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 ... ... @@ -70,7 +70,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Tutorial I: Time Series Analysis}}\\ \small Will be worked on in the exercise session on Wednesday, 11 July 2018.\\[1.5em] \end{center} ... ... @@ -82,7 +82,7 @@ %===================================================================== The following data are made available to you on the course home page\footnote{\url{https://nworbmot.org/courses/complex_renewable_energy_networks/}}: page\footnote{\url{https://nworbmot.org/courses/esm-2018/}}: \begin{verbatim} de_data.csv, gb_data.csv, eu_data.csv, (wind.csv, solar.csv, load.csv). \end{verbatim} ... ... @@ -161,7 +161,7 @@ The time series are normalized to \begin{enumerate}[(a)] \item What is the seasonal optimal mix $$\alpha$$, which minimizes \begin{equation*} \expect{\left[ \alpha W(\cdot) + (1-\alpha) S(\cdot) - L(\cdot) \right]^2} = \frac1T \int_0^T \left[ \alpha W(t) + (1-\alpha) S(t) - L(t) \right]^2 \,\mathrm d t \expect{\left[ \alpha W(t) + (1-\alpha) S(t) - L(t) \right]^2} = \frac1T \int_0^T \left[ \alpha W(t) + (1-\alpha) S(t) - L(t) \right]^2 \,\mathrm d t , \end{equation*} \item How does the optimal mix change if we replace $$A_L \to -A_L$$? ... ... @@ -172,10 +172,10 @@ The time series are normalized to \end{equation*} Express the optimal mix $$\alpha$$ as a function of $$\phi$$. \item A constant conventional power source $$C(t) = 1 - \gamma$$ is now introduced. The mismatch then becomes \begin{equation} \begin{equation*} \Delta(t) = \gamma \left[ \alpha W(t) + (1-\alpha) S(t) \right] + C(t) - L(t) . \end{equation} \end{equation*} Analogously to (a), find the optimal mix $$\alpha$$ as a function of $$0 \leq \gamma \leq 1$$, which minimizes $$\expect{\Delta^2}$$. \end{enumerate} ... ...
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 ... ... @@ -73,7 +73,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Tutorial II: Network Theory and Power Flow}}\\ \small Will be worked on in the exercise session on Friday, 13 July 2018.\\[1.5em] \end{center} ... ... @@ -124,7 +124,7 @@ Consider the simple network shown ins Figure \ref{fig:network}. Calculate in Pyt If you map the nodes to countries like \texttt{0=DK, 1=DE, 2=CH, 3=IT, 4=AT,5=CZ} the network in Figure \ref{fig:network} represents a small part of the European electricity network (albeit very simplified). On the course homepage\footnote{\url{https://nworbmot.org/courses/complex_renewable_energy_networks/}}, you can find the \textit{power imbalance} time series for the six countries for January 2017 in hourly MW in the file \texttt{imbalance.csv}. They have been derived from physical flows as published by ENTSO-E.\footnote{\url{https://transparency.entsoe.eu/transmission-domain/physicalFlow/show}}\\ If you map the nodes to countries like \texttt{0=DK, 1=DE, 2=CH, 3=IT, 4=AT,5=CZ} the network in Figure \ref{fig:network} represents a small part of the European electricity network (albeit very simplified). On the course homepage\footnote{\url{https://nworbmot.org/courses/esm-2018/}}, you can find the \textit{power imbalance} time series for the six countries for January 2017 in hourly MW in the file \texttt{imbalance.csv}. They have been derived from physical flows as published by ENTSO-E.\footnote{\url{https://transparency.entsoe.eu/transmission-domain/physicalFlow/show}}\\ The linear power flow is given by \begin{equation} ... ...
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 ... ... @@ -89,7 +89,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Tutorial III: Storage Optimisation}}\\ \small Will be worked on in the exercise session on Monday, 16 July 2018.\\[1.5em] \end{center} ... ... @@ -97,7 +97,7 @@ \vspace{.5em} %=============== ====================================================== \paragraph{Problem III.1 \normalsize (storage adequacy).}~\\ \paragraph{Problem III.1 \normalsize (storage adequacy without losses).}~\\ %===================================================================== \begin{wrapfigure}{r}{0pt} ... ... @@ -183,7 +183,7 @@ Now we lift the restriction against transmission and allow them to bridge their \end{table} %=============== ====================================================== \paragraph{Problem III.2 \normalsize (storage optimization with PyPSA).}~\\ \paragraph{Problem III.2 \normalsize (storage optimization with PyPSA and losses).}~\\ %===================================================================== Python for Power System Analysis (PyPSA) is a free software toolbox for optimising modern power systems that include features such as variable wind and solar generation, storage units, etc\.. Use the toolbox to extend on your findings in Problem III.1. ... ... @@ -194,6 +194,6 @@ Python for Power System Analysis (PyPSA) is a free software toolbox for optimisi \item Run an investment optimization by calling the \texttt{lopf} function. \item How do your results \texttt{objective} and \texttt{{generators,stores,links}.p\_nom\_opt} compare with the results of III.1(d)? \item Now lift the restriction against transmission and allow North and South to bridge their 500 km separation with a transmission line. How does the cost optimal technology mix change compared to III.1(f)? \item Replace the approximated availability time-series of the wind and the solar generators with the ones from \texttt{availability.csv} computed from reanalysis weather data available on the course homepage\footnote{\url{https://nworbmot.org/courses/complex_renewable_energy_networks/}} and re-run the LOPF. Compare the results! Explain the differences by looking at the cumulative variations relative to the mean of the availability time-series! \item Replace the approximated availability time-series of the wind and the solar generators with the ones from \texttt{availability.csv} computed from reanalysis weather data available on the course homepage\footnote{\url{https://nworbmot.org/courses/esm-2018/}} and re-run the LOPF. Compare the results! Explain the differences by looking at the cumulative variations relative to the mean of the availability time-series! \end{enumerate} \end{document}
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 ... ... @@ -88,7 +88,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Solutions to Tutorial III}}\\ \small Will be worked on in the exercise session on Monday, 16 July 2018.\\[1.5em] \end{center} ... ... @@ -288,9 +288,9 @@ For now, assume the stores are lossless. Losses will be considered in III.2. Without taking losses into account, both regions should choose hydrogen storages. Overall, the North can provide electricity at a lower rate than the South: $$\tilde{P}_{w+h}^N = \frac{104 \cdot 10^9 \eur}{20 \si{\giga\watt}} = 5 \cdot 10^9 \eur \si{\per\giga\watt}$$ $$P_{w+h}^N = \frac{104 \cdot 10^9 \eur}{20 \si{\giga\watt}} = 5 \cdot 10^9 \eur \si{\per\giga\watt}$$ $$\tilde{P}_{s+h}^S = \frac{175 \cdot 10^9 \eur}{30 \si{\giga\watt}} = 6 \cdot 10^9 \eur \si{\per\giga\watt}$$ $$P_{s+h}^S = \frac{175 \cdot 10^9 \eur}{30 \si{\giga\watt}} = 6 \cdot 10^9 \eur \si{\per\giga\watt}$$ % (e) \begin{shaded} ... ... @@ -302,16 +302,16 @@ For now, assume the stores are lossless. Losses will be considered in III.2. % (f) \begin{shaded}\item Now we lift the restriction against transmission and allow them to bridge their 500 km separation with a transmission line. Estimate the cost-optimal technology mix by assuming wind energy in the North is only stored in the North and solar energy in the South is likewise only stored in the South! What would happen if you dropped that assumption?\end{shaded} Because $\tilde{P}_{w+h}^N < \tilde{P}_{w+h}^S$ there will be energy exports from North to South: Because $P_{w+h}^N < P_{w+h}^S$ there will be energy exports from North to South: $$E^N > E^S \quad \text{and} \quad E^N + E^S = 50 \si{\giga\watt}$$ The total price of electricity is given by \begin{align*} P_{tot} & =\frac{ E^N \cdot \tilde{P}_{w+h}^N + E^S \cdot \tilde{P}_{s+h}^S + (E^N - E^S)\cdot 200 \eur\si{\per\kilo\watt}}{E^N + E^S} \\ & = \frac{E^N \cdot \tilde{P}_{w+h}^N + (50\si{\giga\watt} - E^N) \cdot \tilde{P}_{s+h}^S + (2E^N - 50\si{\giga\watt})\cdot 200 \eur\si{\per\kilo\watt}}{E^N + E^S} \\ & = \frac{E^N (\tilde{P}_{w+h}^N - \tilde{P}_{s+h}^S + 400 \eur \si{\per\kilo\watt}) + 50 \si{\giga\watt} (\tilde{P}_{s+h}^S - 200 \eur \si{\per\kilo\watt})}{E^N + E^S} \\ P_{tot} & =\frac{ E^N \cdot P_{w+h}^N + E^S \cdot P_{s+h}^S + (E^N - E^S)\cdot 200 \eur\si{\per\kilo\watt}}{E^N + E^S} \\ & = \frac{E^N \cdot P_{w+h}^N + (50\si{\giga\watt} - E^N) \cdot P_{s+h}^S + (2E^N - 50\si{\giga\watt})\cdot 200 \eur\si{\per\kilo\watt}}{E^N + E^S} \\ & = \frac{E^N (P_{w+h}^N - P_{s+h}^S + 400 \eur \si{\per\kilo\watt}) + 50 \si{\giga\watt} (P_{s+h}^S - 200 \eur \si{\per\kilo\watt})}{E^N + E^S} \\ \end{align*} Now, minimising the term for a choice of $E^N$ will yield ... ... @@ -330,11 +330,17 @@ For now, assume the stores are lossless. Losses will be considered in III.2. Compared to the weighted electricity cost of North and South without transmission \begin{align*} \min \tilde{P}_{tot} & = \frac{20\si{\giga\watt}\cdot 5 \cdot 10^9 \eur \si{\per\giga\watt} + 30\si{\giga\watt}\cdot 6 \cdot 10^9 \eur \si{\per\giga\watt}}{50 \si{\giga\watt}} \\ \min P_{tot} & = \frac{20\si{\giga\watt}\cdot 5 \cdot 10^9 \eur \si{\per\giga\watt} + 30\si{\giga\watt}\cdot 6 \cdot 10^9 \eur \si{\per\giga\watt}}{50 \si{\giga\watt}} \\ & = \frac{280 \cdot 10^9 \eur}{50 \si{\giga\watt}} = 5.6 \cdot 10^9 \eur \si{\per\giga\watt} \end{align*} the system cost could be reduced by approx.\ 7 \%. %=============== ====================================================== \paragraph{Solution III.2 \normalsize (storage optimisation with PyPSA).}~\\ %===================================================================== cf. Jupyter Notebook \end{enumerate} ... ...
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 ... ... @@ -104,7 +104,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Tutorial IV: Electricity Markets}}\\ \small Will be worked on in the exercise session on Tuesday, 17 July 2018.\\[1.5em] \end{center} ... ... @@ -180,7 +180,7 @@ Assume that the demand $D_*$ is constant and insensitive to price, that energy i \end{enumerate} %=============== ====================================================== \paragraph{Problem IV.4 \normalsize (bidding in africa with pypsa).}~\\ % d\paragraph{Problem IV.4 \normalsize (bidding in africa with pypsa).}~\\ %===================================================================== ... ...
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 ... ... @@ -105,7 +105,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Solution IV: Electricity Markets}}\\ \small Will be worked on in the exercise session on Tuesday, 17 July 2018.\\[1.5em] \end{center} ... ... @@ -303,7 +303,7 @@ Assume that the demand $D_*$ is constant and insensitive to price, that energy i \end{enumerate} %=============== ====================================================== \paragraph{Solution IV.4 \normalsize (bidding in africa with pypsa).}~\\ %\paragraph{Solution IV.4 \normalsize (bidding in africa with pypsa).}~\\ %===================================================================== ... ...
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 ... ... @@ -89,7 +89,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Tutorial V: Investment and Large Power Systems\\}} \small Will be worked on in the exercise session on Wednesday, 18 July 2018.\\[1.5em] \end{center} ... ... @@ -135,7 +135,7 @@ Let us suppose that demand is inelastic. The demand-duration curve is given by $\paragraph{Problem V.3 \normalsize (generator dispatch with SciGRID).}~\\ %===================================================================== SciGRID\footnote{\url{https://www.scigrid.de/pages/general-information.html}} is a project that provides an open source reference model of the European transmission networks. In this tutorial, other than previous simple examples, you will examine the economic dispatch of many generators all over Germany and its effect on the power system. The data files for this example and a populated Jupyter notebook are provided on the course homepage\footnote{\url{https://nworbmot.org/courses/complex_renewable_energy_networks/}}. The dataset comprises time series for loads and the availability of renewable generation at an hourly resolution for the year 2011. Feel free to choose a day to your liking; we will later discuss your different outcomes in groups. A few days might be of particular interest: \texttt{2011-01-31} was the least windy day of 2011, \texttt{2011-02-05} was a stormy day with lots of wind energy production, \texttt{2011-07-12} the weather 7 years ago was very sunny day, and \texttt{2011-09-06} was a windy and sunny autumn day. SciGRID\footnote{\url{https://www.scigrid.de/pages/general-information.html}} is a project that provides an open source reference model of the European transmission networks. In this tutorial, other than previous simple examples, you will examine the economic dispatch of many generators all over Germany and its effect on the power system. The data files for this example and a populated Jupyter notebook are provided on the course homepage\footnote{\url{https://nworbmot.org/courses/esm-2018/}}. The dataset comprises time series for loads and the availability of renewable generation at an hourly resolution for the year 2011. Feel free to choose a day to your liking; we will later discuss your different outcomes in groups. A few days might be of particular interest: \texttt{2011-01-31} was the least windy day of 2011, \texttt{2011-02-05} was a stormy day with lots of wind energy production, \texttt{2011-07-12} the weather 7 years ago was very sunny day, and \texttt{2011-09-06} was a windy and sunny autumn day. \begin{enumerate}[(a)] \item Describe the network as well as its regional and temporal characteristics. ... ... @@ -163,7 +163,7 @@ SciGRID\footnote{\url{https://www.scigrid.de/pages/general-information.html}} is %=============== ====================================================== \paragraph{Problem V.4 \normalsize (network clustering).}~\\ %\paragraph{Problem V.4 \normalsize (network clustering).}~\\ %===================================================================== \end{document} No preview for this file type  ... ... @@ -106,7 +106,7 @@ \begin{center} \textbf{\Large Energy System Modelling }\\ {SS 2018, Karlsruhe Institute of Technology}\\ {Institute of Automation and Applied Informatics}\\ [1em] {Institute for Automation and Applied Informatics}\\ [1em] \textbf{\textsc{\Large Solution V: Investment and Large Power Systems}}\\ \small Will be worked on in the exercise session on Wednesday, 18 July 2018.\\[1.5em] \end{center} ... ... @@ -313,7 +313,7 @@ Let us suppose that demand is inelastic. The demand-duration curve is given by$ cf. Jupyter Notebook %=============== ====================================================== \paragraph{Solution V.4 \normalsize (network clustering).}~\\ %\paragraph{Solution V.4 \normalsize (network clustering).}~\\ %===================================================================== \end{document}
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