Modeling tool

The transition modeling was performed with the LUT Energy System Transition model, which optimizes an energy system for given constraints. The simulation is applied for 5-year time periods for the years 2015−2050. For each period, the model defines a cost optimal energy system structure and operation mode for the given set of constraints: power demand, available generation and storage technologies, financial and technical assumptions, and limits on installed capacity for all applied technologies. The model is based on linear optimization and performed in an hourly resolution for an entire year (further details on the workings of the model along with the respective mathematical representation of the target functions can be found in Model section of Methods). The model ensures high precision computation and reliable results. The costs of the entire system are calculated as a sum of the annualized capital expenditures including the weighted average cost of capital (WACC), operational expenditures (including ramping costs), fuel costs and the cost of GHG emissions for all available technologies. The current model version is 2.0.

The LUT Energy System Transition modeling tool simulates and optimizes energy systems including the Power, Heat, and Transportation sectors, and additional Industry sectors, such as Industrial fuels production, Desalination and CO 2 removal. The simulation is performed in full hourly resolution for all hours of a year in single-year steps, where the starting conditions of the simulation depend on the time step assumptions and the previous time step results.

The purpose of the LUT Energy System Transition modeling tool is to assess different possible pathways of energy system development and assist global, national and regional energy strategy planning. Simulations allow investigation of the impact of different policies on the system structure, cost, emissions and the process of development. The model also tests the benefits of energy sectors integration (also called sector coupling), including the Power, Heat, Transportation and Industry sectors (for Industrial fuels production, Desalination and CO 2 removal), as well as evaluates the possibility of additional flexible demand option integration and its impact on the system. The model can be used for:

First, energy system development studies—simulation of the energy system transition from the current structure towards an optimized energy system: In such case, the simulation is performed for several time steps with specific financial and technical assumptions. The simulation starts from the existing energy system structure and the initial conditions of each time step are based on the system structure formed in previous steps. The results provide information on an optimized system structure and operation mode for each step, data on system cost, costs of all the products and elements, and GHG emissions of the system.

Second, feasibility studies—simulation of an optimized energy system structure and operation mode for the given technical and financial constraints: Instead of an energy transition, it is also possible to select an overnight approach, which can provide information on how a newly optimized energy system would look, built under given constraints.

Third, technical analysis—simulation of the system operation with given system structure, resource, technical and financial assumptions: Such simulations can be utilized for energy system robustness assessment to evaluate the range of conditions for which the system can satisfy the demand.

Modeling procedure

The first step of the energy system modeling is data preparation: defining the financial and technical assumptions. The structure of input data is described in the Input data section.

The second step is the scenario specification and simulation: available options are a transition scenario or overnight scenario. For each type of scenario, power, heat, transportation, and industry (industrial fuels production, desalination and CO 2 removal) sectors can be enabled. For the power sector, the simulation can be performed for a centralized system only or with the presence of power prosumers. For each type of simulation, three levels of regional integration can be applied: regional, country-wide, and area-wide. Regional: all regions (nodes) of the energy system are isolated. Country-wide: energy systems are integrated by transmission infrastructure, such as power grids, inside the same country. Area-wide: countries are integrated by transmission infrastructure for the selected area, typically a major region.

The third step is results preparation. After the end of the simulation, the tool collects the optimized results for all model elements in data files and summarizes the main data in a results Excel file. The description of the procedure and the structure of results file are given in the Results preparation section. The overall structure of the modeling procedure is given in Supplementary Fig. 52.

Energy systems operation

The model includes four energy sectors, each of which can also be simulated independently.

Energy systems operation—Power sector

The power sector is divided into a centralized energy system and a power prosumers subsegment. The share of electricity demand related to prosumers can be specified from 0 to 99% of total.

Centralized power system: In the centralized power system all consumption goes through the local AC grid to which the RE generation capacities (PV, wind, hydro, solar thermal electric, geothermal, biomass power plants), fossil and nuclear power plants, and fossil and biomass-based CHP plants are connected. At the same time, the local AC grid is connected to the storage capacities and interregional high voltage direct current (HVDC) and high voltage alternating current (HVAC) grids.

Power prosumers subsegment: PV prosumers represent three types: residential, commercial, and industrial. For each prosumer type, the share of total electricity demand (where the sum of residential, commercial and industrial is equal to the full power sector), grid electricity price, and financial assumptions for PV systems and batteries can be specified. Prosumers have the option to install their own PV generation capacities, Li-ion battery storage sell excess electricity to the centralized power system for a specified feed-in price or buy electricity from the centralized power system at a specified electricity cost. In the standard scenario the share of consumers willing to install their own PV generation capacities increases accordingly to a logistic function in steps of 3, 6, 9, 15, 18, and 20% of the respective segment electricity demand (if grid electricity is cheaper than that from PV generated, the share for the next step remains unchanged). If the power prosumer uses individual heating, generated power can also be used for electrical heating (heating rods and heat pumps). The simplified diagram of the power sector is presented in Supplementary Fig. 53.

Energy systems operation—Heat sector

The heat sector consists of six main segments: industrial high (>1150 °C), medium (100–1150 °C), and low (<100 °C) temperature heat demand, domestic water heating, space heating and cooking biomass demand. All heat shall be generated inside the region. The heat sector is also divided into centralized and individual heating systems.

All industrial heat must be covered by the centralized heat system, shares of centralized water and heating demand must be specified, and this must reflect the share of district heating specific for each region.

All biomass cooking, and the rest of water and heating demands are generated with individual heating systems.

The heat can be generated with CHP plants, solar thermal collectors, individual or centralized fuel-based boilers, electrical heaters, and heat pumps. Industrial high temperature heat demand can be satisfied only with fuel-based heat plants. Medium temperature heat can be also provided by electrical heating. Low temperature heat can also be satisfied by heat pumps, heating rods, solar thermal collectors and recovered heat loss from thermal power plants. Generated heat can be stored in medium or low temperature heat storage. The simplified diagram of the heat sector is presented in Supplementary Fig. 54.

Energy systems operation—transportation sector

The transportation sector is structured into the segments: road, rail, marine and aviation.

Within the road segment a separation is done for light duty vehicles, mainly cars; medium duty vehicles, such as delivery trucks; heavy duty vehicles; and buses. For the four road segments, the following powertrains are available: internal combustion engine, battery electric vehicle (BEV), hybrid plug-in vehicle (PHEV), and hydrogen-based fuel cell vehicles. The share of each type should be specified. BEVs and PHEVs are charged from the grid with “dump charge”—equally at every hour. Later model adjustments for “smart charge” and “vehicle-to-grid (V2G)” are planned.

Within the rail segment two fuel types are available: liquid hydrocarbon fuel (diesel), which can be fossil fuel, biofuel or renewable electricity-based Fischer-Tropsch (FT)-liquid fuel, and electricity. The shares of the fuels shall be selected according to respective projections.

Within the marine segment four fuel types are available: liquid hydrocarbon fuel (diesel), which can be fossil fuel, biofuel or renewable electricity-based FT-fuel; liquefied methane gas, which can be liquefied fossil natural gas, biomethane or renewable electricity-based methane (SNG); liquefied hydrogen (LH2), which is only foreseen as renewable electricity-based hydrogen, and electricity for shorter-distance domestic shipping.

Within the aviation segment three fuel types are available: liquid hydrocarbon fuel (kerosene), which can be fossil-based kerosene, biofuel or renewable electricity-based FT-kerosene; hydrogen, which is only foreseen as renewable electricity-based hydrogen; and electricity for shorter-distance flights.

The simplified diagram of the transportation sector is presented in Supplementary Fig. 55.

Energy systems operation—industry sector

The current model version includes the following industry sectors: industrial fuels production, desalination, and CO 2 removal. The inclusion of further industry sectors, such as cement, steel, chemical industry, metal refining and remaining industrial sectors, is planned for the future.

Industrial fuels production: The energy system can use fossil fuels, as long as it is allowed or affordable, convert biomass to biofuels, and produce renewable electricity-based synthetic fuels in the power, heat or transportation sectors. Currently hydrogen, methane and liquid hydrocarbons production units are integrated in the model.

Methane can be produced from biogas after its purification/upgrading. Then this biomethane can be used in the gas system. The share of biogas which can be upgraded is limited by the urbanization level of the region, but cannot exceed 70% even if the urbanization level is higher. A second option is synthetic natural gas (SNG)—methane produced with methanation reactors from hydrogen and carbon dioxide. The whole power-to-gas (PtG) system includes water electrolysis reactors (assumptions are based on alkaline technology) producing hydrogen from water, CO 2 direct air capturing (DAC) units collecting CO 2 and water from ambient air, and methanation units. Water electrolyzers and DAC units consume power from the system in order to produce H 2 and CO 2 , and then methanation units convert them to synthetic CH 4 .

Liquid hydrocarbons can be produced from biomass by biorefineries, or can be synthesized from H 2 and CO 2 using the FT process. PtG with gas storage and gas turbines can be part of storage for the power sector.

Fossil fuel refineries are not included in the model, and existing capacities of refineries are assumed sufficient to satisfy local consumption of fossil fuels.

The simplified diagram of the industrial fuels production sector is presented in Supplementary Fig. 56.

Desalination sector: Water demand in the region can be covered with Seawater Reverse Osmosis (SWRO) desalination, Multi-Stage Flash (MSF) and Multi-Effect Distillation (MED) technologies. The water is delivered to consumers by distributed piping systems with a respective energy demand, dependent on the distance and altitude from the coast. The water is stored at the production site, which may provide additional flexibility to the desalination system, and can optimize production in order to minimize total system cost. The simplified structure of the desalination sector is presented in Supplementary Fig. 57.

CO 2 removal sector: CO 2 removal demand can be specified for each region in tons of CO 2 per year. This amount of CO 2 will be captured from the atmosphere by DAC units in addition to CO 2 captured for synthetic fuels production. Heat and electricity needed for the DAC operation will be taken from the heat and power sectors, respectively. The simplified structure of the CO 2 removal sector is presented in Supplementary Fig. 58.

Integrated system: Every sector can be modeled individually or as several integrated sectors. Technologies such as PtG, electrical heating (heating rod, heat pumps), steam turbines, SWRO desalination, and FT-fuel production can operate as “bridging technologies” binding different sectors. Flexible power demand from the heat, transportation, industrial fuel production, desalination and CO 2 removal sectors together with better energy management due to bridging technologies can lead to a significant increase in the integrated system efficiency and drop in the total system cost.

Energy system elements

All generation technologies are categorized into renewable-based, biomass-based, fossil-based power generation, renewable-based, biomass-based, fossil-based heat generation and fuel production technologies. Information on renewable-based power generation is summarized in Table 2. Information on biomass-based power generation is summarized in Table 3. Information on fossil-based power generation is summarized in Table 4. Information on renewable-based heat generation is summarized in Table 5. Information on biomass-based heat generation is summarized in Table 6. Information on fossil-based heat generation is summarized in Table 7. Information on fuel production technologies is summarized in Table 8.

Table 2 Renewable-based power generation Full size table

Table 3 Biomass-based power generation Full size table

Table 4 Fossil-fuel-based power generation Full size table

Table 5 Renewables/power-based heat generation Full size table

Table 6 Biomass-based heat generation Full size table

Table 7 Fossil-based heat generation Full size table

Table 8 Fuel production Full size table

All storage options can be divided into three main categories based on the typical energy-to-power ratio: diurnal (E/P ratio less than 24 h), mid-term storage (E/P ratio around 72 h), and long-term storage. Main information about storage technologies included in the model is summarized in Table 9.

Table 9 Storage technologies Full size table

Information on interregional power transmission technologies is summarized in Table 10. Information on water desalination and supply is summarized in Table 11.

Table 10 Power transmission technologies Full size table

Table 11 Water desalination and supply technologies Full size table

Model

The energy system optimization model is based on a linear optimization of the system parameters under a set of applied constraints with the assumption of a perfect foresight of RE power generation and power demand. A multinode approach enables the description of any desired configuration of subregions and power transmission interconnections. The main constraints for the optimization are the matching of all types of generation and demand values for every hour of the applied year, and the optimization criteria is the minimization of the total annual cost of the integrated system (or a sector if only a sector is optimized). The hourly resolution of the model significantly increases the required computation time; however, it guarantees that for every hour of the year the total supply within a subregion covers the local demand and enables a more precise system description including synergy effects of different system components or sectors (sector coupling).

The optimization is performed in a third-party solver. At the moment, the main option is MOSEK ver. 8, but other solvers (e.g. Gurobi, CPLEX, etc.) can also be used. The model is compiled in the Matlab environment in the LP file format, so that the model can be read by most of the available solvers. After the simulation results are parsed back to the Matlab data structure and can be postprocessed for analyses and diagram preparation.

Model—target function

The target of the system optimization is the minimization of the total annual cost of the integrated system (or a sector if only a sector is optimized), calculated as the sum of the annual costs of installed capacities of the different technologies, costs of energy and product generation, and production ramping. This target function includes annual costs of the power, heat, transportation, and industrial (industrial fuels production, desalination and CO 2 removal) sectors. The target function of the applied energy model for minimizing annual costs is presented in Eq. (1) and comprises all hours of a year using the abbreviations: sub-regions (r, reg), generation, storage and transmission technologies (t, tech), capital expenditures for technology t (CAPEX t ), capital recovery factor for technology t (crf t ), fixed operational expenditures for technology t (OPEXfix t ), variable operational expenditures technology t (OPEXvar t ), installed capacity in the region r of technology t (instCap t,r ), annual generation by technology t in region r (E gen t,r ), cost of ramping of technology t (rampCost t ) and sum of power ramping values during the year for the technology t in the region r (totRamp t,r ).

$${\min } {\left( {\mathop {\sum }\limits_{r = 1}^{{\mathbf{reg}}} \mathop {\sum }\limits_{t = 1}^{{\mathbf{tech}}} \left( {{\mathrm {CAPEX}}_t \cdot crf_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {instCap}}_{t,r} + {\mathrm {OPEXvar}}_t \cdot E_{{\mathrm{gen}}\,t,r}} \right.} \hfill \\ +{\left. { {\mathrm {rampCost}}_t \cdot {\mathrm {totRamp}}_{t,r}} \vphantom{\mathop {\sum }\limits_{t = 1}^{{\mathbf{tech}}}}\right)} .$$ (1)

The power prosumers and individual heating users system are realized in an independent submodel with a slightly different target function. The prosumer system is optimized for each subregion independently, even if the subregion is connected to neighbors inside the area. The target function includes annual costs of the prosumer power generation and storage, heating equipment, the cost of electricity required from the distribution grid and the cost of fuels required for boilers. Income of electricity feed-in to the distribution grid is deducted from the total annual cost.

The target function of the applied energy model for minimizing annual costs is presented in Eq. (2) and comprises all hours of a year using the abbreviations: generation and storage technologies (t, tech), capital expenditures for technology t (CAPEX t ), capital recovery factor for technology t (crf t ), fixed operational expenditures for technology t (OPEXfix t ), variable operational expenditures technology t (OPEXvar t ), installed capacity of technology t (instCap t ), annual generation by technology t (E gen t ), retail price of electricity (elCost), feed-in price of electricity (elFeedIn), annual amount of electricity required from the grid (E grid ), annual amount of electricity fed-in to the grid (E curt ).

$${{\mathrm{min}}} \left( {\mathop {\sum }\limits_{t = 1}^{{\mathbf{tech}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {instCap}}_t + {\mathrm {OPEXvar}}_t \cdot E_{{\mathrm{gen}}\,t}} \right.\\ + \, \left. {\vphantom{\sum\limits_{t = 1}^{{\mathbf{tech}}}}} {\mathrm {elCost}} \cdot E_{{\mathrm{grid}}} + {\mathrm {elFeedIn}} \cdot E_{{\mathrm{curt}}}\right).$$ (2)

Model—energy balance constraints

The main constraint for the power sector optimization is the matching of the power generation and demand for every hour of the applied year as shown in Eq. (3). For every hour of the year the total generation within a subregion and electricity import cover the local electricity demand.

$$\begin{array}{*{20}{l}} {\forall h\, \in \,\left[ {1,8760} \right]} \hfill & {\mathop {\sum }\limits_t^{{\mathbf{tech}}} E_{{\mathrm{gen}}\,t} + \mathop {\sum }\limits_r^{{\mathbf{reg}}} E_{{\mathrm{imp}}\,r} + \mathop {\sum }\limits_t^{{\mathbf{stor}}} E_{{\mathrm{stordisch}}\,t}} \hfill \\ {} \hfill & { = E_{{\mathrm{demand}}} + \mathop {\sum }\limits_r^{{\mathbf{reg}}} E_{\exp r} + \mathop {\sum }\limits_t^{{\mathbf{stor}}} E_{{\mathrm{storch}}\,t} + E_{{\mathrm{curt}}} + E_{{\mathrm{other}}}} \hfill \end{array}$$ (3)

Eq. (3) describes constraints for the energy flows of a subregion. Abbreviations: hours (h), technology (t), all modeled power generation technologies (tech), subregion (r), all subregions (reg), electricity generation (E gen ), electricity import (E imp ), storage technologies (stor), electricity from discharging storage (E stordisch ), electricity demand (E demand ), electricity exported (E exp ), electricity for charging storage (E storch ), electricity consumed by other sectors (heat, transport, desalination, industrial fuels production, CO 2 removal) (E other ), curtailed excess energy (E curt ). The energy loss in the HVDC and HVAC transmission grids and energy storage technologies are considered in storage discharge and grid import value calculations.

The heat sector energy balance is defined by three equations: for industrial high temperature heat demand, for industrial high and medium temperature heat demand, and all centralized heat demand. High temperature heat can only be generated by fuel-based boilers (Eq. (4)). Medium temperature heat can also be generated by electrical heating and can be stored in high temperature heat storage and used to produce electricity with steam turbines (Eq. (5)). Low temperature heat can also be provided by heat pumps, electric heating rods and waste heat from other technologies (Eq. (6)).

$$\forall h\, \in \,\left[ {1,8760} \right]\mathop {\sum }\limits_t^{{\mathbf{techHH}}} E_{{\mathrm{gen}}\,t} \ge E_{{\mathrm{demandHH}}},$$ (4)

$$\begin{array}{*{20}{l}} {\forall h \in \left[ {1,8760} \right]} \hfill & {\mathop {\sum }\limits_t^{{\mathbf{techHH}}} E_{{\mathrm{gen}}\,t} + \mathop {\sum }\limits_t^{{\mathbf{techMH}}} E_{{\mathrm{gen}}\,t} + E_{{\mathrm{stordisch}}}} \hfill \\ {} \hfill & { \ge E_{{\mathrm{demandHH}}} + E_{{\mathrm{demandMH}}} + E_{{\mathrm{storch}}} + E_{{\mathrm{other}}}} \hfill \end{array},$$ (5)

$$\forall h\, \in \,\left[ {1,8760} \right]\mathop {\sum }\limits_t^{{\mathbf{tech}}} E_{{\mathrm{gen}}\,t} + \mathop {\sum }\limits_t^{{\mathbf{stor}}} E_{{\mathrm{stordisch}}} = E_{{\mathrm{demand}}} + \mathop {\sum }\limits_t^{{\mathrm{stor}}} E_{{\mathrm{storch}}} + E_{{\mathrm{curt}}} + E_{{\mathrm{other}}}.$$ (6)

Abbreviations: hours (h), technology (t), high temperature heat generation technologies (techHH), medium temperature heat generation technologies (techMH), all heat generation technologies (tech), industrial high temperature heat demand (E demandHH ), industrial medium temperature heat demand (E demandMH ), total centralized heat demand, including industrial, and space heating and water heating demand (E demand ).

Power and heat sector constraints for prosumers have some minor differences. Prosumers can buy electricity from electricity distribution companies (Eq. (7)). Heating of prosumers based on individual heaters includes fuel, RE and electricity-based heaters, but there is no individual heat storage option (Eq. (8)).

$$\forall h\, \in \,\left[ {1,8760} \right]\mathop {\sum }\limits_t^{{\mathbf{tech}}} E_{{\mathrm{gen}}\,t} + \mathop {\sum }\limits_t^{{\mathbf{stor}}} E_{{\mathrm{stordisch}}} \\ = E_{{\mathrm{demand}}} - E_{{\mathrm{grid}}} + \mathop {\sum }\limits_t^{{\mathbf{stor}}} E_{{\mathrm{storch}}} + E_{{\mathrm{curt}}} + E_{{\mathrm{other}}},$$ (7)

$$\forall h\, \in \,\left[ {1,8760} \right]\mathop {\sum }\limits_t^{{\mathbf{tech}}} E_{{\mathrm{gen}}\,t} = E_{{\mathrm {demand}}} + E_{{\mathrm {curt}}}.$$ (8)

Abbreviations: hours (h), technology (t), all modeled power generation technologies (tech), energy generated (E gen ), storage technologies (stor), energy from discharging storage (E stordisch ), energy demand (E demand ), electricity energy for charging storage (E storch ), electricity consumed by heating (E other ), excess energy (E curt ).

Model—power and heat generation

The renewable-based power and heat generation is defined by historical capacity factors for this technology and the optimal installed capacity of this technology (Eq. (9)).

$$\forall h\, \in \,\left[ {1,8760} \right]\,E_{{\mathrm{genRE}}\,h} = {\mathrm {CF}}_{{\mathrm{genRE}}\,h} \cdot {\mathrm {instCap}}_{{\mathrm{genRE}}}.$$ (9)

Abbreviations: hour (h), energy generated by renewable-based generation technology (E genRE ), capacity factor of the technology (CF genRE ), installed capacity in the region of the technology (instCap genRE ).

The fuel-based power and heat generation defined by the optimal installed capacity for this technology (Eq. (10)), availability factor for this technology (Eq. (11)), this technology used fuel available (Eq. (12)), and efficiency of the technology (Eq. (13)).

$$\forall {\mathrm{h}}\, \in \,\left[ {1,8760} \right]E_{{\mathrm{genFU}}\,h} \le {\mathrm {instCap}}_{{\mathrm{genFU}}},$$ (10)

$$\mathop {\sum }\limits_h^{8760} E_{{\mathrm{genFU}}\,h} \le 8760 \cdot {\mathrm {AF}}_{{\mathrm{genFU}}\,h} \cdot {\mathrm {instCap}}_{{\mathrm{genFU}}},$$ (11)

$$\mathop {\sum }\limits_h^{8760} {\mathrm {FU}}_{{\mathrm{genFU}}\,h} \le {\mathrm {totalFU}}_{{\mathrm{genFU}}},$$ (12)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{genFU}}\,h} = {\mathrm {FU}}_{{\mathrm{genFU}}\,h} \cdot {\mathrm {eff}}_{{\mathrm{genFU}}}.$$ (13)

Abbreviations: hour (h), energy generated by fuel-based generation technology (E genFU ), installed capacity in the region of the technology (instCap genFU ), availability factor of the technology (AF genFU ), fuel consumption for the hour h (FU genFU h ), annual fuel consumption for the hour h (totalFU genFU h ), energy conversion efficiency for technology (eff genFU ).

For all technologies, capacity is calculated in output units. For cogeneration the capacity is given in electrical units. For some types of fuel (municipal wastes, industrial biomass wastes, biogas) all available fuel must be consumed for sustainability reasons. Biogas inflow in the system is constant and biogas can be stored only for 48 h.

Model—power and heat storage

Storage technologies are described as energy storage capacity and storage interface capacity. Energy storage capacity limits the maximum state of charge (SoC) of the storage technology and the amount of energy stored (Eq. (14)), while the storage interface capacity limits the maximum power of charge and discharge (Eqs. (15) and (16)). The energy balance constraint for storage technologies is given in Eq. (17).

$$\forall h\, \in \,\left[ {1,8760} \right]{\mathrm {SoC}}_{{\mathrm{stor}}\,h} \le {\mathrm {instCapEn}}_{{\mathrm{stor}}},$$ (14)

$$\forall h\, \in \,\left[ {1,8760} \right]\,E_{{\mathrm{storch}}\,h} \le {\mathrm {instCapInt}}_{{\mathrm{stor}}},$$ (15)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{stordisch}}\,h} \le {\mathrm {instCapInt}}_{{\mathrm{stor}}},$$ (16)

$$\forall h\, \in \, \left[ {1,8760} \right]{\mathrm {SoC}}_{{\mathrm{stor}}\,h} = {\mathrm {SoC}}_{{\mathrm{stor}}\,h - 1} \cdot {\mathrm {selfDisch}}_{{\mathrm{stor}}} \\ + E_{{\mathrm{storch}}\,h} \cdot {\mathrm {eff}}_{{\mathrm{storch}}} - E_{{\mathrm{stordisch}}\,h}/{\mathrm {eff}}_{{\mathrm{stordisch}}}.$$ (17)

Abbreviations: hour (h), storage state of charge for an hour h (SoC stor h ), installed energy capacity of the storage (instCapEn stor ), installed power capacity of the storage (instCapInt stor ), charging energy of the storage for an hour h (E storch h ), discharging energy of the storage for an hour h (E stordisch h ), hourly self discharge of the storage (selfDisch stor ), charge efficiency (eff storch ), discharge efficiency (eff stordisch ).

Model—power transmission

Power transmission is represented by HVDC and HVAC grids. Each line of the grid is bidirectional, but represented in the model as two unidirectional lines: import and export. Capacities of import and export lines are equal to the total power capacity of the interconnection, as shown in Eq. (18). Hourly export/import energy for a subregion is calculated as the sum of all import lines multiplied by this line transmission efficiency minus the sum of all export line energy flows, as shown in Eq. (19). The efficiency of energy transmission by HVDC lines depends on the distance and AC/DC converter pair efficiency, as shown in Eq. (20). The efficiency of energy transmission by HVAC line depends only on distance, as shown in Eq. (21). For both HVDC and HVAC the distance-related losses are calculated in a simplified way.

$$\forall h \in \left[ {1,8760} \right]{\mathrm {line}}_{{\mathrm{import}}\,h} \le {\mathrm {instCap}}_{{\mathrm {line}}};\,{\mathrm {line}}_{{\mathrm{export}}\,h} \le {\mathrm {instCap}}_{{\mathrm {line}}},$$ (18)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{exp}}/{\mathrm{imp}}\,h} = \mathop {\sum }\limits_l^{{\mathbf{lines}}} {\mathrm {line}}_{{\mathrm {import}},l,h} \cdot {\mathrm {eff}}_l - \mathop {\sum }\limits_l^{{\mathbf{lines}}} {\mathrm {line}}_{{\mathrm {export}},l,h},$$ (19)

$${\mathrm {eff}}_l = {\mathrm {eff}}_{{\mathrm {CS}}} \cdot (1 - {\mathrm {distance}} \cdot {\mathrm {EffLoss}}),$$ (20)

$${\mathrm {eff}}_l = 1 - {\mathrm {distance}} \cdot {\mathrm {EffLoss}}.$$ (21)

Abbreviations: hour (h), line (l), energy flow through the power line (line), installed capacity of the power line (instCap line ), exported/imported energy for the region for an hour h (E exp/imp,h ), total energy import efficiency (eff l ), converter pair efficiency (eff CS ), charge length of the line (distance), energy loss in the line (EffLoss).

Model—transportation

Transportation demand is expressed in (metric) ton kilometers (t-km) and passenger kilometers (p-km). Power and fuel consumption for a given mix of transportation means is included in the power, heat and gas (H 2 , CH 4 ) balance equations on the demand side.

Model—industrial sector

Fuel production: The energy system can produce GHG neutral methane for the needs of the power, heat, transportation and industry sectors. The first option is upgrading the available biogas to biomethane. The amount of upgraded biogas cannot be more than the urbanization level of the region, but not more than 70% of all biogas. Biomethane can be stored in the gas storage. The second option is power-to-gas. Hydrogen produced with water electrolysis and CO 2 from DAC units are used as raw materials for the methanation units. Produced SNG can be also stored in the gas storage.

Desalination: In case that desalinated water demand exists in the region, the system has to provide the demanded amount of water every hour. Water storage on the supply side provides flexibility to the system. Desalination units are located on the seashore and they can optimize work in order to decrease the total system cost. The water demand and water storage balance are described in Eqs. (22)–(23).

Water desalination units produce water and store it in water storage. Desalinated water production is limited by optimal capacities of enabled desalination plants and storage technologies (Eqs. (24)–(25)). Power, heat and gas consumption for desalination unit operation as shown in Eqs. (26)–(28) are included in the power, heat and gas balance equations on the demand side. The water pumping electricity demand according to Eq. (29) and cost is calculated based on the pumping capacity of the system, hourly water demand, weighted average length and head of the piping system.

$$\forall h \in \left[ {1,8760} \right]\mathop {\sum }\limits_t^{{\mathbf{tech}}} W_{{\mathrm{des}}\,t,h} + W_{{\mathrm{stordisch}}\,h} - W_{{\mathrm{storch}}\,h} = W_{{\mathrm{demand}}\,h},$$ (22)

$$\forall h\, \in \,\left[ {1,8760} \right]{\mathrm {SoC}}_{{\mathrm{stor}}\,h} = {\mathrm {SoC}}_{{\mathrm{stor}}\,h - 1} + W_{{\mathrm{storch}}\,h} - W_{{\mathrm{stordisch}}\,h},$$ (23)

$$\forall h\, \in \,\left[ {1,8760} \right]W_{{\mathrm{des}}\,t,h} \le {\mathrm {instCapDes}}_t,$$ (24)

$$\forall h\, \in \,\left[ {1,8760} \right]{\mathrm {SoC}}_{{\mathrm{stor}}\,h} \le {\mathrm {instCapStor}},$$ (25)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{heat}}\,h} = \mathop {\sum }\limits_t^{{\mathbf{tech}}} W_{{\mathrm{des}}\,t,h} \cdot {\mathrm {heatCons}}_t,$$ (26)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{el}}\,h} = \mathop {\sum }\limits_t^{{\mathbf{tech}}} W_{{\mathrm{des}}\,t,h} \cdot {\mathrm {elCons}}_t - \mathop {\sum }\limits_t^{{\mathbf{tech}}} W_{{\mathrm{des}}\,t,h} \cdot {\mathrm {elProd}}_t,$$ (27)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{gas}}\,h} = \mathop {\sum }\limits_t^{{\mathbf{tech}}} W_{{\mathrm{des}}\,t,h} \cdot {\mathrm {gasCons}}_t,$$ (28)

$$\forall h\, \in \,\left[ {1,8760} \right]E_{{\mathrm{elPump}}\,h} = \mathop {\sum }\limits_t^{{\mathbf{tech}}} W_{{\mathrm{des}}\,t,h} \times \left( {{\mathrm {elCons}}_{{\mathrm{VPump}}} \cdot {\mathrm {alt}} + {\mathrm {elCons}}_{{\mathrm{HPump}}} \cdot {\mathrm {dist}}} \right).$$ (29)

Abbreviations: hour (h), desalination technology (t), desalinated water (W des ), water storage discharge (W stordisch ), water storage charge (W storch ), water demand (W demand ), installed desalination technology capacity (instCapDes), desalination heat demand (E heat ), desalination electricity demand (E el ), desalination gas demand (E gas ), desalination heat consumption (heatCons), desalination electricity consumption (elCons), desalination electricity production (elProd), desalination gas consumption (gasCons), water pumping electricity demand (E elPump ), horizontal water pumping electricity consumption (elCons HPump ), vertical water pumping electricity consumption (elCons VPump ), pumping distance (dist), pumping altitude difference (alt), water storage state of charge h (SoC stor ), installed capacity of the water storage (instCapStor).

CO 2 removal: The energy system can capture additional amounts of CO 2 from the atmosphere for permanent storage. The CO 2 captured by DAC is stored in CO 2 buffer storage. The system will balance hourly DAC and CO 2 buffer operation in order to balance hourly CO 2 removal demand.

Results preparation and cost calculations

All optimization results are collected and converted from the solver output form to the Matlab structure. This structure contains all information about the system: installed capacities of all system elements, its operation modes, energy, fuel and other product flows.

Data on the structure and operation of the energy system in combination with financial and technical assumptions give the full description of the system. Based on these numbers, it is possible to calculate annual costs of each component and the whole system, allocate costs to specific sectors, calculate costs of products (electricity, heat, synthetic fuels, water) and different components of this costs (primary generation, storage, transmission, curtailment components of electricity prices etc.).

The total annualized cost of the system is calculated as the sum of all sectors costs (Eq. (30)), which includes annualized capital cost and operational costs of all system elements (Eq. (31)):

$$\begin{array}{*{20}{l}} {\mathrm{totalCost}_{{\mathrm{sys}}}} \hfill & = \hfill & {{\mathrm {elSysCost}} + {\mathrm {elProsCost}} + {\mathrm {heatSysCost}} + {\mathrm {heatIndCost}}} \hfill \\ {} \hfill & {} \hfill & { + {\mathrm {transpSysCost}} + {\mathrm {industrSysCost}}}, \hfill \end{array}$$ (30)

$${\mathrm {totalCost}}_{{\mathrm{sys}}} = \mathop {\sum }\limits_{t = 1}^{{\mathbf{tech}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_t + {\mathrm {OPEXvar}}_t \cdot E_{{\mathrm{gen}}\,t},$$ (31)

$${\mathrm {crf}}_t = \frac{{{\mathrm {WACC}} \cdot \left( {1 + {\mathrm {WACC}}} \right)^{N_t}}}{{\left( {1 + {\mathrm {WACC}}} \right)^{N_t} - 1}}.$$ (32)

Abbreviations: total annualized cost of the system (totalCost sys ), annualized cost of the centralized Power sector (elSysCost), annualized cost of the electricity prosumers sector (elProsCost), annualized cost of the centralized heat sector (heatSysCost), annualized cost of the individual heat sector (heatIndCost), annualized cost of the transportation sector (transpSysCost), annualized cost of the industrial sector (industrSysCost), all technologies (tech), technology (t), capital expenditures (CAPEX), capital recovery factor for technology t (crf t ) Eq. (32), annual fixed operational expenditures (OPEXfix), variable operational expenditures (OPEXvar), installed capacity of the technology t (Cap t ), annual output for the technology t (E gen t ), weighted average cost of capital (WACC), lifetime for technology t (N t ).

Total levelized cost of electricity in the system (LCOEtotal) is calculated as the electricity demand weighted average of the centralized power system LCOE (LCOEsys) and prosumers sector LCOE (LCOEpros); the formula is presented in Eq. (33). Centralized power system LCOE is comprised of levelized cost of consumed electricity (LCOEprim), levelized cost of storage (LCOS), levelized cost of curtailed electricity (LCOC), levelized cost of electricity transition (LCOT) and levelized cost of prosumer feed-in reimbursement (LCOFS), Eq. (34). For the prosumer sector, total LCOE is comprised of the levelized cost of consumed electricity (LCOEprim), levelized cost of storage (LCOS), and levelized cost of prosumer feed-in reimbursement (LCOFS), Eq. (35). Levelized cost of generated electricity is calculated as the total annualized cost of the electricity generation system divided by total annual generation (Eq. (36)). In these calculations, operational costs include costs of fuel and GHG emissions cost per unit of generated electricity. The electricity generation systems also include part of the fuel production facilities, which are used for fuel production for power system generators. Levelized cost of consumed electricity is calculated based on the cost of the generated electricity (LCOEgen), excluding electricity lost due to curtailment, storage and transmission system losses (Eq. (37)). Levelized cost of storage is calculated as the annualized cost of storage system equipment and annual cost of electricity losses divided by total electricity consumption (Eq. (38)). Storage systems also include part of the fuel production facilities, which are used for fuel production for the storage system generators (e.g. for power-to-gas−gas-to-power). Levelized cost of curtailment is calculated as the annual cost of curtailed electricity divided by total electricity consumption (Eq. (39)). Levelized cost of transmission is the calculated area total annualized cost of power grid equipment and annual cost of electricity losses divided by total electricity consumption, and multiplied by regional grid utilization weights (Eq. (40)), where regional grid utilization weights are the average of regional shares of total export and import of energy (Eq. (41)).

$${\mathrm {LCOEtotal}}_r = ({\mathrm {LCOEsys}}_r \cdot {\mathrm {El}}_{{\mathrm{consSys}}_r} + {\mathrm {LCOEpros}}_r \cdot {\mathrm {El}}_{{\mathrm{consPros}}_r})/ \hfill \\ ({\mathrm {El}}_{{\mathrm{consSys}}_r} + {\mathrm {El}}_{{\mathrm{consPros}}_r}),$$ (33)

$${\mathrm {LCOEsys}}_r = {\mathrm {LCOEprim}}_r + {\mathrm {LCOS}}_r + {\mathrm {LCOC}}_r + {\mathrm {LCOT}}_r + {\mathrm {LCOFS}}_r,$$ (34)

$${\mathrm {LCOEpros}}_r = {\mathrm {LCOEprim}}_r + {\mathrm {LCOS}}_r - {\mathrm {LCOFS}}_r,$$ (35)

$${\mathrm {LCOEgen}}_r = \frac{{\mathop {\sum }

olimits_{t = 1}^{{\mathbf{Gen}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {OPEXvar}}_t \cdot {\mathrm {El}}_{\mathrm{gen},t,r}}}{{{\mathrm {El}}_{\mathrm{gen},r}}}$$ (36)

$${\mathrm {LCOEprim}}_r = \frac{{{\mathrm {LCOEgen}}_r \cdot ({\mathrm {El}}_{{\mathrm {gen}},r} - {\mathrm {El}}_{{\mathrm {curt}},r} - {\mathrm {El}}_{{\mathrm {storLoss}},r} - {\mathrm {El}}_{{\mathrm {transLoss}},r})}}{{{\mathrm {El}}_{{\mathrm {cons}},r}}},$$ (37)

$$ {{\mathrm {LCOS}}_r =} \hfill \\ \left( {\mathop {\sum }\limits_{t = 1}^{{\mathbf{Stor}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {OPEXvar}}_t \cdot E_{{\mathrm{out}}\,t,r} + {\mathrm {LCOEgen}}_r \cdot {\mathrm {El}}_{{\mathrm{storLoss}}\,r}} \right)/{\mathrm {El}}_{{\mathrm{cons}}\,r},$$ (38)

$${\mathrm {LCOC}}_r = \frac{{{\mathrm {LCOEgen}}_r \cdot {\mathrm {El}}_{{\mathrm{curt}}\,r}}}{{{\mathrm {El}}_{{\mathrm{cons}}\,r}}},$$ (39)

$$\begin{array}{*{20}{l}} {{\mathrm {LCOT}}_r} \hfill & = \hfill & {{\mathrm {RegShare}}_r \cdot \left( {\mathop {\sum }\limits_r^{{\mathbf{Reg}}} \mathop {\sum }\limits_{t = 1}^{{\mathbf{trans}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {OPEXvar}}_t} \right.} \hfill \\ {} \hfill & {} \hfill & {\left. { \cdot {\mathrm {El}}_{{\mathrm{out}}\,t,r} + {\mathrm {LCOEgen}}_r \cdot {\mathrm {El}}_{{\mathrm{transLoss}}\,r}} \right)/{\mathrm {El}}_{{\mathrm{cons}}\,r}}, \hfill \end{array}$$ (40)

$${\mathrm {RegShare}}_r = 0.5 \cdot \frac{{{\mathrm {Import}}_r}}{{\mathop {\sum }

olimits_r {\mathrm {Import}}_r}} + 0.5 \cdot \frac{{{\mathrm {Export}}_r}}{{\mathop {\sum }

olimits_r {\mathrm {Export}}_r}},$$ (41)

$${\mathrm {LCOFS}}_r = \frac{{{\mathrm {feedInTarif}}_r \cdot {\mathrm {El}}_{{\mathrm{prosTogrid}}\,r}}}{{{\mathrm {El}}_{{\mathrm{cons}}\,r}}}.$$ (42)

Abbreviations: region (r), total levelized cost of electricity in the system (LCOEtotal), centralized system levelized cost of electricity (LCOEsys), prosumer sector levelized cost of electricity (LCOEpros), centralized system electricity consumption (El consSys ), prosumer sector electricity consumption (El consPros ), consumed electricity LCOE (LCOEprim), levelized cost of stored electricity (LCOS), levelized cost of curtailed electricity (LCOC), levelized cost of prosumer feed-in reimbursement (LCOFS), generated electricity LCOE (LCOEgen), power generation technologies (Gen), storage technologies (Stor), power transmission technologies (trans), technology (t), capital expenditures (CAPEX), capital recovery factor for technology t (crf t ), annual fixed operational expenditures (OPEXfix), variable operational expenditures (OPEXvar), installed capacity of the technology t (Cap t ), annual output for the technology t (El gen t ), annual electricity generation (El gen ), annual electricity curtailment (El curt ), annual storage loss (El storLoss ), annual grid loss (El transLoss ), annual electricity consumption (El cons ), annual output of storage t (E out t ), annual export of grid technology t (El out t ), electricity exported by region r (Export), electricity imported by region r (Import), feed-in reimbursement (feedInTarif), electricity sold by prosumers to the grid (El prosTogrid ).

The levelized cost of heat (LCOH) is calculated as the weighted average of the centralized and individual system LCOH (Eq. (43)). The centralized heat system LCOH (LCOHsys) and individual heat system LCOH (LCOHind) are calculated as the annualized cost of heat system equipment and annual cost of electricity consumption by heating equipment divided by total heat consumption (Eq. (44,45)). In both formulas, operational expenditures include the cost of fuel and GHG emissions per unit of generated heat. The heat systems also include part of the fuel production facilities, which are used for fuel production for heat generators. Cogeneration plants costs are only included in the power system.

Levelized cost of transportation (LCOM) is calculated as sum of the annualized cost of the entire transport fleet, cost of consumed fuel and electricity, GHG emission cost, divided by transportation demand (Eq. (46)).

Levelized cost of the industrial sector products (LCOP) are: levelized cost of gas (LCOG), liquid fuel (LCOF), water (LCOW), and CO 2 direct air capture (LCOD). These are calculated as the sum of annualized cost of the equipment and cost of annually consumed heat and electricity, divided by total annual consumption of the product (Eq. (47)).

$${\mathrm {LCOHtotal}}_r = ({\mathrm {LCOHsys}}_r \cdot {\mathrm {He}}_{{\mathrm{consSys}}_r} + {\mathrm {LCOHind}}_r \cdot {\mathrm {He}}_{{\mathrm{consInd}}_r})/\hfill \\ ({\mathrm {He}}_{{\mathrm{consSys}}_r} + {\mathrm {He}}_{{\mathrm{consInd}}_r}),$$ (43)

$$\begin{array}{*{20}{l}} {{\mathrm {LCOHsys}}_r} \hfill & = \hfill & {\left( {\mathop {\sum }\limits_{t = 1}^{{\mathbf{heat}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {OPEXvar}}_t \cdot {\mathrm {He}}_{{\mathrm{out}}\,t,r}} \right.} \hfill \\ {} \hfill & {} \hfill & {\left. { + {\mathrm {LCOEsys}}_r \cdot {\mathrm {El}}_{{\mathrm{demSysHeat}}\,r}} \right)/{\mathrm {He}}_{{\mathrm{consSys}}\,r}}, \hfill \end{array}$$ (44)

$$\begin{array}{*{20}{l}} {{\mathrm {LCOHind}}_r} \hfill & = \hfill & {\left( {\mathop {\sum }\limits_{t = 1}^{\mathbf{heat}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {OPEXvar}}_t \cdot {\mathrm {He}}_{{\mathrm{out}}\,t,r}} \right.} \hfill \\ {} \hfill & {} \hfill & {\left. { + {\mathrm {ElPrice}}_r \cdot {\mathrm {El}}_{{\mathrm{demIndHeat}}\,r}} \vphantom{\mathop {\sum }\limits_{t = 1}^{\mathbf{heat}}}\right)/{\mathrm {He}}_{{\mathrm{consInd}}\,r}}, \hfill \end{array}$$ (45)

$${\mathrm {LCOM}}_r = \frac{{\mathop {\sum }

olimits_{t = 1}^{{\mathbf{Mob}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {FuPrice}}_{t,r} \cdot {\mathrm {FuCons}}_{t,r}}}{{{\mathrm {TR}}_{{\mathrm{dem}}\,r}}},$$ (46)

$$\begin{array}{*{20}{l}} {{\mathrm {LCOP}}_r} \hfill & = \hfill & {\left( {\mathop {\sum }\limits_{t = 1}^{{\mathbf{tech}}} \left( {{\mathrm {CAPEX}}_t \cdot {\mathrm {crf}}_t + {\mathrm {OPEXfix}}_t} \right) \cdot {\mathrm {Cap}}_{t,r} + {\mathrm {OPEXvar}}_t \cdot {\mathrm {Pr}}_{{\mathrm{out}}\,t,r}} \right.} \hfill \\ {} \hfill & {} \hfill & {\left. { + {\mathrm {LCOEsys}}_r \cdot {\mathrm {El}}_{{\mathrm{cons}}\,t,r} + {\mathrm {LCOHsys}}_r \cdot {\mathrm {He}}_{{\mathrm{cons}}\,t,r}} \right)/{\mathrm {Pr}}_{{\mathrm{cons}}\,r}}. \hfill \end{array}$$ (47)