# Energy Storage

– yearly electricity demand: 4000 kWh/a

Task 1: a photovoltaic system for your house (understanding economic calculations; 20 points)

The photovoltaic system or the photovoltaic modules have a service life of 25 years (= observation

period) and an output of 10 kWp. The system costs 1,200 € per kWp. The system component inverter

has a purchase price of 150 €/kWp. These costs are already included in the system costs. However,

the inverter only has a service life of 10 years, which means it has to be replaced twice.

The price change factor r is 1.03 and the interest factor q is 1.07.

1.1 What is the residual value of the third inverter? (5 points)

1.2 What is the total annuity of the photovoltaic system? (5 points)

1.3 How high are the electricity generation costs if the photovoltaic system generates 850 kWh/kWp

annually? (5 points)

1.4 How does the value from 2.3 change, if the specific yield increases to 1050 KWh/kWp (real value

of the last 10 years!) due to climate change, the lifetime of the modules increases to 30 years and

that of the inverter to 15 years. The system costs (at the same price for inverters will decrease to

1000 €/kWp. (5 points)

Task 2: Electric car with battery and home energy storage system (40 points)

We would now like to add an electric car to the house. We want to integrate the car into the power

supply of the house, i.e. we take a car that allows charging as well as discharging the battery

(currently only works with CHAdeMO plug, e.g. Nissan Leaf).

Further general conditions:

• Costs for the wallbox: 800 €

• For all components, we assume a service life of 15 a and an interest rate of 2%

• Annual mileage: 10,000 km

• The own consumption quota for the electricity generated from photovoltaics is 50%.

• Electricity purchased from the grid: 30 €ct/kWh

• Otherwise: Data of the photovoltaic systems from task 2

• Tax: e-car: 0 €/a; petrol: 100 €/a

• Insurance: e-car: 1000 €/a; petrol engine 1300 €/a

• Maintenance: e-car: 500 €/a; petrol engine 700 €/a

1.1 What is the cost of approximately one kilowatt hour of home storage (battery) in €/kWh? (3

points)

1.2 How much does a Nissan Leaf (version with 40 kWh battery) cost approximately? (3 points)

1.3 What do you notice when comparing these figures? Can you find an explanation for this? (5

points)

1.4 What is the annual electricity yield from the photovoltaic system? What proportion of this is

fed into the grid? What proportion of this can you use in the house or to charge the car? (5

points)

1.5 What feed-in tariff do you receive annually under either the German EEG regulation or in

your country? (2 points)

1.6 What is the typical consumption of an electric car? (3 points)

1.7 What is the annual electricity demand for the e-car? (5 points)

1.8 How much electrical energy do you have to draw from the grid? (5 points)

1.9 What are the annual costs of supplying electricity to the home and car (as an alternative for a

new e-car, add EUR 0 capital-related costs for the continued use of the old petrol car).

1.10 So take into account the capital costs of the car and the PV system; electricity purchased

from the grid as well as income from feeding electricity into the grid; plus tax, insurance and

maintenance for the car.

Make a distinction between the four cases:

– Electric car without PV

– old petrol engine without PV

– Electric car with PV

– old petrol engine with PV

– What are your conclusions? (10 points)