David Lingfors

Solar Variability Assessment andGrid Integration

Methodology Development and Case Studies

Submitted to the Faculty of Science and Technology, Uppsala University, in partial fulfilmentof the requirements for the degree of Licentiate of Technology, to be publicly examined inLecture Hall 1111, ITC, Lägerhyddsvägen 1, 751 21 Uppsala, Wednesday, November 25 at14:00.

Abstract

Lingfors, D. 2015. Solar Variability Assessment and Grid Integration: MethodologyDevelopment and Case Studies.

During the 21st century there has been a tremendous increase in grid-connected photovoltaic(PV) capacity globally, due to falling prices and introduction of economic incentives. PV sys-tems are in most cases small-scale, installed on residential dwellings, which means that thepower production is widely distributed and close to the end-user of electricity.

In this licentiate thesis distributed PV in the built environment is studied. A methodologyfor assessing short-term (sub-minute) solar variability was developed, which in the continuationof this PhD project could be used to study the aggregated impact on the local distribution gridfrom dispersed PV systems. In order to identify potential locations for PV systems in a futurescenario, methodology was developed to assess the rooftop topography on both local level usingLiDAR data and nationally through building statistics.

Impacts on the distribution grid were investigated through a case study on a rural municipal-ity in Sweden. It was found that the hosting capacity, i.e. the amount of PV power generationthat can be integrated in the grid without exceeding certain power quality measures, is high, atleast 30%. However, the hosting capacity on transmission level needs further investigation. Asa first step a methodology was developed in order to model scenarios for hourly solar powergeneration, aggregated over wide areas, here applied to the whole Swedish power system. Themodel showed high correlation compared to PV power production reported to the Swedishtransmission system operator (TSO). Furthermore, it was used to model scenarios of high PVpenetration in Sweden, which give some indications on the impact on the power system, interms of higher frequency of extreme ramps.

Keywords: Solar Variability, Photovoltaics, Grid Integration, Distributed Generation, GIS

David Lingfors, Department of Engineering Sciences, Solid State Physics, Box 534, UppsalaUniversity, SE-751 21, Uppsala, Sweden

c© David Lingfors 2015

List of papers

This thesis is based on the following papers, which are referred to in the textby their Roman numerals.

I J. Widén, N. Carpman, V. Castellucci, D. Lingfors, J. Olauson, F.Remouit, M. Bergkvist, M. Grabbe, R. Waters, ‘Variability assessmentand forecasting of renewables: A review for solar, wind, wave and tidalresources’, Renewable and Sustainable Energy Reviews, Vol. 44, pp.356-375 (2015).

II D. Lingfors, U. Zimmermann, J. Widén, ‘Characteristics of a low-costsolar irradiance logger’, in Manuscript.

III D. Lingfors, U. Zimmermann, J. Widén, ‘Determining intra-hour solarirradiance variability with a low-cost solar logger network’, inproceedings of the 4th Solar Integration Workshop, pp. 509-513,Berlin, Germany, November 10-11 (2014).

IV D. Lingfors, J. Widén, ‘Development and validation of a wide-areamodel of hourly aggregate solar power generation’, Submitted toEnergy (2015).

V R. Luthander, D. Lingfors, J. Munkhammar, J. Widén,‘Self-consumption enhancement of residential photovoltaics withbattery storage and electric vehicles in communities’, in proceedings ofthe eceee 2015 Summer Study on Energy Efficiency, pp. 991-1002,Presque’île de Giens, France, June 1-6 (2015).

VI D. Lingfors, J. Marklund, J. Widén, ‘Maximizing PV hosting capacityby smart allocation of PV: A case study on a Swedish distributiongrid’, in proceedings of 44th ASES Annual Conference, State College,Pennsylvania, 28-30 July (2015).

Reprints were made with permission from the publishers.

Publications not included in the thesis

VII D. Lingfors, J. Widén, J. Marklund, M. Boork, D. Larsson, ‘Photo-voltaics in Swedish agriculture: Technical potential, grid integration andprofitability’, to be published in proceedings of the ISES Solar WorldCongress 2015, Daegu, Korea, 8-12 November (2015).

VIII J. Munkhammar, J. Rydén, J. Widén, D. Lingfors, ‘Simulating dispersedphotovoltaic power generation using a bimodal mixture model of theclear-sky index’, in proceedings of the 30th European Photovoltaic SolarEnergy Conference (EU-PVSEC), Hamburg, Germany, 14-18 Septem-ber (2015).

IX I. Norberg, O. Pettersson, A. Gustavsson, P. Kovacs, M. Boork, P. Ollas,J. Widén, D. Lingfors, J. Marklund, D. Larsson, D. Ingman, H. Jältorp,‘R 433 Solel i lantbruket - realiserbar potential och nya affärsmodeller[PV in agriculture - Realizable potential and new business models]’, JTI- Swedish Institute of Agricultural and Environmental Engineering, Up-psala, Sweden (2015).

X D. Lingfors, J. Widén, ‘Solenergipotentialen för Blekinges bebyggelseenligt två framtidsscenarier [PV potential for the built environment ofBlekinge county for two future scenarios]’, Technical report 2014:10,Länstyrelsen i Blekinge (2014).

XI D. Lingfors, J. Widén, S. Seipel, ‘Interactive visual simulation for pho-tovoltaic design and planning in the built environment’, in proceed-ings of he 28th European Photovoltaic Solar Energy Conference (EU-PVSEC), pp. 4176-4179, Paris, France, September 30 - October 4 (2013).

XII T. Volotinen, D. Lingfors, ‘Benefits of glass fibers in solar fiber opticlighting systems’, Applied Optics, Vol. 53, Issue 27, pp. 6685-6695(2013).

XIII D. Lingfors, R. Hallqvist, T. Volotinen, ‘Lighting Performance and En-ergy Saving of a Novel Fibre Optic Lighting System’, in proceedings ofCleantech for Sustainable Buildings (CISBAT), pp. 317-322, Lausanne,Switzerland, 4-6 September (2013).

XIV D. Lingfors, T. Volotinen, ‘Illumination performance and energy savingof a solar fiber optic lighting system’, Optics Express Vol. 21, Issue S4,

pp. A642-A655 (2013).

XV S. Seipel, D. Lingfors, J. Widén, ‘Dual-domain visual exploration of ur-ban solar potential’, in proceedings of Eurographics Workshop on UrbanData Modelling and Visualisation, Girona, Spain, 6-10 May (2013).

Notes on my contribution

I contributed with the following in the appended papers:

Paper I, I did the solar forecasting literature survey and wrote about physicaland statistical solar forecasting methods.

Paper II, I built the solar loggers, characterized them, and wrote most of thepaper.

Paper III, I did most of the calculations and writing.

Paper IV, I did the modeling and wrote most of the paper.

Paper V, I did the PV production modeling and wrote about it.

Paper VI, I did the PV production modeling and smart allocation algorithmand wrote most of the paper.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Aim of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Overview of thesis and appended papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 An energy system in change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Perspective on energy systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 The transition of the energy system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Solar energy is already dominating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Transforming solar irradiance into useful energy . . . . . . . . . . . . 72.2.2 Solar energy in the world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 Solar energy in Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 The challenge of high penetrations of PV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 Grid integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Solar variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.3 Assessing solar variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.4 Geographical constraints limiting PV deployment . . . . . . . 132.3.5 Solar resource forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Research gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Methodology and data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Overview of methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 High resolution solar irradiation acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 PV power output on the tilted plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4.1 Solar irradiance on the tilted plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4.2 Modeling PV power output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.5 Roof topography and PV potential in the built environment . . . . . . . 223.5.1 Regional roof topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.5.2 Wide-area roof topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.6 PV scenario modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.7 Grid implications of high PV penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.7.1 Power flow simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.7.2 Increased hosting capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Solar variability assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.1 Validation of the solar logger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.2 Remaining challenges of the solar logger and workforward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.1.3 Correlation of dispersed PV systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Locations with potential for PV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Orientation of building roofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.2 Distribution of PV systems for a high penetration

scenario in Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Grid integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3.1 Hosting capacity in a MV distribution grid . . . . . . . . . . . . . . . . . . . 364.3.2 Impact on the power system for a high penetration

scenario in Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Concluding discussion and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1. Introduction

"You can change the world,You must change the world"

Howard Lyman in Cowspiracy (2014)

Since the start of the new millennium the global photovoltaic (PV) markethas grown almost exponentially, from less than 1 GW in 2000 to almost 180GW in 2014 [1]. The early development was mainly driven by Germany andJapan, the former still world leading by the end of 2014. Currently the demandfor energy increases much faster in Asia than anywhere else in the world,which also is reflected in the PV market. Very soon China is likely to have thehighest installed capacity of all countries. The production of PV modules fromChina has been one of the main driving forces behind the rapid expansion thelast 10 to 15 years.

In Sweden, the interest of PV was low until a subsidy program [2] was in-troduced in 2009, which in combination with decreasing prices on modulesand inverters has stimulated the market. Today, both residential house ownersand companies see the value of PV and with other recently introduced incen-tives [3] the payback time has become reasonable. Some municipalities haveeven set up their own goals on installed capacity [4].

Still the PV penetration in Sweden is low compared to Central Europe; 100times lower than in Germany for instance. However, countries like Germany,Italy and Spain are today experiencing problem with power quality due to thevariability of renewable energy sources, mainly wind and solar. For example,conventional power needs to be ramped in order to meet the increased demandin the afternoon as people come home from their daily activities and since thePV power generation goes down at the same time. This results in a daily pro-file of conventional power demand, popularly referred to as the duck curve byutilities [5]. As costs for PV continues to decrease and cost of conventionalpower increase, a similar future scenario is not unlikely for higher latitudes,like in Sweden. This calls for studies on the integration of PV in higher lati-tudes and what impacts it may have on the power system.

1.1 Aim of the thesisThe main purpose of the licentiate thesis is to develop methodology, which inturn can be used for variability assessment and grid-integration studies of PV

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on different spatiotemporal scales. This can be categorized into three mainaims, which are to:

(a) develop a methodology to assess short-term solar variability,

(b) map potential locations for PV deployment within the built environment,

(c) study the effect of distributed PV on the local power grid and nationalpower system.

Since there is a lack of high resolution data, especially for high-latitudes,the first aim requires some sort of solar irradiance acquisition methodology,as will be addressed in paper II and III. The PV penetration in the Swedishpower system is low today, but may be significant in the future as nuclearpower is shutdown and fuel prices are increasing. It is thus important to de-termine potential locations for PV deployment. Since the Swedish PV markethas expanded over the last years it is possible to develop a model that can pre-dict the future distribution of PV systems based on the current installations asis addressed in paper IV. Furthermore, there is a need to spatially link theselocations with the power system to study what impact the introduction of PVpower generation would have on the local power system as is addressed inpaper V and VI.

1.2 Overview of thesis and appended papersThis licentiate thesis is structured as follows. Section 2 first gives a generalbackground to the status of solar energy in the energy system today, and sec-ondly challenges of solar variability in the power system, more specificallyaddressed in this thesis, are described. Section 3 summarizes the method-ologies used in the appended papers and Section 4 presents the main results.Finally a concluding discussion and future work are presented in Section 5.The results of this licentiate thesis are based on the appended papers:

• Paper I reviews the current research status on variability and forecast-ing assessment for the renewable energy sources; wind, solar, wave andtidal. It was found that it is difficult to compare the methods applied forthe different sources, since the approaches differ as well as the presenta-tion of the results. There is thus a need to study the same methods for allresources for the same spatial and temporal domains and error metrics.

• Paper II describes the design and validation of a silicon-cell based datalogger, developed to measure global solar irradiance at a low cost, butreasonable accuracy. Validation shows that it is accurate compared to

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other similar data loggers and that it captures step changes in solar irra-diance well compared to a commercial thermal pyranometer. It can thusbe used for solar variability studies.

• Paper III presents results from a high resolution network of 6 data log-gers developed in paper II. An exponential isotropic model describingthe site-pair correlation of the loggers was found, similar to what hasbeen reported previously.

• Paper IV presents a PV power model for Sweden based on irradiancedata from the meteorological model STRÅNG and PV system data fromthe Swedish electricity certificate system. The model can be used forfuture scenario modeling of high PV penetration and what impact canbe expected on the power system.

• Paper V studies the PV potential in a community based on high reso-lution LiDAR data. It also shows how self-consumption of PV powercan be enhanced by introducing battery storage, individually owned orshared by the community and/or electric vehicle (EV) home-charging.The study shows that a shared battery is better utilized than individuallyowned are, which increases the self-consumption of the community asa whole, while the impact of EV charging is limited due to mismatchbetween charge patterns and PV power generation.

• Paper VI studies the hosting capacity for PV in a distribution grid of theSwedish rural municipality of Herrljunga. Low resolution LiDAR datais used to identify the potential of roof structures for PV generation andpower-flow simulations are conducted to find the hosting capacity of thegrid. By allocating PV systems in the strongest nodes, the hosting ca-pacity can be increased substantially compared to the baseline case.

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2. Background

In this chapter the background of the thesis is presented. First in Section 2.1 ageneral background of today’s energy system is presented and in Section 2.2the role of solar energy in the ebergy system. In Section 2.3 the challengeof solar variability and the integration of solar energy in the power system ispresented, which more specifically links to the work of this thesis. Finally,identified research gaps are presented in Section 2.4.

2.1 An energy system in change2.1.1 Perspective on energy systemsEnergy has always been in the service of humans, ever since we learned tocontrol fire. The main driving force of the industrial revolution is often con-sidered to be the invention of the steam engine, which made wind and watermills for power transmission obsolete and production efficiency could be in-creased by moving factories from the rivers to urban areas with abundance ofcheap working force. Coal and oil, with high energy density, have been avail-able at almost no cost throughout the last century, providing the foundationof the modern society. Before Silent Spring was published in 1962, writtenby Rachel Carson [6], little attention was given the environmental impact ofhuman activities in general, including the use of energy. Climate change dueto emissions of greenhouse gases was pointed out as early as 1896 by SvanteArrhenius [7]. However, still during the 1970’s, scientists did not agree onwhether we saw a global cooling effect due to increased amount of aerosolsin the atmosphere or a warming effect due to greenhouse gas emissions [8].Not until 1985 with the development of more sophisticated computer models aconsensus among scientists was formed around the anthropological impact onclimate change during the International Conference on the Assessment of theRole of Carbon Dioxide and of Other Greenhouse Gases in Climate Variationsand Associated Impacts in Villach, Austria [9]. Nuclear power was one solu-tion, but with the Three Mile Island and Chernobyl accidents in near memorythere was a growing opinion against a transition to nuclear power by the endof the 1980’s [10].

2.1.2 The transition of the energy systemBy the time of the Villach conference, energy from renewable sources wasmade up mainly of hydropower, but the take-off for wind power in the US

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1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

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Figure 2.1. Primary energy consumption in the world for different energy sourcesbetween 1965 and 2014 [12]

started in the 1980’s with Europe catching up in the 1990’s, mainly due toGermany and Denmark [11]. We now see photovoltaic (PV) power generationfollowing the same development as wind energy. Figure 2.1 shows the globalproduction from different sources over time. In 2014 primary energy demandfrom hydropower was 6.8% and other renewables made up by wind (1.2%),geothermal (0.9%), biomass (0.5%) and solar (0.3%). Renewables are gainingmarket shares of the global primary energy mix, but the challenge is that thedemand for fossil fuels is increasing faster in absolute numbers, mainly due tothe strong economic growth in Asia, as Figure 2.2 demonstrates. China, whichis the biggest user of fossil fuels today, sees other reasons than mitigation ofclimate gas emissions. The air quality in the densely populated cities is ofgreat concern and China is also one of the main drivers for the development ofrenewable technologies today. Critical voices from the public and scientists,symbolized by the work of the Intergovernmental Panel on Climate Change(IPCC) have forced politicians and world leaders to act. The work has beenintensified through and the numerous climate conferences the past 25 years,the transition towards a renewable energy system seems likely.

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Figure 2.2. Use of primary energy in different regions of the world between 1965 and2014 [12].

2.2 Solar energy is already dominatingMost energy used today derives from the sun. Oil, coal and gas originate fromplants remolded under high pressure for millions of years to high-density en-ergy sources. Wind and wave energy stems from solar irradiance heating theair. Hydropower origin from the evaporation of water due to the solar irradi-ance which later fills up the water reservoirs through precipitation. Sourcesthat are not driven by solar energy are geothermal, nuclear and tidal energy,the latter a result of the gravitational pull from the moon.

2.2.1 Transforming solar irradiance into useful energyIn less than an hour, solar energy hitting the surface of the earth can providethe world’s energy demand for a whole year [12]. Site-specifically the avail-ability of solar energy is limited by the rotation of the earth resulting in diur-nal and seasonal variations, but also shading and weather conditions such asclouds and mist limit the availability. Nevertheless, achieving cost efficiency iswhat today limits the implementation of solar energy conversion technologies.There are different ways of utilizing the solar irradiance. Passive use throughwindows for space heating and day-lighting has been around for thousands ofyears. Solar absorbers can be used for hot water and space heating and cen-tralized plants, where mirrors are concentrating the solar beams to heat steam,are being used to generate electricity in some places. On research level there

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is artificial photosynthesis, which mimics the photosynthesis in plants to pro-duce hydrogen. Lastly, solar cells can convert solar irradiance directly intoelectricity.

2.2.2 Solar energy in the worldPhotovoltaics (PV) is the main technology for direct conversion of solar en-ergy today. From being an expensive technology for space applications thetechnology is now widely used in applications ranging from cellphone charg-ers to large-scale PV fields. The system cost of PV has decreased substan-tially the last decade, making it competitive or close to competitive withoutsubsidies in some parts of the world. This is more common on islands and inareas without an existing power system where so called fuel parity has beenreached, meaning that PV installations are compensated by the fuel savings[1]. For grid-connected PV systems subsidies are still needed in many regionsto compensate for the difference between cost of electricity from the grid andgenerated from PV. Once PV is competitive without these subsidies grid par-ity has been reached. The early adopters of PV have been Germany, for whichgenerous feed-in tariffs have been offered the PV power producer, and Japan,where investment subsidies have resulted in a large PV market, concentratedto the residential sector. The introduction of subsidy programs has not en-tirely been a success story. In Denmark annual net-metering was introducedin 2012, which led to an installation rate 20 times higher than the previousyear, and high public costs [13]. Similar boom- and bust cycles have beenseen in many European countries, such as Spain, Bulgaria and the Czech Re-public, due to immature subsidy programs [1]. There are however indicationsthat grid-parity is being reached in several countries. For instance [14] claimsthat grid parity has been reached in 2014 for high consuming households inBrazil, Mexico, Germany, Italy, Australia and Japan. The grid parity conceptis however complex and depends on what assumptions that are made and whatsector that is analyzed [1]. Figure 2.3 shows the accumulated installed capac-ity of PV between 2005 and 2014 for different regions. Germany still has thelargest PV capacity but the installation rate has stagnated the last few yearsdue to decreased feed-in tariffs, which means that China is the probable worldleader when 2015 is summarized.

2.2.3 Solar energy in SwedenIn Sweden the PV penetration is low compared to the rest of Europe. Only0.06% of the power demand is covered by PV [15], which can be comparedto Italy, which is the country that has the highest PV penetration in the worldof nearly 8% [1]. The available solar irradiance in Sweden is often mistakenfor being too low for PV applications, when it actually is almost as good as

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2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

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Others

Figure 2.3. Accumulated installed PV capacity for different countries of the worldbetween 2005 and 2014 [1].

Central Europe [16]. However, this is not the main obstacle for PV deploymentin Sweden. The Swedish electricity mix consists of mainly hydro and nuclearpower, but also about 10% wind power. The power demand has decreased thelast few years which has led to an excess of power and low electricity prices.Not only solar energy is considered expensive but nuclear power plants areplanned to shut down within a few years due to loss of profitability and thewind power expansion has stagnated [17, 18]. However, a PV subsidy programintroduced in 2009 has given the Swedish PV market some push forward [2,15]. At the introduction, granted applicants were compensated for 60% ofthe system costs, but the level has decreased continuously to 20% in 2016.The interest has exceeded the available funds by far, which according to somecritics has slowed the market as potential PV producers wait for more fundsto be available before installing [19]. After net-metering was discussed forseveral years, instead a tax discount was introduced in 2015 [3], giving the PVpower producer some compensation for electricity fed into the grid. On top ofthat, some electricity suppliers’ compensation for sold PV power well exceedsthe electricity spot price, which means that selling the electricity has becomemore beneficial than to self-consume in some regions [15]. In the long runthis would be unsustainable from a grid perspective and electricity suppliersare likely to decrease the compensation as the PV market grows.

9

2.3 The challenge of high penetrations of PVThis Section gives a brief overview of current research on grid integration ofsolar power including some theory behind solar variability, what implicationit has on the power system and how it can be assessed. Finally some differentforecasting methods are described. A more thorough review of solar variabil-ity assessment and forecasting can be found in paper I.

2.3.1 Grid integrationThe variable nature of many renewable energy sources, such as wind, solaror tidal imposes challenges for the power grid operator. The challenge is notonly the transition from a power system dominated by fossil fuels itself, butthe integration of renewables in the power system, which originally was de-signed for centralized non-intermittent power plants. Traditionally there havebeen two concerns for the grid operator when it comes to power quality; (I) thevoltage quality, which is the impact of supply voltage on equipment, and (II)the current quality, which is equipment current impacting the grid and otherusers [20]. When distributed generation is introduced a third (III) quality as-pect is added, the tripping of generators caused by voltage fluctuations. Duringthese fluctuations generators trip in order not to interfere with the protectionequipment of the feeder and to avoid islanding of parts of the grid, whichcould be dangerous for maintenance personnel. Such an island would haveproblem maintaining normal frequency and voltage equipment might be dam-aged [20]. Distributed generators are therefore often equipped with protectionequipment which is automatically activated at power quality deviations dis-connecting it from the power system. The main challenge for the power sys-tem arise when multiple generators trip almost simultaneously for the samereason. Such events have happened in Italy 2003 [21], in Germany 2006 [22]and affecting most people, in India 2012 [23].

As distributed generation becomes more common, the grid operator mightwant to be ready to host the increased amount without risking the power qual-ity deviations described above. This upper limit of integrable distributed gen-eration is referred to as the hosting capacity of the grid. One simple, but oftenexpensive method to increase the hosting capacity is to reinforce the grid withthicker or new feeders. Other, dynamic methods that have been given a lot ofattention are curtailment of power at times of high voltages (see for instance[24]), real and reactive power control in the PV inverter [25] and demand-sidemanagement, for which the latter has been shown to be difficult to motivateeconomically for the PV owner [26]. Storage, most commonly in batteries[27, 28] is also one solution, a special case is to use the batteries of the ve-hicle, a concept referred to as vehicle to grid [29]. These dynamic methods,need to react both on the current load and power generation in the grid and thefuture. Hence, one of the main challenges is the forecasting of both load and

10

generation, which is difficult, due to the variability of distributed generationlike PV and wind power.

2.3.2 Solar variabilitySolar variability has two causes. It is mainly caused by the motion of theearth, rotating around its own axis and around the sun. Site-specific solarvariability follows diurnal and seasonal patterns, which become more promi-nent further away from the equator. This deterministic part of the variability iswell-known and can be described by mathematical formulas. There is howeveralso a stochastic component, caused by weather, in particular moving clouds.These changes happen over shorter time periods from seconds, during partlycloudy conditions, to a few days due to weather fronts.

The growing interest for PV power generation the last 20 years has mo-bilized researchers to enhance the understanding of the short-term variabilityinduced by cloud fields, since it is relevant for grid operators (see for instance[30, 31, 32, 33, 34, 35, 36, 37, 38, 39]). To remove the deterministic part ofthe variability two indices have been developed, namely the clearness indexand the clear-sky index. The first is defined as the ratio of the irradiance onthe earth surface to the extraterrestrial irradiance on top of the atmosphere.The clear-sky index, Kt∗, derives from the ratio of the ground irradiance to theclear sky irradiance, which is the irradiance at clear-sky for a given locationand time. The clear-sky irradiance depends on the position of the sun and onthe content of water vapor and aerosols in the atmosphere [40]. Once solarirradiation data with intra-hourly resolution have become available it has beenshown that the clearness index has a bimodal probability distribution, whosepeaks corresponds to clear and cloudy conditions respectively [41, 42, 43].Probabilistic models to reproduce this bimodality has been suggested, for in-stance in [44, 45].

What has been given special concern when characterizing solar variabilityis the ramp rate, originally used to describe the change in power over sometime period for a generator [46]. The step change in clear sky index can thus bedefined as ΔKt∗Δt for the time interval Δt. For a single location the variabilitycan be defined as the standard deviation of the change over some time periodT corresponding to the sum of time intervals Δt [32]:

σT (ΔKt∗Δt) =√

Var(ΔKt∗Δt). (2.1)

Since PV power generation in most regions is distributed it is interesting tostudy the impact on the power system from many aggregated PV systems. Theaggregated variability of the measured irradiance or PV power output fromdispersed sites has found to be lower than for a single site (e.g. [30, 33]).This is referred to as the smoothing effect and is central in solar variabilitystudies. The smoothing effect is illustrated in Figure 2.4 as the mean of the

11

12:20 12:25

Time (HH:MM)

0

100

200

300

400

500

600

GH

I (W

/m2)

Ind. siteMean

Figure 2.4. Global horizontal irradiance (GHI) with time steps of 1 s for 8 sites within340 m, on a partly cloudy day in September, 2014 in Uppsala, Sweden. The meanGHI of all sites is presented in bold. From paper III.

measured global horizontal irradiance (GHI) at 8 sites within 340 m and with1 s sampling interval (from paper III). Passing clouds causes fast fluctuationsat individual sites, but these are efficiently smoothed if looking at the meanirradiance at each time step of all sites. If separating the sites in distancesufficiently they become uncorrelated. The aggregated variability of N uncor-related identical ground sensors or PV systems can be expressed as [32]:

σN =1√N

σi, (2.2)

where σi is the variability for a single site, from Equation 2.1.

2.3.3 Assessing solar variabilitySolar variability can be assessed in many different ways. For some regionsthe solar irradiance has been measured with ground sensors and collected indatabases (see for instance [47]). Some of these databases are more thoroughlydescribed in [48]. In some cases, when measured irradiance is not sufficient,meteorological models are combined with measured data to create a griddeddata set, such as PVGIS, which provides daily values for Europe and Africa[49]. Semi-empirical models uses satellite images as inputs to derive the so-lar irradiance, for instance the SolarAnywhere model [50]. The highest spatial

12

resolution of these data sets is 250 m [51]. For higher resolution, both spatiallyand temporally ground measurements are thus needed. Thermal pyranometersfor ground measurements are considered the most accurate, since the sensoris designed as a black body radiator, like the sun, and thus sensitive to the fullsolar spectrum. The sensor, normally a metallic strip, is heated by the solarirradiance. The bending of the strip corresponds to the intensity of the solarirradiance [52]. However, due to the thermal intertia of the sensor, the thermalpyranometer is not recommended when very fast fluctuations are measuredsince the response-time is too long (a few seconds). For very fast fluctuationsphotoelectric sensors are better suited, due to the very short response-time.The accuracy is however worse, since the spectral bandwidth is limited [52].Other advantages are however the low cost compared to the thermal pyranome-ter and the simple construction (see for instance [53, 54, 55, 56]).

2.3.4 Geographical constraints limiting PV deploymentIn order to quantify the aggregated variability of solar irradiance or PV poweroutput it is important to map potential sites for PV deployment. Solar variabil-ity can be studied considering any arbitrary combination of sites across a givenregion. However, PV are not likely to be deployed just anywhere, based solelyon solar irradiance conditions. For instance, infrastructure in terms of roadsand power grid are needed and land-use should preferably not stand in conflictwith other possible applications or natural values. For the last decade there hasbeen a growing interest of creating solar maps or PV potential studies based ongeo-referenced data sets (for a comprehensive review, see [57]). For instance[58] developed a method to estimate the usable land-area for large PV fieldsin Ontario, Canada. More concern has been given the PV potential in the builtenvironment. Since existing roof structures and facades, in most cases, are notcompeting with other potential applications, the power can be used directly inthe building. Buildings are also most often connected to the grid. For largerregions, like countries or continents, the potential for PV in the built environ-ment has been estimated using statistics on building typologies from differenttime periods [59, 60, 61].

If the local PV potential for a city district up to municipality level is sought,the computational power of geographical information systems (GIS) can beused to make more detailed analysis of the building topography. The past fewyears GIS environments have been used to make solar maps to highlight thePV potential on existing roof structures. Some are using statistics or aerialimages [61, 62, 63]. In [64] a 3D model of a city district was created, throughmeasurements using a laser distance device. Recently LiDAR (Light Detec-tion And Ranging) data of high resolution has become readily available inmany regions of the world, especially in urban areas, automating the creationof 3D urban models. In short, LiDAR data is gathered by emitting light pulses

13

towards an object, which results in a point cloud that can be used to character-ize the morphology of the object. More specific for this context, satellites, air-planes or helicopters gather information about the ground surface by sendingout several signals of which some are reflected on canopies and other obstruc-tive objects. The time delay of the returns of the original signal can be used todistinguish for instance trees from ground or building surfaces. Methods fordistinguishing buildings from ground have also been developed, e.g. in [65].

LiDAR data has thus been used for PV potential studies on roof structures,e.g. in [66, 67], and in some cases also facades have been considered [68, 69].In Sweden a tool called SEES (Solar Energy on Existing Structures) was de-veloped [70], which has since then been used to produce solar maps for sev-eral Swedish cities. Google recently launched solar maps for some US cities,which suggests that these maps will be more common globally [71]. So farsolar maps have merely been used to estimate the PV potential of a region orto help property owners to identify roof structures with high solar irradiation.The next step would be to connect solar maps to the power grid infrastruc-ture in order to identify bottle necks in the grid in case of high penetration ofrenewables. Some work has already been done, for instance [72] developeda solar cadastre which highlights the bottlenecks of the Salzburg distributiongrid. There is however room for more research.

2.3.5 Solar resource forecastingForecasting solar irradiance has become increasingly important for transmis-sion and distribution system operators in markets with high penetration of PV.Even though comprehensive research has been conducted the last decade, stillonly a few utilities use solar forecasts for planning and operation of their grid[73]. For the utility, forecasts on two time domains are of interest; day-aheadforecasts (<48h) for resource planning and scheduling and intraday for loadfollowing and dispatch of conventional power to avoid real-time regulationas far as possible [73]. The Nordic power system is regulated mainly by hy-dropower from Sweden and Norway. For smaller hydro stations the flexibilityis relatively high. However, larger hydropower plants are supplied by waterfrom reservoirs some distance upstream, hence there is a time delay from themoment the water is untapped until it reaches the power station. Minimizingthe forecast error of variable energy sources is thus important since the oper-ation of larger hydropower plants need to be planned in advance. One shouldalso bear in mind that all hydropower stations downstream a large water reser-voir are affected, also the smaller ones, complicating the planning of the powersystem further.

Figure 2.5 (from paper I) presents an overview of different forecast tech-niques of solar, wind and wave energy and in what spatial and temporal do-mains they are best suited. For sub-minute forecasting, persistence models are

14

1Temporal resolution (h)

10 100 10000.1

100

10

1

0.1

0.01

Spat

ial r

esol

utio

n (k

m)

GFSgfsGFSgfsgGFSgfsGFSgfsGFSgfs

Solar Wind Wave

TSI

Satellite Images

Intra-hour Intra-day Day ahead

Persistence Statistical Physical

Figure 2.5. Recommended forecasting methods for wind, solar and wave power ondifferent spatiotemporal domains. The idea of the figure including the regions forsolar forecasting methods build on Fig. 4 in [87] here extended with data for wind andwave forecasting methods. From paper I.

preferred. In a persistence model the clear-sky index is predicted to remainunchanged some time ahead. Wind and wave energy are not experiencingsuch fast fluctuations as solar, thus the persistence model works over longertime periods and spatial extent. Forecasting models can roughly be dividedinto statistical and physical models. As Figure 2.5 shows statistical modelsare preferred at higher spatial and temporal (<6h) resolution, with some ex-ceptions; a total sky imager (TSI) [74, 75] or satellite images [76, 77, 78] canbe used to analyze the evolution of cloud fields. Statistical models can furtherbe categorized into time-series modeling, such as auto-regressive (AR) mod-els often combined with moving average (MA) and exogenous (X) input (e.g.[79]) and learning algorithms for which artificial neural networks (ANN) havebeen studied immensely the past few years (see [80] for a summary). For long-term forecasting, from a few hours to days physical models referred to as nu-merical weather prediction (NWP) models are used, which except from solarirradiance, take other atmospheric data as input, such as wind fields, tempera-ture, air pressure and humidity. Examples of NWP models are SolarAnywhere[50, 81], GFS (Global Forecasts System) [82], ECMWF (European Centre forMedium-Range Weather Forecasts) [83], NAM (North American Mesoscale)[84] and RR (Rapid Refresh) [85] (for a comprehensive review and compari-son of the models see [81, 86]).

15

2.4 Research gapsThe previous sections have highlighted some interesting research topics thatcould be further investigated, since there are still research gaps to be filled.Here these gaps are summarized and linked to the appended papers in this the-sis. The following research gaps have been identified:

• High-latitude conditions are characterized by distinct seasonal variationsin power demand, high in winter and low in summer. For the solar irra-diance availability it is the other way around, which implies that specialstudies of the solar variability and its impact on the power system are re-quired for high latitudes. This is addressed in all of the appended papers.

• High resolution irradiance data is needed to better understand short-term (sub-minute) solar variability caused by passing clouds. This re-quires a methodology to assess solar irradiance data, which is not exten-sively available today. Furthermore, data collected for several spatiallydispersed sites would contribute to an increased understanding of theaggregated short-term variability over a region and could be used in thedevelopment and validation of new models. This is addressed in paperII and III.

• High resolution mapping of the built environment is important in orderto assess potential locations for PV deployment. As discussed in Section2.3.4 solar maps are not new and has been produced for many urban ar-eas worldwide. However, the link between potential locations for PV inthe built environment and the impact on the grid is often missing. Thisis addressed in paper V and VI.

• Impacts on the local power system are mutually linked with the pre-vious bullet point. Localities that are likely to be used for future PVdeployment in the built environment, should be combined with studieson actual distribution grids with real end-user consumption data. This isaddressed in paper VI.

• Impacts on the national power system need to be studied for high-latitudeconditions. In the Nordic power system, hydropower plays an importantrole in balancing of power and enables a relatively high penetration ofrenewable energy sources in the power system compared to southernEurope. A first step to quantify this potential is taken in paper I wherethe existing research on variability assessment and forecasting for solar,wind, wave and tidal energy is addressed. In paper IV a PV model forSweden is developed which could be extended to a larger region.

16

3. Methodology and data

In this chapter methodologies and data used in the appended papers are pre-sented. Data is briefly presented in Section 3.1 and summarized in Table 3.1.In Section 3.3 - 3.7 the methodologies will be further described in the sameorder as they appear in Table 3.2. Since paper I is a review, thus only concernswork of others, it is not included in Table 3.1 and 3.2.

3.1 DataSolar irradiance data for paper II and III was collected with the solar logger.For paper IV and VI hourly global horizontal and direct normal irradiancefrom the meteorological model STRÅNG was used, which covers northernEurope with a resolution of 11 × 11 km [88]. 1-minute data used in paperV was obtained from the Swedish Meteorological and Hydrological Institute(SMHI) for Norrköping (N58.58◦, E16.15◦), Sweden. High resolution LiDARdata are in some cases collected in cities for urban planning. This was donefor the densely populated areas in Uppsala municipality (UM) and could thusbe used in paper V. Low resolution LiDAR data on the other hand, are readilyavailable for almost all of Sweden through the geodata cooperation agreementbetween universities and the Swedish land survey authority, collected in or-der to create a new national elevation model [89]. This data was validatedagainst the high resolution data in Uppsala in paper X and was also used inpaper VI to map potential roof tops for PV power generation. Statistics ofthe building footprints on county level, used in paper IV, was obtained fromStatistics Sweden [90]. Maps of the building footprint and property borderswhere also obtained within the geodata cooperation agreement. PV systemdata, including installed capacity, location, date of connection and expectedannual power production was provided from the Swedish Energy Agency [91].Hourly Swedish power consumption and PV power production were obtainedfrom the Swedish TSO [92]. Lastly, hourly consumption data for about 5 000customers, and line impedances of the distribution grid of Herrljunga Elek-triska AB (HEAB) were provided for the grid integration analysis in paperVI.

3.2 Overview of methodologiesThe methodologies used in this thesis are listed in Table 3.2 and are linked toeach other as follows. A methodology for assessing high resolution solar irra-

17

diance data is presented in Section 3.3, and could be used for future studies ondistribution grid level. However, here irradiance data of lower resolution wasused from elsewhere to compute the PV power on the tilted plane, explainedin Section 3.4. To quantify the PV potential in the built environment, rooftopswere identified with both high and low resolution following the methods inSection 3.5.1 and 3.5.2 respectively. Once potential rooftops are identified,future scenarios of PV deployment can be conducted, described in Section3.6, and the impact on the distribution grid can be studied, described in Sec-tion 3.7.1 and 3.7.2.

Table 3.1. Data used in each paper of the thesis.

Data Ref. Paper

II III IV V VI

Solar irradiance- Solar Logger (<1 min) - � �- Hourly [88] � �- Minute SMHI �LiDAR- High resolution (50 pt/m2) UM �- Low resolution (0.5-1 pt/m2) [89] � �Temperature [93] � �Building footprint statistics [90] �Building footprint map [94] � �Property map [94] �PV system data for Sweden [91] �Swedish power consumption [92] �Swedish PV power production [92] �Herrljunga grid HEAB �

Table 3.2. Methodologies used in each paper of the thesis.

Methodology Section PaperII III IV V VI

Irradiation acquisition 3.3 � �PV power on tilted plane 3.4 � � �Roof topography mapping 3.5- Regional (GIS) 3.5.1 � �- Wide-area (Statistics) 3.5.2 �PV scenario modeling 3.6 � �Power flow simulations 3.7.1 �Smart allocation 3.7.2 �

18

Figure 3.1. The solar logger. Both sides of the printed junction box (middle and right)and the junction box for which the electronics are kept (left). The white circle in themiddle of the junction box lid is the PTFE window, under which the photodiode isplaced.

3.3 High resolution solar irradiation acquisitionThere is a lack of high resolution solar irradiance data for the Nordic coun-tries. SMHI has collected hourly values at 12 sites in Sweden since 1983 [95]and as Table 3.1 shows 1-minute data has been collected for Norrköping for afew years and STRÅNG provides gridded data for northern Europe [88], butwith a rather low accuracy of 30% root mean square error (RMSE) for hourlyglobal horizontal irradiance (GHI) and 57% RMSE for direct normal irradi-ance (DNI) of individual sites [96]. In order to study sub-hourly solar vari-ability, irradiance need to be assessed in another way. Therefore a data loggerwas developed, initially started as a bachelor project [97], that can collect solarirradiance data with high resolution, here after referred to as the solar logger(SL). The design is described in detail in paper II. In short the global solar irra-diance is diffusely transmitted through a polytetrafluoroethylene (PTFE) win-dow and detected by a BPW34 silicon photodiode [98]. The time is measuredby a software real-time clock, which utilizes an external 32.768 kHz quartzcrystal and is updated via a global-positioning (GPS) module every other hour[99]. It also measures temperature by a DS18B20 digital thermometer [100].All electronics is controlled by an ATMEGA328(P) micro-controller [101]programmed in C. Figure 3.1 shows the printed circuit board of the SL and thejunction box in which the electronics are kept during operation. The perfor-mance of the SL was validated against a commercial Kipp & Zonen CMP11secondary standard pyranometer [102], in terms of instantaneous irradianceand step changes of the irradiance on different time scales.

3.4 PV power output on the tilted planeIn this section the methodology for calculating the PV power output on thetilted plane is described. First the methodology for deriving the solar irradi-ance on the tilted plane is presented in Section 3.4.1 and secondly a model

19

for the PV power generation in Section 3.4.2. The methodologies are used inpaper IV, V and VI.

3.4.1 Solar irradiance on the tilted planeIrradiance data are in most cases available for the horizontal plane as beam(Gb) and diffuse (Gd) part and since PV systems often are tilted to maximizethe output or to match the load, a model is needed to calculate the irradianceon the tilted plane. No model development was carried out within this thesisand the model used in the appended papers is therefore only briefly describedhere. The irradiance on the tilted plane can be calculated following the Hayand Davies model described in [103], which is also summarized in [104]. Allimportant angles for computing the irradiance on the tilted plane is presentedin Figure 3.2. The global solar irradiance is normally separated into threeparts:

GT = GbT +GdT +GgT , (3.1)

where GbT , GdT and GgT is the beam, diffuse and ground-reflected componentof the irradiance respectively. The beam component depends on the positionof the sun in the sky and the content of water vapor and aerosols in the at-mosphere. The diffuse part is, in the Hay and Davies model, considered asisotropic, meaning that it is uniformly distributed from all directions. This isa simplification, but it has been shown that the model perform well comparedto other more sophisticated models [105]. The angle of incidence, θ , can becalculated from all angles in Figure 3.2 as:

cosθ =sinδ sinφ cosβ− sinδ cosφ sinβ cosγ+ cosδ cosφ cosβ cosω+ cosδ sinφ sinβ cosγ cosω+ cosδ sinβ sinγ sinω

(3.2)

For a horizontal plane Equation 3.2 simplifies as:

cosθZ = cosδ cosφ cosω + sinδ sinφ . (3.3)

From θ and θZ , GbT can be computed as:

GbT =cosθcosθZ

Gb. (3.4)

The diffuse irradiance on the tilted plane, GdT is calculated as:

GdT = Gd

[(1−Ai)

(1+ cosβ

2

)+

cosθcosθZ

Ai

], (3.5)

20

(a)

LlocEarth

Sun

Ecliptic

Celestialequator

23.45°

(b)

Figure 3.2. a) Angles describing the sun position including the declination angle (δ ),hour angle (ω) and the longitude or local meridian (Lloc). b) Angles used to computethe solar irradiance on the tilted plane including the zenith angle (θZ), surface tilt (β ),surface azimuth angle (γ) and latitude (φ ). Reproduced with permission from [106].

where Ai is the anisotropic index calculated as the ratio of the beam irradianceon the horizontal plane to the theoretical beam irradiance if the atmospheredid not exist. Finally the ground-reflected irradiance GgT can be calcultaed as:

GgT = (Gb +Gd)ρg

(1− cosβ

2

), (3.6)

where ρg is the reflectance or albedo of surrounding objects seen by the plane,such as trees, buildings and ground. For colder climates this may vary sig-nificantly with season due to snow coverage. The model does not considershading from surrounding objects, such as trees and other buildings. Since thebeam component is most affected by shading, it was set to zero for cosθ <cosθlim, where the value of θlim was searched in order to optimize the modelin paper IV (see Section 3.6).

3.4.2 Modeling PV power outputIf no losses are assumed the DC output from a PV array can med modeled as:

Pdc = AGT ηSTC, (3.7)

where A is the area of the PV array and ηSTC is the PV module efficiency atstandard test conditions (STC), assumed to be 15% in all papers appended inthis thesis. The conversion efficiency of the PV cell is affected by the celltemperature, which in turn depends on the incident solar irradiance and theambient temperature. The conversion efficiency can be calculated from [107]as:

21

ηc = ηSTC

[1−μ

(Ta −Tc,STC +GT

Tc,NOCT −Ta,NOCT

GNOCT(1−ηSTC)

)], (3.8)

where μ = −0.0047 ◦C −1 is the temperature coefficient for cell efficiency,Ta is the ambient temperature, Tc,STC = 25 ◦C is the cell temperature at STCand Tc,NOCT , Ta,NOCT = 20 ◦C and GNOCT = 800 W/m2 are cell temperature,ambient temperature and incident radiation at what is used to be referred to asthe nominal operating cell temperature (NOCT). If temperature is consideredthe DC output of the PV array would be:

Pdc = AGT ηc. (3.9)

If losses in the inverter are neglected the AC output of the system is Pac =Pdc. However, including the inverter could be important as the generatedpower from a PV array at high solar irradiance could exceed the rated power ofthe inverter, leading to high DC powers being cut by the inverter. The Sandiainverter performance model was used to for the AC output power as [108]:

Pac = Pac0Pdc −Ps0

Pdc0 −Ps0, (3.10)

for Pdc values between Ps0 and Pdc0, where Pac0 is the rated inverter AC power(same as the rated PV power), Pdc0 is the rated DC input power of the in-verter, here assumed to 3.3% higher than rated PV power and Ps0 is the in-verter threshold power, i.e. the lowest DC input that gives an AC output, hereassumed to 0.5% of rated PV power. Below Ps0 the output is zero and abovePdc0 it is limited to Pac0.

3.5 Roof topography and PV potential in the builtenvironment

In this section building statistics and GIS are presented as means to assess thetopography of the built environment and the potential for PV power genera-tion. The methodologies were applied in paper IV, V and VI.

3.5.1 Regional roof topographyRegional roof topography in the built environment was assessed using LiDARdata and building footprints in a GIS environment, corresponding to the workin paper V and VI. An overview of input data (grey boxes) and model steps(white boxes) is presented in Figure 3.4, including the PV power generation

22

Figure 3.3. Aerial LiDAR image of the studied area in Paper VI showing the yearlysolar irradiation. The buildings included in the study are numbered from 1 to 21.

modeling, described in Section 3.4. This section will focus on the method-ology, which was somewhat similar for paper V and VI, but with some dif-ferences, mainly due to the resolution of the available LiDAR data (see Table3.1). References to the boxes in Figure 3.4 will be presented in italics in thefollowing.

From the LiDAR data a digital surface model (DSM) was derived (BuildingDSM). The building footprint map, provided by the Swedish land survey au-thority [94], was used to distinguish rooftops from other features. In ArcGIS[109] the Solar Analyst was used to compute the annual solar radiation (An-nual GT) on the roof tops [110]. The Solar Analyst considers shading fromsurrounding objects, such as trees and other buildings. Thus rooftops interest-ing for PV power generation can be identified.

In paper V, LiDAR data of high resolution (50 pt/m2) was used, which madeit possible to classify azimuths of the roof segments with high accuracy. Theclassification procedure is summarized in Figure 3.5. For each building, rastercells (0.4 × 0.4 m) of the building DSM were assigned the nearest peak of akernel density estimation of the azimuths of all cells. In this way the mainroof segments could be identified, for which cells with deviant azimuths wereexcluded. Normally these excluded cells represents the fringe of the roof orroof installations, such as chimneys, and is thus not suitable for PV. The kerneldensity method (more thouroghly described in paper V) works well for simpleroof structures such as the pitched roofs in the residential area studied see Fig-ure 3.3). For more complex roof structures, some kind of clustering of rastercells would be desirable to distinguish roof segments of similar azimuth fromeach other. Next, the irradiance on the tilted plane (GT Model) was computed,following the method in Section 3.4. In the last step (PV model), only cells

23

Minute+GHorDHor

PV Prod.(Building)

GTiltModel

Solar Analyst

BuildingFootprint

High ResLiDAR

Filter>X kWh

LiDARBuilding

DSM

AnnualGT

MinuteGT

ClassifyAzimuth

PVModel

a) Paper V b) Paper VI

GTiltModel

Solar Analyst

BuildingFootprint

Low ResLiDAR

Hourly+GHorDHor

Filter>X kWh

LiDARBuilding

DSM

PropertyMap

AnnualGT

HourlyGT

GridData

GridPotential

PowerFlow

PV prod.(Bus)

PVModel

Figure 3.4. Flow charts of the methodologies used in papers V and VI to derive thePV potential with a) high resolution on building level in a community or city and b)low resolution aggregated on medium voltage buses in a distribution grid. Grey boxesrepresents data and white model steps.

having annual solar irradiance exceeding 950 kWh/m2 were considered for PVdeployment (Filter > X kWh).

In paper VI, the resolution of the available LiDAR data was lower (0.5-1pt/m2) [89], making the method used for high-resolution LiDAR data non-applicable. The low resolution LiDAR data was validated against high res-olution data in paper X and the validation is presented in Figure 3.6. Thelow resolution data captures the annual solar irradiation well, as Figure 3.6a) shows, at least for high irradiation levels (> 800 kWh/m2,yr). For thelow-resolution data the mean tilt of the building roofs is higher than for thehigh-resolution data as Figure 3.6 b) reveals. This is probably caused by thetilt being over-exaggerated at the fringe of the roof. The tilt in each rastercell is estimated from the altitude of surrounding cells, which means that cellsrepresenting ground will influence the mean tilt of the roof to a larger extentwhen low-resolution data are used. This probably also explains the relativeerror |GH −GL|/GH , where GH and GL is the total solar irradiance on each

24

Figure 3.5. Example of identification procedure of the most suitable roof segmentfor PV installation and its azimuth angle for a building. (1) is the Kernel densityestimation of the azimuths of all raster cells of the roof, (2) are the identified azimuthsof the (in this case two) roof segments, (3) marks the azimuth of the most suitableroof segment, (4) is a histogram of all the azimuths and (5) only for raster cells withan annual solar irradiance of >950 kWh/m2,yr. Bins of (5) reaching above the dashedline (10 % of max bin) are assigned to the nearest azimuth peak (2) along the x-axis.From paper V.

building for the high- and low resolution data set respectively. Figure 3.6 c)shows that the relative error is higher for smaller buildings. Hence the rooffringe represents a larger share of the total roof area. Since the main objectiveof paper VI was to study the impact of the aggregated PV power generationon the medium voltage level of a distribution grid, the lower level of accu-racy compared to high resolution data presented in Figure 3.6, was consideredacceptable. Here the azimuth and tilt of each cell was categorized (see Fig-ure 3.7 for an example), for which the irradiance on the tilted plane and thePV power generation was pre-calculated for each of the categories in order tosave computational time. The PV power production was finally aggregated onthe medium voltage (MV) bus that the building was connected to (PV prod.(Bus)). Buildings where linked to their corresponding MV bus spatially in Ar-cGIS [109] through the coordinates of the MV buses found in the grid dataand the property map [94].

3.5.2 Wide-area roof topographyIn paper IV statistics of the building footprint on county level [90] was used tomodel the aggregated PV power generation of the Swedish electricity marketbidding areas (see Figure 4.5). In order to keep the model simple it was fit-

25

0 0.2 0.4 0.6 0.8 1Share of cells

0

500

1 000

1 500kW

h/m

2,y

r(a)

HighLow

0 30 60 90Cell tilt (°)

0

50

100

150

200

250

Num

ber

of b

uild

ings

(b)

HighLow

0 500 1000 1500 2000 2500 3000Roof area (m2)

0

0.5

1

|GH

- G

L|/G

H

(c)

ind. buildingsmean

Figure 3.6. Validation of low resolution LiDAR data, against high resolution data, on504 buildings in Uppsala. The figure shows in a) the cumulative distribution of annualirradiance per raster cell, in b) a histogram of the mean roof tilt of each building andin c) the relative error |GH −GL|/GH in total irradiance of low resolution comparedto high resolution. From paper X.

ted against historical data assuming one fixed value of the tilt β and azimuthγ for all PV systems. As discussed in Section 2.3.4 this is a simplificationand the actual PV system orientation depends on roof typography, which inturn depends on the type of building and current architectural preferences bythe time it was built. The model in paper IV comprises the aggregated PVgeneration of Sweden, which means that the level of detail on the orientationof the individual buildings become less important than if looking at a limitedarea. Since building footprints were not available for each of the 1960 uniqueSwedish localities (city or small village), it was calculated as:

Al =Nl

NcAc, (3.11)

where Nl is the number of residents of locality l, Nc and Ac are the number orresidents and building footprint area of county c. The building foot print wasweighted on county level rather than national because difference in popula-tion density gives a lower footprint area per capita in more densely populatedcountys. Higher resolution than county level was not available.

26

-100 0 100

Azimuth (°)

0

20

40

60

80T

ilt (°)

All available roofs

0 500 1000 1500kW

-100 0 100

Azimuth (°)

0

20

40

60

80

Tilt

(°)

Irradiance > 700 kWh/m2/y

0 200 400 600kW

-100 0 100

Azimuth (°)

0

20

40

60

80

Tilt

(°)

Irradiance > 1000 kWh/m2/y

0 50 100kW

Figure 3.7. Potential PV generation capacity on agricultural building roofs in theHerrljunga grid, with three different requirements on annual irradiance. Note that thescale of the color bar differs between the subfigures. From paper VII.

3.6 PV scenario modelingIn paper IV a model was developed, intended to be used for scenario model-ing for different penetrations of PV in the power system. First scenarios wereapplied on Sweden, but it will also be tested for other regions. The model wasfirst trimmed against reported PV power production data for 2014 reported tothe Swedish TSO [92]. An overview of the model development is presentedin Figure 3.8, for which gray boxes represents data and white boxes modelsteps. References to the boxes in Figure 3.4 will be presented in italics. Adetailed description of the model can be found in paper IV. Hourly irradiancedata from STRÅNG [88] and data for PV systems within the Swedish elec-tricity certificate system were used as inputs to the model. The numbers inFigure 3.8 indicates the order of the iteration processes to find the best modelparameters. Since tilts and azimuths of the systems were unknown, fixed val-ues were sought, which gave the lowest unbiased RMSE or standard error forthe model compared to reported data (1). Shading (2) was modeled by find-ing an optimum cosθlim (see Section 3.4). Temperature and inverter models,described in Section 3.4.2, were considered for being either included or not(Y/N) in the PV model (3-4). When the first results of the model were ana-lyzed it was noted that the bias was significant. The reason for this seemedto be a discrepancy between reported and expected power production stated inthe PV system data [91]. Hence, some of the self-consumed production wasnot reported to the TSO. Therefore a self-consumption correction (SCC) wasconducted, which lowered the bias substantially. The model was validated for2012 and 2013 respectively.

Next scenarios of high PV penetration could be developed from the model.In order to find a likely distribution of PV systems, since this will affect theaggregated power output a weighting function (WF) was developed, which

27

Temp(Y/N)

GTiltModel PV Sys.

Location

Hourly+GHorDHor

HourlyGT

PVModel

TiltAzimuth

LiDARStandardError

cos lim

Shading

Inverter(Y/N)

1 2

43

5

Done

1

4

PV Sys.Wp

SCC

Validate

PV Sys.Exp prod.

3 1BiasCorrect

Figure 3.8. Flow chart of the model development in paper IV. Gray boxes representsdata, and white boxes model steps. The numbers represent iteration loops to find bestmodel parameters.

consider the building footprint area Al from Equation 3.11, and the solar irra-diation Gl for a normal year at each location as:

WF = AlGnl , (3.12)

where n was derived by fitting the WF against the current distribution of PVsystems within the PV subsidy program [2].

3.7 Grid implications of high PV penetrationIn the design and operation of a transmission or distribution grid it is importantto study the dynamics of the grid when different levels of distributed renewableenergy sources are integrated. In [20] it is suggested that power flows shouldbe measured to allow better planning of the operation of the power system.This is however often difficult to motivate economically, especially in a distri-bution grid, and it could even be difficult to find good grid candidates with highpenetration of distributed generation. If grid structure and line impedances areknown, power-flow simulations could be performed to investigate the hostingcapacity of the grid, and ways to increase it.

3.7.1 Power flow simulationsFor the power flow simulations the Newton-Raphson method was used in orderto solve the power flow equations of the system. The method was initially

28

implemented in Matlab [111] by Widén and is more thoroughly described in[106].

3.7.2 Increased hosting capacityOne important aspect in the transforming to a renewable energy system is toincrease its hosting capacity for intermittent power generation (see Section2.3.1. A method was developed to increase the PV hosting capacity in the dis-tribution grid and was applied on the medium voltage (MV) grid in Herrljunga(paper VI). When running power flow simulations, it was noted that for somenodes of the grid the maximum hourly voltage over the year increased substan-tially when PV was introduced, while other nodes stayed almost unaffected.By allocating more PV in the strong nodes of the grid and less in the weak, thehosting capacity could be increased. This was done by lowering the annualirradiation threshold level from 950 to 700 kWh/m2, hence allowing PV mod-ules on more roof segments. This pushed the maximum voltage well above theovervoltage margin (1.05 p.u.) of the MV grid in several nodes. PV systemswas then removed in weak nodes following the steps in Figure 3.9 until theovervoltage margin was not exceeded in any node or hour during the year. Inthis way a new hosting capacity of the grid could be found.

V > 1.05 p.u.?max

Power flow simulation of this hour

Validate for full year

Identify most common hour of max Voltage

Find node i ofhighest voltage

PV in node i?

Yes No

Remove PV systems in

node i

Remove PVsystems in

neighbor node

NoYes

Power flow simulation

V > 1.05 p.u.?max

NoYes Done

Figure 3.9. Flow chart of the smart allocation methodology from paper VI for increas-ing the PV hosting capacity in the grid.

29

4. Results

This chapter summarizes the results from the appended papers. In Section4.1 results from paper II and III are summarized corresponding to the firstaim of the thesis (see Section 1.1), to assess high resolution solar variability.In Section 4.2 results from paper IV, V and VI corresponding to the secondaim is presented, to map potential locations for PV deployment within thebuilt environment. Finally in Section 4.3 results from paper IV, V and VI arepresented corresponding to the third aim, the impact of distributed PV on thepower system.

4.1 Solar variability assessmentHere the results of assessing high resolution solar irradiance and variabilitythrough the solar logger, from paper II and III, are presented.

4.1.1 Validation of the solar loggerThe intention of the solar logger (SL) described in Section 3.3 and in paperII is to capture high resolution global solar irradiance with reasonable accu-racy and low cost. The uncalibrated output of the SL follows an almost linearrelationship with a commercial Kipp & Zonen CMP11 thermal pyranome-ter, a quadratic calibration only improves the RMSE marginally compared tothe linear as Figure 4.1 shows. The performance is in line with previouslypresented loggers [56, 112, 54, 55, 113, 53, 114, 115]. The SL should alsocapture short-term (seconds to a few minutes) solar variability. Step changesof the SL compared to the Kipp & Zonen pyranometer are presented in Figure4.2 for different time scales. Due to the response time (< 5s) and samplinginterval of the Kipp & Zonen pyranometer the shortest time step is limited to10 seconds. As can be expected the correlation increases with time scale.

4.1.2 Remaining challenges of the solar logger and work forwardIn the field tests of the SL, the accuracy of the solar irradiance acquisitionis high, but still some challenges need to be solved before the SL can oper-ate with confidence for a longer time period without maintenance, preferablyfrom a few months up to a year. The battery consumption is too high and varies

31

Solar logger (a.u.)0

100

200

300

400

500

600

700

800

900

1000

Pyr

anom

eter

(W

/m2)

RMSE of linear fit: 16.9 W/m2

RMSE of quadratic fit: 16.5 W/m2

linear fitquadratic fit

Figure 4.1. Linear and quadratic fit of the SL data to measured solar irradiance by aKipp & Zonen CP11 secondary standard pyranometer. From paper II.

1 0.5 0 0.5 11

0.5

0

0.5

1

t = 10 s

RMSE of y = x: 0.029

CSI step change, Solar Logger ( )

CS

I ste

p ch

ange

, Pyr

anom

eter

()

RMSE of y = x: 0.015

t = 1 min t = 5 min

RMSE of y = x: 0.014

t = 30 s

RMSE of y = x: 0.020

scattery = x

1 0.5 0 0.5 11

0.5

0

0.5

1

1 0.5 0 0.5 11

0.5

0

0.5

1

1 0.5 0 0.5 11

0.5

0

0.5

1

1 0.5 0 0.5 11

0.5

0

0.5

1

Figure 4.2. Step change of CSI for a SL on the x-axis and for the Kipp & ZonenCMP11 secondary standard pyranometer on the y-axis, repeated for averaged CSIover four different time scales; 10 s, 30 s, 1 min and 5 min. RMSE (-) of the idealmatch (y=x) is presented for each plot. From paper II.

32

between individual loggers from 3 to 7 weeks when logging every second. In-creasing the sampling interval should increase the life time of the batteries,but the power consumption of the components is not yet fully examined. Onesolution when applicable is to connect the SL to the power grid, but still oneof the most important features is its flexibility and non-dependance of the grid,like for projects in developing countries, with regular black-outs or no accessto the grid. A second version is under development, and early results, notpresented in paper II, indicate lower power consumption, mainly due to a lesspower consuming GPS unit, but also due to software updates. The secondchallenge is air and moisture penetrating the junction box where the electron-ics of the SL are kept, even though the box is IP67 classed. Condensed watercauses corrosion on the circuit board and eventually the SL short-circuits. Twosolutions have been identified for this issue. First the junction box could bemade tighter or replaced by a better box and equipped with silica gel. Thesecond solution is to add a ventilation hole strategically, still with the risk ofhaving water filling the box during heavy rainfall.

4.1.3 Correlation of dispersed PV systemsOnce a robust data acquisition method is found, short-term solar variabilitycan be studied. In paper III this was done by placing six SL along a 120 mstraight line on a building roof top with a clear view of the sky (cf. Figure 2in paper III). The Pearson cross-correlation coefficient was computed for eachstation-pair and a exponential model was derived similar to previous modelsfor wind [116, 117] and solar power [118, 33, 37]:

ρ = e−λ

di, jΔt1/2 , (4.1)

where λ [m-1s1/2] is an empirical fit parameter, di, j is the distance betweenstation i and j and Δt is the time length of the step change. However, sucha model does not take the direction of the cloud movements into account. Ina study on Hawaii it was shown that the along- and cross-wind correlationsdiffer significantly [119]. In the study, wind and cloud direction was highlycorrelated, which may not be the case for other locations. More recently [120]developed an improved model for the correlation in the direction of cloudmovement. The SL could be used to validate such a model. The station-pair cross correlations of the clear sky index step change for different timescales are presented in Figure 4.3 including the exponential model in 4.1 as areference. The value of λ differs slightly depending on time scale (cf. β inTable 1 of paper II).

33

0 50 100 150

Distance, di,j

(m)

0.2

0.4

0.6

0.8

1

ross

-co

rrel

atio

n

t = 10 s

0 50 100 150

Distance, di,j

(m)

0

0.2

0.4

0.6

0.8

1

ross

-co

rrel

atio

n

t = 30 s

0 50 100 150

Distance, di,j

(m)

0

0.2

0.4

0.6

0.8

1

ross

-co

rrel

atio

n

t = 60 s

0 50 100 150

Distance, di,j

(m)

0

0.2

0.4

0.6

0.8

1

ross

-co

rrel

atio

n

t = 1 s

ID = 00f4ID = 1477ID = 1488ID = 1483ID = 1434ID = 146bExponential Fit

Figure 4.3. Cross-correlations of the clear sky index step change as a function ofdispersion distance for different time scales; Δt. The exponential fit model of Equation4.1 is also presented. Modified from paper III.

4.2 Locations with potential for PVAs earlier discussed in Section 3.5 utilizing existing roof structures for PV isbeneficial for several reasons, such as placing power generation close to theend-user and efficient use of land area. Here results are presented of map-ping the built environment on different levels, from low resolution aggregatedon county level in paper IV (Section 4.2.2) to high resolution on individualbuilding level in paper V and VI (Section 4.2.1).

4.2.1 Orientation of building roofsThe orientation or azimuth of a PV system typically follow the orientation ofthe south-most facade of the building, and should therefore in average facesouth if assuming uniform distribution of building orientations. This assump-tion was made in paper IV, for which the whole of Sweden was studied. Fora given region it is however not always the case as was shown in paper X,where the PV potential of the Swedish county of Blekinge was investigated,covering an area of about 3 000 km2. As one can see in Figure 4.4 a) it wasfound that buildings are more likely oriented in north-south or east-west ratherthan somewhere in between. One theory is that the topography of Blekingewith water run-off in the north-south direction (see Figure 4.4 b)) results in

34

-90 -60 -30 0 30 60 90Orientation (°)

0

5000

10000

15000N

umbe

r of b

uild

ings

(a) (b)

Figure 4.4. a) Histogram of the orientation of the south-most long side of buildings inthe Blekinge county and b) water streams in Blekinge county. From paper X.

Table 4.1. Azimuth (γ), tilt (β ), roof area (A) and installed power (P) for each of the21 houses studied in paper V. Definition of azimuth angle: [-90◦, 0◦, 90◦] = [east,south, west], tilt angle: [0◦, 90◦] = [horizontal, vertical]. From paper V.

No. γ (◦) β (◦) A (m2) P (Wp) No. γ (◦) β (◦) A (m2) P (Wp)

1 -15 27 43.8 4500 11 -15 32 44.8 45002 -19 24 87.0 4500 12 -17 26 69.5 45003 -15 32 42.5 4500 13 -15 26 69.0 45004 -19 31 41.0 4500 14 - - 0.2 -5 73 26 32.5 4500 15 -19 32 52.6 45006 75 32 27.0 4050 16 - - 6.1 -7 74 30 37.0 4500 17 -15 42 24.0 36008 72 32 21.5 3230 18 -16 42 40.4 45009 - - 8.5 - 19 73 30 15.7 236010 74 22 42.4 4500 20 31 34 71.4 4500

21 76 27 20.3 3050

both infrastructure and building stock being arranged either in parallel or per-pendicular to the water streams which have shaped the landscape. Since theorientation of PV systems is one of the features impacting the solar variabil-ity, regional patterns, like the one in Blekinge, is thus sometimes of interest tostudy when modeling the aggregated power generation from PV. In paper Van even smaller area was studied (see Figure 3.3). In modern cities, buildingsare naturally arranged according to the street grid, and this is also true for thecity district studied in paper V. The kernel density method used to determinethe azimuth of the roof segment best suited for PV was found to predict theazimuth well, with an RMSE of only 2.1◦. The identified azimuth angle, meantilt, total area and installed capacity of the identified roof segments for all 21buildings are presented in Table 4.1. For some buildings, the available roofarea was considered not sufficient for PV (<10 m2).

35

Table 4.2. Model performance evaluated for 2012 and 2013 respectively, where MAEis the mean absolute error and ΔP is the step change in power production. All errormeasures are presented as percentage of installed capacity and also the correlationcoefficient is presented. NPV represents the number of installed PV systems by the endof the year. From paper IV.

2012 2013

NPV 123 462nMAE 1.3% 1.1%bias 0.2% 0.2%nRMSE 2.4% 2.2%nRMSE ΔP, 1h 1.5% 1.3%nRMSE ΔP, 4h 3.1% 2.8%Correlation 0.97 0.99

4.2.2 Distribution of PV systems for a high penetration scenarioin Sweden

In paper IV a model was developed that was trimmed against hourly PV powerproduction (see Section 3.6), reported to the Swedish TSO. The model repro-duced the production with high accuracy. For instance the correlation was0.97 and 0.99 for the evaluation years 2012 and 2013 respectively as Table 4.2shows. In Section 3.6 a weighting function (see Equation 3.12), developed inpaper IV, was presented. It could be used to model possible locations for PVover a larger area. In Figure 4.5 a) the actual distribution of PV systems in theSwedish PV subsidy program [2] is presented (unfilled black circles) and alsothe modeled distribution of the same PV systems using the weighting function(filled gray circles). In Figure 4.5 b) a scenario of 8 TWh annual power pro-duction is presented, corresponding to 6% of the power demand for Sweden.This penetration level was chosen with regard to the current penetration levelin Germany [121]. The impact on the Swedish power system for this scenariois presented in Section 4.3.2.

4.3 Grid integrationIn this section results regarding the impact on the grid from PV is presented,first on low- and medium voltage level (from paper V and VI) in Section 4.3.1,and on national level (from paper IV) in Section 4.3.2.

4.3.1 Hosting capacity in a MV distribution gridIn paper V batteries were used to increase the self-consumption of a smallcommunity of 21 residential houses (see Section 3.5.1). The largest increase

36

10°E 15° E 20° E 25° E

55 °N

60 °N

65 °N

70 °N

0 200 400 600 km100

SE1

SE2

SE3

SE4 > 100 MW10 - 100 MW1 - 10 MW< 1 MW

10°E 15° E 20° E 25° E

55 °N

60 °N

65 °N

70 °N

0 200 400 600 km100

SE1

SE2

SE3

SE4

ModeledSubsidy program> 1 MW0.1 - 1 MW0.01 - 0.1 MW< 0.01 MW

(a) (b)Figure 4.5. a) Map of Sweden showing electricity market bidding areas SE1-4, the ac-tual distribution of PV systems in the Swedish subsidy program (unfilled black circles)and the modeled distribution (filled gray circles). The size of the circles represents theinstalled capacity in each locality, in total 52 MW across the country. b) A scenarioof 8.4 GW installed PV capacity, corresponding to an annual power production of 8TWh. Note that the scale of the markers differs between a) and b). From paper IV.

37

MV bus0 50 100 150 200 250

Vol

tage

()

1

1.02

1.04

1.06

1.08

1.1

1.12>700 kWh/m2yr>700 kWh/m2yr (SA)>950 kWh/m2yrOvervoltage margin

(a) (b)

Figure 4.6. a) The simulated maximum voltage in each MV bus in the Herrljungadistribution grid, when the annual solar irradiance level of 950 and 700 kWh/m2, isapplied, the latter before and after smart allocation. b) The MV buses representedin a map of Herrljunga (black border). The sizes of the dots represents the installedcapacity and the colors the maximum overvoltage. From paper VI.

in self-consumption was obtained for a shared battery. An increased self-consumption would probably also increase the hosting capacity of the low-voltage grid of the community. Batteries are however still an expensive alter-native for grid-connected PV systems [122]. The hosting capacity could alsobe increased through the smart allocation (SA) method applied in paper VI,where PV installations only were allowed in the strongest nodes of the grid(see Section 3.7.2). Power flow simulations on the Herrljunga MV grid gave ahosting capacity of 32% if PV deployment was allowed in all nodes, but onlyon roof segments with annual solar irradiation exceeding 900 kWh/m2. How-ever, by applying the SA method, the hosting capacity increased to 74%. Thisis presented in Figure 4.6 as the maximum voltage magnitude over the yearof 2014 for each node. The solid line in Figure 4.6 a), representing the SAmethod, lies close to the overvoltage margin (1.05 p.u.), but never exceeds it.The maximum voltage is also presented spatially in Figure 4.6 b). Worth not-ing is that the strongest nodes, experiencing lower maximum voltages (yellowon the map), are situated in the urban areas of the municipality. Theoreti-cally there is still room for increasing the hosting capacity even more in thesenodes, but as will be discussed in the next section, the distribution grid is alsointeracting with the transmission grid for which other constraints apply.

4.3.2 Impact on the power system for a high penetration scenarioin Sweden

In Figure 4.3 we saw how the correlation of sites decreases with distance. Asdescribed in Section 2.3.2 dispersing PV systems has a smoothing effect onthe aggregated variability. In paper IV the outcome of introducing PV in Swe-

38

Table 4.3. Extreme step changes for load only, corresponding to today’s Swedishpower system, and for 6% and 74% of PV penetration respectively. The 1% percentilesare included and also the fraction of time for which the extremes in the load onlyscenario are exceeded in the high PV penetration scenarios. Modified from paper IV.

1h 4hLoad 6% PV 74% PV Load 6% PV 74% PV

Max [GWh] 2.35 4.50 56.6 5.74 7.68 88.8Min [GWh] -1.37 -4.77 -59.8 -4.39 -7.87 -87.1Max perc. [GWh] 1.95 2.01 18.9 4.89 5.14 58.4Min perc. [GWh] -1.11 -1.41 -18.9 -3.74 -4.13 -58.9% of time >maxLoad - 0.16 17.0 - 0.18 20.6% of time <minLoad - 1.07 19.5 - 0.69 21.2

den corresponding to 6 % of the total power demand was examined in termsof change in extreme step changes. Figure 4.7 shows duration curves of the1 and 4 hour step changes (or ramps) before (load) and after introducing 6%of PV (net load). In Table 4.3 extreme step changes before and after introduc-ing a vast amount of PV is presented. Not only the 6% scenario, but a 74%scenario is included corresponding to the hosting capacity in the Herrljungamedium voltage grid presented in paper VI. The local distribution grid maywell handle such a high PV penetration, but Herrljunga is interconnected tothe transmission grid and will thus influence the higher voltage level of thepower system. If assuming that all local distribution grids in Sweden canhandle a penetration level of 74%, how would extreme step changes be influ-enced compared to the load-only case? In Figure 4.8 a) the maximum and 1%percentile of 1h up- and down ramps are presented as a function of PV pen-etration in the Swedish power system determined from the model developedin paper IV (see Section 3.6). From the figure, one can see that maximumup- and down-ramps stay unaffected until a PV penetration of 3% and 1.5%respectively is reached. Corresponding figures for the percentiles are 9% and5.5% respectively. The x-axis only stretches to the 10% penetration level asthe curves follow a linear trend after this. Figure 4.8 b) shows the time fractionof up- and down ramps exceeding the extreme ramps in the load-only case asa function of PV penetration level in the Swedish power system. Figure 4.8a) gives an idea of the hosting capacity in Sweden. What is also important isthe timing of the ramping events and the capacity of balancing the power, forexample can hydropower provide the need of regulation during sunny summerdays? Key figures for penetration levels of the 6% and 74% penetration arepresented in Table 4.3, which also includes 4h ramps.

39

0 20 40 60 80 100

Time [%]

-8

-6

-4

-2

0

2

4

6

8

Ste

p ch

ange

[GW

h]

Load, 1hNet load, 1hLoad, 4hNet load, 4h

Figure 4.7. Duration curves of 1 and 4 hour step changes for load only and for load mi-nus PV production (net load) representing 6% of the Swedish annual power demand.Determined with the model developed in paper IV.

0 2 4 6 8 10PV penetration [%]

1

2

3

4

5

6

7

8

9

1h ra

mp

[GW

h/h]

Max upMax downMax up 1% percentileMax down 1% percentile

0 20 40 60 80 100PV penetration [%]

0

5

10

15

20

25

Tim

e fra

ctio

n [%

]

% of time > Max up (load only)% of time > Max down (load only)

(a) (b)

Figure 4.8. a) Maximum and 1% percentile of 1h up- and down ramps as a functionof PV penetration in the whole Swedish power system. b) Fraction of time of whichthe 1h up- and down- ramps are exceeding the extreme ramps in the load only case asa function of PV penetration level in the Swedish power system. Determined with themodel developed in paper IV.

40

5. Concluding discussion and future work

Here the implications of the results in the appended papers are shortly dis-cussed with emphasis on future work, since this thesis only reports the firsthalf of the PhD-project. The validation of the solar logger showed that the ac-curacy is in line with similar data loggers. The low-cost has made it possibleto produce several loggers, and the next step will be to distribute them in thecity of Uppsala, Sweden. The collected data will be used to evaluate differentPV systems installed in Uppsala, to verify mathematical models describing thesolar variability, developed within the research group [120] and to study theimpact of short-term (1-min) solar variability on the local distribution grid.

To study the impacts of PV variability on the national or Nordic level, anaccurate model for the variability in total future aggregated PV generationis required. The smart allocation method, presented in paper VI, could beused to increase the hosting capacity. However, as the results showed, thedistribution grid is strong and can host at least 30% PV, which is in line withprevious studies [123]. The smart allocation method could be a useful toolfor the distribution system operator (DSO) in forming new business models.For example the DSO could rent rooftops based on the analysis in paper VIwith the criteria of high annual irradiation and access to a strong connectionnode in the distribution grid. Still the problem remains with over-productionduring clear summer days with low demand, meaning there will be a net-flow of power out on the transmission grid. Storage in batteries could help toincrease the self-consumption on distribution level. This will be investigatedin future studies on the distribution grid in Herrljunga.

What would limit the hosting capacity in the transmission grid in high-latitudes is not fully understood, but important factors are the capacity of bal-ancing power and short-term regulation. Hydropower from Sweden and Nor-way will continue to play an important role, but it might reach its full capacityif renewable energy sources would continue to be integrated in the power sys-tem, especially if the Nordic electricity market (Nordpool) would be integratedin the European market.

The model developed in paper IV reproduced the reported PV power pro-duction with high accuracy as Table 4.2 shows. The correlation of 0.97 and0.99 for the evaluation years 2012 and 2013 are higher than what has beenreported earlier for similar wide-area models [124, 125]. The model is cur-rently applied in a study on the Nordic countries where the aggregated vari-ability from four different renewable and intermittent energy sources are stud-ied, namely wind, wave, tidal and solar energy. This study will thus build onboth paper I and paper IV.

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Acknowledgements

This licentiate thesis was made possible with the support from a number ofpersons. First, I would like to thank STandUP for energy for partial fundingof my PhD project. I would like to express my sincere gratitude to my mainsupervisor senior lecturer Joakim Widén, for introducing me to the researchfield of solar variability and for his patience in answering my many questions.His guidance helped me throughout my research and writing of this thesis. Iwould also like to thank my co-supervisors senior lecturer Uwe Zimmermannfor introducing me to the world of electronics and Professor Ewa Wäckelgårdfor discussions on the holistic approach to energy systems research.

I would like to thank Peter Svedlindh, head of the division of Solid StatePhysics at Uppsala University, for letting me carry out my PhD project at thedivision. I thank my fellow colleagues in the Built Environment Energy Sys-tem Group (BEESG) Annica, Joakim M, Magnus and Rasmus for stimulatingdiscussions on all aspects of the energy system, and all other colleagues atSolid State Physics.

Thanks to Herrljunga Elektriska AB and especially CEO Anders Mannikoff,for providing distribution grid data, which made some of the work presentedhere, and hopefully future work possible. Thanks also to the county adminis-trative board of Blekinge and the Swedish Energy Agency for project funding.

Thanks to Uppsala climate protocol and the people working on a road mapfor a climate neutral Uppsala 2050, for a wider perspective on the role ofenergy systems in the society.

I would like to thank my partner Lovisa Larsson for encouraging me to pro-ceed through the challenges of the project and for making me a better person.Finally, I would also like to thank my family for believing in me, especially myfather, also a researcher, for discussing ethics and good practices in research.

43

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