Open model-based analysis of a 100% renewable and sector-coupled energy system -- The case of Germany in 2050
Preprint Submitted to Applied Energy. Page of Modeling and Analysis of 100% Renewable Sector-Coupled Energy System for Germany
Md. Nasimul Islam Maruf Highlights ● An open model approach for analyzing a 100% renewable-based and sector-coupled energy system is proposed. ●
An hourly optimization tool based on the open energy modeling framework is developed to investigate the German energy system. ●
Scenario results show that a 100% renewable-based system for supplying electricity and building heat is feasible in Germany in 2050 under different conditions. ●
Annual investment costs vary between 17.6 – 26.6 bn €/yr for the volatile generators, 23.7 – 28.8 bn €/yr, and a minimum 2.7 – 3.9 bn €/yr for electricity and heat storage. ●
Sensitivity analyses show that optimum grid expansion and storage usage storage maximize the flexibility of the system and decrease the overall investment cost.
Abstract
The ambitious energy target to achieve climate-neutrality in the European Union (EU) energy system raises the question of the feasibility of using only renewables across all energy sectors. Germany, as one of the leading industrialized countries of the EU, has adopted several climate action plans for the realistic implementation and maximum utilization of renewable energies in its future energy system. The literature review shows a clear gap in comprehensive techniques describing an open modeling approach for analyzing fully renewable and sector-coupled energy systems. This paper outlines an open modeling technique for analyzing the feasibility of the 100% renewable-based and sector-coupled energy system in Germany. It identifies the capacities and investment costs for different components and briefly evaluates the flexibility aspects of the system in terms of transmission grid expansion, energy storage, and dispatchable loads. Based on the open energy modeling framework (Oemof), an hourly optimization tool 'OSeEM-DE' is developed to investigate the German energy system. The model results show that a 100% renewable-based and sector-coupled system for electricity and building heat is feasible in Germany under different conditions. The investment capacities and component costs depend on the parametric variations of the developed scenarios. According to the model results, the annual investment costs vary between 17.6 – 26.6 bn €/yr for the volatile generators, and between 23.7 – 28.8 bn €/yr for the heat generators. Besides, the model suggests an investment of a minimum of 2.7 – 3.9 bn €/yr for electricity and heat storage. A comparison of the OSeEM-DE results with Fraunhofer ISE study reports shows that the percentage-wise energy mix composition and the Levelized Cost of Electricity (LCOE) from the model are within the plausible ranges. Finally, sensitivity analyses indicate that storage expansion and optimum grid extension between Northern and Southern Germany can maximize the provision of flexibility to the system and decrease the overall investment cost.
Keywords:
Broader Context
This research contributes to open energy modeling challenges to analyze 100% renewable-based energy systems for integrated energy sectors. Additionally, it contributes to the studies of renewable energy utilization and the understanding of energy transition in the German context. The research illustrates an in-depth methodology for developing fully renewable and cross-sectoral energy system models and delineates the technique for scenario-based energy system analysis. It advances the understanding of the feasibility of the integrated system and shows the required capacities and investment for its components to stay within the available potentials of renewable resources. The study reveals the possibility of using power-to-heat devices such as electric heat pumps and using biomass-based combined heat and power plants to eliminate the dependency on fossil fuels for heat generation. The study also shows the interrelation between grid and storage Department of Energy and Environmental Management, Europa-Universität Flensburg, Flensburg, Germany; Postal Address: Auf dem Campus 1b (Room: VIL 108), 24943 Flensburg, Germany; E-mail: [email protected]; Phone: +494618053007.
Preprint Submitted to Applied Energy. Page of expansion can impact the provision of the flexibility of the energy system. To summarize, the model and the analysis technique will be useful for investigating similar energy systems, especially in the North Sea region. Nomenclature
Abbreviations
ACAES ASHP Capex CHP CSP DE Dispa-SET DSM ENTSO-e EU FOM GHG GSHP H LCOE Li-ion LP MERRA MILP NDE NPV NS O&M Oemof OPSD OSeEM-DE P2H P2G PHS PV PyPSA Redox ROR SDE TES VOM WACC ZNES Adiabatic Compressed Air Energy Storage Air Source Heat Pump Capital Expenditure Combined Heat and Power Concentrated Solar Power Germany Unit commitment and optimal dispatch model Demand-side Management European Network of Transmission System Operators for Electricity European Union Fixed Operation and Maintenance Greenhouse Gas Ground Source Heat Pump Hydrogen Levelized Cost of Electricity Lithium-ion Linear Programming Modern-Era Retrospective analysis for Research and Application Mixed-Integer Linear Programming Northern Germany Net Present Value North Sea Operation and Maintenance Open Energy Modelling Framework Open Power System Data Open Sector-coupled Energy Model for Germany Power-to-Heat Power-to-Gas Pumped Hydro Storage Photovoltaic Python for Power System Analysis Vanadium Redox Run-of-the-River Southern Germany Thermal Energy Storage Variable Operation and Maintenance Weighted Average Cost of Capital Center for Sustainable Energy Systems
Symbols 𝑡 Timestep 𝑇 Set of all timesteps 𝑏 Bus 𝐵 Set of all buses 𝑙 Load 𝐿 Set of all loads 𝑣 Volatile generator 𝑉 Set of all volatile generators ℎ Heat pump 𝐻 Set of all heat pumps 𝑠 Storage 𝑆 Set of all storages 𝑚 Transmission line 𝑀 Set of all transmission lines
Variables 𝑥 𝑏,𝑖𝑛𝑓𝑙𝑜𝑤 Input flow to bus 𝑏 𝑥 𝑏,𝑜𝑢𝑡𝑓𝑙𝑜𝑤 Output flow from bus 𝑏 𝑥 𝑙𝑓𝑙𝑜𝑤 Load flow of load 𝑙 𝑥 𝑣𝑓𝑙𝑜𝑤 Flow of volatile generator unit 𝑣 𝑥 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 Endogenous capacity of volatile generator unit 𝑣 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,𝑐𝑎𝑟𝑟𝑖𝑒𝑟 Carrier flow of CHP unit 𝑐ℎ𝑝
Preprint Submitted to Applied Energy. Page of 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 Electricity flow of CHP unit 𝑐ℎ𝑝 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,ℎ𝑒𝑎𝑡 Heat flow of CHP unit 𝑐ℎ𝑝 𝑥 ℎ,𝑓𝑟𝑜𝑚𝑓𝑙𝑜𝑤 Electricity flow from the electricity bus for heat pump unit ℎ 𝑥 ℎ,𝑡𝑜𝑓𝑙𝑜𝑤 Heat flow to the heat bus for heat pump unit ℎ 𝑥 𝑠𝑙𝑒𝑣𝑒𝑙 Energy level of storage unit 𝑠 𝑥 𝑠,𝑖𝑛𝑓𝑙𝑜𝑤 Input flow to storage unit 𝑠 𝑥 𝑠,𝑜𝑢𝑡𝑓𝑙𝑜𝑤 Output flow from storage unit 𝑠 𝑥 𝑝ℎ𝑠𝑙𝑒𝑣𝑒𝑙 Energy level of pumped hydro storage unit 𝑝ℎ𝑠 𝑥 𝑝ℎ𝑠𝑓𝑙𝑜𝑤,𝑜𝑢𝑡 Output flow of pumped hydro storage unit 𝑝ℎ𝑠 𝑥 𝑝ℎ𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 Endogenous inflow profile of pumped hydro storage unit 𝑝ℎ𝑠 𝑥 𝑚,𝑓𝑟𝑜𝑚𝑓𝑙𝑜𝑤 Flow from a bus through the transmission line 𝑚 𝑥 𝑚,𝑡𝑜𝑓𝑙𝑜𝑤 Flow to a bus through the transmission line 𝑚 Parameters 𝑐 𝑙𝑝𝑟𝑜𝑓𝑖𝑙𝑒 Exogenous profile of load 𝑙 𝑐 𝑙𝑎𝑚𝑜𝑢𝑛𝑡 Total amount of load 𝑙 𝑐 𝑣𝑝𝑟𝑜𝑓𝑖𝑙𝑒 Exogenous profile of volatile generator 𝑣 𝑐 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 Maximum capacity potential of volatile generator 𝑣 𝑐 𝑐ℎ𝑝𝑏𝑒𝑡𝑎 Power loss index of CHP 𝑐 𝑐ℎ𝑝𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 Electrical efficiency of CHP 𝑐 𝑐ℎ𝑝𝑡ℎ𝑒𝑟𝑚𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 Thermal efficiency of CHP 𝑐 𝑐ℎ𝑝𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑖𝑛𝑔_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 Condensing efficiency of CHP 𝑐 𝑏𝑖𝑜𝑚𝑎𝑠𝑠𝑎𝑚𝑜𝑢𝑛𝑡 Absolute amount of biomass commodity 𝑐 ℎ𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 Conversion efficiency (Coefficient of Performance, i.e., COP) of heat pump unit ℎ 𝑐 𝑠𝑙𝑜𝑠𝑠_𝑟𝑎𝑡𝑒 Loss rate of storage unit 𝑠 𝑐 𝑠𝑒𝑡𝑎_𝑖𝑛 Charging efficiency of storage unit 𝑠 𝑐 𝑠𝑒𝑡𝑎_𝑜𝑢𝑡 Discharging efficiency of storage unit 𝑠 𝑐 𝑠𝑟𝑜𝑢𝑛𝑑𝑡𝑟𝑖𝑝_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 Round Trip efficiency of storage unit 𝑠 𝑐 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 Maximum power capacity of storage unit 𝑠 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 Maximum energy capacity of storage unit 𝑠 𝑐 𝑝ℎ𝑠𝑙𝑜𝑠𝑠_𝑟𝑎𝑡𝑒 Loss rate of pumped hydro storage unit 𝑝ℎ𝑠 𝑐 𝑝ℎ𝑠𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 Efficiency of pumped hydro storage unit 𝑝ℎ𝑠 𝑐 𝑝ℎ𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 Exogenous inflow profile of pumped hydro storage unit 𝑝ℎ𝑠 𝑐 𝑚𝑙𝑜𝑠𝑠 Loss on transmission line 𝑚 𝑐 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 Marginal cost 𝑐 𝑉𝑂𝑀
Variable operation and maintenance cost 𝑐 𝑐𝑎𝑟𝑟𝑖𝑒𝑟_𝑐𝑜𝑠𝑡 Carrier cost 𝜂 Efficiency 𝑐 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 Capacity cost 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 Energy capacity cost of storage 𝑐 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 Annuity cost 𝑐 𝑐𝑎𝑝𝑒𝑥 Capital expenditure cost 𝑐 𝑊𝐴𝐶𝐶
Weighted Average Cost of Capital 𝑐 𝐹𝑂𝑀
Fixed operation and maintenance Cost 𝑛 Lifetime 𝑐 𝐴𝐼𝑉
Annual investment cost 𝑐 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 Optimized capacity cost 𝑐 𝑇𝐼𝑉
Total Investment cost 𝑐 𝐿𝐶𝑂𝐸
Levelized cost of electricity 𝐼 𝑛 Initial cost of investment expenditure 𝑀 𝑛 Sum of all O&M costs 𝐹 𝑛 Sum of all fuel Costs 𝐸 𝑛 Sum of all electrical energy produced 𝑟 Discount rate
Preprint Submitted to Applied Energy. Page of
1. Introduction
A clear rulebook was adopted for the practical implementation of the Paris Agreement in December 2018 at the United Nations Climate Conference (COP24) in Katowice, which delineated a world-wide climate action plan to mitigate climate change by reducing global warming to 1.5° C if possible [1]. To achieve a climate-neutral society with net-zero greenhouse gas (GHG) emissions across all sectors by 2050, the European Commission endorsed a strategic long term vision in line with the Paris Agreement for the European Union (EU) [2]. The North Sea (NS) region can be seen as a representative area to demonstrate the feasibility and plausible pathways for achieving the ambitious target of net-zero emission across all the sectors in an energy system [3]. As a leading industrialized nation of the NS region and the EU, Germany already adopted a climate action plan for the realistic implementation of extensive GHG neutrality across all the energy sectors by 2050 [4]. This ambitious energy target requires 'reinvention' of energy systems to be technically feasible and economically viable, guarantying realistic solutions to ensure affordability, reliability, and sustainability [5]. The overcapacity of volatile generators in a 100% renewable-based energy system leads to excess energy in the electricity grid. A relatively new approach known as 'sector coupling' can use this surplus energy efficiently [6]. Sector coupling has emerged as a new concept in energy and climate policy discussions in recent years. The 'Climate Action Plan 2050' and the 'Green Paper on Energy Efficiency' reflect the high political significance of sector coupling, among other things in Germany [4,7]. Sector coupling can make a decisive contribution to the achievement of ambitious climate protection goals through increased use of renewable electricity in the heating and transport sectors and industry to substitute fossil fuels. The expansion of renewable energies in Germany will increase the need for grid expansion, particularly in local distribution grids for solar photovoltaic (PV) and onshore wind plants, and in the area of transmission grids for offshore wind power. The current power system of Germany has many fossil fuel-based and nuclear-based power plants in Southern Germany. A gradual exit from fossil fuel and nuclear power will require shifting to renewables from offshore wind plants in Northern Germany. Therefore, there will be a need for transmission grid expansion from North to South at the same time. The transmission grid operators and the federal government of Germany have accelerated the development of Grids from Northern to Southern Germany, with 4,650 kilometers to be constructed by 2025 [8]. Figure 1 shows the status of grid expansion in Germany in which the expansion plan from north to south along with other grids in planning and development stages are illustrated [9].
Figure 1: Current status of electricity transmission network planning and development in Germany. The orange, red, and yellow lines show that many North-South grid extension projects are in the planning and development phase. Source: Federal Network Agency of Germany (Bundesnetzagentur) 2020 [9].
Preprint Submitted to Applied Energy. Page of Flexibility and sector coupling can bring renewable energies into the various energy sectors in high proportions and raises energy efficiency potentials effectively. By adopting solutions like power-to-heat (P2H) technologies (such as electric heat pumps), and power-to-gas (P2G) technologies (such as Hydrogen storage via electrolysis); the transformation of energy between different energy sectors can be made even more independent of the supply and demand. Flexibility can be offered in various ways, for example, shifting heat pump or electric vehicle loads in private households, and even shifting the energy consumption in industries as a part of an integrated, sector-coupled network. However, the energy flow should be smartly and effectively managed between the sectors to stabilize the network operation while keeping the system flexible and efficient [10].
2. State of the Art and Research Question
In the last two decades, both 'sector coupling' and '100% renewable energy systems' have been subjects of interest for energy researchers globally, as reviewed by the Author in an earlier article [3]. Several pieces of research investigated 100% or near-100% renewable energy systems from the national perspectives. Such investigation includes energy system analysis of Australia, Barbados, Belgium, Brazil, Canada, China, Colombia, Costa Rica, Croatia, Denmark, Finland, France, Germany, Great Britain, Iceland, India and the SAARC region, Iran, Ireland, Italy, Japan, Macedonia, New Zealand, Nigeria, Norway, Pakistan, Paraguay, Portugal, Saudi Arabia, Seychelles, Tokelau, Turkey, Ukraine, the United Kingdom, the United States, and Uruguay [11–52]. Other than these national studies, there are many other 100% renewable system studies larger than national energy systems covering the World, North-East Asia, the ASEAN region, Europe and its neighbors, Europe, South-East Europe, and the Americas [53–66]. Similarly, there are also regional level studies on 100% system for Hvar (Croatia), Mecklenburg-Vorpommern (Germany), Schleswig-Holstein (Germany), Orkney (Scotland), Samsø and many other regions (Denmark), and the Åland Islands (Finland), and the Canary Islands (Spain) [67–70]. Nonetheless, most of these studies focus on 100% renewable-based electricity systems. Only a few consider energy transition pathways for reaching the target, including all the relevant sectors such as heating, cooling, transport, and gas [71]. In German energy system analyses, several studies focus on individual energy sectors such as the heating market, transportation, future electricity market. For achieving the energy transition towards climate-neutrality, Schmid et al. identified and characterized actors who can put the energy transition into practice, but they focused on the power sector only [72]. In a similar publication, Lehmann and Nowakowski analyzed three scenarios for the future electricity system in Germany [73]. Robinius et al. reviewed sector coupling scenarios for Germany linking electricity and transport sectors [6,74]. Gullberg et al. described how the interconnection between Norway and Germany could ensure a low-carbon energy future [75]. Scholz et al. identified the bottlenecks of using only renewables for the energy transition [76]. Schroeder et al. compared different scenarios to investigate the need for grid expansions in Germany [77]. Although there are various modeling and analysis on the German energy transition towards climate neutrality, most of them focus either on specific aspects of an individual energy sector or the markets and actors linked with the energy system. A few studies outline a detailed techno-economic analysis using 100% renewables, including multiple energy sectors in Germany. Palzer and Henning showed that a 100% renewable energy system for power and heat is technically possible, and the overall annual cost for the system will be comparable to today's price. However, their analysis assumes that the building sector, the heat requirement is reduced by 60% in the future compared to today's demand, and their analyzing tool REMod-D is not an open-source model. In another recent publication, Hansen et al. concluded that the full energy system transition towards 100% renewables by 2050 in Germany is technically and economically possible, but resource potentials, mainly biomass, is a big challenge for this transition. Hansen et al. used EnergyPLAN for their analysis, a popular free-to-use simulation tool for modeling 100% systems for all energy sectors. However, it is not possible to analyze the capacity expansion mechanism and reach an optimum solution using EnergyPLAN [78]. A literature review by Maruf shows that there is a clear research gap in applying cross-sectoral holistic approaches using comprehensive open modeling techniques for analyzing 100% renewable and sector-coupled models in Germany and the other countries in the NS region [3]. Therefore, based on the scope of further research on this subject, the following research question is formulated–
How feasible is it to transform towards a 100% renewable energy system for both power and heat sectors in Germany by 2050?
Answering the main research question raises additional questions on the overall energy mix, investment cost and capacities, the issue of grid expansion within Germany, and different flexibility aspects of the system; which formulates the following sub-research questions–
Preprint Submitted to Applied Energy. Page of In which capacities such a system can be implemented? What are the estimated investment costs for the different system components? What are the flexibility aspects of grid expansion, storages, and dispatchable loads in such a system?
The main objective of the paper is to design, develop, and investigate an open-source energy model for Germany for both power and heat sectors. The model analyzes different scenarios to investigate moderate to extreme conditions to determine the plausible energy mix and required investment in component-wise capacities and costs. The model considers dividing the German energy system into two sub-national regions so that the grid expansion from Northern to Southern Germany can be analyzed. It also helps to understand the underlying energy flow mechanism and the role of different energy components from both national and sub-national perspectives. The analysis of the heating sector in this model is limited to the use of building heat, including space heating and domestic hot water demands. The study does not consider the inclusion of industrial process heating demands using renewables. Section 3 describes the methodology of the model, which consists of the architecture of the model and its component-wise mathematical description. Section 4 describes the details of the working mechanism of the developed model and the input data used for the analysis. Section 5 describes the development of different scenarios. Section 6 presents and compares the scenario results and examines the details of the system based on the research questions. Section 7 summarizes the results and concludes with the future steps of the research.
3. Methodology
The optimization model follows a hybrid approach where the current technology capacities are exogenously defined, and the future investment capacities are endogenously determined. System boundaries, according to technology potentials, are set to avoid any unrealistic solution based on overestimation. The 'Open Sector-coupled Energy Model for Germany (OSeEM-DE)' is an application constructed using 'Oemof Tabular'- python-based linear programming (LP) optimization tool under the open energy modeling framework (Oemof) [79]. As shown in Figure 2, the two German sub-national energy system nodes are Northern Germany (NDE) and Southern Germany (SDE). NDE consists of Schleswig-Holstein, Lower Saxony, Bremen, Hamburg, and Mecklenburg-Vorpommern, and SDE consists of the remaining eleven states of Germany. The power exchange between NDE and SDE is possible using the transshipment approach via NDE-SDE Link.
Figure 2: The German national energy system with two sub-national nodes, NDE (shown using blue color) and SDE (shown using green color). Map source: Wikimedia Commons [80].
Figure 3 illustrates the Oemof-based OSeEM-DE energy system model. The volatile components of the model are onshore wind, offshore wind, Solar Photovoltaic, and hydro Run-of-the-River (ROR) plants. The fuel input of the Combined Heat and Power (CHP) plants comes from biomass resources. Besides CHP, Air Source Heat Pump (ASHP) and Ground Source Heat Pump (GSHP) can generate heat. The storage options are Pumped Hydro Storage (PHS), Lithium-ion (Li-ion) battery, Vanadium Redox (Redox) flow battery, Hydrogen (H ) storage, and Adiabatic Compressed Air Energy Storage (ACAES). The heat storage option is Thermal Energy Preprint Submitted to Applied Energy. Page of Storage (TES) using hot water tanks. NDE and SDE energy systems are almost identical, except that offshore wind and ACAES components are only available in NDE.
Figure 3: Simplified block diagram of the Oemof-based OSeEM-DE model for Germany showing NDE and SDE nodes.
The OSeEM-DE model follows the formulation methodology using Oemof Solph described by Hilpert, where the maximum potential constrains the volatile renewable sources, total biomass amount, and storage capacities [81]. The transmission capacity between NDE and SDE and the heat storage capacities are also limited exogenously. The upper limit for the P2H technologies are subject to optimization but depends on the availability of electricity. The different components of the energy system and their mathematical formulations are as follows, where 𝑥 denotes the endogenous variables, and 𝑐 denotes the exogenous parameters used in the model. There are three types of buses in the energy model: electrical, heat, and fuel bus. Since all flows into and out of a bus are balanced, for the set of all buses 𝑏 ∈ 𝐵 , sum of all input flows 𝑥 𝑏,𝑖𝑛𝑓𝑙𝑜𝑤 to a bus 𝑏 must be equal to the sum of all output flows 𝑥 𝑏,𝑜𝑢𝑡𝑓𝑙𝑜𝑤 : ∑ 𝑥 𝑏,𝑖𝑛𝑓𝑙𝑜𝑤 (𝑡) = ∑ 𝑥 𝑏,𝑜𝑢𝑡𝑓𝑙𝑜𝑤 (𝑡) ∀𝑡 ∈ 𝑇, ∀𝑏 ∈ 𝐵 (1) Two types of loads are considered in the energy model: electricity and heat. The heat load consists of space heat and domestic hot water. For the set of all loads 𝑙 ∈ 𝐿 , the load flow 𝑥 𝑙𝑓𝑙𝑜𝑤 at every time step 𝑡 must be equal to the product of two exogenously given inputs: profile value of the load 𝑐 𝑙𝑝𝑟𝑜𝑓𝑖𝑙𝑒 at time step 𝑡 , and the total amount of the load 𝑐 𝑙𝑎𝑚𝑜𝑢𝑛𝑡 : 𝑥 𝑙𝑓𝑙𝑜𝑤 (𝑡) = 𝑐 𝑙𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) . 𝑐 𝑙𝑎𝑚𝑜𝑢𝑛𝑡 ∀𝑡 ∈ 𝑇, ∀𝑙 ∈ 𝐿 (2) The volatile generators in the model are onshore and offshore wind, solar PV, and hydro ROR plants. These components are connected to electricity buses. The offshore wind component is available only in NDE. For all the volatile generators 𝑣 ∈ 𝑉 , the flow 𝑥 𝑣𝑓𝑙𝑜𝑤 at every time step 𝑡 must be equal to the product of the capacity 𝑥 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 and the profile value of the volatile generator 𝑐 𝑣𝑝𝑟𝑜𝑓𝑖𝑙𝑒 : 𝑥 𝑣𝑓𝑙𝑜𝑤 (𝑡) = 𝑥 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (𝑡). 𝑐 𝑣𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) ∀𝑡 ∈ 𝑇, ∀𝑣 ∈ 𝑉 (3) The endogenously obtained capacity of the generator 𝑥 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 at every time step 𝑡 must be less than or equal to the maximum capacity potential of the volatile component 𝑐 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 : Preprint Submitted to Applied Energy. Page of 𝑥 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (𝑡) ≤ 𝑐 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 ∀𝑡 ∈ 𝑇, ∀𝑣 ∈ 𝑉 (4) Since the model is 100% RES-based, the CHP plants use only biomass resources as fuel. Thus, biomass goes into the fuel bus, which later goes as the input of CHP, as shown in Figure 3. The CHP runs in extraction turbine mode, as shown by (5 – 7), according to Mollenhauer et al. [82]. (5) shows the relation between the input carrier flow 𝑥 𝑐 ℎ 𝑝,𝑓𝑙𝑜𝑤,𝑐𝑎𝑟𝑟𝑖𝑒𝑟 and the two output flows: electrical output flow 𝑥 𝑐 ℎ 𝑝𝑓𝑙𝑜𝑤,𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 and heat output flow 𝑥 𝑐 ℎ 𝑝𝑓𝑙𝑜𝑤, ℎ 𝑒𝑎𝑡 , at every time step 𝑡 . (6) shows the relationship between the two output flows. 𝑐 𝑐 ℎ 𝑝𝑏𝑒𝑡𝑎 is the power loss index, which is derived using (7). 𝑐 𝑐 ℎ 𝑝𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 , 𝑐 𝑐 ℎ 𝑝𝑡 ℎ 𝑒𝑟𝑚𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 and 𝑐 𝑐 ℎ 𝑝𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑖𝑛𝑔_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 denote the electrical, thermal and condensing efficiencies of the CHP unit, respectively. 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑡) = 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 (𝑡) + 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,ℎ𝑒𝑎𝑡 (𝑡) . 𝑐 𝑐ℎ𝑝𝑏𝑒𝑡𝑎 𝑐 𝑐ℎ𝑝𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑖𝑛𝑔_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ∀𝑡 ∈ 𝑇 (5) 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 (𝑡) ≥ 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,ℎ𝑒𝑎𝑡 (𝑡). 𝑐 𝑐ℎ𝑝𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝑐 𝑐ℎ𝑝𝑡ℎ𝑒𝑟𝑚𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ∀𝑡 ∈ 𝑇 (6) 𝑐 𝑐ℎ𝑝𝑏𝑒𝑡𝑎 = 𝑐 𝑐ℎ𝑝𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑖𝑛𝑔_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 − 𝑐 𝑐ℎ𝑝𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝑐 𝑐ℎ𝑝𝑡ℎ𝑒𝑟𝑚𝑎𝑙_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 (7) Equation (8) models the limited availability of biomass commodities where the aggregated inflows are constrained by the absolute amount of the biomass commodity 𝑐 𝑏𝑖𝑜𝑚𝑎𝑠𝑠𝑎𝑚𝑜𝑢𝑛𝑡 : ∑ 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤,𝑐𝑎𝑟𝑟𝑖𝑒𝑟 (𝑡) ≤ 𝑐 𝑏𝑖𝑜𝑚𝑎𝑠𝑠𝑎𝑚𝑜𝑢𝑛𝑡 ∀𝑡 ∈ 𝑇 (8) In addition to CHPs, two types of heat pumps are used to supply heat loads in the model: ASHP and GSHP, the latter being the more efficient but expensive option. Oemof Solph's conversion component, which converts power to heat, is used for modeling both heat pumps. Therefore, a conversion process of one input flow 𝑥 ℎ ,𝑓𝑟𝑜𝑚𝑓𝑙𝑜𝑤 (electricity flow from the electricity bus) and one output 𝑥 ℎ ,𝑡𝑜𝑓𝑙𝑜𝑤 (heat flow to the heat bus) and a conversion factor 𝑐 ℎ ,𝑡𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 (conversion efficiency i.e., coefficient of performance of the heat pump) at every time step 𝑡 models all the heat pumps ℎ ∈ 𝐻 : 𝑥 ℎ,𝑡𝑜𝑓𝑙𝑜𝑤 (𝑡) = 𝑥 ℎ,𝑓𝑟𝑜𝑚𝑓𝑙𝑜𝑤 (𝑡). 𝑐 ℎ,𝑡𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ∀𝑡 ∈ 𝑇, ∀ℎ ∈ 𝐻 (9) In addition to PHS, the other electricity storage technologies used in the model are Li-ion and Redox batteries, ACAES, and H storage. Hot water-based TES is the only heat storage component in both NDE and SDE. Oemof Solph's generic storage formulations are used to model all the storage components except PHS. For all these storages 𝑠 ∈ 𝑆 , the mathematical model includes the input and output flows and the storage level: 𝑥 𝑠𝑙𝑒𝑣𝑒𝑙 (𝑡) = 𝑥 𝑠𝑙𝑒𝑣𝑒𝑙 (𝑡 − 1). (1 − 𝑐 𝑠𝑙𝑜𝑠𝑠_𝑟𝑎𝑡𝑒 ) + 𝑐 𝑠𝑒𝑡𝑎_𝑖𝑛 . 𝑥 𝑠𝑓𝑙𝑜𝑤,𝑖𝑛 (𝑡) − 𝑥 𝑠𝑓𝑙𝑜𝑤,𝑜𝑢𝑡 (𝑡)𝑐 𝑠𝑒𝑡𝑎_𝑜𝑢𝑡 ∀𝑡 ∈ 𝑇, ∀𝑠 ∈ 𝑆 (10) Where 𝑥 𝑠𝑙𝑒𝑣𝑒𝑙 indicates the storage energy level, 𝑐 𝑠𝑙𝑜𝑠𝑠_𝑟𝑎𝑡𝑒 marks the loss rate for the storage, 𝑥 𝑠𝑓𝑙𝑜𝑤,𝑖𝑛 and 𝑥 𝑠𝑓𝑙𝑜𝑤,𝑜𝑢𝑡 indicates the input and output flows, and 𝑐 𝑠𝑒𝑡𝑎_𝑖𝑛 and 𝑐 𝑠𝑒𝑡𝑎_𝑜𝑢𝑡 denotes the charging and discharging efficiencies of the storage. The charging and discharging efficiency is formulated from the roundtrip efficiency using 𝑐 𝑠𝑒𝑡𝑎 =√𝑐 𝑠𝑟𝑜𝑢𝑛𝑑𝑡𝑟𝑖𝑝_𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 . The input and output flows 𝑥 𝑠𝑓𝑙𝑜𝑤 are constrained by the maximum power capacity Preprint Submitted to Applied Energy. Page of 𝑐 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 as shown in (11). The energy level 𝑥 𝑠𝑙𝑒𝑣𝑒𝑙 is constrained by the maximum energy capacity 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 as shown in (12). 𝑥 𝑠𝑓𝑙𝑜𝑤 (𝑡) ≤ 𝑐 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 ∀𝑡 ∈ 𝑇, ∀𝑠 ∈ 𝑆 (11) 𝑥 𝑠𝑓𝑙𝑜𝑤 (𝑡) ≤ 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 ∀𝑡 ∈ 𝑇, ∀𝑠 ∈ 𝑆 (12) The PHS are modeled as storage units with a constant inflow and possible spillage: 𝑥 𝑝ℎ𝑠𝑙𝑒𝑣𝑒𝑙 (𝑡) = 𝑥 𝑝ℎ𝑠𝑙𝑒𝑣𝑒𝑙 (𝑡 − 1). (1 − 𝑐 𝑝ℎ𝑠𝑙𝑜𝑠𝑠_𝑟𝑎𝑡𝑒 ) + 𝑥 𝑝ℎ𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) − 𝑥 𝑝ℎ𝑠𝑓𝑙𝑜𝑤,𝑜𝑢𝑡 (𝑡)𝑐 𝑝ℎ𝑠𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ∀𝑡 ∈ 𝑇 (13) Where 𝑥 𝑝 ℎ 𝑠𝑙𝑒𝑣𝑒𝑙 indicates the pumped hydro storage energy level, 𝑐 𝑝ℎ𝑠𝑙𝑜𝑠𝑠_𝑟𝑎𝑡𝑒 marks the loss rate for the PHS, 𝑥 𝑝 ℎ 𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 indicates the endogenous inflow profile, 𝑥 𝑝 ℎ 𝑠𝑓𝑙𝑜𝑤,𝑜𝑢𝑡 denotes the output flow from the PHS, and 𝑐 𝑝 ℎ 𝑠𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 marks the efficiency of the PHS. The hydro inflow is constrained by an exogenous inflow profile: 𝑝ℎ𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) ≤ 𝑐 𝑝ℎ𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) ∀𝑡 ∈ 𝑇 (14) Therefore, if the inflow exceeds the maximum storage capacity, spillage is possible by setting 𝑥 𝑝 ℎ 𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 to lower values. The spillage at time step 𝑡 can therefore be defined by 𝑐 𝑝 ℎ 𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) − 𝑥 𝑝 ℎ 𝑠𝑝𝑟𝑜𝑓𝑖𝑙𝑒 (𝑡) . The electricity transmission between two energy systems via NDE-SDE Link is modeled using the transshipment approach, which facilitates simple electricity exchange (import-export) after considering a transmission loss factor. Therefore, transmission lines 𝑚 ∈ 𝑀 are modeled according to the following mathematical formulation: 𝑥 𝑚,𝑓𝑟𝑜𝑚𝑓𝑙𝑜𝑤 (𝑡) = (1 − 𝑐 𝑚𝑙𝑜𝑠𝑠 ). 𝑥 𝑚,𝑡𝑜𝑓𝑙𝑜𝑤 (𝑡) ∀𝑡 ∈ 𝑇, ∀𝑚 ∈ 𝑀 (15) Where 𝑥 𝑓𝑟𝑜𝑚,𝑚𝑓𝑙𝑜𝑤 indicates the flow from the supplying energy system, 𝑥 𝑚,𝑡𝑜𝑓𝑙𝑜𝑤 indicates the flow to the receiving energy system, and 𝑐 𝑚𝑙𝑜𝑠𝑠 indicates the loss on transmission line 𝑚 . The marginal costs 𝑐 𝑣,𝑐 ℎ 𝑝, ℎ ,𝑠𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 are calculated based on the variable operation and maintenance (VOM) cost 𝑐 𝑣,𝑐 ℎ 𝑝, ℎ ,𝑠𝑉𝑂𝑀 , carrier cost 𝑐 𝑣,𝑐 ℎ 𝑝, ℎ ,𝑠𝑐𝑎𝑟𝑟𝑖𝑒𝑟_𝑐𝑜𝑠𝑡 , and the efficiency of the corresponding technology 𝜂 𝑣,𝑐ℎ𝑝,ℎ,𝑠 : 𝑐 𝑣,𝑐ℎ𝑝,ℎ,𝑠𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 = 𝑐 𝑣,𝑐ℎ𝑝,ℎ,𝑠𝑉𝑂𝑀 + 𝑐 𝑣,𝑐ℎ𝑝,ℎ,𝑠𝑐𝑎𝑟𝑟𝑖𝑒𝑟_𝑐𝑜𝑠𝑡 𝜂 𝑣,𝑐ℎ𝑝,ℎ,𝑠 (16) The capacity costs for volatile generators, CHP and heat pumps 𝑐 𝑣,𝑐 ℎ 𝑝, ℎ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 are calculated based on the fixed operation and maintenance (FOM) cost 𝑐 𝑣,𝑐 ℎ 𝑝, ℎ 𝐹𝑂𝑀 , and the annuity of the corresponding technology 𝑐 𝑣,𝑐ℎ𝑝,ℎ𝑎𝑛𝑛𝑢𝑖𝑡𝑦 , as shown in (17). The annuity 𝑐 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 is calculated using (18), which consist of the initial capital expenditure 𝑐 𝑐𝑎𝑝𝑒𝑥 , the weighted average cost of capital 𝑐 𝑊𝐴𝐶𝐶 , and the lifetime of the investment 𝑛 for the respective technology. 𝑐 𝑣,𝑐ℎ𝑝,ℎ𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 = 𝑐 𝑣,𝑐ℎ𝑝,ℎ𝐹𝑂𝑀 + 𝑐 𝑣,𝑐ℎ𝑝,ℎ𝑎𝑛𝑛𝑢𝑖𝑡𝑦 (17) 𝑐 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 = 𝑐 𝑐𝑎𝑝𝑒𝑥 . (𝑐 𝑊𝐴𝐶𝐶 . (1 + 𝑐
𝑊𝐴𝐶𝐶 ) 𝑛 ((1 + 𝑐 𝑊𝐴𝐶𝐶 ) 𝑛 − 1) (18) In the case of storages, the capacity costs 𝑐 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 and the storage capacity costs 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 are calculated using (19 – 20): Preprint Submitted to Applied Energy. Page of 𝑐 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 = 𝑐 𝑠,𝑝𝑜𝑤𝑒𝑟𝑎𝑛𝑛𝑢𝑖𝑡𝑦 (19) 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 = 𝑐 𝑠𝐹𝑂𝑀 + 𝑐 𝑠,𝑒𝑛𝑒𝑟𝑔𝑦𝑎𝑛𝑛𝑢𝑖𝑡𝑦 (20) Where, 𝑐 𝑠,𝑝𝑜𝑤𝑒𝑟𝑎𝑛𝑛𝑢𝑖𝑡𝑦 is the annuity cost of storage power , and 𝑐 𝑠,𝑒𝑛𝑒𝑟𝑔𝑦𝑎𝑛𝑛𝑢𝑖𝑡𝑦 is the annuity cost of storage energy. These two annuities are calculated using the formulation of (18). 𝑐 𝑠𝐹𝑂𝑀 is the fixed operation and maintenance cost (FOM) of energy storage. In addition to these modeling equations, some costs are calculated and analyzed after a successful model run, based on the optimization results. The annual investment cost 𝑐 𝐴𝐼𝑉 is calculated multiplying the annuity 𝑐 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 and the optimized capacity 𝑐 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 , as shown in (21). The total investment (overnight) investment cost 𝑐 𝑇𝐼𝑉 is calculated multiplying the capital expenditure 𝑐 𝑐𝑎𝑝𝑒𝑥 , and the optimized capacity 𝑐 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 , as shown in (22). Furthermore, the Levelized Costs of Electricity 𝑐 𝐿𝐶𝑂𝐸 is calculated from the ratio of the Net Present Value (NPV) of total costs of over lifetime (including fixed and variable operation and maintenance costs, fuel costs, and the discount rate), and the NPV of the electrical energy produced over the lifetime, as shown in (23). 𝑐 𝐴𝐼𝑉 = 𝑐 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 . 𝑐 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (21) 𝑐 𝑇𝐼𝑉 = 𝑐 𝑐𝑎𝑝𝑒𝑥 . 𝑐 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (22) 𝑐 𝐿𝐶𝑂𝐸 = ∑ (𝐼 𝑛 + 𝑀 𝑛 + 𝐹 𝑛 )(1 + 𝑟) 𝑛 ∑ 𝐸 𝑛 (1 + 𝑟) 𝑛 (23) Where 𝐼 𝑛 indicates the initial cost of investment expenditures (same as 𝑐 𝑐𝑎𝑝𝑒𝑥 ), 𝑀 𝑛 indicates the sum of all operation and maintenance expenditures (sum of 𝑐 𝑉𝑂𝑀 and 𝑐 𝐹𝑂𝑀 ), and 𝐹 𝑛 indicates the fuel expenditure (such as the carrier cost of biomass), 𝐸 𝑛 indicates the sum of all electrical energy generation, 𝑟 indicates the discount rate (same as 𝑐 𝑊𝐴𝐶𝐶 ), and 𝑛 indicates the lifetime. The objective function is created from all instantiated objects which use all operating costs and investment costs arguments: 𝑚𝑖𝑛: ∑ 𝑥 𝑣𝑓𝑙𝑜𝑤 (𝑡). 𝑐 𝑣𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 ⏞ 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔_𝑐𝑜𝑠𝑡 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑒 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟𝑣,𝑡 + ∑ 𝑥 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 . 𝑐 𝑣𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 ⏞ 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡_𝑐𝑜𝑠𝑡 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑒 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟𝑣 + ∑ 𝑥 𝑐ℎ𝑝𝑓𝑙𝑜𝑤 (𝑡). 𝑐 𝑐ℎ𝑝𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 ⏞ 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔_𝑐𝑜𝑠𝑡 𝐶𝐻𝑃 𝑐ℎ𝑝,𝑡 + ∑ 𝑥 𝑐ℎ𝑝𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 . 𝑐 𝑐ℎ𝑝𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 ⏞ 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡_𝐶𝐻𝑃 𝑐ℎ𝑝 + ∑ 𝑥 ℎ𝑓𝑙𝑜𝑤 (𝑡). 𝑐 ℎ𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 ⏞ 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔_𝑐𝑜𝑠𝑡 𝐻𝑒𝑎𝑡 𝑃𝑢𝑚𝑝 ℎ,𝑡 + ∑ 𝑥 ℎ𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 . 𝑐 ℎ𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 ⏞ 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡_𝑐𝑜𝑠𝑡 𝐻𝑒𝑎𝑡 𝑃𝑢𝑚𝑝ℎ + ∑ 𝑥 𝑠𝑓𝑙𝑜𝑤 (𝑡). 𝑐 𝑠𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙_𝑐𝑜𝑠𝑡 ⏞ 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔_𝑐𝑜𝑠𝑡 𝑆𝑡𝑜𝑟𝑎𝑔𝑒𝑠,𝑡 + ∑ 𝑥 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 . 𝑐 𝑠𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 + 𝑥 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 . 𝑐 𝑠𝑠𝑡𝑜𝑟𝑎𝑔𝑒_𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦_𝑐𝑜𝑠𝑡 ⏞ 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡_𝑐𝑜𝑠𝑡 𝑆𝑡𝑜𝑟𝑎𝑔𝑒𝑠 (24)
4. Model
The underlying concept of the OSeEM-DE model uses the formulation of LP and mixed-integer linear programming (MILP) from a generic object-oriented structure of Oemof Solph, which allows creating models on different levels of detail using predefined components and an optional formulation of expressions and constraints. Figure 4 shows a summary of the OSeEM-DE model input and output.
Preprint Submitted to Applied Energy. Page of Figure 4: Input and output of the OSeEM-DE model
The input data used in the model are the capacities and potentials of renewable energy-based power plants (such as wind, PV), heat generation technologies (such as CHP, heat pump), electricity and heat demands, transshipment capacity, storage capacities, and their potential. Also, operating costs (i.e., marginal cost) and the investment costs (i.e., capacity cost) for all the considered technologies are provided as input. After solving the model using open model solvers, the results are post-processed using Oemof Tabular's post-processing scripts. The output of the model provides information on the generation mix, investment capacities according to the provided capacities and available potential, balance in each of the buses, import/export between energy systems (in this case between NDE and SDE), filling level of the storages and the shadow prices. Python language is used for scripting the model according to the flowchart shown in Figure 5. After starting the necessary packages (such as pandas, facades, post-processing), input data, and result directories are set up, and input data are read from external .csv files. Different scenarios are built in this stage with different datasets, which are further discussed in the scenario development part of this paper. The input datasets are pre-processed before importing them to the input .csv files. After the input dataset is read, the energy system is created, and different buses are created and added to the energy system using Oemof Solph. Then different components (such as power, heat, and storage components) are added to the energy system from Oemof Tabular's 'Facades' classes. Then the energy model is created and solved using Oemof Solph. After successful optimization, results are post-processed and written to several .csv files using Oemof Tabular's post-processing tool, which are later illustrated using Oemof Tabular's 'Plots' tool.
Preprint Submitted to Applied Energy. Page of Figure 5: OSeEM-DE Model development
The model optimizes investment and operation for a full year of historical hourly data, with 2011 chosen as the primary representative year because of its average wind conditions, high solar irradiation (representing the expected warm condition in 2050 due to the climate change), slightly lower overall heating demand, and duration of maximum heating demand during the wintery days [83]. 4.1.1. Electricity and Heat Load The hourly electricity load data based on the
ENTSO-e statistical database are obtained from the
Open Power System Data (OPSD) Project [84,85]. Hourly normalized time series are obtained from the electricity load data for both NDE and SDE energy systems based on population-based clustering. The total electricity demand for Germany in 2050, based on the representative year, is 532.77 TWh el , of which NDE accounts for 96.6 TWh el , and SDE accounts for 436.16 TWh el . The hourly heat load data based on the When2Heat Project are obtained from the
OPSD Project database [84,86,87]. Heat demand time series for space heat and hot water for Germany are obtained separately from the
When2Heat profiles and are clustered and normalized for use as inputs of the model. The total heat demand for Germany in 2050, based on the representative year, is 648.53 TWh th . Total space heating demand accounts for 533.6 TWh th, of which NDE accounts for 96.75 TWh th , and SDE accounts for 436.85 TWh th . Total hot water demand accounts for 114.92 TWh th, of which NDE accounts for 20.83 TWh th , and SDE accounts for 94.08 TWh th . 4.1.2. Volatile Generator Normalized onshore wind profiles based on MERRA-2 datasets are obtained separately for NDE and SDE energy systems from the
Renewables Ninja Project . Normalized offshore wind profiles based on
MERRA-2 datasets are also obtained from the
Renewables Ninja Project . Similarly, normalized solar PV profiles based
Preprint Submitted to Applied Energy. Page of on MERRA-2 datasets are obtained separately for NDE and SDE energy systems from the
Renewables Ninja Project [88]. Hydro inflow data for the ROR plants are obtained and normalized from the
Dispa-SET Project database [89]. The current capacity and potential data are obtained or calculated from the
Agency for Renewable Energies , Deutsche WindGuard , Limes-EU
Project , ZNES , ANGUS II Project , and
PyPSA Project databases [90–97]. Table 1 shows the capacity and available potential data for the volatile generators in 2050.
Table 1.
Capacity and potential for volatile generators in the German energy system in 2050
Energy System Onshore Wind [GW el ] Offshore Wind [GW el ] Solar PV [GW el ] Hydro ROR [GW el ] NDE Capacity 22.12 6.66 7.56 0.09 Available Potential 49.88 76.94 55.77 0.06
SDE
Capacity 31.79 - 37.66 4.2 Available Potential 118.81 - 188.07 1.1
Germany
Total Capacity 53.91 6.66 45.23 4.29 Total Available Potential 168.69 76.94 243.84 1.16
Hotmaps Project for forest residues, livestock effluents, and agricultural residues [98]. According to the calculation for a full year, the available potential for biomass in NDE is 141.1 PJ, and in SDE, it is 493.23 PJ, totaling 634.33 PJ for the whole of Germany. For the current capacities, it is assumed that the existing biomass and biogas-based power plants are converted to CHP plants by 2050. Therefore, 4.74 GW CHP in NDE and 8.86 GW CHP in SDE energy systems are assumed to be installed and fully operational by 2050. The current heat pump capacities are considered zero, and their investment potentials are not constrained. However, since heat pumps are P2H devices, their investment capacities depend upon limited available power from the potentially constrained volatile generators. 4.1.4. Storage The capacity and available maximum potential data for storage investments are described in Table 2. Data for Li-ion and Redox flow batteries, H storages, and ACAES are obtained from the ANGUS II Project scenarios for Germany in 2050 [97]. PHS data are obtained from the
Dispa-SET Project dataset [89]. For batteries, H storage, and TES, it is assumed that 18% of the total potential of Germany is available for NDE, and the rest is available for SDE. Table 2.
Capacity and maximum potential for storage investments
Energy System Li-ion [GW el ] Redox [GW el ] Hydrogen [GW el ] ACAES [GW el ] PHS [GW el ] TES* [GW th ] NDE Capacity 0 0 0 0.29 0.34 0 Available Potential 2.82 0.17 1.82 3.43 - 1.8
SDE
Capacity 0 0 0 - 0.82 0 Available Potential 12.83 0.76 8.28 - - 8.2
Germany
Capacity 0 0 0 0.29 8.57 0 Available Potential 15.65 0.93 10.1 3.43 - 10 *Own assumption
The energy storage potentials for the batteries, H storage, and ACAES investment are subject to optimization. The storage potential for the existing ACAES plant in Huntorf is 0.58 GWh el [99]. Inflow data for PHS are derived from the Dispa-SET Project 's scaled inflow dataset and the current PHS capacity of Germany. Storage
Preprint Submitted to Applied Energy. Page of capacities for PHS are taken from the Dispa-SET Project dataset, which is 1.7 GWh el for NDE, and 717 GWh el for SDE [89]. PHS investment is excluded because of the limited expansion capacity. A loss rate of 1% for PHS and 1.4% for TES are considered in the model [83,89,97]. 4.1.5 Transmission Line The transmission lines in between NDE and SDE energy systems (NDE-SDE Link) are modeled as transshipment capacities with line loss. The total transmission capacity is set and varied exogenously for different scenarios. A line loss of 4% is considered for all the cases according to the IEA data for German transmission lines [100]. The investment capacity costs are based on annuity and fixed operation and maintenance (O&M) costs, and the marginal costs are based on variable O&M costs, the carrier costs, and the efficiencies. The carbon costs are not considered in the marginal costs since the system is 100% renewable. The required data for calculating the costs, such as capital expenditure, lifetime, the Weighted Average Cost of Capital (WACC), storage capacity cost, carrier cost, fixed and variable O&M costs, efficiencies, and maximum hours for storages, are taken from various references, which are summarized in Table A.1 in Appendix A.
5. Scenarios
Three scenarios, namely
Base , Conservative , and
Progressive , are developed and analyzed to answer the research questions in different conditions. The volatile generator inputs remain the same in all scenarios. The existing PHS and ACAES capacities also stay the same. The variation of the other parameters for different scenarios is shown in Table 3.
Table 3.
Parametric variation for different scenarios
Scenario Electricity Demand [TWh el ] Total Heat Demand [TWh el ] Total Grid Capacity [GW el ] Biomass Available Potential [PJ] Electricity Storage Potential* [GW el ] Heat Storage Potential [GW th ] Base
Conservative
Progressive : 10.1 *In addition to these investment potentials, the existing storage capacities of PHS and ACAES are considered for all three scenarios. In the base scenario, it is assumed that electricity and heating demands remain the same as the representative year (2011) in 2050. For storage, Li-ion batteries, PHS, and ACAES (NDE) are considered. The full biomass potential from forest residues, livestock effluents, and agricultural residues in Germany is used as CHP input. For the electrical storage, Li-ion and Redox batteries up to their maximum potentials are used. Besides, half of the total ACAES potential is considered for investment.
In the conservative scenario, it is assumed that the electricity demand will increase by 10% than the base scenario in 2050. The heating demand is kept the same as the base scenario. For the grid transmission from NDE to SDE, a reduced transfer capacity is considered. To handle the excess electrical demand, an additional
Preprint Submitted to Applied Energy. Page of
10% biomass import is considered on top of the full potential of Germany. For storage, ACAES and Redox investment possibilities are omitted, and only Li-ion battery investment is considered.
In the progressive scenario, it is assumed that both the electricity and heat demands (both space and hot water) will reduce by 10% than in the base scenario in 2050. For the grid transmission from NDE to SDE, increased maximum capacity is considered. The maximum usage of biomass is reduced by 10%. All types of electrical (including H ) and heat storages are optimized for investment up to their full potentials.
6. Results & Discussions
All three scenarios reach feasible optimization solutions. Therefore, it is possible to meet the electricity, space heat, and hot water demand in Germany with its renewable resources. However, in the conservative scenario, it is observed that with higher electricity demand and reduced storage and grid capacities, additional biomass import is necessary. Scenario-wise details on the sufficiency of the German energy system to balance supply and demand in both NDE and SDE are discussed below. 6.1.1 Base Scenario Figure 6 (a) shows the variation of generation and demand in the electricity bus of the NDE energy system for the base scenario in 2050. In NDE, offshore wind can be seen as the dominant resource, providing 188.43 TWh el over the year. Onshore wind is the second-most prevalent resource that supplies a total of 155.19 TWh el . Other resources such as CHP, solar PV, and Hydro ROR plants provide 39.19 TWh el , 17.4 TWh el , and 0.4 TWh el, respectively. Figure 6 (b) shows the percentage-wise use of different electricity generators over the year in the NDE energy system for the base scenario. (a) (b) (c) (d) Figure 6: Optimization results of the electricity buses in the base scenario in 2050 (a) supply-demand variation for NDE (b) %-wise use of electricity generators for NDE (c) supply-demand variation for SDE (d) %-wise use of electricity generators for SDE. Figure 6 (c) shows the variation of generation and demand in the electricity bus of SDE for the base scenario in 2050. In SDE, solar PV is the most dominant resource, supplying 269.38 TWh el over the year. Onshore wind is the second-most prevalent resource delivering a total of 197.98 TWh el . CHP and Hydro ROR plants provide 61.71 TWh el and 14.56 TWh el, respectively. Figure 6 (d) shows the percentage-wise use of different generators in the SDE energy system for electricity generation. Preprint Submitted to Applied Energy. Page of The light green lines in Figure 6 (a) and Figure 6 (c) indicate electrical energy transmission via the NDE-SDE link. The majority of electricity transmission is from NDE to SDE, which shows a total export of 122.22 TWh el from NDE to SDE to supply the electricity shortage in the SDE energy system. On the other hand, the electricity shortage in NDE is much less, since only 3.3 TWh el was delivered from SDE to NDE over the year. Figure 7 (a) shows the variation of heat supply and demand and the usage of TES in the heat bus of NDE for the base scenario in 2050. GSHP is the most dominant heat supplier, supplying 66.86 TWh th over the year. CHP and ASHP provide the rest of the heat demand, 39.19 TWh th and 16.11 TWh th respectively. The heat storages are used throughout the year up to their exogenously given maximum potential, 1.35 GW th . Figure 7 (b) shows the percentage-wise use of different generators in the NDE energy system for heat generation. (a) (b) (c) (d) Figure 7: Optimization results of the heat buses in the base scenario in 2050 (a) supply-demand variation for NDE (b) %-wise use of heat generators for NDE (c) supply-demand variation for SDE (d) %-wise use of heat generators for SDE. Figure 7 (c) shows the variation of supply-demand and heat usage in SDE for the base scenario in 2050. GSHP dominates the other heat generators by a considerable margin, supplying more than 86% (460.7 TWh th ) of the total heat generation over the year. CHP provides 61.1 TWh th, and ASHP provides 13.47 TWh th to meet the rest of the demand. The heat storages are used throughout the year up to their maximum potential, 6.15 GW th . Figure 7 (d) shows the percentage-wise use of heat generators in SDE. Figure 8 (a) shows the usage of electricity storage over the year in NDE for the base scenario. Besides using the full capacities of existing ACAES and PHS plants, the optimization suggests an additional investment of 0.15 GW el of ACAES, 2.82 GW el Li-ion, and 0.17 GW el Redox batteries. Similarly, in SDE, while the existing full capacity of PHS is used for most of the year, an additional investment of 12.83 GW el Li-ion and 0.76 GW el Redox batteries are suggested, as shown in Figure 8 (b). Therefore, in the base scenario, the model suggests full utilization of the exogenously provided maximum capacities for both Li-ion and Redox batteries and partial utilization of the ACAES potential for the German energy system. (a) (b) Figure 8: Electricity storage usage in the base scenario in 2050 (a) NDE (b) SDE
Preprint Submitted to Applied Energy. Page of el and 155.19 TWh el . Solar PV, CHP, and hydro ROR plants supply 67.97 TWh el , 43.11 TWh el , and 0.4 TWh el , respectively. Since the electricity demand is increased compared to the base scenario, the excess demand is met by the additional offshore, solar PV, and CHP installations. Figure 9 (b) shows the percentage-wise use of different electricity generators over the year in NDE for the conservative scenario. (a) (b) (c) (d) Figure 9: Optimization results of the electricity buses in the conservative scenario in 2050 (a) supply-demand variation for NDE (b) %-wise use of electricity generators for NDE (c) supply-demand variation for SDE (d) %-wise use of electricity generators for SDE. Figure 9 (c) shows the variation of generation and demand in the electricity bus of the SDE energy system for the conservative scenario in 2050. While solar PV, onshore wind, and hydro ROR plants provide the same amount of energy as in the base scenario, the excess electricity demand is met by installing additional CHP plants, providing 67.83 TWh el over the year. Figure 9 (d) shows the percentage-wise use of different electricity generators over the year in the SDE energy system for the conservative scenario. In SDE, onshore, solar PV, and hydro ROR capacities are already installed to their maximum capacities in both base and conservative scenarios. Therefore, the excess demand in SDE can be met by the additional biomass-based CHP, offshore, and solar PV facilities in NDE. Consequently, an increase in the electricity export totaling 143.16 TWh el over a year from NDE to SDE is observed. On the contrary, the export from SDE to NDE reduces to a total of 0.04 TWh el since there are more offshore and PV installations in NDE in the conservative scenario than in the base scenario. Figure 10 (a) shows the variation of heat supply and demand and the usage of TES in the heat bus of NDE for the conservative scenario in 2050. The heat generator order remains the same as the base scenario in the conservative scenario, where GSHP, CHP, and ASHP supply 65.04 TWh th , 43.11 TWh th, and 18.5 TWh th, respectively. The heat storages are used up to their reduced maximum potential of 0.9 GW th . Figure 10 (b) shows the percentage-wise use of different heat generators for the conservative scenario in NDE. Preprint Submitted to Applied Energy. Page of (a) (b) (c) (d) Figure 10: Optimization results of the heat buses in the conservative scenario in 2050 (a) supply-demand variation for NDE (b) %-wise use of heat generators for NDE (c) supply-demand variation for SDE (d) %-wise use of heat generators for SDE. Figure 10 (c) shows the heat supply-demand variation and TES usage in the heat bus of SDE for the conservative scenario in 2050. The heat generator order remains the same as the base scenario, where GSHP, CHP, and ASHP supply a yearly total of 457.73 TWh th , 67.7 TWh th, and 8.2 TWh th, respectively. The heat storages are used throughout the year to their reduced maximum potential, i.e., 4.1 GW th . Figure 10 (d) shows the percentage-wise use of different heat generators for the conservative scenario in SDE. In the conservative scenario, besides the existing PHS and ACAES capacities, only Li-ion battery investment is considered. Figure 11 (a) shows the usage of electricity storages over the year in NDE for the conservative scenario, where the optimization suggests an additional investment of the full available capacity of Li-ion batteries (i.e., 2.81 GWel). Figure 11 (b) shows a similar pattern for SDE, where the model suggests an additional investment of 12.83 GW el Li-ion batteries. (a) (b) Figure 11: Electricity storage usage in the conservative scenario in 2050 (a) NDE (b) SDE el over the year. Energy generation from offshore wind, CHP, and solar PV plants decrease in this scenario, with a total supply of 101.17 TWh el , 35.27 TWh el , and 8.11 TWh el, respectively. Hydro ROR supply remains the same (i.e., 0.4 TWh el ) in all three scenarios. Figure 12 (b) shows the percentage-wise use of the electricity generators for the progressive scenario in NDE. Preprint Submitted to Applied Energy. Page of (a) (b) (c) (d) Figure 12: Optimization results of the electricity buses in the progressive scenario in 2050 (a) supply-demand variation for NDE (b) %-wise use of electricity generators for NDE (c) supply-demand variation for SDE (d) %-wise use of electricity generators for SDE. Figure 12 (c) shows the supply-demand variation in the electricity bus of SDE for the progressive scenario in 2050. The total energy supplying merit order remains the same, with solar PV being the most dominant resource, followed by onshore wind, CHP, and hydro ROR plants, supplying 250.22 TWh el , 197.98 TWh el , 55.92 TWh el, and 14.56 TWh el respectively. While onshore wind and hydro ROR supply remain the same, supply from solar PV and CHP is reduced than the other two scenarios because of the reduced electricity and heat demand. Figure 12 (d) shows the percentage-wise use of the electricity generators in SDE. With reduced electricity and heat demand but further storage options, electricity export from NDE to SDE is much reduced than the previous two scenarios, totaling 94.56 TWh el over the year. On the other hand, comparatively less offshore wind, CHP, and solar PV installations in NDE expanded NDE-SDE grid connection, and additional storage flexibility in both NDE and SDE helps to balance the demand of the NDE with more power from the south. Therefore, in the progressive scenario, a total of 6.26 TWh el is transferred from SDE to NDE, which is higher than both base and conservative scenarios. Figure 13 (a) shows the variation of heat supply and demand and the usage of TES in the heat bus of NDE for the progressive scenario in 2050. With the same merit order of the other two scenarios, GSHP, CHP, and ASHP produce 58.74 TWh th , 35.27 TWh th, and 13.2 TWh th throughout the year. The heat storages are used throughout the year up to their maximum potential of 1.8 GW th . Figure 13 (b) shows the percentage-wise use of different heat generators for the progressive scenario in NDE. (a) (b) Preprint Submitted to Applied Energy. Page of (c) (d) Figure 13: Optimization results of the heat buses in the progressive scenario in 2050 (a) supply-demand variation for NDE (b) %-wise use of heat generators for NDE (c) supply-demand variation for SDE (d) %-wise use of heat generators for SDE. Figure 13 (c) shows the supply-demand variation and TES usage in the heat bus of SDE for the progressive scenario in 2050. The merit order remains the same as the other two scenarios where GSHP, CHP, and ASHP provide 409.28 TWh th , 51.6 TWh th, and 22.53 TWh th, respectively. The heat storages are used up to their increased maximum potential of 8.2 GW th . Figure 13 (d) shows the percentage-wise use of different heat generators for the progressive scenario in SDE. Figure 14 shows the usage of electricity storage over the year in NDE and SDE for the progressive scenario. In addition to the investment in batteries up to their max potentials (i.e., 15.65 GW el investment for Li-ion and 0.93 GW el investment for Redox), the model suggests an additional investment of 0.51 GW el in ACAES. Although Hydrogen storage is one of the inputs of this scenario, the optimization does not suggest the installation of H storage in any of the energy systems. (a) (b) Figure 14: Electricity storage usage in the progressive scenario in 2050 (a) NDE (b) SDE el , investment in 168.69 GW el (i.e., the maximum onshore wind potential) is necessary for all three scenarios for Germany, of which 49.88 GW el is in the NDE, and 118.81 GW el is in the SDE energy system. Therefore, the model suggests maximum utilization of the available potential of all onshore wind energy in Germany. In the case of offshore wind plants shown by Figure 15 (b), on top of the existing 6.66 GW el , the base scenario suggests installing 54.4 GW el , the conservative scenario recommends installing 76.94 GW el (i.e., the maximum offshore wind potential), and the progressive scenario suggests installing 26.13 GW el capacities. Preprint Submitted to Applied Energy. Page of (a) (b) (c) (d) Figure 15: Scenario-wise comparison of installed capacity and required investments for volatile generators in Germany (a) onshore wind (b) offshore wind (c) PV (d) hydro ROR plants. For solar PV, as shown in Figure 15 (c), in addition to the existing 45.23 GW el capacity, the base and conservative scenarios suggest utilizing the full solar potential of Southern Germany, i.e., 188.07 GW el in the SDE energy system. Contrarily, the progressive scenario in SDE suggests a reduced solar PV installation of 172 GW el . In Northern Germany, where solar PV potential is comparatively less, the model suggests installing 8.65 GW el in the base scenario and 55.77 GW el in the conservative scenario (maximum solar PV potential). Interestingly, the progressive scenario suggests that no additional solar PV installation is necessary for NDE. In the case of Hydro ROR plants shown by Figure 15 (d), both the NDE and SDE systems for all three scenarios suggest capacity increment up to the maximum available potentials, i.e., 0.06 GW el in NDE and 1.1 GW el in SDE, on top of the existing 4.29 GW el in Germany. 6.2.1.2 Volatile Generator Investment Cost Figure 16 shows the technology-wise investment costs of the volatile generators for NDE and SDE and the total costs for each of the scenarios in Germany. As shown in Figure 16 (a), the annual investment cost remains the same in all three scenarios for onshore wind plants (9.84 bn €/yr) and hydro ROR plants (0.19 bn €/yr). For offshore wind, the annual investment is 7.92 bn €/yr, which increases in the conservative scenario (11.2 bn €/yr) and decreases in the progressive scenario (3.8 bn €/yr). Similarly, in solar PV, the base scenario investment of 4.33 bn €/ yr goes high in the conservative scenario (5.37 bn €/yr) and goes low in the progressive scenario Preprint Submitted to Applied Energy. Page of (3.79 bn €/yr). Figure 16 (b) compares the total investment cost for all volatile generators in the German energy system for different scenarios. The annual investment cost for all the volatile generators is 22.28 bn €/yr, which increases by more than 19% in the conservative scenario (26.6 bn €/yr) and decreases by around 21% in progressive scenario (17.62 bn €/yr). (a) (b) Figure 16: Scenario-wise comparison of investment costs for volatile generators in Germany (a) technology-wise comparison (b) total investment cost for all volatile generators. The primary vertical axis (left) shows the total investment cost for the whole time-horizon in billion euros (shown as stacked columns), and the secondary vertical axis (right) shows the annual investment cost in billion euros/year (shown in markers). th investment, the conservative scenario requires an increased 181.86 GW th investment, and the progressive scenario requires a decreased 154.93 GW th investment in Germany. (a) (b) Figure 17: Scenario-wise comparison of installed capacity and required investments for CHP and Heat Pump in Germany (a) CHP (b) Heat Pump (GSHP and ASHP). Preprint Submitted to Applied Energy. Page of Although the heat demand did not change in the conservative scenario, heat generator installations increases because of the following reasons: Since volatile generators are already installed up to their maximum potential, increased CHP installations are required to meet the additional electricity demand; 2.
Reduced grid transfer capacity minimizes the scope for power exchange between the grids and hence lessen the scope of P2H conversion with power from the other energy system. This circumstance enforces the model to install additional local heat pumps in individual energy systems; 3.
Heat generation in this energy system is dependent upon both electrical (because of P2H) and heat storage. Since both electrical and heat storages are reduced in the conservative scenario, supply-demand balancing requires additional heat generators. This additional heat generator in the conservative scenario also results in surplus heat in both energy systems at different hours over the year. Nevertheless, this problem of additional heat investment is minimized in the progressive scenario where we have reduced electricity and heat demands, increased grid transfer capacity, and increased electrical and heat storage. Therefore, the investment in both CHPs and heat pumps are lowered in the progressive scenario, as shown in Figure 17. 6.2.2.2 CHP and Heat Pump Investment Cost Figure 18 shows the technology-wise investment costs of the CHPs and heat pumps for NDE and SDE and the total costs for each of the scenarios in Germany. As shown in Figure 18 (a), the annual investment cost for CHPs in the base scenario is 8.71 bn €/yr, which increases to 9.34 bn €/yr in the conservative scenario, and decreases to 7.39 bn €/yr in the base scenario. Similarly, for heat pumps, the base scenario investment of 18.47 bn €/yr increases to 19.44 bn €/yr in the conservative scenario, and decreases to 16.28 bn €/ yr in the progressive scenario. Figure 18 (b) compares the total investment cost for all CHPs and heat pumps in the German energy system for different scenarios. The annual investment cost for all the heat generators is 27.18 bn €/yr, which increases by more than 5% in the conservative scenario (28.78 bn €/yr), and decreases by around 13% in the progressive scenario (23.67 bn €/yr). (a) (b) Figure 18: Scenario-wise comparison of investment costs for CHP and heat pump in Germany (a) technology-wise comparison (b) total investment cost for all heat generators (CHPs & heat pumps). The primary vertical axis (left) shows the total investment cost for the whole time-horizon in billion euros (shown as stacked columns), and the secondary vertical axis (right) shows the annual investment cost in billion euros/year (shown in markers). as an input, the model does not suggest any investment in H storage. Figure 19 (a) and Figure 19 (b) shows the required investment capacities of Li-ion and Redox batteries. Both batteries are used up to their maximum given potential, whenever used as an input. According to Figure 19 (a), for a total of 15.65 GW el Li-ion batteries, the total optimized energy capacity is 102 GWh el (NDE=18.32 GWh el , SDE=83.42 GWh el ). As shown in Figure 19 Preprint Submitted to Applied Energy. Page of (b), for 0.93 GW el Redox batteries in Germany, the total optimized energy capacity is 3 GWh el (NDE= 0.56 GWh el , SDE=2.52 GWh el ) . However, the ACAES are used partially with an optimized power of 0.15 GW el and optimized energy storage of 2.5 GWh el in the base scenario, and an increased optimized capacity of 0.51 GW el and optimized energy storage of 5 GWh el in the progressive scenario, as shown in Figure 19 (c). Figure 19 (d) shows the usage of TES capacities up to their maximum exogenous potential, with the total optimized energy storage capacity varying in between 360 GWh th (conservative) and 720 GWh th (progressive). (a) (b) (c) (d) Figure 19: Scenario-wise comparison of required power and energy storage investments for electrical and heat storages in Germany (a) Li-ion (b) Redox (c) ACAES (d) TES. The primary vertical axis (left) shows the power capacity in GW el /GW th (shown as stacked columns), and the secondary vertical axis (right) shows the energy storage capacity GWh el /GWh th (shown in markers). th . As the storage capacity goes down to 360 GWh th in the conservative scenario, the yearly investment reduces to 1.1 bn €/yr. In the progressive scenario, the annual investment again increases to 2.21 bn €/yr, since the total storage capacity of Germany increases to 720 GWh th . Figure 20 (b) shows the total investment costs Preprint Submitted to Applied Energy. Page of for all storages in Germany according to the model results. The annual investment for all storages is 3.29 bn €/yr in the base scenario, which decreases by more than 18% to 2.67 bn €/yr in the conservative scenario with reduced storage provisions, and increases by around 17% to 3.86 bn €/yr in the progressive scenario with high storage provisions. (a) (b) Figure 20: Scenario-wise comparison of investment costs for electrical and heat storages in Germany (a) technology-wise comparison (b) total investment cost for all storages. The primary vertical axis (left) shows the total investment cost for the whole time-horizon in billion euros (shown as stacked columns), and the secondary vertical axis (right) shows the annual investment cost in billion euros/year (shown in markers). el , which can increase to 1074 TWh el in the conservative scenario with excess demand, less storage, and reduced grid capacity; and decrease to 818 TWh el in the progressive scenario with reduced demand, more storage, and increased grid capacity. The energy mix also shows that, while all three scenarios need maximum offshore wind and hydro ROR, additional solar PV, offshore wind, and CHP supply the rest of the demand. The base scenario mix comprises 37% onshore wind, 19% offshore wind, 30% solar PV, 10% CHP, and 0.01% hydro ROR plants. The progressive scenario shows similar results: 43% onshore wind, 12% offshore wind, 31% solar PV, 11% CHP, and 0.01% hydro ROR. These two results can be compared with the study by Fraunhofer Institute, where they concluded that in an 85% system, the electricity generation is close to 800 TWh el , of which onshore wind is 47%, offshore wind is 16%, and solar PV is 22% [101]. Therefore, the results from the OSEeM-DE model suggest that a transformation towards 100%-system is feasible by 2050, and the energy mix (in merit order) consists of onshore wind, solar PV, offshore wind, CHP, and hydro ROR plants. CHPs can replace the remaining 15% fossil-fuel-based generation of the 85% system in the Fraunhofer study using the available biomass potential in Germany without importing from other countries. Such a system can also co-exist with a heat sector integrated model incorporating P2H technologies such as heat pumps. It is evident from Figure 21 (b), which compares the heat generation mixes from different scenarios. The heat generation is 657 TWh th in the base scenario, and 660 TWh th in the conservative scenario. Although the heat demand remained the same in both scenarios, the latter shows a higher generation because of less heat storage provision and reduced transfer capacity between systems. However, with less demand, more heat storage capacity, and more grid transfer capacity, the progressive scenario yields a reduced heat generation of 590 TWh th . Preprint Submitted to Applied Energy. Page of (a) (b) Figure 21: Scenario-wise comparison for energy generation (a) electricity generation (b) heat generation The heat generation in all three scenarios also shows that heat pumps dominate the heat generation (around 80%), and biomass-CHPs cover the rest of the demand. In heat pumps, the comparatively more efficient GSHPs are preferable over comparatively less expensive ASHPs. Though the model considers only CHPs and heat pumps, other renewable applications such as electric boiler, solar heating, biofuel heating, hydrogen heating, geothermal heating should be investigated for producing heat, primarily process heating in industries. Excess generation from renewables is a challenge that needs to be solved using a combination of plausible solutions. The OSeEM-DE results show that the least amount of excess generation occurs in the progressive scenario, indicating the apparent solution of using more storages. Also, the developed model is currently an island model with no interconnection between neighboring countries. A German energy system and its neighboring countries can reduce the curtailment problem with reduced optimized generation and storage capacities. Furthermore, demand response activities and the inclusion of the transport sector with electric vehicles are also needed to reduce the curtailment or utilize the excess generation. The Levelized cost of electricity (LCOE) is calculated from the optimization results according to (23) (See Section 3.9). These LCOE values are close to another study report from Fraunhofer ISE, which illustrated a range of learning curve-based predictions of LCOEs in Germany through 2035 [102]. Table 4 compares the LCOE values according to the OSeEM-DE model results and the Fraunhofer ISE's study. The comparison shows that the scenario results for onshore and offshore wind and solar PV technology from OSeEM-DE are within the range predicted in the Fraunhofer ISE report for the year 2035; however, for biomass, the OSeEM-DE results indicate higher LCOE values, resulting from the high fuel cost of biomass.
Table 4: LCOE comparison of Fraunhofer ISE study report values and OSeEM-DE model results
Technology Levelized Cost of Electricity [€ cent/kWh] Fraunhofer ISE Study (2035) [102] OSeEM-DE Model (2050)
Onshore Wind 3.49 - 7.09 4.99 Offshore Wind 5.67 - 10.07 6.34 - 6.93 Solar PV 2.41 - 4.70 3.56 - 3.73 Biomass/Biogas 10.14 - 14.74 (Biogas) 19.47 - 20.26 (Biomass)
Preprint Submitted to Applied Energy. Page of el vs. 436.16 TWh el ). Similarly, in the conservative scenario, around 29% of the SDE electrical demand comes from NDE (143.17 TWh el vs. 479.78 TWh el ), and in the progressive scenario, around 24% of the SDE demand comes from NDE (94.57 TWh el vs. 392.55 TWh el ). A sensitivity analysis is conducted to inspect the effect of grid expansion on power and heat generator investments, energy transfer, storage. For this analysis, the base scenario is modified where all the storage capacities (including ACAES) are optimizable up to their maximum potentials, and the grid capacity (i.e., the NDE-SDE link) varies in between 25 GW el and 40 GW el . As shown in Figure 22 (a), with the grid expansion from 25 GW el to 40 GW el , the offshore wind investment is reduced by 15% from 59.75 GW el to 50.68 GW el , and the solar PV is reduced by 22% from 241.22 GW el to 188.07 GW el . The onshore wind and hydro ROR investment remain the same. Similarly, the requirement of heat pump installation also decreases by 5% (171.37 GW th vs. 171.21 GW th ). However, while increasing grid expansion results in decreasing capacities of offshore wind plants, relatively less expensive biomass-based CHPs replace a share of the curtailed offshore generation. Therefore, CHP installation increases by 2% (66.97 GW vs. 68.30 GW) with the grid expansion from 25 GW el to 40 GW el . Figure 22 (b) shows the increase in the total amount of electricity transfer from between NDE and SDE for increasing grid capacities. For the grid expansion from 25 GW el to 40 GW el , an increase of 2.5% (119.64 TWh el vs. 122.72 TWh el ) from NDE to SDE is observed. On the other hand, from SDE to NDE, though the transfer amount is much less in comparison with NDE to SDE, a sharp increment rate can be observed (0.21 TWh el vs. 6 TWh el ) when the grid capacity expands. (a) (b) Figure 22: Effect of grid capacity expansion between Northern and Southern Germany (a) investment in electricity and heat generators. The varying values of offshore wind, solar PV, CHP, and heat pumps are shown using lines, and the steady onshore wind and hydro ROR capacities are shown using columns (b) total annual electrical energy transfer between NDE and SDE. Two different vertical axes are used for showing the exchange, the primary vertical one (left) for NDE to SDE, and the secondary vertical one (right) for SDE to NDE. Regarding storage, the results for power and energy capacities for all the storage remained constant for all grid capacities, which indicated the maximum usage of the exogenously provided potentials. Therefore, the impact on the storage capacities for the expansion of the grid could not be measured using this sensitivity analysis. However, it is evident that the grid expansion facilitates a smoother balance between the two systems resulting through an increased electricity exchange, thus requiring overall less investment offshore wind, solar PV, and heat pump installations. Therefore, the expansion of the electrical grid between Northern and Southern Germany should be considered as a promising option for supporting a 100% renewable-based sector-coupled system for Germany. However, the cost of grid expansion vs. investment in generation facilities, which has not been conducted in this research, must be investigated to reach an optimum solution and draw a conclusion.
Preprint Submitted to Applied Energy. Page of el , and the batteries (Li-ion and Redox), H storage, and TES are gradually doubled from their current maximum exogenous potential. The ACAES and PHS capacities are not expanded since spatial constraints limit their maximum potentials. As shown in Figure 23 (a), with the increase in storage capacities, the onshore wind, solar PV, and hydro ROR capacities do not change, but the offshore investment drops by more than 47% (55.53 GW el vs. 29.1 GW el ) when the storages are doubled. Similarly, both CHP and heat pump investment decreased by more than 13% (62.5 GW vs. 54.32 GW) and 6% (189.87 GW th vs. 177.39 GW th ), respectively. Hence, increased storage options offer additional flexibility to curtail peak/reserve capacities for the energy system. On the other hand, electricity exchange decreases from NDE to SDE by more than 9% (113.88 GW el vs. 102.77 GW el ) when the storage capacity is doubled, as shown in Figure 23 (b). Contrarily, the electricity transmission from SDE to NDE is almost a straight line, with a much lower value. The decrease of investment in offshore wind, CHP, and heat pumps and the reduced energy transfer from NDE to SDE indicate that storage expansion in local energy systems can be another viable flexibility option for reducing investment in generation capacities and grid expansion. (a) (b) Figure 23: Effect of storage expansion from current capacity (0%) to double capacity (100%) (a) investment in electricity and heat generators. The varying values of offshore wind, CHP and heat pumps are shown using lines, and the steady onshore wind, solar PV and hydro ROR capacities are shown using columns (b) total annual electrical energy transfer between NDE and SDE. Two different vertical axes are used for showing the exchange, the primary vertical one (left) for NDE to SDE, and the secondary vertical one (right) for SDE to NDE. Nevertheless, considering the limited reserve capacity of cobalt and vanadium, expanding the battery capacities is a matter of further investigation. The sensitivity analysis for storage expansion also reveals the usage of Hydrogen storages in three instances (0%, 20%, and 40%) when the grid capacity was comparatively low (20 GW el , which is low in comparison with the base, conservative and progressive scenario capacities), and the Preprint Submitted to Applied Energy. Page of other storage options were not sufficient. This result indicates the possibility of Hydrogen storage as another plausible alternative, especially for local energy systems, when other resources for batteries are not adequate, and when the grid expansion is limited. In addition to H storage, the use of Norwegian large hydro capacities is another promising storage option for the future German energy system. Nevertheless, this requires additional investment in interconnection capacities between Norway and Germany and is subject to policy discussions between them.
7. Conclusion
The analysis shows that a 100% renewable energy system for both power and (building) heat sectors are feasible for moderate (progressive) to extreme (conservative) scenario considerations. For onshore wind and hydro ROR investments, maximum potentials should be utilized to meet the demand. In contrast, in the case of PV and offshore wind turbines, the investment capacities depend upon variation in electricity and heat demand, transmission grid expansion, available biomass potential, and storage provisions. The energy mix of such a system is composed of all the possible volatile generator resources, biomass resources, and the already existing renewable capacities. For electrical storage, pumped hydro, ACAES, and batteries are preferred over Hydrogen as storage options. In volatile generator investments, the scenario analysis shows that a fixed investment of 168.69 GW el onshore wind and 1.16 GW el hydro ROR plants are necessary, along with varying investments of 26.13 – 76.94 GW el offshore wind and 172 – 243.84 GW el solar PV capacities for the three developed scenarios. Onshore wind plants require the maximum annual investment is required (9.84 bn €/yr), and hydro ROR plants require minimum annual investment (0.19 bn €/yr), while offshore wind and solar PV requires varying investments in different scenarios (3.8 – 11.2 bn €/yr for offshore wind and 3.79 – 5.37 bn €/yr for solar PV). The total cost for the volatile generators in Germany, therefore, can vary in between 17.62 bn €/yr and 26.6 bn €/yr, which sums up to 312 – 450 bn € over the lifetime. Heat generator capacities vary for CHPs between 58.26 GW th and 73.62 GW th , while the heat pump acts as a more preferred alternative heating option for buildings, requiring 154.93 – 181.86 GW th installations for Germany. The cost varies accordingly, for CHPs in between 7.39 bn €/yr and 9.34 bn €/yr, and the heat pumps in between 16.28 bn €/yr and 19.44 bn €/yr. The total cost for the heat generators in Germany, therefore, varies in between 23.67 bn €/yr and 28.78 bn €/yr, which sums up to 316 – 385 bn € over the lifetime. For storages, while partial investment is suggested for ACAES varying from 0.15 GW el to 0.51 GW el , batteries are preferred over Hydrogen storages for all three scenarios. Existing PHS and ACAES capacities are used throughout the year, and the TES are utilized to their maximum exogenous capacities. The total cost of power and storage shows that maximum investment is required for Li-ion batteries (1.57 bn €/yr), and TES storage capacities (1.1 – 2.21 bn €/yr). With minimum storage provision in the conservative scenario and maximum storage provision in the progressive scenario, the total cost for electrical and heat storages in Germany varies in between 2.67 bn €/yr (conservative) and 3.86 bn €/yr (progressive), which sums up to around 33 – 48 bn € over the full lifetime. The energy mix comparison with the Fraunhofer Study suggests that a transformation towards 100%-system according to the results from the OSeEM-DE model is feasible by 2050, where the energy mix consists of onshore wind, solar PV, offshore wind, CHP, and hydro ROR plants. The biomass-CHP is a promising option to replace the 15% fossil-fuel-based generation of the 85% system of the Fraunhofer study, and the optimized results from the OSeEM-DE model shows that the German potential is sufficient to meet this requirement. The LCOE results from the OSeEM-DE model have been compared with another Fraunhofer study, which shows that the values are close to each other, except for biomass, which is higher in the OSeEM-DE results because of high biomass cost. The flexibility of the system was examined via sensitivity analysis of the grid and storage capacities. It is observed that with grid expansion, the cost of offshore wind, solar PV, and heat pump decreases, but the CHP investment increases slightly. On the other hand, with the gradual expansion of storage, offshore wind, CHP, and heat pump investment, and the amount of energy transfer from NDE to SDE decreases. Therefore, maximum utilization of the storage usage and optimum grid expansion can provide additional flexibility to the system and decrease the overall investment cost. The cost of grid expansion vs. investment in generation and storage facilities must be investigated to reach the optimum solution. The limited capacity of battery materials should also be taken into consideration. A possible alternative storage solution is Norwegian hydro storages with the interconnection between Norway and Germany, which is subject to further investigation. Preprint Submitted to Applied Energy. Page of There are several limitations of the developed model and scenarios. Firstly, the transmission grids were modeled as transshipment capacities between two nodes only, which does not reflect the realistic power system. Therefore, the investment cost for the grid expansion could not be estimated and presented in the paper. Secondly, the heating sector does not include industrial heating demand (i.e., process heat). Thirdly, Concentrated Solar Power (CSP) and other renewable-based plants (such as geothermal) were not included in the optimization. The inclusion of these components can ease the need for only CHP and heat pumps as heat generators and cover a portion of the electricity demand. However, since process heating is also excluded in this model, these two renewable options are likely to play a vital role in meeting partial process heating demand. Fourthly, the storage of synthetic gas produced by renewable electricity in P2G converters was not considered in the model. Finally, the import and export of electricity between countries, which is an essential part of the combined energy transition towards the climate-neutrality of the EU, was not considered in the model. Nonetheless, the developed open modeling tool OSeEM-DE paves the pathway towards modeling and analyzing plausible sector-coupled scenarios for 100% renewable-based national and sub-national energy systems, especially in the NS region. At the same time, this study shows how different energy mix options and their component-wise investment capacities and costs can be investigated using the model; hence the case of Germany can be followed for other similar regions to conduct the feasibility analysis of 100% renewable-based sector-coupled systems. Moreover, the study also reveals that sensitivity analyses can help in identifying the flexibility aspects of the system in future energy infrastructure. On this background, the following plans are outlined for future steps of this research- 1.
Integration of the German transport sector, with a particular focus on electric vehicles as dispatchable loads; 2.
Inclusion of industrial heating demand, and other possible renewable resources, and demand-side management (DSM) potentials in the German energy sector; 3.
Interconnection between the neighboring countries of Germany and analyze the impact of grid exchange in the EU context; 4.
Inclusion of Norwegian pumped hydro storage and investigation into its possible consequences; 5.
Replication and enhancement of the current model for other areas of the NS region.
Data:
Data, source codes, and results of the model is available in the following Github repository: github.com/znes/OSeEM-DE
Funding:
This research is a part of the ENSYSTRA project which received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No: 765515
Acknowledgments:
This work was supported by the ENSYSTRA network and by the Center for Sustainable Energy Systems (ZNES) by Europa-Universität Flensburg and the Flensburg University of Applied Sciences. The author would like to thank the Openmod Community and Oemof developers for spreading the idea of open-data and open-science in energy system modeling. The author acknowledges the supervision, guidance and support from Prof. Dr. Olav Hohmeyer, Prof. Dr. Bernd Möller, Dr. Fredrik Hedenus, Simon Hilpert, and Martin Söthe throughout the project.
Conflicts of Interest:
The author declares no conflict of interest.
Appendix A
The input data for cost calculation are obtained from various project databases [90–97, 101–102], which are summarized in Table A.1
Table A.1.
Input Cost Data for OSeEM-DE Model O n s h o re W i nd O ff s h o re W i nd S o l a r P V H y d r o ( R O R ) B i o m a ss L i - i o n H R e d ox P H S A S H P G S H P ACA E S TE S Capex (€/kW)
Lifetime (Years)
25 25 25 50 30 20 22.5 25 50 20 20 30 30
Preprint Submitted to Applied Energy. Page of WACC
Variable O&M Cost (€/MWh)
0 0 0 0 11.3 1 1 1 0 0 0 1 0
Fixed O&M Cost (€/kWh)
35 80 25 60 100 10 10 10 20 36.75 49 10 0.38
Storage Capacity Cost (€/kWh) - - - - - 187 0.2 70 - - - 40 38
Carrier Cost (€/MWh) - - - - 34.89 - - - - - - - -
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