Download Calculation of the Amortization time for a „Grid connected“ System.

1. Lesson Two: Solar Energy
1.1
Aims of the lesson
Giving a brief overview about Solar Power
Enabling you to dimension an off-grid photovoltaic system
1.2
Timetable
The Lesson should be about 45 to 50 Minutes long. Here is our timetable:
8 minutes: Introduction into Photovoltaic cells and „Off Grid“ Systems
5 minutes: Dimensioning of an „Off Grid“ System
8 minutes: Introduction into „Grid connected“ Systems, Advancements and Amortization
2 minutes: Calculation of the Amortization time for a „Grid connected“ System.
15 minutes: Groupwork
rest (about 7 minutes): presentation of the solution
1.3
Input
1.3.1 Types of Photovoltaic cells
monocrystalline cells:
This type of cells is one of the most common. Mon crystalline cells cost about 5 to 10€ per W
of output Power. This i s a high price, but the efficiency of these cells is about 15 to 17%,
which is much better then most of the other cell - types. Because of the high efficiency, you
typically need an area of about 6 m^2 to generate one kWp of output power.
multicrystalline cells:
This type of cells is the second type, that is used very much. These cells cost about 3€ per W of
output power. The disadvantage of this type is the low efficiency. The efficiency is about 10 to 13%.
As a result, the area, you need for the same output power, has to be bigger than the area, needed by
monocrystalline cells.
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1.3.2 Photovoltaic Systems
Photovoltaic systems produce about 0,5 percent of the electrical power needed in Europe
and about 1.5 percent worldwide.
The two types of Photovoltaic systems are „Off Grid“ and „Grid connected“.
The differences between those two types are, that an off grid system, doesn‘t need a
connection to the public electricity grid. It can be installed nearly everywhere. The german
word used for this type of system is "Inselanlage" or in english "Island System"; this is a very
appropriate word for this system, because it could be useed on a tiny island too. A grid
connected system needs the public electricity grid. Another difference is, that with an off
grid system, the produced energy has to be stored. The grid connected system feeds the
produced power directly into the public electricity grid.
„Off Grid“ Systems:
The so called „regulator“ gets it‘s power from the Photovoltaic cells and charges the battery
in a economic way. By using a regulator, the lifetime of the battery can be extended. The
Inverter converts the Direct Current (DC) from the battery into an Alternating Current (AC).
The Voltage at the AC-Side is 230V. The inverter can only convert a limited amount of power,
so it has to be powerful enough for the connected devices. The battery buffers the energy so
that you can use it, whenever you need it.
„Grid connected“ Systems:
The idea behind this system is, that every house is a small power station. The Photovoltaic
modules are normally multycrystalline, because monocrystalline cells would be too
expensive. The cable from the Photovoltaic Cells goes into a Isolator. An Isolator is nothing
more than a BIG manual Circuit breaker. Normally this Breaker is closed, but if you have to
repair something, you have to open the circuit because you can't turn off Photovoltaic
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modules otherwise. The inverter has the same function as a inverter in a „Off Grid“ System,
but normally it's more powerful. The produced power is counted by a meter and feeds into
the public electricity grid.
Dimensioning of an „Off Grid“ Photovoltaic system.
There are a couple of appliances in the circuit which need together 300W (
). All
connected devices should work for 8 hours without sunlight (t). The efficiency of the inverter
( ) is 88% and the battery voltage is 12V. The battery should be charged within 8 hours
(tsun). Because of the bad mounting angle and the efficiency grade of the charging regulator,
the efficiency ( ) decreases to 70%. The cell - type is monocrystalline.
The first thing you have to do is calculating the needed capacity of the battery:
Then you have to calculate the needed output power of the photovoltaic cells:
The last step is to calculate the needed Area for the Photovoltaic cells.
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Advancement
If you produce too much electricity with your PV system, you can sell it to your supplier and
get money for it. This money is called „Advancement“. Of course you have to use a gridconnected solar system. The amount of Advancement depends on the country and the
energy supplier. The following table shows the average Advancement in different countries:
Country
Advancement
Amortisation time
(10000€, 2MW/year)
Austria
Germany
Poland
15 ct/kWh
35 years
20 ct/kWh
25 years
17 ct/kWh
30 years
Calculation of the Amortization time for a „Grid connected“ System.
With this formula, the Balance of the Photovoltaic system can be calculated. Here is am
example:
The system costs 10.000€, you get 1.500€ Support, your system produces 2.000 kWh per
year, the Advancements is 0,15€ per kWh and you have to spend 20€ per year for
maintenance. If you want to know the balance in 10 years, n would be 10.
This means, that the system‘s actual cost is 5700€.
To calculate the time of Amortization, the formula has to be rearranged.
By setting the Balance to zero, you get a number of years. After that time, your System paid
for itself. Every produced kWh after that goes directly into your pocket.
With the Data from the first example, we get a time of about 30 years.
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1.4
Task for Group work
1.4.1 Scaling of an off-grid photovoltaic system
An off grid solar system should be dimensioned. There are a couple of appliances in the
circuit which need together 300W, 230 V. All connected devices should work for 8 hours
without sunlight (t). The efficiency of the inverter ( ) is 88% and the battery voltage is
12V. During one day (8 hours of sunlight) the battery should be loaded up.
calculate the capacity of the battery
How much output power must the solar panel have, if you want to charge the battery
completely within 8 hours (tsun) of sunshine. Because of the bad mounting angle, the
efficiency ( ) decreases to 70%.
How big is the area of the solar panels if you use monocrystaline photovoltaic cells?
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1.4.2 Rate of Solar Energy in the Fuel Mix
The table below shows the development of the fuel mix in Europe. Think about the missing
percentages and discuss.
1.4.3 Calculate the time of amortisation of a grid-connected Photovoltaic system.
Standards:
CostsPV: 20.000€
Support: 2.500€
EPV: 4000kWh
Advancement: 20ct/kWh
Costs per year : 25€
n... years
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1.5
Solution of Group work (for the teacher)
1.5.1 Scaling of an off-grid photovoltaic system
Calculate the capacity of the battery
How much output power must the solar panel have, if you want to charge the battery
completely within 8 hours (tsun) of sunshine. Because of the bad mounting angle, the
efficiency ( ) decreases to 70%.
How big is the area of the solar panels if you use monocrystaline photovoltaic cells?
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1.5.2 Rate of Solar Energy in the Fuel Mix
1.5.3 Calculate the time of amortization of a grid-connected Photovoltaic system.
1.6
Future innovations
1.6.1 Examples:
Solar energy powered car:
pro: no CO2 emission
con: only short distances  „CityCar“
Solar display:
pro: The photovoltaic cell is located underneath the display  no extra area needed
con: The display would be very expensive
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