Abstract - DiVA portalkth.diva-portal.org/smash/get/diva2:1115150/FULLTEXT01.pdf · 2017. 6. 26. · av villan. En k anslighetsanalys utf ors f or att studera inverkan av batteri

Keywords: PV battery system; battery control; self-consumption; economic ana-lysis.

AbstractThe aim of this project is to find the optimal size battery for an already installed PVsystem in a family house in Southern Sweden. First, the existing system is modelledand 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 batterycapacity on the electricity fluxes between the house and the grid. The profitabilityof the project is then investigated, considering the current tariff schemes for thehouse and for the ”average” Swedish house. Eventually the possibility of applyingprice-dependent control strategies to the battery is investigated.

The primary conclusion is that a battery installation is not profitable for the studiedhouse whether the incentives provided by the Swedish government are consideredor not. Yet a subsidized installation would be profitable for a house subject to theaverage Swedish electricity price. Another conclusion is that the current hourlyvolatility in the electricity price is not high enough to make reasonable the use ofprice dependent battery control strategies. Their use would lead to better econom-ical performance, with respect to the simplest battery control strategy, in case ofincreased volatility.

Sammanfattning

Malet av det har projektet ar att hitta batteri med den basta storleken for en ex-isterande solcellssystem i en villa i Sodra Sverige. Forst, det existerande systemetmodelleras och valideras. Sedan byggs en ny modell som innehaller ett batteri. Iden har modellen antas att malet av batteriet ar att maximera sjalvkonsumptionav villan. En kanslighetsanalys utfors for att studera inverkan av batteri kapacitetpa el flussmedel mellan villan och natet. Darefter, lonsamheten av projektetet un-dersoktes, med tanke pa den befintliga tariffsystem for den utforskade villan ochden ”genomsnitt” Svenska villa. Slutligen, mojligheten att tillampa prisberoendebatterikontrollstrategier undersoks.

Den primara slutsats ar att en batteriinstallation ar inte lonsam for den studer-ade villa, med eller utan bidrag. Anda en subventionerad installation skulle varalonsam for ett hus som utsatts for genomsnitt svenska elpriset. En annan slutsatsar att den nuvarande volatilitet i elpriset ar inte tillrackligt hog for att gora lampligden anvandning av prisberoende batterikontrollstrategier. Deras anvandning skulleleda till battre ekonomisk prestanda, med avseende pa den enklaste batteristrategi,om prisvolatilet okningar.

Acknowledgement

I would like to show my gratitude to Konstatin Kostov, my supervisor in AcreoSwedish 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 workingon it.

Thanks also to Teresita Qvarnstrom and Hans Persbeck for providing me with usefuldata.

I am also deeply grateful to Nelson Sommerfeldt, my supervisor at KTH, for beingalways available for feedbacks and his very valuable comments and suggestions thatallowed me to improve my work.

I would also like to thank my friends Raphael and Roberto for their support duringthese months and the time dedicated to discuss with me part of my work.

Lastly, my deepest gratitude goes to my parents, for their continuous supportthroughout my years of studies. Without it reaching this goal would have beenmuch harder.

Contents

List of Figures i

List of Tables iii

Units iv

Abbreviations v

Subscripts vii

1 Introduction 11.1 Electricity storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Residential electricity storage . . . . . . . . . . . . . . . . . . . . . . 31.3 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Scope and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Case study 82.1 The Swedish electricity market and PV policies . . . . . . . . . . . . 8

2.1.1 PV support . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 The house . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Current system modelling 123.1 Electricity demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Electricity generation system . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.1 PV panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.2 Inverter modelling . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 PV battery system modelling 284.1 System configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 System modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2.1 AC-DC bidirectional inverter . . . . . . . . . . . . . . . . . . 30

4.2.2 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3 Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4 Techno-economic analysis . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Performances under different tariff schemes and control strategies 405.1 Tariff schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Control strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2.1 Solar control (SC) . . . . . . . . . . . . . . . . . . . . . . . . . 435.2.2 Purchase control (PC) . . . . . . . . . . . . . . . . . . . . . . 465.2.3 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. . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Electricity fluxes of the house in 2014. . . . . . . . . . . . . . . . . . 11

3.1 Year profile of electricity consumption. Resolution: 1 day. . . . . . . . 153.2 Percentage load curves for Mondays. 1 hour and 15 minutes resolution. 163.3 Scheme of the electrical system . . . . . . . . . . . . . . . . . . . . . 173.4 Main irradiance profiles. . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 Irradiance data sample. . . . . . . . . . . . . . . . . . . . . . . . . . . 203.6 Characteristic and power curves of a PV panel . . . . . . . . . . . . . 213.7 Movement of the operation point due to MPPT imprecision . . . . . 233.8 Inverter efficiency curves . . . . . . . . . . . . . . . . . . . . . . . . . 233.9 Modelled electricity fluxes 1-3 July 2014 - Resolution 15 minutes. . . 243.10 Comparison of the modelled and real systems . . . . . . . . . . . . . 253.11 Error in the estimation of the electricity produced by the PV system 253.12 Error in the estimation of the electricity produced by the PV system

- Irradiance dependence . . . . . . . . . . . . . . . . . . . . . . . . . 263.13 Error in the estimation of the electricity bought from the grid . . . . 27

4.1 DC coupled PV battery system scheme . . . . . . . . . . . . . . . . 294.2 AC coupled PV battery system scheme . . . . . . . . . . . . . . . . . 294.3 AC/DC bidirectional converter efficiency curve . . . . . . . . . . . . 314.4 Sensitivity analysis: self-consumption and self-sufficiency vs battery

capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5 Sensitivity analysis: electricity bought and sold vs battery capacity . 344.6 Batteries comparison, electricity bought and sold every month . . . . 354.7 8 kWh Li-ion battery charge during the sunniest day of January . . . 354.8 NPV vs battery capacity with the current economical input . . . . . 374.9 NPV vs battery capacity with different retail electricity prices . . . . 384.10 NPV vs battery capacity with different battery costs . . . . . . . . . 384.11 NPV vs battery capacity with different battery costs. Electricity

price: 0.19 e/kWh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

i

LIST OF FIGURES

5.1 Annual average Nord Pool wholesale electricity price . . . . . . . . . 415.2 Average grid price for a single family house in Sweden . . . . . . . . 415.3 Modelled electricity price on the 1st January 2017 . . . . . . . . . . 425.4 Solar control. Step 1-4 . . . . . . . . . . . . . . . . . . . . . . . . . . 445.5 Solar control. Step 5-7 . . . . . . . . . . . . . . . . . . . . . . . . . . 455.6 Purchase control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.7 NPV of the battery investment with TS1 applied . . . . . . . . . . . 485.8 NPV of the battery investment with TS5 applied . . . . . . . . . . . 485.9 NPV of the battery investment with TS20 applied . . . . . . . . . . 495.10 NPV of the battery investment in a house without PV panels . . . . 49

ii

List of Tables

3.1 Monthly and average daily consumption during year 2014 . . . . . . . 133.2 Months shaving factors . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3 Inverter efficiency table. Efficiency in [%] . . . . . . . . . . . . . . . 24

4.1 Components characteristics for the economical analysis . . . . . . . . 37

5.1 Retail price items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

iii

Units

A ampere°C degree centrigradece euro centse euroK kelvinkW kilowattkWh kilowatthourMW megawattMWh megawatthourSEK Swedish crownV voltW watt

iv

Abbreviations

AC Alternating currentBC Base controlc Specific costC CapacityCAES Compressed energy storageCHP Combined heat and powerDC Direct currentDOD Depth of dischargeDSM Demand side managementE EnergyEPC Engineering procurement and constructioneT Electricity taxFc−g View factor collector-groundFc−s View factor collector-sunFC Fuel cellG Irradiancegc Green certificategs Green supportHP Heat PumpI Currenti discount rateIC Investment costLi-Ion Lithium IonMPP Maximum power pointMPPT Maximum power point trackingNaS Sodium sulfurNiCd Nickel cadmiumnp Network priceNPV Net persent valueO&M Operation and maintenancePC Purchase controlPHS Pumped hydro storagePV Photovoltaic

v

Abbreviations

R Revenuerp Retailer priceSC Self-consumption or Solar controlSMES Superconduction magnetic energy storageSMHI Swedish meteorological and hydrological instituteSOC State of chargeSPC Solar-purchase controlSS Self-sufficiencyT TemperatureTMY Typical meteorological yearV Voltagewp Wholesale priceβ Tilted angleη Efficiencyρ Reflectivityθ Incidence angleθz Zenith angle

vi

Subscripts

amb Ambientb Batterybc Battery chargebd Battery dischargebn Beam normald Diffuseel Electricityh HorizontalI Inverteri Incidencein Inputmax maximummin minimumMPP Maximum power pointMPPT Maxumum power point trackingoc Open circuitOP Operationout OutputPV Panelsc Short circuitSTC Standard conditionst Tilted

vii

Chapter 1

Introduction

The environmental policy in Sweden, as in the European Union, is guided towardsan increase of use of renewable energies [1]. In 2014, more than 50% of the grossfinal energy consumption of Sweden was provided by renewable energies. Biomassand waste, followed by hydropower, were the most exploited renewable sources; theyrespectively contributed to the total renewable energy generation for around 61%and 33%. Wind energy contributed for around 6% and solar energy contribute wasstill 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 PVcapacity in Sweden nearly doubled every year, and the capacity installed in 2015 is1.5 times the one installed in 2014; the total capacity installed at the end of 2015was around 125 MW[3]. Figure 1.1 [3] shows the trend of the installed PV capacityin Sweden.

Figure 1.1: Installed PV capacity in Sweden.

The most common application for PV systems, in Sweden, is residential. They are

1

Chapter 1. Introduction

installed both as stand-alone systems or grid-connected. In the first case, the systemis provided with a battery; the produced electricity is directly used by the houseloads or stored for later use. In the second case, the system is, nowadays, usuallynot provided with a battery; the electricity is directly used by the house loads or fedinto 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 itwould not be possible to reach a high share of solar energy without using storingdevices. Besides, because of the highly fluctuating nature of this energy source, themassive presence of grid-connected PV panels can cause instabilities in electricalgrids [4]. Therefore, every grid, depending on its robustness, has a theoretic limitfor renewable energy penetration. The presence of storage in the grid increases thislimit.

Some electricity storage technologies are available, their goal is to compensate thefluctuations in the grid and/or store energy for long periods. The characteristics ofsome 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 pumpedfrom a downhill reservoir to an uphill reservoir, during this process electricityis consumed. When the electricity price is high, the water flows from the upperlevel reservoirs to the down level reservoir. The water flow activates downhillturbines 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 energydensity and high power density technology. The main drawback is the need ofspecific 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 acceleratethe cylinder, the faster the cylinder rotates the more energy is stored. Torecover the stored energy, the cylinder is slowed down; in this case the electri-cal motor works as a generator to produce electricity. The efficiency stronglydepends on the storage time, because of the high self-discharge; the overallinstantaneous efficiency can be 90%. Because of the high self-discharge thistechnology is suitable more for frequency control of the grid rather than longperiod storage. Another drawback is the high cost [5];

2


� compressed air energy storages (CAES): CAES system are high capacityenergy storages. In a CAES system, low price electricity is used to compressair and store it in a underground geologic formation. To recover the energy thecompressed air is used to run a turbine. The compressed air can also be usedas oxidant in the combustion chamber of a natural gas power plant. Energycan thus be stored for periods up to one year thanks to the low leakages. Themain drawback of this technology is the necessity of a natural cavern to storethe air [5];

� superconducting magnetic energy storages (SMES): superconductorsare materials that have zero electrical resistance when their temperature isbelow a certain critical temperature (some degrees above 0 K); the result is thatthere are no Joule losses associated to electricity flowing in these materials.Electricity can be injected and extracted very fast from SMES, this makesthem suitable for fast fluctuation compensation. To maintain the materials inthe state of superconductors refrigeration is necessary. The losses associatedwith the refrigeration systems are the only ones, so the overall efficiency of thesystem depends on the storing time of electricity; efficiencies up to 98% canbe reached. The drawbacks of these system are linked to the high price andcomplex infrastructures need in case of big capacity installations [6];

� hydrogen: an energy vector whose production is energy-intensive. Hydrogencan be produced by an electrolyzer that, consuming electricity, splits water intohydrogen and oxygen. The hydrogen is stored into a tank and then combinedwith air oxygen inside a fuel cell (FC), the recombination process produceselectricity and does not require any combustion reaction. FC are suitable forresidential sector, yet the overall efficiency of the process is 35% and the costsare 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 usetoday is for portable devices. Their application in the residential sector hasstarted to be studied, since they can be used to store the electricity generatedby installed PV panels in the houses. Because of the short lifetime, highdisposal impact and high cost, high capacity battery storages are still notcompetitive 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.

3


Installing a storage device in a residential PV system both makes the system moredispatchable, allowing the use of solar energy even during non-sunny periods, andreduces 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 theself-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 houseloads and the percentage of electricity demand that is satisfied by the PV system inthe house.

Among the electricity storages for residential sector, fuel cells end electrolizers havelower 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 makethe system more profitable. This depends on many factors:

� cost of the installation: the higher the cost of the installation, the lowerthe probability that the system is profitable;

� tariff scheme: the higher the gap between the price at which electricity issold 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 wellwith 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: acost-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 waythe system could be more profitable than if only used to maximize self-consumption[9].

Other solutions, besides storage, are available to increase electricity self-consumptionin a house with installed PV panels. The possibility of shifting the house loads inthe houses so to match the electricity generation or the fluctuations of the electricityprice during a day (usually referred as demand side management (DSM) or demandresponse), 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; thismeans that they can be operated when there is excess of electricity production.This solution still presents some limits compared to a storage installation, due tothe impossibility to shift some house loads (light, television, cooking appliances);

4


the available literature [10] shows that, on average, the percentage increase in theSC 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 importantparameter to take into account is its capacity. A larger capacity battery is capableof increasing self-consumption, however the marginal benefit must be compared tomarginal cost. Performing a techno-economical analysis is necessary to ensure thereturn on the investment and minimize its payback time.

The objective of this master thesis is to show how to size a battery for an alreadyexisting residential PV system. It also aims at verifying whether the conditions foradding a battery to a PV system in Sweden already subsist or under which condi-tions this kind of investment would become profitable. Different control algorithmsare used for the battery, depending on the electricity tariff scheme considered. Thetechno-economical performances of each investigated system are discussed.

1.4 Scope and limitations

The case study is a single family house in Vaxjo, Southern Sweden. As input forthe developed model, the weather data of this location, the monthly consumptiondata of the family living in the house and the characteristic of the PV installationalready present on the house roof are used.

The dependence of solar irradiation on the locality does not allow to consider theoutcomes of this study valid for many locations. It should also be considered thatthe 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 modelsare obtained is clearly explained; the same models can be used for any location andany loads by changing the input data.

The models developed allow to optimize the battery size for an already existingPV installation, the same approach cannot be used if the goal is to optimize thedesign of the whole PV-battery system. Eventually it is not aim of this project tocompare the installation of a battery to other possible techniques to increase theself-consumption of the house.

5


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 datato validate the model.

3. Two different types of battery (lead acid and lithium ion) are then inserted inthe 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 tariffscheme and market conditions are analyzed and the necessary conditions tomake the investment profitable are discussed.

5. Hourly tariff schemes are considered and new price optimized control strategiesare investigated to increase the profitability of the battery.

1.6 Previous work

Many researchers are now focusing on the methods to increase self-consumption inhouses 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 systemsunder 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-inelectricity. 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 thegreatest influence on the flexibility of the modelled systems. The investment costswere not considered in the study, since the comparison was between the same systemwith or without control.

Lorenzi and Silva [11] created a demand response model for two different systemsin a Portuguese single family house with low energy consumption. The first systemis characterized by PV system, electrical boiler and battery. The second system iscomposed only by the PV system and the electrical boiler. The Portuguese tariffscheme was used. The system without battery performs economically better than

6


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 economicallyconvenient.

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 trendin the battery price and feed-in tariffs, in the long term, PV-battery systems will becheaper 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 smallPV-battery systems are already profitable

Thygesen and Karlsson [14] performed a study on a single-family house in Vasteras,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 systemsshowed that, when the same level of self-consumption is reached, the system withhot water tank is more profitable.

Mulderet al. [15] conducted a study based on Belgium households. They comparedtwo 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 electricitypurchase price and battery price. The study shows that starter lead acid batterieswere 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 retailprices, in Germany. The tariff incentivizes smart-operating storages, that wouldallow decreasing the influence of the PV system on the electrical grid. Under theseconditions 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.

7

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, butdepends on demand and offer.

The wholesale electricity market is part of the Nord Pool power market, that alsoincludes Norway, Finland, Denmark, Lithuania, Latvia and Estonia. The NordPool provides day-ahead and intraday markets. Most of the trading occurs in theday-ahead market (Elspot), that provides prices changing hour by hour [17]. Thewholesale prices can vary significantly from hour to hour depending on which powerplants are available to deliver electricity. This means that the price are low whencheap 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 possiblecontracts available for the customers:

� floating price: the price changes from month to month. It is adjusted accordingto 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 theelectricity price for the consumers. Four parts contribute to the electricity price:

8

Chapter 2. Case study

electricity, grid, green certificates and taxes. The meaning of green certificates isexplained in the next subsection.

2.1.1 PV support

Different PV support policies exist in Sweden. Here the ones known by the authorof this thesis are listed [3]:

� installation rebate: since 2006 the Swedish government introduced subsidiesfor PV installations, in the form of partial refund for the installation cost. Asthe installation cost of PV panels has been decreasing every year, also the per-centage of rebate has been decreasing, in particular for residential installationsthe maximum coverage of the installation costs dropped from 60% in 2009 to20% in 2015 ;

� green certificates: since 2003 every electricity generator must have a mini-mum amount of green certificates. Green certificates are gained by producingrenewable electricity: one certificate is given per MWh of renewable electricityproduced. They can also be bought and sold in a open market [20]. Applyingfor green certificates implies additional bureaucratic and economical burdens,that not necessarily lead to significant economical advantages for residentialPV systems. As a consequence green certificates are not a relevant contributeto these installations;

� guarantees of origin: documents that state the origin of the electricity. Since2010 each electricity producer receives a guarantee per MWh of electricityproduced. The guarantees can be sold and bought in the same way as thegreen certificates. The customers can then choose their electricity source.Applying for guarantees of origin is not compulsory, but voluntary. Theircontribute to PV support is negligible;

� grid compensation: most electricity, in Sweden, is produced in the Northand consumed in the South. This implies significant transmission losses. Res-idential PV systems produce electricity in the same area where the electricityis consumed. As a consequence less transmission losses are associated to it. APV electricity producer can apply for grid compensation: the producer earnsbetween 0.2 and 0.7 ceper kWh fed into the grid.

� tax-credit: since 2015 it is possible for prosumers (electricity producers andconsumers at the same time) to apply for tax-credit. The prosumer receivesa tax reduction of 6.2 ceper kWh fed into the grid. The tax-credit is givenfor 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 measurewill be in force for a long period.

9


While the installation of PV system has been economically supported since 2006,no measures to support the increase of self-consumption of building provided withthese systems existed until November 2016. Now the installation of a storage systemcan be refunded up to 60% of the storage cost [21].

2.2 The house

A single family house in Vaxjo, Southern Sweden, is used for this case study. Thehouse is shown in figure 2.1.

Figure 2.1: House used as case study.

The house was designed by Sustainable houses in Smaland, an association of com-panies in construction business that aims at designing energy-efficient houses. Itis a net-zero energy house, meaning that the energy consumed during the wholeyear 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 inthe roof). The heating is underfloor. The lighting consists of LED with motionsensors. The washing machine and dishwasher are connected to the hot water tankthrough a heat exchanger, that preheats the cold water from the tap with the hotwater from the hot water tank, in this way the heat load due to these devices isonly 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 areinstalled 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 houseare available. They are shown in figure 2.2.

10


Figure 2.2: Electricity fluxes of the house in 2014.

Figure 2.2 shows that although, during spring and summer, the electricity producedis 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 houseprovides constant prices for buying electricity during the day and no feed-in tariffsfor the electricity fed into the grid. This means that increasing self-consumptionwould bring economic benefits for the family living in the house.

11

Chapter 3

Current system modelling

The electricity consumption, production, sale and purchase data for the house areavailable 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 temporalresolution suggested for this kind of project [22].

In this chapter it is shown how the annual electricity load curve and electricitygeneration 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 monthlyelectricity 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 theelectricity demand from year to year, and that having only one year values is not astrong limitation for the validity of the results. From the available data, the averagedaily consumption for every month is calculated. This leads to the results shown intable 3.1. The values for January are far lower than the values for December. Forprivacy 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 atthe beginning of January, so to get a very low electricity demand at the beginning ofJanuary 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 ofthe same month. Then, some modifications are done in order to have a differentvalue 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 aremodified to shave the gaps between the months (see ”Shaving procedure”);

12

Chapter 3. Current system modelling

� the daily consumption values of all the days of the months are modified, addingor subtracting a certain percentage of the average daily consumption to itsvalue, according to a specific pattern (see ”Peaking procedure”).

Month Monthly electricity Average dailyconsumption [kWh] consumption [kWh]

January 634 20February 792 28

March 693 22April 520 17May 516 17June 579 19July 550 18

August 482 16September 491 16October 628 20

November 876 29December 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) areobtained by imposing, for each month, the equality between the electricity demandat the end of the month and at the beginning of the following month. In this waytwelve 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 isthe shaving factor for the same month. As the values at the beginning of Januaryand at the end of December do not have to match, as the family is assumed not to bein the house at the beginning of January, only eleven equations are available, whilethere are twelve unknowns. One value has to be imposed arbitrarily. The value forJune is the one chosen arbitrarily: the average electricity demand in May, June andJuly is similar, the length of the days is almost constant in June, meaning that theload due to lighting is almost constant; therefore a factor equal to 0 is imposed. Thefactors obtained are shown in table 3.2. The shaving factors are applied so that inevery month there are ten days when the demand is higher than during the averageday and ten days when the demand is lower. Differently, in January half of the daysare characterized by lower demand, half by higher demand.

13


Month Shaving factor [%]January 60February 11

March 14April 12May 12June 0July 6

August 5September 5October 16

November 20December 3

Table 3.2: Months shaving factors

Peaking procedure

The factors used to avoid shaved differences between close days (here referred aspeaking 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 typesof 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 thedaily electricity demand for the day associated to ”type #”. ”Type 1” is applied todays 1,6,7. ”Type 2” is applied to day 2. ”Type 3” is applied to day 3. ”Type 4” isapplied to day 4. ”Type 5” is applied to day 5. Every type is applied cyclically everyseven days, like in the week. The cycle is applied until day 28 of each month, ”type1” is applied from day 29 to 30/31. This means that each type day, in one month, isnot necessarily associated with the same day of the week in another month. This isdone because creating such an algorithm is easier than creating one that associates

14


always the same day type to the same day of the week; as the choice of the factorsand the applied scheme is arbitrary, though the easier algorithm is less elegant andconsistent, 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 totalenergy 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, iscreated 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 typesof dwellings [23]. The load curves for family houses without electric heating areused. The resolution of the curves available in the literature is 1 hour. From thesecurves, new curves with 15 minutes resolution are generated. To generate the newcurves, 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

15


hours during the workdays. During those hours the energy consumed in onehour 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 consumedduring the hour is considered base load; then is equally spread on the fourtime intervals contained in the hour. The remaining energy is spread on theintervals randomly. This makes the algorithm capable of capturing the spikesin the demand of the house.

The load curve for Mondays is shown in figure 3.2. It is shown together with the 1hour 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, meaningthat Mondays have the same percentage curve, Tuesdays have the same percentagecurve etc. In this way the load curve for the whole year with 15 minutes resolutionis obtained.

3.2 Electricity generation system

The electricity generation system consists of 20 PV panels, connected in series. Thepanels are mounted on the house roof with 45° inclination. The nominal power ofthe whole PV system is 4.9 kW. When the solar irradiation reaches the panels, DC

16


is produced. The DC produced by the panels is then converted into AC by a solarinverter. The AC can be fed into the house, if there is demand. Otherwise it is fedinto the grid. When the electricity produced by the PV system is not enough tosatisfy the internal load of the house, the extra electricity that is needed comes fromthe 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 theincident irradiance, Gi and panel temperature TPV [24].

Irradiance

The 2014 values of irradiance for Vaxjo are available on the Swedish meteorologicaland hydrological institute (SMHI) website [25]. The available values are the hourlydata for global horizontal irradiance (Gh); the necessary inputs for the PV panelsmodelling are values of global irradiance on a 45° tilted surface, with 15 minutesresolution. 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 minutesresolution are originated.

The irradiance on a tilted surface is calculated as follows [26]:

Gt = Gbncosθ +GdFc−s + ρGhFc−g (3.2)

17


Gh is given. The beam normal irradiance (Gbn) is calculated by using the DIRINTmodel, it allows to calculate Gbn as a function of Gh, zenith angle θz, day of the yearand atmospheric pressure. A Matlab function, given by Sandia National Laborato-ries, was used to perform the model [27]. The diffuse horizontal irradiance (Gd) iscalculated 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−sand 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 valuesof irradiance are compared with the values of the clear sky irradiance, that meansthe 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 ASHRAEmodel 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 is90% 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 theDIRINT model;

3. sunny/cloudy (SC) or cloudy/sunny (CS): the hour is considered SC/CSif 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 isconsidered SCS if the hours before and after are both VS. Similarly forthe CSC case;

5. variable (VV): the hour is considered VV if none of the previous schemeis applicable.

� different algorithms are applied according to the type of hour, it must beconsidered that the profile always follows the clear sky profile, if not otherwisespecified:

1. during the hour, the irradiance has the same profile as the clear skyirradiance;

18


2. the irradiance is uniform during the hour. It does not follow the clearsky profile;

3. the first two intervals of the hour are considered sunny/cloudy, the lasttwo intervals of the hour are considered cloudy/sunny. The irradianceof the sunny part of the day is considered equal to 90% [29] of the clearsky irradiance. The irradiance of the cloudy part of the day is calculatedso that the average irradiance during the whole hour is correct. If thisalgorithm leads to values of irradiance lower than the clear sky diffuseradiation, then the following algorithm is used: the irradiance of thecloudy part of the hour is considered equal to the diffuse radiation andis not linked to the clear sky profile, the irradiance of the sunny part ofthe hour is calculated so that the average irradiance is correct;

4. the first and last intervals are considered sunny/cloudy, the second andthird 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. Fourrandom values, so that their sum is 100, are generated, one per interval ofthe hour. The global radiation during the hour is the sum of the diffuseradiation plus a certain percentage (given by the random number) of thedifference between the global and the diffuse radiations. The process isiterated 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 introducedby this model on the 1 hour averaged values is shown. You can notice that atthe sunrise and at the sunset the 1 hour average and then the 15 minutes averageirradiances can be higher than the clear sky irradiance. It means that the model isnot accurate when the sun is low on the horizon.

Panel temperature

The panels temperature was not measured. The panel temperature is functionof irradiance, air temperature and wind velocity, yet for semplicity an empiricalcorrelation with the ambient temperature and the solar irradiance only is used [30]:

TPV = Tamb + k ·Gi (3.6)

The constant k depends on the mounting type of PV panels. For panels installedon 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.

19


Figure 3.4: Main irradiance profiles.

Figure 3.5: Irradiance data sample.

20


Panel operation

For every possible combination of Gi and TPV , the panel can produce electricity withdifferent values of voltage and current. The curves representing IPV as function ofVPV are called characteristic curves. An example of possible characteristic curve isshown 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 itscharacteristic curve at which the panel has to work in order to reach the maximumefficiency. This point is called maximum power point (MPP). To produce the max-imum possible power, given the environment conditions, the panels should work attheir MPP. The panels work on a point that is the MPP, or close to it thanks to theMPP tracking (MPPT) algorithm, present in solar converters.

In the developed model, the open circuit voltage (Voc) of the panel is considereddependent only on TPV , while the short circuit current (Isc) is considered dependentonly on Gi.The dependence of Isc on TPV and the dependence of Voc on Gi are neglected in thismodel.

These are the correlations used [31]:

Isc = IscNOCT· Gi

GSTC

(3.7)

Voc = VocSTC·(

1 + (TPV − TSTC) · kv100

)(3.8)

21


The maximum power point current (IMPP ) and maximum power point voltage(VMPP ) are then considered proportional to the Isc and Voc:

IMPP = IMPPSTC· IscIscSTC

(3.9)

VMPP = VMPPSTC· VocVocSTC

(3.10)

In the model of the PV panel it is supposed that the MPPT efficiency is 100%, thenthe output of every single PV panel is characterized by IMPP and VMPP .

Since the system is composed by 20 PV panels in series, the total generated voltageis 20VMPP .

IMPP and 20VMPP are the input values for the inverter, in the case when the MPPTefficiency is 100%.

3.2.2 Inverter modelling

The inverter keeps the PV panels working at their MPP and convert the DC intoAC. The inverter does not follow the MPP of the panels with 100% precision. Totake into account the energy losses introduced by this error, the variable ηMPPT isintroduced; it is assumed ηMPPT = 0.98 [32]. It is assumed that the imprecision ofthe inverter in tracking the MPP leads to the underestimation of the VMPP , so thepanels actually work on a point of their characteristic curve that is slightly on theleft 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 observedthat while VOP does not coincide with VMPP , IOP is almost the same as IMPP . Theinputs for the inverter are then: Iinv = IMPP , Vinv = ηMPPT · 20VMPP .The inverterefficiency depends on the power and voltage of the electricity that enters in theinverter. The inverter datasheet gives the efficiency curves as function of outputpower and input voltage for a bigger model than the one installed in the house. It isassumed that the same curves can be used for the installed model. The curves areshown in figure 3.8. From the datasheet curves, a bidimensional table, reporting theefficiency 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 throughbilinear interpolation of the values in the table. The output power of the PV systemis then calculated as follows:

P = ηinv · ηMPPT · 20PMPP (3.11)

22


Figure 3.7: Movement of the operation point due to MPPT imprecision

Figure 3.8: Inverter efficiency curves

23


V[V]\P[W] 115 262 518 772 1026 1537 2049 3077 4111 5100440 87 95.7 96.6 97 97.2 97.2 97.1 97 96.8 96.5580 87 96.2 97.1 98 98.1 98.3 98.1 98 97.8 97.2800 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 electricityconsumption, generation, sale and purchase curves, with a 15 minutes resolution. Itis not practical to show these curves for the whole year. The curves are shown forthe 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 wasobserved in chapter 2: why the amount of electricity bought in summer is aroundhalf of the total electricity consumed in the same season, although the electricityproduced is more than the electricity consumed. You can see that the time whenmost 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

24


to compare the results of the modelled system with the real data. The results of themodel 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 errorsare shown in figure 3.11.

Figure 3.11: Error in the estimation of the electricity produced by the PV system

25


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 ofthe PV model for low values of irradiance; in figure 3.12 it is possible to seethat the highest values of imprecision are actually related to the lowest valuesof irradiance: for low values of irradiance the lower the irradiance, the higherthe relative error. For higher values of irradiance the relative error does notshow any dependence on the irradiance. The relative error on the productionover 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, itis possible that the behaviour of the family in this month was far from theaverage behaviour. Except for June, during spring and summer the modelunderestimates the matching between the production and the consumption ofelectricity, it could then be modified accordingly. Yet, since it is not possibleto know the real behaviour of the family and the overall error of the model isacceptable (0.3%), the model based on the average Swedish behaviour is theone used also for the remainder of the study.

26


Figure 3.13: Error in the estimation of the electricity bought from the grid

27

Chapter 4

PV battery system modelling

After obtaining the PV system model, and after verifying its reliability, the originalmodel can be modified, implementing the presence of a battery. In this chapter thepossible configurations for the new system are examined. The details of the newsystem and the way it is modelled are explained. The results obtained are finallyshown 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 area more mature technology than the bidirectional AC/DC converters;

– higher storing efficiency: the electricity is stored directly after beingproduced; there are less conversion steps, and thus losses, than in the ACcoupling systems.

This system is represented in figure 4.1;

� AC-coupled systems: the battery is connected, through a bidirectionalAC/DC converter, to the output of the grid inverter.

Advantages:

– easier to apply to an already existing PV system: there are notimportant modifications to the system, the battery can be considered anadded device in the house;

28

Chapter 4. PV battery system modelling

– possibility to store the electricity buying it from the grid: thesolar inverter only operates in one direction, putting the battery beforeit 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

29


For the analysed case, as the PV system is already installed in the house, addinga battery using an AC-coupled configuration is easier than using a DC-coupledconfiguration. The AC-coupled system is then investigated. This configuration alsoallows 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 exactlythe 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 isdifferent. In this chapter a system where the battery installed is used to maximizeself-consumption is studied. When electricity is produced, it is first fed into thehouse, to satisfy the electricity demand, then it is used to charge the battery andlast it is fed into the grid. When the electricity required by the house is bigger thanthe 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 thebattery.

4.2.1 AC-DC bidirectional inverter

The AC/DC bidirectional inverter has the task of converting AC into DC, that canbe fed into the battery, when the battery operates in charging mode. It converts DCinto AC when the battery operates in discharging mode. The AC used in chargingmode 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 maximizeself-consumption, the AC is always provided by the solar converter.

The efficiency curve for this component has been taken from the literature [35]. Thesame 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. Sincethe 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/DCbidirectional inverter considered is 5 kW. The values shown in figure 4.3 are thenscaled 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 thebattery, do not work in this conditions.

30


Figure 4.3: AC/DC bidirectional converter efficiency curve

4.2.2 Battery

Different battery technologies, their efficiencies (η), and lifetimes with respect todepth of discharge (DOD) are listed below:

� Lead acid [36]: η = 72-78%, 1000-2000 cycles at 70% DOD, self-dischargeis a significant problem, contains toxic heavy metals, is the most mature andcheapest 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 Powerwall1 [37]:

� ηbc = ηbd=0.96;

31


� SOCmin=0 %;

� SOCMax=100%.

The values used for the Lead Acid battery are the following [13]:

� ηbc = ηbd=0.9;

� SOCmin=30%;

� SOCMax=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 underits minimum SOC. The energy fed into the battery is then calculated as:

Ein = ηAC/DC · ηbc · (EPVnet − Eload) (4.1)

The energy released by the battery when required by the load is calculated as:

Eout =Eload − EPVnet

ηDC/AC · ηbd(4.2)

Equation 4.1 is only valid when the input energy in the battery does not cause thebattery SOC to go over the maximum SOC. In this latter case part of the energyproduced by the PV panels is fed into the grid. Equation 4.2 is only valid when theoutput energy from the battery does not cause the battery SOC to go under theminimum SOC. In this latter case part of the energy demanded by the house loadsis fed by the grid.

4.3 Performances

Once the PV battery system is modelled, its behaviour, varying with the batterysize, can be studied. The studied parameters are the total electricity sold and boughtduring the year, the self-sufficiency and the self-consumption of the house.

The self-sufficiency indicates the percentage of electricity load satisfied by the PVsystem:

SS =35040∑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∑i=1

EPV,i − Esold,i

EPV,i

(4.4)

32


Figures 4.4 shows the trend of self-consumption and self-sufficiency with the batterysize.

Figure 4.4: Sensitivity analysis: self-consumption and self-sufficiency vs batterycapacity

The values of self-consumption are higher for the Lead acid batteries than for theLI-Ion batteries, when the same net battery size is considered (the different DODshould be taken into account, it means that a 30 kWh lead acid battery should becompared with a 15 kWh Li-ion battery). This is due to the lower efficiency of thelead acid batteries: more electricity is required to recharge the battery, thereforeless electricity is fed into the grid. Higher values of self-sufficiency are reached withthe 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-sufficiencyfrom around 25% to slightly more than 40%. Adding a 16 kWh lead acid batteryto the existing system increases the self-sufficiency from around 25% to slightly lessthan 40%. For battery capacities of respectively 8 kWh and 16 kWh the Li-Ion andLead Acid self-sufficiency curves present a knee, it means that the marginal benefitsof increasing battery sizes become significantly lower.

Investigating how the different DOD and efficiencies influence the optimal size ofthe battery it is observed that both a smaller operating range of SOC and lower

33


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 effectof 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, asfunction of the battery size. An 8 kWh Li-Ion battery reduces the electricity boughtfrom 5870 kWh to 4710 kWh. It reduces the electricity sold from 2840 kWh to 1410kWh. It means that a reduction of 1160 kWh in the electricity bought correspondsto a reduction of 1430 kWh in the electricity sold. From the differences, it can bededuced that the bought price of electricity must be significantly higher than theselling price so that the savings overcome the lost revenues from sales. A 16 kWhlead acid battery reduces the electricity bought from 5870 kWh to 4770 kWh. Itreduces the electricity sold from 2840 kWh to 1310 kWh. In this case a reduction of1100 kWh in the electricity bought corresponds to a reduction of 1490 kWh in theelectricity 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 canbe observed that although the presence of the battery, even in winter when the solarradiation is low, part of the electricity produced is sold. This can be due to thefact that in sunny days the battery can be totally recharged, or that the electricityproduced 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 intothe grid. To answer this question a more detailed analysis of the sunniest day inJanuary is performed, only the Li-Ion battery is considered. The results are shown

34


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

35


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 batterycapacity: increasing the battery size would only affect the summer months, not thewinter. This should be taken into account when doing projects for summer housesin 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 toinvest on this kind of installation. The parameter used in this thesis to evaluate thefeasibility of the investment is the net present value (NPV) of the investment, thatis the difference between the present values of cash inflows and outflows over thelifetime of the investment. An investment is considered profitable only if its NPV isgreater than 0.

NPV = −IC +

lifetime∑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 + EPC%) + cI · CI(1 + EPC%) (4.6)

The revenue (R) consists of the discounted savings in the electricity bill, thanks tothe 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. Thecosts for the inverter and the lead-acid battery given in [13] refers to 2013. For thebattery, a 7.6% cost decrease per year is stated in the same paper. For the inverter, acost decrease of 10% per year is assumed, as stated by the Deutsche Bank [38]. Thecosts for 2016 are then derived, and are the ones shown in the table. The currentretail electricity price for the house is 1.1 SEK, which corresponds to around 0.114e/kWh [39], no feed-in tariffs are considered. The real discount rate is consideredequal to 4%, the inflation is assumed equal to 2%.

36


Inverter Lead-Acid Battery Li-Ion BatterySpecific Cost 0.14 e/W 145 e/kWh+146 e/kW 450 e/kWh

Lifetime (years) 15 8 15EPC 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 atthe 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 batterycapacity 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 isprofitable. What conditions would make the investment profitable are studied.

Figure 4.9 shows how the NPV varies if the tariff scheme varies. Investing on aLead acid battery would never be economically feasible under the considered tariffschemes, while a Li-Ion battery would have a positive NPV (around 500 ewith a 7kWh battery) for an electricity purchase cost of 0.30 e/kWh. Considering that theaverage electricity price for a household in Sweden is 0.19 e/kWh and the highestelectricity price in Europe is 0.30 e/kWh, in Denmark [40], it is logical to thinkthat a change in the electricity price able to make a battery profitable is unlikely tohappen in the foreseeable future.

37


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 isconsidered.

Figure 4.10: NPV vs battery capacity with different battery costs

A decrease in the battery price below 150 e/kWh guarantees the possibility of prof-itable investments. This means that battery prices should decrease of around 2

3. A

Li-Ion battery price drop of around 50% is expected by the end of 2020 [41]; thismeans that at least before 2020 investing on a battery will be not feasible for this

38


particular house.

Another investigation is done considering the average electricity price in Sweden:0.19 e/kWh, and different battery costs. The results are shown in figure 4.11.

Figure 4.11: NPV vs battery capacity with different battery costs. Electricity price:0.19 e/kWh

In this case, if the battery price drops to 250 e/kWh installing a battery starts to befeasible. This scenario suggests that if electricity prices rise and battery prices fall,in the near future batteries could be economically interesting in Sweden even with-out installation rebate; taking into account the refund on the battery installation,this investment is already profitable.

39

Chapter 5

Performances under different tariffschemes and control strategies

So far the real retail electricity price has been considered constant during all the yearsof the simulations, the nominal price varied only because of inflation. In reality alsothe real electricity price varies, some contracts provide electricity prices changingfrom year to year or from month to month; some contracts can also provide priceschanging from hour to hour. Some battery control strategies can take advantage ofsub-daily tariff schemes. These possibilities are explored in this chapter.

5.1 Tariff schemes

The retail electricity price is composed by many cost items, their values can changefrom contract to contract. The values assumed for year 2014 are reported in table5.1 [17], [42], [43].

Cost item Value Growth rateWholesale price (wp) See [17] See [17]Green support (gs) 0.3 ce/kWh 0%/yearNetwork price (np) 3.2 ce/kWh See figure 5.2Retailer profit (rp) 0.5 ce/kWh 0%/yearElectricity tax (eT) 3 ce/kWh 1%/year

VAT 25 % 0%/yearGreen certificates (gc) 1.7 ce/kWh 0%/year

Table 5.1: Retail price items

The value of wholesale price of electricity changes from hour to hour in the dayahead Nord Pool electricity market and the average annual wholesale price can varystrongly from year to year [17]. In particular in Sweden, because of the high shareof hydropower and the use of electrical heaters and heat pumps for heating, it is

40

Chapter 5. Performances under different tariff schemes and controlstrategies

highly influenced by the weather conditions [18]. Figure 5.1 shows how the annualaverage real (prices referred to 2015) wholesale electricity price varied from 2001 to2015 [17].

Figure 5.1: Annual average Nord Pool wholesale electricity price

The growth rate of the network price already takes into account inflation; the nomi-nal grid price for a single family house in Sweden increases almost linearly with time[43]. Its trend from 2001 to 2015 is shown in figure 5.2.

Figure 5.2: Average grid price for a single family house in Sweden

41


From these information three tariff schemes with prices varying hour by hour arecreated and used with the already mentioned control strategy for the battery andwith the new ones that are described later on in this chapter. The proposed tar-iff schemes provide prices changing hour by hour for 15 years, from year 2017 toyear 2031. The real wholesale prices during these years are considered the same asfrom year 2001 to 2015. The difference among the tariff schemes is the volatilityin the wholesale electricity prices, meaning the relative difference between the aver-age wholesale price during the day and the wholesale price during each hour. Thevolatility v has a different value every hour of the day and is here defined as:

vi =wpi,av − wpi

wpi,av(5.1)

where wpi is the wholesale price for the hour ”i” and wpi,av is the average wholesaleprice during the day.

The nominal electricity price p for the hour ”i” of the year ”y” is then calculated inthe following way:

pi,y = (wpi,av,y − vi,ywpi,av,y + gs+ rp+ eTy) · V AT · πy + gc · πy + npy (5.2)

Three different tariff schemes are then derived: TS1 considers the real volatility inthe Nord pool market, TS5 takes into account a volatility that is 5 times the realone, analogously TS20. The nominal electricity price for the the 1st of January 2017is shown in figure 5.3.

Figure 5.3: Modelled electricity price on the 1st January 2017

42


5.2 Control strategies

Different control strategies from the one seen before (base control) can be appliedto the battery. The new types of control are applicable when the electricity pricechanges from hour to hour, or anyway the price of electricity is not constant duringa day. To apply these controls it is necessary to know the electricity loads, theelectricity price and the house electricity generation 24 hours in advance.

5.2.1 Solar control (SC)

This control provides a different way to charge and discharge the battery with therespect to the base control. It does not provide buying electricity from the grid tostore it into the battery, the only electricity stored is the one produced by the PVpanels. Applying this control leads to increase the electricity self-consumption whenthe electricity price is high and decrease it when the electricity price is low.

The control consists of the following steps (for a better understanding also see theflow charts in figures 5.4 and 5.5):

1. the base control is simulated for 1 day, the information about the SOC of thebattery, the use of the inverter, the direct use of PV produced electricity andthe electricity bought in every time interval are calculated and saved;

2. for every time interval ”i” it is checked if:

� during ”i” energy from the battery is used;

� among the following ”n” hours there are time intervals when the priceis higher than during the interval ”i” and if during those time intervalselectricity is bought from the grid; these intervals are referred as ”j”. ”n”is the minimum between the number of hours before the electricity pricebecomes lower then the price during ”i” and 24 (number of hours in oneday);

3. if both the conditions of step 2 are satisfied, the battery energy previouslyused during ”i” is saved to be used during the intervals ”j”, then used duringthe interval ”i” if still available.

4. step 2 and 3 are repeated again, with the difference that ”n” is always 24;

5. for every time interval ”i” it is checked if:

� during ”i”, energy from the PV panels is used;

� among the following ”n” hours there are time intervals ”j” during which itwould be cheaper to use electricity produced by the PV panels and stored

43


during the time interval ”i”, rather then use the energy produced during”i” in the interval ”i” and buy the electricity during the time interval ”j”.”n” is the minimum between the number of hours before the electricityprice becomes lower then the price during ”i” and 24;

6. if both the conditions of step 5 are satisfied, the PV electricity is first storedin the battery for later us during intervals ”j”, then used during ”i” if stillavailable.

7. step 5 and 6 are repeated again, with the difference that ”n” is always 24.

Figure 5.4: Solar control. Step 1-4

44


Figure 5.4 shows steps 1-4 of the control: the flow chart represents steps 1-3. Thesame flow chart, without he parts circled in red, is step 4.

Figure 5.5 shows steps 5-7 of the control:the whole flow chart represents steps 5-6.The same flow chart, without the part circled in red, is step 7.

Figure 5.5: Solar control. Step 5-7

During all the steps it is checked that the inverter is never overused, although itshould never happen because designed to be able to store all the PV panels produc-tion, and that the battery is never overcharged or under discharged. For a betterunderstanding ot the steps 4 and 7 read the explanation given in the followingparagraph for step 3 of the purchase control.

45


5.2.2 Purchase control (PC)

This control strategy applies to a house with no PV panels, it provides buying andstoring electricity from the grid for later use in the house if doing so is cheaper thandirectly buying electricity when the loads require it. The strategy consists of thefollowing steps (for a better understanding also see the flow chart in figure 5.6):

1. for every time interval ”i” it is checked if among the following ”n” hours thereare time intervals ”j” during which it would be cheaper to use electricity boughtand stored during the time interval ”i” rather then buying the electricity di-rectly during the time interval ”j”.”n” is the minimum between the number ofhours before the electricity price becomes lower then the price during ”i” and24;

2. if it is the case, during ”i” electricity is bought and stored for later use duringthe hours ”j”.

3. point 1 and 2 are repeated with the difference that now ”n” is always 24.

Figure 5.6 shows steps 1-3 of the control: the flow chart represents steps 1-2. Thesame flow chart, without he parts circled in red, is step 3. Point 1 and 2 guaranteethat electricity is first bought and stored at the minimum available price during the24 hours. It is possible that, because of the inverter limits, not all the electricityneeded during a hour with high electricity price can be bought during the previoushour with the minimum price; point 3 guarantees that, if still cheaper than directlybuying and using, electricity is bought and stored for later use even at a higher pricethan the minimum. It is always checked that the inverter is not overused and thebattery is not overcharged or under discharged.

Some considerations on the lifetime of the battery must be done when this typeof control is used. The battery lifetime depends on the cycling. On the solar bat-tery catalogues the lifetime is usually given in term of years, as regular daily chargingand discharging is assumed and from the number of cycles the number of years isderived. When the PC is applied, the battery cycling can be strongly irregular, thenit must be checked that the number of cycles really performed by the battery is notbigger then the number of cycles the battery can perform. The number of cyclesalready performed is calculated as [12]:

nc =Ebd

Cb

(5.3)

It is assumed that the lifetime given in the battery data sheet, 15 years, correspondsto 6000 cycles [44].

46


Figure 5.6: Purchase control

5.2.3 Solar + purchase control (SPC)

This control is a combination of the previous two controls. The solar control isapplied first, then the output SOC, inverter use and electricity purchase are used asinput for the purchase control.

5.3 Results

The system behaviour is simulated with the four control strategies described in thispaper (BC, SC, PC and SPC) and the tariff schemes TS1, TS5 and TS20. PC isapplied to a case when there is no solar or any other electricity generation in thehouse, while the other controls take into account the solar generation of the house

47


during the TMY. Figures 5.7, 5.8, 5.9 show the profitability of the battery systemwith the control strategies BC, SC, SPC, respectively for the tariff schemes TS1,TS5 and TS20. Two different battery specific costs are considered: 450 e/kWh,that is the price considered so far for the Li-Ion battery, and 180 e/kWh that is thecost of the battery if 60% of the investment is refunded.

Figure 5.7: NPV of the battery investment with TS1 applied

Figure 5.7 shows that, with the current value of wholesale price volatility, installinga battery is not feasible even considering the refund, besides the performance of thebattery does not change depending on the control applied.


Figure 5.8 shows that with a volatility 5 times bigger than the current one the

48


application of SC or SPC has an impact on the performance of the battery, if theSPC is applied to the battery and the installation cost is 60% refunded, the instal-lation would be profitable .


Figure 5.9 shows that if the battery expense is refunded and the volatility is 20times bigger than the actual one, buying a battery can be profitable whatever thecontrol strategy is; although applying a solar-purchase control strategy would leadto higher revenues.

The possibility of installing a battery in a house without PV system is also ana-lyzed, the only applicable control strategy is PC. The profitability of the system isshown in figure 5.10.

Figure 5.10: NPV of the battery investment in a house without PV panels

49


The installation of a battery in a house without local electricity generation is notprofitable with the current volatility in the price, yet it would be if the volatilitywere 20 times higher; the possibility to increase the volatility should be consideredby the electricity authority if you want to use residential storage systems as solutionto increase the renewable energies share in the electricity production.

50

Chapter 6

Conclusions

Though the installed PV capacity in Sweden is still negligible, the investments init are increasing. The decision of the Swedish government to finance batteries in-vestments can be interpreted as the forecast of a future where distributed electricityproduction could strongly influence the electricity grid.

The results of this study show that a 10 kWh battery installation can increasethe PV-produced electricity self-consumption of a house from 40% to 75%. Yet itis impossible to have a unique conclusion stating whether installing a battery in ahouse provided with PV panels is profitable or not in Southern Sweden. Three mainconclusions can be deduced from the analysis performed:

� assuming that the electricity price varies only because of inflation, installinga battery in the house used for the analysis is not profitable at the moment,even if the battery expense refund is considered;

� assuming that the electricity price varies only because of inflation, installing abattery in a house that has the same characteristics as the one analyzed in thisthesis, but for which the electricity price is 0.19 e/kWh or higher, is alreadyprofitable if the battery expense refund is considered;

� the current volatility in the electricity price is not enough to make the appli-cation of tariff schemes depending control strategies evidently more profitablethan the application of the simple base control commonly used for solar bat-teries.

The possibility to have general results is limited by the high variability in the elec-tricity prices from contract to contract; besides there is a variable that is not takeninto account in this study: the possibility to have revenues from electricity sale.

It should also be considered that the evolution of the prices in the future yearsis not certain, as strongly dependent on the Swedish energy policy and climate con-ditions; performing an analysis considering different scenarios would allow to give

51

Chapter 6. Conclusions

more general results.

Another limitation of the study is that the only considered way to increase thevolatility in the customer electricity price is to increase the volatility in the whole-sale electricity price; it does not represent the only possible way, other ways, suchas not constant electricity taxes, could be investigated.

This study was also limited by keeping a constant PV surface. The optimizationfrom scratch of a PV-battery system can lead to different results than the optimiza-tion of a battery installation for an already existing PV system.

52

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56

Appendix I: solar angles

Solar declination in [°]:

δ = 23.45 · sin(

360284− n

365

)n: day of the year.

Equation of time:

ET = 229.2(0.000075+0.001868cos(B)−0.032077sin(B)−0.014615cos(2B)−0.04089sin(2B))

B = (n− 1)360

365Noon time:

hn = 12 +l − lref

15− ET (+1)

l: longitude.lref= reference longitude.

Hour angle in [°]:ω = (h− hn) · 15

h: standard time

Zenith angle:cos(θz) = cos(Φ)cos(δ)cos(ω) + sin(Φ)sin(δ)

Φ: latitude.

Solar azimuth:

sin(γs) =cos(δ)sin(ω)

sin(θz)

Incident angle on a tilted surface:

cos(θ) = cos(θz)cos(β) + sin(θz)sin(β)cos(γs − γ)

β: surface inclination.γ: surface azimuth.

viii

Appendix II: panel characteristics

ix

Appendix III: invertercharacteristics

x

Documents

Abstract - DiVA portalkth.diva-portal.org/smash/get/diva2:1115150/FULLTEXT01.pdf · 2017. 6. 26. · av villan. En k anslighetsanalys utf ors f or att studera inverkan av batteri