Sizing and modeling a microgrid containing renewable energy production, energy storage, electrical vehicles and other green technologies

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DEGREE PROJECT IN ELECTRICAL ENGINEERING TECHNOLOGY, SECOND CYCLE, 30 CREDITS

STOCKHOLM, SWEDEN 2020

Sizing and modeling a microgrid containing

renewable energy production, energy storage, electrical

vehicles and other green technologies

YOSEF GEBRESILASSIE

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Sizing and modeling a microgrid containing renewable energy

production, energy storage, electrical vehicles and other green technologies

Author

Yosef Gebresilassie

Master in Electrical Engineering KTH Royal Institute of Technology

Examiner

Hans Edin

KTH Royal Institute of Technology

Supervisor

Daniel Månsson

KTH Royal Institute of Technology

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Abstract

Optimal design of a microgrid containing renewable energy sources in a residential sector is important to have a technical and economical feasible investment. In this project a microgrid (MG) for a house cooperative in Hudiksvall, Sweden has been studied. The aim of this study is to estimate how the electric vehicles (EVs) will aid the MG assuming different availabilities.

Furthermore, this study aims to investigate optimal sizes of photovoltaic (PV) power and solar collectors for the households as well as possible energy storage capacity to increase the self-consumption.

To study the role of the EVs in aiding the MG a simulation was carried in MATLAB/SIMULINK. To estimate the optimal sizes of the PV cells a life cycle cost assessment (LCCA) was carried out. The optimal output from the SC was estimated by using the f -chart method.

The results from this study points out that a higher EV capacity will be required when the EVs are available for longer hours of the day, which is mainly due to the large share of PV power produced and the limited range of charging/discharging capacity of the EV battery. The LCCA shows that a high PV capacity will lead to a low net present value and a longer payback period. The sensitivity analysis which was carried out indicates that the PV system investment is mostly sensitive to the investment cost. The f -chart method gives the recommended values for SC output and an estimation of the thermal energy storage capacity.

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Sammanfattning

Ett mikronät som innehåller olika förnyelsebara energikällor behöver designas optimalt för kunna ha en både ekonomisk och teknisk genomförbar investering.

I detta projekt studerades ett mikronät för en bostadsförening i Hudiksvall.

Syftet med detta projekt var att studera hur elbilar kommer att kunna försörja nätet vid olika tillgänglighetstider hos bilarna.Utöver det syftade det här projektet också på att uppskatta den optimala effekten på solceller och solfångare för bostadsföreningen samt möjligheterna för energilagring för att utöka konsumtionen av närproducerad el och värme.

En simulering i MATLAB/SIMULINK utfördes för att studera elbilarnas roll i att försörja mikronätet. För att få en bild av den optimala effekten på solcellerna utfördes en livscykelkostandsanalys. Den optimala effekten för solfångarna har beräknats genom f -chart metoden.

Resultaten från denna studie visar att högre batterikapacitet på elbilar kommer att krävas när elbilarna är kopplade till mikronätet för längre perioder. Detta beror på den höga effektproduktionen från solcellerna samt den begränsade nivån för laddning/urladdning av elbilarnas batteri. Livcykelkostnadsanalysen gav ett lägre nuvärde samt längre återbetalningsperioder då en högre kapacitet på solcellerna installerades. Känslighetsanalysen som utfördes visar att nuvärdet av investeringen är mest känslig för investeringskostnaden. Med f -chart metoden kunde slutsatser gällande optimal solfångare och termisk energilagring dras.

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Acknowledgements

The thesis has been conducted in collaboration with BRF Stenberg and the department of electrical engineering at KTH Royal Institute of Technology.

I would like thank my supervisor at KTH, Daniel Månsson for his continuous support and input. I would like also to thank Klas Boman for his input during the thesis and for being always available for discussion and questions. I would like also to thank Mats Andersson from Energi Banken for his support and input about the pilot project. I would like also to thank my examiner at KTH, Hans Edin.

A special thanks to Yang Jiao for the help and guidance during the thesis and for being available for questions and discussions.

A big thanks to my family for their continuous support, love and encouragement, with out you this journey would have been impossible guys !

I would like also to thank my friends for their continuous love and kindness, which made this journey possible. I am also grateful to my mates at KTH, ”Harambe”

for the shared love and laughter throughout the years.

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1 Introduction

Clean, affordable, reliable and sustainable energy is one of the sustainable development goals set by the United Nations [25]. Several countries around the world including Sweden have set future goals to increase the share of renewable energy sources (RESs). In Sweden the target is to reach 100% renewable electricity by 2040 [12] [23].

In the last decade the share of renewable energy have been growing in Sweden in terms of wind power and solar power [10]. The photovoltaic (PV) technology have shown a strong growth especially in the residential sector, which can depend on the governmental direct subsidy systems to develop the PV power market in Sweden [18]. The trend of distributed energy generation especially located at the end user side can lead to more efficient and environmental friendly alternative to conventional energy systems [2].

One of the alternatives to the conventional centralized energy generation is microgrids (MGs). Unlike centralized energy generation where the generation is located at one end and consumption at the other end, MGs contains decentralized energy systems which are located near to the end user. A microgrid system can contain several subsystems including, energy generation units, energy storage systems (ESS) and energy management systems. MGs can be stand-alone systems where the MG system is not connected to the main grid, those systems are applicable for remote areas. The majority of MGs are grid-tied where prosumers can produce and consume electricity [40].

One of the challenges with the emerging RESs is their intermittent behaviour.

This nature of RESs introduces a new uncertainty for power utilities to forecast the output energy from those sources. The forecast is vital to plan future power generation, due to the limited inertia in the power system there must be a balance between the generated and consumed electricity [26]. Several technologies in form of energy storage are the main expectations to deal with this problem. Energy storage in form of batteries specifically lithium ion batteries have shown continuous development in the area. Nevertheless, the large price of batteries is the main obstacle to fully adapt the technology. Mass production

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and enhancement of the technology can have part in resolving the issue [4].

1.1 Background

In the transition of fossil energy to green energy sources, ESS of different types play an important role to optimize the use of intermittent renewable energy sources such as wind- or solar power as well as to improve the stability and reliability of the power systems.

In the future a microgrid can contain these different green technologies but also electrical vehicles (EVs), heat pumps and systems for the capture of waste heat and more. An energy hub (EH) is the collection of subsystems in which the energy from the above-mentioned sources can be exchanged to fully utilize these energy sources and carriers. Examples would be to store the excess power produced from PV cells as heat, utilize the battery of an EV to supplement PV cells for the load demand, turn excess energy from heat pumps and solar collectors into electricity etc. The final end-goal would be an optimized self-sufficient microgrid with a minimized carbon footprint even capable of creating revenue by selling power and services to the grid [24].

In this project a small microgrid containing solar cells and solar collectors, electrical vehicles, thermal energy storage (accumulator tank) and heat pumps, as well as a number of dwellings will be analyzed in the preparation for its construction.

1.2 Purpose

For a microgrid, as described above, there are several design variables that will affect the long-term utilization of it. The solar cell output, ESS capacity, EV utilization cycle, heat and electricity usage etc. are all important for creating synergy and to form a microgrid that is technical, economical and environmentally optimal. In the project announced here a small microgrid is in the process of being built at housing cooperative (BRF) Stenberg in Hudiksvall, Sweden and investigations into the optimal design choices to be made here is of interest.

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1.3 Goal

The main goal of this thesis is to investigate the following questions, assuming that the microgrid will have different load (heat and electricity) demands:

- What are the required capacities for the EVs battery and the thermal energy storage ?

- What are the optimal sizes (ouputs) for the solar cells and the solar collectors

?

- Using published aging models for EV batteries, how can the EVs aid the microgrid assuming various availabilities ?

1.4 Methodology

In this master thesis the following methodologies have been used to carry out the tasks of the project:

1. A literature review about microgrid modeling and simulation have been carried out. Different existing models in MathWorks have been studied and used as the background for the study. Investigations into PV modules, batteries and bi-directional DC-DC converters was conducted.

2. Economic analysis for PV power investment was conducted. Peak shifting for cost savings was also studied.

3. A method known as f -chart was used to estimate solar collectors thermal power output.

4. Data collection from different sources was performed.

The microgrid simulation was carried out in MATLAB/SIMULINk software provided by MathWorks. The software provides a toolbox, Simpowersystems to perform physical modeling. Numerical analysis for optimal solar cells and solar collectors output have been carried out.

Data regarding the load profile (electricity) at BRF Stenberg in form of monthly consumption was provided by the landlord in Stenberg. A more detailed data was

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used, Reference Energy Disaggregation Data Set (REDD) [15], which represent electricity consumption for several homes. It is a high-frequency current/voltage data for instantaneous power consumption for these homes. Electricity spot prices is obtained from Nord Pool, which is responsible for the power market in Europe [28]. Climate data is obtained from SMHI, the Swedish meteorological and hydrology institute [32]. Data regarding the PV power in Sweden is obtained from a survey report made by the Swedish Energy Agency [18].

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2 Theoretical Background

2.1 Solar Energy

To estimate the output power from solar collectors and solar cells a fundamental understanding about solar energy is needed. The solar radiation obtained from the sun without been scattered by the atmosphere is known as direct solar radiation or beam radiation. In contrast, the solar radiation obtained after its direction been changed is known as diffuse radiation. The sum of those two radiations is called global solar radiation. Most of the data measurements which exist today are for global solar radiations on horizontal surfaces. Solar irradiance, W/m²is the rate of incident solar power on a horizontal surface per a unit area.

Similarly, solar irradiation or radiant exposure, J/m²is the solar irradiance on a horizontal surface per a unit area and over a certain time interval [5].

2.1.1 Beam Radiation

Several parameters are important to define, so that relations for solar radiations above surfaces can be derived. Some geometrical relations can be derived for a plane oriented in relation to the sun. The following angles are important to mention which some of are given in Figure 2.1, [5] ;

ϕ, is the angular location, latitude, north or south of the equator, north positive and south negative;−90^◦ ⩽ ϕ ⩽ 90^◦.

δ, is the declination, which is the sun angular position when the sun is on the local meridian in relation to the plane of the equator, north positive;−23.45^◦⩽ δ

⩽ 23.45^◦.

β, is the slope, this is the tilt angle between the plane of the solar panel or collector; 0^◦⩽ β ⩽ 180^◦. When β is bigger than 90^◦it means that the surface has a downward-facing component.

θ, is known as the angle of incidence. It is the angle between a normal line to a solar cell and the beam radiation.

ω, is known as the hour angle, which is the sun displacement to the east or west

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Figure 2.1: (a) geometrical angles between the sun and a surface on a horizontal plane (b) Plane view of the Sun and the solar azimuth angle [5]

of the meridian as a result of earth rotation.

γ, If we project the normal of the surface to the horizontal plane, the deviation of it from the local meridian can be given by the surface azimuth angle. Zero degrees indicates south location, east negative and west positive; −180^◦ ⩽ γ ⩽ 180^◦.

θ_z, is the zenith angle, this is the angle of incidence of the beam radiation on any horizontal surface.

α_s, is the solar altitude angle, which is the angle between the horizontal plane and the line of the sun or the beam radiation.

γ_s, is the solar azimuth angle, which describe the angular displacement of the beam radiation and the horizontal plane from the south, where the beam radiation is projected on the horizontal plane.

The declination angle can be obtained from the following relation [5],

δ = 23.45sin(360284 + n

365 ) (1)

The recommended values for the declination angles, for |ϕ| less than 66.5^◦ are given in Figure 2.2, which are obtained by using Equation (1), where n is the day of the year [5].

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Figure 2.2: Recommended average days for months, values of n by months and declination angles for each month [5]

2.1.2 Extraterrestrial Radiation

Extraterrestrial radiation is the radiation that will be received from the Sun in the absence of atmosphere. This radiation can be obtained according to [5], from Equation (2);

H_o = 24× 3600Gsc

π (1 + 0.033cos360n

365 )× (cos(ϕ)cos(δ)sin(ωs) + πωs

180sin(ϕ)sin(δ)) (2) In Equation (2) G_sc is the solar constant (1367 W /m²) and ω_s is the sunset hour angle in degrees given by;

ω_s = arccos[−tan(δ)tan(ϕ)] (3)

2.1.3 Estimation of solar radiation on tilted surfaces

The ratio between the monthly average daily solar radiation on a horizontal surface (H) and the average monthly daily extraterrestrial radiation (H₀) is known as the average clearness index (K_T) [5].

K_T = H

H₀ (4)

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The monthly average daily solar radiations on inclined/tilted planes (H_T) or surfaces can be calculated by;

H_T = RH (5)

Ris defined as the ratio between the radiation on tilted surfaces and the horizontal plane, which is given by;

R = (1− H_d

H )Rb+ Hd(1 + cos(β)

2H ) + ρ(1− cos(β)

2 ) (6)

In Equation (6) R_b is the ratio of the average beam radiation on tilted surface in relation to that on a horizontal surface. The ground reflectance is presented by ρ.

The monthly average daily diffuse solar radiations H_dis derived from a correlation obtained from [5];

For ω_s⩽ 81.4^◦and 0.3⩽ KT ⩽ 0.8,

H_d

H = 1.391− 3.560KT + 4.189K_T²− 2.137KT

3 (7)

For ω_s> 81.4^◦and 0.3⩽ KT ⩽ 0.8,

H_d

H = 1.311− 3.022KT + 3.427K_T²− 1.821KT

3 (8)

In Equation (6), R_bcan be obtained from,

Rb = cos(ϕ− β)cos(δ)sin(ω^′s) + ω^′_s(π/180)sin(ϕ− β)sin(δ)

cos(ϕ)cos(δ)sin(ω_s) + ω_s(π/180)sin(ϕ)sin(δ) (9) ω_s^′ , is the sunset hour angle for the tilted or inclined plane, given by;

ω_s^′ = min[ω_s, arccos[−tan(ϕ − β)tan(δ)]] (10)

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Figure 2.3: Cross section for a flat solar collector [5]

2.1.4 Solar Collectors

Solar collector is a heat exchanger which can transform a solar energy to heat.

Flat-plate solar collectors are designed for applications where required energy is 100^◦C above the ambient temperature. Those collectors use both beam and diffuse solar radiation, they do not require sun tracking and they have low maintenance cost which makes them preferable for residential buildings.

In Figure 2.3 we can observe a cross section for a flate plate SC, often a liquid transport medium is used to absorb the sun energy through the ”black” absorber plate of the collector. The covers are to reduce convection and the insulation helps to reduce conduction losses. The circulation pumps used to transport the transport medium are estimated to consume about 2-2.5 % of the total energy obtained from the SC [5]. Typical properties required for the transport medium are high heat capacity, low freezing point and cheap price.

The heat balance equation for a SC during steady state can be determined by,

Q_u = A_c[S− UL(T_pm− Ta)] (11)

here Q_u is useful output energy from the SC, S is the solar radiation absorbed by a SC, U_Lis the SC overall loss coefficient, A_cis the SC area, T_ais the ambient temperature and T_pmis the temperature of the absorber plate.

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2.2 Thermal Energy Storage

Thermal energy storage (TES) is useful in solar thermal applications to manage the mismatch between power supply and demand. Three important parts of a TES are; heat transfer mechanism, a containment system and a storage medium. TES technologies which are widely used are, sensible heat storage, latent heat storage and thermochemical heat storage. At the present time molten salt and synthetic oil are frequently used in sensible heat storage materials in large scale concentrating solar power (CSP) systems [14].

2.2.1 Sensible Heat Energy Storage

In this type of TES temperature shifting of storage medium is used without a phase change of the medium. Sensible heat storage is preferable due its low cost and simplicity. The solar energy is stored in a storage medium which is usually liquid or solid, where the storage capacity depends on the energy density (energy per a unit mass) and the thermal diffusivity (rate of heat release and extraction) [14].

Water based storage is preferable sensible heat storage for residential applications due its low cost and simplicity. Water stratifies naturally where hot water flows to the top due its low density and cold water remains in the bottom. Water tank (WT) also known as accumulator tanks (AT) are often made of stainless steel and surrounded by thick insulation. Typical applications for water tanks with solar collectors and electric heater for domestic hot water (DHW) is given in Figure 2.4. The direct mode is when the SC heat transfer medium (water in this case) is directly mixed with water tank storage medium. In the indirect mode the opposite is valid where the transfer medium of the SC is released to the water through a heat exchanger (HE) [17] [14].

2.2.2 Latent Heat Energy Storage

In latent heat storage (LHS) technologies phase shifting materials (PCMs) are used, those PCMs have the ability to absorb and release energy through physical state change. The PCMs used are often preferred to have high energy density and low volume variation during phase change to minimize the containment

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Figure 2.4: (a) direct mode (b)indirect mode [17]

volume. Some of the commonly used PCMs are, Paraffin wax, Palmitic acid and salt hydrates [9].

2.3 Solar Thermal Power and Heat Pumps

Systems which combine both solar energy and heat pumps are known as solar heat pump systems (SHPs). In such systems photovoltaic can be used to generate electricity or SC to generate heat, in some applications the combinations of both can be used [29]. The main objective of combining those two technologies is to decrease the electricity consumption for the heating load.

The SC can be used in parallel or series with the heat pump. In the series configuration as shown in Figure 2.5a the SC acts like an extra source for the heat pump either exclusively or as an additional with another source. It can be directly connected to heat pump or through a storage medium [30].

In parallel system configurations both the heat and the SC independently supply the heat load via one or more storage tanks, Figure 2.5b. Due to the simplicity of the design, installation and control of this configuration, they are more dominant in the market [30].

Solar photovoltaic systems are integrated with heat pumps to increase the rate of self-consumption of the generated electricity. In some countries due to the expensive prices of electricity compared to the locally produced, people have found it as an alternative to increase the locally consumed electricity [11].

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(a) Series system

(b) Parallel system

Figure 2.5: Solar heat pump system with series and parallel configurations [30]

2.4

f

-chart Method

There are several methods which are used to study solar thermal processes. The important design parameters for a solar thermal process is the collector area, collector type, storage capacity, fluid flow rates and heat exchanger sizes. TRNSYS is a transient process simulation program used to study solar energy applications.

A component library exist in the program which can help to perform physical modeling of solar collectors and other relevant components. Simulations carried out in this program are often yearly simulations where system performance is of interest. Meteorological data for several sites are available in this program to carry

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Ranges of Design parameters 0.6⩽ (τα)n⩽ 0.9 5⩽ (F_R^′A_c)⩽ 120m² 2.1⩽ (UL)⩽ 8.3 W /m²^◦C

30⩽ β ⩽ 90^◦ 83⩽ (UA)h⩽ 667W /^◦C

Table 2.1: Design parameters for f -chart method [5]

out simulations [5].

There is also other numerical methods used to estimate the solar collector performance for a given input set of data. The f -chart method is used to estimate the fraction (f ) of the total heat load (space heating and hot water) supplied by a solar heating system. This method is common for residential applications and is derived from correlations obtained through several simulations for solar heating systems. Furthermore, the method is developed for a standard storage capacity of 75 liters of water per square meter solar collector area. The f -chart method is developed for various system configuration such as liquid and air systems. In the liquid systems, liquid is used as a heat transfer medium from the collector and air is used for air systems [3] [5].

The ranges of design parameters used to develop the f -chart method are given in Table 2.1. U_L is the solar collector overall loss coefficient. The average normal transmittance-absorptance product is given by (τ α)_n. The collector heat exchanger factor is given by (F_R^′) multiplied by A_C, which is the SC area. The tilt angle of the SC is presented by β and (U A)_h is the building overall energy loss coefficient, U is the loss coefficient constant and A is building areas which present the heat losses. Moreover, there are other design variables which are vital for the f -chart method, for example F_Rwhich is the heat removal factor. This heat removal factor of the SC represents the ratio of the useful energy gain from the SC if the whole SC surface was at the fluid inlet temperature [5].

As mentioned earlier the f -chart method is a correlation obtained from various empirical results of several simulation of case studies of solar systems. The dimensionless parameters used in the f -chart method are given in equations (12) and (13).

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X = Collector Energy Losses

Total heating load (12)

Y = Total Energy Absorbed by Collector

Total heating load (13)

Equations (12) and (13) can be numerically obtained from Equations (14) and (15). Some of those parameters are mentioned earlier. New parameters in those Equations are, L which is the total heating load for a month, ∆t is total number of seconds in a month, T_a is the monthly average ambient temperature, T_{r ef} is the empirical reference temperature (100 ^◦C), H_T is the monthly average daily radiation incident on collector (J/m²), N is the number of days in a month and (τ α)is the monthly average transmittance-absorptance product [3].

X = F_RU_L× (F_R^′

F_R)× (Tr ef)× ∆t × Ac

L (14)

Y = F_R(τ α)_n× F_R^′

F_R × τ α

(τ α)_n × HTN × A_c

L (15)

Parameters F_RU_L and F_R(τ α)_n are constants obtained from test results of the respective collector. The factor ^F_F^R^′

R is a correction term for the different temperature drops between the collector and the storage tank. Similarly _{(τ α)}^{τ α}

n is the ratio between the average transmittance-absorptance product and the normal transmittance-absorptance product. Those parameters are collector specific which are obtained via some experimental tests mentioned in [5].

For liquid heat transfer medium systems the fraction (f ) can be determined from Equation (16). The annual load (F) supplied by the solar thermal system can be determined by Equation (17), which is the sum of all monthly fractions divided by the yearly load.

f = 1.029Y − 0.065X − 0.245Y² + 0.0018X²+ 0.0215Y³ (16)

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Figure 2.6: f-chart method using liquid heat transfer and storage media [5]

F =

∑∑fiLi

L_i (17)

The f -chart method is limited and can only be used for X and Y values given in Figure 2.6.

2.5 Photovoltaic Technology

The PV market is defined as a total nationally installed PV application with a PV capacity of at least 40 W. The ratio installed PV power is continuously growing in Sweden, in 2018 approximately a total of 150 MWp was installed and the cumulative installed capacity was above 400 MWp (Figure 2.7). The grid- connected distributed PV systems have been dominating in the recent years as shown in Figure 2.7 due to the direct capital subsidy from the government and the falling prices of the PV modules (observe Figure 2.9). Those grid-connected systems can be divided into residential systems with a capacity of 0-20 kWp, small commercial systems with a capacity 0-20 kWp and larger-scale commercial systems which are bigger than 20 kWp. Those systems are often roof-mounted systems [18].

The electricity generation in Sweden is dominated by nuclear and hydro power as shown in Figure 2.8. Since the electricity market is dominated by stable nuclear

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Figure 2.7: Annual installed PV capacity and cumulative installed capacity in Sweden [19]

Figure 2.8: Electricity generation in Sweden 2016 [18]

and hydro power the average electricity prices are low [18].

2.5.1 PV System Prices

In recent years as mentioned earlier PV system prices have been declining. This can depend on the decreased prices of PV modules over the last decade due to the continuous improvement of the technology. Another reason can be the growing PV market in Sweden where installation firms are continuously increasing. The cost structure for a PV system obtained from five Swedish installation companies is given in Figure 2.10, here it can be observed that the system prices is largely dominated by the module prices and installation costs [18].

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Figure 2.9: Average prices for grid-connected PV systems (excluding VAT) [19]

Figure 2.10: Average cost structure for grid-connected commercial PV system (40- 60) kWp [18]

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Figure 2.11: Average electricity spot prices in SE3 (Stockholm) 2018 [18]

2.5.2 Electricity Prices

The trading market for electricity in Sweden and other Nordic countries is Nordpool, which is responsible for the spot prices based on demand and supply of electricity. In 2011 the Swedish electricity network got divided in four electricity bidding areas (SE1-SE4) by the Swedish National Grid (Svenska Kraftnät). This is due to the high electricity production in the north and higher demand in the south than the north. This mismatch lead to some transmission capacity problems between those bidding areas. Those electricity areas will help to recognize where the reinforcement of the grid is needed and where the production should be increased. The electricity spot prices for 2018 in Stockholm is given in Figure 2.11.

2.5.3 Capital Subsidy and Financial Incentives For PV Development in Sweden

The governmental support for the PV market in Sweden started in form of direct capital support where 70 % of the installations costs was covered if the PV-system was built in a public building [18]. Those governmental capital support policies have been changing through out the years. According to the Swedish Energy Agency in 2019, it was possible to obtain a compensation which is up to 20% of the total PV-system cost [8].

Electricity green certificate is one of the governmental support policy to promote

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Figure 2.12: Average certificate prices [18]

PV power in Sweden. The idea of those certificates is that any ”green” electricity producer will get one certificate for each MWh generated electricity. Those certificates can latterly be sold at the market. The buyers are different electricity stakeholders which have an obligation (quota obligation) to buy the certificates at the market price. This system was introduced in 2003. The certificate prices follows the market price, if the generated ”green” electricity is high the prices goes down and the opposite if the generated electricity is low [38]. The certificate price over the years is given in Figure 2.12.

Guarantees of origin (GOs) is another support policy which is similar to the green certificate system. The GOs are electronic documents obtained for each MWh produced electricity. Those documents are sold at the market price where the buyers are often utility companies who want to sell ”green” energy. The prices of GOs are often difficult to obtain but the market value is estimated to 10 SEK per MWh [18].

Another governmental support is the tax credit for microproducers. This policy was introduced in January 2015, the credit is 0.6 SEK/kWh for renewable electricity. To receive this compensation some rules must be followed. Firstly, the excess electricity from the PV system must be feed in a the same connection point as electricity is received and the ampere fuse at the connection point should not exceed 100 amperes. The upper limit is that the PV system owner can only receive a tax credit for a maximum 30 000 kWh renewable electricity [18].

Grid benefit composition is another form of revenue obtained for the reduced transmission losses. The scale of this compensation depends on the electrical area of the produced renewable electricity. This compensation varies between 0.02 and 0.10 SEK/kWh. The compensation value use to be higher in the Southern parts of

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the country due to the high transmission losses [19].

2.6 Electric Vehicles

Electric vehicles (EVs) can have a major role in the future as a back up to the main power system. Since most of the hours during the day EVs are parked, vehicle- to-grid (V2G) technology can be adapted to aid the grid/micro-grid during peak hours. Different studies indicate that 1% peak shifting of demand can lead to cost savings up to 3.9 % [39] [34].

Lithium-ion (Li-Ion) batteries are dominant in EV applications. The capacity of the batteries are often determined in ampere-hours (Ah) or kWh. Terminologies used to determine the available capacity in an EV is the state of charge (SoC). The depth of discharge (DoD) of battery is the amount or capacity which is used from a fully charged battery. The life-time of the battery is often determined by so called state-of-health (SoH), which is the remaining capacity of the battery that can be charged [16].

2.6.1 Generic Battery Model

A generic Li-Ion battery model can be presented by a controlled voltage source in series with a constant resistance. The charge and discharge relations are given in the following equations, in general the coefficients for charge and discharge can be different (Equations (18) and (19)) [35].

discharge model (i^∗ > 0)

f₁(it, i∗, i) = E0− (K × Q

Q− it × i∗) − (K × Q

Q− it × it) + Aexp(−B × it) (18)

charge model (i^∗ < 0)

f₂(it, i∗, i) = E0−(K × Q

it + 0.1× Q×i∗)−(K × Q

Q− it×it)+Aexp(−B ×it) (19)

In the equations,

- E₀is the nonlinear voltage, in V - Q is the battery capacity, in Ah

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Figure 2.13: Discharging Characteristic [22]

- B is the exponential capacity, in Ah⁻1 - A is the exponential voltage, in V - it is the extracted capacity, in Ah

- i∗ is the low-frequency current dynamics, in A - i is the battery current, in A

- K is the polarization constant, in V /Ah or know as the polarization resistance

In Figure 2.13 the yellow area represents the exponential area where the voltage drops exponentially, the upper limit is where the battery is fully charged. The grey area presents the section where the battery can be utilized until the battery reaches the nominal capacity after that the battery discharges rapidly. This model is available in MATLAB/SIMULINK SimpowerSystems library for lithium-ion batteries [35].

2.6.2 Battery Aging

A battery life time can be expressed as the sum of calendar life and cycle life. Those expressions depends on several parameters. The cycle degradation and calendar degradation (D^caland D^cyc) are given in Equations (20) respectively (21).

D^cal = S_t(t)S_σ(σ)S_T(T_C) (20)

D^cyc =

∑N i

S_δ(δ)S_σ′(σ^′)S_T′(T_c^′) (21)

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In Equation (20), S_t(t) is the function of elapsed time t(s); S_σ(σ) is a function of σ average state of charge and S_T(T_C) is function of T_C average battery cell temperature. In the cycle degradation relation, i stands for one cycle of charge and discharge while N presents the total number of cycles; S_δ(δ) is the function of depth of discharge (δ), S_σ′(σ^′)is the function of the average state of charge (σ^′) during charging and discharging; similarly S_T′(T_c^′)is the function of the average cell temperature (T_c^′) during a charging and discharging event [34].

S_t(t)S_σ(σ)is can be given by Equation (22), where σ_ref is the reference SoC (50%), Kσ and K_tare constants.

S_t(t)S_σ(σ) = e^K^σ^(σ^−σ^ref⁾K_tt (22)

Similary S_δ(δ)S_σ′(σ^′) can be determined by Equation (23), K_{δ 1} and K_δ2 are constants [34]

S_δ(δ)S_σ′(σ^′) = e^K^σ^(σ^′^−σ^ref⁾K_{δ 1}δ^K^δ² (23)

In Figure 2.14 the battery life cycle can be observed for different DoD, higher DoD results in rapid aging of the battery. To prevent that different battery management systems are used to keep the DoD within optimal limits. Studies indicates that a battery end life is when its reaches a SoH of 80%, where 100% is the SoH for a healthy and new battery [34] [21]. The SoH of 80% is the level where noticeable changes in the battery can be observed.

2.7 DC-Bus Microgrid System

Microgrid systems can have either a DC-bus or an AC-bus. A DC-bus system is relevant to small scale micro-grid applications. AC-bus systems can have some issues regarding reactive power control, synchronization and bus stability.

Different systems connected to a DC-bus can be, PV cells often via a DC/DC boost converter, DC load, AC load via an DC/AC inverter [27].

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Figure 2.14: Depth of discharge versus cycle life of lithium-ion battery [21]

2.7.1 DC/DC Converter

DC-DC converters are used to take an input DC voltage and produce an out put voltage which is often at a different voltage level. This is done through fast switching by using input signals. Today most of the DC-DC converters consists of insulated gate bipolar transistors (IGBTs) and metal oxide silicon effect transistors (MIDFETs) due to their good quality of switching in terms of power ratings and switching frequency [41].

In microgrid applications, the converter can be used to couple a battery system to a DC-bus. Bi-directional DC-DC converters are used to control the power flow between the battery and the DC-bus [31].

2.8 Life Cycle Cost Analysis

Life cycle cost analysis (LCCA) is used to compare various investment costs and revenues over a given life time. A set of data is used as an input, for example;

investment costs, degradation rate, discount/interest rate. The output of such a study can be cash flows over the years and the net present value of the investment.

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Since this study is related to a PV system the expected life time for the PV system is about 20 years, [13] [1].

2.9 Electricity Prices in Sweden

There are two main actors in the Swedish electricity market which are important for end-users or consumers. Those two actors are known as the retailer (electricity provider) and the distribution system operator (DSO). The DSO is responsible that the consumers have electricity at their household meters. The DSO operator is also responsible for the maintenance and operation of the distribution grid. The tariff payed by the consumers to the DSO consists of two parts (fixed charge and a flexible charge). The fixed charge depends on the fuse rating on the consumer side. The flexible charge is based on the average electricity consumption of the consumer [36] [37].

The electricity provider (retailer) can be chosen freely by the electricity consumer.

The retailer is responsible to deliver electricity to end-users based on the Nord Pool market. The consumer can chose to have a variable tariff, fixed tariff or a mixed tariff. The variable tariff is a hourly real time tariff based on the market price, which is given a day ahead by Nord Pool. The fixed tariff as it sound is a constant price payed by the consumer for each kWh energy. The mixed tariff is a combination of the variable and fixed tariff. To obtain price arbitrage in this study, the end-user is assumed to have a variable tariff contract. An additional cost paid by the consumer is the value added tax (VAT) or ”moms” and energy taxes [6].

The total electricity cost is the sum of costs paid to the DSO and the retailer as well as VAT and energy taxes, which is given in Equation (24). The average electricity price in Sweden for 2019 for an average size villa was 2.15 SEK/kWh, this price include average costs for DSO and electricity retailers as well as average energy taxes and VAT [7].

E_cost = Retailer_cost+ DSO_cost (24)

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3 Case Study and Data Analysis

This project is performed for BRF Stenberg. Stenberg is an old rural property with a distance of 3 km from the city center of Hudiksvall, Sweden, Figure 3.1. In the last 40 years this property have developed from a traditional ”farmhouses” to modern buildings for work and living. The idea here is to have a microgrid system with a grid-tied PV system, EVs, solar thermal collectors with accumulator tanks and a heat pump. The goal is to have an optimal design which is economically and technically feasible. The ultimate future goal is to become energy self-sufficient or off-grid.

Figure 3.1: BRF Stenberg Hudiksvall [33]

The estimated monthly electricity consumption in BRF Stenberg is about 4084 KWh. The energy demand in form of space heating and domestic hot water (DHW) is given in Figure 3.2. A pilot study was conducted for BRF Stenberg by Energi Banken. In this study a simulation for the annual electricity generation from a PV installation on three roofs was performed. One of the roofs belong to the

”Studion” house southern roof, the other two roofs belongs to eastern and western

”Lagårn”, look at Figure 3.1. This study is performed for a PV system with a peak power of 68 kW. The Simulations were carried out in a software program called PVsol, where climate data for Hudiksvall is used. The yearly electricity output from the PV installation is given in Figure 3.3 (a). The total yearly production is estimated to 52 MWh per a year.

In the simulation three inverters (SMA Tripower) were included, two with the

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Figure 3.2: BRF Stenberg monthly heat demand

Figure 3.3: (a) Yearly PV generation (b) PV generation for a day in June

nominal power of 25 kW and the third with 10 kW. The PV modules used in the simulation were monocrystalline silicon solar cells with a peak power of 310 W each. The simulation takes consideration to shading effects by the trees around the houses. The estimated investment cost for this system is about 750 thousand Swedish Krona (SEK). PV energy output for a day in June is given in Figure 3.3 (b).

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4 Methods

4.1 Microgrid Simulation

The goal of this simulation is to study how the EVs will aid the microgrid considering different EV availabilities. The microgrid simulation was performed in the software MATLAB/SIMULINK ver.R2019a provided by MathWorks. A DC-bus system was designed with a reference voltage of 500 V, given in Figure 4.1.

Figure 4.1: Microgrid System

The PV power data from the pilot project was used for the simulation (Figure 3.3 (b)). Since the data for the PV power was hourly data, a higher resolution data from an open source called ”PVOutput” was used. Those measurement are for every 9 minutes. The PVOutput data was scaled up to match the hourly output power from Figure 3.3 (b). The scaled data which is used as the PV model output in the simulation is given in Figure 4.2.

4.1.1 PV Model

The PV modules in Figure 4.1 was modelled by a current source in parallel with a diode. The diode turns off when the current flow is zero from the PV and it also does not consider zero currents.The objective of the diode is to oppose the current flowing in the reverse side when the PV is not generating. Due to the non ideal behaviour of the PV modules, a shunt resistance and series resistance are included in the circuit, Figure 4.3. By using the PV power from Figure 4.2, the PV

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Figure 4.2: PV generation using scaled data for a day in June

current I_{P V} was obtained. The output voltage from the PV system to the DC bus is set to 500 V (V in Figure 4.3) .

Figure 4.3: Equivalent circuit for a PV cell

4.1.2 Load Profile for the households

The load profile of the households in Stenberg can be seen as the electricity consumption for several households (AC load in Figure 4.1). The daily electricity consumption for the households in Stenberg is about 135 kWh. To present the load for those several households in Stenberg, electricity consumption for several households from the REDD data base was used and added up as Figure 4.4 shows.

The data from REDD was scaled up to match the total energy consumption in

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Stenberg (135 kWh/day).

Figure 4.4: Load Profile Stenberg

4.1.3 Battery Model

A generic Li-ion battery model (section 2.6.1) is used to represent the EVs in the microgrid where they can charge and discharge based on the voltage level of DC-bus. The link between the battery and the DC-bus is a bidirectional DC-DC converter (BDC), given in Figure 4.5 (b). The BDC operates in two modes, either charging or discharging mode. In the charging mode, the signal Q2 is on and Q1 is off, the opposite is valid for the discharging mode. Those signals are generated via a PWM block from Simpowersystems. A PI-controller is used to generate those signals to the PWM. The PI controller, controls the DC-bus voltage and generates a duty cycle for the IGBTs of the BDC. If the voltage in the DC-bus is less than 500 V it means that the battery must discharge to the microgrid, if it is above 500 V the battery is charged by the surplus PV generation.

Moreover, a three-phase DC-AC inverter is used in this Simulation have an 97%

efficiency and is obtained from MathSWorks. This inverter is connecting the DC- bus and the load profile of Stenberg. The power grid in Figure 4.1 was presented by a battery connected to the DC-bus to track the power mismatch.

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Figure 4.5: (a) Battery used in Simulation (b) Bidirectional DC-DC converter

4.1.4 Study Cases

In this study a 24-hour simulation for the microgrid was performed. The simulation can be divided in four scenarios; the first scenario is when the microgrid is not connected to the grid (island mode). In this scenario the EVs are available the whole day.

In the second scenario the EVs are at work between 8 am - 6 pm and there is a possibility to charge at work. In this case, it is assumed that EVs will be able to aid the microgrid directly when they are connected again. In this scenario the microgrid is connected to the main grid so that the load can be matched when the EVs are away. When the EVs arrive to the microgrid, it is assumed that they have the same SoC as when the left.

The third scenario is similar to the second, the only difference is that the EVs in this scenario can not charge at work. A resistance of 20 ohm was used to represent the lost power from the battery during the traveling hours. The resistance value is chosen randomly to estimate the power losses.

In the fourth scenario, it is assumed that it is a weekend day where the EVs are not available between 10 am - 2 pm. Since the EVs are not available for a short period in this scenario, it is assumed that they are not charged when they are away. To present the the power losses for being on the road a resistance with 8 ohm was

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used. This resistance is obtained from the ratio of hours that the EVs was not available in this scenario in relation to scenario 2 (_10hrs^4hrs ∗ 20ohms).

the load profile in Figure 4.4 and PV power in Figure 4.2 are used in all four scenarios.

4.2 Thermal Model

To model the solar thermal collectors output in Stenberg the f -chart method was used. The data required for this method are; monthly average daily radiation incident on collector MJ/m², the average monthly ambient temperature (T_a) and the monthly load profile. The monthly thermal load profile for Stenberg is given in Figure 3.2. The average ambient temperature for Hudiksvall was obtained from SMHI, the data is for 2019, the measurements are daily measurement (one at 06:00 am and the other at 06:00 pm), Figure 4.6. The monthly average daily global radiation on horizontal surfaces were obtained from a station measurement at Borlänge due to the lack of data at Hudiksvall. The data is hourly measurements for 2019 from SMHI, Figure 4.7.

Figure 4.6: Average monthly temperature Hudiksvall

The f -chart method was implemented by using the following relations;

• The recommended declination angles are used from Figure 2.2.

• The extraterrestrial radiation is determined by using Equation (2), the latitude of Hudiksvall is ϕ = 61.7^◦ north. The sunset hour (ω_s) is derived from Equation (3).

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Figure 4.7: Global monthly average daily irradiance

• Equations (4)-(10) are used to to calculate the monthly average daily solar radiation on tilted surfaces (H_T). The tilted angle of the solar collector here is assumed to be 40^◦. The ground reflectance (ρ) is assumed to be 0.2.

• By using Equations (12)-(17) the fraction energy applied by the solar thermal collector was obtained.

4.3 Life Cycle Cost Analysis

To evaluate the economical aspect of the project a life cycle cost assessment (LCCA) was carried out to decide the optimal PV capacity for Stenberg.

Economical indicators were obtained for different PV sizes. To get a view of the parameters which will have a huge impact on the investment a sensitivity analysis was conducted. Cost savings by peak shifting was studied, where the EVs are used for this case.

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5 Result

In this chapter results obtained from the study are presented. The first section presents the results for the microgrid simulation at Stenberg. In the second section the thermal modeling results are presented. In the third section results for the economic analysis are given.

5.1 Microgrid Simulation Stenberg

5.1.1 First Scenario

In Figure 5.1 the microgrid power simulation is given when the system is in islanding mode. The EVs are assumed to be available the whole day. It can be observed that the EVs are supplying the load when the sun is not shining. On the contrary, during the day the EVs are charging with the surplus PV power. The negative power indicates that the EVs are charging and the positive power the they are discharging.

Figure 5.1: MG Simulation Stenberg Case 1

The battery current and voltage are given in Figure 5.3. The sign convention used here is that a positive current indicates discharging and negative current indicates charging of the EVs. When the simulation begins, the battery is assumed to have a SoC of 40 %. In Figure 5.2 the battery SoC is given, the SoC is increasing when

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Figure 5.2: EVs battery SoC Case 1

Figure 5.3: (a) Battery Current (b) Battery Voltage Case 1

there is surplus PV power and decreasing when the load demand is exceeding PV generation.

5.1.2 Second Scenario

The second scenario is when the EVs between (8am - 6pm) are either on the road or work, the microgrid in this case is connected to the grid. The EVs in this case have the possibility to charge at work. In Figure 5.4 the simulation for the microgrid is given, it can be observed that during the morning both the grid and the EVs are supplying the load.When the EVs are not available the surplus PV

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generation is injected to the power grid. When the EVs are available again at 6 pm, they start to supply the load in the microgrid. A spike can observed in grid power when the EVs are connected to the microgrid, this caused due to the sudden undamped interruption of power from the grid in the simulation.

Figure 5.5: EVs Battery SoC Case 2

In Figure 5.5 the SoC for the simulation is given. The SoC in this case is assumed to be 85 % when the simulation starts. Figures 5.6 (a) and (b) are the battery current and voltage during the simulation. In both Figures a similar spike as the

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mentioned before can be observed which is also due to the sudden interruption of the power grid. By observing the battery current and voltage the charging and discharging hours can be observed. Similarly as previous case the sign convention used here is that negative power and current indicates the charging of the EVs.

5.1.3 Third Scenario

The third scenario illustrate when the EVs does not have the possibility to charge at work. The unavailability hours for the EVs are similar to the previous case.

In Figure 5.7 the microgrid simulation is given, in this case both the battery and the grid are supplying the load when the PV generation is not meeting the load demand. Since the EVs have not a possibility to charge at work, when they are connected again to the microgrid at 6 pm, they will start to charge first, latterly they will be able to discharge to the microgrid. At 6 pm sudden peaks of the grid power can be observed in Figure 5.7 this is due to the sudden plug-in of the EVs to the microgrid. The peak indicates that the EVs are charging from the grid and latterly discharging to the microgrid.

In Figure 5.8 the battery SoC is given where the battery charging/discharging can be observed for the whole day. The linear decrease of the SoC is as the result of the constant resistance (20 ohms). The spikes in battery current and voltage indicates the sudden connection of the EVs to the MG, Figures 5.9 (a) and (b).

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5.1.4 Fourth Scenario

The fourth scenario is when the EVs are not available between 10 am - 2 pm. In Figure 5.10, it can be observed that the EVs are aiding the microgrid early in the mourning hours. During the time when the EVs are not available a constant power can be observed which represents the power loss of the EVs on the road. When the EVs are connected to the MG again they will start to charge with the surplus

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PV power. The EVs are aiding the MG when PV power is not available. In Figure 5.11 the EVs SoC can be observed.The EVs battery current and voltage are given in Figures 5.12 (a) and (b). The spikes in this scenario represent also the sudden grid interruption.

Figure 5.10: MG simulation Case 4

For those four scenarios different EV capacities are required, the values are given in Table 5.1. Those are the battery capacities that will be required for each case to fulfill the charging/discharging range of the battery (SoC 30-90 %). This range is chosen to increase the life-time of the battery.

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Figure 5.12: (a) Battery Current (b) Battery Voltage Case 4 Scenario Capacity [kWh]

1 320

2 250

3 190

4 300

Table 5.1: EV Capacity with a SOC of (30 - 90%)

The peak power capability that battery/EVs needs to handle for each scenario is given in Table 5.2. This is the peak power reached in the battery during the microgrid simulation for each scenario. To increase the cycle life of the batteries it is recommended to keep the peak power below the values in Table 5.2.

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Scenario Peak Power Capability [kW]

1 35

2 23

3 129

4 23

Table 5.2: Peak power capability for each scenario

5.2 Thermal Modeling Stenberg

As mentioned earlier to evaluate the average yearly output from the solar thermal collectors some design parameters regarding the physical property of the SC are required. The parameters used for this study are for a flat-plate solar collectors given in Table 5.3 obtained from [5].

Design Parameters F_RU_L 4 W/m² F_R(τ α)_n 0.74

F_R^′

FR 0.97

τ α

(τ α)n 0.96

Table 5.3: Design parameters for f -chart method [5]

The average monthly daily irradiance on the solar collector during a year time is given in Figure 5.13. As expected the solar irradiance is higher during the sunny months of the year.

In Figure 5.14 the ratio of the energy supplied to the heat load (space heating and DHW) by the heat pump and the SC is given for different SC areas. For larger areas of the SC a higher share of solar energy is obtained.

In Figure 5.15 the yearly energy supplied by a SC and heat pump for a SC area 0f 60 m²is given. It can be observed that during the sunny months of the year the energy demand can entirely be supplied by the solar thermal collectors.

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Figure 5.13: Irradiance on SC

Figure 5.14: Annual supplied energy by heat pump and SC as the function of SC area

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Figure 5.15: Annual energy supply with a 60m²solar thermal collector

5.3 Economic Analysis

5.3.1 LCCA PV Stenberg

In this section results regarding the LCCA for the PV installtion is given. The main output parameters from this study are the net present value (NPV) and the return of investment (ROI). Input data used to perform the study are listed below, some of them are already mentioned in the theory section.

- To estimate the economic value of the generated PV electricity, the yearly average spot prices from Nordpool were used. This data is for the electric area SE2. The average electricity spot price for 2019 was 0.40 SEK/kWh excluding energy taxes and VAT [28].

- The market prices for electricity green certificates and guarantee of origin are estimated to be 100 SEK/MWh respective 10 SEK/MWh.

- The PV system price is assumed to be around 11500 SEK/kWp.

- The governmental support for the total investment cost is 20 %.

- The tax reduction compensation is 0.6 SEK/kWh produced PV electricity, the upper limit is 30000 kWh (18000 SEK).

- The grid owner compensation for transmission losses is assumed to be 0.06

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SEK/kWh.

- The interest rate or discount rate of the banks is assumed to be 3 %.

- The yearly degradation rate of PV system is around 0.4 % [20].

- The life time of the PV system is assumed to be 20 years.

Cash flows for different PV-system capacities are in given in Figures 5.16-5.21. In the first years the cash flow is negative due to the high investment cost.

Figure 5.16: Annual accumulated cashflow for a 40 kWp system

PV capacity [KWp] NPV [SEK]

40 129057

50 104604

60 71963

68 45862

80 6695

90 -25946

Table 5.4: NPV for different PV capacities

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5.3.2 Sensitivity Analysis

A sensitivity analysis was conducted to investigate the parameters which will highly impact the investment due to their variation. Parameters studied here are;

investment cost, prices for ”green” certificate and guarantee of origin, electricity spot prices and tax reduction compensation. Those parameters are changed

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between -15% and 15% from their previous chosen values. The output of this analysis is the fluctuation of the NPV for the variation of the chosen investment parameters.

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Figure 5.22: Sensitivity Analysis

5.3.3 EVs Economic Analysis

To estimate the profit obtained by having the EVs in the microgrid for the different scenarios, Equations (25-27) are used. The income in Equation (25) is obtained from the surplus PV energy, here assumed,to be sold to the grid at spot price, in Figures 5.4, 5.7 and 5.10 it can be seen as P_Gridless than zero. The cost in Equation