Market value of PV battery systems for autonomous rural energy supply

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International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Energy Procedia 158 Energy Procedia 00(2019) (2017)1188–1193 000–000 Kong, China International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong 10 International Conference on Applied Energy (ICAE2018), 22-25 www.elsevier.com/locate/procedia August 2018, Hong Kong, China th Kong, China 10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong 10 Conference on Energy 22-25 August 2018, Hong Market value of PV battery systems for autonomous rural energy Kong, China(ICAE2018), 10th International International Conference on Applied Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, China Market value of PV battery systems for autonomous rural energy Kong, Chinafor autonomous rural energy supply Market value of PV battery systems

supply Market value of PV battery systems for autonomous rural energy Market value of PV battery systems autonomous rural energy supply a, b Market value of International PV battery systems for autonomous rural energy The 15th Symposium onfor District Heating andcCooling Alexander Kies *, Jakub Jurasz , Paweł B. Dąbek supply b c Alexander Kiesa,a,*, Jakub Jurasz , Paweł B. Dąbek supply b c Germany supply Frankfurt Institute for Advanced Studies, University Frankfurt, Frankfurt Main 60438, Alexander Kies *,Goethe Jakub Jurasz , Paweł B.amDąbek Assessing the feasibility of using the heat demand-outdoor AGH University, Kraków 30-059, Poland a, b c Germany Frankfurt Institute for Advanced Studies, Goethe University Frankfurt, Frankfurt am Main 60438, Alexander Kies Jakub Jurasz B. Dąbek a,*,Goethe b, Paweł c Germany Wroclaw University of Environmental and Life30-059, Science, Wrocław 50-375, Poland Frankfurt Institute for Advanced Studies, University Frankfurt, Frankfurt am Main 60438, Alexander Kies *, Jakub Jurasz B. Dąbek AGH Kraków Poland a,University, b, Paweł c Alexander Kies *, Jakub Jurasz , Paweł B. Dąbek temperature function for a long-term district heat demand forecast AGH University, Kraków 30-059, Poland Wroclaw UniversityStudies, of Environmental and Life Frankfurt, Science, Wrocław 50-375, Poland Frankfurt Institute for Advanced Goethe University Frankfurt am Main 60438, Germany a

b

a a

c

b

a a Frankfurt a

c

b

cWroclaw Institute for Advanced Goethe University Frankfurt, Frankfurt am Main 60438, Germany UniversitybStudies, of Environmental and Life30-059, Science, Wrocław 50-375, Poland AGH University, Kraków Poland Frankfurt Institute for AdvancedbStudies, Goethe University Frankfurt, Frankfurt am Main 60438, Germany University, 30-059, Poland a,b,ccWroclaw University a bAGH a Kraków b Wrocław 50-375, Poland c c of Environmental and Life Science, AGH University, Kraków 30-059, Poland c Wroclaw University of Environmental and Life Science, Wrocław 50-375, Poland Abstract c Wroclaw University of Environmental and Life Science, Wrocław 50-375, Poland a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Solar photovoltaics (PV) panels combination with batteries are often proposed a solution provide stable power supply Veoliain Recherche & Innovation, 291 Avenue Dreyfous Daniel,as78520 Limay,toFrance c in rural areas. PV generation is mostly dominated by the solar -diurnal cycle and has, some countries, already started have Abstract Solar photovoltaics (PV)Systèmes panels in combination with batteries are proposed asAlfred ainsolution to 44300 provide stableFrance power to supply Département Énergétiques et Environnement IMToften Atlantique, 4 rue Kastler, Nantes,

I. Andrić

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

Abstract Solar photovoltaics (PV) panels in combination with batteries are often proposed as ainsolution to provide stablestarted power to supply influence on the price distribution on the electricity market. in rural areas. PVdaily generation is mostly dominated by the solar diurnal cycle and has, some countries, already have Abstract in areas. PVstudy generation is mostly dominated by the solar diurnal cycle and has, someincountries, already have In rural thisphotovoltaics work, thepanels performance and of rural PV-battery hybrid ato future renewable Polishto power Solar (PV) in combination with batteries are often proposed assystems ainsolution provide stablestarted power supply influence on we the daily price distribution on optimisation the electricity market. Solar photovoltaics (PV) panels in combination with batteries are often proposed as a solution to provide stable power supply influence on the daily price distribution on the electricity market. system. We use data onthe generation to study PVof and battery deployment. Together aprovide power system optimisation in rural areas. PV generation is mostly dominated by the solar diurnal cycle and has, someinwith countries, already started to have In thisphotovoltaics work, we study performance and optimisation rural PV-battery hybrid systems ato future renewable Polish power Solar (PV) panels in potentials combination with batteries are often proposed as ainsolution stable power supply in rural areas.we PVstudy generation is mostly dominated bystudy the of solar diurnal cycle and has,systems inatsome countries, already topower have hybrid a future renewable Polish In this work, the performance and optimisation rural PV-battery Abstract and dispatch model for the Polish power system, we market values when selling theinwith national market forstarted different CO 2 influence onuse the daily distribution on thetoelectricity market. system. We data onprice generation potentials study PVsolar and battery deployment. Together a power system optimisation in rural areas. PV generation is mostly dominated by the diurnal cycle and has, in some countries, already started to have influence on the daily price distribution on the electricity market. and battery deployment. Together with a power system optimisation system. We use data on generation potentials to study PV price scenarios. We show that optimal orientations with respect to tilt/azimuth are subject to change as the PV share grows In this work, we study the performance and optimisation of rural PV-battery hybrid systems in a future renewable Polish power and dispatch model for the Polish power system, we study market values when selling at the national market for different CO 2 influence on the daily price distribution on the electricity market. In work, we study the performance and optimisation ofmarket rural PV-battery hybrid systems innational a futuresolutions renewable Polish power and dispatch model for the Polish power system, weshares study values when at theeffective market different CO 2 the District heating networks are commonly addressed inPV the literature as one ofselling the most for decreasing andthis that the use benefit batteries grows for higher of renewables. system. We data onthe generation potentials to study and battery deployment. Together a power optimisation price scenarios. Wefrom show that optimal orientations with to tilt/azimuth are subject toa change as system thefor PV share grows In this work, we study performance and optimisation ofrespect rural PV-battery hybrid systems inwith future renewable Polish power system. Wegas useemissions data on generation potentials to study PV respect and battery deployment. Together with a power system optimisation price scenarios. We show that optimal orientations with to tilt/azimuth are subject to change as the PV share grows greenhouse from the building sector. These systems require high investments which are returned through the model for Polish power system, weshares study market values when selling at the with national market for different CO 2heat and dispatch that We the use benefit batteries grows for higher of renewables. system. datafrom on the generation potentials to study PV and battery deployment. Together a power system optimisation and dispatch model for the Polish power system, weshares study market values when selling at the national market for different CO 2 that the benefit from batteries grows for higher of renewables. and sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Copyright © 2018 Elsevier Ltd. All rights reserved. pricedispatch scenarios. Wefor show optimal tilt/azimuth are subject changemarket as thefor PVdifferent share grows and model the that Polish powerorientations system, we with studyrespect marketto values when selling at the to national CO 2 price scenarios. We show that optimal orientations with respect to tilt/azimuth are subject to change as the PV share grows th prolonging the investment return period. Selection and peer-review under responsibility of the scientific committee of the International on Applied and that the from batteries grows for higher shares of renewables. Copyright ©benefit 2018 Ltd.optimal All rights reserved. price scenarios. WeElsevier show that orientations with respect to tilt/azimuth are10 subject to changeConference as the PV share grows © 2019 The Authors. Published by Elsevier Ltd. and that(ICAE2018). the from batteries grows for higher shares of renewables. Copyright ©benefit 2018 Elsevier Ltd. rights reserved. The main scope of this paper is toAll assess the feasibility of using the heat demand – outdoor temperature function for demand Energy Selection and peer-review under responsibility of the scientific committee of the 10th International Conference onheat Applied and that benefit from batteries grows for higher shares of renewables. This is anthe open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. TheConference district is on consisted of 665 Copyright ©under 2018 Elsevier Ltd. All rights reserved. Energy (ICAE2018). Peer-review responsibility of the scientific committee of ICAE2018 – The 10th International Applied Copyright © 2018 Elsevier Ltd. All rights reserved. th Energy (ICAE2018). buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: energy storage; photovoltaics; battery, hybrid power system Selection and peer-review responsibility of the scientific committee of the 10th International Conference on Applied Copyright © 2018 Elsevier under Ltd. All rights reserved. Energy. Selection and peer-review under responsibility of power the scientific committee of thethe 10therror, International Conference on values Applied renovation scenarios were developed (shallow, intermediate, deep). To estimate obtained heat demand were Keywords: energy storage; photovoltaics; battery, hybrid system Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Keywords: energy storage; photovoltaics; hybrid power compared with results from a dynamicbattery, heat demand model,system previously developed and validated by the authors. Energy (ICAE2018). The results energy showed that when only weather is considered, Keywords: storage; photovoltaics; battery,change hybrid power system the margin of error could be acceptable for some applications 1. Introduction Keywords: storage; photovoltaics; battery, power (the error inenergy annual demand was lower than hybrid 20% for all system weather scenarios considered). However, after introducing renovation Keywords: energy storage; photovoltaics; battery, hybrid power system 1. Introduction 1. Introduction scenarios, the error value increased up to 59.5% (depending on the capacities weather andhave renovation scenarios combination Around the world, large amounts of renewable generation been installed. Major aimsconsidered). behind The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the 1. Introduction transformations of power systems are climate change mitigation and increased sustainability. Around the world, large amounts of renewable generation capacities have been installed. Major aims behind 1. Introduction decrease inthe theworld, numberlarge of heating hoursofofrenewable 22-139h during the heating season have (depending on the combination of weather and Around amounts generation capacities been installed. Major aims behind 1. Introduction Climate change of haspower directsystems effect onare renewable potentials [1,2] and exploitation of renewables has the reverse transformations climate change mitigation andthe increased sustainability. renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on transformations of power systems climate change andthe increased sustainability. Around the world, large amounts of renewable generation have installed. Major aims behindthe effect ofchange mitigating climate change. Wind, hydro andmitigation photovoltaics (PV) are been the major renewable technologies. Climate has direct effect onare renewable potentials [1,2]capacities and exploitation offor renewables has the reverse Around the world, large amounts of renewable generation capacities have been installed. Major aims behindand coupled scenarios). The values suggested could be used to modify the function parameters the scenarios considered, Climate change has direct effect renewable potentials [1,2]capacities and exploitation of renewables has the reverse transformations of power systems are climate change mitigation andthe increased sustainability. Around the world, large amounts renewable generation have been installed. Major aims behind PV, unlike wind and hydro, is dueon toof its comparably low investment barrier considered torenewable be ideal for decentrally effect of mitigating climate change. Wind, hydro and photovoltaics (PV) are the major technologies. improve the accuracy of heat demand estimations. transformations of power systems are climate change mitigation and increased sustainability. effect of mitigating climate change. Wind, hydro and photovoltaics (PV) are the major renewable technologies.

Climate change has direct effect potentials [1,2] and exploitation of renewables the reverse transformations power systems are climate mitigation andthe increased sustainability. organized energy systems, where electricity ischange created andinvestment consumed locally. However, itsbe generation potential is PV, unlike windof and hydro, is dueon torenewable its comparably low barrier considered to ideal has for decentrally Climate change has direct effect on renewable potentials [1,2] and the exploitation of renewables has the reverse PV, unlike wind and hydro, is due to its comparably low investment barrier considered to be ideal for decentrally effect of mitigating climate change. Wind, hydro and photovoltaics (PV) are the major renewable technologies. Climate change has direct effect on renewable potentials [1,2] and the exploitation of renewables has the reverse mostly dominated by the diurnal cycle and therefore neither dispatchable nor able to provide a constant baseload. energy systems, where electricity is created and consumed locally. However, its generation potential is ©organized 2017 The Authors. Published by Elsevier Ltd. effect of mitigating climatewhere change. Wind, hydro and and photovoltaics (PV) areHowever, the majorits renewable technologies. organized energy systems, electricity is created consumed locally. generation potential is PV, unlike wind and hydro, due to Wind, itsand comparably low investment barrier considered torenewable be ideal for decentrally effect mitigating change. hydro and photovoltaics (PV) are the to major technologies. Due toofdominated the characteristics ofis PV power generation, batteries are seen as anor natural complementary to PV panels. mostly byclimate the diurnal therefore neither dispatchable able provide a constant baseload. Peer-review under responsibility of thecycle Scientific Committee of The 15th International Symposium on District Heating and PV, unlike wind and hydro, is due to its comparably low investment barrier considered to be ideal for decentrally mostly dominated by the diurnal cycle and therefore neither dispatchable nor able to provide a constant baseload. organized energy systems, where electricity is created and consumed locally. However, its generation potential is PV, unlike wind and hydro, is due to its comparably low investment barrier considered to be ideal for decentrally Cooling. Most are lithium-ion which are batteries already used in many astoofpotential today, but Due topromising theenergy characteristics of PVbatteries, power generation, are seen as a technological natural complementary PV panels. organized systems, where electricity is created and consumed locally. However, itsdevices generation is Due to the characteristics of PV power generation, batteries are seen as a natural complementary to PV panels. mostly dominated by the diurnal cycle and therefore neither dispatchable nor able to provide a constant baseload. organized energy systems, where electricity is created and consumed locally. However, its generation potential is Most promising arebylithium-ion batteries, which are already used in manynor technological devices as of today, but mostly dominated the diurnal cycle and therefore neither dispatchable able to provide a constant baseload. Mosttopromising arebyForecast; lithium-ion which are batteries already used in many technological devices astoofPV today, but Keywords: Heatcharacteristics demand; change Due the ofClimate PVbatteries, power generation, are seen as anor natural panels. mostly dominated the diurnal cycle and therefore neither dispatchable able tocomplementary provide a constant baseload. Due to the characteristics of PV power generation, batteries are seen as a natural complementary to PV panels. Mosttopromising are lithium-ion which are batteries already used in many devices astoofPV today, but Due the characteristics of PVbatteries, power generation, are seen as a technological natural complementary panels. Most promising are lithium-ion batteries, which are already used in many technological devices as of today, but Most promising are lithium-ion batteries, which are already used in many technological devices as of today, but * Corresponding author. Tel.: +49 69 798 47698;

E-mail©address: [email protected] * Corresponding author. Tel.: +49 69 798by47698; 1876-6102 2017 The Authors. Published Elsevier Ltd. * Corresponding author. Tel.: of +49 798 47698; E-mail address: [email protected] Peer-review under responsibility the69Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 ©address: 2019 The Authors. Published by Elsevier Ltd. E-mail [email protected] 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Corresponding author. Tel.:under +49 69 798 47698; This* is an open access article the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) th * Corresponding author. Tel.:Elsevier +49 69Ltd. 798 All 47698; Selection peer-review under responsibility of thecommittee scientific of the–10 Conference on Appliedon Energy E-mailand address: [email protected] 1876-6102 Copyright © 2018 rights reserved. committee Peer-review under responsibility of 69 the798 scientific of ICAE2018 TheInternational 10th International Conference Applied Energy. * Corresponding author. Tel.: +49 47698; E-mail address: [email protected] (ICAE2018). 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy 10.1016/j.egypro.2019.01.305 E-mailand address: [email protected] th Selection peer-review under responsibility the scientific (ICAE2018). 1876-6102and Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10 International Conference on Applied Energy 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. (ICAE2018). th Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. committee of the 10th International Conference on Applied Energy Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). (ICAE2018).

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Alexander Kies et al. / Energy Procedia 158000–000 (2019) 1188–1193 Author name / Energy Procedia 00 (2018)

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are mostly not cost-competitive for grid storage application and whose non-linear behaviour (e.g., aging, selfdischarge) is not fully understood. Other options to partially integrate renewable energy include system-friendly renewables [3], optimal angle/tilt combinations of solar PV modules [4] demand side management [5], transmission grid extensions [6] or sector coupling [7,8]. Hybrid systems to combine different renewable sources have seen certain attention in the research community as well. Common combinations include PV and hydro [9-11] or wind-PV-hydro [12]. In this paper, we investigate three aspects: First, we investigate the cost-optimal generation mix in a Polish power system in dependency of the CO2 price. Second, we study market values of rural PV systems in dependency of tilt/azimuth for different CO2 prices, where these local PV systems are treated as a price maker and prices are taken as local marginal prices from the system optimisation. Third, we investigate the potential benefit of batteries on the market value of PV for two CO 2 price scenarios. 2. Data

power

Time series of renewable generation for wind and photovoltaics, which were used in the system optimisation of the Polish power system, were obtained from the open power system database (open-power-system-data.org). For decentral energy supply, we investigated different azimuth/tilt combinations with respect to their usefulness for installing PV panels in terms of the slope and aspect of the roof, as well as the potential shading (Fig. 1). The analysis of corresponding potentials involved around 1900 buildings from the municipality of Piechowice (area 43.22 km2, coordinates 505120N, 15378E; PL92: N: 328869340234, E: 255802263661), Poland. Potential tilts and azimuths were divided into 5 estimates for azimuth: E, SE, S, SW, W as well as 13 estimates of tilts in 13 steps by 5° in the range of 2.5° to 62.5°

power

E

W

N

time

S Connection to the national power system

power

time

time

Typical daily electricity load profile

Power generation from photovoltaics

Fig. 1. Conceptual design of rural energy supply.

3. Methodology

Figure 1: Conceptual design of rural energy supply

We model the Polish power system via a linear program that minimises system cost. It is treated as an island system, i.e., exchange with neighboring countries is not considered. Furthermore, transmission constraints within the country are neglected (copperplate approximation). The objective reads: min (∑𝑠𝑠 𝑐𝑐𝑠𝑠 𝐺𝐺𝑠𝑠 + ∑𝑠𝑠,𝑡𝑡 𝑜𝑜𝑠𝑠 𝑔𝑔𝑠𝑠 (𝑡𝑡)) 𝑔𝑔,𝐺𝐺

(1)

Author name / Energy Procedia 00 (2018) 000–000 Author name / Energy Procedia 00 (2018) 000–000 Alexander Kies et al. / Energy Procedia 158 (2019) 1188–1193

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3 3

Author name / Energy Procedia 00 (2018) 000–000 3 Here, cs are the investment costs for generation capacity, os are the marginal costs of energy generation, Gs are the capacities of generators and gs are the time series of dispatch. The index s runs over all considered energy Here, cs are the investment costs for generation capacity, os are the marginal costs of energy generation, Gs are the technologies, wind, PV, conventional sources andobatteries. A list ofcosts all of energy carrier types G used, Here, cs are thee.g. investment costs for generation capacity, energy generation, are the s are the marginal capacities of generators and gs are the time series of dispatch. The index s runs over all considereds energy corresponding modelling and details theirseries cost assumptions The all dispatch of hydro and arewell the as time of dispatch. are Thegiven indexin sTable runs I.over considered energy capacities of generators gs as technologies, e.g. wind, PV, conventional sources and batteries. A list of all energy carrier types used, the bio power is not optimised. Instead,sources they areand assumed to provide baseload. technologies, e.g.explicitly wind, PV, conventional batteries. A list aofconstant all energy carrier types used, the corresponding modelling details as well as their cost assumptions are given in Table I. The dispatch of hydro and In addition to the objective, multiple constraints haveassumptions to be satisfied: corresponding modelling details as well as their cost are given in Table I. The dispatch of hydro and bio power is not explicitly optimised. Instead, they are assumed to provide a constant baseload. To ensure stable power system operation, thethey demand must be tomatched the actual power generation and/or bio power is not explicitly optimised. Instead, are assumed provideby a constant baseload. In addition to the objective, multiple constraints have to be satisfied: storage flows times: multiple constraints have to be satisfied: In addition to at theallobjective, To ensure stable power system operation, the demand must be matched by the actual power generation and/or To ensure stable power system operation, the demand must be matched by the actual power generation and/or storage flows at all times: ∑𝑠𝑠 𝑔𝑔𝑠𝑠flows (𝑡𝑡) −at𝑑𝑑(𝑡𝑡) = 0 ↔ 𝜆𝜆𝑡𝑡 ⋁ 𝑡𝑡 (2) storage all times:

∑𝑠𝑠 𝑔𝑔𝑠𝑠 (𝑡𝑡) − 𝑑𝑑(𝑡𝑡) = 0 ↔ 𝜆𝜆𝑡𝑡 ⋁ 𝑡𝑡 (2) (𝑡𝑡)the ∑𝑠𝑠 𝑔𝑔d𝑠𝑠 is − demand. 𝑑𝑑(𝑡𝑡) = 0𝜆𝜆↔ 𝜆𝜆𝑡𝑡 ⋁shadow 𝑡𝑡 (2) where price that is used as a market price to calculate market value in the second 𝑡𝑡 is the part ofdthe results section. where is the demand. 𝜆𝜆 is the shadow price that is used as a market price to calculate market value in the second where d is the demand. 𝜆𝜆𝑡𝑡 is the shadow priceunit that is is used as a market price to calculate market in the second The dispatch g or storage constrained by its maximal capacity G s value multiplied by the s of a generator part of the results section.𝑡𝑡 part of the results section. corresponding hourly capacity factor g ̅ , which is for renewable sources determined by the weather: 𝑠𝑠 The dispatch gs of a generator or storage unit is constrained by its maximal capacity G s multiplied by the The dispatch gs of a generator or storage unit is constrained by its maximal capacity G s multiplied by the corresponding hourly capacity factor g̅𝑠𝑠 , which is for renewable sources determined by the weather: corresponding capacity factor g̅𝑠𝑠 , which is for renewable sources determined by the weather: 0 ≤ 𝑔𝑔𝑠𝑠,𝑡𝑡 ≤ ̅̅̅̅𝐺𝐺 ghourly (3) 𝑠𝑠,𝑡𝑡 𝑠𝑠,𝑡𝑡 ⋁ 𝑡𝑡 , 𝑠𝑠

0 ≤ 𝑔𝑔𝑠𝑠,𝑡𝑡 ≤ ̅̅̅̅𝐺𝐺 g 𝑠𝑠,𝑡𝑡 𝑠𝑠,𝑡𝑡 ⋁ 𝑡𝑡 , 𝑠𝑠 (3) ≤ g̅̅̅̅𝐺𝐺 (3) ≤ 𝑔𝑔𝑠𝑠,𝑡𝑡 capacity ⋁ 𝑡𝑡 , 𝑠𝑠time series per renewable technology is based on historical data, i.e., the distribution The0 hourly 𝑠𝑠,𝑡𝑡 𝑠𝑠,𝑡𝑡factor of within the country therenewable historical distribution. Thecapacities hourly capacity factor time reflects series per technology is based on historical data, i.e., the distribution The hourlycapacities capacity factor time series per renewable technology is based on historical i.e., the distribution Maximum are assumed to be unlimited. Fordistribution. conventional generators, dispatchdata, is purely constrained by of capacities within the country reflects the historical of within thei.e. country reflects thecapacities installed capacity, g̅𝑠𝑠 (𝑡𝑡) = 1.0. the historical distribution. Maximum capacities are assumed to be unlimited. For conventional generators, dispatch is purely constrained by Storage consistency ensured via to thebestorage stateFor of charge 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡 generators, dispatch constraint: Maximum capacitiesisare assumed unlimited. conventional dispatch is purely constrained by the installed capacity, i.e. g̅ (𝑡𝑡) = 1.0. the installed capacity, i.e. g̅𝑠𝑠𝑠𝑠 (𝑡𝑡) = 1.0. Storage consistency is ensured via the storage state of charge 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡 dispatch constraint: 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡consistency = 𝜂𝜂0 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡−1 + 𝜂𝜂1 𝑔𝑔𝑠𝑠,𝑡𝑡 − 𝜂𝜂2−1 𝑔𝑔 𝑠𝑠, 𝑡𝑡𝑠𝑠,𝑡𝑡> dispatch 1 (5) constraint: Storage is ensured via𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 the storage state of charge⋁𝑆𝑆𝑆𝑆𝑆𝑆 𝑠𝑠,𝑡𝑡, 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑ℎ 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡 = 𝑆𝑆𝑆𝑆𝑆𝑆|𝑡𝑡| (6) 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡 = 𝜂𝜂0 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡−1 + 𝜂𝜂1 𝑔𝑔𝑠𝑠,𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝜂𝜂2−1 (5) −1 𝑔𝑔𝑠𝑠,𝑡𝑡, 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑ℎ ⋁ 𝑠𝑠, 𝑡𝑡 > 1 = 𝜂𝜂 𝑆𝑆𝑆𝑆𝑆𝑆 + 𝜂𝜂 𝑔𝑔 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − 𝜂𝜂 𝑔𝑔 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑ℎ 𝑠𝑠, 𝑡𝑡 > 1 (5) 𝑆𝑆𝑆𝑆𝑆𝑆 ⋁ 0 𝑠𝑠,𝑡𝑡−1 𝑠𝑠,𝑡𝑡 where standing1 losses and 𝜂𝜂1 2and𝑠𝑠,𝑡𝑡, 𝜂𝜂2 efficiencies of the corresponding charging and discharging 0 describes 𝑆𝑆𝑆𝑆𝑆𝑆𝜂𝜂𝑠𝑠,𝑡𝑡 = 𝑆𝑆𝑆𝑆𝑆𝑆 (6) |𝑡𝑡| 𝑠𝑠,𝑡𝑡 (6) 𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠,𝑡𝑡 =In𝑆𝑆𝑆𝑆𝑆𝑆 |𝑡𝑡| processes. addition, a cyclic state-of-charge is enforced. where 𝜂𝜂 describes standing losses and 𝜂𝜂 and 𝜂𝜂 efficiencies of the corresponding charging and discharging where 𝜂𝜂00 describes standing losses and 𝜂𝜂11 and 𝜂𝜂22 efficiencies of the corresponding charging and discharging processes. In addition, a cyclic state-of-charge is enforced. 4. Cost assumptions processes. In addition, a cyclic state-of-charge is enforced.

4. Cost assumptions Cost assumptions have been adopted from a publication by JRC [14]. They are briefly summarised in Table I. 4. Cost assumptions Annualised cost are calculated by assuming an annuity of 8.6% for all assets except PV, where the annuity is Cost assumptions have been adopted from a publication by JRC [14]. They are briefly summarised in Table I. assumed to be 5.7%. Cost assumptions have been adopted from a publication by JRC [14]. They are briefly summarised in Table I. Annualised cost are calculated by assuming an annuity of 8.6% for all assets except PV, where the annuity is Annualised cost are calculated by assuming an annuity of 8.6% for all assets except PV, where the annuity is assumed to 1. be 5.7%. cost assumptions for generation and storage technologies originally based on value estimates from JRC. Table assumed to beAnnualised 5.7%. Technology Capital Marginal Efficiency Table 1. Annualised cost assumptions for generation andOvernight storage technologies originally based on value estimates from JRC. Table 1. Annualised cost assumptions for generation and storage technologies originally based estimates from JRC. Cost Generation Coston value Dispatch/Uptake Technology Overnight Capital Marginal Efficiency [Euro/GW/a] [Euro/MWh] Technology Overnight MarginalCost Efficiency CostCapital Generation Dispatch/Uptake Cost Generation Cost Dispatch/Uptake OCGT 49.400 187.0 0.39 [Euro/GW/a] [Euro/MWh] [Euro/GW/a] [Euro/MWh] Onshore Wind 127.450 0.015 1 OCGT 49.400 187.0 0.39 OCGT 49.400 187.0 0.39 PV 61.550 0.010 1 Onshore Wind 127.450 0.015 1 Onshore Wind 127.450 0.015 1 Lignite 159.000 33.0 0.38 PV 61.550 0.010 1 PV 61.550 0.010 1 Hard Coal 133.200 45.0 0.39 Lignite 159.000 33.0 0.38 Lignite 159.000 33.0 0.38 Battery 120.389 0 0.900/0.900 Hard Coal 133.200 45.0 0.39 Hard Coal 133.200 45.0 0.39 Battery 120.389 0 0.900/0.900 Battery 120.389 0 0.900/0.900

5. Results 5. Results First, we analyse the results of the optimisation of the Polish power system. 5. Results Fig. 2 (left) shows the Polish generation mix in dependency of the CO2 price as a result of the previously introduced First, we analyse the results of the optimisation of the Polish power system. lignite is the most competitive technology but is optimisation problem. It is shown at diminishing First, we analyse the results of the that optimisation of theCO Polish power system. 2 prices Fig. 2 (left) shows the Polish generation mix in dependency of the CO2 price as a result of the previously introduced prices rise. Above prices of 20 Euro per ton, renewables become cost-competitive replaced byshows hard coal as COgeneration Fig. 2 (left) the Polish mix in dependency of the CO price as a result of the previously introduced 2 2 optimisation problem. It is shown that at diminishing CO2 prices lignite is the most competitive technology but is optimisation problem. It is shown that at diminishing CO2 prices lignite is the most competitive technology but is replaced by hard coal as CO2 prices rise. Above prices of 20 Euro per ton, renewables become cost-competitive replaced by hard coal as CO2 prices rise. Above prices of 20 Euro per ton, renewables become cost-competitive

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replacing lignite, while the share of hard coal continues growing, as well. The share of hard coal continues to grow until CO2 prices are slightly above 30 Euros per ton, while lignite is completely irrelevant at this point. In addition, it can be observed that relative market values (calculated according to Eq. 6) of renewables decrease as generation shares increase. This can be attributed to profile-related values [13], as growing shares of renewables exhibit greater influence on price patterns. PV has a relative market value of around 80% at a CO 2 price of 0 Euros/ton, which grows slightly to around 90% at 20 Euro/ton, but monotonously decreases afterwards, as PV shares start to grow rapidly. For wind, relative market value monotonously decreases with growing CO 2 prices, but starts from a comparably high level of more than 120% and, once CO2 prices reach values above 20 Euros/ton, stays a constant number of percentage points above the value for PV.

Figure 2: Left: Optimal generation mix in dependency of the CO2 price. Right: Relative market value of wind and PV in dependency of the CO2 price.

Figure 3: Relative market values for CO2 price of 0 and 30 Euro/ton (left / right).

Next, we study the market value of PV systems in dependency of tilt and azimuth. First, we cost-optimise a purely decentral PV-battery supply (i.e., no exchange with the national grid) for the described municipality of Piechowice, where we limit installed capacity per tilt/azimuth combination to 1 MW and find an installed capacity of 16.5 MW distributed among combinations as well as a battery with an energy capacity of 104.6 MWh. Capacities are installed south-facing (azimuth 180 degree) and south-east facing (azimuth 135) at high tilts of 30 degree and more, where capacity factors are highest and therefore levelised cost of electricity is lowest. Different tilts and azimuth have different feed-in profiles causing different values of generated energy. Taking shadow prices 𝜆𝜆𝑡𝑡 from the system optimisation, one can calculate the relative market value 𝜗𝜗 (relative to a constant feedin profile) as ∑ 𝑔𝑔𝑡𝑡 𝜆𝜆𝑡𝑡 ̅̅̅ 𝑡𝑡 𝑔𝑔𝑡𝑡 𝜆𝜆𝑡𝑡

𝜗𝜗 = ∑𝑡𝑡

where 𝜆𝜆̅𝑡𝑡 is the average price.

(7)

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Figure 4: relative market value for CO2 price of 80 Euro/ton.

Fig. 3-4 show relative market value for three different CO2 prices of 0, 30 and 80 Euro/ton. At a CO2 price of zero, south-facing modules of high tilt have highest market values. At these CO 2 prices, virtually no PV system is within the optimal national mix, hence no influence of PV on price statistics is exerted. The high market value of PV with this tilt/azimuth combination indicates a large agreement with load patterns, which dominate prices. At prices of 30 Euro, where PV has a share in the generation mix of approximately 15% and wind of another 25%, the picture has already changed: now, west-facing modules are optimal, albeit differences are small. At a price of 80 Euros, this pattern is even further pronounced and relative differences in market value are up to 10%. At those prices, wind and PV contribute around 60% of the generation mix. It can therefore be concluded, that price patterns under these circumstances are dominated by generation instead of demand. Next, we allow for additional battery storage to increase the market value of PV without considering the cost of the battery. Fig. 5 shows relative market value of PV power in combination with a battery of different energy capacities. No limits on charging/discharging rates are assumed. In addition, the battery can only store produced PV power, but sell it at any time. At 30 Euro/ton, relative market value increase is around 20% for an energy capacity that is equal to the nominal PV capacity times 1 hour. At a storage capacity of 6 hours times the nominal capacity, the market value is roughly doubled. For a CO2 price of 80 Euro/ton, where renewables have considerable influence on market prices, the market value already doubles at an energy capacity of 1 hour times the capacity and a 6-hour storage increases it by around 5 times.

Figure 5: Relative market value of PV battery systems in dependency of the storage size.

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6. Discussion and conclusions In this paper, two aspects are investigated. First, the market value of PV panels for different tilt/azimuth combinations is studied. For low CO2 prices, market values tend to be highest for south-facing modules. This can likely be attributed to the resemblance of generation profiles of south-facing modules to demand patterns. If CO2 prices increase, a paradigm shift can be observed: west-facing modules have the highest relative market value. This is likely because prices are not dominated by the demand anymore, but instead by non-dispatchable generation. Furthermore, it can be concluded from this fact that the PV time series, which influences price statistics, is likely dominated by south-facing modules. However, relative market value differences between different combinations of tilt and azimuths remain in all cases below 10%. Therefore, it seems likely that levelised cost of electricity differences have the largest impact on profitability of PV systems and concrete feed-in pattern differences are of minor importance. Second, the effect of a battery on the market value of solar PV is shown. Especially at high CO2 prices of 80 Euro/ton, where renewables wind and PV contribute a noticeable share to the overall generation mix in the national power system of around 60%, batteries provide a huge increase in market value, which is around 4-5 times higher than at a CO2 price of 30 Euro/ton. Acknowledgements A. Kies is financially supported by Stiftung Polytechnische Gesellschaft and the R&D project NetAllok (FKZ03ET4046A), financed by the Federal Ministry of Economic Affairs and Energy (BMWi). Parts of this work were submitted to the 3rd International Hybrid Power Systems Workshop 2018. We thank the reviewers for their helpful comments. References [1] Schlott, Markus, et al. "The Impact of Climate Change on a Cost-Optimal Highly Renewable European Electricity Network." arXiv preprint arXiv:1805.11673 (2018). [2] Kozarcanin, Smail, Hailiang Liu, and Gorm Bruun Andresen. "Climate change impacts on large-scale electricity system design decisions for the 21st Century." arXiv preprint arXiv:1805.01364 (2018). [3] Hirth, Lion, and Simon Müller. "System-friendly wind power: How advanced wind turbine design can increase the economic value of electricity generated through wind power." Energy Economics 56 (2016): 51-63. [4] Chattopadhyay, Kabitri, et al. "The impact of different PV module configurations on storage and additional balancing needs for a fully renewable European power system." Renewable Energy 113 (2017): 176-189. [5] Johansson, Viktor, et al. "Value of wind power–Implications from specific power." Energy 126 (2017): 352-360. [6] Kies, Alexander, Bruno U. Schyska, and Lueder von Bremen. "Curtailment in a highly renewable power system and its effect on capacity factors." Energies 9.7 (2016): 510. [7] Schaber, Katrin, Florian Steinke, and Thomas Hamacher. "Managing temporary oversupply from renewables efficiently: Electricity storage versus energy sector coupling in Germany." International Energy Workshop, Paris. 2013. [8] Brown, T., et al. "Synergies of sector coupling and transmission extension in a cost-optimised, highly renewable European energy system." Energy 160 (2018): 720-739 [9] Jurasz, Jakub, and Bartłomiej Ciapała. “Solar–hydro hybrid power station as a way to smooth power output and increase water retention.” Solar Energy, 173, 675-690. [10] Francois, Baptiste, et al. "Complementarity between solar and hydro power: Sensitivity study to climate characteristics in Northern-Italy." Renewable energy 86 (2016): 543-553. [11] Ming, Bo, et al. "Optimizing utility-scale photovoltaic power generation for integration into a hydropower reservoir by incorporating long-and short-term operational decisions." Applied Energy 204 (2017): 432-445. [12] Jurasz, Jakub. "Modeling and forecasting energy flow between national power grid and a solar–wind–pumpedhydroelectricity (PV–WT–PSH) energy source." Energy conversion and management 136 (2017): 382-394. [13] Edenhofer, Ottmar, et al. "On the economics of renewable energy sources." Energy Economics 40 (2013): S12-S23. [14] Carlsson, J., et al. "ETRI 2014-Energy technology reference indicator projections for 2010-2050." European Commission, Joint Research Centre, Institute for Energy and Transport, Luxembourg: Publications Office of the European Union (2014).