Commit 7ef55aae authored by Markus Millinger's avatar Markus Millinger
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Updated supplementary material

parent 9e6999a5
......@@ -388,61 +388,67 @@ This work was funded by the Helmholtz Association of German Research Centers and
\newpage
\section*{Supplementary material}
\subsection*{Model description}
BENOPT is a fully deterministic, bottom-up, perfect foresight, linear optimisation model for modelling cost-optimal and/or GHG abatement optimal allocation of renewable energy carriers and materials across power, heat and transport sectors. The sectors are further divided into sub-sectors. The model has an up to hourly resolution (in the power sector), which can be aggregated depending on the task.
\subsubsection*{Variable Renewable Energy developments}
For the VRE generation, i.e. on- and offshore wind and solar photovoltaic (PV), hourly generation time series as well power load for Germany for the years 2016-18 were used \cite{OpenPowerSystemData.2019}.
%The future development of (a) power demand as well as (b) on- and offshore wind and solar PV capacities, and (c) capacity factors (C$_f$, the ratio of actual output to the maximum possible output of a power plant, over a period of time) were assumed for 5-year time steps from 2020 until 2050 according to the defined scenario conditions (Section \ref{ch:scenarios}).
The generation time series data are normalized and scaled \cite{Tafarte.2014,Tafarte.2019} according to the assumed capacity expansions and their capacity factor developments. The power load time series are likewise scaled to comply with the assumed development of total annual power demand.
%Electricity generation from river hydro power was modelled as a fixed feed-in to the production time series, with an invariable electricity generation (MW) totalling the projected energy generation volume (TWh) in the respective year.
The resulting time series for VRE and hydro power production are then subtracted from the power load time series on an hourly basis for each time step, resulting in hourly time series for the residual load that model the development of electricity generation and consumption from 2020 until 2050.
The residual load data are then sorted, resulting in residual load duration curves (RLDC) for every 5 years. These are then interpolated to obtain RLDCs for each year between 2020-2050.
The main goal functions used are minimising cost and maximising GHG abatement. The allocation of resources across transport, power and heat sectors (further divided into sub-sectors) is optimised simultaneously, enabling a systems perspective where the opportunity costs are minimised and thus sub-optimal solutions avoided, which would occur if only considering single sectors or pathways (as in standard life-cycle analyses).
\subsubsection*{Greenhouse gas emissions}
The total GHG emissions $\varepsilon_{tot,j}^{(t)}$ [kgCO$_{2}$eq GJ$_{fuel}^{-1}$] of option $j$ at time-point $(t)$ are calculated a sum of all emissions in the different stages of the process (Eqn. \ref{eq:ghgEmis}): $F$, feedstock cultivation; $T_1$, transport of the biomass to the conversion facility; $P_1$, first process step (with allocation factor $\alpha_{1}$); $P_2$, second process step ($\alpha_{2}$); transport of the fuel to the fuelling station $T_2$. The input data is all related to the feedstock input [t$_{FM}$], except for the final fuel transport, whereby a conversion to GJ$_{fuel}$ is performed through division by feedstock energy content $e_j$ [GJ t$_{FM}^{-1}$] multiplied by fuel conversion efficiency $\eta_j$. The inputs for the feedstock cultivation are on a hectare basis, thus a division by yield $Y_j$ [t$_{FM}$ ha$^{-1}$] is necessary. The emissions of all process steps preceding the end of $P_1$ are allocated to the fuel according to $\alpha_{1}$, whereas those preceding the end of $P_2$ are additionally allocated according to $\alpha_{2}$.
The GHG emissions $\varepsilon_{i,t}$ [kgCO$_{2}$eq GJ$_{fuel}^{-1}$] of option $i$ at time-point $t$ are calculated a sum of all emissions in the different stages of the process (Eqn. \ref{eq:ghgEmis}), with $F$, feedstock (ERE, electricity mix, biomass residues or crop cultivation); $T_1$, transport of the biomass to the conversion facility; $P_1$, first process step (with allocation factor $\alpha_{1}$); $P_2$, second process step ($\alpha_{2}$); transport of the energy carrier to the usage or fuelling station $T_2$. The emissions of all process steps preceding the end of $P_1$ are allocated to the fuel according to $\alpha_{1}$, whereas those preceding the end of $P_2$ are additionally allocated according to $\alpha_{2}$, divided by the feedstock specific energy content $e_{f}$ multiplied with the feedstock-technology specific conversion efficiency.
For each input to any process, for all inputs $k$ belonging to the respective process steps, the input amount $\dot{m}_{k,j}^{(t)}$ is multiplied by its emission factor $\varepsilon_k^{(t)}$. Byproducts which are not considered in the allocation, but through a credit, are denoted $cr$.
For each input to any process, for all inputs $k$ belonging to the respective process steps, the input amount $\dot{m}_{k,j,t}$ is multiplied by its emission factor $\varepsilon_{k,t}$. Byproducts which are not considered in the allocation, but through a credit, are denoted $cr$.
\begin{figure}[H]
\begin{equation}\label{eq:ghgEmis}
\begin{split}
\varepsilon_{tot,j}^{(t)} = & \frac{\alpha_{1} \alpha_{2}}{e_{j} \eta_{j}} \left( \frac{1}{Y_{j}^{(t)}}\sum_{k\in F} \dot{m}_{k,j}^{(t)} \varepsilon_{k}^{(t)} + \sum_{k\in T_1} \dot{m}_{k,j}^{(t)} \varepsilon_{k}^{(t)} + \sum_{k\in P_1} \dot{m}_{k,j}^{(t)} \varepsilon_{k}^{(t)} - \dot{m}_{cr,j}^{(t)} \varepsilon_{cr}^{(t)} \right) \\
&+ \frac{\alpha_{2}}{e_{j} \eta_{j}} \left( \sum_{k\in P_2} \dot{m}_{k,j}^{(t)} \varepsilon_{k}^{(t)} - \dot{m}_{cr,j}^{(t)} \varepsilon_{cr}^{(t)} \right) + \sum_{k\in T_2} \dot{m}_{k,j}^{(t)} \varepsilon_{k}^{(t)}
\varepsilon_{i,t} = & \frac{\alpha_{1} \cdot \alpha_{2}}{e_{f} \cdot \eta_{i,f}} \left( \varepsilon_{feed} + \sum_{k\in T_1} \dot{m}_{k,i,t} \cdot \varepsilon_{k,t} + \sum_{k\in P_1} \dot{m}_{k,i,t} \cdot \varepsilon_{k,t} - \dot{m}_{cr,j,t} \cdot \varepsilon_{cr,t} \right) \\
&+ \frac{\alpha_{2}}{e_{f} \cdot \eta_{i}} \left( \sum_{k\in P_2} \dot{m}_{k,i,t} \cdot \varepsilon_{k,t} - \dot{m}_{cr,i,t} \cdot \varepsilon_{cr,t} \right) + \sum_{k\in T_2} \dot{m}_{k,i,t} \cdot \varepsilon_{k,t}
\end{split}
\end{equation}
\end{figure}
Please refer to \citet{Millinger.2018b} for a more thorough description of the GHG calculations.
The inputs for the feedstock cultivation are on a hectare basis, thus a division by yield $Y_j$ [t$_{FM}$ ha$^{-1}$] is necessary for crops to calculate the emissions $\varepsilon_{feed,crop}$ (Eqn. \ref{eq:cropGHG}). The emissions of residues $\varepsilon_{feed,res}$ and ERE $\varepsilon_{feed,ere}$ are assumed to be zero in the standard version, while the electricity mix emissions $\varepsilon_{feed,elmix}$ are set in the scenarios.
\begin{equation}\label{eq:cropGHG}
\varepsilon_{feed,crop} = \frac{1}{Y_{f,t}}\sum_{k\in F} \dot{m}_{k,j,t} \varepsilon_{k,t}
\end{equation}
Please refer to \citet{Millinger.2018b} for a more detailed description of the GHG calculations.
\subsubsection*{Feedstock costs}
The crop prices are derived by using wheat as a benchmark, with other crops set to achieve the same profit per hectare. The hectare profit for wheat is calculated as the market price p$_w^{(t)}$ [\texteuro \ t$_{FM}^{-1}$] times yield Y$_w^{(t)}$ [$t_{FM}$ ha$^{-1}$] minus production costs c$_w^{(t)}$ [\texteuro \ ha$^{-1}$]. Other crops are to achieve this profit per ha, adding production costs c$_i^{(t)}$ [\texteuro \ ha$^{-1}$]. The prices are then divided with the yield Y$_i^{(t)}$ [$t_{FM}$ ha$^{-1}$] to come up with a market price p$_i^{(t)}$ [\texteuro \ $t_{DM}^{-1}$] of feedstock $i$. Over time, this results in a market price development including opportunity costs for each feedstock (Eqn. \ref{eq:feedPrice}).
The crop prices are derived by using wheat as a benchmark, with other crops set to achieve the same profit per hectare. The hectare profit for wheat is calculated as the market price p$_{w,t}$ [\texteuro \ t$_{FM}^{-1}$] times yield Y$_{w,t}$ [$t_{FM}$ ha$^{-1}$] minus production costs c$_{w,t}$ [\texteuro \ ha$^{-1}$]. Other crops are to achieve this profit per ha, adding production costs c$_{f,t}$ [\texteuro \ ha$^{-1}$]. The prices are then divided with the yield Y$_{f,t}$ [$t_{FM}$ ha$^{-1}$] to come up with a market price p$_{f,t}$ [\texteuro \ $t_{DM}^{-1}$] of feedstock $f$. Over time, this results in a market price development including opportunity costs for each feedstock (Eqn. \ref{eq:feedPrice}).
%\begin{flushleft}
\begin{equation}\label{eq:feedPrice}
p_i^{(t)} = \left( p_w^{(t)} Y_w^{(t)} - c_w^{(t)} + c_i^{(t)} \right) {Y_i^{(t)}}^{-1}
p_{f,t} = \left( p_{w,t} \cdot Y_{w,t} - c_{w,t} + c_{f,t} \right) {Y_{f,t}}^{-1}
\end{equation}
%\end{flushleft}
Please refer to \citet{Millinger.2018d} for a more thorough description of the crop costs.
For the biomass residues, each type $\phi_{f,t}$ is divided into three equally large groups for each time-point, with the price for the categories set to the minimum value, the average of the minimum and maximum values and the maximum value, respectively. The span is given exogenously.
For the biomass residues, each type $\phi_{f,t}$ is divided into three equally large groups for each time-point, with the price for the categories set to the minimum value, the average of the minimum and maximum values and the maximum value, respectively. The span is given exogenously and in the standard setting follows the set price increase of wheat.
\subsubsection*{Optimal material and energy allocation}
BENOPT is a fully deterministic, bottom-up, perfect foresight, linear optimisation model for modelling cost-optimal and/or GHG abatement optimal allocation of renewable energy carriers and materials across power, heat and transport sectors. The sectors are further divided into sub-sectors. The model has an up to hourly resolution, which can be aggregated depending on the task.
The price of ERE and electricity mix is likewise set exogenously, and may be set to vary over time.
The main goal functions used are minimising cost and maximising GHG abatement. The allocation of resources across transport, power and heat sectors (further divided into sub-sectors) is optimised simultaneously, enabling a systems perspective where the opportunity costs are minimised and thus sub-optimal solutions avoided, which would occur if only considering single sectors or pathways (as in standard life-cycle analyses).
\subsubsection*{Variable Renewable Energy developments}
For the VRE generation, i.e. on- and offshore wind and solar photovoltaic (PV), hourly generation time series as well power load can be used from \citet{OpenPowerSystemData.2019}, with the years 2016-18 used in the standard setting for Germany.
The future development of power demand as well as on- and offshore wind and solar PV capacities, capacity factors (C$_f$, the ratio of actual output to the maximum possible output of a power plant, over a period of time) and electricity storage capacities are assumed for 5-year time steps from 2020 until 2050 according to defined scenario conditions. Electricity generation from river hydro power can be modelled as a fixed feed-in to the production time series, with an invariable electricity generation (MW) totalling the projected energy generation volume (TWh) in the respective year.
The generation time series data are normalized and scaled \cite{Tafarte.2014,Tafarte.2019} according to the assumed capacity expansions and their capacity factor developments. The power load time series are likewise scaled to comply with the assumed development of total annual power demand.
The resulting time series for VRE and hydro power production are then subtracted from the power load time series on an hourly basis for each time step, resulting in hourly time series for the residual load that model the development of electricity generation and consumption from 2020 until 2050.
The residual load data are then sorted, resulting in residual load duration curves (RLDC) for every 5 years. These are then interpolated to obtain RLDCs for each year between 2020-2050.
\subsubsection*{Optimal material and energy allocation}
An optimal resource allocation without requiring sub-sectoral renewable fuel targets is enabled through a two-stage modelling. First, the total possible GHG abatement under the given restrictions is maximised (Eqn. \ref{eqn:ghg}), with $\varepsilon_{tot}$ being the total GHG abatement, given by the avoided reference fossil fuel emissions $\varepsilon_{sub,t}$ multiplied by the relative end conversion efficiency to the sub-sector specific service, compared to the sub-sector specific reference option (e.g. for road transport the Tank-To-Wheel (TTW) relative fuel economy compared to an Otto ICEV) $\omega_{i}$ of the energy carrier type $i$, minus the production emissions $\varepsilon_{i,t}$, multiplied by the production of the renewable fuel $\pi_{i,t}$, at time point $t$. The factor $\omega_{i}$ ensures that the fuel economy for a given transport service is being compared, and thus a Well-to-Wheel (WTW) analysis is performed.
\begin{equation}\label{eqn:ghg}
\varepsilon_{max} = \sum_{i,t} (\varepsilon_{sub} \cdot \omega_{i} - \varepsilon_{i,t}) \cdot \pi_{i,t}
\end{equation}
Second, the resulting maximal total GHG abatement is set as a boundary condition (Eqn. \ref{eq:ghgtarget}), which can be step-wise reduced in runs where the costs are minimised (Equation \ref{eqn:cost}), with the total cost $C_{tot}$ being the sum of the cost $C_{i,t}$ for each option multiplied by the production at each time-point.
Second, the resulting maximal total GHG abatement is set as a boundary condition (Eqn. \ref{eq:ghgtarget}), which can be step-wise reduced in runs where the costs are minimised (Eqn. \ref{eqn:cost}), with the total cost $C_{tot}$ being the sum of the cost $C_{i,t}$ for each option multiplied by the production at each time-point.
\begin{equation}\label{eq:ghgtarget}
\varepsilon_{tot} = a \cdot \varepsilon_{max}, \quad a \in [0,1]
......@@ -498,13 +504,13 @@ Capacity expansion is subject to the sum of a constant ramp factor $r_{min}$ and
\kappa_{i,t+1}^+ \geqslant r_{max} \quad \forall (i,t) \in (I,T)\\
\end{equation}
The required land for each option is given by the production, divided by yield $Y_{i,t}$ [PJ$_{feed}$ Mha$^{-1}$] times conversion efficiency $\eta_{i,t}$ [PJ$_{fuel}$ PJ$_{feed}^{-1}$]. The total land use cannot surpass $\Lambda_{t}$ at any time point.
The required land for each option is given by the production, divided by yield $Y_{i,t}$ [PJ$_{feed}$ Mha$^{-1}$] times conversion efficiency $\eta_{i,t}$ [PJ$_{fuel}$ PJ$_{feed}^{-1}$]. The total land use cannot surpass $\Lambda_{t}$ at any time point (Eqn. \ref{eq:landUseTot}).
\begin{equation}\label{eq:landUseTot}
\Lambda_{t} \geqslant \sum_{i,f \in \Lambda,s}\pi_{i,f,s,t} \left( Y_{f,t} \cdot \eta_{i,f,t} \right)^{-1} \quad \forall (i,f,s,t) \in (I,F,S,T)
\end{equation}
The land use $\lambda_{f,t+1}$ by any given crop type at time ($t+1$) can be maximally increased by $r_{min,\Lambda} + r_{\Lambda} \cdot \lambda_{f,t}$.
The land use $\lambda_{f,t+1}$ by any given crop type at time ($t+1$) can be maximally increased by $r_{min,\Lambda} + r_{\Lambda} \cdot \lambda_{f,t}$ (Eqn. \ref{eq:landUseCrop}).
\begin{equation}\label{eq:landUseCrop}
\lambda_{f,t+1} \leqslant r_{min,\Lambda} + r_{\Lambda} \cdot \lambda_{f,t} \quad \forall (f,t) \in (F,T)
......@@ -559,7 +565,7 @@ Parameters and decision variables are summarised in Tables \ref{tab:nomenclature
%pwrMixMax Maximum power usage from mix for EVs and H2 production (PJ)
%solveOption solveoption (1=costMin 0=ghgMax)
\textbf{[To be completed!]}
\begin{table}[!htb]\centering
\begin{footnotesize}
\caption{\footnotesize{Parameters in the modelling. Values are given if they are constant across all dimensions (I=fuel option; F=Feedstock; S=sector; T=time) and scenarios. If the values differ between dimensions and/or scenarios, "Diff" is stated. Decision variables are "Free".}}
......@@ -606,7 +612,6 @@ Parameters and decision variables are summarised in Tables \ref{tab:nomenclature
\end{footnotesize}
\end{table}
Processes based on energy crops, biomass residues as well as power-based fuel options (electrofuels) are included. For electrofuels options, surplus power is assumed as the main source, with the power mix assumed additionally in certain scenarios. In order to capture the complexities involved in a sufficient detail, an intra-annual temporal resolution is required. The electrofuel plant capacities are endogenously adapted in order to capture the cost trade-off between electrofuel capacity and the achievable capacity factor which is determined by the surplus power curve.
%
%\begin{table*}[!htb]\centering
% \begin{footnotesize}
......@@ -629,8 +634,6 @@ Processes based on energy crops, biomass residues as well as power-based fuel op
% \end{footnotesize}
%\end{table*}
The power demand which is not covered by PV, wind or hydro (see below) is set as an upper demand for dispatchable power options. The dispatchable power options included here are fuel cells powered by hydrogen, as well as gas turbines powered by biomethane. The demand is divided into 50 intra-year steps, similarly to the surplus power. This is again done in order to more accurately capture the cost of covering the peak residual loads. The biomass and hydrogen used for dispatchable power decreases the renewable fuel production potential for transport (and vice versa). The optimal usage is determined endogenously within the model.
\end{document}
\endinput
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