PHYS-E6570 Solar Energy Engineering Exercise 9 March 28, Sizing a self-sufficient solar electricity system for a cottage television

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1 PHYS-E6570 Solar Energy Engineering Exercise 9 March 28, Sizing a self-sufficient solar electricity system for a cottage television Design a solar electricity system (solar cells and a battery) for a TV in a summer cottage. The system is used from April to September. The maximum temperature of the solar cells is 50 C and design temperature 28 C. The power of the solar cells is reduced by 0.5%/ C as temperature increases (current is a constant). The load is a B/W TV working off a 12 V battery. The TV consumes 20 W of power and it is watched 3 hours a day. The maximum depth of discharge of the battery is 75 %, efficiency 95 % and the voltage of one cell in full charge is 2.35 V. Voltage loss over a back diode is 0.8 V. The battery needs to be sufficient for operation during a 10 day dark period. The tilting angle of the solar batteries is 60. The irradiation intensities corresponding to this angle are in the table below. The battery is in full charge, when the watching period begins. Mitoita aurinkosähköjärjestelmä (kennosto ja akku) kesämökkitelevisiota varten. Järjestelmän käyttöaika on huhtikuusta syyskuuhun. Aurinkoparistojen maksimilämpötila on 50 C ja mitoituslämpötila 28 C. Paristojen teho heikkenee lämpötilan kasvaessa 0,5 %/ C (virta pysyy vakiona). Kuormana on 12 V:n akulla toimiva mv-televisio, jonka tehonkulutus on 20 W ja katseluaika 3 tuntia vuorokaudessa. Akun maksimipurkaussyvyys on 75%, hyötysuhde 95% ja yhden kennon jännite täydessä latauksessa 2,35 V. Jännitehäviö estodiodin yli on 0,8 V. Akun varassa on tultava toimeen 10 vrk:n pimeä aika. Aurinkoparistojen kallistuskulma on 60, jota vastaavat säteilyintensiteetit ovat alla olevassa taulukossa. Akku on katselukauden alkaessa täydessä latauksessa. kk 60 o taso kwh/m Sizing and economic considerations of a grid-connected solar electricity system We shall consider a typical Finnish house of a four person family: floor area 120 m 2, electric heating and annual electricity consumption kwh/a. The house is located in Espoo and it has a ridge roof, whose long side is in southwest-northeast axis (see figure on page 2). a) How large fraction of the energy consumption of the family could be covered with a gridconnected solar electricity system (system efficiency 10%), if the entire roof area would be covered with solar panels? How much solar electricity is annually produced in the northwest face of the roof compared to southeast? b) We shall consider two options: a solar panel system covering the entire roof and panels that cover only the southeast face of the roof. I both cases estimate the price of the solar electricity produced with the system, when the net investment costs of the system including the installation on the roof are 10 /Wp for which the family takes a loan for years with a 6% interest and demands a payback time of 20 years. 1

2 c) Repeat the calculations of parts a) and b) for a house, whose long façade faces directly south and the tilting angle of the roof is optimal. d) What would be the price of solar electricity, if the same roof system were located in solar belt in Phoenix, Arizona? Tarkastellaan tyypillistä suomalaista nelihenkisen perheen omakotitaloa: lattiapinta-ala 120 m 2, sähkölämmitys, vuosittainen sähkön kulutus kwh/a. Espoossa sijaitsevassa talossa on harjakatto, jonka pitkä sivu on lounas-koillis-suunnassa (ks. kuva s. 2). a) Kuinka suuri osa perheen energian kulutuksesta voitaisiin kattaa verkkoon kytketyllä aurinkosähköjärjestelmällä (järjestelmähyötysuhde 10%), jos koko kattopinta-ala peitettäisiin aurinkopaneeleilla? Paljonko saadaan aurinkosähköä vuodessa katon luoteenpuoleiselta sivulta verrattuna kaakonpuoleiseen sivuun? b) Tarkastellaan kahta vaihtoehtoa: koko katon peittävää paneelistoa, ja vain kaakonpuoleisen katon sivun peittävää paneelistoa. Arvioi kummassakin tapauksessa PV-järjestelmällä tuotetun aurinkosähkön hinta, kun järjestelmän investointikustannukset katolle asennettuna on 10 /Wp, jota varten perhe ottaa vuoden lainan 6%:n korolla, ja vaatii järjestelmän takaisinmaksuajaksi 20 vuotta. c) Toista a) ja b) kohdan laskut talolle, jonka pitkä julkisivu on suoraan etelään, ja katon kallistuskulma optimaalinen. d) Mikä olisi aurinkosähkön hinta, jos sama optimi aurinkokattojärjestelmä sijaitsisi aurinkovyöhykkeellä Phoenixissä Arizonassa? 3. Simple economic calculations of grid-connected photovoltaic systems TU Delft OpenCourseWare, Solar Cells" by Miro Zeman, licensed under CC BY-NC-SA 3.0 a) What must be the production costs of a PV system, which generates electricity at a price that is comparable with the price of conventional electricity? b) What are the costs of this system per Wattpeak? Given: The efficiency of PV modules that comprise the PV system is 14% and the lifetime of the modules is 20 years. The PV system is located in The Netherlands where the average price for conventional electricity is 0.10 per kwh. The average energy per unit area delivered by sunlight during one year is in The Netherlands 1000 kwh/(m 2 year). We neglect the conventional electricity price change due to inflation or other circumstances.)

3 4. Simple sizing calculations of grid-connected photovoltaic systems TU Delft OpenCourseWare, Solar Cells" by Miro Zeman, licensed under CC BY-NC-SA 3.0 a) How big area of a roof must be covered with PV modules in order to generate an average household annual use of electricity? b) How expensive must the PV system be in order to deliver electricity at the same price, as is the price of conventional electricity? Given: The efficiency of PV modules that comprise the PV system is 12% and the lifetime of the modules is 20 years. The PV system is located in The Netherlands where the average price for conventional electricity is 0.10 per kwh and the average energy per unit area delivered by sunlight during one year is 1000 kwh/(m 2 year). The household average electricity use is 2500 kwh per year.

4 Tables Figure 1. Monthly (1 12, kwh/m 2, mth) and annual (Q, kwh/m 2, a) radiation sums for differently oriented and shadowed surfaces in Helsinki. T = tilt angle from horizontal plane ( ), A = azimuth angle ( ) (deviation from south), H = shadowing of the horizon

5 ( ). Source [1]. Figure 2. Monthly (1 12, kwh/m 2, mth) and annual (Q, kwh/m 2, a) radiation sums for differently oriented and shadowed surfaces in Arizona. T = tilt angle from horizontal plane ( ), A = azimuth angle ( ) (deviation from south), H = shadowing of the horizon ( ). Source [1].

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