Blowout Week 70 featured Tesla’s new 7 kWh and 10 kWh lithium-ion battery storage units. Will they allow households with rooftop solar PV systems to store enough surplus solar power to fill domestic demand throughout the year without the need to import grid power when the sun isn’t shining? It all depends on how much storage is needed and how much it costs, and in this post I present ball-park estimates of storage requirements and costs for domestic rooftop solar installations calculated using the following simplifying assumptions:

Household consumption is 5,000 kWh/year. (About right for Western Europe, low for the US, high for most of the rest of the world.) Household demand is constant through the year at 13.7 kWh/day, or 0.57 kWh/hour. The impacts of changes in cloud cover are ignored. The storage requirements generated by diurnal fluctuations in solar output are insignificant relative to the storage requirements generated by seasonal fluctuations. The storage batteries are 100% efficient, with no conversion losses and no charge/discharge restrictions. Solar panels are inclined south at the optimum angle for maximum annual generation.

Four rooftop solar cases are considered: at the Equator, at latitude 20 north, at latitude 40 north and at latitude 60 north. To generate 5,000 kWh in a year we need 3.8 kW of installed PV capacity on the Equator (load factor 15%), 3.4 kW at latitude 20N (load factor 17%), 3.6 kW at latitude 40N (load factor 16%) and 5.7 kW at latitude 60N (load factor 10%). The load factors are from the Estimating global solar PV load factors post.

Figure 1 shows annual solar output in kWh/square meter/day for the four cases using five-day averages (data from PVeducation). It plots module output from fixed solar panels inclined south at the angle that generates maximum annual generation (which is the same as latitude only on the Equator. Optimum panel inclinations are 18 degrees relative to the horizontal at latitude 20N, 35 degrees at 40N and 49 degrees at 60N.) The most notable feature is the seasonal variation in solar output, which ranges from 13% at the Equator and 45% at latitude 20N to a factor of 2.6 at 40N and a factor of 36 at 60N:

Figure 1: Annual solar output by latitude for the four cases considered



Discussing these cases in sequence:

Rooftop solar system on the Equator:

Figure 2 plots annual solar generation against household demand for a rooftop solar PV system on the Equator. The data on this and following Figures are adjusted so that the system generates 5,000 kWh per year (68.5 kWh every five days). The green-shaded areas show periods where the rooftop system generates more power than the household needs and the pink-shaded areas show where it generates less. The amount of battery storage needed to store the surplus power for re-use during deficit periods is given by the total number of kWh in the green (or pink) shaded area:

Figure 2: Annual solar generation versus demand for a solar system on the Equator

A solar PV system on the Equator does not need large amounts of storage because solar generation doesn’t change much through the year and because the solar cycle is only six months rather than a year long. The total storage requirement is 48 kWh, equivalent to 3.5 days of average generation, and this can be filled with five Tesla 10kWh wall units costing 5 X $3,500 = $17,500, exclusive of installation. This, however, still more than doubles the cost of the system. (Installation costs for the solar panels would be about $15,000 assuming $4,000 per installed kilowatt and 3.8 kW installed).

Rooftop solar system at latitude 20 north

Figure 3 plots the data for this latitude. Even though we are still in the tropics the storage requirement increases significantly. To fill winter demand the household now has to store 285 kWh of surplus summer generation, requiring 29 Tesla 10kWh wall units costing $101,500.

Figure 3: Annual solar generation versus demand for a solar system at latitude 20N



Rooftop solar system at latitude 40 north

Figure 4 plots the data for this latitude. To fill winter demand the batteries now have to store 676 kWh of surplus summer generation, requiring 68 Tesla 10kWh wall units costing $238,000.

Figure 4: Annual solar generation versus demand for a solar system at latitude 40N



Rooftop solar system at latitude 60 north

Figure 5 plots the data. To meet winter demand at this latitude the batteries have to store 1,522 kWh of surplus summer generation, requiring 153 Tesla 10kWh wall units costing $535,500 and weighing 15.3 tons:

Figure 5: Annual solar generation versus demand for a solar system at latitude 60N



Even with these rough numbers it’s hard to see how anyone living any distance from the Equator is going to be able to justify the cost of installing enough batteries to go off-grid with a domestic rooftop solar PV installation.

Finally, Figure 6 plots storage requirements as a percentage of annual generation against latitude for the four cases considered. The percentages will be the same regardless of the size of the installation.

Figure 6: Battery storage requirements versus latitude.

