The background to this work is the assumption that solar electricity will play an important role in the future electricity system. If solar electricity will stand for a large part of the electricity production, the situation may arise instantaneous that the access of solar electricity exceed the demand, and if the produced electricity not can be stored or exported, this electricity will be seen as an overproduction which can not be used.

The goal with this study is the following:

• Calculate how much solar electricity that can be installed in Sweden without overproduction of solar electricity. The basis is use of Swedish climatic data and today’s electricity consumption.

• Calculation of how large the overproduction are if the more solar electricity is produced, that is if we allow the solar electricity production instantaneous exceed the electricity consumption.

• In the calculations solar radiation data from several sites are used for studying how the solar electricity production may vary in different sites. This can answer the question if low production in some parts of the country (for example due to overcast weather) is compensated by more clear weather in other parts of the country.

• Calculation of the optimal direction of PV modules in Sweden if large areas are installed. This can answer the question if it is possible to direct the modules to other directions than south to maximize the electricity production without causing overproduction of electricity.

• The calculations will be performed with several years of climatic data to see the difference between the years.

One limitation with the study is that the calculations are performed only for Swedish circumstances and with Swedish data, although the Swedish electricity grid today is a part of a larger North European electricity system. One reason is that this was a limited study, and calculations with data for a larger region should demand a lot of expensive data. However, it can be assumed that when overproductions will arise in Sweden, which is during daytime in summer, the situation often will be similar in neighbour countries, which limits the possibility for export of excess electricity produced by PV technology.

Furthermore, two simplifications are used in the calculations.

• It is assumed that it is possible to distribute the produced solar electricity in the electricity grid without restrictions

• It is assumed that all electricity produced by PV installations up to the point when the production equals the consumption can be consumed. This means that it is assumed that all other electricity production in Sweden can be shut down when this occur.

The last simplification is questionable, since there in reality always are electricity productions which can not be turned of without loosing production, and this is further discussed in chapter 4. However, the main goal with this study is to find the approximate size on how much PV that can be installed, and for this the approximations are acceptable.

1. Method

The climatic data used are hourly mean values for ambient temperature, direct and diffuse radiation for five Swedish sites (see table 1), spread over the country. We assume that the distribution of PV installations in the future will be according to the population distribution, and therefore the different climatic data are weighted according to how large parts of the Swedish population that live near the different sites. Climatic data for the full years 1988-1991 was used.

Table 1. Swedish sites with climatic data used in the study. Site Latitude Population- distribution [%] Optimal tilt [degrees] Optimal azimuth [degrees] Lund 55,8 25 35 10 Goteborg 57,8 25 40 15 Stockholm 59,2 30 40 5 Borlange 60,5 10 40 5 Lulea 65,5 10 45 10

To get data for the electricity use, we use hourly data from [1] for 1996-2005. The optimal should have been to use data for the same years as we had climatic data, but when we study the profile of the electricity usage between different years, the difference is small. If we compare a certain period for several years (for example the first week in a certain month), the large difference is not between years, but between weekdays (Monday-Friday) and weekends (Saturday-Sunday). A typical profile for the electricity usage was therefore created from the data, and it was assumed that this profile was representative for the years of climatic data that where studied (1988-1991).

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Figure 1. Average electricity use in Sweden during 1996-2005. During the weekends, the

electricity use decrease. Data from [1].

In the calculations, the simplification is done that the PV modules have 10% system efficiency, independent on module temperature and irradiation level. By comparing the calculated produced electricity with the assumed used electricity the same hour, it is possible to calculate how large PV area that correspond to the need during critical hors (daytime, summer). It is also possible to calculate what happens if another distribution of modules over Sweden is assumed (other to what corresponds to the population distribution), what happens if the PV modules is directed to other directions than south, and what happens if the PV area in Sweden is larger than the area needed to precisely avoid overproduction.

2.

Result

Figure 3 shows the electricity production from grid-connected solar electricity during four years when the solar cell area has been chosen so the electricity production during sunny summer days exactly matches the electricity demand (marked with stars in the figure). This area corresponds to 128 Mm2 PV area (referred to as A0 in this text). It is assumed that this area is divided between the sites according to the population distribution and that the modules have optimal tilts and azimuths according to table 1. If we assume that the modules are equal distributed over the five sites, the maximum possible electricity from the sun before overproduction starts is the same (approx. 9,5% of the total electricity consumption in the country), which is shown in table 2. Furthermore it is seen that the maximum possible solar cell area before overproduction starts is 5-10% larger if the PV modules are divided between the sites, compared to concentrating all the PV production at a single site. This effect is due to a more uniform production since local extreme weather conditions are dampened with country wide PV production.
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Figure 4 shows how large part of the Swedish electricity production that can be covered if the solar cell area is larger than A If the total solar cell area is 2 * A almost 18% of the electricity need (blue line) can be covered by solar electricity while the overproduction is slightly less than 6%. If the PV area is 3 * A 23% of the electricity need can be covered, while the overproduction is

amply 18%, etc. Figure 5, which can be of academically interest, shows how a large part of the electricity production that can be covered in the total PV area is substantially larger than A0. The

maximum amount of the Swedish electricity use that can be covered direct by PV (without storage), is by natural reasons 50% since the PV cells don’t give any output during night-time, but then over 90% of the possible generated solar electricity can not be used due to overproduction.

Table 2. Possible PV area before production of solar electricity starts to exceed the electricity demand. A0 is the maximum PV area in Sweden before solar electricity production starts to exceed the demand. City Name 2 (A0) ( m ) Electric Demand met by PV at Ao ( % ) Lund (0.25) 118,356,000 8.98 Goteborg (0.25) 114,270,000 8.51 Stockholm (0.30) 120,326,000 8.80 Borlange (0.10) 116,565,000 8.64 Lulea (0.10) 117,982,000 8.28 Sweden (by population) 128,265,000 9.488 Sweden (even by city) 129,006,000 9.49

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In [2] results are also presented on how sensitive it is to direct the PV modules direct to south. For ’’small” PV areas, below A the output will be only 75% if the modules are directed to east and

west, compared to if they are directed to south. When the total PV area starts to exceed 2 * A the

direction of the PV modules get less important, but still the largest output is if the modules are directed to the south. The calculations also show that if the total PV area is equal to or larger than 4

• A it is favourable to direct the PV modules (with equal areas) to south-east and south-west instead of south since this generates a more even electricity production over the day.