskadSi momuSave sezonuri hesis

24

eleqtruli datvirTva. Sedegad simZlavreTa balansidan

gamomdinare Seicvleba Tbosadgurebis datvirTvebic. Seicvleba

aseve aqtiuri simZlavris danakargebi gadacemis qselSi.

eleqtrosadgurebs da eleqtrosistemebs gaaCniaT garkveuli

saxis ekonomikuri maCveneblebi kerZod: margi qmedebis

koeficienti; pirveladi energoresursis xvedriTi xarji;

pirveladi energoresursis fardobiTi nazrdi. qselSi

simZlavris danakargebis fardobiTi nazrdi da a.S., romelTa

ricxviTi mniSvnelobebi bevradaa damokidebuli sistemis

sadgurebis eleqtrul datvirTvaze drois mocemul intervalSi.

aRniSnulidan gamomdinare, wyalsacavian hesebze dagrovebuli

wylis maragis racionaluri xarjvis amocana ganxiluli unda

iqnes am hesebTan kaskadSi momuSave sezonuri hesebis

energetikul maxasiaTebelTa gaTvaliswinebiT. amrigad,

wyalsacavSi dagrovebuli wylis maragis xarjvis amocana

kompleqsuri xasiaTis amocanaa 1,2.

saqarTvelos energosistema Tavisi specifiurobiT gamoirCeva.

kerZod, wyalmcirobis periodSi (zamTris sezoni), roca

Tbosadgurebi muSaobaSia hidroeleqtrosadgurebis mier

gamomuSavebuli eleqtroenergiis xvedriTi wili 70% da metia.

amasTan qveynis wyalsacavian hesebTan kaskadSi sakmarisad didi

raodenobis sezonuri hesebi muSaoben. aseTi saxis wyalsacavian

hesebs warmoadgens 7.

engurhesi, romelTanac kaskadSi muSaobs vardnilhesi 14.

amJamad vardnilhesi 24 ar muSaobs. vardnilhesi 1

Tavismxriv wyalsacaviani hesia.

Saorhesi, romelTanac kaskadSi muSaobis aseve

wyalsacaviani hesi tyibulhesi da Camodinebaze momuSave

varcixehesi 14.

Jinvalhesi, romelTanac kaskadSi muSaobs zahesi da

orTaWalhesi.

xramhesi 1, romelTanac kaskadSi muSaobs xramhesi 2.

25

engurhesidan vardnilhes 1-mde wylis dinebis xangrZlivoba

Seadgens daaxloebiT erT saaTs (nax.1). amitom datvirTvis

grafikzec droSi daZvra iqneba erTi saaTi. rac imas niSnavs, rom

mocemul saaTze engurhesis wyalsacavze ganxorcielebuli

cvlileba vardnilhesisTvis grafikze aisaxeba erTi saaTis

Semdeg.

Saorhesidan tyibulhesamde wylis dinebis xangrZlivoba

Seadgens 30 wuTs, tyibulhesidan varcixehesamde dinebis

xangrZlivoba aris 5 sT da 30 wT (nax.2). Sesabamisad am

xangrZlivobiT iqneba daZruli cvlilebebi datvirTvis grafikze.

Jinvalhesidan zahesamde wylis Cadinebis dro aris 5 sT,

xolo orTaWalhesamde – 11 sT. (nax.3). e.i. Jinvalhesis

wyalsacavze drois mocemul momentSi ganxorcielebuli

cvlileba (wyalsacavis Sevseba – damuSaveba) kaskadSi momuSave

zahessa da orTaWalhesze es cvlileba moxdeba drois aRniSnuli

xangrZlivobebis dagvianebiT.

xramhesi 1-dan – xramhesi 2-mde wylis dinebis xangrZlivoba

aris 2 sT (nax.4). amitom xramhesi 1-is wyalsacavis cvlileba

(Sevseba – damuSaveba) xramhes 2-ze moxdeba 2 sT-is dagvianebiT.

nax. 1. enmomu

ngurhesis uSave vard

da masTandnilhesis

n kaskadSisqema

i

26

naxx.2 Saorheaseve wyal

esis da malsacavian

sTan kaskan tyibul

adSi momuhesis sqem

uSave ma

27

nax.3 J

Jinvalhesizahesis

is da masTda orTaW

Tan kaskadWalhesis s

dSi momuSsqema.

ave

28

nax.4 xramhesi IxrI da masTaramhesi II-i

an kaskadSis sqema

Si momuSavve

29

30

$ 1.2. Camodinebaze momuSave kaskaduri hesis

muSaobis reJimis gansakuTrebuloba.

sezonuri hesi, romelic drois mocemul momentSi muSaobs

mdinareSi wylis bunebrivi Camonadenis xarjze, zogierTi

gamonaklisis garda (xanmokle uxvi naleqi dRis drois mcire

monakveTSi), dReRamis intervalSi faqtiurad anviTarebs erTi

da igive sididis simZlavres, anu misi SesaZlo simZlavre

ganpirobebulia mdinareSi wylis bunebrivi xarjiT.

rogorc avRniSneT, roca sezonuri (anu Camodinebaze

momuSave) hesi Sedis wyalsacaviani hesis kaskadSi, maSin misi

datvirTvis grafiki Seicvleba maregulirebel hesze wyalsacavis

Sevseba-damuSavebis grafikis Sesabamisad.

maSasadame, kaskadSi momuSave sezonuri hesi garkveulwilad

(muSaobis reJimis xasiaTiT) maregulirebeli hesis rols

asrulebs. am rolis efeqturi Sesruleba miiRweva

maregulirebeli hesis muSaobis grafikTan SeTanxmebiTa da

eleqtrosistemis jamuri datvirTvis grafikis dafarvaSi

kaskadSi momuSave sezonuri hesis monawileobis grafikis

Sesabamisi dadgeniT. swored amaSi gamoixateba Camodinebaze

momuSave kaskaduri hesis muSaobis reJimis gansakuTrebuloba

(Tavisebureba), romlis racionaluri gamoyenebis SemTxvevaSi

SeiZleba miRweuli iqnes energosistemis ekonomikuri

maCveneblebis garkveuli xarisxiT gaumjobeseba.

sailustraciod ganvixiloT Semdegi saxis martivi magaliTi.

gansaxilvel eleqtrosistemaSi kaskadSi muSaobs xuTi hesi.

(nax.5)

nax.5 kaskadSi momuSave hesebis sqema

hesi-- I

hesi-- II

3sT 1sT

hesi-- III hesi-- IV hesi-- V

1sT 1sT

31

amasTan hesi-I da hesi-II warmoadgens wyalsacavian hess, xolo

hesi-III, hesi-IV da hesi-V ki sezonurs.

am hesebis dadgmuli simZlavreebia PIdadg 240 mgvt, PIIdadg

160 mgvt, PIIIdadg 160 mgvt, PIVdadg 80 mgvt, PVdadg 120

mgvt.

miviRoT, rom sadguris muSa dawnevebis Sesabamisad wylis

erTidaigive xarjvisas, am hesebis ganviTarebuli simZlavre

erTmaneTTan Semdeg TanafardobaSia; I 1,5 II, II III, III 2 IV,

IVdadg V.

wyali I-hesidan II-hesamde bunebrivi dinebiT aRwevs 3 saaTSi;

II-dan III-mde 1 sT-Si; III-dan IV-Si 1 sT-Si; IV-hesidan V-hesamde 1

sT-Si.

CavTvaloT, rom mocemuli dReRamis intervalSi mdinareSi

wylis bunebrivi Camonadenis xarjze TiToeuli sadguris mier

ganviTarebuli simZlavre Seadgens misi dadgmuli simZlavris

50%-s (50%-iani uzrunvelyofa)

sistemis dReRamuri datvirTvis grafikis dafarvaSi, garda

zemoT aRniSnuli eleqtrosadgurebisa, kidev monawileobs

Tbosadguri, romlis simZlavre VI 60 mgvt da arakaskaduri

sezonuri hidrosadgurebi, romelTa jamuri simZlavre VII 40

mgvt.

aRniSnul sadgurebs Soris sistemis datvirTvis ganawilebis

grafiki naCvenebia naxazi 6-ze, rogorc am naxazidan Cans 21_22

saaTis intervalSi hesi-I muSaobs 140 mgvt datvirTviT. sawyisi

monacemebis Sesabamisad mdinareSi wylis bunebrivi Camonadenis

xarjze am sadgurs SeuZlia ganaviTaros 120 mgvt. e.i. es sadguri

Tavisi wyalsacavidan damatebiT iRebs 20 mgvt simZlavris

ekvivalenturi wylis raodenobas. wylis es moculoba 3 saaTis

Semdeg iqneba hesi-II_ze, anu 0_1 saaTis intervalSi. wylis am

moculobiT hesi-II ganaviTarebs.

II , ,93,33 mgvt.

32

magram es sadguri am saaTze muSaobs 80 mgvt datvirTviT. e.i.

13,33 mgvt simZlavris Sesabamisi wylis raodenobiT is avsebs

Tavis wyalsacavs.

ganvixiloT 22_23 saaTis intervali. am intervalSi hesi-I

muSaobs 100 mgvt datvirTviT. e.i. am saaTze hesi Tavis

wyalsacavSi tovebs (wyalsacavs Seavsebs) 20 mgvt simZlavris

ekvivalenturi raodenobis wyals. am hesze namuSevari wyali (100

mgvt) hesi II-ze iqneba 1_2 saaTis intervalisTvis da hesi II wylis

am moculobis mixedviT ganaviTarebs

II ,66,67mgvt. simZlavres.

faqtiurad es sadguri drois am monakveTSi muSaobs 80 mgvt

datvirTviT, e.i. Tavis wyalsacavidan damatebiT iRebs 80-66,67=

13,33 mgvt simZlavris ekvivalentur wyals.

ganvixiloT 23_24 saaTis intervali. am intervalSi hesi-I

muSaobs 60 mgvt. datvirTviT. e.i. es sadguri drois am

intervalSi wyalsacavSi itovebs 120 60 60 mgvt simZlavris

ekvivalenturi raodenobis wyals drois am intervalSi hesi I-ze

namuSevari wyali 3 saaTis Semdeg e.i. 2_3 saaTis intervalSi

iqneba hesi II-ze, romelic drois am intervalSi muSaobs isev 80

mgvt datvirTviT. anu is wyalsacavidan damatebiT aiRebs 20 mgvt

simZlavris ekvivalentur wyals.

amave principiT gagrZeldeba hesi I da hesi II sadgurebis

muSaoba dReRamis sxva intervalSic.

ganvixiloT hesi-III, hesi-IV, da hesi-V sadgurebis muSaobis

reJimebi. rogorc avRniSneT hesi-II-dan moyolebuli yovel

momdevno sadguramde wylis Cadinebis xangrZlivobaa 1 saaTi.

23_24 saaTis intervalSi hesi-II muSaobs 80 mgvt datvirTviT da

amave datvirTviT III 80 mgvt imuSavebs hesi-III 1 saaTis Semdeg,

anu 0_1 saaTis intervalSi. e.i. aseve 1 saaTis Semdeg, anu 1_2

saaTis intervalSi hesi-IV imuSavebs IV 40 mgvt-iT da

kidev 1 saaTis Semdeg anu 2_3 saaTis intervalSi hesi-IV

imuSavebs IV IV · 40 60 mgvt datvirTviT.

33

amrigad, wyalsacavian hesebze muSaobis reJimebis cvlilebiT

icvleba kaskadSi momuSave hesebis muSaobis reJimebi da

Sesabamisad, miviRebT Tbosadguris reJimis Secvlis

SesaZleblobas. ganxiluli magaliTidan Cans, rom sezonuri

hesebis mier ganviTarebuli simZlavre Seesabameba mdinareSi

wylis dReRamur realuri Camodinebas. maregulirebel hesebze ki

saWiro gaxda wyalsacavidan maragis gamoyeneba an piriqiT.

(warmodgenil naxazze Tbosadguris datvirTva aRebulia

mudmivad). Tbosadguris datvirTvis grafikis Secvla SeiZleba

mibmuli iqnes dReRamis intervalSi saTbobis xarjis minimumis

pirobasTan, rac amocanis optimaluri gadawyvetis SemTxvevaSi

garkveuli sididis ekonomikur efeqts mogvcems.

es miuTiTebs mas, rom wyalsacavian hesebTan erTad sezonuri

hesebis muSaobis reJimis SecvliT SeiZleba mivaRwioT

Tbosadguris muSaobis optimalur reJims, anu is vamuSaoT

misTvis yvelaze ufro xelsayrel pirobebSi _ saTbobis

xvrdriTi xarji Seadgendes minimalurs.

34

Nnax. 6

35

I Tavis daskvna

am TavSi xazgasmiTa gamaxvilebuli yuradReba

maregulirebeli hesis kaskadSi dinebis mixedviT qvemoT momuSave

sezonuri hesis muSaobis specifiurobaze. am sezonuri hesis mier

dReRamis ganmavlobaSi gamomuSavebuli eleqtroenergiis

moculoba, (anu misi dReRamuri datvirTvis grafiki).

damokidebulia ara marto mdinareSi wylis bunebrivi Camonadenis

moculobaze, aramed masTan kaskadSi (dinebis mixedviT zemoT)

momuSave wyalsacaviani hesis wyalsacavis Sevseba _ damuSavebis

reJimze.

aRniSnulia, rom wyalsacavSi dagrovebuli wylis

racionaluri gamoyenebis mizniT dReRamuri grafikis

SemuSavebisas gaTvaliswinebuli unda iyos, rogorc TviT

wyalsacaviani hesis, aseve masTan kaskadSi momuSave sezonuri

hesis energetikuli maxasiaTeblebi. aqedan gamomdinare, naCvenebia,

rom wyalsacavSi dagrovebuli wylis racionaluri xarjvis

amocanis amoxsna kompleqsur midgomas moiTxovs, romlis drosac

gaTvaliswinebuli unda iqnes wylis bunebrivi dinebis

xangrZlivoba wyalsacaviani hesidan sezonur hesamde.

naCvenebia, rom wyalsacavis Sevseba _ damuSavebis grafikis

kompleqsuri midgomiT SemuSavebis gziT, miiRweva ra sezonuri

hesis datvirTvis marTva, SesaZlebelia kidev ufro gaumjobesdes

Tbosadgurebis muSaobis ekonomikuri maCveneblebiT anu mTeli

sistemis maStabiT, kidev ufro daixvewos eleqtrosadgurebs

Soris aqtiuri datvirTvis optimaluri ganawilebis amocana.

36

Tavi 2 eleqtrosadgurebis energetikuli

maxasiaTeblebi

$2.1 samanevro maxasiaTeblebi

energosistemaSi muSaobs sxvadasxva tipis eleqtrosadgurebi,

maT Soris yvelaze meti xvedriTi wili uWiravs Tbo da

hidrosadgurebs. eleqtrosadgurebis muSaobis reJimis SerCeva

mimdinareobs eleqtroenergiis gamomuSavebaze minimaluri

xarjebis uzrunvelyofis moTxovniT. am moTxovnis miRweva

SesaZlebelia im SemTxvevaSi Tu arsebobs detaluri informacia

eleqtrosadguris energetikuli maxasiaTeblebis Sesaxeb.

eleqtrosadgurebis muSaobis reJimebi dgindeba datvirTvis

grafikis dafarvisas. datvirTvis grafikis dafarvaSi

monawileobs sadguris muSa simZlavre, anu muSaobisTvis

mzadyofnis simZlavre.

eleqtrosadgurebis jamur muSa simZlavresa da maT jamur

datvirTvas Soris sxvaoba warmoadgens simZlavris rezervs,

romelic Sedgeba civi da cxeli rezervisagan. simZlavris cxeli

rezervi es igive mbrunavi rezervia.

datvirTvis grafikSi hidrosadguris monawileobis reJimi

muSa simZlavris farglebSi unda uzrunvelyofdes energiis

dReRamuri limitis srulad aTvisebas. am grafikSi

Tboeleqtrosadgurebis muSaobis reJimi, maTi muSaobis

efeqturobis amaRlebis mizniT, unda iyos met_naklebadD

stabiluri, anu naklebad cvalebadi.

Tec-is muSaobis reJimis gansazRvrisas iTvaliswineben, rom am

tipis eleqtrosadgurebis ZiriTadi daniSnulebaa Tburi

datvirTvis dafarva, xolo kondensaciuri eleqtrosadgurebis

datvirTva dReRamis intervalSi unda xdebodes saTbobis

optimaluri gamoyenebis pirobiT.

yvela eleqtrosadguri normalur reJimSi unda

monawileobdes sixSiris da nakadganawilebis regulirebaSi,

xolo avariul reJimSi simZlavreTa marTvaSi. Yyovelive es

37

damokidebulia sadguris agregatTa manevrirebis unarsa da

marTvis avtomaturi sistemis efeqtur muSaobaze. sadguris

manevrirebis unari ganisazRvreba datvirTvis da regulirebis

diapazoniT.3,4

datvirTvis diapazoni. Tu -uri agregatisTvis xangrZlivad

dasaSveb minimalur da maqsimalur datvirTvas Seadgens

Sesabamisad ,min da ,maq maSin agregatisTvis datvirTvis

diapazoni

დატვ., %P ,მაქს P ,მინ

P ,მაქს· 100

am diapazonis farglebSi SesaZloa icvlebodes damxmare

mowyobilobaTa Semadgenloba, an amorTuli iqnes calkeuli

avtomaturi regulatori. im konkretuli energoblokisTvis,

romlisTvisac მაქს ,ნომ datvirTvis diapazoni SeiZleba

ganisazRvros minimaluri dasaSvebi datvirTvis mixedviT

დატვ., % 1 ,,მინ · 100

sadac ,მინ,,მინ

,ნომ

agregatis minimaluri dasaSvebi datvirTvis fardobiTi

mniSvneloba.

TboeleqtrosadgurebisTvis minimaluri dasaSvebi datvirTva

ganpirobebulia orTqlis turbinis da qvabdanadgaris muSaobis

reJimebiT, qvabdanadgaris tipiT da damokidebulia sawvavis

saxeobaze. blokebisaTvis romlebic muSaoben mazuTze an airze

minimaluri dasaSvebi datvirTvis diapazoni 50%_ze metia,

naxSirze momuSave energoblokebisaTvis ki 40%-mdea.

hidroeleqtrosadgurebisaTvis minimaluri dasaSvebi datvirTva

praqtikulad ar izRudeba.

regulirebis diapazoni. es datvirTvis is intervalia, romlis

farglebSi agregatis datvirTva SeiZleba icvlebodes

avtomaturad ZiriTadi da damxmare mowyobilobebis

Semadgenlobis Secvlis gareSe. am farglebis nebismieri

datvirTvisas teqnologiuri avtomatikis regulatorebi unda

38

muSaobdes Seuferxeblad. saWiroebis SemTxvevaSi SeiZleba

avtomaturad icvlebodes maTi parametrebi, raTa regulirebis

diapazonis mTel intervalSi uzrunvelyoT avtomaturi

regulireba.

$2.2 agregatTa energetikuli maxasisaTeblebiA

normaluri eqspuataciis pirobebSi energosistemis

optimaluri marTvis erTerT ZiriTad amocanas warmoadgens

sistemis eleqtrosadgurebs Soris datvirTvis optimaluri

ganawileba, rac gulisxmobs energetikuli, SromiTi da fuladi

resursebis efeqtur gamoyenebas da amavdroulad momxmarebelTa

saimedo da uwyvet energomomaragebas. aRniSnuli amocanis

gadawyveta sakmaod rTulia.

eleqtroenergiis warmoebis, gadacemisa da ganawilebis

procesSi energosistemis TiToeuli elementis, danadgar-

mowyobilobebis muSaobis efeqturoba damokidebulia mTel rig

teqnikur-ekonomikur maxasiaTeblebze, romelTa Soris

mniSvnelovani roli uWiravs eleqtrosadgurebis (agregatebis)

energetikul maxasiaTeblebs. eleqtrosadgurebis energetikuli

maxasiaTebeli miiReba sadguris calkeuli hidro Tu

TbomowyobilobaTa analogiuri maxasiaTeblebis safuZvelze. maT

ricxvs miekuTvneba: saxarjo, xvedriTi da diferencialuri

maxasiaTeblebi 1,2.

saxarjo maxasiaTebeli aris damokidebuleba generatoris

(sadguris) mier ganviTarebul simZlavresa da pirvaladi

energoresursis xarjs Soris.

da (1)

sadac, – wylis xarji hidrosadgurze (hidroagregatze), m3/wm;

– saTbobis xarji turboagregatze, kg/sT.

_ generatoris (sadguris) mier ganviTarebuli

simZlavre, mgvt.

39

zogadad saxarjo maxasiaTebels aqvs Cazneqili mrudis saxe

(nax.7(a))

sadguris mimarTebaSi ganixileba xvedriTi maxasiaTebeli.

xvedriTi maxasiaTebeli aris energoresursis xarji agregatis

mier ganviTarebul erTeulovan simZlavreze.

qQ

P მ /წმ

მგვტ da b

B

P

კგ/სთ

მგვტ (2)

xvedriTi maxasiaTebeli xasiaTdeba erTi eqstremumiT

(nax.7(b)) am maxasiaTebelze gansakuTrebul interess warmoadgens

wertili, romelic xasiaTdeba pirveladi energoresursis

xvedriTi xarjis minimumiT. Aam wertilიs Sesabamis datvirTvas

ekonomikur datvirTvas uwodeben, romlis drosac agregatis

(sadguris) margi qmedebis koeficienti 1

122,45 , 101,94 maqsimaluria

diferencialuri maxasiaTebeli ganixileba pirveladi

energoresursis nazrdis datvirTvis nazrdTan fardobis saxiT:

da

roca datvirTvis nazrdi usasrulod mcirea, maSin

diferencialur maxasiaTebels aqvs saxe:

da (3)

Ooptimizaciis amocanebSi am maxasiaTebels pirveladi

energoresursis fardobiT nazrds uwodeben. es maxasiaTebeli

ZiriTadad wrfewirs warmoadgens. (nax.7(g))

40

Nnax.7 saxrjo (a), xvedriTi (b), diferencialuri (g), maxasiaTeblebi

$2.3 eleqtrosadgurebis energetikuli

maxasiaTeblebis dadgenis gzebi

energosistemis reJimebis optimizaciis amocanebis

gantolebaTa sistemaSi eleqtrosadguris saxarjo maxasiaTebeli

erTerTi ZiriTadi gantolebaa, romelic am amocanebSi kavSiris

gantolebas warmoadgens. amasTan miRebulia igi Cawerili iqnes

meore rigis polinomis saxiT 2

wm

m3,2bpap 0QQ da sT

kg,2bpapB 0B (4)

sadac: Q0, B0 - uqmi svlis xarjia;

a ,b polinomis pirveli da meore rigis SesakrebTa

koeficientebi, Sesabamisad. A

am parametrTa (koeficientebis) saTanadod SerCevis

pirobebSi (4) saxeSi Cawerili saxarjo maxasiaTebeli sakmarisi

sizustiT asaxavs realobas.

saxarjo maxasiaTeblis agebis safuZvels SeiZleba

warmoadgendes rogorc qarxnuli monacemebi, aseve naturaluri

gazomvebis Sedegebi. Qqarxnuli monacemebi eqspluataciis

pirobebSi icvleba da, amitom, saWiroa periodulad Catardes

naturaluri gazomvebi. naturaluri gazomvebi saSualebas

gvaZlebs davadginoT saqarxno monacemebis droSi cvlilebis

a)

max

PP P

min

q,b

q,b, B,Q

g) b)

41

dinamika da, aqedan gamomdinare, aseTi gazomvebis Sedegebi ufro

miaxloebulia realobasTan.

eqsperimentiT (naturaluri gazomvebis) monacemebis

safuZvelze analizuri gamosaxulebis misaRebad visargeble

umciresi kvadratebis meTodiT5

��� �� min2

dxb

a

(x)-f(x)M

ATu integralis nacvlad gamoviyenebT jamis formulas, gveqneba

min)()(2

1

n

iii xxf M (5)

sadac: )( ixf _ saZiebeli analizuri funqcia;

)( ix _ eqsperimentiT (gazomviT) miRebuli ordinatTa ix abcisis

dros Cvens SemTxvevaSi

hidroagregatze saangariSo gamosaxuleba (romelic saZiebelia),

xolo i

Q)( ix _ amave agregatebze eqsperimentiT miRebuli

wylis xarji datvirTvis dros.

aseve, - Tboagregatze saZiebeli

saangariSo gamosaxuleba da - eqsperimentiT miRebuli

saTbobis xarji datvirTvis dros.

(4) gamosaxulebis gaTvaliswinebiT (.5) miiRebs saxes:

Μ

da

Μ

miRebuli gamosaxulebis minimizaciis pirobidan gamomdinare

vRebulobT gantolebaTa Semdeg sistemas

42

0

0

0

hidroagregatebisTvis

da

0

0

0

TboagregatebisTvis

romelTa amoxsnis safuZvelze davadgenT saxarjo maxasiaTeblis

gamomsaxveli polinomis , , , koeficientebs. mopovebuli

statistikuri informaciis safuZvelze dagenil iqna

saqarTvelos Tbo da hidrosadgurebis agregatebze pirveladi

energoresursis xarjis saangariSo gamosaxulebebi

.

winamdebare naSromSi warmodgenilia Catarebuli

eqsperimentebis safuZvelze engurhesis, Jinvalhesis, xramhesi 1-is,

varcixehes 1,2 hidrosadgurebis hidroagregatebze wylis xarjis

mniSvnelobebi sxvadasxva datvirTvebis dros, xolo danarCeni

hidrosadgurebs wylis xarjis mniSvnelobebi sxvadasxva

datvirTvebis dros, dadgenili iqna am hesebis muSaobis

statistikuri monacemebis mixedviT (sapasporto monacemebi da

sxva saxis informacia). 1,12

cxril 1-Si warmodgenilia sxvadasxva datvirTvebis dros

eleqtrosadgurebis eqsperimentiTa da saangariSo gamosaxulebiT

miRebuli xarjis ricxviTi mniSvnelobebi.

mocemul cxrilidan Cans, rom cdomileba, gansazRvravs

0.06%-s, maSasadame hidroagregatebze wylis xarjis saangariSo

gamosaxuleba maRali sizustiT asaxavs realobas. es imis

maCvenebelia, rom gamoTvlebiT miRebuli saxarjo maxasiaTeblis,

saangariSo gamosaxuleba SeiZleba gamoviyenoT saqarTvelos

energosistemis reJimebis optimizaciis amocanebSi.

43

Tboeleqtrosadgurebis saxarjo maxasiaTeblis saangariSo

gamosaxulebis misaRebad visargebleT xvedriTi xarjis Sesaxeb

mopovebuli informaciiT. kerZod, gardabnis Tbosadguris me-9

blokisTvis, roca is muSaobs P=270 mgvt simZlavriT, xv=356

gr/kvtsT. aseve me-3, me-4 blokebisTvis, roca isini datvirTulni

arian P=130 mgvt, qxv=384,4 gr/kvtsT. #1,2 airturbinebisTvis,

roca P=55 mgvt, qxv= 414.4 gr/kvtsT.

zemoT aRwerili meTodiT davadgineT saxarjo

maxasiaTeblebis gamomsaxveli polonomebis B0, da

koeficientebi aRniSnuli maxasiaTeblis saangariSo

gamosaxulebebs aqvs cxril 2-Si naCvenebi saxe.

qvemoT 821 naxazebze warmodgenilia saxarjo maxasiaTeblebis

grafikebi. Savi feris mrudi miRebulia eqsperimentis

(naturaluri gazomvebis) monacemebiT, xolo wiTeli feris mrudi

ki saangariSo gamosaxulebiT (meore rigis polinomi). am

naxazebidan aSkarad Cans, rom maT Soris gansxvaveba,

praqtikulad ar aris.

44

cxr.1 hidrsadgurebis saxarjo maxasiaTebeli saangariSo gamosaxuleba

sadguri

dawneva,

m

datvir- Tva, mgvt

wylis xarji m3/wm

cdomileba saxarjo maxasiaTebeli

eqsperi-menti

saanga-

rი So gamos.

∆ m3/wm

∆ %

engurhesi

360

260 220 170 100

81,05 68 53

34,06

81 68 53 34

0,05 0 0

0,06

0,06 0 0

0,01

11,24+0,20 +14· 10

xramhesi 1

370

37,8 31,66 23

14,73

12 9,8 7,3 4,7

12 10 7,5 5

0 0,2 0,2 0,3

0 0.02 0.03 0.06

0,907+0,27 +6· 10

varcixehesi

15,5

23 19,97 14,06 9,03

174,9 150 109 73

174,35 150 109 73

0,6 0 0 0

0.03 0 0 0

5,55+6,58 +1,8· 10

Jinvalhesi

128

32,5 27,49 19,92 13,05

28,78 24,11 18 12

28,7 24 17,8 12

0,08 0,1 0,2 0

0.003 0.004 0.01 0

1,.39+0.80 +1,2· 10

orTaWalhesi 11

6 5,02 3,48 2,52

76 63 45 34

75,8 63.1 45,9 34

0,08 0,1 0,9 0

0.002 0.001 0.02 0

9,33+8,9 +3,6· 10

Saorhesi 478

9,6 7,76

5,65 3.61 3,61

2,5 2 1,5 1

2,5 2 1,5 1

0 0 0 0

0 0 0 0

0.209+0,21 +3· 10

tyibulhesi

293

20 16 11,5 8,85

8,5 7 5 4

8,5 7

4,97 4

0 0

0,03 0

0 0

0.006 0

1,29+0,27 +4,7· 10

xramhesi 2

330

55 46,65 21,95 22,99

20 17 12 9

19,96 17,02 12 9

0,04 0,02 0 0

0.002 0.001 0 0

1.776+0.30 +5· 10

vardnilhesi

59

73,33 55 36,7 18,3

143 106,2 72,2 37

142.8 106 72,1 37

0,2 0,2 0,1 0

0.001 0.002 0.001 0

3,79+2,8 +2,3· 10

zahesi 1

20

12 9,96 7,05 5

77 63 46 32,5

76,8 63 46 32,5

0,2 0 0 0

0.003 0 0 0

3,024+5,81 +2,7· 10

zahesi 2 20

3,2 2,4 1,6 0,8

20,5 15,3 10 5,12

20,5 15 10 5,14

0 0,3 0

0,02

0 0.02 0

0.004

0,27+5,93 +1,2· 10

45

cxr.2 Tbosadgurebis saxarjo maxasiaTebelebis saangariSo gamosaxulebebi

gardabnis Tbosadguri

datvir-Tva,mgvt

saTbobis xarji cdomileba saxarjo maxasiaTebeli saangariSo gamosaxuleba eqspe-

rimentiT saangari-

So gamosax.

∆ kg/sT

∆ %

me-9 bloki

100 200 260 300

40000 71500 92690 107100

39970 71610 92476 107170

30 -110 214 -70

0.0075 -1.54 0.23 -0.065

12250 257,6P 0.196

me-3,4 bloki 80 100 120 140 160

31200 38000 44640 51240 57880

33000 39000 45000 51900 58101

18000 1000 360 660 221

0.06 0.03 0.008 0.01 0.004

7614.9+272.71 +0.293

airturbina #1, 2

10 30 42 55

7500 12900 17190 22770

7591 12962 17271 22817

91 62 81 47

0.01 0.005 0.005 0.002

5517.1+170.38 +2.617

46

nax.8

nax.9

47

nax.10

nax.11

48

nax.12

nax.13

49

nax.14

nax.15

50

nax.16

nax.17

51

nax.18

nax.19

52

nax.20

nax.21

53

$2.4 eleqtrosadgurebis ekvivalenturi

energetikuli maxasiaTeblebi

energosistemis muSaobis reJimebis optimizaciis amocanaTa

Soris erTerT ZiriTad amocanas warmoadgens eleqtrosadgurebs

Soris aqtiuri datvirTvis optimaluri ganawileba. umravles

SemTxvevaSi yovel eleqtrosadgurze dadgmulia ori da meti

agregati. muSaobaSi CarTul agregatTa Semadgenloba

ganapirobebs am sadguris da, aseve, mTeli sistemis muSaobis

ekonomikurobasa da saimedoobas.

Tbo da hidroeleqtrosadgurebs Soris aqtiuri datvirTvis

ganawilebis amocana iTvaliswinebs yoveli saangariSo periodis

calkeuli droiTi intervalisTvis ganisazRvros

eleqtrosadgurebis optimaluri datvirTva da, amavdroulad,

ganxorcieldes agregatTa Semadgenlobis Sigasasadguro

optimizacia.

Sigasasadguro optimizaciisTvis aucilebelia gagvaCndes

sadguris ekvivalenturi energetikuli maxasiaTeblebi, romelic

sadguris datvirTvisa da muSaobaSi CarTul agregatTa ricxvis

funqciaa.

ekvivalentur energetikul maxasiaTebels, romelic

calkeul droiT intervalSi sadgurebs Soris aqtiuri

datvirTvis optimaluri ganawilebis amocanis amoxsnisas

gamoiyeneba, sistemis mocemuli datvirTvis dros uzrunvelyofs

rogorc sadgurebis, aseve, mTeli sistemis muSaobis optimalur

maCveneblebs. sadguris ekvivalenturi energetikuli

maxasiaTeblis saangariSo gamosaxuleba dadgindeba sadguris

calkeul agregatTa energetikuli maxasiaTeblebis mixedviT.

sadguris ekvivalenturi maxasiaTeblis dadgena sakmarisad

rTulia, gansakuTrebiT, ganivi kavSirebis mqone energoblokebis

SemTxvevaSi. roca sadguris energoblokebi warmoadgenen

erTnairi energetikuli maxasiaTeblis mqone monoblokebs, maSin

54

sadguris ekvivalenturi saxarjo maxasiaTeblis ageba SedarebiT

martivia 1,19.

sadguris agregatis energetikuli maxasiaTebeli, rogorc

ukve aRiniSna sasurvelia warmoadgendes meore rigis polinoms.

sadguris ekvivalenturi saxarjo maxasiaTeblis asagebad

vsargeblobT informaciiT sadguris agregatTa mdgomareobis

Sesaxeb, rac gulisxmobs imas, rom sadguris yoveli agregati

SeiZleba iyos gaCerebuli an muSa mdgomareobaSi. am

TvalsazrisiT, Tu sadgurze dgas n raodenobis agregati, maSin

maTi mdgomareobis kombinaciaTa raodenoba, zogadad Seadgens

2n-s, rac mTeli sistemis masStabiT warmoadgens

mravalganzomilebian amocanas.

amocanis gamartivebis mizniT ganvixiloT SemTxveva, roca

sadgurze dgas erTnairi saxarjo maxasiaTeblis mqone

agregatebi, muSaobaSi CarTuli raodenobis ekvivalenturi

maxasiaTebeli, zogadad, iqneba

2P pbaTT kkk k0,

sadac: k0,T - pirveladi energoresursis uqmi svlis xarji, roca

muSaobaSi CarTulia raodenobis monobloki;

kk ba , - Sesabamisi koeficientebi muSaobaSi CarTuli imave

raodenobis agregatebis SemTxvevaSi

Tu sadguris jamuri datvirTvaa P da muSaobaSi CarTulia

k raodenobis agregati, maSin erTi agregatis datvirTva iqneba:

.k

pP 1

aqedan gamomdinare erT Tboblokze (igulisxmeba

monobloki) pirveladi energoresursis xarji iqneba

2

1

k

pb

k

paTT 0 ,

xolo muSaobaSi CarTuli raodenobis monoblokebze

SemTxvevaSi, pirveladi energoresursis jamuri xarji

55

2

k

pb

k

paTkTk 0

anu

21bp

kapkTTk 0 (7)

maSasadame, (6) da (7) gamosaxulebaTa Sedarebis

safuZvelze monoblokebiani TbosadgurebisTvis SegviZlia

davweroT

0kTT k .0 ; aak da bk

bk

1

analogiurad SeiZleba ganisazRvros hidrosadgurebis

ekvivalenturi saxarjo maxasiaTebelic, magram unda

gaviTvaliswinoT, rom hidrosadgurebis hidroteqnikur nawilSi

aris saerTo sadawneo nageboba, saerTo saderivacio arxi an

sadawneo gvirabi Tu sadawneo milsadeni. amitom ekvivalenturi

energetikuli maxasiaTeblis dadgena zemoT naCvenebi martivi

algoriTmiT ar moxerxdeba. sakiTxis gadawyvetis mizniT

gamoyenebuli iqna mravalwliani dakvirvebis safuZvelze

mopovebuli statistikuri informacia. am informaciis analizis

Sedegad SesaZlebeli gaxda dagvedgina agregatTa k -1

Semadgenlobidan k Semadgenlobaze gadasvlis e.w. optimalobis

koeficienti , romelic sxvadasxva hesisaTvis, zogadad

sxvadasxvaa. am koeficientis gamoyenebiT SesaZlebeli gaxda

dagvedgina hidrosadguris ekvivalenturi saxarjo saangariSo

gamosaxuleba 19.

hidrosadguris ekvivalenturi saxarjo saangariSo

gamosaxulebas, zogadad, aqvs Semdegi saxe

,2,0 np

k

bapkk QQ (8)

56

sadac uqmi svlis xarji k,0Q

warmoadgens pirveladi

energoresursis uqmi svlis xarjs k raodenobis agregatis

erTdrouli muSaobisas.

agregatTa nebismieri SemadgenlobisaTvis agebuli

ekvivalenturi saxarjo maxasiaTeblebis safuZvelze sadguris

jamuri datvirTvisagan damokidebulebaSi SesaZlebelia

dadgindes muSaobaSi CarTul agregatTa optimaluri ricxvi.K -1

raodenobis agregatTa Semadgenlobidan k raodenobis agregatTa

Semadgenlobaze gadasvlis ekonomikuri mizanSewoniloba

ganisazRvreba sadguris im 1kP , k ekonomikuri datvirTviT (nax.22),

romlis drosac pirvaladi energoresursis xarji k -1 da k

raodenobis agregatebis SemTxvevaSi erTnairia.

kk QQ 1 (9)

nax. 22 k -1 Semadgenlobidan k Semadgenlobaze gadasvlis ekonomikuri

datvirTvis gansazRvra amasTan, rogorc naxazidan Cans

1kQ ( ),1 kkPP kQ ( ),1 kkPP

da

1kQ ( >)> ,1 kkPP kQ ( )> ,1 kkPP  

-1

P

1kP, k

57

(8)-is Tanaxmad (9) Caiwereba Semdeg saxeSi

,1 ,1

2

,1,0,1

2

,11,0kkkkk

kkkkk pk

bapp

k

bap

QQ

am tolobidan;

,)1(

1,1

2

1,0,0kk

kk pbkk

QQ

(10)

sadguris (agregatis) muSaobis erTerT ekonomikur

maCvenebels warmoadgens margi qmedebis koeficienti (mqk) romlis

saangariSo gamosaxulebas hidrosadgurebisTvis, zogadad aqvs

Semdegi saxe

,

94.10194.101

2,0 p

k

bap

pp

k

QHQH (11)

am gamosaxulebis mixedviT SeiZleba dadgenili iqnas

sadguris is )1kP (ek, ekonomikuri AdatvirTva, romlis drosac

sadguris mqk iqneba maqsimaluri, kerZod pirobidan

0

vRebulobT

b

kP k

k,0

)1

Q(ek, (12)

nPk )1( ,,, )1kP (ek, ,, kkP ,1 datvirTvebisas ),( P koordinatTa

sistemis P RerZze (nax. 23) SeiZleba gaaCndeT sxvadasxva

urTierTmdebareoba:

nek PkPP kkk )1( ,1)1(

1)1( ,

kkk PPkP ,1)2(

1)2( )1( nek

kkk PPPk ,1)3(

1)3()1( ekn

58

P

1

2

3k

)1)1(

kP (ek,

kkP ,1)1(

1)2(

kP eknPk )1( kkP ,1

)2(

1)3(

kP ek

kkP ,1)3(

nkP

nax.23 agregatTa Semadgenlobis ekonomikuri datvirTvis

intervalebi m.q.k.-is SefasebiT

am utolobaTa analizi gviCvenebs, rom 1k

Semadgenlobidan k Semadgenlobaze gadasvlis ekonomikuri

mizanSewonilobis koeficienti SeiZleba icvlebodes

sxvadasxva farglebSi:

pirvel SemTxvevaSi

1)1(

)1

n

(ek,

Pk

P k (13)

meore SemTxvevaSi gamomdinare iqedan, rom agregatTa

datvirTva nominalurze metad ararekomindirebulia,

koeficienti mkacrad miaxloebulia 1-Tan.

mesame SemTxvevaSi ki, imave mizeziT, rac meore SemTxvevaSi,

=1.

zogadad, SeiZleba ZalaSi davtovoT (12) gamosaxuleba.

59

sxvadasxva hidrosadgurebis statistikur informaciaTa

kompleqsurma analizma, saSualeba mogvca koeficientis

dasadgenad visargeblobT Semdegi TanafardobiT

1)1(

,1)1(

nPk

P kkk anu n

PkP kkk )1( )1(

,1 (14)

Aam Tanafardobis gaTvaliswinebiT SegviZlia davadginoT

uqmi svlis jamuri xarji agregatTa sxvadasxva Semadgenlobisas.

amisaTvis visargebloT (9) gamosaxulebiT, romelic (14)

gamosaxulebis gaTvaliswinebiT miiRebs saxes

22)1(21,0,0 )1(

)1(

1nPkb

kkk

kk

QQ

anu , )1( 2)1(2

1,0,0 nPbk

k kkk

QQ

imis gaTvaliswinebiT, rom damatebiT erTi agregatis

CarTvam ar unda gamoiwvios pirveladi resursis uqmi svlis

xarjis gazrda 1,0Q -ze metad, gvaqvs

02)1(2

1 Q

nPbk

k k

anu

1)1(

)1(2

20

k

Pkb

k

n

Q

am gamosaxulebis (14) –Si CasmiT vRebulobT

b

kkP kk

0,1

)1( Q

agregatTa mocemuli Semadgenlobis Sesabamisi

ekvivalenturi energetikuli maxasiaTebeli gaTvaliswinebuli

iqneba eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis amocanis amoxsnisas.

60

P

nax.24 agregatTa Semadgenlobis ekonomikuri datvirTvis

intervalebi saxarji maxasiaTebliT

roca kk

P,1<P < 1, kkP , pirveladi energoresursis ekonomia

miiRweva Tu muSaobaSi CarTuli iqneba k raodenobis agregati

(nax.24).

statistikuri informaciis damuSavebis safuZvelze,

saqarTvelos hidrosadgurebisaTvis davadgineT

koeficientebis mniSvnelobebi cxrli 3

cxr.3 ekonomikuri mizanSewonilobis _ koeficienti saqarTvelos hidrosadgurebisTvis

miRebuli koeficientis gamoyenebiT dadginda saqarTvelos

hidrosadgurebis ekvivalenturi maxasiaTeblebi. agreTve

dadginda ekonomikuri datvirTvis zRvrebi, romlebic mocemulia

4 cxrilSi. sadguris ekvivalenturi maxasiaTeblis saSualebiT,

moxdeba sadguris optimaluri datvirTvis gansazRvra, xolo

ekonomikuri datvirTvis zRvrebi saSualebas mogvcems

ganvaxorcieloT Sigasasadguro optimizacia.

hesi hesi hesi engurhesi 0.96 varcixehesi 0,87 orTaWalhesi 0,88 vardnilhesi 0,87 tyibulhesi 0,97 xrami 1 0,.94 lajanurhesi 0,94 Saorhesi 0,96 xrami 2 0,87 rionhesi 0,94 Jinvalhesi 0,96 zahesi 0.87

1

-1

T,Q

1kP k kP, 1k

61

cxr.4 ekvivalenturi saxarjo maxasiaTebali da ekonomikuri datvirTvis zRvrebi

eleqtrosadguris

dasaxeleba CarTul

agregatTa

raodenoba

#

CarTul agregatTa

ekvivalenturi

saxarjo maxasiaTebali

ekonomikuri

datvirTvis

farglebi,mgvt

engurhesi 1

2

3

4

5

11,24 0,202 0,1 · 10 14,35 0,202 0,5 · 10 18,18 0,202 0,33 · 10 22,13 0,202 0,25 · 10 26,02 0,202 0,2 · 10

0 220 220 440 440 660 660 880

880 1300

xramhesi 1

1

2

3

0,91 0,27 0,6 · 10 1,28 0,27 0,3 · 10 1,73 0,27 0,2 · 10

0 37,8 38 75

75 112

Jinvalhesi

1

2

3

4

1,397 0,802 0,12 · 10 1,96 0,802 0,6 · 10 2,62 0,802 0,4 · 10 3,28 0,802 0,3 · 10

30 32,5 32,5 55 55 70

Saorhesi 1

2

3

4

0,21 0,21 3 · 10 0,39 0,21 0,15 · 10 0,47 0,21 0,1 · 10 0,61 0,21 0,75 · 10

0 9 9 18

18 27 27 36

tyibulhesi 1

2

3

4

1,29 0,27 4,7 · 10 2,12 0,27 2,35 · 10 3,1 0,27 1,57 · 10 4,1 0,27 1,17 · 10

0 20 20 40 40 60 60 80

vardnilhesi

1

2

3

3,79 1,8 1,3 · 10 6,5 1,8 0,65 · 10 9,0 1,8 0,43 · 10

0 60 60 115

115 220

xramhesi 2

1

2 1,78 0,3 0,5 · 10 2,36 0,3 0,25 · 10

0 55 55 110

zahesi 1

1

2 3,02 5,81 0,3 · 10 4,67 5,81 1,5 · 10

0 12 12 24

zahesi 2

1

2

3

4

0,27 5,93 0,13 0,7 5,93 0,65 1,1 5,93 0,43 · 10 1,4 5,93 0,33 · 10

0 3,2 3,2 6,4 6,4 9,6

9,6 12,8

orTaWalhesi

1

2

3

9,3 8,9 0,37 14,4 8,9 0,19 19,7 8,9 0,12

0 6 6 12

12 18

varcixehesi 1

2 14,87 6,17 3,3 · 10 21,5 6,17P 1,7 · 10

0 23 23 46

62

II Tavis daskvna

eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis ekonomikuri efeqti damokidebulia, rogorc

energoblokebis, aseve calkeuli eleqtrosadgurebis

energetikuli maxasiaTeblebis da maT Soris saxarjo

maxasiaTeblebis, aRmweri maTematikuri modelis utyuarobis

xarisxze. am TavSi, gavaanalizeT ra, rogorc qarxnuli, aseve

naturaluri gazomvebis statistikuri informacia

energoblokebis Sesaxeb, umciresi kvadratebis meTodiT,

davadgineT rogorc energoblokebis saxarjo maxasiaTeblebi,

aseve calkeuli eleqtrosadgurebis ekvivalenturi saxarjo

maxasiaTebeli meore rigis polinomis saxiT.

naCvenebia, rom miRebuli analizuri gamosaxulebis mixedviT

gansazRvruli pirveladi energoresursis xarjis ricxviTi

mniSvneloba maRali sizustiT emTxveva naturaluri gazomvebis

Sedegebs.

amave TavSi, agregatebis saxarjo maxasiaTeblebis

maTematikuri modelis safuZvelze, gadaWrili iqna muSaobaSi

CarTuli agregatebis optimaluri ricxvis amocana anu

dadgenili iqna sadguris datvirTvis ekonomikuri intervalebi

muSaobaSi CarTuli agregatebis raodenobis gaTvaliswinebiT.

calke cxrilis saxiTaa warmodgenili saqarTvelos yvela

wyalsacaviani hesisa da am hesebTan kaskadSi momuSave sezonuri

hesebis saxarjo maxasiaTeblebi da datvirTvis ekonomikuri

maCveneblebi muSaobaSi CarTuli agregatebis ricxvis mixedviT.

63

Tavi 3. optimizaciis amocanis gantolebaTa sistema

$3.1 gantolebaTa sistemis struqtura

optimizaciis amocanis gantolebaTa sistema sawarmoo

teqnologiuri procesis teqnikur-ekonomikur maCveneblebs

akavSirebs gamosakvlevi obieqtis muSaobis ZiriTad saxasiaTo

parametrebTan, romlebic amocanis saZiebel parametrebs

warmoadgens.

nebismieri teqnologiuri procesis optimizaciis maTematikuri

modeli zogadad Seicavs gantolebaTa xuT jgufs; efeqturobis

gantoleba (miznis gantoleba), kavSiris gantoleba, SezRudvis

gantoleba da utoloba, optimaluri marTvis gantoleba,

adaptaciis gantoleba 1,2,3.

efeqturobis gantoleba warmoadgens sawarmoo

teqnologiuri procesis mimdinareobis maxasiaTebeli teqnikur-

ekonomikuri maCveneblis maTematikur gamosaxulebas im saZiebeli

parametrebis mimarT, romlebic gavlenas axdenen procesis

mimdinareobaze. kerZod, eleqtroenergetikul sferoSi

optimizaciis erTerTi amocanis mizans warmoadgens

eleqtroenergiis gamomuSavebis procesis warmarTva pirveladi

energoresursis minimaluri xarjis pirobebSi. am SemTxvevaSi

saTbobis xarjis minimumis moTxovna warmoadgens amocanis

kriteriums.

amocanaTa Soris SeiZleba aRmoCndes iseTi, romlis

Sefaseba unda ganxorcieldes sxvadasxva kriteriumebis

erTdrouli gaTvaliswinebiT, aseT SemTxvevaSi miznis funqciis

Sedgena garTulebulia da moiTxovs specifiur midgomas.

miznis funqcia anu efeqturobis gantoleba kriteriumis

miTiTebiT Caiwereba Semdegnairad

, ,

sadac: – Semaval cvladTa simravle;

– saZiebelia anu gamomaval cvladTa simravle.

64

kavSiris gantoleba aRwers kavSirs teqnologiuri

procesis Semaval da gamomaval parametrebs Soris

.

am damokidebulebas warmoebis teqnologiuri procesis

maxasiaTebels uwodeben. igi SeiZleba warmodgenili iqnes

cxrilebis an mrudebis saxiT. optimizaciis amocanebis

amoxsnisTvis ufro moxerxebulia kavSiris gantoleba

warmodgenili iqnas analizuri saxiT. (agregtis saxarjo

maxasiaTebeli). eleqtroenergetikaSi kavSiris gantolebis saxiT

ganixileba agregatTa saxarjo maxasiaTeblebi.

SezRudvis gantolebebi da SezRudvis utolobebi

warmoadgens SezRudvebs, romlebic daedeba teqnologiuri

procesis Semaval an gamomaval parametrebs tolobis an

utolobis saxiT. es SezRudvebi gamosaxaven im pirobebs, rac

aucileblad unda Sesruldes teqnologiuri procesis

ganxorcielebisas.

SezRudvis gantoleba, romelic warmoadgens kavSirs

teqnologiuri procesis gamosaval parametrebs Soris, zogadad,

SeiZleba Caiweros Semdeg saxeSi.

, … … 0

, … … 0

, … … 0

sadac: – SezRudvis gantolebaTa raodenoba;

– saZiebel parametrTa raodenoba.

imisaTvis, rom optimizaciis amocanas gaaCndes alternatiuli

amoxsnebi, romelTa Soris unda moiZebnos saukeTeso

(optimaluri), aucilebelia sruldebodes piroba . im

SemTxvevaSi Tu , maSin amocanas ar gaaCnia amonaxsni, xolo

im SemTxvevaSi roca , maSin gantolebaTa sistemas aqvs

erTaderTi amonaxsni, romelic, zogadad, ar warmoadgens

saukeTesos.

65

SezRudvis utoloba SeiZleba iyos calmxrivi an ormxrivi. es

utoloba gviCvenebs Semaval da gamomaval cvladebis dasaSveb

zRvrebs. saZiebeli cvladisaTvis SezRudva SeiZleba Caiweros

Semdegnairad (ormxrivi utoloba):

x ,მინ x x ,მაქს.

SezRudva SeiZleba iyos mkacri da aramkacri. mkacri

SezRudvis darRveva dauSvebelia, radganac man SeiZleba

gamoiwvios elementis dazianeba. aramkacri SezRudvis

darRvevisas SeiZleba adgili hqondes uaryofiT movlenas

(maCveneblebis gauareseba), magram ar gamoiwvios avariuli

situacia.

optimaluri marTvis anu optimizaciis gantoleba

saSualebas gvaZlevs ganvaxorcieloT procesis optimaluri

marTva. igi miiReba miznis, kavSirisa da SezRudvis gantolebaTa

erToblivi gaTvaliswinebiT da warmoadgens kavSirs saZiebel

cvladebsa da optimizaciis amocanis mizans Soris.

adaptaciis gantoleba iTvaliswinebs teqnologiur

procesSi miwodebuli realur informaciasa da sawyis

informacias Soris gansxvavebas. es imas niSnavs, rom

optimizaciis amocanis amonaxsni, romelic miiReba

prognozirebuli informaciis safuZvelze, moiTxovs

koreqtirebas, radganac arsebuli realuri informacia

garkveulwild gansxvavdeba prognozirebul informaciisagan.

adaptaciis gantolebis daniSnulebaa prognozirebuli da

realuri sawyisi informaciebis safuZvelze dadgenili

amoxsnebis realizaciisas miRebul efeqtebs Soris gansxvaveba

dayvanili iqnes minimumamde.

66

$3.2 optimizaciis gantolebaTa sistemis

amoxsnis meTodika

3.2.1 optimizaciis amocanis amoxsnis pirdapiri

meTodi

mocemulia miznis funqcia

,

sadac Semavali parametrebi ganisazRvreba kavSiris

gantolebebiT

, … …

, … …

, … …

(15)

saZiebeli parametrebi erTmaneTTan dakavSirebulia kavSiris

gantolebiT

, … … 0

, … … 0

, … … 0

(16)

da SezRudvis utolobebi

x ,მინ x x ,მაქს

x ,მინ x x ,მაქს

x ,მინ x x ,მაქს

(17)

optimizaciis amocanis mizania moiZebnos cvladTa iseTi

mniSvnelobebi, romlebic daakmayofilebs (16) da (17) saxis

SezRudvebs da uzrunvelyofs miznis funqciis eqstremums.

Tu miznis funqciaSi Semaval cvladebs SevcvliT (15)

gamosaxulebaTa mixedviT, maSin miznis funqcia gamoisaxeba

mxolod saZiebeli cvladebiT 1,2.

, . … … (18)

optimizaciis amocanis amoxsnisas pirdapiri meTodis

mixedviT (16) gantolebaTa sistemidan amovxsniT , …

67

saZiebel cvladebs danarCeni , … sidideebis

saSualebiT.

, … ,

, …

, …

(19)

, … cvladebi warmoadgenen damoukidebel saZiebel

cvladebs, xolo , … cvladebi ki damokidebul saZiebel

cvladebs. (18) miznis funqciaSi (19) cvladTa SetaniT gveqneba;

Φ Φ , … (20)

amrigad, miznis funqcia Seicavs saZiebel cvlads. am

funqciis eqstremumi ganisazRvreba calkeuli cvladis mixedviT

funqciis kerZo warmoebulebis nulTan tolobis pirobidan

Φ 0

Φ 0

Φ 0

(21)

am gantolebaTa sistemidan amovxsniT , … saZiebel

cvladebs, romelTa (19)-Si Casmis Semdeg dadgindeba danarCeni

, … – cvladebi.

saZiebeli cvladebis mniSvnelobebis dadgenis Semdeg

Semowmdeba (17) SezRudvis utolobebi. Tu es utolobebi yvela

cvladis mimarT sruldeba, maSin optimizaciis amocanis amoxsna

damTavrebulia. Tu erTi an ramdenime cvladisTvis romelime

utoloba dairRva, maSin am cvlads vaniWebT mis zRvrul

ricxviT mniSvnelobas imisda mixedviT, Tu romel mxares dairRva

SezRudva. am ricxviTi mniSvnelobebis gaTvaliswineba

optimizaciis amocanis yvela gantolebaSi, gamoiwvevs saZiebel

cvladTa Semcirebas da amocanis amoxsna Catardeba xelmeored

saZiebel cvladTa Semcirebuli raodenobis pirobebSi. (17)

utolobaTa Semowmeba unda moxdes amocanis yoveli amoxsnis

Semdeg, sanam aRniSnuli utolobaTa sistema ar dakmayofildeba

yvela cvladis mimarT.

68

3.2.2 optimizaciis amocanis amoxsnis lagranJis

ganusazRvrel mamravlTa meTodi

optimizaciis amocanaTa amoxsnisas gamoiyeneba lagranJis

ganusazRvrel mamravlTa meTodi, romlis dros (18) saxeSi

Cawerili miznis funqciis eqstremumis nacvlad ganixileba

lagranJis funqciis eqstremumi, romelic Caiwereba Semdegi

saxiT1,2,9

∑ (22)

sadac: –(16) saxis SezRudvis gantolebebi;

– mudmivi mamravlebi, romelTac lagranJis

ganusazRvrel mamravlebs uwodeben.

yvela saZiebeli cvladis mixedviT funqciis kerZo

warmoebulis nulTan gatolebiT miiReba gantolebaTa sistema

∑ 0

∑ 0

∑ 0

(23)

am gantolebaTa sistemaSi Sedis raodenobis saZiebeli

sidide. kerZod, raodenobis saZiebeli cvladebi , … da

raodenobis lagranJis mamravlebi , … ... .

(16) da (23) gantolebaTa raodenoba aseve Seadgens -s

rac sakmarisia saZiebeli cvladebis dasadgenad.

amoxsnis Semdeg moxdeba (16) utolobebis Semowmeba da

saZiebel cvladTa mimarT Catardeba igive procedurebi, rac

zemoT iyo aRwerili ($3.2.1).

lagranJis meTodis gamoyenebisas yvela saZiebeli cvladi

miiReba, rogorc damoukidebeli cvladi. am meTodis upiratesoba

mdgomareobs imaSi, rom miznis funqciis da SezRudvis

gantolebaTa arawrfivoba amocanis amoxsnisas ar qmnis

damatebiT siZneleebs, rac pirdapiri amoxsnis meTodis

69

gamoyenebisas gantolebaTa arawrfivoba SeiZleba gadaulaxav

problemad iqces.

$3.3 amocanis maTematikuri modeli

optimizaciis amocanis xasiaTis, Sinaarsisa da miznis

Sesabamisad, SeiZleba visargebloT sruli an gamartivebuli

maTematikuri modeliT. sruli maTematikuri modeli Seicavs

xuTive saxis gantolebebs. gamartivebul maTematikur models

miekuTvneba SefasebiTi da optimizaciuri modeli. SefasebiTi

maTematikuri modeli ar Seicavs marTvisa da adaptaciis

gantolebebs, xolo optimizaciuri modeli ki ar Seicavs

mxolod adaptaciis gantolebas 1,2,9.

SefasebiTi modeliT sargeblobisas kavSirisa da SezRudvis

gantolebebis (utolobebis) safuZvelze xdeba miznis funqciis

gamoTvala, rac saSualebas iZleva Sefasdes teqnologiuri

procesis mimdinareobis esa Tu is varianti. optimizaciuri

modeli, romelic damatebiT Seicavs marTvis gantolebas,

amocanis amoxsnis Sedegad gvaZlevs cvladTa simravles,

romelTa realizaciisas miRweuli iqneba mizani – teqnologiuri

procesis mimdinareobis saukeTeso varianti.

maTematikuri modelis saxe mniSvnelovnad damokidebulia

arsebuli informaciis sizusteze da optimizaciis meTodze.

eleqtroenergetikaSi SeiZleba gamoyenebuli iqnes

maTematikuri programirebis esa Tu is meTodi imisda mixedviT

miznis da SezRudvebis gantolebebi (utolobebi) warmoadgens

wrfiv Tu arawrfiv funqciebs. im SemTxvevaSi, roca miznis

funqcia da SezRudvis gantolebebi da utolobebi saZiebeli

cvladebis mimarT wrfivi funqciebia, farTod gamoiyeneba

diferencialuri gamoTvlebi, romelTa ricxvs miekuTvneba

pirdapiri amoxsnis meTodi, lagranJis ganusazRvrel mamravlTa

meTodi da variaciuli gamoTvlebi.

optimizaciis amocanis amoxsna niSnavs teqnologiuri

procesis maxasiaTebeli parametrebis moZiebas, romlebic

70

uzrunvelyofen miznis funqciis eqstremums SezRudvis yvela

saxis gantolebaTa da utolobaTa dacvis pirobebSi.

SezRudvis utolobaTa sistema optimizaciis amocanaSi

SeiZleba gaTvaliswinebuli iqnes ori sxvadasxva xerxiT.

pirveli maTgani gulisxmobs SezRudvis gaTvaliswinebas rogorc

damatebiT pirobas saZiebeli sididis amonaxsnis koreqtirebis

TvalsazrisiT, xolo meore xerxi gulisxmobs SezRudvis

utolobis gaTvaliswinebas e.w. sajarimo funqciis saxiT.

ganvixiloT Tbohidrosadgurebs Soris aqtiuri datvirTvis

optimaluri ganawilebis amocana. eleqtrosistemis optimizaciis

mTeli ciklisaTvis maregulirebeli hesebis datvirTvebi

Tbosadgurebis datvirTvebTan erTad warmoadgens saZiebel

sidideebs. am SemTxvevaSi kriteriums warmoadgens Tbosadgurze

saTbobi xarjis minimumi.

maSasadame, eleqtrosadgurebs Soris aqtiuri datvirTvis

optimaluri ganawilebis amocanis miznis funqcia Caiwereba

Semdeg saxeSi1,2,3

∑ ∑ , (24)

sadac: _ drois is intervali, romlis ganamavlobaSi

eleqtruli sistemis jamuri datvirTva SeiZleba

CavTvaloT mudmiv sidided (simartivisTvis aiReben

1sT);

intervalTa saerTo raodenoba gansaxilvel

periodSi;

, -ur Tbosadgurebze saTbobis saaTuri xarji

intervalSi;

,,0”_ indeqsi miniWebuli aqvs mabalansirebel

Tbosadgurs;

Tbosadgurebis saerTo ricxvi.

kavSiris gantolebebs warmoadgens Tbohidrosadgurebis

saxarjo maxasiaTeblebi meore rigis polinomis saxiT2

, , , kg/sT 0,1,2, … (25)

71

da

, , , , m3/wm , . . (26)

, _ -ur Tbosadgurze saTbobis saaTuri xarji, kg/sT;

_ -ur hidrosadgurze wylis wamuri xarji, m3/wm.

_ hidrosadgurebis saerTo ricxvi

SezRudvis gantolebaTa saxiT gvaqvs:

a) aqtiuri simZlavris balansis gantoleba yoveli

intervalisaTvis

W , ∑ P , ∑ P, ∑ Pდან.სადგ Pდატვ, 0 (27)

m _ maregulirebeli hidrosadgurebis saerTo ricxvi

b) yoveli maregulirebeli hidrosadgurisTvis wylis limiti

dReRamis intervalSi

, 3600 · ∑ , ,ლიმ 0 , . . (28)

sadac: ლიმ – -uri hesisTvis dReRamuri limiti (m3/dReRame).

SezRudvis utolobaTa saxiT gvaqvs

,მინ ,მაქ da ,მინ ,მაქ . (29)

SevadginoT lagranJis funqcia

, ∑ ,

anu

= ∑ ∑ , , , ,

∑ ∑ , ∑ , dan.sadg.t

Pმომხ _ )+∑ m 3600 ∑ , , , ,ლიმ (30)

am gamosaxulebaSi τ =1, xolo , warmoadgens lagranJis

ganusazRvrel mamravlTa simravles.

lagranJis funqcia (30) gavawarmooT cvladis mixedviT

da gavutoloT nuls

72

,, 1 ∆

∆ ,0

,, 1 ∆

∆ ,0

,

, 1 ∆

∆ ,0

,, 1 ∆

∆ ,0

(31)

am gantolebaTa sistemaSi:

, 2b , -uri Tbosadgurze saTbobis fardobiTi

nazrdi drois drois intervalSi;

∆

∆ ,. qselSi aqtiuri simZlavris danakargebis

fardobiTi nazrdi -uri kondesaciuri sadguris

kvanZisaTvis.

lagranJis funqciis (30) gavawarmoT cvladis mixedviT

da gavutoloT nuls

, 1 ∆

∆3600 , , 0

, 1 ∆

∆3600 , , 0

, 1 ∆

∆3600 , , 0

, 1 ∆

∆3600 , , 0

(32)

am gantolebaTa sistemaSi:

, 2b , -uri hidrosadgurisaTvis wylis fardobiTi

nazrdi drois intervalSi;

∆

∆ ,. -uri hesis kvanZisaTvis qselSi aqtiuri simZlavris

danakargebis fardobiTi nazrdi.

Tu CavTvliT, rom qselSi aqtiuri simZlavris danakargebi

ar aris damokidebuli eleqtrosadgurebis datvirTvebze (es

daSveba pirvel miaxloebaSi misaRebia), maSin saZiebel , da

73

, cvladebis mixedviT funqciis minimizaciis moTxovna gvaZlevs

Semdegi saxis gantolebaTa sistemas

, 0 1,2 …

3600 , 0 1. .

A

miRebul gantolebaTa sistemaSi mamravlis gamoricxvis

Semdeg vRebulobT

, 3600λ , ,

anu

, , … , 3600 , 3600 ,

3600 , = (33)

(33) gantolebaTa sistema (27) gamosaxulebasTan (aqtiuri

simZlavris balansi) erTad warmoadgens Tbosadgurebsa da

maregulirebel hidroeleqtrosadgurebs Soris aqtiuri

datvirTvis optimaluri ganawilebis ZiriTad da, amasTan,

aucilebel pirobas 1,2.

miRebuli gantolebebidan SeiZleba dadgindes mamravlis

fizikuri arsi am gantolebebidan

kg/m3

Aanu

,

sadac warmoadgens mabalansirebeli Tbosadguris simZlavres.

Tu warmoebulebs SevcvliT mcire nazrdebiT miviRebT

(34)

74

Tu romelime -uri maregulirebel hidrosadgurze datvirTva

Seicvleba sididiT, maSin igi unda dabalansdes

mabalansirebeli sadguris mier, e.i. maSasadame gvaqvs

kg/m3 (35)

e.i. mamravli gviCvenebs hidrosadgurze wylis xarjis

erTi erTeuliT (m3) Secvlisas ra raodenobiT Seicvleba

saTbobis xarji (kg) mabalansirebel Tbosadgurze. mas mocemuli

hidrosadgurisTvis hidroresursis gamoyenebis efeqturobis

koeficients uwodeben.

niSani `minusi~ miuTiTebs, rom -ur maregulirebel

hidrosadgurze wylis xarjis zrda Tbosadgurze gamoiwvevs

saTbobis xarjis Semcirebas da piriqiT.

(31)-is da (32)-is gaTvaliswinebiT

(36)

radgan sistemis maqsimaluri datvirTvis reJimSi, rogorc

mabalansirebeli Tbosadguri, aseve calkeuli maregulirebeli

hesi daaxloebiT (8085)% datvirTviT muSaobs, SegviZlia

mamravli miaxloebiT ase CavweroT:

. . დადგ

, , .დადგ (37)

aq zeda indeqsi (0) miuTiTebs mas, rom mamravlis

mniSvneloba aRebulia miaxloebiT (nulovani miaxloebiT) da

amocanis amoxsnis procesSi iteraciuli gziT dazustdeba.

–sidideebis gamoTvlis Semdeg SegviZlia ganvsazRvroT P

Semdegi gamosaxulebidan

P , ∑ a 2b P , a ∑µ P ,

,a ∑ Pდან.სადგ Pდატვ,

∆P 0 (38)

75

xolo , da , saZiebeli cvladebi viangariSoT Semdegi

gamosaxulebebiT

, 2 , (39)

, 2 , (40)

cvladTa mniSvnelobebi unda Semowmdes SezRudvis

utolobiT. Tu romelime maTgani dairRva, maSin (38)-Si Caismeba am

cvladis qveda an zeda zRvruli mniSvneloba imisda mixedviT Tu

romel mxares dairRva SezRudvis utoloba mocemuli

cvladisTvis, romlis Semdeg ganisazRvreba , axali

mniSvneloba da Semdeg (39) da (40) gamosaxulebebiT , da ,

Sesabamisad. es procedura gagrZeldeba manam, sanam SezRudvis

utolobebi ar dakmayofildeba yvela saZiebeli cvladisaTvis.

amis Semdeg saWiroa Semowmdes yoveli maregulirebeli

hidrosadgurisTvis wylis limiti dReRamis intervalSi. yoveli

saaTisaTvis. TiToeuli hesisaTvis gamoiTvleba wylis

dReRamuri xarji

3600 · ∑ , , , (41) romlis Semdeg ganisazRvreba wylis dReRamuri xarji

hidrosadgurze.

Tu TiToeuli hesisTvis dasaSvebze metad ar

gansxvavdeba mocemuli ,ლიმიტ sididisagan, maSin angariSi

damTavrebulad CaiTvleba. Tu romelime hesze wylis xarji

metad gansxvavdeba limitisagan, maSin saWiroa dazustdes -is

mniSvneloba Semdegi gamosaxulebiT

λ λ 1Q

Q ,ლიმიტ, (42)

romlis Semdeg gameorebiT CatardebaE(39-40) gantolebaTa

sistemis amoxsnis procedura.

76

$3.4 maTematikuri modeli saqarTvelos

eleqtrosistemis magaliTze

saqarTvelos energosistemaSi aris Tbosadgurebi: me-9, me-3,

me-4 energoblokebi da airturbinuli sadguri ori blikiT,

maregulirebeli hidrosadgurebi: engurhesi, xramesi 1, Jinvalhesi,

Saorhesi, tyibulhesi da maTTan kaskadSi momuSave sezonur

hidrosadgurebi: vardnilhesi, xramhesi 2, zahesi, orTaWalhesi,

varcixehesi.

energosistemis datvirTvis optimaluri ganawilebis amocanis

kriteriums warmoadgens, saangariSo periodSi Tbosadgurze

energoresursis (saTbobis) jamuri xarjis minimumebi.

Sesabamisad miznis funqcias aqvs saxe

აირტ, აირტ, (43)

kavSiris gantolebebis saxiT ganixileba Tbo da

hidroeleqtrosadguris saxarjo maxasiaTeblebi muSaobaSi

CarTuli agregatebis Semadgenlobis gaTvaliswinebiT romelic

dadgenilia $2.3 –Si da romlebic kavSirs amyarebs sadguris

(mgvt) datvirTvasa da pirveladi energoresursis kg/sT an

m3/wm xarjs Soris.

me-9 bloki

T 12250 257.61P 0.196

me-3,4 bloki

T 7614.9 272.71P 0.293

#1,2 airturbina

5517.1+170.38P+2.617P

engurhesi

11,24 0,202 0,1 · 10

14,35 0,202 0,5 · 10

18,18 0,202 0,33 · 10

22,13 0,202 0,25 · 10

26,02 0.202 0.2 · 10

77

xramhesi 1

0,91 0,27 0,6 · 10

1,28 0,27 0,3 · 10

1,73 0,27 0,2 · 10

    Jinvalhesi

1,397 0,802 0,12 · 10

1,96 0,802 0,6 · 10

2,62 0,802 0,4 · 10

3,28 0,802 0,3 · 10

Saorhesi

0,21 0,21 0.33 · 10

0,39 0,21 0,15 · 10

0,47 0,21 0,1 · 10

0,61 0,21 0,75 · 10

tyibulhesi

1,29 0,27 4,7 · 10

2,12 0,27 2,35 · 10

3,1 0,27 1,57 · 10

4,1 0,27 1,17 · 10

vardnilhesis

3,79 1,8 1,3 · 10

6,5 1,8 0,65 · 10

9,0 1,8 0,43 · 10

xramhesi 2

1,78 0,3 0,5 · 10

2,36 0,3 0,25 · 10

 

 

78

zahesi 1 ( ori agregati TiToeuli 12 mgvt)

3,02 5,81 3 · 10

4,67 5,81 1,5 · 10

zahesi 2- ( oTxi agregati TiToeuli 12 mgvt)

0,27 5,93 13 · 10

0,7 5,93 6,5 · 10

1,1 5,93 4,3 · 10

1,4 5,93 3,3 · 10

orTaWalhesi

9,3 8,9 0,37

14,4 8,9 0,19

19,7 8,9 0,12

varcixehes 1,2,3,4

14,87 6,17 3,3 · 10

21,5 6,17P 1,7 · 10

am gamosaxulebebSi indeqsi 1,2,3,4 miuTiTebs muSaobaSi

erTdroulad CarTuli hidroagregatebis raodenobas.

SezRudvis gantolebaTa saxiT gvaqvs:

a) aqtiuri simZlavris balansis gantoleba dReRamis

intervalSi yoveli saaTisaTvis

∑ wyalsac. ∑ kaskad. ∑ danarC. ∑ Tbo. ∑ momxm ∆ (44)

sadac:

∑ wyalsac. eng. xr1. Jinv. Saori. tyib.

∑ kaskad. vard.. xr2. zah1,2. orTaW. varc. 1,2,3,4.

∑ dan. gum 1. gum2.+ rioni. laj. CiT. xad.

sacx. TeTrix. marty. awh. bJuJa. mcire.

∑ Tbo. me_9. me_3,4. airt.1,2.

b) yoveli maregulirebeli (wyalsacaviani)

hidrosadgurisTvis wylis limiti dReRamis intervalSi

79

Weng. =3600∑ Qენგ. Qლიმ. 0

Wხრ.1. =3600∑ Qხრ. . Qხრ. .ლიმ. 0

Wჟინვ. =3600∑ Qჟინვ. Qჟინვ.ლიმ. 0

Wშაორი. =3600∑ Qშაორი. Qშაორი.ლიმ. 0

Wტყიბ,. =3600∑ Qტყიბ. Qტყიბ.ლიმ. 0

sadac: , _ -uri sadgurze wylis xarji saaTze, m3/wm;

, _ -uri sadguris wylis xarjvis dReRamuri limiti

m3/dReRame

SezRudvis utolobaTa saxiT gvaqvs ekonomikuri datvirTvis

(mgvt) intervalebi, romlebic dadgenilia $2.3-Si da naCvenebia

(4) cxrilSi.

engurhesi

muSaobaSi CarTulia: erTi agregati 0 220

ori agregati 220 440

sami agregati 440 660

oTxi agregati 660 880

xuTi agregati 880 1300

xramhesi 1

muSaobaSi CarTulia: erTi agregati 0 37,8

ori agregati 37,8 75

sami agregati 75 112

Jinvalhesi

muSaobaSi CarTulia: erTi agregati 30 32,5

ori agregati 32,5 55

sami agregati 55 70

aq erTi agregatis SemTxvevaSi qveda zRvari 30 mgvt

ganpiribebulia q. Tbilisis wyalmomaragebis moTxovnebis

gaTvaliswinebiT.

Saorhesi

muSaobaSi CarTulia: erTi agregati 0 9

80

ori agregati 9 . 18

sami agregati 18 27

tyibulhesi

muSaobaSi CarTulia: erTi agregati 0 20

ori agregati 20 40

sami agregati 40 60

oTxi agregati 60 80

vardnilhesi

muSaobaSi CarTulia: erTi agregati 0 60

ori agregati 60 . 115

sami agregati 115 220

xramhesi 2

muSaobaSi CarTulia: erTi agregati 0 55

ori agregati 55 . 110

zahesi 1

muSaobaSi CarTulia: erTi agregati 0 12

ori agregati 12 . 24

zahesi 2

muSaobaSi CarTulia: erTi agregati 0 3,2

ori agregati 3,2 6,4

sami agregati 6,4 9,6

oTxi agregati 9,6 12,8

orTaWalhesi

muSaobaSi CarTulia: erTi agregati 0 6

ori agregati 6 . 12

sami agregati 12 18

varcixehesi

muSaobaSi CarTulia: erTi agregati 0 23

ori agregati 23 . 46

SegviZlia SevadginoT lagranJis funqcia:

81

=∑ 12250 257.6Pმე 0.196Pმე 7614.9 272.71Pმე

0.293Pმე 7614.9 272.71Pმე 0.293 Pმე 5517.1

170,38Pაირტ, 2,617 Pაირტ, 5517.1 170,38Pაირტ, 2,617 Pაირტ, )

+ ∑ ( eng. xr1. Jin. Saori. tyib. me_9. me_3,4. Pმე

Pairt.1+ Pაირტ. Pvard.. xrami 2. zah1 Pზაჰ. PorTaW. varc1 ვარც.

ვარც, + ვარც. გუმ. gum2 rioni. laj. CiT. xad.gum

gum2 rioni. laj. CiT. xad. sacx. TeTrix. marty

awh. bJuJa. mcire._ momxm ∆ )+eng.3600∑ 26,02 0.202P

0.2 · 10 P Qენგ.ლიმიტ λხრ. 3600 ∑ 1,73 0,27P 0,2 · 10

Qხრ. .ლიმიტ λჟინ[3600∑ 3,28 0,802P 0,3 · 10 P Qჟინვ.ლიმიტ ®

λშაორ. 3600∑ 0,61 0,21 0,75 · 10 Qშაორ.ლიმიტ λტყიბ.[3600

∑ 4,1 0,27 1,17 · 10 Qტყიბ.ლიმიტ

xazgasmiT unda avRniSnoT, rom saxarjo maxasiaTeblebi

aRebulia im SemTxvevisTvis, roca sadgurze muSaobaSi CarTulia

yvelაAAagregati. maTiM optimaluri Semadgelobis dadgena

moxdeba kompiuterul programaSi Sesabamisi algoriTmis

mixedviT.

rogorc $3.3-Si iyo aRniSnuli , warmoadgens lagranJis

ganusazRvrel mamravlTa simravles. igi gviCvenebs

hidrosadgurze wylis xarjis erTi erTeuliT (m3) Secvlisas ra

raodenobiT Seicvleba saTbobis xarji (kg) mabalansirebel

Tbosadgurze (Cven SemTxvevaSi mabalasirebeli Tbosadguria me-9

bloki).

gaangariSebis sawyis (pirvel) etapze SeiZleba ganvsazRvroT

TiToeuli maregulirebeli hesis sidide (37) gamosaxulebis

Sesabamisad:

λენგმე მე . ·Pმე ,დადგ

ენგ ენგ , , ენგ.დადგ=

. · . · . ·

. · . · . ·0.401kg/m3

ხრ. = . · . · . ·

. · . · · . · .0.320 kg/m3

82

ჟინ.. · . · . ·

. · . · . · .0.117 kg/m3

λშაორ.. · . · . ·

. · . · . · .0.391 kg/m3

λტყიბ.. · . · . ·

. · . · . ·0.238 kg/m3

im SemTxvevaSi, roca romelime maregulirebeli sadgurisaTvis

wylis dReRamuri xarji dasaSvebze metad gansxvavdeba

limitisagan, maSin saWiroa am sadgurisaTvis dazustdes

mamravlis miRebuli mniSvneloba (42) formuliT.

$3.5 optimizaciis amocanis

amoxsnis meTodis SerCeva

$2.3-Si aRiniSna, rom Camoyalibebuli optimizaciis amocanis

amoxsna SesaZlebelia pirdapiri meTodiT da lagranJis

ganusazRvrel mamravlTa meTodiT.

rogorc detalurma analizma gviCvena, eleqtroenergetikuli

xasiaTis amocanebis, erZod eleqtrosadgurebs Soris

datvirTvis optimaluri ganawilebis amocanis amoxsnisTvis ufro

moxerxebuli aRmoCnda grafikuli meTodi.

eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis ZiriTad pirobas warmoadgens sadgurze pirveladi

energoresursis fardobiTi nazrdis toloba (gamosaxuleba 33,

$2.3)

… 3600 3600

sadac: _mabalasirebeli Tbosadguris pirveladi

energoresursis fardobiTi nazrdi;

, … _fadobiTi nazrdi TbosadgurebisaTvis;

, … _fardobiTi nazrdi

hidrosadgurebisTvis.

83

eleqtrosadgurebs Soris datvirTvis optimaluri

ganawilebis grafikuli meTodi gulisxmobs sadgurebis

datvirTvaTa gansazRvras pirveladi energoresursis fardobiTi

nazrdis grafikebis gamoyenebiT. amisaTvis saWiroa aigos

fardobiTi nazrdis 2b grafikebi yvela

eleqtrosadgurisTvis (nax.25)

nax.25 fardobiTi nazrdis grafikebi

gaangariSebis sawyis etapze viRebT pirveladi

energoresursis fardobiTi nazrdis raime mniSvnelobas,

risTvisac sakmarisia SevirCioT mabalansirebeli sadguris

datvirTvas dReRamis mocemul saaTze sistemis jamuri

datvirTvis Seabamisad. am sididis mixedviT ganvsazRvravT

2b da, Sesabamisad, pirveladi energoresursis

fardobiTi nazrdis grafikebis daxmarebiT (nax.25) davadgenT

sadgurebis … … . … . mniSvnelobebs, romelTa

mixedviT gamovTvliT aqtiuri simZlavris ubalansobas

∆Pუბ ∑ P Pდანარჩ.სადგ Pმომხ._∆P

Tu aqtiuri simZlavris ubalansoba dasaSveb farglebSia,

maSin sadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis amocana amoxsnilia mocemuli saaTisaTvis.

winaaRmdeg SemTxvevaSi ubalansobis proporciulad Seicvleba

84

mabalansirebeli sadguris datvirTvis mniSvneloba da

amoxsnis procedura daiwyeba Tavidan. es iteraciuli procesi

gagrZeldeba manam, sanam aqtiuri simZlavris ubalansoba

winaswar SerCeul sidideze naklebi ar gaxdeba.

III Tavis daskvna

am TavSi Catarebulia eleqtrosistemaSi eleqtrosadgurebs

Soris aqtiuri datvirTvis ganawilebis optimizaciis amocanis

gantolebaTa sistemis analizi. ganxilulia aseTi saxis

amocanaTa amoxsnis meTodebi da Sefasebulia am meTodebis

gamoyenebis sferoebi.

sadgurTa saxarjo maxasiaTebelTa maTematikuri

gamosaxulebebis safuZvelze Sedgenilia miznis fuqcia,

SezRudvis gantolebaTa da SezRudvis utolobaTa sistema.

dasmuli amocanis Sesabamisad miznis funqcias warmodgens

Tbosadgurebze pirveladi energoresursis anu saTbobis jamuri

xarji, SezRudvis gantolebis saxiT ganixileba energosistemaSi

aqtiuri simZlavris balansis gantoleba, xolo SezRudvis

utolobaTa saxiT ganixileba energoblokebis minimaluri da

maqsimaluri dasaSvebi datvirTvebi.

eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis Tematikuri modeli Cawerilia konkretulad

saqarTvelos energosistemis magaliTze.

amave TavSi naCvenebia, rom dasmuli amocanis amoxsnisas

kompiuterizaciis TvalsazrisiT, ufro moxerxebulia

gamoyenebuli iqnes amocanis amoxsnis grafikuli meTodi, rac

gulisxmobs pirveladi enrgoresursis fardobiTi nazrdis

tolobas yvela eleqtrosadgurisaTvis.

85

gamoTvlilia da TiToeuli maregulirebeli hesisTvis

mocemulia lagranJis mamravlis ricxviTi mniSvnelobebi,

romelic am hesis hidroresursis gamoyenebis efeqturobis

koeficients warmoadgens.

 

 

 

86

Tavi 4. amocanis amoxsnis algoriTmizacia-programireba

$4.1. sawyisi informaciis momzadeba

optimizaciis amocanis amoxsna grafikul meTodiT

ganxorcielda saTanado algoriTmis safuZvelze. romelSic,

,,Visual Basic”-is programul enaze Seiqmna programa, romlis

saSualebiTac sadgurebs Soris aqtiuri datvirTvis optimaluri

ganawileba Sesrulda am sadgurebze muSaobaSi CarTuli

agregatebis optimaluri ricxvis dadgenasTan erTad. rac Seexeba

Sigasasadguro optimizacia ganxorcieldeba sadguris

ekvivalenturi maxasiaTeblis bazaze, romelic dadgenilia $2.3.-Si

da Setanilia cxril 4-Si.

optimizaciis gantolebaTa sistema, rogorc ukve avRniSneT

moicavs miznis funqcias (43), aseve SezRudvis gantolebebs

da utolobebs. SezRudvis gantoleba Cvens SemTxvevaSi

warmoadgens balansis gantolebas (44).

programuli gaangariSebis sawyis etapze, sawyis informaciad

aRebulia ekvivalenturi saxarjo maxasiaTebeli sadgurze

dadgmuli yvela agregatis gaTvaliswinebiT.

engurhesi _ (xuTi agregati)

26,02 0.202 0.2 · 10

xramhesi _ (sami agregati)

1,73 0,27 0,2 · 10

Jinvalhesi _ (oTxi agregati)

3,28 0,802 0,3 · 10

Saorhesi _ (oTxi agregati)

0,61 0,21 0,75 · 10

tyibulhesi _ (oTxi agregati)

4,1 0,27 1,17 · 10

vardnilhesis _ (sami agregati)

9,0 1,8 0,43 · 10

xramhesi 2 _ (ori agregati)

2,36 0,3 0,25 · 10

87

zahesi 1 ( ori agregati TiToeuli 12 mgvt)

4,67 5,81 1,5 · 10

zahesi 2- ( oTxi agregati TiToeuli 12 mgvt)

1,4 5,93 0,33 · 10

orTaWalhesi _ (sami agregati)

19,7 8,9 0,12

varcixehes 1,2,3,4_ (ori agregati)

21,5 6,17P 1,7 · 10

pirvel miaxloebaSi SeirCeva engurhesis pirobiTi

fardobiTi nazrdi da gavrceldeba igi mTeli sistemisaTvis

სისტ. ენგ. ენგ. 2 ენგ. ენგ. ენგ. (45)

Semdeg tolobidan ganisazRvreba maregulirebel

sadgurebze aqtiuri datvirTva i0. i·λ2b·λ

. kerZod,

ხრ,სისტ. ხრ. .· ხრ

ხრ. · ხრ.

ჟინვ.სისტ. ხჟინვ.. ჟინვ

2bჟინვ· ჟინვ

შაორსისტ. შაორ.· შაორ

2bშაორ·შაორ

ტყიბ.სისტ. ტყიბ.. ტყიბ

2bტყიბ.· ტყიბ.

მესისტ. მე . მე

2bმე .· მე .

am tolobbebSi calkeuli sadgurebisaTvis mudmivi sididea

da ar aris damokidebuli muSaobaSi CarTuli agregatTa

raodenobaze, xolo icvleba sadgurze muSaobaSi CarTul

agregatTa ricxvis Sesabamisad (ix. cxr. 4)

88

sadgurebs Soris aqtiuri datvirTvis optimaluri ganawilebis

amoxsnis pirvel etapze, mosalodnelia, rom ama Tu im sadgurze

muSaobaSi CarTuli agregatTa maqsimaluri Semadgenloba iyos

araoptimaluri, amitom saWiroa Semadgenlobis koreqtireba, rac

gaangariSebis Semdeg etapze Sesruldeba.

aRsaniSnavia, rom mocemuli sadguris agregatTa

Semadgenlobis Secvla ganxorcieldeba sadguris ekvivalenturi

saxarjo maxasiaTeblis SecvliT (cxr.2.4), rac gamoiwvevs

sadgurebs Soris datvirTvis optimaluri ganawilebis

koreqtirebas.

ris Semdeg, dReRamis mocemul saaTze dadgindeba

maregulirebeli sadgurebis optimaluri datvirTva da

agregatTa optimaluri Semadgenloba. agregatTa am

Semadgenlobis Sesabamisi saxarjo maxasiaTeblis mixedviT

ganisazRvreba wylis xarji mocemul hidrosadgurze m3/wm.

Qენგ. Q ენგ. b Pენგ,

Qხრ1. Q ხრ. b Pხრ.

Qჟინვ, Q ჟინვ. b Pჟინვ

Qშაორ, Q შაორ. b Pშაორ,

Qტყიბ.Q ტყიბ. b Pტყიბ,

sadac _ agregatTa optimaluri Semadgenloba dReRamis

mocemul saaTze.

rogoc $1.1-Si iyo aRniSnuli maregulirebel

hidrosadgurebTan kaskadSi muSaobs sezonuri hidrosadgurebi

Semdegi sqemiT:

engurhesi vardnilhesi;

Saorhesi tyibulhesi varcixehesi 1,2,3,4;

Jinvalhesi zahesi orTaWalhesi;

xramhesi 1 xramhesi 2.

aqedan gamomdinare mocemul saaTze maregulirebeli

hidrosadgurebis wylis dadgenili xarji ∆ drois Semdeg

Caedineba sezonur kaskadur hesSi, rac am hesis saxarjo

89

maxasiaTeblis Sesabamisad saSualebas mogvcems ganvsazRvroT

misi aqtiuri datvirTva.

P ∆

· Q Q Qშემ

sadac sezonuri kaskaduri hesi;

uri maregulirebeli hidrosadguri, romlis kaskadSi

muSaobs uri sezonuri hesi;

შემ sezonur hesisi Semonadeni.

am gamosaxulebaSi , da aRebulia im SemTxvevisTvis,

roca mocemul sezonur hesze muSaobaSi CarTulia yvela

agregati. miRebuli sididis mixedviT SeirCeva agregatTa

optimaluri Semadgenloba am sagurze (cxr.4) da ganmeorebiT

dadgindeba P ∆ datvirTva.

aseTi gaangariSebebi maregulirebel hesebze da sezonur

hesebze Sesruldeba dReRamis ganmavlobaSi yovel saaTisTvis.AA

Semdeg ganisazRvreba wylis xarji dReRamis intervalSi

yvela maregulirebel hesze: Qენგ ∑ Q ,ენგ,

Qხრ. ∑ Q ,ხრ, , Qჟინვ ∑ Q ,ჟინვ, Qშაორ. ∑ Q ,შაორ., Qტყიბ ∑ Q ,ტყიბ. da

TiToeuli maregulirebeli hesiiTvis Sefasdeba wylis

dReRamuri limitis gamoyenebis faqti.

gamoTvlaTa am ciklis gamoTvlebi damTavrebulad CaiTvleba

Tu TiToeuli maregulirebeli hesisTvis sruldeba piroba

Q Q ლიმ ∆ ,

sadac ∆ wylis dReRamuri xarjis dasaSvebi cdomilebaa.

Tu romelime maregulirebel hidrosadgurze ar Sesruldeba

aRniSnuli utoloba, maSin Sesabamisad am HhesisTvis moxdeba λ

mamravlis koreqtireba (42) formuliT.

$4.2 amocanis algoriTmi

1. 1

90

2. sist ,danarC sadac ,danarC vard.. xr. 2. zah1 zah.2

orT. varc. 1,2,3,4. danarC

3. eng. 0,6 · Cawers eng. ujraSi

4. Tu 0 eng. 220 ki, maSin aiRebs 1.1 da gadava me-9-ze, Tu

ara, maSin gadava me-5-ze.

5. Tu 220 eng. 440 ki, maSin aiRebs 1.2 da gadava me-9-ze,

Tu ara, maSin gadava me-6-ze.

6. Tu 440 eng. 660 ki, maSin aiRebs 1.3 da gadava me-9-ze,

Tu ara, maSin gadava me-7-ze.

7. Tu 660 eng. 880 ki, maSin aiRebs 1.4 da gadava me-9-ze,

Tu ara, maSin gadava me-8-ze.

8. Tu 880 eng. 1300 ki, maSin aiRebs 1.2 da gadava me-9-ze.

9. sist eng. 2 eng.· eng. eng.

10. xr.1 . . · .

, · , Cawers xr.1. ujraSi

11. Tu xr.1 0 ki, maSin xr.1 0 da gadava 17-ze da ara 12-ze.

12. Tu xr.1 112 ki, maSin xr.1 112 da gadava 17-ze, Tu ara,

maSin gadava13-ze.

13. Tu 0 xr.1 37,8 ki, maSin aiRebs 2,1 -s da gadava 16-ze, Tu

ara maSin gadava 14-ze

14. Tu 37,8 75 ki, maSin aiRebs 2,2 -s da gadava 16-ze, Tu

ara maSin gadava 15-ze.

15. Tu 75 112 ki maSin aiRebs 2,3 -s da gadava 16-ze.

16. xr.1. · ,

· ,

17. Cawers xr.1. ujraSi

18. Jin.. · ,

, · ,

19. Tu Jin 30 ki, maSin Jin 30 gadava 26-ze, Tu ara maSin

gadava 20-ze.

20. Tu Jin 30 ki, maSin Jin 90 gadava 26-ze, Tu ara maSin

gadava 21-ze.

21. Tu 30 32,5 ki, maSin aiRebs 3,1 -s da gadava 25-ze, Tu

ara maSin gadava 22-ze.

91

22. Tu 32,5 55 ki, maSin aiRebs 3,2 -s da gadava 25-ze, Tu

ara maSin gadava 23-ze.

23. Tu 55 70 ki, maSin aiRebs 3,3 -s da gadava 25-ze, Tu

ara maSin gadava 24-ze.

24. Tu 70 90 ki, maSin aiRebs 3,4 -s da gadava 25-ze.

25. Jin.. · ,

· ,

26. . Cawers Jin.. ujraSi.

27. Saori.. · ,

, · ,

28. Tu Saori 0 ki, maSin Saori 0 gadava 35-ze, Tu ara maSin

gadava 29-ze.

29. Tu Saori 38 ki, maSin Saori 38 gadava 35-ze, Tu ara maSin

gadava 30-ze.

30. Tu 0 9 ki, maSin aiRebs 4,1 -s da gadava 34-ze, Tu

ara maSin gadava 31-ze.

31. Tu 9 18 ki, maSin aiRebs 4,2 -s da gadava 34-ze, Tu

ara maSin gadava 32-ze.

32. Tu 18 27 ki, maSin aiRebs 4,3 -s da gadava 34-ze, Tu

ara maSin gadava 33-ze.

33. Tu 27 38 ki, maSin aiRebs 4,4 -s da gadava 34-ze.

34. Saori.სისიტ. ·LAM ,

B ·LAM , Cawers 35-Si

35. Saori -Si

36. ty.სისიტ. · ,

, · ,

37. Tu ty. 0 ki, maSin ty. 0 gadava 44-ze, Tu ara maSin gadava

38-ze.

38. Tu ty. 80 ki, maSin ty. 80 gadava 44-ze, Tu ara maSin

gadava 39-ze.

39. Tu 0 20 ki, maSin aiRebs 5,1 -s da gadava 43-ze, Tu

ara maSin gadava 40-ze.

40. Tu 20 40 ki, maSin aiRebs 5,2 -s da gadava 43-ze, Tu

ara maSin gadava 41-ze.

92

41. Tu 40 60 ki, maSin aiRebs 5,3 -s da gadava 43-ze, Tu

ara maSin gadava 42-ze.

42. Tu 60 80 ki, maSin aiRebs 5,4 -s da gadava 43-ze.

43. ty.სისიტ. · ,

, · ,

44. ty. -Si

45 ty.

· ,

· , ·38

46. Tu m/s. 100 ki, maSin m/s. 100 gadava 48-ze, Tu ara maSin

gadava 47-ze.

47. Tu m/s. 100 ki, maSin m/s. 100 gadava 48-ze, Tu ara maSin

gadava 48-ze.

48. m/s. Cawers m/s. -ujraSi

49. სისიტ · ,

, · ,

50. Tu 210 ki, maSin 210 gadava 52-ze, Tu ara maSin

gadava 51-ze.

51. Tu 270 ki, maSin 100 gadava 52-ze, Tu ara maSin

gadava 52-ze.

52. Cawers -ujraSi.

53. სისიტ. · ,

· , · , Cawers 55-Si.

54. Tu 80 ki, maSin 80 gadava 55-ze, Tu ara maSin gadava

54-ze.

55. Tu 140 ki, maSin 140 gadava 55-ze, Tu ara maSin

gadava 55-ze.

56. Cawers -ujraSi.

57. სისიტ. · ,

· , · , Cawers 4 -Si.

58. Tu 80 ki, maSin 80 gadava 59-ze, Tu ara maSin gadava

58-ze.

59. Tu 140 ki, maSin 140 gadava 59-ze, Tu ara maSin

gadava 59-ze.

60. Caiwerebas -ujraSi.

93

61. a/t სისიტ. · ,

· ,

62. Tu a/t. 0 ki, maSin a/t. 0 gadava 66-ze~, Tu ara maSin

gadava 62-ze.

63. Tu a/t. 110 ki, maSin a/t. 110 gadava 66-ze~, Tu ara maSin

gadava 63-ze.

64. Tu 0 55 ki, maSin aiRebs 9,1 -s da gadava 65-ze, Tu

ara maSin gadava 64-ze.

65. Tu 60 80 ki, maSin aiRebs 9,2 -s da gadava 65-ze.

66. a/t სისიტ. · ,

· ,

67. Cawers a/t.. ujraSi.

68. ub. ∑ 613 eng. xr.1 Jin. Saori ty. m/s ,

a/t(1-2)

69. Tu ub. 10 ki, gadava70-ze, Tu ara maSin gadava 69-ze.

70. eng. eng. 0,2 ub. Caiweros eng. ujraSi da gadava

4-ze.

71. ,eng

72. eng. 1, 1 1, ·

73. ,eng. Cawers eng. ujraSi.

74. vard.

, · ,

· , Caiwereba

79-Si.

75. Tu vard. 220 ki, maSin vard. 220 Caiwereba vard.

Tu ara maSin gadava 74-ze.

76. Tu 0 vard. 60 ki, maSin aiRebs 11,1 -s gadava 77-ze,

Tu ara maSin gadava 75-ze.

77. Tu 60 vard. 115 ki, maSin aiRebs 11,2 -s gadava 77-ze,

Tu ara maSin gadava 76-ze.

78. Tu 115 vard. 220 ki, maSin aiRebs 11,3 -s gadava 77-

ze.

79. vard.

, · ,

· ,

94

80. Caiwereba vard. ujraSi.

81. Tu 1 24 ki vard Caiwereba vard ujraSi.

82. ,xr.1. 2, 2 2, · Caiwereba xr.1. ujraSi.

83. xr.2

, · , . ,

· , Caiwereba

xr.2 – ujraSi.

84. Tu xr.2 110 ki, maSin xr.2 110 Caiwereba xr.2 –

ujraSi da gadava 84-ze, Tu ara gadava 81-ze.

85. Tu 0 xr.2 55 ki, maSin aiRebs 12,1 -s da gadava 83-ze,

Tu ara gadava 82-ze.

86. Tu 55 xr.2 110 ki, maSin aiRebs 12,2 -s da gadava 83-

ze.

87. xr.2

, · , . ,

· , Caiwereba

xr.2 – ujraSi.

88. Tu 1 24 ki, maSin xr.2 Caiwereba xr.2 ujraSi.

89. Jin. 30 0 30 32,5

90. ,Jin. 3, 3 3, · Caiwereba

Jin. ujraSi.

91. z.1

, · , .

· , Caiwereba z.1 –

ujraSi.

92. Tu z.1 24 ki maSin z.1 24 Caiwereba z.1 ujraSi

da gadava 91-ze, Tu ara gadava 88-ze.

93. Tu z.1 12 ki, maSin aiRebs 13,1 -s da gadava 90-ze, Tu

ara gadava 89-ze.

94. Tu z.1 24 ki, maSin aiRebs 13,2 -s da gadava 90-ze.

95. z.1

, · , .

· , Caiwereba z.1 –

ujraSi.

96. Tu z.1 24 ki, maSin z.1 Caiwereba z.1 ujraSi.

95

97. z.2

, · , .

· , Caiwereba z.2 –

ujraSi.

98. Tu z.2 12,8 ki maSin z.2 ujraSi Caiwereba da

gadava 99-ze, Tu ara gadava 94-ze.

99. Tu 0 z.1 3,2 ki, maSin aiRebs 14,1 -s da gadava 97ze,

Tu ara gadava 95-ze.

100. Tu 3,2 z.1 6,4 ki, maSin aiRebs 14,2 -s da gadava 98-

ze, Tu ara gadava 96-ze.

101. Tu 6,4 z.1 9,6 ki, maSin aiRebs 14,3 -s da gadava 98-

ze, Tu ara gadava 97-ze.

102. Tu 9,6 z.1 12,8 ki, maSin aiRebs 14,4 -s da gadava 98-

ze,

103. z.2

, · Q , Qჟინვ.

· ,

104. Tu 5 24 ki maSin z.2 Caiwereba z.1 ujraSi.

105. orT.

, · , ჟინვ.

· , Caiwereba

orT. – ujraSi.

106. Tu orT. 18 ki maSin orT. Caiwereba orT.

ujraSi da gadava 106-ze, Tu ara gadava 102-ze.

107. Tu 0 orT. 6 ki, maSin aiRebs 15,1 -s da gadava 108-

ze, Tu ara gadava 103-ze.

108. Tu 6 z.1 12 ki, maSin aiRebs 15,2 -s da gadava -ze,

Tu ara gadava 104-ze.

109. Tu 12 z.1 18 ki, maSin aiRebs 15,3 -s da gadava 105-

ze,

110. orT.

, · , ჟინვ.

· ,

111. Tu 11 24 ki maSin orT. Caiwereba orT.

ujraSi.

96

112. Saori ,Saori. 4, 4 4, · Caiwereba

Saori. ujraSi.

113. ty. ,ty. 5, 5 , · Caiwereba

ty. ujraSi.

114. varc.

, · , .

· ,

115. Caiwereba orT. – ujraSi, orT. – ujraSi, orT. –

ujraSi, orT. – ujraSi,

116. Tu varc.1 46 ki, maSin varc.1 46 da Caiwereba

varc.1 ujraSi, analogiuria varc.2, varc.3, varc.4

ujraSi.

117. Tu 0 varc.1 46 ki, maSin aiReba 17,1 gadeava 113-ze,

Tu ara gadava 112-ze.

118. Tu 23 varc.1 46 ki, maSin aiReba 17,2 gadeava 113-ze.

119. varc.1

, · , .

· ,

120. Caiwereba varc1 varc.2, varc.3, varc.4 ujraSi.

121. Tu 6 24 ki maSin varc.1 Caiwereba varc.1

ujraSi.

122. Tu 7 24 ki maSin varc.2 Caiwereba varc.2

ujraSi.

123. Tu 8 24 ki maSin varc.3 Caiwereba varc.3

ujraSi.

124. Tu 9 24 ki maSin varc.4 Caiwereba varc.4

ujraSi.

125. 1

126. Tu 24 ki, maSin gadava 2-ze, Tu ara gadava 120-ze.

127. 1

128. ub. eng. xr.1. Jin. Saori. tyib m/s vard.. xrami

2. zah. orTaW. varc. 1,2,3,4. Cam.hes.)

129. Tu უბ. 0 ki maSin gadava 115-ze, Tu ara gadava 123-ze.

ენგ. ენგ. 0,2 უბ. ჩაიწერება ენგ. ujraSi.

97

130. dabrundeba 4-ze.

131. ენგ. ∑ ენგ.

132. Tu ენგ. ენგ.ლიმ. 0,03 ენგ.ლიმ. Tu ki gadava 128-ze, Tu ara

gadava 127-ze.

133. ენგ. ენგ. · ენგ.ლიმ. ენგ.

ენგ.ლიმ. Caiwereba ენგ. ujraSi.

134. ხრ. ∑ ,ხრ.

135. Tu ხრ. ხრ1 .ლიმ. 0,03 ხრ. ლიმ. Tu ki gadava 131-ze, Tu

ara gadava 130-ze.

136. ხრ. ხრ. · ხრ. ლიმ. ხრ.

ხრ. ლიმ. Caiwereba ხრ. ujraSi.

137. .ჟინ. ∑ ,ჟინ.

138. Tu ჟინ. ჟინ.ლიმ. 0,03 ჟინ.ლიმ. Tu ki gadava 134-ze, Tu ara

gadava 133-ze.

139. ჟინ. ჟინ. · ჟინ.ლიმ. ჟინ.

ჟინ.ლიმ. Caiwereba ჟინ. ujraSi.

140. შაორი ∑ ,შაორი

141. Tu შაორი. შაორი.ლიმ. 0,03 შაორი.ლიმ. Tu ki gadava 137-ze,

Tu ara gadava 136-ze.

142. შაორი შაორი · შაორი.ლიმ. შაორი

შაორი.ლიმ. Caiwereba შაორი ujraSi.

143. ტყ. ∑ ,ტყ.

144. Tu ტყ. ტყ.ლიმ. 0,03 ტყ.ლიმ. Tu ki gadava 140-ze, Tu ara

gadava 139-ze.

145. ტყ. ტყ. · ტყ.ლიმ.. ტყ.

ტყ.ლიმ. Caiwereba შაორი ujraSi.

146. Tu .ლიმ. .

.ლიმ.1 0,03 ტყ.ლიმ. Tu ki gadava 141-ze, Tu ara

gadava 4-ze.

147. Tu რეალ.

ლიმ.1 0,03

damTavreba, dabeWdva

98

$4.3 aqtiuri datvirTvis optimaluri ganawileba

saqarTvelos eleqtrosistemaSi kompiuteruli

programis meSveobiT (2008 wlis 17dekemberi)

zemoT aRniSnuli kompiuteruli programis meSveobiT

ganxorcielda optimizaciis amocanis amoxsna saqarTvelos

energosistemis magaliTze. kerZod ganxiluli iqna 2008 wlis 17

dekemberi.

sawyis informaciad programaSi Setanilia sistemis

yovelsaaTuri datvirTva, cxr.5, maregulirebeli

hidrosadgurebis dReRamuri limiti cxr.6.

cxr.5 sistemis datvirTva

cxr.6 wylis dReRamuri limiti

sadguri limiti, Q m3/dR

engurhesi 7665217.39

xramhesi 1 486486.48

Jinvalhesi 310000

Saorhesi 307457.544

tyibulhesi 1511262.8

dro,

sT

datvirTva,

mgvt

1 917

1 857

3 810

4 774

5 810

6 800

7 841

8 928

dro,

sT

datvirTva,

mgvt

17 1197

18 1346

19 1404

20 1399

21 1343

22 1292

23 1208

24 1064

dro,

sT

datvirTva,

mgvt

9 1133

10 1196

11 1216

12 1202

13 1185

14 1187

15 1229

16 1202

99

yoveli sadgurisaTvis mudmivi sididea agregatTa

nebismieri SemadgenlobisTvis, da icvleba muSaobaSi

CarTul agregatTa ricxvis Sesabamisad.

cxr.7 sadgurebis , , sidideebi

sadguri ,m3/wm

,kg/sT

engurhesi 11.24 0.202 0.1· 10

14.35 0.5· 10

18.18 0.33· 10

22.13 0.25· 10

26.02 0.2· 10

xramhesi 1 0.91 0.27 0.6· 10

1.28 0.3· 10

1.73 0.2· 10

Jinvalhesi 1.39 0.802 0.12· 10

1.96 0.6· 10

2.62 0.4· 10

3.28 0.3· 10

Saorhesi 0.21 0.21 0.33· 10

0.39 0.15· 10

0.47 0.1· 10

0.61 0.75· 10

tyibulhesi 1.29 0.27 4.7· 10

2.12 2.35· 10

3.1 1.57· 10

4.1 1.17· 10

vardnilhesi 3.79 1.8 1.3· 10

6.5 0.65· 10

9 0.43· 10

xramhesi 2 1.78 0.3 0.5· 10

2.36 0.25· 10

zahesi 1 3.02 5.8 3· 10

100

4.67 1.5· 10

zahesi 2 0.27 5.93 13· 10

0.7 6.5· 10

1.1 4.3· 10

1.4 3.3· 10

orTaWalhesi 9.3 8.9 0.37

14.4 0.19

19.7 0.12

varcixehesi

1,2,3,4

14.87 6.17 3.3· 10

21.5 1.7· 10

me-9 bloki 12250 257.6 0.305

me-3,4 bloki 7614.9 272.7 0.196

#1,2 airturbina 5517.1 170.38 2.617

maregulirebeli hidrosadgurebisTvis sawyis informaciaSi

Setanilia λ _ mamravlis mniSvneloba, cxr.8 romlis

koreqtireba moxdeba limitis dacvis mizniT

cxr.8 _ mamravlis mniSvneloba

hidrosadguri , kg/m3

engurhesi 0.401

xramhesi 1 0.320

Jinvalhesi 0.117

Saorhesi 0.391

tyibulhesi 0.238

dReRamis yoveli saaTisaTvis sruldeba balansis

gantoleba (29), SezRudvis utolobaTa saxiT gvaqvs ekonomikuri

datvirTvis zRvrebi (cxr.4)

eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis pirobas warmoadgens fardobiTi nazrdebis toloba

(35). rogorc $4.1.-Si aRiniSna სისტ. . pirvel miaxloebaSi

gamoiTvleba engurhesis pirobiTi nazrdi da gavrceldeba igi

mTeli sistemisaTvi e.i სისტ. ენგ.

101

mocemuli saaTisTvis viRebT engurhesis aqtiur datvirTvas

sistemis jamuri datvirTvis Sesabamisad mocemuli saaTisaTvis

Pენგ 0,6 · P sist, sadac, _ P sist sistemis jamuri datvirTvaa

mocemuli saaTisTvis. koeficienti _ 0,6 aRebulia .pirobiTad

Sesabamisad ganvsazRvravT ენგ. is mniSvnelobas (45)

gamosaxulebiT da davadgenT sadgurebis aqtiur datvirTvebs

mocemuli saaTisTvis. Semdeg procesi warimarTeba algoriTmi 4.2-

is Sesabamisad. (ix danarTi)

qvemoT warmodgenilia (cxr.9, nax.26) 2008 wlis 17 dekembrs

realurad arsebuli (sse-is sadReRamiso uwyisi mixedviT)

sadgurebis datvirTuloba, moxmareba da kompiuteruli

programis sauZvelze gaangariSebiT miRebuli monacemebi (cxr.10

da nax.27) igive moxmarebisa da maregulirebeli sadgurebis im

dRes arsebuli wylis limitis dacviT.

102

17 dekemberi 2008 weli (faqtiuri

cxr.9

saaTi

maregulireblebi hidrosadgurebi

mez.sis

t

Tbosa-dgurebi

kaskadSi momuSave hidrosadgurebi

sez

onu

ri

moxmareb

a

enguri

xrami

1

Jinval

i

Sao

ri

tyibuli

me-4 b

loki

me 9-l

oki

vardni

lhesi

xrami

2

zahes

i 1

zahes

i 2

orTaW

ala

varcix

ehes

i 1

varcix

ehes

i 1

varcix

ehes

i 1

varcix

ehes

i 1

1 160  35 32 20 52 62 141 201 0 22 12 80 95 917

2 110  7 32 1 32 97 141 201 0 14 12 80 95 827 3 110  7 32 1 52 69 140 201 0 6 12 80 95 810 4 55  7 32 1 52 83 141 205 0 6 12 80 95 774 5 76  7 32 1 52 97 142 205 0 6 12 80 95 810

6 100  7 32 1 32 83 142 205 0 6 12 80 95 800

7 140  7 32 1 32 83 143 205 0 6 12 80 95 841

8 225 7 32 1 34 83 143 205 0 6 12 80 95 928

9 310 7 32 20 34 111 143 208 50 6 12 100 95 1133

10 400 7 32 20 34 90 143 205 50 3 12 100 95 1196

11 400 19 32 20 51 83 141 208 50 0 12 100 95 1216

12 400 19 32 20 51 69 141 208 50 0 12 100 95 1202

13 380 11 32 20 51 83 139 207 50 0 12 100 95 1185

14 380 11 32 20 51 83 141 207 50 0 12 100 95 1187

15 380 55 32 20 51 90 139 207 50 0 12 100 88 1229

16 380 11 32 20 51 97 141 214 50 0 12 100 88 1202

17 380 11 45 20 51 83 141 210 50 0 12 100 88 1197

18 475 31 65 20 51 97 139 212 50 0 12 100 88 1346

19 500 7 65 20 51 97 141 212 50 55 12 100 88 1404

20 475 19 65 20 51 104 142 212 50 55 12 100 88 1399

21 426 20 65 20 51 97 141 212 50 55 12 100 88 1343

22 350 41 65 20 51 97 141 216 50 55 12 100 88 1292

23 270 41 65 20 51 97 141 212 50 55 12 100 88 1208

24 170 41 45 20 38 90 139 210 50 55 12 100 88 1064

103

nax.26 sistemis datvirTvis grafiki (faqtiuri)

 

104

 17 dekemberi 2008 weli

(programiT)

cxr.10

saaTi

maregulireblebi hidrosadgurebi

mez.sis

t

Tbosa-dgurebi

kaskadSi momuSave hidrosadgurebi

sez

onu

ri

moxmareb

a

enguri

xrami

1

Jinval

i

Sao

ri

tyibuli

me-4 b

loki

me 9-l

oki

vardni

lhesi

xrami

2

zahes

i 1

zahes

i 2

orTaW

ala

varcix

ehes

i 1

varcix

ehes

i 1

varcix

ehes

i 1

varcix

ehes

i 1

1 206  10,8 32,7 10,8 33,6 -12 140 264 46.5 28 8 4 5 11,8 12 11,3 11,3 95 917

2 167  9,1 29,1 9,8 29,5 -22.4 139 248 34.3 25 8 4 5 11,8 12 11,7 11,3 95 827 3 163  8,8 28,4 9,3 28,7 -23.3 139 246 29.3 22 8 4 5 11,7 12 11,8 11,3 95 810 4 148  8,2 26,9 8,7 26,9 -27.7 135 240 28 21 7 4 5 11,5 12 11,8 11,7 95 774 5 166  8,8 28,4 9,2 28,7 -22.2 139 247 27 21 7 3 6 11,3 12 11,7 11,8 95 810 6 162  8,6 28 9,1 28,2 -23 138 245 29 21 6 3 6 11 11 11,5 11,8 95 800 7 183  9,4 29,6 9,7 30,1 -17.8 140 254 28 21 6 3 6 10,6 11 11,3 11,7 95 841 8 230 11 33,1 10,9 34,1 -5.3 140 270 31 21 6 3 6 10,3 11 11 11,6 95 928 9 368 14,8 41,2 13,8 43 31.6 140 270 38 22 6 3 6 10,3 10 10,6 11,6 95 1133 10 399 15,9 43,6 14,7 45,7 39.4 140 270 55 23 7 3 5 10,2 10 10,3 10,9 95 1196 11 408 16,4 44,4 14,9 46,5 42.1 140 270 58 26 5 3 5 10,3 10 10,3 10,6 95 1216 12 397 16,1 43,9 14,8 45,9 39 140 270 60 27 5 3 5 10,3 10 10,2 10,3 95 1202 13 386 15,8 43,2 14,6 45,2 35.8 140 270 57 28 6 3 5 10,4 10 10,3 10,3 95 1185 14 387 15,8 43,3 14,6 45,3 36.5 140 270 57 28 7 4 4 10,6 10 10,3 10,1 95 1187 15 421 16,6 44,9 15,1 47,1 45.6 140 270 57 27 7 4 4 11,1 11 10,4 10,3 88 1229 16 398 16,1 43,9 14,8 45,9 39 140 270 61 27 7 4 4 11,3 11 10,6 10,3 88 1202 17 396 16 43,7 14,7 45,8 38.8 140 270 58.6 28 7 4 4 11,4 11 11,1 10,3 88 1197 18 501 18,7 49,5 16,7 51,8 67 140 270 58 28 7 4 4 11,3 11 11,3 10,6 88 1346 19 531 19,8 51,8 17,5 54,1 74.7 140 270 70 27 7 4 5 11,3 11 11,4 11,1 88 1404 20 521 19,7 51,6 17,5 53,9 72.2 140 270 74 30 7 4 5 11,3 11 11,3 11,3 88 1399 21 482 18,7 49,4 16,7 51,7 62 140 270 73 31 7 4 5 11,4 11 11,3 11,3 88 1343 22 451 17,8 47,4 16 49,6 53 140 270 68.7 31 7 4 5 11,3 11 11,3 11,3 88 1292

23 395 16,2 44,1 14,8 43.8 38 140 270 64 30 8 4 5 11,3 11 11,4 11,3 88 1208

24 300 13,5 38,4 12,8 40 12.9 140 270 58 29 8 4 5 11,7 11 11,3 11,3 88 1064

105

nax.27 sistemis datvirTvis grafiki (programiT)

106

rogorc analizma gviCvena engurhesze am dRes realurad

gaxarjuli wylis moculoba iyo 7665217.39 m3 da jamuri

gamomuSaveba mgvtsT, xolo wylis imave moculobis

pirobebSi programiT gaangariSebisas engurhesis jamurma

gamomuSavebam SeadginaA mgvtsT, rac imis

damadasturebelia, rom roca sadgurze ganxorcieldeba

agregatTa optimizacia, erTdaigive wylis moculobiT

SesaZlebeli gaxda meti energiis miReba. swored amis

saSualebiT Tu im dRes ruseTis energosistemidan faqtiurad

ganxorcielda 2125 mgvtsT energiis importi, programiT miRebul

SedegSi es sidide Semcirda 577 mgvtsT-mde. aseve, ganvsazRvreT

me-9 Tboblokze saTbobis xarji da mis mier gamomuSavebuli

eleqtroenergia. analizma aCvena, rom am energoblokze saTbobis

xvedriTi xarji, sistemis datvirTvis optimaluri ganawilebisas

Seadgena xv=356 gr/kvtsT, maSin roca faqtiuri reJimiT

muSaobisas saTbobis xvedriTi xarji iyo, xv=359 gr/kvtsT e.i

me-9 bloki muSaobda optimalur reJimSi, anu misTvis xelsayrel

pirobebSi.

107

1. IV Tavis daskvna

am TavSi, Sedgenili algoriTmis mixedviT, gaanalizebulia

,,Visual Basic” programul eniT _ ganxorcielebuli optimizaciis

amocanis amoxsnis Sedegebi saqarTvelos energosistemis

magaliTze.

rogorc aRniSnuli iyo sezonuri hesis datvirTvis grafiki

damokidebulia ara marto mdinareSi wylis bunebriv Camonadenze,

aramed masTan kaskadSi (dinebis mixedviT zemoT) momuSave

wyalsacaviani hesis wyalsacavis Sevseba_damuSavebis reJimze.

swored sezonuri hesisi muSaobis am specifiurobis

gaTvaliswinebiT SesaZlebelia gaumjobesdes Tbosadguris

muSaobis ekonomikuri maCvenebeli da mTeli sistemis masStabiT

ganxorcieldes sadgurebs Soris aqtiuri datvirTvis

optimaluri ganawileba am sadgurebze muSaobaSi CarTuli

agregatebis optimaluri ricxvis dadgenasTan erTad.

Sigasasadguro optimizacia xorcieldeba sadguris

ekvivalenturi maxasiaTeblis bazaze, romelic winaswar iqna

dadgenili.

zemoT aRniSnuli kompiuteruli programis saSualebiT

ganxorcielda optimizaciis amocanis amoxsna saqarTvelos

energosistemis magaliTze. konkretulad ganxiluli iyo 2008

wlis 17 dekemberi.

rogorc analizma gviCvena, programiT ganxorcielebuli

optimizaciis amocanis amoxsniT miRebuli Sedegebis mixedviT

engurhesis mier, im dRes wylis arsebuli limitis dacviT,

gamomuSavebuli iqna ufro meti energia _ 8168 mgvtsT, vidre

faqtiurad _ 7052 mgvtsT. sistemaSi aqtiuri datvirTvis

optimaluri ganawilebisas, me-9 enrgoblokze saTbobis xvedriT

xarjma Seadgina 356 gr/kvtsT, nacvlad faqtiuri 359 gr/kvtsT-isa.

gazarda am energoblokis dReRamuri gamomuSaveba (6333 mgvtsT,

nacvlad faqtiuri 4988 mgvtsT-isa).

108

Sedegad dReRamis intervalSi mniSvnelovnad Semcirda

eletroenergiis importi (577 mgvtsT, nacvlad faqtiuri 2125

mgvtsT-isa). Sedgenili programis mixedviT yvela wyalsacaviani

hidrosadgurebis wylis dReRamuri limiti gamoyenebuli iqna

srulad, TiTqmis 100%-iT

109

2. ექსპერიმენტული ნაწილი

naSromis oTxive Tavis analizis daskvnebi gamyarebulia

eqsperimentuli modelirebis SedegebiT. III, IV TavebSi

SemuSavebuli maTematikuri meTodebisa da modelebis safuZvelze

Visual Basic-is programul enaze Seqmnilia programa.

programa mocemulia danarTis saxiT.

110

3. daskvna

xazgasmiTaa aRsaniSnavi hesis kaskadSi dinebis mixedviT

qvemoT momuSave sezonuri hesis muSaobis specifiuroba. am

sezonuri hesis mier dReRamis ganmavlobaSi gamomuSavebuli

eleqtroenergiis moculoba, (anu misi dReRamuri datvirTvis

grafiki). damokidebulia ara marto mdinareSi wylis bunebrivi

Camonadenis moculobaze, aramed masTan kaskadSi (dinebis

mixedviT zemoT) momuSave wyalsacaviani hesis wyalsacavis

Sevseba _ damuSavebis reJimze.

sayuradReboa, rom wyalsacavSi dagrovebuli wylis

racionaluri gamoyenebis mizniT dReRamuri SemuSavebisas

gaTvaliswinebuli unda iyos, rogorc TviT wyalsacaviani hesis,

aseve masTan kaskadSi momuSave sezonuri hesis energetikuli

maxasiaTeblebi. aqedan gamomdinare, wyalsacavSi dagrovebuli

wylis racionaluri xarjvis amocanis amoxsna kompleqsur

midgomas moiTxovs, romlis drosac gaTvaliswinebuli unda

iqnes wylis bunebrivi dinebis xangrZlivoba wyalsacaviani

hesidan sezonur hesamde.

wyalsacavis Sevseba _ damuSavebis grafikis kompleqsuri

midgomiT SemuSavebis gziT, miiRweva ra sezonuri hesis

datvirTvis marTva, SesaZlebelia kidev ufro gaumjobesdes

Tbosadgurebis muSaobis ekonomikuri maCveneblebi, anu mTeli

sistemis masStabiT kidev ufro daixvewos eleqtrosadgurebs

Soris aqtiuri datvirTvis optimaluri ganawilebis amocana.

eleqtrosadgurebs Soris aqtiuri datvirTvis optimaluri

ganawilebis ekonomikuri efeqti damokidebulia, rogorc

energoblokebis, aseve calkeuli eleqtrosadgurebis

energetikuli maxasiaTeblebis da, maT Soris saxarjo

maxasiaTeblebis, aRmweri maTematikuri modelis utyuarobis

xarixze. rogorc qarxnuli, aseve naturaluri gazomvebis

statistikuri informaciis gaanalizebiT, energoblokebis

Sesaxeb, umciresi kvadratebis meTodiT, dadginda rogorc

111

energoblokebis saxarjo maxasiaTeblebi, aseve calkeuli

eleqtrosadgurebis ekvivalenturi saxarjo maxasiaTebeli meore

rigis polinomis saxiT. miRebuli analizuri gamosaxulebis

mixedviT gansazRvruli pirveladi energoresursis xarjis

ricxviTi mniSvneloba maRali sizustiT emTxveva naturaluri

gazomvebis Sedegebs.

agregatebis saxarjo maxasiaTeblebis maTematikuri modelis

safuZvelze, gadaWrili iqna muSaobaSi CarTuli agregatebis

optimaluri ricxvis amocana anu dadgenili iqna sadguris

datvirTvis ekonomikuri intervalebi muSaobaSi CarTuli

agregatebis raodenobis gaTvaliswinebiT.

Catarda eleqtrosistemaSi eleqtrosadgurebs Soris

aqtiuri datvirTvis ganawilebis optimizaciis amocanis

gantolebaTa sistemis analizi. ganxiluli da Sefasebuli iqna

aseTi saxis amocanaTa amoxsnis meTodebi da am meTodebis

gamoyenebis sferoebi.

sadgurTa saxarjo maxasiaTebelTa maTematikuri

gamosaxulebebis safuZvelze Sedgenilia miznis fuqcia,

SezRudvis gantolebaTa da SezRudvis utolobaTa sistema.

dasmuli amocanis Sesabamisad miznis funqcias warmodgens

Tbosadgurebze pirveladi energoresursis anu saTbobis jamuri

xarji, SezRudvis gantolebis saxiT ganixileba energosistemaSi

aqtiuri simZlavris balansis gantoleba, xolo SezRudvis

utolobaTa saxiT ganixileba energoblokebis minimaluri da

maqsimaluri dasaSvebi datvirTvebi. eleqtrosadgurebs Soris

aqtiuri datvirTvis optimaluri ganawilebis Tematikuri modeli

Cawerilia konkretulad saqarTvelos energosistemis magaliTze.

dasmuli amocanis amoxsnisas kompiuterizaciis TvalsazrisiT,

ufro moxerxebulia gamoyenebuli iqnes amocanis amoxsnis

grafikuli meTodi, rac gulisxmobs pirveladi enrgoresursis

fardobiTi nazrdis tolobas yvela eleqtrosadgurisaTvis.

gamoTvlilia da TiToeuli maregulirebeli hesisTvis

mocemulia lagranJis mamravlis ricxviTi mniSvnelobebi,

112

romelic am hesis hidroresursis gamoyenebis efeqturobis

koeficients warmoadgens.

Sedgenili algoriTmis mixedviT gaanalizda ,,Visual Basic”

programul eniT _ ganxorcielebuli optimizaciis amocanis

amoxsnis Sedegebi saqarTvelos energosistemis magaliTze.

rogorc iyo aRniSnuli sezonuri hesis datvirTvis grafiki

damokidebulia ara marto mdinareSi wylis bunebriv Camonadenze,

aramed masTan kaskadSi (dinebis mixedviT zemoT) momuSave

wyalsacaviani hesis wyalsacavis Sevseba_damuSavebis reJimze.

swored sezonuri hesis muSaobis am specifiurobis

gaTvaliswinebiT SesaZlebelia gaumjobesdes Tbosadguris

muSaobis ekonomikuri maCvenebeli da mTeli sistemis masStabiT

ganxorcieldes sadgurebs Soris aqtiuri datvirTvis

optimaluri ganawileba am sadgurebze muSaobaSi CarTuli

agregatebis optimaluri ricxvis dadgenasTan erTad.

Sigasasadguro optimizacia ganxorcieldeba sadguris

ekvivalenturi maxasiaTeblis bazaze, romelic winaswar iqna

dadgenili.

zemoT aRniSnuli kompiuteruli programis saSualebiT

ganxorcielda optimizaciis amocanis amoxsna saqarTvelos

energosistemis magaliTze. konkretulad ganxiluli iyo 2008

wlis 17 dekemberi.

rogorc analizma gviCvena, programiT ganxorcielebuli

optimizaciis amocanis amoxsniT miRebul Sedegbis mixedviT

engurhesis mier im dRes wylis arsebuli limitis dacviT

gamomuSavebuli iqna ufro meti energia _ 8168 mgvtsT, vidre

faqtiuri reJimiT _ 7052 mgvtsT. sistemaSi aqtiuri datvirTvis

optimaluri ganawilebisas me-9 enrgoblokze saTbobis xvedriT

xarjma Seadgens 356 gr/kvtsT, nacvlad faqtiuri 359 gr/kvtsT-isa.

amasTan, optimaluri ganawilebis amocanis amoxsnis Sesabamisad

gazarda am energoblokis dReRamuri gamomuSaveba (6333 mgvtsT,

nacvlad faqtiuri 4988 mgvtsT-isa).  

113

dReRamis intervalSi Semcirda eleqtroenergiis

importi(577 mgvtsT, nacvlad faqtiuri 2125 mgvtsT-isa).

114

danarTi

programis teqsti

Pdat(1) = 917: Pdat(2) = 827: Pdat(3) = 810: Pdat(4) = 774: Pdat(5) = 810: Pdat(6) = 800: Pdat(7) = 841 Pdat(8) = 928: Pdat(9) = 1133: Pdat(10) = 1196: Pdat(11) = 1216: Pdat(12) = 1202: Pdat(13) = 1185: Pdat(14) = 1187 Pdat(15) = 1229: Pdat(16) = 1202: Pdat(17) = 1197: Pdat(18) = 1346: Pdat(19) = 1404: Pdat(20) = 1399: Pdat(21) = 1343 Pdat(22) = 1292: Pdat(23) = 1208: Pdat(24) = 1064: Pdat(25) = 917: Pdat(26) = 827: Pdat(27) = 810: Pdat(28) = 774 Pdat(29) = 809: Pdat(30) = 800: Pdat(31) = 850: Pdat(32) = 928: Pdat(33) = 1133: Pdat(34) = 1196: Pdat(35) = 1216 For i = 1 To 35 Pdato(i) = Pdat(i) Next i LAM(1, 1) = 0.401: LAM(1, 2) = 0.401: LAM(1, 3) = 0.401: LAM(1, 4) = 0.401: LAM(1, 5) = 0.401 LAM(2, 1) = 0.32: LAM(2, 2) = 0.32: LAM(2, 3) = 0.32: LAM(2, 4) = 0.32: LAM(2, 5) = 0.32 LAM(3, 1) = 0.117: LAM(3, 2) = 0.117: LAM(3, 3) = 0.117: LAM(3, 4) = 0.117: LAM(3, 5) = 0.117 LAM(4, 1) = 0.391: LAM(4, 2) = 0.391: LAM(4, 3) = 0.391: LAM(4, 4) = 0.391: LAM(4, 5) = 0.391 LAM(5, 1) = 0.238: LAM(5, 2) = 0.238: LAM(5, 3) = 0.238: LAM(5, 4) = 0.238: LAM(5, 5) = 0.238 QLim(1) = 7665218: QLim(2) = 486487: QLim(3) = 3100000: QLim(4) = 307458: QLim(5) = 1511263 NN = 0 For i = 1 To 14 RIONI(i) = 95: KN(i) = 0 Next i For i = 15 To 24 RIONI(i) = 88 Next i For i = 25 To 35 RIONI(i) = 95: Next i 'For i = 1 To 35 'Pdat(i) = Pdato(i) - RIONI(i) 'Next i N = 10 For i = 1 To N KN(i) = 0 NG(i) = 1 HHH(i) = 0 Next i st = 0 ' Pdat min=330 Pdat max=2340 KK = 1 nk = 1 Psum = 0 For i = 1 To NFor j = 1 To 5'LAM(i, j) = 0 Q(i, j) = 0 b(i, j) = 0pzv (i, j) = 0Next ja(i) = 0 Next iFor i = 1 To N For j = 1 To 5 For k = 1 To 2 max(i, j, k) = 0 Next k Next j

115

max(1, 1, 1) = 0: max(1, 1, 2) = 220 max(1, 2, 1) = 220: max(1, 2, 2) = 440 max(1, 3, 1) = 440: max(1, 3, 2) = 660 max(1, 4, 1) = 660: max(1, 4, 2) = 880 max(1, 5, 1) = 880: max(1, 5, 2) = 1300 'enguri Psadmax(1) = 1300 max(2, 1, 1) = 0: max(2, 1, 2) = 37.8 'xrami-1 max(2, 2, 1) = 37.8: max(2, 2, 2) = 75 max(2, 3, 1) = 75: max(2, 3, 2) = 112 max(2, 4, 1) = 75: max(2, 4, 2) = 112 max(2, 5, 1) = 75: max(2, 5, 2) = 112 Psadmax(2) = 112 max(3, 1, 1) = 0: max(3, 1, 2) = 32.5 'Jinvali max(3, 2, 1) = 32.5: max(3, 2, 2) = 55 max(3, 3, 1) = 55: max(3, 3, 2) = 70 max(3, 4, 1) = 70: max(3, 4, 2) = 90 max(3, 5, 1) = 70: max(3, 5, 2) = 90 Psadmax(3) = 90 max(4, 1, 1) = 0: max(4, 1, 2) = 9 'Saori max(4, 2, 1) = 9: max(4, 2, 2) = 18 max(4, 3, 1) = 18: max(4, 3, 2) = 27 max(4, 4, 1) = 27: max(4, 4, 2) = 38 max(4, 5, 1) = 27: max(4, 5, 2) = 38 Psadmax(4) = 38 max(5, 1, 1) = 0: max(5, 1, 2) = 20 'Tkibuli max(5, 2, 1) = 20: max(5, 2, 2) = 40 max(5, 3, 1) = 40: max(5, 3, 2) = 60 max(5, 4, 1) = 60: max(5, 4, 2) = 80 max(5, 5, 1) = 60: max(5, 5, 2) = 80 Psadmax(5) = 80 mezomin = Val(Text1.Text) mezomax = Val(Text2.Text) Psadmin(1) = 0 Psadmin(2) = 0 Psadmin(4) = 0 Psadmin(5) = 0 Psadmin(3) = 0 If mezomin = 0 And mezomax = 0 Then mezomin = -100 mezomax = 100 End If max(6, 1, 1) = mezomin: max(6, 1, 2) = mezomax 'mezobeli sistema max(6, 2, 1) = mezomin: max(6, 2, 2) = mezomax 'mezobeli sistema max(6, 3, 1) = mezomin: max(6, 3, 2) = mezomax 'mezobeli sistema max(6, 4, 1) = mezomin: max(6, 4, 2) = mezomax 'mezobeli sistema max(6, 5, 1) = mezomin: max(6, 5, 2) = mezomax 'mezobeli sistema Psadmin(6) = mezomin: Psadmax(6) = mezomax c3 = 1 - Check1.Value max(7, 1, 1) = 80 * c3: max(7, 1, 2) = 140 * c3 'BLOKI 3 max(7, 2, 1) = 80 * c3: max(7, 2, 2) = 140 * c3 'BLOKI 3 max(7, 3, 1) = 80 * c3: max(7, 3, 2) = 140 * c3 'BLOKI 3 max(7, 4, 1) = 80 * c3: max(7, 4, 2) = 140 * c3 'BLOKI 3 max(7, 5, 1) = 80 * c3: max(7, 5, 2) = 140 * c3 'BLOKI 3 Psadmin(7) = 80 * c3: Psadmax(7) = 140 * c3 max(8, 1, 1) = 80: max(8, 1, 2) = 140 'Bloki4 max(8, 2, 1) = 80: max(8, 2, 2) = 140 max(8, 3, 1) = 80: max(8, 3, 2) = 140

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max(8, 4, 1) = 80: max(8, 4, 2) = 140 max(8, 5, 1) = 80: max(8, 5, 2) = 140 Psadmin(8) = 80: Psadmax(8) = 140 'N4 bloki c9 = 1 - Check2.Value max(9, 1, 1) = 210 * c9: max(9, 1, 2) = 260 * c9 'Bloki 9 max(9, 2, 1) = 210 * c9: max(9, 2, 2) = 260 * c9 max(9, 3, 1) = 210 * c9: max(9, 3, 2) = 260 * c9 max(9, 4, 1) = 210 * c9: max(9, 4, 2) = 260 * c9 max(9, 5, 1) = 210 * c9: max(9, 5, 2) = 260 * c0 Psadmin(9) = 210 * c9: Psadmax(9) = 260 * c9 'N9 bloki cair = 1 - Check3.Value max(10, 1, 1) = 0 * cair: max(10, 1, 2) = 55 * cair 'Air1,2 max(10, 2, 1) = 55 * cair: max(10, 2, 2) = 110 * cair 'Air1,2 max(10, 3, 1) = 55 * cair: max(10, 3, 2) = 110 * cair 'Air1,2 max(10, 4, 1) = 55 * cair: max(10, 4, 2) = 110 * cair 'Air1,2 max(10, 5, 1) = 55 * cair: max(10, 5, 2) = 110 * cair 'Air1,2 Psadmin(10) = 0: Psadmax(10) = 110 * cair 'Air1,2 sax(1) = "enguri": pzv(1, 1) = 0: pzv(1, 2) = 1300: a(1) = 0.202: b(1, 1) = 0.0001: b(1, 2) = 0.00005: b(1, 3) = 0.00003: b(1, 4) = 0.000025: b(1, 5) = 0.00002: Q(1, 1) = 11.25: Q(1, 2) = 14.35: Q(1, 3) = 18.18: Q(1, 4) = 22.13: Q(1, 5) = 26.02: 'LAM(1, 1) = 0.411: LAM(1, 2) = 0.411: LAM(1, 3) = 0.411: LAM(1, 4) = 0.411: LAM(1, 5) = 0.411 sax(2) = "xrami 1": pzv(2, 1) = 0: pzv(2, 2) = 112.8: a(2) = 0.27: b(2, 1) = 0.0006: b(2, 2) = 0.0003: b(2, 3) = 0.002: b(2, 4) = 0.0002: b(2, 5) = 0.0002 Q(2, 1) = 0.9: Q(2, 2) = 1.28: Q(2, 3) = 1.73: Q(2, 4) = 1.73: Q(2, 5) = 1.73: LAM(2, 1) = 0.328: LAM(2, 2) = 0.328: LAM(2, 3) = 0.328: LAM(2, 4) = 0.328: LAM(2, 5) = 0.328 sax(3) = "Jinvali": pzv(3, 1) = 0: pzv(3, 2) = 80: a(3) = 0.802 b(3, 1) = 0.0012: b(3, 2) = 0.0006: b(3, 3) = 0.0004: b(3, 4) = 0.0003: b(3, 5) = 0.0003 Q(3, 1) = 1.4: Q(3, 2) = 1.96: Q(3, 3) = 2.62: Q(3, 4) = 3.28: Q(3, 5) = 3.28: 'LAM(3, 1) = 0.117: LAM(3, 2) = 0.117: LAM(3, 3) = 0.117: LAM(3, 4) = 0.117: LAM(3, 5) = 0.117 sax(4) = "Saori": pzv(4, 1) = 0: pzv(4, 2) = 38.4: a(4) = 0.21: b(4, 1) = 0.003: b(4, 2) = 0.0015: b(4, 3) = 0.001: b(4, 4) = 0.00075: b(4, 5) = 0.00075 Q(4, 1) = 0.21: Q(4, 2) = 0.33: Q(4, 3) = 0.47: Q(4, 4) = 0.61: Q(4, 5) = 0.61: 'LAM(4, 1) = 0.391: LAM(4, 2) = 0.391: LAM(4, 3) = 0.391: LAM(4, 4) = 0.391: LAM(4, 5) = 0.391 sax(5) = "tyibuli": pzv(5, 1) = 0: pzv(5, 2) = 80: a(5) = 0.27: b(5, 1) = 0.0047: b(5, 2) = 0.0024: b(5, 3) = 0.0016: b(5, 4) = 0.0012: b(5, 5) = 0.0012 Q(5, 1) = 1.29: Q(5, 2) = 2.12: Q(5, 3) = 3.1: Q(5, 4) = 4.1: Q(5, 5) = 4.1 'LAM(5, 1) = 0.238: LAM(5, 2) = 0.238: LAM(5, 3) = 0.238: LAM(5, 4) = 0.238: LAM(5, 5) = 0.238 sax(6) = "MEZOBELI": pzv(6, 1) = -100: pzv(6, 2) = 100: a(6) = 368: b(6, 1) = 0.305: b(6, 2) = 0.305: b(6, 3) = 0.305: b(6, 4) = 0.305: b(6, 5) = 0.305 Q(6, 1) = 1.29: Q(6, 2) = 2.12: Q(6, 3) = 3.1: Q(6, 4) = 4.1: Q(6, 5) = 4.1 LAM(6, 1) = 1: LAM(6, 2) = 1: LAM(6, 3) = 1: LAM(6, 4) = 1: LAM(6, 5) = 1 sax(7) = "me 3bloki": pzv(7, 1) = 80 * c3: pzv(7, 2) = 140 * c3: a(7) = 272.7: b(7, 1) = 0.293: b(7, 2) = 0.293: b(7, 3) = 0.293: b(7, 4) = 0.293: b(7, 5) = 0.293

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Q(7, 1) = 7614.9: Q(7, 2) = 7614.9: Q(7, 3) = 7614.9: Q(7, 4) = 7614.9: Q(7, 5) = 7614.9 LAM(7, 1) = 1: LAM(7, 2) = 1: LAM(7, 3) = 1: LAM(7, 4) = 1: LAM(7, 5) = 1 sax(8) = "me 4 bloki": pzv(8, 1) = 80: pzv(8, 2) = 140: a(8) = 272.7: b(8, 1) = 0.293:: b(8, 2) = 0.293: b(8, 3) = 0.293: b(8, 4) = 0.293: b(8, 5) = 0.293 Q(8, 1) = 7614.9 LAM(8, 1) = 1: LAM(8, 2) = 1: LAM(8, 3) = 1: LAM(8, 4) = 1: LAM(8, 5) = 1 sax(9) = "me 9 bloki": pzv(9, 1) = 210: pzv(9, 2) = 270: a(9) = 259.5: b(9, 1) = 0.152: b(9, 2) = 0.152: b(9, 3) = 0.152: b(9, 4) = 0.152: b(9, 5) = 0.152 Q(9, 1) = 9500 LAM(9, 1) = 1: LAM(9, 2) = 1: LAM(9, 3) = 1: LAM(9, 4) = 1: LAM(9, 5) = 1 sax(10) = "airturbina1+2": pzv(10, 1) = 0: pzv(10, 2) = 110: a(10) = 170.38 b(10, 1) = 2.617: b(10, 2) = 2.617 / 2: b(10, 3) = 2.617 / 2: b(10, 4) = 2.617 / 2: b(10, 5) = 2.617 / 2 Q(10, 1) = 5517 Q(10, 2) = 11034 LAM(10, 1) = 1: LAM(10, 2) = 1: LAM(10, 3) = 1: LAM(10, 4) = 1: LAM(10, 5) = 1 max(11, 1, 1) = 0: max(11, 1, 2) = 73.3 'vardnili max(11, 2, 1) = 73.3: max(11, 2, 2) = 146 max(11, 3, 1) = 146: max(11, 3, 2) = 210 max(11, 4, 1) = 146: max(11, 4, 2) = 210 max(11, 5, 1) = 146: max(11, 5, 2) = 210 max(12, 1, 1) = 0: max(12, 1, 2) = 55 'xrami-2 max(12, 2, 1) = 55: max(12, 2, 2) = 110 max(12, 3, 1) = 55: max(12, 3, 2) = 110 max(12, 4, 1) = 55: max(12, 4, 2) = 110 max(12, 5, 1) = 55: max(12, 5, 2) = 110 max(13, 1, 1) = 0: max(13, 1, 2) = 12 'Zahesi-1 max(13, 2, 1) = 12: max(13, 2, 2) = 24 max(13, 3, 1) = 12: max(13, 3, 2) = 24 max(13, 4, 1) = 12: max(13, 4, 2) = 24 max(13, 5, 1) = 12: max(13, 5, 2) = 24 max(16, 5, 1) = 23: max(16, 5, 2) = 46 max(17, 1, 1) = 0: max(17, 1, 2) = 23 'Varcixe-2 max(17, 2, 1) = 23: max(17, 2, 2) = 46 max(17, 3, 1) = 23: max(17, 3, 2) = 46 max(17, 4, 1) = 23: max(17, 4, 2) = 46 max(17, 5, 1) = 23: max(17, 5, 2) = 46 max(18, 1, 1) = 0: max(18, 1, 2) = 23 'Varcixe-3 max(18, 2, 1) = 23: max(18, 2, 2) = 46 max(18, 3, 1) = 23: max(18, 3, 2) = 46 max(18, 4, 1) = 23: max(18, 4, 2) = 46 max(18, 5, 1) = 23: max(18, 5, 2) = 46 max(19, 1, 1) = 0: max(19, 1, 2) = 23 'Varcixe-4 max(19, 2, 1) = 23: max(19, 2, 2) = 46 max(19, 3, 1) = 23: max(19, 3, 2) = 46 max(19, 4, 1) = 23: max(19, 4, 2) = 46 max(19, 5, 1) = 23: max(19, 5, 2) = 46 Psadmin(11) = 0 Psadmax(11) = 210 'Vardnili Psadmin(12) = 0 Psadmax(12) = 110 'Xrami-2

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Psadmin(13) = 0 Psadmax(13) = 24 'Zaesi-1 Psadmin(14) = 0 Psadmax(14) = 16 'Zaesi-2 Psadmin(15) = 0 Psadmax(15) = 18 'Ortacala Psadmin(16) = 0 Psadmax(16) = 46 'Varcixe-1 Psadmin(17) = 0 Psadmax(17) = 46 'Varcixe-2 Psadmin(18) = 0 Psadmax(18) = 46 'Varcixe-3 Psadmin(19) = 0 Psadmax(19) = 46 'Varcixe-4 sax(11) = "vardnili": pzv(11, 1) = 0: pzv(11, 2) = 210: a(11) = 1.8: b(11, 1) = 0.0013: b(11, 2) = 0.00065: b(11, 3) = 0.00043: b(11, 4) = 0.00043: b(11, 5) = 0.00043 ': b(9, 2) = 0.00065: b(9, 3) = 0.00065: 'b(9, 4) = 0.00065: b(9, 5) = 0.00065: Q(11, 1) = 3.79: Q(11, 2) = 6.5: Q(11, 3) = 9: Q(11, 4) = 9: Q(11, 5) = 9: LAM(11, 1) = 0.052 ': LAM(1, 2) = 0.411: LAM(1, 3) = 0.411: LAM(1, 4) = 0.411: LAM(1, 5) = 0.411 sax(12) = "xrami-2": pzv(12, 1) = 0: pzv(12, 2) = 110: a(12) = 0.3: b(12, 1) = 0.0005: b(12, 2) = 0.00025: b(12, 3) = 0.00025: b(12, 4) = 0.00025: b(12, 5) = 0.00025 Q(12, 1) = 1.78: Q(12, 2) = 2.36: Q(12, 3) = 2.36: Q(12, 4) = 2.36: Q(12, 5) = 2.36 LAM(12, 1) = 0.292 sax(13) = "zahesi-1": pzv(13, 1) = 0: pzv(13, 2) = 24: a(13) = 5.81: b(13, 1) = 0.03: b(13, 2) = 0.015: b(13, 3) = 0.015: b(13, 4) = 0.015: b(13, 5) = 0.015 Q(13, 1) = 3.02: Q(13, 2) = 4.67: Q(13, 3) = 4.67: Q(13, 4) = 4.67: Q(13, 5) = 4.67 LAM(13, 1) = 0.016 sax(14) = "zahesi-2": pzv(14, 1) = 0: pzv(14, 2) = 16: a(14) = 5.93: b(14, 1) = 0.13: b(14, 2) = 0.065: b(14, 3) = 0.043: b(14, 4) = 0.033: b(14, 5) = 0.033 Q(14, 1) = 0.27: Q(14, 2) = 0.7: Q(14, 3) = 1.1: Q(14, 4) = 1.4: Q(14, 5) = 1.4 LAM(14, 1) = 0.015 sax(15) = "orTaWala": pzv(15, 1) = 0: pzv(15, 2) = 18: a(15) = 8.9: b(15, 1) = 0.37: b(15, 2) = 0.19: b(15, 3) = 0.12: b(15, 4) = 0.12: b(15, 5) = 0.12 Q(15, 1) = 9.3: Q(15, 2) = 14.4: Q(15, 3) = 19.7: Q(15, 4) = 19.7: Q(15, 5) = 19.7 LAM(15, 1) = 0.008 sax(16) = "varcixe-1": pzv(16, 1) = 0: pzv(16, 2) = 46: a(16) = 6.17: b(16, 1) = 0.033: b(16, 2) = 0.017: b(16, 3) = 0.017: b(16, 4) = 0.017: b(16, 5) = 0.017 Q(16, 1) = 14.87: Q(16, 2) = 21.5: Q(16, 3) = 21.5: Q(16, 4) = 21.5: Q(16, 5) = 21.5 LAM(16, 1) = 0.013 sax(17) = "varcixe-2": pzv(17, 1) = 0: pzv(17, 2) = 46: a(17) = 6.17: b(17, 1) = 0.033: b(17, 2) = 0.017: b(17, 3) = 0.017: b(17, 4) = 0.017: b(17, 5) = 0.017 Q(17, 1) = 14.87: Q(17, 2) = 21.5: Q(17, 3) = 21.5: Q(17, 4) = 21.5: Q(17, 5) = 21.5 LAM(17, 1) = 0.013 sax(18) = "varcixe-3": pzv(18, 1) = 0: pzv(18, 2) = 46: a(18) = 6.17: b(18, 1) = 0.033: b(18, 2) = 0.017: b(18, 3) = 0.017: b(18, 4) = 0.017: b(18, 5) = 0.017 Q(18, 1) = 14.87: Q(18, 2) = 21.5: Q(18, 3) = 21.5: Q(18, 4) = 21.5: Q(18, 5) = 21.5 LAM(18, 1) = 0.013 sax(19) = "varcixe-4": pzv(19, 1) = 0: pzv(19, 2) = 46: a(19) = 6.17: b(19, 1) = 0.033: b(19, 2) = 0.017: b(19, 3) = 0.017: b(19, 4) = 0.017: b(19, 5) = 0.017

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Q(19, 1) = 14.87: Q(19, 2) = 21.5: Q(19, 3) = 21.5: Q(19, 4) = 21.5: Q(19, 5) = 21.5 LAM(19, 1) = 0.013 For i = 1 To 35 Pkaskad(i) = 0 Next i LAM(1, 1) = LAM(1, 1) MMM: For i = 1 To 5 aa(i) = a(i) * LAM(i, 1) * 3600 For j = 1 To 5 BB(i, j) = b(i, j) * LAM(i, 1) * 3600 Next j Next i For i = 6 To 10 aa(i) = a(i) For j = 1 To 5 NG(i) = 0 BB(i, j) = b(i, j) Next j Next i aa(1) = aa(1): aa(2) = aa(2): aa(3) = aa(3): aa(4) = aa(4): aa(5) = aa(5): LAM(1, 1) = LAM(1, 1): LAM(2, 1) = LAM(2, 1): LAM(3, 1) = LAM(3, 1): LAM(4, 1) = LAM(4, 1): LAM(5, 1) = LAM(5, 1): BB(1, 1) = BB(1, 1): BB(1, 2) = BB(1, 2): BB(1, 3) = BB(1, 3): BB(1, 4) = BB(1, 4): BB(1, 5) = BB(1, 5): BB(2, 1) = BB(2, 1): BB(2, 2) = BB(2, 2): BB(2, 3) = BB(2, 3): BB(2, 4) = BB(2, 4): BB(2, 5) = BB(2, 5): BB(3, 1) = BB(3, 1): BB(3, 2) = BB(3, 2): BB(3, 3) = BB(3, 3): BB(3, 4) = BB(3, 4): BB(3, 5) = BB(3, 5): BB(4, 1) = BB(4, 1): BB(4, 2) = BB(4, 2): BB(4, 3) = BB(4, 3): BB(4, 4) = BB(4, 4): BB(4, 5) = BB(4, 5): BB(5, 1) = BB(5, 1): BB(5, 2) = BB(5, 2): BB(5, 3) = BB(5, 3): BB(5, 4) = BB(5, 4): BB(5, 5) = BB(5, 5): For i = 1 To 24 H(i) = 0 For j = 11 To 19 P(j, i) Next j Next i LAM(1, 1) = LAM(1, 1): LAM(2, 1) = LAM(2, 1): LAM(3, 1) = LAM(3, 1): LAM(4, 1) = LAM(4, 1): LAM(5, 1) = LAM(5, 1) LAMO(1, 1) = LAM(1, 1): LAMO(3, 1) = LAM(3, 1): LAMO(4, 1) = LAM(4, 1): LAMO(5, 1) = LAM(5, 1) LAM2(3, 1) = 0.10922: LAM2(4, 1) = 0.361: LAM2(5, 1) = 0.21 'For T = 1 To 20 jj = 0 sisjami = 0 For i = 1 To 24 sisjami = sisjami + Pdato(i) Next i For i = 1 To 24 AT(i) = Pdato(i) / sisjami

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Next i For i = 1 To 24 Qxrami1(i) = QLim(2) * AT(i) / 3600 Qjinvali(i) = QLim(3) * AT(i) / 3600 Qshaori(i) = QLim(4) * AT(i) / 3600 Qtkibuli(i) = QLim(5) * AT(i) / 3600 P(2, i) = (-a(2) + Sqr(a(2) ^ 2 - 4 * b(2, 5) * (Q(2, 5) - Qxrami1(i)))) / (2 * b(2, 5)) P(3, i) = (-a(3) + Sqr(a(3) ^ 2 - 4 * b(3, 5) * (Q(3, 5) - Qjinvali(i)))) / (2 * b(3, 5)) P(4, i) = (-a(4) + Sqr(a(4) ^ 2 - 4 * b(4, 5) * (Q(4, 5) - Qshaori(i)))) / (2 * b(4, 5)) P(5, i) = (-a(5) + Sqr(a(5) ^ 2 - 4 * b(5, 5) * (Q(5, 5) - Qtkibuli(i)))) / (2 * b(5, 5)) Next i For saati = 1 To 24 For i = 2 To 5 For j = 5 To 1 Step -1 If (i >= 6 Or i = 3) And P(i, saati) <= Psadmin(i) Then P(i, saati) = Psadmin(i) End If If P(i, saati) >= max(i, j, 1) And P(i, saati) <= max(i, j, 2) Then Breal(i) = b(i, j) End If 'If P(3, saati) >= 30 And i = 3 Then GoTo MNB Next j Next i Call kaskaduri Next saati For i = 1 To 24 Pdat(i) = Pdato(i) - P(2, i) - P(3, i) - P(4, i) - P(5, i) - P(11, i) - P(12, i) - P(13, i) - P(14, i) - P(15, i) - P(16, i) - P(17, i) - P(18, i) - P(19, i) - RIONI(i) Next i oi = 0 AXALI: For saati = 1 To 24 If oi = 0 Then P(1, saati) = 0.6 * Pdat(saati) For i = 1 To 5 NG(1) = 0 If P(1, saati) > max(1, i, 1) And P(1, saati) < max(1, i, 2) Then Breal(1) = BB(1, i) NG(1) = i End If Next i e(1) = ((a(1) + 2 * b(1, 2) * P(1, saati))) * LAM(1, 1) * 3600 For i = 1 To 5 If P(1, saati) >= max(1, i, 1) And P(1, saati) <= max(1, i, 2) Then QT(1, saati) = Q(1, i) + a(1) * P(1, saati) + b(1, i) * P(1, saati) ^ 2 Exit For End If Next i P(11, saati + 1) = (-a(11) + Sqr(a(11) ^ 2 - 4 * b(11, 5) * (Q(11, 5) - QT(1, saati) - 10))) / (2 * b(11, 5)) If P(11, saati + 1) > Psadmax(11) Then P(11, saati + 1) = Psadmax(11)

121

For j = 5 To 1 Step -1 If P(11, saati + 1) >= max(11, j, 1) And P(11, saati + 1) <= max(11, j, 2) Then Breal(11) = b(11, j) Qreal(11) = Q(11, j) Exit For End If Next j P(11, saati + 1) = (-a(11) + Sqr(a(11) ^ 2 - 4 * Breal(11) * (Qreal(11) - QT(1, saati) - 10))) / (2 * Breal(11)) 'P(11, saati) = P(11, saati) If saati + 1 > 24 Then P(11, saati + 1 - 24) = P(11, saati + 1) For i = 6 To 9 P(i, saati) = (e(KK) - a(i)) / (2 * b(i, 1)) If i = 7 Then P(7, saati) = c3 * P(7, saati) If i = 9 Then P(9, saati) = c9 * P(9, saati) If i = 10 Then P(10, saati) = cair * P(10, saati) Next i If P(10, saati) < 55 Then b(10, 1) = 2.617 If P(10, saati) > 55 Then b(10, 1) = 1.309 P(10, saati) = (e(KK) - a(10)) / (2 * b(10, 1)) For i = 6 To 10 If P(i, saati) <= Psadmin(i) Then P(i, saati) = Psadmin(i) End If If P(i, saati) >= Psadmax(i) Then P(i, saati) = Psadmax(i) End If Next i Jami(saati) = 0 For j = 1 To 19 Jami(saati) = Jami(saati) + P(j, saati) Next j Pubal(saati) = Pdato(saati) - Jami(saati) - RIONI(saati) If Abs(Pubal(saati)) > 1 Then P(1, saati) = P(1, saati) + 0.2 * Pubal(saati) Next saati c = 0 For i = 1 To 24 c = c + QT(1, i) * 3600 Next i Qubal = QLim(1) - c If Abs(Qubal) > 0.003 * QLim(1) Then LAM(1, 1) = LAM(1, 1) * Sqr((QLim(1) + c) / (2 * QLim(1))) oi = 0 For i = 1 To 24 '35 Picture3.Print " ", i, Jami(i) = 0 For j = 1 To 19

122

Jami(i) = Jami(i) + P(j, i) Next j Jami(i) = Jami(i) + RIONI(i) For j = 11 To 19 'QLim(1) = 7665218 'c = 0 'For i = 1 To 24 'c = c + QT(1, i) * 3600 'Next i 'c = c

'Next

For i = 0 To 23 X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = P(9, i + 1) * MS U = 0Y1 = 9000 - c Y2 = 900 - U Picture3.Line (X1, Y1)-(X2, Y2), RGB(555, 0, 0), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(8, i + 1) * MS U = U + (P(8, i + 1)) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(0, 440, 0), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(7, i + 1) * MS U = U + P(7, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(0, 0, 550), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(10, i + 1) * MS U = U + P(10, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(90, 0, 99), BF 'c = c + P(6, i + 1) * MS 'U = U + P(6, i + 1) * MS 'Y1 = 9000 - U 'Y2 = 9000 - c 'Picture3.Line (X1, Y1)-(X2, Y1 + MS * (P(4, i + 1))), RGB(0, 110, 99), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(2, i + 1) * MS U = U + P(2, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c

123

Picture3.Line (X1, Y1)-(X2, Y2), RGB(90, 110, 0), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(3, i + 1) * MS U = U + P(3, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(490, 0, 444), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(4, i + 1) * MS U = U + P(4, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(5, i + 1) * MS U = U + P(5, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c icture3.Line (X1, Y1)-(X2, Y2), RGB(50, 150, 130), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(11, i + 1) * MS U = U + P(11, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(5, 50, 430), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(12, i + 1) * MS U = U + P(12, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(25, 50, 2), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(13, i + 1) * MS U = U + P(13, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(35, 530, 30), BF X1 = 600 + i * 500 X2 =600 + (i + 1) * 500 c = c + P(14, i + 1) * MS U = U + P(14, i + 1) * MS Y1 = 9000 - U Y2 = 9000 – c Picture3.Line (X1, Y1)-(X2, Y2), RGB(75, 50, 70), BF X1 = 600 + i * 500

124

X2 = 600 + (i + 1) * 500 c = c + P(15, i + 1) * MS U = U + P(15, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(5, 550, 5), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(16, i + 1) * MS U = U + P(16, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(65, 50, 460), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(17, i + 1) * MS U = U + P(17, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(75, 70, 70), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(18, i + 1) * MS U = U + P(18, i + 1) * MS Y1 = 9000 – U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(75, 670, 70), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(19, i + 1) * MS U = U + P(19, i + 1) * MS Y1 = 9000 - U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(375, 70, 70), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + RIONI(i + 1) * MS U = U + RIONI(i + 1) * MS Y1 = 9000 – U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(555, 0, 0), BF X1 = 600 + i * 500 X2 = 600 + (i + 1) * 500 c = c + P(1, i + 1) * MS U = U + P(1, i + 1) * MS Y1 = 9000 – U Y2 = 9000 - c Picture3.Line (X1, Y1)-(X2, Y2), RGB(0, 440, 0), BF 'X1 = 600 + i * 500 'X2 = 600 + (i + 1) * 500 'c = c + P(6, i + 1) * MS 'U = U + P(6, i + 1) * MS 'Y1 = 9000 – U 'Y2 = 9000 – c 'Picture3.Line (X1, Y1)-(X2, Y2), RGB(0, 0, 0), BF

125

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