Exercises on Photovoltaics

Exercises on Photovoltaic 1) What are the Fermi level, the conduction band and the valence band? 2) What is the band gap of silicon? 3) Explain the principle of a p-n junction with reference to the depletion region. 4) Explain the generation of electricity in a solar cell. 5) Draw and explain the structure of a PV cell. 6) What are the typical efficiencies of monocrystalline, polycrystalline silicon cells, and non-silicon cells? 7) Draw the current-voltage graph of a typical photovoltaic module and explain the concepts of short circuit current, open circuit voltage and maximum power point 8) State 4 drawbacks and 4 advantages of photovoltaics. 9) The band gap of GaAs is 1.4 eV. Calculate the optimum wavelength of light for photovoltaic generation in a GaAs solar cell. 10) a) Give the equation for the I–V characteristic of a p–n junction diode in the dark. b) If the saturation current is 10−8 Am−2, calculate and draw the I– V characteristic as a graph to 0.2V. 11) a) What is the approximate photon flux density (photon s−1 m−2) for AM1 solar radiation at 0.8 kWm−2? b) AM1 insolation of 0.8kWm−2 is incident on a single Si solar cell of area 100 cm2. Assume 10% of photons cause electron–hole separation across the junction leading to an external current. What is the short circuit current Isc of the cell? Sketch the I–V characteristic for the cell. 26) A small household-lighting system is powered from a nominally 8V (i.e. four cells at 2V) storage battery having a 30Ah supply when charged. The lighting is used for 4.0 h each night at 3.0A. Design a suitable photovoltaic power system that will charge the battery from an arrangement of Si solar cells. a How will you arrange the cells? b How will the circuit be connected?

c How will you test the circuit and performance?

28) What is the best fixed orientation for power production from a photovoltaic module located at the South Pole?

29) Einstein won the Nobel Physics Prize in 1905 for explaining the photoelectric effect, in which light incident on a surface can lead to the emission of an electron from that surface with energy: E = hν−Φ where hν is the energy of a photon of light and Φ is a property of the surface. a) What are the main differences and similarities between the photoelectric effect and the photovoltaic effect? b)

Discuss how, if at all, the photoelectric effect could be used to yield useful energy.

30) The band gap of intrinsic Si at 29

O

C is 1.14 eV. Calculate the probability

function exp (−Eg/2kT) for electrons to cross the full band gap by thermal excitation. 31) A Si photovoltaic module is rated at 50W with insolation 1000Wm −2 as for peak insolation on Earth. What would be its peak output on Mars? (Data: Mean distance of the Sun from Earth is 1.50×1011 m; from Mars 2.28×1011 m.’ 32) For a Photovoltaic (PV) powered calculator, please calculate the following: (a) The PV material on a PV powered calculator is a rectangle measuring 20 mm by 5 mm. What is its area in mm2? (b) Its efficiency, to convert power from the sun into electrical power for the calculator, is 10%. How much power input is required to get a power output of one mW? (c) What is the light intensity (in mW per mm2) that is necessary to get this power output from the PV material in the calculator? (d) On a bright sunny day the amount of light from the sun is 1000 W per 1m2.

Show that this is equivalent to 1 mW per 1 mm2. How much power output does the PV material in the calculator produce on this day?

33) On a sunny day a PV cell with an area of 10 cm by 10 cm will deliver a current of 2 A and a voltage of 0.5 V. (a) How much power does this PV cell produce? (b) How many of these cells are needed to produce 15 W electrical power? (This is the power necessary for one low energy light bulb, which provides the same level of light as an old style 60W light bulb.) (c) What is the total area of PV material (in m2) to produce 15 Watts? (d) How many of these low energy light bulbs can be lit when the area of PV material is 1 m2?

34) One PV module has 48 monocrystalline silicon PV cells. The area of each cell is a pseudo square with an area of 12 cm by 12 cm. (a) What is the area of one PV cell (assume that each PV cell is a true square)? (b) What is the total area of PV material in this PV module (in m2)? (c) The efficiency of one PV cell to convert energy from the sun into electricity is about 16.4%. How much power from the sun is required to get 100 W of electrical power output from one PV cell? (d) On a very bright sunny day the amount of light from the sun is 1000 W/m2. How much power would this PV module produce at this time?

35) The Sun-Seeker, a PV powered light aircraft, uses `about 700' silicon PV cells connected in an array which supplies up to 120 V. (a) Assuming a maximum voltage of 0.5 V per PV cell, how do you think the PV cells are arranged and exactly how many PV cells are in the PV array?

(b) Each PV cell is a rectangle measuring 140 mm by 100 mm. What is the area of one PV cell and the total area of PV material? (c) With an incident light intensity of 800 W/m 2, the total power output from the PV array is 288 W. What is the energy efficiency of the PV cells? What type of silicon PV material are the PV cells made from?

36) (a) A PV module consist of 40 PV cells. Each PV cell measures approx. 100 mm by 100 mm. What is the area of one PV module? (Assume that the PV module area is the sum of the cell areas. This is a valid assumption because the PV cells are very closely packed into the special PV modules.) (b) If each PV cell supplies 2.5 A and 0.5 V (at light intensity of 1000W/m 2), what is the power output and the efficiency of one PV module? (c) Considering the efficiency, PV cell size and shape what type of PV material are the PV cells made from? (d) There are 100 PV modules in the whole PV array. What is the total area and the maximum power output of the PV array?

37) Imagine a family living in Africa. They have no grid connection and hence no electricity so they intend to buy a Solar Home System (SHS). This will allow them to have light and to watch TV in the evening. You must help them to look at their electricity requirement to see what size of SHS will provide enough electricity. In Africa, where their home is, the energy from the sun averages 6 kWh/m 2 each day. That means the energy provided from the sun is equivalent to a light intensity of 1000W/m2 for six hours each day. In fact there would be about 12 hours of sunlight during which time the light intensity would vary but the daily total would be 6 kWh/m2. (a) The PV module in a SHS has a power output of 50 Wp. Assuming that the module operates at 25°C (i.e. at STC), how much electricity will it provide every day?

(b) The family wants to have one light in the main room of the house, one light in the kitchen and one on a table where the children do their homework. Of course they would use low energy light bulbs, which require between seven and twenty Watts. (Equivalence of low energy light bulbs to standard light bulbs: 7 W @ 40 W, 11 W @ 60 W, 16 W @ 75 W & 20 W @ 100 W). Which light bulbs would it be best to use for the different lamps and why? (c) Assume that the main light is used for four hours a day, the kitchen light for two hours per day and the table light for three hours each day. How much electrical energy does each light use each and what is the total daily requirement of the lights? What power output would a PV module require to supply this electricity? (d) The family also likes to watch TV. If their television requires 50 W and they watch every day for two hours, what is its daily electrical energy requirement? (e) Does the PV module in the SHS supply enough energy for all their needs? (f) Discuss the result.