Family Smith is interested in buying a solar energy system. After some search on internet they have found two different systems that they are considering. System A is a PV system based on multicrystalline silicon solar cells and System B is a PV system based on amorphous silicon solar cells.

System A: The efficiency of the multicrystalline silicon module amounts to 15%. The dimensions of the solar module are 0.5m by 1.0m. Each module has 75 Wp output. The modules cost 60€ each.

System B: The amorphous silicon solar modules have an efficiency of 6%. The dimensions of the solar modules amount to 0.5m by 1.0m. The output of each module is 30 Wp. The modules cost 20€ each. The advanage of the amorphous silicon solar modules is that they perform better on cloudy days in which there is no direct sunlight. Installed in the Netherlands, this system gives, on a yearly basis, 10% more output per installed Wp than the multicrystalline silicon modules.

Both systems are grid-connected using a 900 Wp inverter. The total price of the inverter, the cables, the installation and other costs amounts to € 1000. The solar modules are to be installed on a shed. The roof of the shed can only support 10 m² of solar modules.

In the Netherlands a PV system having multicrystalline silicon module generates on average 850 Wh per Wp in one year. The performance of both types of modules is guaranteed for 20 years. The price of electricity from the grid is € 0.23/kWh. Assume that all the power produced by the PV system is completely consumed by the Smith family.

a) How much (peak) power (in Wp) can be installed for system A given the peak power of the inverter and the area available on the shed?

b) How much (peak) power (in Wp) can be installed for system B given the peak power of the inverter and the area available on the shed?


c) What is the price of a kWh of electricity (in €/kWh) generated by system A?


d) What is the price of a kWh of electricity (in €/kWh) generated by system B?


e) Family Smith is eligible for a municipal subsidy for sustainable energy that amounts to 15% of the initial costs of the PV system. Using this subsidy, how many years does system A need to be operational to earn the own investment back (assume that the electricity price of € 0.23/kWh does not change).

f) The same question as e) but for system B.

900

600
0.112
0.12

900

600
0.112
0.12
8.309
9.22

Are you from India?

We are going to build a PV system on a roof of 10m2, and we have two possible PV modules:

(1) A first generation module with efficiency ç=18% and cost of 0.80€/Wp.

(2) A second generation PV module with efficiency ç=10% and cost of 0.40€/Wp.

The non-modular costs are 100€/m2.

Note that the irradiance under standard test conditions is 1000W/m2.

What is the cost in € of implementing a PV system for the entire roof using first generation technologies?

What is the cost in € of implementing a PV system for the entire roof using second generation technologies?

Family Smith is eligible for a municipal subsidy for sustainable energy that amounts to 15% of the initial costs of the PV system. Using this subsidy, how many years does system A need to be operational to earn their own investment back (assume that the electricity price of €0.23/kWh does not change)?

Excellent

a) To calculate the peak power (in Wp) that can be installed for system A, we need to determine the maximum number of modules that can be installed on the shed's roof. The available area on the roof is 10m².

Let's calculate the area occupied by each module:
Area per module = length × width
Area per module = 0.5m × 1.0m = 0.5m²

Now, let's calculate the maximum number of modules:
Maximum number of modules = Total available area ÷ Area per module
Maximum number of modules = 10m² ÷ 0.5m² = 20 modules

The peak power (in Wp) that can be installed for system A is the product of the number of modules and the power output per module:
Peak power for system A = Number of modules × Power output per module
Peak power for system A = 20 modules × 75 Wp/module = 1500 Wp

Therefore, system A can have a peak power of 1500 Wp.

b) Similarly, to calculate the peak power (in Wp) that can be installed for system B, we'll follow the same process.

Peak power for system B = Number of modules × Power output per module
Peak power for system B = Total available area ÷ Area per module × Power output per module
Peak power for system B = 10m² ÷ 0.5m² × 30 Wp/module
Peak power for system B = 600 Wp

Therefore, system B can have a peak power of 600 Wp.

c) To calculate the price of a kWh of electricity (in €/kWh) generated by system A, we need to consider the total cost of the PV system, including the modules, inverter, installation, and other costs.

Total cost of system A = Number of modules × Cost per module + Cost of inverter and other components
Total cost of system A = 20 modules × €60/module + €1000
Total cost of system A = €1200 + €1000
Total cost of system A = €2200

Next, let's calculate the total energy generated by system A in one year:
Total energy generated by system A = Peak power of system A × Average energy generated per Wp
Total energy generated by system A = 1500 Wp × 850 Wh/Wp = 1275000 Wh = 1275 kWh

The price of a kWh of electricity generated by system A is the total cost divided by the total energy generated:
Price of electricity from system A = Total cost of system A ÷ Total energy generated by system A
Price of electricity from system A = €2200 ÷ 1275 kWh = €1.725/kWh

Therefore, the price of a kWh of electricity generated by system A is €1.725/kWh.

d) Similarly, to calculate the price of a kWh of electricity (in €/kWh) generated by system B, we'll follow the same process.

Total cost of system B = Number of modules × Cost per module + Cost of inverter and other components
Total cost of system B = 10 modules × €20/module + €1000
Total cost of system B = €200 + €1000
Total cost of system B = €1200

Total energy generated by system B = Peak power of system B × Average energy generated per Wp
Total energy generated by system A = 600 Wp × 850 Wh/Wp = 510000 Wh = 510 kWh

Price of electricity from system B = Total cost of system B ÷ Total energy generated by system B
Price of electricity from system B = €1200 ÷ 510 kWh = €2.353/kWh

Therefore, the price of a kWh of electricity generated by system B is €2.353/kWh.

e) To calculate the number of years system A needs to be operational to earn the own investment back (assuming the electricity price of €0.23/kWh does not change), we need to consider the annual savings in electricity costs compared to the grid.

Annual savings from system A = Total energy generated by system A × Price of electricity from the grid
Annual savings from system A = 1275 kWh × €0.23/kWh = €293.25

Total investment after subsidy = Total cost of system A - Municipal subsidy
Total investment after subsidy = €2200 - 0.15 × €2200
Total investment after subsidy = €2200 - €330
Total investment after subsidy = €1870

Years to earn back the investment = Total investment after subsidy ÷ Annual savings from system A
Years to earn back the investment = €1870 ÷ €293.25 ≈ 6.37 years

Therefore, it will take approximately 6.37 years for system A to earn the own investment back.

f) Similarly, to calculate the number of years system B needs to be operational to earn the own investment back (assuming the electricity price of €0.23/kWh does not change), we'll follow the same process.

Annual savings from system B = Total energy generated by system B × Price of electricity from the grid
Annual savings from system B = 510 kWh × €0.23/kWh = €117.30

Total investment after subsidy = Total cost of system B - Municipal subsidy
Total investment after subsidy = €1200 - 0.15 × €1200
Total investment after subsidy = €1200 - €180
Total investment after subsidy = €1020

Years to earn back the investment = Total investment after subsidy ÷ Annual savings from system B
Years to earn back the investment = €1020 ÷ €117.30 ≈ 8.7 years

Therefore, it will take approximately 8.7 years for system B to earn the own investment back.

Cheater

a) 765

c)0.232