The relationship between the size of a battery and self-sufficiency in a household that is connected to the grid and uses solar panels
L.P. van Velzen
22 th June 2020
Pre-MSc Research Paper
The relationship between the size of a battery and self-sufficiency in a household that is connected to the grid and uses solar panels
By
L.P. van Velzen
Date: 22nd of June 2020 University: University of Groningen Faculty: Faculty of Economics and Business Author: L.P. (Lars) van Velzen Student number: S4148290 Email: l.p.van.velzen@student.rug.nl Address: Nieuweweg 40-6 9711TH Groningen
Phone number: 0655957082 Supervisor: J.E. Fokkema
Word count: 6000
Executive summary
How can batteries and solar panels combined contribute to a better environment and increase self-sufficiency of a household? By using the synergistic effects of combined battery power and solar power. The outcomes of this research is a paper addressing the main research question: What is the relationship between the size of a battery and the self-sufficiency in a household that is connected to the grid and uses solar panels. Prior research indicates that using solar panels and batteries have an economical advantage and could help to peak shaving as well as the capacity needed to achieve this. The research gap that will be investigated in this research is the relationship of solar panels combined with batteries and the application of variable grid rates to get insight on the performance of the self-sufficiency. Self-sufficiency is calculated by using the amount of renewable energy and divide it by the total used energy. When the most ideal situation is calculated, this will be compared with a regular household to determine the self-sufficiency difference. This will determine whether the regular household or the battery household will be more self- sufficient. The results of whether a battery could offer an economical effort are calculated on an hourly base and will result in savings/expenses during a year. The application of a small battery has the highest contribution to self-sufficiency although this could be increased by using a slightly bigger battery while 100% self-sufficiency is not achievable because of the size of the battery and solar panels. The contribution of variable grid prices does not have a contribution to self-sufficiency and does not offer an economic advantage.
Table of contents
Executive summary 3
Table of contents 4
List of tables 5
List of Figures 6
1. Introduction 7
2. Theoretical framework 8
3. Method 10
3.1. Conceptual model 10
3.2. Experimental setup 12
4. Results 14
5. Discussion and Conclusion 16
References 17
Appendix 1, Order of actions 19
Appendix 2, Supply and Demand profiles 20
Appendix 3, Self-sufficiency increment with solar power and battery capacity 22
List of Tables
Table 1, Component list of used parameters in the calculations. ... 10
Table 2, Conducted experiment list ... 12
Table 5, Variable grid rates compared to single rate grid prices with variable battery and solar power capacity. ... 15
Table 6, Order of actions taken in order in a household with solar power. ... 19
Table 7, Order of actions taken in a household in order without solar power. ... 19
Table 7, Self-sufficiency percentage in households without a battery and only using solar power. ... 22
Table 7, Cost savings with solar panels and without a battery when using single rates or variable rates. ... 23
Table 8, Self-sufficiency and self-sufficiency increment of common situations in households with solar power and batteries with a battery capacity of 1 kWh. ... 22
Table 9, Self-sufficiency and self-sufficiency increment of common situations in households with solar power and batteries with a battery capacity of 4 kWh. ... 23
Table 10, Self-sufficiency and self-sufficiency increment of common situations in households with solar power and batteries with a battery capacity of 8 kWh. ... 23
List of Figures
Figure 1, Conceptual mode of the relationship of battery storage and solar power in a household. ... 10
Figure 2, Logic flow diagram of a household without battery and with solar panels which uses the solar energy first and after that it uses grid power. ... 11
Figure 3, Logic flow diagram of a household with a battery and solar panels which uses power in the order of solar power, battery power and grid power. ... 11
Figure 4, Logic flow diagram of a household with battery and grid charging capabilities, to charge a battery in advance, this could be used when energy prices are lower and it is profitable to buy energy in advance. ... 12
Figure 5, kWh consumption during the year for a household consuming 4400 kWh a year. ... 20
Figure 6, kWh consumption during the year of a household with a total energy consumption of 4400 kWh. ... 20
Figure 7, Average solar panel efficiency during the hours of the day for a period of one year. ... 21
Figure 8, Efficiency of solar panels during the days of the year, this graph includes the hours without sunlight. ... 21
Figure 9, Self-sufficiency of a households without a battery and only using solar panels. ... 22
Figure 10, Self-sufficiency in households with solar power and batteries with a battery capacity ... 14
1. Introduction
How can batteries and solar panels combined contribute to a better environment and increase self-sufficiency of a household. By using the synergistic effects of combined battery power and solar power.
The reduction of carbon dioxide emission is a broadly discussed subject. The burning of fossil fuel causes carbon dioxide which causes air pollution and is one of the leading environmental concerns (Wilcoxen, 1993). “Earth’s climate is changing as a result of human activities, particularly from energy use, and that further change is inevitable” (Sims, 2004). The known environmental impact of fossil fuels has caused the increased use and advancement of renewable energies (Ordóñez, Jadraque, Alegre, & Martínez, 2010). Sustainable energy technology developments have the ability to mitigate climate change and decrease the devastating impact on the environment
Reaching a 100% self-sufficient household by carrying out a decentralized strategy has the ability to mitigate pollution.
The increment of self-sufficiency results in decreasing carbon dioxide emission because self-sufficiency increases because of self- generated energy. This can be achieved by the use of solar panels and batteries. However, this raises the question of the size and capacity of the batteries. To be entirely energy sufficient would require huge batteries and excessive amounts of solar panels, this is not feasible in regular households. If a household is 100% self-sufficient it is grid-independent. Therefore, there won’t be any pollution. And this means a household can be environmental friendly.
Using solar panels offers a viable solution for environmental problems (Ordóñez et al., 2010). Solar panels are easy to implement on houses, and therefore one of the easiest consumer initiatives for carbon dioxide reduction. To reduce pollution and the emission of carbon dioxides, the use of renewable energy sources could take a huge step forward to mitigate climate change in the energy sector.
By replacing the conventional energy resources with renewable energy sources, the challenges of filling the energy demand gap arises. Whit conventional energy resources such as coal and gas power plants depend on fossil resources, renewable methods depend on the amount of wind or sun during the day. During the night, solar energy generation is not possible, this is only possible within a couple of hours of the day. When applying renewable resources to a household means that when not storing the energy or having a backup, the household could have a demand gap in energy resources caused by the dependence of light and wind. To fill the energy gap, one possible outcome could be storing the energy in batteries. “Energy storage utilizing batteries is acknowledged as one of the foremost vital and efficient ways of stabilizing and balancing electricity power networks.” (Al Zyoud
& Abu Elhaija, 2019)
The problem using this method is the charging cycle to match supply and demand. This means that during the day there could be more energy generated than is required, this energy could be used for storage but how much needs to be stored and the frequency of the storage, has yet to be determined. The demand for households is not homogenous and depends on several factors seasonal fluctuations in energy demand and time. During the winter, electricity usage is higher than during the summer (Hekkenberg, Benders, Moll, & Schoot Uiterkamp, 2009) and the energy consumption during the day is higher than during the night (Karjalainen, 2011). “Power management and stability assurance are critical tasks in modern grids.” (Palizban & Kauhaniemi, 2016) As a result, grid balancing is also an important topic. When an entire city uses solar panels and delivers to the grid during the day, the grid receives huge amounts of power while during the night it does not receive any power. Due to this, it is of huge importance to store energy to overcome the grid balancing issue. An essential component to overcome this problem is to increase self-sufficiency by using battery storage to balance the grid.
To investigate this relationship, it is important to know when to store energy generated during the day to match the demand during the night. When matching supply and demand in a household, by generating, storing, and using renewable energy, it should be (theoretical) possible to be able to have an electrical self-sustaining household. However, this means that the batteries used for storage during the day need to be huge and therefore not realistic. Given this, there should be a relationship between the size of the battery, the number of solar panels, and self-sufficiency. This will be evaluated by making a distinction between a household with a battery and a control group without a battery to determine the added value of self-sufficiency by using a battery.
When the supply of energy is high, it is assumed that the price will drop. When the supply is low, the price could rise. The battery can be used to store energy during times when the price is low and consume during the time when the price is high. This could resolve in an economical effort when using the battery in combination with solar panels and variable energy costs.
Variable grid prices might have an impact on the costs. When there is much supply and less demand there could be a peak in the electricity grid. This would result in a decreasing price. These fluctuations within grid prices could have an advantage when combined with a battery. Purchasing energy when it is cheap and consuming this energy when the price is high.
The outcomes of this research is a paper addressing the main question: What is the relationship between the size of a
battery and self-sufficiency in a household that is connected to the grid and uses solar panels. This will result in a percentage
combined with an analysis of the amount of power consumed and delivered from/to the grid. This will give insight in how to use
the battery and solar panels in an optimal way to be as much self-sufficient. Furthermore, the self-sufficiency will be described on
a scale of grid consumption. Giving an overall insight in how to achieve a self-sustaining household. The research includes a
literature review, graphs, and calculations when to provide, deliver, or store energy. Section 2 explains the theoretical framework
followed by the method in section 3 and the findings in section 4. The paper ends with the discussion and the conclusion in section
5 which answers the main question and will describe the limitations and avenues for further research.
2. Theoretical framework
In this section, prior research regarding the application of solar panels and batteries will be analysed and compared to each other.
Prior research indicates that using solar panels and batteries have an economical advantage and could help to peak shaving as well as the capacity needed to achieve this. The research gap that will be investigated in this research is the relationship of solar panels combined with batteries and the application of variable grid rates combined with solar panels and batteries to get insight into the performance of the self-sufficiency.
Solar panels are applied nation-wide for example for both, industry and private sector. In this paper, self-sufficiency of a household and the relation between a battery and solar panels will be described. In the majority of the cases, the generated energy surplus from solar panels is directly delivered to the grid by an automated electrical system. Due to the excessive amount of power generated during the day and the inability to store the power, this is an inevitable consequence. The other option, throwing away the energy, is not eco-efficient. By storing a certain amount of energy in a battery, the grid dependency reduces, and the self-sufficiency increases.
Prior research describes that the timing of charging a battery could be economically efficient by adding rules in the charging cycle of the battery and the grid consumption/delivery(Ren, Grozev, & Higgins, 2016). With the use of solar panels the reduction of grid consumption increases(Ren et al., 2016). In this research, multiple types of households with, without and the combination of solar panels and batteries are compared. The conducted research is limited as it only provides economic advantages. The most self-sufficient situation is not described due to the fact that only 7 situations are compared. In this research, more cases will be analysed as well as the combination with variable grid rates. The paper by McKenna (2013) describes the economical effort and gives an in-depth analysis of the application of lead-acid batteries with the environmental impact. Charging the battery during the surplus of the day and use it during the night avoids expenses to the grid(McKenna, McManus, Cooper, &
Thomson, 2013). The conducted research describes that there is no economic advantage to use lead-acid batteries and the environmental impact due to the production is also negative(McKenna et al., 2013). The paper limits itself to the most environmental ideal situation. It only describes several cases without optimizing the parameters of battery capacity and solar power. However, it lacks optimizing the case by evaluating battery power and solar panels as parameters, this will be conducted in this research. The battery capacities have significantly increased since 2012 due to technological advances in battery capacity.
Today, the most appropriate battery storage technology are lithium-ion batteries, these are used in power stations(Zhu, Hu, Xu, Jin, & Shui, 2020). A major difference is the lifetime of a battery as the number of charging cycle are increased(Friesen et al., 2017).
Therefore, the conclusion of the economic advantage and environmental impact can be questioned.
Other research estimates the battery size for peak-shaving. “The results suggest typical system sizes range from 5 kWh/2.6 kW for low electricity intensity homes to 22 kWh/5.2 kW for electricity intense homes with electric space heating.”(Leadbetter & Swan, 2012) It shows that the use of a battery could achieve peak demand reductions of between 42%
and 49%(Leadbetter & Swan, 2012) and concludes that batteries can far or less be used to fill the gap in demand and excessive surplus. This means that the use of a battery is already proved to be useful, but this research limits itself to peak shaving and to the same factors as the McKenna (2013) paper. The paper helps to identify the upper and lower limits regarding the capacity of the battery.
The research by Leadbetter & Swan (2012) is used as a starting position for the determination of battery capacity.
Although the paper only focuses on peak-shaving and not on the application of solar panels. This research combines the use of solar panels and batteries and is therefore different than the paper by Leadbetter & Swan (2012). Other research concludes that the value for the customers can be increased “with battery storage by enhancing the load management and outage protection attributes of solar panels”(Hoff, Perez, & Margolis, 2007).
This paper explains that the economic advantages are not the important factors, the focus is on the comparison self- sufficiency. However, investing in battery power could be profitable in the long run without having drawbacks on the self- consumption rate(Naumann, Karl, Truong, Jossen, & Hesse, 2015).
Although there is various research conducted about the application of batteries(Leadbetter & Swan, 2012)(McKenna et al., 2013) and the application of solar panels(Ordóñez et al., 2010), there is no scientific research about the comparison of the efficiency of both solar-powered houses and solar-powered houses with batteries to get the most environmental ideal situation and the highest self-sufficiency. The comparison of these two situations is missing in the literature, especially the efficiency comparison of both cases. This is therefore seen as the most critical research gap.
There is also a gap in the literature about the effect of variable grid prices with the uses of solar panels and batteries in a household when purchasing and storing energy in advance. The literature describes that there is an effect of the application of solar panels with batteries(Ren et al., 2016) although that research is conducted in other parts of the world, this research focusses to the Netherlands and is limited to variable grid prices. This also implies for the self-sufficiency of this type of household.
The variable grid prices in combination with solar panels are not yet described although demand management with
variable prices is described in the literature(Gottwalt, Ketter, Block, Collins, & Weinhardt, 2011). In this paper, the use of household
equipment and variable energy prices is investigated although households can only expect low benefits and is limited. The
combination to use renewable energy sources such as solar panels and batteries is not investigated. Other research concludes
that the use of variable grid prices “can support grid stability during demand peak hours”(Ruppert, Hayn, Bertsch, & Fichtner,
2016). The use of a battery in combination with solar panels has a relationship with self-sufficiency when using 50% of the average
daily energy production(Velik, 2014). Although this research does not focus on the capacity of solar panels. The variable rates used
in the research are only used for cost calculations and not for buying energy in advance to create an economical effort. These
rates do not vary by day and are thus the same during the year. Furthermore, the calculations are based on seasons and not on an hourly base.
In this research, the missing information regarding the relationship between battery capacity, solar power and self- sufficiency is investigated. This will be conducted with multiple experiments. This includes the calculations of households with and without a battery combined with variable grid prices.
3. Method
In this section, the description of the research is highlighted. It is explained how the research is executed in a logical step-by-step approach. This will be described with several graphs and tables to understand the decisions made for the calculations.
3.1. Conceptual model
To help describe the relationship the conceptual model of the research question is shown in figure 1. The conceptual framework explains the causal relations of the research by showing the main components.
Figure 1, Conceptual model of the relationship of battery storage and solar power in a household.
When storing energy in a battery several factors are important to determine the capacity such as size and type. The size can increase along with the capacity, although the capacity should be reasonable. After generating the power from solar panels, it will be consumed or stored this depends on the demand of power. The amount of power that is generated and consumed, without using any power from the grid during the year is the self-sufficiency. The problem is what is the most self-sufficient situation when using solar panels and a battery, this has to be determined under what conditions optimal self-sufficiency exists by using battery power and solar panels. To determine this the included and excluded variables used in the experiments are explained in table 1. The results are accompanied by several graphs with a possible intersection for the most self-sufficient household.
Table 1, Component list of used parameters in the calculations.
Component Detail Parameter Included/excluded Comment
Household Energy demand kWh Included Liander data
Hourly data Hours Included Data is hourly based
Battery Charging losses Excluded No losses due to charging
Discharge losses Excluded No losses due to consuming
Capacity kWh Included Variable
Degrading Excluded No losses due to lifetime
Type Excluded Type is not determined
Solar panels Energy supply kWh Included PVGIS data
Capacity kWp Included Variable
Hourly data Hours Included Data is hourly based
Transformation losses Excluded No transformation losses
Grid Energy delivered kWh Included Power delivered to the grid
Energy consumed kWh Included Power consumed from the grid
Losses Excluded No losses in cables
The flowchart of a regular household is shown in figure 2. In this chart, the only decision is whether there is solar power or not. If there is solar power it will be consumed and the excessive energy will be delivered and sold to the grid, when there is no solar power all the energy will be consumed and bought from the grid. The order of actions is described in section 3.1 and appendix 1.
Figure 2, Logic flow diagram (number 1) of a household without battery and solar panels which uses solar energy first and after that, it uses
grid power.
Figure 3 describes the processes of a household with a battery. The most important decision in the figure is the availability of solar power. When solar power is available, the energy will be consumed in the first place and then stored in the battery. When the battery is fully stored the excessive energy will be delivered to the grid and sold. When there is no solar power available the energy stored in the battery will be consumed. When the battery is empty and there is no solar power available, the energy will be consumed and purchased from the grid. A household with a battery uses a much more complex flow chart with four decision blocks and 5 processes. The extra decision blocks and processes are used to store or consume electricity to/from a battery.
Figure 3, Logic flow diagram (number 2) of a household with a battery and solar panels which uses power in the order of solar power, battery
power and grid power.
Figure 4 describes the processes of a household with a battery and variable grid rates. The figure is the same as figure 3 but includes an option to buy energy from the grid. This is only available when there is no solar power and there is space available in the battery.
Figure 4, Logic flow diagram (number 3) of a household with battery and grid charging capabilities, to charge a battery in advance, this could
be used when energy prices are lower and it is profitable to buy energy in advance.
3.2. Experimental setup
In this section, the multiple conducted experiments are described. A brief overview of these experiments is shown in table 2.
Table 2, Conducted experiment list
Experiment Number of
experiments Battery Capacity
(kWh) Solar power
capacity (kWp) Variable
grid rates Prospect (hour) Flow
diagram
Base case, solar power 25 0 1-25 No 0 1
Extreme value, solar power 10000 0 10000 No 0 1
Solar power with battery 625 1-25 1-25 No 0 2
Solar power with battery 12 0 1-12 Yes 0 3
Solar power with battery 4 0, 5 0, 5 Yes 1 3
Solar power with battery 2 5 0, 5 Yes 2 3
Solar power with battery 2 5 0, 5 Yes 3 3
Solar power with battery 2 10 0, 5 Yes 3 3
To understand self-sufficiency in a household a regular household needs to be compared with a battery household, in the experiment this will be considered as the base case. Self-sufficiency is the annual overall self-generated percentage of electricity.
To calculate this, all incoming and outgoing flow of electricity need to be known. This will be conducted on an hourly based during a period of one year. The lifetime drawbacks of the battery and solar panels are out of the scope of this research as well as the efficiency factor for solar panels and batteries. In this research, the data Is already in energetic values, therefore the efficiency does not have to be considered.
The actions when there is solar power are always consuming the electricity, there is no maximum of energy that will be consumed from the solar panels. The second action is storing, this only applies when there is excessive electricity and is limited to the amount of storage capacity. The last action is selling to the grid, this only applies when there is excessive power from solar power, and when the batteries are fully loaded. The actions when there is no solar power available are in the first place consuming from the battery, this is limited to the stored amount of energy in the battery. The next action is buying from the grid. This only applies when there is no solar power and no energy in the batteries.
To determine the used electricity for a household of 5 persons in The Netherlands hourly data of Liander will be used.
The used data is from 2009 this is because there is no more recent data available(Liander, 2009). Solar power efficiency and data is gathered from PVGIS. These two sources are the main sources for data used for the supply and demand calculations, energy profiles regarding Liander and PVGIS are stated in Appendix 2.
The assumption is made that most home solar installations have 6 to 22 panels installed(Peter van der Wilt, 2019). This
means that the actual capacity of solar arrays varies between 2 kWp and 8 kWp. The battery capacity used in households can vary
between 4 and 22 kWh, this is shown in prior research. With the arrival of the Tesla Powerwall this can be confirmed(Tesla, 2019).
Powerwalls have a continuous capacity of 5kWh. Installing four of them would fit in every average home.
The first part is to determine the efficiency of a household with solar panels. The efficiency of a household, the bases case, with solar panels will lie in-between 0% and 100%. After this, the efficiency of a household with solar panels and batteries will be analysed to find the optimal parameter conditions. This will also lie in-between 0% and 100%. The solar panel capacity varies between 0 and 25 kWp. This is because it covers most of the household capacity. The battery capacity also varies between 0 and 25 kWh. This is because of prior research. With this data 675 calculations are made. This is done with Oracle Crystal Ball to simulate in Excel. For all simulations, the battery storage at the start is 0 kWh.
Although the economical effort will be calculated, the capital expenditure of the equipment will not be included in the calculations. This is due to the difference in prices of the equipment. When the annual profit/costs are calculated the return on investment calculation can be conducted for the specific equipment. The calculations are modular and easy to adjust for example the different solar panels, efficiency factors, and battery capacity. The energy prices are average price rates of power companies in the Netherlands. These will be consumed and delivery rates. When the most ideal situation is calculated, this will be compared with a regular household to determine the self-sufficiency. This will determine whether the regular household or the battery household will be more self-sufficient. The results whether a battery could offer an economical effort are calculated on an hourly base and will result in savings/expenses during a year.
The final part will analyse whether the use of a battery poses an economically viable solution with variable grid prices. To determine whether variable grid prices affect the costs, several cases are analysed. The single rate is 0,22 euro and the total amount of kWh is 4473,7(Pricewise, 2020). This is based on the Liander data and multiplied by 1.2 to get to a more average kWh consumption of a household of 5 persons during the year(Energiesite, 2020). The variable energy rates are gathered from Entsoe(Entsoe, 2019), however, the prices are for the industry and have been divided by 1000 and multiplied by 5,3 to match an average annual price of 0,22 euro per kWh(Pricewise, 2020). The price for delivering to the grid is set at 0,07 euro (Gaslicht, 2012).
The use of batteries is excluded in the first experiment. The solar power set between 1 and 12 kWp. The output data of this experiment will compare the economic advantages of single rate grid prices and variable grid prices.
When storing energy at times when the energy is at fewer costs and use this energy during peak hours. In the calculations, this will be limited to 5 hours in advance. The simulations will look if the hourly rate is less than the average of the following 5 hours, if that is the case, the energy will be bought in advance. There will only be energy purchased in advance when there is no solar power available. Furthermore, the calculations are based on 1, 2, and 3 hours of solar power in advance. This means that the generated electricity needs to be 0 in 1, 2, and 3 hours in advance.
Prior studies confirmed that the use of a battery in combination with solar panels could be effective in obtaining higher self-sufficiency. However, the exact relationship was not yet determined.
.
4. Results
In this section, the results of the calculations and will be described and substantiated. This will be done by calculations in Excel.
The used parameters for the results are solar power, battery capacity, self-sufficiency, and the economic advantage. These will be compared and analysed.
With the use of only solar panels, the maximum calculated self-sufficiency that can be achieved is 49,3%. This is an experiment to determine the maximum self-efficiency for further comparison. With this experiment, the variables used to examine the highest possible self-sufficiency are 10.000 solar panels with a regular household. Self-sufficiency does not increase further when more solar panels are used. This gives insight into the maximum achievable self-efficiency, although it is not realistic in a household, it is only used as an extreme condition. This is because of the lack of energy during the night. More common self- sufficiency varies between 20,5% and 43,0% more variables are shown in table 6 in appendix 3. As seen in figure 5, excessive amounts of solar panels do not contribute to higher self-sufficiency when not using a battery.
To determine the battery size, 625 calculations have been made, varying from 0 to 25 kWp solar power and battery capacity. This is seen in figure 5.
Figure 5, Self-sufficiency in households with solar power and batteries with battery capacity data shown in appendix 3 table 11.
The use of a battery is useful from 1 kWh on. From 1 kWh to 4 kWh it is useful to use a battery to increase self-sufficiency because of the steepest angle in self-sufficiency increment. This varies between 22,8% and 51,0% more values can be seen in table 7 in appendix 3. This means that the highest contribution to self-sufficiency is accomplished with a small battery. When using more than 8 kWh of battery capacity self-sufficiency increment will be less but the overall contribution to self-sufficiency increases.
When using even more battery capacity self-sufficiency will increase. The 4 kWh is set due to prior research and the 4 kWh is a point where the average curve of figure 10 flattens. S elf-sufficiency increment varies between 23,1% and 71,9% more variables are shown in table 8 in appendix 3. The last step is to set the battery capacity to 8 kWh this is due to the less steep angle of self-sufficiency increment , this varies between 23,1% and 83,0% more variables are shown in table 9 in appendix 3. The values indicate a positive contribution of solar power and batteries to the self-sufficiency. The more battery capacity is available the more the self-sufficiency increases. Although the curve flattens after the 8 kWh battery capacity.
If solar power can be increased to 20 kWp, the self-sufficiency would increase gradually. For example, the use of 20 kWp and a combination of 10kWh batteries would result in 90,1% self-sufficient. For the efficiency factor of 96,2%, there needs to be a minimum of 25 kWp of solar power combined with a battery of 25 kWh. This is, however not realistic and cannot be achieved in households. To get an even more self-sufficiency of 99,9%, both of the parameters need to exceed at least 80.
0,0 20,0 40,0 60,0 80,0 100,0 120,0
0 kWp 1 kWp 2 kWp 3 kWp 4 kWp 5 kWp 6 kWp 7 kWp 8 kWp 9 kWp 10
kWp 11
kWp 12
kWp 13
kWp 14
kWp 15
kWp 16
kWp 17
kWp 18
kWp 19
kWp 20
kWp 21
kWp 22
kWp 23
kWp 24
kWp 25
kWp
Self-sufficiency(%)
Solar power (kWp) Self-Sufficiency compaed to battery capacity
0 kWh 1 kWh 2 kWh 3 kWh 4 kWh 5 kWh 6 kWh
7 kWh 8 kWh 9 kWh 10 kWh 11 kWh 12 kWh 13 kWh
14 kWh 15 kWh 16 kWh 17 kWh 18 kWh 19 kWh 20 kWh
21 kWh 22 kWh 23 kWh 24 kWh 25 kWh
When the self-sufficiency increases this results in cost savings because self-sufficiency increases due to the self-generated electricity. Self-sufficiency level is linear related to cost saving. By using a battery, it could be possible to store energy during the night and use it during the day. This is only possible when the battery is not fully charged. The same effect is investigated when combined with variable grid rates. The results of this experiment are shown in table 8. When using variable grid prices the use of a battery could have an economical effort, but this needs to be compared with the base case of variable grid prices. Variable rates depend on the supply of power. During the day, the supply is higher than during the night. This results in variable energy costs.
When comparing the costs of a single rate with variable rates in a household without a battery in all cases using a single energy rate is cheaper. All variables are shown in table 10 in appendix 3
When combining the variable energy rates with a battery, as can be seen in table 5, the highest self-sufficiency (65,8%) can be achieved by a single grid price. Although variable grid prices do not affect the total costs when not using solar panels and batteries, in this case using variable grid rates is more expensive than a single rate. However, when using a bigger battery of 10kWh, the economical effort is 134,36 compared to 133,44. When using the battery for storage during the time that the power is cheaper will result in an economical effort. Although this is only relevant when using solar panels and having further energy consumption data available.
Table 3, Variable grid rates compared to single rate grid prices with variable battery and solar power capacity.
Battery capacity (kWh)
Solar power
(kWp) Prospect
(hours) Variable grid price (y/n) Self-
Sufficient (%)
Energy bought (euro)
Energy sold
(euro) Total (euro)
0 0 0 No 0,0 962,22 0,00 962,22
5 0 0 No 0,0 962,22 0,00 962,22
0 5 0 No 37,1 605,34 307,67 297,76
5 5 0 No 65,8 328,98 194,62 134,36
0 0 1 Yes 0,0 1001,67 0,00 1001,67
5 0 1 Yes 0,0 843,29 0,00 843,29
0 5 1 Yes 37,1 646,54 307,67 338,87
5 5 1 Yes 48,6 431,70 262,67 169,27
5 0 2 Yes 0,0 843,29 0,00 843,29
5 5 2 Yes 50,5 416,33 254,80 161,53
5 0 3 Yes 0,0 843,33 0,00 843,92
5 5 3 Yes 54,1 392,00 240,87 151,13
10 0 3 Yes 0,0 839,54 0,00 839,54
10 5 3 Yes 56,8 363,34 229,90 133,44
The combination of using solar power, batteries, and variable grid rates do not have a contribution to self- sufficiency. This is because the calculations are based on the economic advantage. In the first case with 5kWp solar power, 5kWh battery capacity, and without variable grid rates, the self-sufficiency is 65,8% this is in all cases higher. The 1-hour prospect has a 48,6% of self-sufficiency, the 2-hour prospect has a 50,5% of self-sufficiency and the 3-hour prospect a 56,8%
of self-sufficiency. What can be seen is that self-sufficiency increases while the hourly prospect increases.
The application of a small battery has the highest contribution to self-sufficiency although this could be increased by using a slightly bigger battery while 100% self-sufficiency is not achievable because of the size of the battery and solar panels. The contribution of variable grid prices does not have a contribution to self-sufficiency and does not offer an economic advantage.
5. Discussion and Conclusion
In this section, the research question that contributed to the research gap “What is the relationship between the size of a battery self-sufficiency in a household that is connected to the grid and uses solar panels?” is answered. The main findings and limitations will be discussed and avenues for further research are provided.
When using solar panels only the maximum self-sufficiency is 49,3%, this is an extreme value and could not be achieved in practice due to the fact that this would need more than 1000 kWp of solar power. This value is calculated to determine the maximum. The most convenient factors vary between 20,5% and 43,0% when using between 1 and 12 kWp of solar power. This could be increased when combined with batteries.
The use of batteries has a positive increasing contribution to self-sufficiency. The highest contribution is achieved between 1 and 4 kWh this is because of the steepest angle on figure 5. When using solar power that varies between 1 and 12 kWh self-sufficiency varies between 22,8% and 71,9%. When using a battery capacity of 4 to 8 kWh self-sufficiency varies between 23,1% and 83,0%. If both of the parameters are increased the self-sufficiency does so, although this does not give the highest contribution since the relationship is not linear. After the 8 kWh mark on figure 5 the curve flattens meaning that self-sufficiency increases but not as much as before. Self-sufficiency increases the most when combining a battery with solar power. The greatest contributor is solar power. The more solar power available, the more is excessive power is available that consequently can be stored in the battery. Thus, the battery does not need to have the same capacity as the solar panels because there is always energy that will be consumed. The recommended capacity for batteries lies between 4 and 8 kWp depending on the installed solar panel capacity. This would have the highest contribution to self-sufficiency. The range of the battery is in line with the previous research.
When using variable grid prices with solar power that varies between 1 and 12 kWp and without a battery, the energy costs with variable rates are in all cases higher. This can be clarified because when the solar panels do not generate electricity the variable rates are on average higher than the single rate. The savings decrease while solar power increases. This could be clarified because there is more peak power available.
When solar power is combined with variable grid rates there is no positive contribution to self-sufficiency, this could be due to calculations that are based on the economic advantage. However, self-sufficiency increases as the time prospect increases.
This means that if the prospect is more than 3 hours it could lead to self-sufficiency increment although this is not possible to oversee how much electricity will be consumed in the future. When combining solar power, battery capacity and variable grid rates there is no economic advantage. In all case the expenses with variable rates are higher than the single grid rates.
The relationship between the size of a battery and self-sufficiency when using solar power is positive increasing when using a minimum amount of battery capacity varying between 1 and 8 kWp and using solar power capacity varying between 1 and 12 kWp. This has however only a positive effect when there is a single rate grid price. When using more battery capacity or solar power self-sufficiency will increase slightly. This means that if an average household wants to be more self-sufficient, the only prerequisites are solar power and battery capacity. This would quickly result in a self-sufficiency of more than 50%.
The research is limited to that the self-sufficiency could be more specific when the actual solar panel capacity is available, this is not the case. If this data was available it would result in more detailed information about self-sufficiency of households instead of a range of capacity with a forthcoming self-sufficiency. Furthermore, the data used for variable grid prices are based on day-ahead prices from the industry, the use of a multiplication factor of 5,3 could be reduced if the actual grid prices on average are lower than the single rate grid prices.
Further research could include the effect of self-sufficiency to a village. This would include the effect of multiple self- sufficient households on the power grid, the effect of energy prices and the effect of households purchasing and selling power to each other. In this research, the multiplication factor of 5.3 it could theoretical be lowered if a village is seen as an industry and would have the same benefits of the variable grid rates. It could also include the prospect on self-sufficiency. If the prospect time increases this could result in an even better economical effort when variable grid prices are available. Also, the 3 hours ahead is not available in real-time situations, therefore there needs to be a prognosis of the consumption in the forthcoming hours. The accuracy of this needs to be further investigated. Further research may also include battery losses and lifetime losses to get a more precise performance indication.
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Appendix 1, Order of Actions
All flowcharts follow a certain order when it comes to decisions about whether to consume, store or sell energy. All calculations are executed on each hour of the year and are all done in a certain order. This applies to all three logic flow diagrams. This order is shown in table 9 and table 10.
Table 4, Order of actions taken in order in a household with solar power.
Action
1 Consume from solar panels
2 Store
3 Sell to grid
Table 5, Order of actions taken in a household in order without solar power.
Action
1 Consume from battery 2 Buy from grid
Appendix 2, Supply and Demand profiles
The data from PVGIS and Liander has been analysed in excel to give an insight the average consumption and power generation during the day. The average consumption of electricity during the day can be seen in figure 7 and figure 8. In the figures can be seen that the demand for electricity varies during the day, this is an important aspect due to the determination of the size of the battery. The demand for electricity depends on the season and the time of the day. During the summer, the energy consumption is lower than during the winter. The consumption of electricity is also higher at the end of the day.
Figure 6, kWh consumption during the year for a household consuming 4400 kWh a year.
Figure 7, kWh consumption during the year of a household with a total energy consumption of 4400 kWh.
The solar panel data is an efficiency factor, this factor is multiplied with the solar panel capacity to get the actual generated power. The profile of the efficiency of a panel during the day can be seen in figure 8 and the efficiency during the year in figure 9. During the day, the energy is generated and during the night there is no energy generated. And during the summer months, the panels generate more power than during the winter.
0 50 100 150 200 250 300
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
kWh consumption (year)
Hour of the day
Average kWh consumption per hour during the year
0 2 4 6 8 10 12 14 16
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311 321 331 341 351 361
Energy consumption (kWh)
Day of the year
kWh consumption per dayduring the year
Figure 8, Average solar panel efficiency during the hours of the day for a period of one year.
Figure 9, Efficiency of solar panels during the days of the year, this graph includes the hours without sunlight.
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Solar power efficiency
Hour of the day
Average solar power availability per hour during the year
0 0,05 0,1 0,15 0,2 0,25 0,3
1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311 321 331 341 351 361
Average eficnency of solar panels (%)
Dayof the year
Efficency of solar panels per day during the year
Appendix 3, Self-sufficiency increment with solar power and battery capacity
All the calculations are conducted in Excel, an output of these data is provided to review the precise self-sufficiency concerning the parameters in-between 1 and 12 kWp. The self-sufficiency of households with solar power varying between 1 and 12 kWp and without battery capacity is shown in table 6.
Table 6, Self-sufficiency in households without a battery and only using solar power.
Solar power (kWp) Self-Sufficiency (%)
1 20,5
2 28,5
3 32,6
4 35,2
5 37,1
6 38,5
7 39,6
8 40,5
9 41,3
10 42,0
11 42,5
12 43,0
The graph of self-sufficiency without a battery can be seen in figure 10. The relationship between bot parameters is not linear.
The curve flattens after 8kWh and flattens even more after 22kWh. This means that excessive amounts of solar power do not contribute to even higher self-sufficiency.
Figure 10, Self-sufficiency of a households without a battery and only using solar panels.
Efficiency of households with solar power varying between 1 and 12 kWp and battery capacity of 1, 4, and 8 kWp. These are the points on figure 10 where there is a steepest angle. The values of the battery capacity of 1, 4, and 8 kWp are shown in table 7, 8 and 9.
Table 7, Self-sufficiency and self-sufficiency increment of common situations in households with solar power and batteries with a battery capacity of 1 kWh.
Solar Power (kWp) Battery Capacity (kWh) Max Self-Sufficiency (%) Self-Sufficiency Increase by battery (%)
1 1 22,8 2,3
2 1 33,8 5,3
3 1 39,0 6,4
4 1 42,1 6,9
5 1 44,3 7,2
6 1 45,9 7,4
7 1 47,1 7,5
0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 50,0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Self-Sufficiency (%)
Solar power (kWh)
Self sufficiency of a household comapared to solar power
