Classic silicon semiconductor solar cells, for example, are sold with a peak power of 300 watts for 400 euros:
The manufacturer states: 295 kWh per year with a south orientation, 260 kWh with an east/west orientation. This is an average of 0.75 kWh per day. With an average day length of 12 hours (which is the same everywhere on our globe), that's only 750/12 ≈ 60 watts, averaged over the day. (We do not include the night.) This results in a purchase price of 6700 € per generated kilowatt (averaged over the year).
In the following we compare this technology and this price with our concepts.
We do not convert the energy of the solar radiation directly into electrical energy, but first into heat and then into electrical energy, because the structural components for the production of such energy converters are remarkably cheaper than the large-area silicon semiconductor chips:
At the heart of our approach is the conversion of sunlight into heat. These are thermosolar panels. It's just a black painted metal surface that collects solar heat. Inside, a liquid (e.g. oil) flows, carrying away the thermal energy for further processing. Oil is more efficient than water, because the higher temperature improves the COP (coefficient of performance) of the downstream thermal engine.
Requirements:
→ Largest possible surface area
→ Inexpensive production
→ If necessary, tracking with the position of the sun.
→ Temperature optimization of the liquid (oil).
The most cost-effective solution is a flat thin-walled metal sheet (with beads for mechanical stability), or a set of thin-walled tubes. In the case of electrical power generation, a high operating temperature optimizes thermodynamic efficiency (COP) according to the second law of thermodynamics. In the case of supplying a refrigerator and for water production, the oil temperature must be adapted to the consumer (steam engine or compressor-refrigerator, also absorber-refrigerator).
-> If we drive a steam engine with the thermal energy from the internal fluid, to further drive an electric generator, it is like following:
The higher the upper temperature, the better the efficiency (COP). For example, if we can work with T cold =27°C and T hot =300°C, we get η≈47%. For T hot =500°C, it would give us a COP of η≈61%. The flow rate of the heat transfer oil (from the thermosolar collector to the steam engine) must be matched to the power dissipated by the steam engine by means of a suitable control/regulation system (temperature-resistant oil pump required) to achieve temperature-constant operation of the steam engine. The electrical power generator must be adapted to the output-power of the steam engine.
In the case of fixed thermosolar collectors, operation with a power, which is variable in a
relatively wide range, must be made possible.
In the case of tracked thermosolar collectors (rotation according to the position of the
sun), the variation of the power is less pronounced.
The decision on possible tracking (or not) arises in the course of development work from the
answer to the question: Which solution is more cost-efficient for the same power output - tracking
or large-area thermosolar collectors ?
Costs for the sheet metal: Thin-walled sheet steel can be obtained in Germany ready for shipment in small sheets (of sufficient thickness) for 30 Euros per square meter. In Africa or Asia it is much cheaper. To be on the safe side, I calculate pessimistically and use this above mentioned price, knowing that large quantities from the metal manufacturer on coil, are much cheaper. Two plates, one on the bottom and one on the top, between which the oil runs, makes less than 60 €/m².
Let us now calculate the achieved thermal power: the solar constant is = 1.368 kW/m².
Yield 12 hours per day at 40% (because of absorption of solar radiation in the atmosphere and because of the movement of the sun, again calculated pessimistically) gives 550 watts · 12 hours = 6600 Wh every day per square meter of collector surface. We remain at 550 watts per hour of thermal power daily average per square meter of solar collector area.
Achieved mechanical power: With this thermal power we drive a steam engine, optimally a Sterling engine. Since (due to mechanical friction losses and due to heat losses), experience shows that the real efficiency reaches about two thirds of the ideal efficiency, we calculate η ≈ ⅔ · 47% ≈ 30%
=> The average mechanical power in the daily mean is approx. 30% · 550 watts ≈ 165 watts (conservative estimation of the value).
Electrical power achieved: Power generators usually have a good efficiency (COP) between 90% and 95%. So, related to the 165 watts of mechanical power just calculated, we can expect 150 watts of electrical power, per square meter of solar collector area. This is the calculation for sunny weather in sunny Asia and Africa. For German conditions, we would expect about 60 watts per square meter.
Comparison of efficiencies: So the efficiency of our thermal solar cells is
about the same as the efficiency of the photovoltaic semiconductor solar cells.This is normal.
Comparison of purchase cost: This is our advantage.
Photovoltaic semiconductor solar cells are typically in the range of 220 ... 250 €/m², as can
be easily researched on the Internet.
For the same power, our thermal solar cells are well below 60 €/m², plus the cost of the
sterling engine plus power generator.
A realistic price for a steam engine is about 8000 ... 10000 € for a 40 ... 50 kW engine,
thus about 200 €/kW. If I convert the price of 200 €/kW to the solar cell area at 150 Watt/m², I
get 200/1000*150 = 30 € per m² solar cell area. This means that for the energy coming from 1 m² of
thermal solar cell area, I have to spend 30 € to convert the thermal energy into mechanical energy
of a rotating shaft.
We can find power generators conveniently and quickly on the Internet, including diesel
engine with 5kW under 1000 €. If we leave away the diesel engine, then it becomes much cheaper,
thus I estimate 10 kW for 1000 € (without diesel engine, which we do not need). That is half of
what we needed for the steam engine. So that comes to 15 € per m² of solar panel area.
Thus, we have for the thermo-solar cell:
- 60 €/m² for the solar heat collector
- 30 €/m² for the steam engine
- 15 €/m² for the electricity generator
- Makes in total 105 €/m² with about the same efficiency as the semiconductor solar cell.
If I calculate the semiconductor solar cell with an average of 235 €/m² (see above), then we
have to calculate only 105 €/m² for our thermo-solar cells with the same efficiency (COP) and the
same power. That gives a price saving of 130 €/m², corresponding to 55% cheaper. So our thermal
solar cells cost a bit less than half of the semiconductor solar cells, with the same power and the
same efficiency. I have calculated at European prices clearly to the disadvantage of our
thermo-solar cell, whereby in reality, I expect that the production at African or Asian price level
turns out still clearly more favorably for our thermo-solar cell.
Summary: Our thermo-solar cells cost (noticeably) less than half of classical semiconductor
solar cells, reaching the same performance.