Ero sivun ”Energiatasemalli” versioiden välillä
pEi muokkausyhteenvetoa |
p (→Vastaus) |
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| Rivi 10: | Rivi 10: | ||
Lineaarinen ohjelmointiongelma muodostuu seuraavasti. | Lineaarinen ohjelmointiongelma muodostuu seuraavasti. | ||
Koskien jokaista tuotantoyksikköä: olkoon x<sub>i</sub> voimalan aktiviteetti. Otetaan myös muuttuja y<sub>j</sub> merkitsemään kunkin energiatyypin ali- ja ylijäämiä. | |||
The objective function is the function we are optimising. Each production unit has a unit profit per activity denoted by a<sub>i</sub> which is determined by the amount of different input commodities (e.g. coal) per amount of different output commodities (i.e. electricity and heat) and their market prices. Also, lets say we want to make sure that district heat demand is always met when possible and have a large penalty factor for each unit of heat demand not met (1M€ in the model). In addition, it must be noted that excess district heat becomes wasted so it counts as loss. Let these deficit and excess related losses be denoted by b<sub>j</sub>. The whole objective function then becomes: sum(x<sub>i</sub>a<sub>i</sub>) + sum(y<sub>j</sub>b<sub>j</sub>). | The objective function is the function we are optimising. Each production unit has a unit profit per activity denoted by a<sub>i</sub> which is determined by the amount of different input commodities (e.g. coal) per amount of different output commodities (i.e. electricity and heat) and their market prices. Also, lets say we want to make sure that district heat demand is always met when possible and have a large penalty factor for each unit of heat demand not met (1M€ in the model). In addition, it must be noted that excess district heat becomes wasted so it counts as loss. Let these deficit and excess related losses be denoted by b<sub>j</sub>. The whole objective function then becomes: sum(x<sub>i</sub>a<sub>i</sub>) + sum(y<sub>j</sub>b<sub>j</sub>). | ||
The values of variables are constrained by equalities and inequalities: the sum of production of a commodity is equal to its demand minus deficit plus excess, activity is constrained by the maximum capacity and all variables are non-negative by definition. | The values of variables are constrained by equalities and inequalities: the sum of production of a commodity is equal to its demand minus deficit plus excess, activity is constrained by the maximum capacity and all variables are non-negative by definition. | ||
This can be efficiently solved by computers for each given instance. Production wind-up and wind-down is ignored, since time continuity is not considered. As a consequence fuel limits (e.g. diminishing hydropower capacity) are not modelled completely either. | This can be efficiently solved by computers for each given instance. Production wind-up and wind-down is ignored, since time continuity is not considered. As a consequence fuel limits (e.g. diminishing hydropower capacity) are not modelled completely either. | ||
Versio 13. elokuuta 2015 kello 15.08
Kysymys
Mikä on energiatase ja miten se mallinnetaan?
Vastaus
Laskemalla yhteen tietyn ajanjakson sisällä tuotettu energia ja vähentämällä siitä kulutettu energia saadaan energiatase. Koska sähköverkossa ja kaukolämpöverkossa ei ole merkittäviä energian varastointimekanismeja, täytyy taseen olla lyhyellä aikavälillä käytännössä nolla. Kun tarkastellaan tietyn alueen (kuten Helsingin) energiatasetta, voidaan olettaa, että sähköä voidaan viedä ja tuoda kansainvälisillä markkinoilla. Kaukolämpöverkon energia täytyy kuitenkin tuottaa paikallisesti. Tämä muodostaa taustan tärkeälle kysymykselle siitä, kuinka optimoidaan tuotanto niin ettei synny merkittäviä vajauksia, minimoidaan tappiot ja maksimoidaan voitot. Osittain tämä ongelma ratkeaa todellisen maailman markkinavoimien avulla.
Viimeisin energiatasemallimme käyttää lineaarisia ohjelmointityökaluja optimaalisen aktiviteettitason löytämiseen joukolle tuotantoyksiköitä päämallin simuloimissa tilanteissa. Päämalli on vastuussa päätöksentekoon liittyvistä asioista, kun taas energiataseen optimointi ainoastaan simuloi todellisen maailman markkinoiden toimintaa.
Lineaarinen ohjelmointiongelma muodostuu seuraavasti. Koskien jokaista tuotantoyksikköä: olkoon xi voimalan aktiviteetti. Otetaan myös muuttuja yj merkitsemään kunkin energiatyypin ali- ja ylijäämiä.
The objective function is the function we are optimising. Each production unit has a unit profit per activity denoted by ai which is determined by the amount of different input commodities (e.g. coal) per amount of different output commodities (i.e. electricity and heat) and their market prices. Also, lets say we want to make sure that district heat demand is always met when possible and have a large penalty factor for each unit of heat demand not met (1M€ in the model). In addition, it must be noted that excess district heat becomes wasted so it counts as loss. Let these deficit and excess related losses be denoted by bj. The whole objective function then becomes: sum(xiai) + sum(yjbj).
The values of variables are constrained by equalities and inequalities: the sum of production of a commodity is equal to its demand minus deficit plus excess, activity is constrained by the maximum capacity and all variables are non-negative by definition.
This can be efficiently solved by computers for each given instance. Production wind-up and wind-down is ignored, since time continuity is not considered. As a consequence fuel limits (e.g. diminishing hydropower capacity) are not modelled completely either.
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