Keywords: PV battery system; battery control; self-consumption; economic ana- lysis.
Abstract
The aim of this project is to find the optimal size battery for an already installed PV system in a family house in Southern Sweden. First, the existing system is modelled and validated. Then a new model including a battery is built. In this model it is as- sumed that the aim of the battery is to maximize the self-consumption of the house.
A sensitivity analysis is performed in order to study the influence of the battery capacity on the electricity fluxes between the house and the grid. The profitability of the project is then investigated, considering the current tariff schemes for the house and for the ”average” Swedish house. Eventually the possibility of applying price-dependent control strategies to the battery is investigated.
The primary conclusion is that a battery installation is not profitable for the studied house whether the incentives provided by the Swedish government are considered or not. Yet a subsidized installation would be profitable for a house subject to the average Swedish electricity price. Another conclusion is that the current hourly volatility in the electricity price is not high enough to make reasonable the use of price dependent battery control strategies. Their use would lead to better econom- ical performance, with respect to the simplest battery control strategy, in case of increased volatility.
Sammanfattning
M˚alet av det h¨ar projektet ¨ar att hitta batteri med den b¨asta storleken f¨or en ex- isterande solcellssystem i en villa i S¨odra Sverige. F¨orst, det existerande systemet modelleras och valideras. Sedan byggs en ny modell som inneh˚aller ett batteri. I den h¨ar modellen antas att m˚alet av batteriet ¨ar att maximera sj¨alvkonsumption av villan. En k¨anslighetsanalys utf¨ors f¨or att studera inverkan av batteri kapacitet p˚a el flussmedel mellan villan och n¨atet. D¨arefter, l¨onsamheten av projektetet un- ders¨oktes, med tanke p˚a den befintliga tariffsystem f¨or den utforskade villan och den ”genomsnitt” Svenska villa. Slutligen, m¨ojligheten att till¨ampa prisberoende batterikontrollstrategier unders¨oks.
Den prim¨ara slutsats ¨ar att en batteriinstallation ¨ar inte l¨onsam f¨or den studer- ade villa, med eller utan bidrag. ¨And˚a en subventionerad installation skulle vara l¨onsam f¨or ett hus som uts¨atts f¨or genomsnitt svenska elpriset. En annan slutsats
¨
ar att den nuvarande volatilitet i elpriset ¨ar inte tillr¨ackligt h¨og f¨or att g¨ora l¨amplig den anv¨andning av prisberoende batterikontrollstrategier. Deras anv¨andning skulle leda till b¨attre ekonomisk prestanda, med avseende p˚a den enklaste batteristrategi, om prisvolatilet ¨okningar.
Acknowledgement
I would like to show my gratitude to Konstatin Kostov, my supervisor in Acreo Swedish ICT, the company where I wrote my master thesis, for the great opportu- nity to work on this project and the freedom and trust he gave me while working on it.
Thanks also to Teresita Qvarnstr¨om and Hans Persbeck for providing me with useful data.
I am also deeply grateful to Nelson Sommerfeldt, my supervisor at KTH, for being always available for feedbacks and his very valuable comments and suggestions that allowed me to improve my work.
I would also like to thank my friends Rapha¨el and Roberto for their support during these months and the time dedicated to discuss with me part of my work.
Lastly, my deepest gratitude goes to my parents, for their continuous support throughout my years of studies. Without it reaching this goal would have been much harder.
Contents
List of Figures i
List of Tables iii
Units iv
Abbreviations v
Subscripts vii
1 Introduction 1
1.1 Electricity storage . . . 2
1.2 Residential electricity storage . . . 3
1.3 Thesis Objective . . . 5
1.4 Scope and limitations . . . 5
1.5 Methodology . . . 6
1.6 Previous work . . . 6
2 Case study 8 2.1 The Swedish electricity market and PV policies . . . 8
2.1.1 PV support . . . 9
2.2 The house . . . 10
3 Current system modelling 12 3.1 Electricity demand . . . 12
3.2 Electricity generation system . . . 16
3.2.1 PV panels . . . 17
3.2.2 Inverter modelling . . . 22
3.3 Model validation . . . 24
4 PV battery system modelling 28 4.1 System configuration . . . 28
4.2 System modelling . . . 30
4.2.1 AC-DC bidirectional inverter . . . 30
4.2.2 Battery . . . 31
4.3 Performances . . . 32
4.4 Techno-economic analysis . . . 36
5 Performances under different tariff schemes and control strategies 40 5.1 Tariff schemes . . . 40
5.2 Control strategies . . . 43
5.2.1 Solar control (SC) . . . 43
5.2.2 Purchase control (PC) . . . 46
5.2.3 Solar + purchase control (SPC) . . . 47
5.3 Results . . . 47
6 Conclusions 51
Appendix I viii
Appendix II ix
Appendix III x
List of Figures
1.1 Installed PV capacity in Sweden. . . 1
2.1 House used as case study. . . 10
2.2 Electricity fluxes of the house in 2014. . . 11
3.1 Year profile of electricity consumption. Resolution: 1 day. . . 15
3.2 Percentage load curves for Mondays. 1 hour and 15 minutes resolution. 16 3.3 Scheme of the electrical system . . . 17
3.4 Main irradiance profiles. . . 20
3.5 Irradiance data sample. . . 20
3.6 Characteristic and power curves of a PV panel . . . 21
3.7 Movement of the operation point due to MPPT imprecision . . . 23
3.8 Inverter efficiency curves . . . 23
3.9 Modelled electricity fluxes 1-3 July 2014 - Resolution 15 minutes. . . 24
3.10 Comparison of the modelled and real systems . . . 25
3.11 Error in the estimation of the electricity produced by the PV system 25 3.12 Error in the estimation of the electricity produced by the PV system - Irradiance dependence . . . 26
3.13 Error in the estimation of the electricity bought from the grid . . . . 27
4.1 DC coupled PV battery system scheme . . . 29
4.2 AC coupled PV battery system scheme . . . 29
4.3 AC/DC bidirectional converter efficiency curve . . . 31
4.4 Sensitivity analysis: self-consumption and self-sufficiency vs battery capacity . . . 33
4.5 Sensitivity analysis: electricity bought and sold vs battery capacity . 34 4.6 Batteries comparison, electricity bought and sold every month . . . . 35
4.7 8 kWh Li-ion battery charge during the sunniest day of January . . . 35
4.8 NPV vs battery capacity with the current economical input . . . 37
4.9 NPV vs battery capacity with different retail electricity prices . . . . 38
4.10 NPV vs battery capacity with different battery costs . . . 38
4.11 NPV vs battery capacity with different battery costs. Electricity price: 0.19 e/kWh . . . 39
LIST OF FIGURES
5.1 Annual average Nord Pool wholesale electricity price . . . 41
5.2 Average grid price for a single family house in Sweden . . . 41
5.3 Modelled electricity price on the 1st January 2017 . . . 42
5.4 Solar control. Step 1-4 . . . 44
5.5 Solar control. Step 5-7 . . . 45
5.6 Purchase control . . . 47
5.7 NPV of the battery investment with TS1 applied . . . 48
5.8 NPV of the battery investment with TS5 applied . . . 48
5.9 NPV of the battery investment with TS20 applied . . . 49
5.10 NPV of the battery investment in a house without PV panels . . . . 49
List of Tables
3.1 Monthly and average daily consumption during year 2014 . . . 13
3.2 Months shaving factors . . . 14
3.3 Inverter efficiency table. Efficiency in [%] . . . 24
4.1 Components characteristics for the economical analysis . . . 37
5.1 Retail price items . . . 40
Units
A ampere
°C degree centrigrade ce euro cents
e euro
K kelvin
kW kilowatt kWh kilowatthour
MW megawatt
MWh megawatthour SEK Swedish crown
V volt
W watt
Abbreviations
AC Alternating current BC Base control
c Specific cost
C Capacity
CAES Compressed energy storage CHP Combined heat and power DC Direct current
DOD Depth of discharge
DSM Demand side management
E Energy
EPC Engineering procurement and construction eT Electricity tax
Fc−g View factor collector-ground Fc−s View factor collector-sun FC Fuel cell
G Irradiance gc Green certificate gs Green support
HP Heat Pump
I Current
i discount rate IC Investment cost Li-Ion Lithium Ion
MPP Maximum power point
MPPT Maximum power point tracking NaS Sodium sulfur
NiCd Nickel cadmium np Network price NPV Net persent value
O&M Operation and maintenance PC Purchase control
PHS Pumped hydro storage PV Photovoltaic
Abbreviations
R Revenue
rp Retailer price
SC Self-consumption or Solar control
SMES Superconduction magnetic energy storage
SMHI Swedish meteorological and hydrological institute SOC State of charge
SPC Solar-purchase control SS Self-sufficiency
T Temperature
TMY Typical meteorological year
V Voltage
wp Wholesale price β Tilted angle η Efficiency ρ Reflectivity θ Incidence angle θz Zenith angle
Subscripts
amb Ambient
b Battery
bc Battery charge bd Battery discharge
bn Beam normal
d Diffuse
el Electricity
h Horizontal
I Inverter
i Incidence
in Input
max maximum
min minimum
MPP Maximum power point
MPPT Maxumum power point tracking oc Open circuit
OP Operation
out Output
PV Panel
sc Short circuit
STC Standard conditions
t Tilted
Chapter 1 Introduction
The environmental policy in Sweden, as in the European Union, is guided towards an increase of use of renewable energies [1]. In 2014, more than 50% of the gross final energy consumption of Sweden was provided by renewable energies. Biomass and waste, followed by hydropower, were the most exploited renewable sources; they respectively contributed to the total renewable energy generation for around 61%
and 33%. Wind energy contributed for around 6% and solar energy contribute was still negligible [2].
Solar energy, though, thanks to the decreasing price of solar installations, has be- come a cheap energy source also in Sweden. From 2010 to 2014, the installed PV capacity in Sweden nearly doubled every year, and the capacity installed in 2015 is 1.5 times the one installed in 2014; the total capacity installed at the end of 2015 was around 125 MW[3]. Figure 1.1 [3] shows the trend of the installed PV capacity in Sweden.
Figure 1.1: Installed PV capacity in Sweden.
The most common application for PV systems, in Sweden, is residential. They are
Chapter 1. Introduction
installed both as stand-alone systems or grid-connected. In the first case, the system is provided with a battery; the produced electricity is directly used by the house loads or stored for later use. In the second case, the system is, nowadays, usually not provided with a battery; the electricity is directly used by the house loads or fed into the electrical grid when the loads do not absorb all the generated electricity.
The grid-connected systems represent most of the PV installed capacity.
1.1 Electricity storage
Like other renewable sources, solar energy is not dispatchable, meaning the gen- eration of electricity cannot be controlled to correlate with demand. Therefore it would not be possible to reach a high share of solar energy without using storing devices. Besides, because of the highly fluctuating nature of this energy source, the massive presence of grid-connected PV panels can cause instabilities in electrical grids [4]. Therefore, every grid, depending on its robustness, has a theoretic limit for renewable energy penetration. The presence of storage in the grid increases this limit.
Some electricity storage technologies are available, their goal is to compensate the fluctuations in the grid and/or store energy for long periods. The characteristics of some electricity storage technologies are summarised below:
pumped hydro storages (PHS): the most established technology for large- scale electricity storage. When the electricity price is low, water is pumped from a downhill reservoir to an uphill reservoir, during this process electricity is consumed. When the electricity price is high, the water flows from the upper level reservoirs to the down level reservoir. The water flow activates downhill turbines which convert the potential energy of the water into mechanical en- ergy, then the mechanical energy is converted into electricity by a generator.
The round trip efficiency varies between 65-80%. It is a both high energy density and high power density technology. The main drawback is the need of specific geographical conditions to install a hydro-power plant and a PHS;
flywheels: a flywheel consists of a cylindrical mass rotating in a vacuum en- vironment to reduce the friction losses. An electric motor is used to accelerate the cylinder, the faster the cylinder rotates the more energy is stored. To recover the stored energy, the cylinder is slowed down; in this case the electri- cal motor works as a generator to produce electricity. The efficiency strongly depends on the storage time, because of the high self-discharge; the overall instantaneous efficiency can be 90%. Because of the high self-discharge this technology is suitable more for frequency control of the grid rather than long period storage. Another drawback is the high cost [5];
Chapter 1. Introduction
compressed air energy storages (CAES): CAES system are high capacity energy storages. In a CAES system, low price electricity is used to compress air and store it in a underground geologic formation. To recover the energy the compressed air is used to run a turbine. The compressed air can also be used as oxidant in the combustion chamber of a natural gas power plant. Energy can thus be stored for periods up to one year thanks to the low leakages. The main drawback of this technology is the necessity of a natural cavern to store the air [5];
superconducting magnetic energy storages (SMES): superconductors are materials that have zero electrical resistance when their temperature is below a certain critical temperature (some degrees above 0 K); the result is that there are no Joule losses associated to electricity flowing in these materials.
Electricity can be injected and extracted very fast from SMES, this makes them suitable for fast fluctuation compensation. To maintain the materials in the state of superconductors refrigeration is necessary. The losses associated with the refrigeration systems are the only ones, so the overall efficiency of the system depends on the storing time of electricity; efficiencies up to 98% can be reached. The drawbacks of these system are linked to the high price and complex infrastructures need in case of big capacity installations [6];
hydrogen: an energy vector whose production is energy-intensive. Hydrogen can be produced by an electrolyzer that, consuming electricity, splits water into hydrogen and oxygen. The hydrogen is stored into a tank and then combined with air oxygen inside a fuel cell (FC), the recombination process produces electricity and does not require any combustion reaction. FC are suitable for residential sector, yet the overall efficiency of the process is 35% and the costs are very high [7].
batteries: devices that convert electricity into chemical energy and vice-versa.
The round trip efficiency can vary between 75% and 93%. Their main use today is for portable devices. Their application in the residential sector has started to be studied, since they can be used to store the electricity generated by installed PV panels in the houses. Because of the short lifetime, high disposal impact and high cost, high capacity battery storages are still not competitive with PHS and CAES.
Most of the storing technologies mentioned are grid-scale, while hydrogen and bat- teries can also be applied on a residential scale.
1.2 Residential electricity storage
As most of the PV installations in Sweden are residential, a way to allow the in- crease the share of solar energy would be coupling storages and PV installations.
Chapter 1. Introduction
Installing a storage device in a residential PV system both makes the system more dispatchable, allowing the use of solar energy even during non-sunny periods, and reduces the influence of the system on the electrical grid, as the amount of elec- tricity fed into the grid decreases. The storage, indeed, leads to an increase of the self-consumption (SC) and self-sufficiency (SS) of the house: respectively the per- centage of energy produced by the PV installation that is consumed by the house loads and the percentage of electricity demand that is satisfied by the PV system in the house.
Among the electricity storages for residential sector, fuel cells end electrolizers have lower efficiencies than batteries and are more expensive [8]. As a consequence bat- teries are nowadays the most commercially available technology for residential elec- tricity storage.
Including a battery in a PV system, to increase self-consumption, could also make the system more profitable. This depends on many factors:
cost of the installation: the higher the cost of the installation, the lower the probability that the system is profitable;
tariff scheme: the higher the gap between the price at which electricity is sold and bought, the higher the probability that the system is profitable;
load curve of the house: if the load curve of the house matches very well with the electricity generation curve, installing a storage is not as necessary, meaning the storage may not be used frequently enough to make it profitable.
Finally, if an electricity tariff scheme with sub-daily price variations is applied: a cost-optimal control can be applied and the storage can be used to store electricity (both produced by the PV panels or bought from the grid) when the price is low, and use and possibly sell the stored electricity when the price is high. In this way the system could be more profitable than if only used to maximize self-consumption [9].
Other solutions, besides storage, are available to increase electricity self-consumption in a house with installed PV panels. The possibility of shifting the house loads in the houses so to match the electricity generation or the fluctuations of the electricity price during a day (usually referred as demand side management (DSM) or demand response), is another investigated option. Some appliances that require high power (dishwashers, washing machines, tumble dryers, electrical boilers or heat pumps), can be operated at any time, or have anyway a certain degree of flexibility; this means that they can be operated when there is excess of electricity production.
This solution still presents some limits compared to a storage installation, due to the impossibility to shift some house loads (light, television, cooking appliances);
Chapter 1. Introduction
the available literature [10] shows that, on average, the percentage increase in the SC due to DSM implementation is lower than the one due to a battery installation.
1.3 Thesis Objective
When deciding to install a battery in a residential PV system, the most important parameter to take into account is its capacity. A larger capacity battery is capable of increasing self-consumption, however the marginal benefit must be compared to marginal cost. Performing a techno-economical analysis is necessary to ensure the return on the investment and minimize its payback time.
The objective of this master thesis is to show how to size a battery for an already existing residential PV system. It also aims at verifying whether the conditions for adding a battery to a PV system in Sweden already subsist or under which condi- tions this kind of investment would become profitable. Different control algorithms are used for the battery, depending on the electricity tariff scheme considered. The techno-economical performances of each investigated system are discussed.
1.4 Scope and limitations
The case study is a single family house in V¨axj¨o, Southern Sweden. As input for the developed model, the weather data of this location, the monthly consumption data of the family living in the house and the characteristic of the PV installation already present on the house roof are used.
The dependence of solar irradiation on the locality does not allow to consider the outcomes of this study valid for many locations. It should also be considered that the average behavior of a Swedish family is used to model the loads, this further re- duces the scope of applicability of the results of this paper. Yet the way the models are obtained is clearly explained; the same models can be used for any location and any loads by changing the input data.
The models developed allow to optimize the battery size for an already existing PV installation, the same approach cannot be used if the goal is to optimize the design of the whole PV-battery system. Eventually it is not aim of this project to compare the installation of a battery to other possible techniques to increase the self-consumption of the house.
Chapter 1. Introduction
1.5 Methodology
The objectives are met through Matlab models created for the purpose. The proce- dure is divided into many steps:
1. The performance of the existing system during one year is estimated by cre- ating a mathematical systems model, including; demand curves, irradiation, PV generation, and inverter losses.
2. The performance of the model are compared with one year of available data to validate the model.
3. Two different types of battery (lead acid and lithium ion) are then inserted in the model, the control of the batteries aims at maximizing the self-consumption.
The technical performances of the new systems are investigated.
4. The techno-economic performances of the batteries under the current tariff scheme and market conditions are analyzed and the necessary conditions to make the investment profitable are discussed.
5. Hourly tariff schemes are considered and new price optimized control strategies are investigated to increase the profitability of the battery.
1.6 Previous work
Many researchers are now focusing on the methods to increase self-consumption in houses provided with PV systems, and on their economical feasibility.
Salpakari and Lund [9] developed different physical models for a house in South- ern Finland. The models include a PV system, a heat pump (HP), thermal storage, battery and shiftable loads. They studied the behaviour of the modelled systems under a cost-optimal control. They showed that if a hourly price tariff is applied, cost-optimal control leads to savings and to a significant reduction of the feed-in electricity. It is also possible to reduce the feed-in electricity to zero without a sig- nificant decrease of the savings. The HP with storage tank and the battery has the greatest influence on the flexibility of the modelled systems. The investment costs were not considered in the study, since the comparison was between the same system with or without control.
Lorenzi and Silva [11] created a demand response model for two different systems in a Portuguese single family house with low energy consumption. The first system is characterized by PV system, electrical boiler and battery. The second system is composed only by the PV system and the electrical boiler. The Portuguese tariff scheme was used. The system without battery performs economically better than
Chapter 1. Introduction
the PV-battery system, due to the high installation cost of the battery. The battery- system is the best solution to increase self-consumption, although not economically convenient.
Weniger, Tjaden and Quaschning [12] showed that in Germany, a PV system with- out battery is cheaper than a PV-battery system. Yet, considering the existing trend in the battery price and feed-in tariffs, in the long term, PV-battery systems will be cheaper than simple PV-system. On the other hand Hoppmann, Volland et al. [13]
assess that, in Germany, with no feed-in tariffs or self-consumption premiums small PV-battery systems are already profitable
Thygesen and Karlsson [14] performed a study on a single-family house in V¨aster ˙as, Sweden. Two storing strategies were considered: a lead acid battery and a hot wa- ter tank with electrical heater to assist a heat pump. The analysis of the systems showed that, when the same level of self-consumption is reached, the system with hot water tank is more profitable.
Mulderet al. [15] conducted a study based on Belgium households. They compared two batteries available on the market: a starter lead acid battery and a Li-Ion bat- tery. The study considers different tariff schemes and variations both in electricity purchase price and battery price. The study shows that starter lead acid batteries were already attractive in 2012 without subsidies, while Li-Ion could become attrac- tive in 2017 if an electricity price increase of 4% per year, starting from 2013, occurs.
Schreiber and Hochloff [16] proposed a capacity-dependent tariff to add to the retail prices, in Germany. The tariff incentivizes smart-operating storages, that would allow decreasing the influence of the PV system on the electrical grid. Under these conditions it is shown that both a non-optimally controlled and an optimally con- trolled PV-battery system are cheaper than a PV system without energy storage.
Chapter 2 Case study
2.1 The Swedish electricity market and PV poli- cies
In Sweden, both the wholesale and the retail electricity markets are deregulated, it means that the electricity price is not influenced by direct state regulations, but depends on demand and offer.
The wholesale electricity market is part of the Nord Pool power market, that also includes Norway, Finland, Denmark, Lithuania, Latvia and Estonia. The Nord Pool provides day-ahead and intraday markets. Most of the trading occurs in the day-ahead market (Elspot), that provides prices changing hour by hour [17]. The wholesale prices can vary significantly from hour to hour depending on which power plants are available to deliver electricity. This means that the price are low when cheap electricity sources, such as hydro and nuclear, are enough to meet the demand;
but can rise much when other sources (CHP, gas turbines) are required [18].
The retail electricity market involves over 120 retailers. There are three possible contracts available for the customers:
floating price: the price changes from month to month. It is adjusted according to the Nord Pool prices;
fixed price: the price stays constant for one, two or three year;
hourly pricing: the price follows the Nord Pool day-ahead market.
The floating price contract is the most common one [19].
The variety of available contracts makes it impossible to assess unequivocally the electricity price for the consumers. Four parts contribute to the electricity price:
Chapter 2. Case study
electricity, grid, green certificates and taxes. The meaning of green certificates is explained in the next subsection.
2.1.1 PV support
Different PV support policies exist in Sweden. Here the ones known by the author of this thesis are listed [3]:
installation rebate: since 2006 the Swedish government introduced subsidies for PV installations, in the form of partial refund for the installation cost. As the installation cost of PV panels has been decreasing every year, also the per- centage of rebate has been decreasing, in particular for residential installations the maximum coverage of the installation costs dropped from 60% in 2009 to 20% in 2015 ;
green certificates: since 2003 every electricity generator must have a mini- mum amount of green certificates. Green certificates are gained by producing renewable electricity: one certificate is given per MWh of renewable electricity produced. They can also be bought and sold in a open market [20]. Applying for green certificates implies additional bureaucratic and economical burdens, that not necessarily lead to significant economical advantages for residential PV systems. As a consequence green certificates are not a relevant contribute to these installations;
guarantees of origin: documents that state the origin of the electricity. Since 2010 each electricity producer receives a guarantee per MWh of electricity produced. The guarantees can be sold and bought in the same way as the green certificates. The customers can then choose their electricity source.
Applying for guarantees of origin is not compulsory, but voluntary. Their contribute to PV support is negligible;
grid compensation: most electricity, in Sweden, is produced in the North and consumed in the South. This implies significant transmission losses. Res- idential PV systems produce electricity in the same area where the electricity is consumed. As a consequence less transmission losses are associated to it. A PV electricity producer can apply for grid compensation: the producer earns between 0.2 and 0.7 ceper kWh fed into the grid.
tax-credit: since 2015 it is possible for prosumers (electricity producers and consumers at the same time) to apply for tax-credit. The prosumer receives a tax reduction of 6.2 ceper kWh fed into the grid. The tax-credit is given for an amount of kWh that is lower or equal to the amount of kWh bought, anyway no more than 30,000 kWh. There are no guarantees that this measure will be in force for a long period.
Chapter 2. Case study
While the installation of PV system has been economically supported since 2006, no measures to support the increase of self-consumption of building provided with these systems existed until November 2016. Now the installation of a storage system can be refunded up to 60% of the storage cost [21].
2.2 The house
A single family house in V¨axj¨o, Southern Sweden, is used for this case study. The house is shown in figure 2.1.
Figure 2.1: House used as case study.
The house was designed by Sustainable houses in Sm˚aland, an association of com- panies in construction business that aims at designing energy-efficient houses. It is a net-zero energy house, meaning that the energy consumed during the whole year is roughly equal to the renewable energy produced on site. The house is pro- vided with cellulose insulation (40 cm insulation in the walls, 50 cm insulation in the roof). The heating is underfloor. The lighting consists of LED with motion sensors. The washing machine and dishwasher are connected to the hot water tank through a heat exchanger, that preheats the cold water from the tap with the hot water from the hot water tank, in this way the heat load due to these devices is only partially satisfied by electricity. Around 17 m2 of vacuum tubes for water heat- ing and 20 PV panels with a rating power of 4.9 kW for electricity generation are installed on the roof. The heating system is connected to the district heating system.
The monthly data of electricity produced, consumed, bought and sold by the house are available. They are shown in figure 2.2.
Chapter 2. Case study
Figure 2.2: Electricity fluxes of the house in 2014.
Figure 2.2 shows that although, during spring and summer, the electricity produced is more than the electricity consumed, in the same period around half of the elec- tricity consumption is provided by the grid. The current tariff applied to the house provides constant prices for buying electricity during the day and no feed-in tariffs for the electricity fed into the grid. This means that increasing self-consumption would bring economic benefits for the family living in the house.
Chapter 3
Current system modelling
The electricity consumption, production, sale and purchase data for the house are available with the resolution of 1 month. Such a resolution is not enough to opti- mally size a battery to install in the system. A 15 minutes resolution is the temporal resolution suggested for this kind of project [22].
In this chapter it is shown how the annual electricity load curve and electricity generation curve for the house are obtained. The curves have 15 minutes resolution.
3.1 Electricity demand
The available initial data to model the load curve of the house are the monthly electricity consumption data for year 2014. As the heating is not provided by elec- tricity, it is reasonable to assume that there are no differences, due to climate, in the electricity demand from year to year, and that having only one year values is not a strong limitation for the validity of the results. From the available data, the average daily consumption for every month is calculated. This leads to the results shown in table 3.1. The values for January are far lower than the values for December. For privacy reasons it has not been possible to ask the family living in the house for ex- planations. To create the model it is assumed that the family was not in the house at the beginning of January, so to get a very low electricity demand at the beginning of January and a demand comparable with the one of February at the end of the month.
At first it is considered that the consumption was the same for all the days of the same month. Then, some modifications are done in order to have a different value of electricity daily consumption every day.
The modifications done on the average daily consumption are explained below:
the daily consumption values of the first and last days of the months are modified to shave the gaps between the months (see ”Shaving procedure”);
Chapter 3. Current system modelling
the daily consumption values of all the days of the months are modified, adding or subtracting a certain percentage of the average daily consumption to its value, according to a specific pattern (see ”Peaking procedure”).
Month Monthly electricity Average daily consumption [kWh] consumption [kWh]
January 634 20
February 792 28
March 693 22
April 520 17
May 516 17
June 579 19
July 550 18
August 482 16
September 491 16
October 628 20
November 876 29
December 1109 36
Table 3.1: Monthly and average daily consumption during year 2014
Shaving procedure
The factors to shave the gaps among the months (here referred as shaving factors) are obtained by imposing, for each month, the equality between the electricity demand at the end of the month and at the beginning of the following month. In this way twelve equations with twelve unknown can be obtained; each equation is in the form:
M · (1 ± m%) = M+1· (1 ± (m+1)%) (3.1) where M is the daily average electricity demand for the generic month M and m is the shaving factor for the same month. As the values at the beginning of January and at the end of December do not have to match, as the family is assumed not to be in the house at the beginning of January, only eleven equations are available, while there are twelve unknowns. One value has to be imposed arbitrarily. The value for June is the one chosen arbitrarily: the average electricity demand in May, June and July is similar, the length of the days is almost constant in June, meaning that the load due to lighting is almost constant; therefore a factor equal to 0 is imposed. The factors obtained are shown in table 3.2. The shaving factors are applied so that in every month there are ten days when the demand is higher than during the average day and ten days when the demand is lower. Differently, in January half of the days are characterized by lower demand, half by higher demand.
Chapter 3. Current system modelling
Month Shaving factor [%]
January 60
February 11
March 14
April 12
May 12
June 0
July 6
August 5
September 5
October 16
November 20
December 3
Table 3.2: Months shaving factors Peaking procedure
The factors used to avoid shaved differences between close days (here referred as peaking factors) are chosen arbitrarily and are the same for every month:
f1=10%
f2=15%
Without considering the changes made by the shaving factors, there are five types of day in each month:
Type 1: M1=M;
Type 2: M2=M+f1*M;
Type 3: M3=M-f1*M;
Type 4: M4=M+f2*M;
Type 5: M5=M-f2*M;
where M is the daily average electricity demand for the generic month M, M# is the daily electricity demand for the day associated to ”type #”. ”Type 1” is applied to days 1,6,7. ”Type 2” is applied to day 2. ”Type 3” is applied to day 3. ”Type 4” is applied to day 4. ”Type 5” is applied to day 5. Every type is applied cyclically every seven days, like in the week. The cycle is applied until day 28 of each month, ”type 1” is applied from day 29 to 30/31. This means that each type day, in one month, is not necessarily associated with the same day of the week in another month. This is done because creating such an algorithm is easier than creating one that associates
Chapter 3. Current system modelling
always the same day type to the same day of the week; as the choice of the factors and the applied scheme is arbitrary, though the easier algorithm is less elegant and consistent, it does not necessarily imply bigger errors in the results.
Changing the daily data is made in such a way not to modify the values of the total energy consumption during each month. The profile obtained is shown in figure 3.1.
Figure 3.1: Year profile of electricity consumption. Resolution: 1 day.
Then, a percentage daily load curve (see fig.3.2), with 15 minutes resolution, is created for every day of the week. Two different daily load curves, one for the work- days and the other one for the holidays, are available for Sweden, for different types of dwellings [23]. The load curves for family houses without electric heating are used. The resolution of the curves available in the literature is 1 hour. From these curves, new curves with 15 minutes resolution are generated. To generate the new curves, four values of energy consumption have to be derived (one every 15 minutes) from the single value of energy consumption per hour, given in the literature.
To do that, two different parts of the day are considered:
when people don’t use any device: night during the weekends, night plus work
Chapter 3. Current system modelling
hours during the workdays. During those hours the energy consumed in one hour is considered equally spread on the 4 time intervals contained in the hour;
when people could use the electrical devices: 12.5% of the energy consumed during the hour is considered base load; then is equally spread on the four time intervals contained in the hour. The remaining energy is spread on the intervals randomly. This makes the algorithm capable of capturing the spikes in the demand of the house.
The load curve for Mondays is shown in figure 3.2. It is shown together with the 1 hour resolution load curve.
Figure 3.2: Percentage load curves for Mondays. 1 hour and 15 minutes resolution.
Then its own percentage load curve is applied to every day of the year, meaning that Mondays have the same percentage curve, Tuesdays have the same percentage curve etc. In this way the load curve for the whole year with 15 minutes resolution is obtained.
3.2 Electricity generation system
The electricity generation system consists of 20 PV panels, connected in series. The panels are mounted on the house roof with 45° inclination. The nominal power of the whole PV system is 4.9 kW. When the solar irradiation reaches the panels, DC
Chapter 3. Current system modelling
is produced. The DC produced by the panels is then converted into AC by a solar inverter. The AC can be fed into the house, if there is demand. Otherwise it is fed into the grid. When the electricity produced by the PV system is not enough to satisfy the internal load of the house, the extra electricity that is needed comes from the grid.
A simplified scheme of the system is shown in figure 3.3.
Figure 3.3: Scheme of the electrical system The datasheets for the components can be found in the Appendix.
3.2.1 PV panels
The operation of a PV panel: the output voltage and current, depends on the incident irradiance, Gi and panel temperature TP V [24].
Irradiance
The 2014 values of irradiance for V¨axj¨o are available on the Swedish meteorological and hydrological institute (SMHI) website [25]. The available values are the hourly data for global horizontal irradiance (Gh); the necessary inputs for the PV panels modelling are values of global irradiance on a 45° tilted surface, with 15 minutes resolution. From Gh, the values of irradiance on a 45° tilted surface (Gt) are calcu- lated first with 1 hour resolution; then from the hourly data, data with 15 minutes resolution are originated.
The irradiance on a tilted surface is calculated as follows [26]:
Gt = Gbncosθ + GdFc−s+ ρGhFc−g (3.2)
Chapter 3. Current system modelling
Gh is given. The beam normal irradiance (Gbn) is calculated by using the DIRINT model, it allows to calculate Gbnas a function of Gh, zenith angle θz, day of the year and atmospheric pressure. A Matlab function, given by Sandia National Laborato- ries, was used to perform the model [27]. The diffuse horizontal irradiance (Gd) is calculated as follows [26]:
Gd = G − Gbncosθz (3.3)
ρ is the ground reflectivity, a reference value: ρ = 0.2 is used. The view factors Fc−s and Fc−g are calculated as:
Fc−s = 1 + cosβ
2 (3.4)
Fc−g = 1 − cosβ
2 (3.5)
where β is the tilted surface angle from horizontal.
To obtain the 15 minutes resolution data from the 1 hour resolution data, the values of irradiance are compared with the values of the clear sky irradiance, that means the one received by the collector if there were no clouds during the whole time.
Several models are available to calculate the clear sky irradiance [28], the ASHRAE model is used here [26]. The following procedure is followed:
every hour is classified as type 1, 2, 3, 4 or 5:
1. very sunny (VS): the hour is considered sunny if the global irradiance is 90% higher than the global clear sky irradiance.
2. very cloudy (VC): the hour is considered very cloudy if the global irra- diance is lower than 110% of the diffuse irradiance calculated with the DIRINT model;
3. sunny/cloudy (SC) or cloudy/sunny (CS): the hour is considered SC/CS if it is not VS nor VC, but the hour before/after is VS;
4. sunny/cloudy/sunny (SCS) or cloudy/sunny/cloudy (CSC): the hour is considered SCS if the hours before and after are both VS. Similarly for the CSC case;
5. variable (VV): the hour is considered VV if none of the previous scheme is applicable.
different algorithms are applied according to the type of hour, it must be considered that the profile always follows the clear sky profile, if not otherwise specified:
1. during the hour, the irradiance has the same profile as the clear sky irradiance;
Chapter 3. Current system modelling
2. the irradiance is uniform during the hour. It does not follow the clear sky profile;
3. the first two intervals of the hour are considered sunny/cloudy, the last two intervals of the hour are considered cloudy/sunny. The irradiance of the sunny part of the day is considered equal to 90% [29] of the clear sky irradiance. The irradiance of the cloudy part of the day is calculated so that the average irradiance during the whole hour is correct. If this algorithm leads to values of irradiance lower than the clear sky diffuse radiation, then the following algorithm is used: the irradiance of the cloudy part of the hour is considered equal to the diffuse radiation and is not linked to the clear sky profile, the irradiance of the sunny part of the hour is calculated so that the average irradiance is correct;
4. the first and last intervals are considered sunny/cloudy, the second and third intervals are considered cloudy/sunny. Then it proceeds as ex- plained for type 3;
5. variable: in this case the profile does not follow the clear sky profile. Four random values, so that their sum is 100, are generated, one per interval of the hour. The global radiation during the hour is the sum of the diffuse radiation plus a certain percentage (given by the random number) of the difference between the global and the diffuse radiations. The process is iterated until none of the values is higher than the clear sky irradiance.
In figure 3.4 the possible profiles are shown. In figure 3.5 the variability introduced by this model on the 1 hour averaged values is shown. You can notice that at the sunrise and at the sunset the 1 hour average and then the 15 minutes average irradiances can be higher than the clear sky irradiance. It means that the model is not accurate when the sun is low on the horizon.
Panel temperature
The panels temperature was not measured. The panel temperature is function of irradiance, air temperature and wind velocity, yet for semplicity an empirical correlation with the ambient temperature and the solar irradiance only is used [30]:
TP V = Tamb+ k · Gi (3.6)
The constant k depends on the mounting type of PV panels. For panels installed on a sloped roof, k = 24 °C/kW [30] can be used.
The air temperature for Vaxjo is available with 1 hour resolution. The tempera- ture is considered constant during the whole hour.
Chapter 3. Current system modelling
Figure 3.4: Main irradiance profiles.
Figure 3.5: Irradiance data sample.
Chapter 3. Current system modelling
Panel operation
For every possible combination of Gi and TP V, the panel can produce electricity with different values of voltage and current. The curves representing IP V as function of VP V are called characteristic curves. An example of possible characteristic curve is shown in figure 3.6.
Figure 3.6: Characteristic and power curves of a PV panel
The power curve has a maximum. It means that there is a specific point of its characteristic curve at which the panel has to work in order to reach the maximum efficiency. This point is called maximum power point (MPP). To produce the max- imum possible power, given the environment conditions, the panels should work at their MPP. The panels work on a point that is the MPP, or close to it thanks to the MPP tracking (MPPT) algorithm, present in solar converters.
In the developed model, the open circuit voltage (Voc) of the panel is considered dependent only on TP V, while the short circuit current (Isc) is considered dependent only on Gi.
The dependence of Isc on TP V and the dependence of Vocon Gi are neglected in this model.
These are the correlations used [31]:
Isc = IscN OCT · Gi GST C
(3.7)
Voc= VocST C ·
1 + (TP V − TST C) · kv 100
(3.8)
Chapter 3. Current system modelling
The maximum power point current (IM P P) and maximum power point voltage (VM P P) are then considered proportional to the Isc and Voc:
IM P P = IM P PST C · Isc
IscST C (3.9)
VM P P = VM P PST C · Voc
VocST C (3.10)
In the model of the PV panel it is supposed that the MPPT efficiency is 100%, then the output of every single PV panel is characterized by IM P P and VM P P.
Since the system is composed by 20 PV panels in series, the total generated voltage is 20VM P P.
IM P P and 20VM P P are the input values for the inverter, in the case when the MPPT efficiency is 100%.
3.2.2 Inverter modelling
The inverter keeps the PV panels working at their MPP and convert the DC into AC. The inverter does not follow the MPP of the panels with 100% precision. To take into account the energy losses introduced by this error, the variable ηM P P T is introduced; it is assumed ηM P P T = 0.98 [32]. It is assumed that the imprecision of the inverter in tracking the MPP leads to the underestimation of the VM P P, so the panels actually work on a point of their characteristic curve that is slightly on the left of the MPP. In figure 3.7 you can see how the operation point moves on the char- acteristic curve, due to the tracking imprecision. From figure 3.7 it can be observed that while VOP does not coincide with VM P P, IOP is almost the same as IM P P. The inputs for the inverter are then: Iinv = IM P P, Vinv = ηM P P T · 20VM P P.The inverter efficiency depends on the power and voltage of the electricity that enters in the inverter. The inverter datasheet gives the efficiency curves as function of output power and input voltage for a bigger model than the one installed in the house. It is assumed that the same curves can be used for the installed model. The curves are shown in figure 3.8. From the datasheet curves, a bidimensional table, reporting the efficiency of the inverter as function of input power and voltage has been deduced.
It is shown in table 3.3.
The efficiency for any given input voltage and power is then calculated through bilinear interpolation of the values in the table. The output power of the PV system is then calculated as follows:
P = ηinv· ηM P P T · 20PM P P (3.11)
Chapter 3. Current system modelling
Figure 3.7: Movement of the operation point due to MPPT imprecision
Figure 3.8: Inverter efficiency curves
Chapter 3. Current system modelling
V[V]\P[W] 115 262 518 772 1026 1537 2049 3077 4111 5100
440 87 95.7 96.6 97 97.2 97.2 97.1 97 96.8 96.5
580 87 96.2 97.1 98 98.1 98.3 98.1 98 97.8 97.2
800 87 94 95.7 96.7 97.2 97.3 97.5 97.5 97.2 97
Table 3.3: Inverter efficiency table. Efficiency in [%]
3.3 Model validation
The models described in the previous paragraphs allow to compute the electricity consumption, generation, sale and purchase curves, with a 15 minutes resolution. It is not practical to show these curves for the whole year. The curves are shown for the first three days of July in figure 3.9
Figure 3.9: Modelled electricity fluxes 1-3 July 2014 - Resolution 15 minutes.
Thanks to the high resolution of figure 3.9, it is possible to understand what was observed in chapter 2: why the amount of electricity bought in summer is around half of the total electricity consumed in the same season, although the electricity produced is more than the electricity consumed. You can see that the time when most electricity is produced does not coincide with the time when most of electric- ity is consumed. The highest amount of electricity is consumed during the evening, when the panels are not producing. The battery then, should store the energy pro- duced during the day and release it during the evening and night.
From the 15 minutes resolution data, the monthly data are calculated, in order
Chapter 3. Current system modelling
to compare the results of the modelled system with the real data. The results of the model are shown in figure 3.10 together with the measured data.
Figure 3.10: Comparison of the modelled and real systems Figure 3.10 leads to the observations listed below.
the electricity generation is estimated with a relative error lower than 3% dur- ing every month but January, November and December. The detailed errors are shown in figure 3.11.
Figure 3.11: Error in the estimation of the electricity produced by the PV system
Chapter 3. Current system modelling
Figure 3.12: Error in the estimation of the electricity produced by the PV system - Irradiance dependence
The lower accuracy during the winter months is due to the unreliability of the PV model for low values of irradiance; in figure 3.12 it is possible to see that the highest values of imprecision are actually related to the lowest values of irradiance: for low values of irradiance the lower the irradiance, the higher the relative error. For higher values of irradiance the relative error does not show any dependence on the irradiance. The relative error on the production over the whole year is 0.7%.
3.13 shows that the error on the electricity bought model is lower than 5%
but in June, July and August. In particular the error reaches 12% in June.
In this month the real consumption curve shows an unexpected local peak, it is possible that the behaviour of the family in this month was far from the average behaviour. Except for June, during spring and summer the model underestimates the matching between the production and the consumption of electricity, it could then be modified accordingly. Yet, since it is not possible to know the real behaviour of the family and the overall error of the model is acceptable (0.3%), the model based on the average Swedish behaviour is the one used also for the remainder of the study.
Chapter 3. Current system modelling
Figure 3.13: Error in the estimation of the electricity bought from the grid
Chapter 4
PV battery system modelling
After obtaining the PV system model, and after verifying its reliability, the original model can be modified, implementing the presence of a battery. In this chapter the possible configurations for the new system are examined. The details of the new system and the way it is modelled are explained. The results obtained are finally shown and discussed.
4.1 System configuration
Different PV-battery system configurations are possible [33] [34]:
DC-coupled systems: the battery is connected, through a battery charger, to the output of the PV panels, before the grid inverter.
Advantages:
– availability of components: the bidirectional DC/DC converters are a more mature technology than the bidirectional AC/DC converters;
– higher storing efficiency: the electricity is stored directly after being produced; there are less conversion steps, and thus losses, than in the AC coupling systems.
This system is represented in figure 4.1;
AC-coupled systems: the battery is connected, through a bidirectional AC/DC converter, to the output of the grid inverter.
Advantages:
– easier to apply to an already existing PV system: there are not important modifications to the system, the battery can be considered an added device in the house;
Chapter 4. PV battery system modelling
– possibility to store the electricity buying it from the grid: the solar inverter only operates in one direction, putting the battery before it does not allow to recharge the battery from the grid;
This system is represented in figure 4.2.
Figure 4.1: DC coupled PV battery system scheme
Figure 4.2: AC coupled PV battery system scheme
Chapter 4. PV battery system modelling
For the analysed case, as the PV system is already installed in the house, adding a battery using an AC-coupled configuration is easier than using a DC-coupled configuration. The AC-coupled system is then investigated. This configuration also allows to use the system in a smart grid, to buy electricity when the price is low.
This possibility is investigated chapter 5.
4.2 System modelling
Up to the grid inverter the new system, configuration and components, is exactly the same as the previously discussed system. Because of the insertion of the battery, as in figure 4.2, the way electricity is provided to the house loads and to the grid is different. In this chapter a system where the battery installed is used to maximize self-consumption is studied. When electricity is produced, it is first fed into the house, to satisfy the electricity demand, then it is used to charge the battery and last it is fed into the grid. When the electricity required by the house is bigger than the electricity provided by the PV panels, the demand is first met by the battery, last by the electrical grid. This type of battery control is here reffered as base control (BC).
The new components in the system are the AC/DC bidirectional inverter and the battery.
4.2.1 AC-DC bidirectional inverter
The AC/DC bidirectional inverter has the task of converting AC into DC, that can be fed into the battery, when the battery operates in charging mode. It converts DC into AC when the battery operates in discharging mode. The AC used in charging mode can be supplied both by the grid converter (so the PV panels) and the grid.
As in the model analysed in this chapter, the only aim of the battery is to maximize self-consumption, the AC is always provided by the solar converter.
The efficiency curve for this component has been taken from the literature [35]. The same curve is used both in charging and discharging mode. It is shown in figure 4.3.
The model found in the literature has a nominal input power of 5.3 kW. Since the maximum input power of the solar inverter is 5.1 kW and its maximum effi- ciency for 5.1 kW input power is 97.2%, the maximum input power of the AC/DC bidirectional inverter considered is 5 kW. The values shown in figure 4.3 are then scaled accordingly. No efficiency values are given for output power lower than 10%
of the nominal output power. It is then considered that the inverter, and thus the battery, do not work in this conditions.
Chapter 4. PV battery system modelling
Figure 4.3: AC/DC bidirectional converter efficiency curve
4.2.2 Battery
Different battery technologies, their efficiencies (η), and lifetimes with respect to depth of discharge (DOD) are listed below:
Lead acid [36]: η = 72-78%, 1000-2000 cycles at 70% DOD, self-discharge is a significant problem, contains toxic heavy metals, is the most mature and cheapest technology;
Nickel cadmium (NiCd) [36]: η = 72-78%, 3000 cycles at 100% DOD, self-discharge is a significant problem, contains toxic heavy metals;
Sodium sulfur (NaS) [36]: η = 89%, 2500 cycles at 100% DOD, no self- discharge, high operating temperature;
Lithium ion (Li-Ion) [37]: η = 92.5%, 15 years at 100% DOD, expensive.
The most diffuse technologies on the market are the lead acid and the Li-Ion bat- teries. Both these typologies are considered in this project.
The values used for the LI-Ion battery are the ones given for Tesla’s Powerwall 1 [37]:
ηbc = ηbd=0.96;
Chapter 4. PV battery system modelling
SOCmin=0 %;
SOCM ax=100%.
The values used for the Lead Acid battery are the following [13]:
ηbc = ηbd=0.9;
SOCmin=30%;
SOCM ax=80%.
No self-discharge or capacity fade losses are considered at this point of the project.
The battery is never charged over its maximum SOC and never discharged under its minimum SOC. The energy fed into the battery is then calculated as:
Ein = ηAC/DC· ηbc· (EP Vnet − Eload) (4.1) The energy released by the battery when required by the load is calculated as:
Eout = Eload− EP Vnet
ηDC/AC· ηbd (4.2)
Equation 4.1 is only valid when the input energy in the battery does not cause the battery SOC to go over the maximum SOC. In this latter case part of the energy produced by the PV panels is fed into the grid. Equation 4.2 is only valid when the output energy from the battery does not cause the battery SOC to go under the minimum SOC. In this latter case part of the energy demanded by the house loads is fed by the grid.
4.3 Performances
Once the PV battery system is modelled, its behaviour, varying with the battery size, can be studied. The studied parameters are the total electricity sold and bought during the year, the self-sufficiency and the self-consumption of the house.
The self-sufficiency indicates the percentage of electricity load satisfied by the PV system:
SS =
35040
X
i=1
Eload,i− Ebought,i
Eload,i (4.3)
The self-consumption indicates the percentage of electricity produced that is con- sumed inside the house; so that is not fed into the grid.
SC =
35040
X
i=1
EP V,i− Esold,i
EP V,i (4.4)
Chapter 4. PV battery system modelling
Figures 4.4 shows the trend of self-consumption and self-sufficiency with the battery size.
Figure 4.4: Sensitivity analysis: self-consumption and self-sufficiency vs battery capacity
The values of self-consumption are higher for the Lead acid batteries than for the LI-Ion batteries, when the same net battery size is considered (the different DOD should be taken into account, it means that a 30 kWh lead acid battery should be compared with a 15 kWh Li-ion battery). This is due to the lower efficiency of the lead acid batteries: more electricity is required to recharge the battery, therefore less electricity is fed into the grid. Higher values of self-sufficiency are reached with the Li-Ion batteries. This is due to the higher efficiency of the Li-Ion batteries.
Adding a 8 kWh Li-Ion battery to the existing system increases the self-sufficiency from around 25% to slightly more than 40%. Adding a 16 kWh lead acid battery to the existing system increases the self-sufficiency from around 25% to slightly less than 40%. For battery capacities of respectively 8 kWh and 16 kWh the Li-Ion and Lead Acid self-sufficiency curves present a knee, it means that the marginal benefits of increasing battery sizes become significantly lower.
Investigating how the different DOD and efficiencies influence the optimal size of the battery it is observed that both a smaller operating range of SOC and lower
Chapter 4. PV battery system modelling
battery efficiencies lead the knees of the studied curves to be moved towards right, yet the effect of a smaller operating range of SOC is more significant than the effect of reduced efficiencies.
Figure 4.5: Sensitivity analysis: electricity bought and sold vs battery capacity
Figure 4.5 shows the total values of electricity bought and sold in one year, as function of the battery size. An 8 kWh Li-Ion battery reduces the electricity bought from 5870 kWh to 4710 kWh. It reduces the electricity sold from 2840 kWh to 1410 kWh. It means that a reduction of 1160 kWh in the electricity bought corresponds to a reduction of 1430 kWh in the electricity sold. From the differences, it can be deduced that the bought price of electricity must be significantly higher than the selling price so that the savings overcome the lost revenues from sales. A 16 kWh lead acid battery reduces the electricity bought from 5870 kWh to 4770 kWh. It reduces the electricity sold from 2840 kWh to 1310 kWh. In this case a reduction of 1100 kWh in the electricity bought corresponds to a reduction of 1490 kWh in the electricity sold.
In figure 4.6 the 8 kWh Li-ion and 16 kWh lead acid battery configurations perfor- mances are compared with the ones of the current model, month by month. It can be observed that although the presence of the battery, even in winter when the solar radiation is low, part of the electricity produced is sold. This can be due to the fact that in sunny days the battery can be totally recharged, or that the electricity produced has often a non sufficient power to be fed into the battery, without con- siderably loosing efficiency in the components of the system; it is therefore fed into the grid. To answer this question a more detailed analysis of the sunniest day in January is performed, only the Li-Ion battery is considered. The results are shown
Chapter 4. PV battery system modelling
in figure 4.7.
Figure 4.6: Batteries comparison, electricity bought and sold every month
Figure 4.7: 8 kWh Li-ion battery charge during the sunniest day of January
Figure 4.7 shows that the battery is not fully charged at the end of the day, it
Chapter 4. PV battery system modelling
can be deduced that, during the shortest days of the year, only the electricity pro- duced when the solar irradiation is low, is sold. This limits the optimal battery capacity: increasing the battery size would only affect the summer months, not the winter. This should be taken into account when doing projects for summer houses in Sweden and places where the summer and winter insulation vary a lot.
4.4 Techno-economic analysis
A techno-economic analysis is necessary to understand whether it is feasible to invest on this kind of installation. The parameter used in this thesis to evaluate the feasibility of the investment is the net present value (NPV) of the investment, that is the difference between the present values of cash inflows and outflows over the lifetime of the investment. An investment is considered profitable only if its NPV is greater than 0.
N P V = −IC +
lif etime
X
year=1
Ryear− O&Myear (4.5) The investment cost (IC) consists of the cost of the components (bidirectional in- verter and battery) and the engineering, procurement and construction (EPC) costs:
IC = cb· Cb(1 + EP C%) + cI· CI(1 + EP C%) (4.6) The revenue (R) consists of the discounted savings in the electricity bill, thanks to the presence of the battery:
R = cel· (El.bought|withoutbattery− El.bought|withbattery)
(1 + i)year (4.7)
The operation and maintenance (O&M ) costs take into account the necessary ex- penses for the scheduled check of the system:
O&M = cO&M · CI
(1 + i)year (4.8)
The specific costs for the components are shown in table 4.1 [37] [13]. If not other- wise specified the installation refund for the battery is not taken into account. The costs for the inverter and the lead-acid battery given in [13] refers to 2013. For the battery, a 7.6% cost decrease per year is stated in the same paper. For the inverter, a cost decrease of 10% per year is assumed, as stated by the Deutsche Bank [38]. The costs for 2016 are then derived, and are the ones shown in the table. The current retail electricity price for the house is 1.1 SEK, which corresponds to around 0.114 e/kWh [39], no feed-in tariffs are considered. The real discount rate is considered equal to 4%, the inflation is assumed equal to 2%.
Chapter 4. PV battery system modelling
Inverter Lead-Acid Battery Li-Ion Battery Specific Cost 0.14 e/W 145 e/kWh+146 e/kW 450 e/kWh
Lifetime (years) 15 8 15
EPC 8% 8% 8%
O&M 0 22 e/kW/year 0
Table 4.1: Components characteristics for the economical analysis
The model is modified and takes into account the capacity fade losses of the battery, considered constant during the lifetime of the component. The useful capacity at the end of the life of the battery is 80%. The weather data use as input are the typ- ical meteorological year (TMY) data. The dependence of the NPV on the battery capacity is shown in figure 4.8.
Figure 4.8: NPV vs battery capacity with the current economical input
Figure 4.8 shows that with the current economical conditions, no investment is profitable. What conditions would make the investment profitable are studied.
Figure 4.9 shows how the NPV varies if the tariff scheme varies. Investing on a Lead acid battery would never be economically feasible under the considered tariff schemes, while a Li-Ion battery would have a positive NPV (around 500 ewith a 7 kWh battery) for an electricity purchase cost of 0.30e/kWh. Considering that the average electricity price for a household in Sweden is 0.19 e/kWh and the highest electricity price in Europe is 0.30 e/kWh, in Denmark [40], it is logical to think that a change in the electricity price able to make a battery profitable is unlikely to happen in the foreseeable future.
Chapter 4. PV battery system modelling
Figure 4.9: NPV vs battery capacity with different retail electricity prices
Another investigated scenario is a reduction in the price of batteries. In partic- ular the Li-Ion battery is investigated. The current electricity price for the house is considered.
Figure 4.10: NPV vs battery capacity with different battery costs
A decrease in the battery price below 150e/kWh guarantees the possibility of prof- itable investments. This means that battery prices should decrease of around 23. A Li-Ion battery price drop of around 50% is expected by the end of 2020 [41]; this means that at least before 2020 investing on a battery will be not feasible for this
