Abstract
The recent development of renewable energy sources (RES) challenges energy systems and opens many new research questions. Energy System Models (ESM) are important tools to study these problems. However, including RES into ESM strongly increases the model complexity, because one needs to model the fluctuant, weather-dependent electricity production from RES with a high level of granularity. This leads to long execution times. To deal with this issue, our objective is to reduce the input time series of ESM without losing their energy-related key characteristics, such as weather-dependent fluctuations in production or peak demands. This task is challenging, because of the variety and high-dimensionality of the data. We describe a carefully engineered data-processing pipeline to reduce energy time series. We use Self-Organizing Maps, a specific kind of neural network, to select “representative days”. We show that our approach outperforms the existing ones with respect to the quality of ESM results, and leads to a significant reduction of ESM execution times.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 2153
Funding source: Bundesministerium für Wirtschaft und Energie
Award Identifier / Grant number: 03ET4023A-F
Funding statement: This work was partially supported by the DFG Research Training Group 2153: “Energy Status Data – Informatics Methods for Its Collection, Analyses and Exploitation” and the BEAM-ME Project (ID: 03ET4023A-F) founded by the Federal Ministry for Economic Affairs and Energy.
About the authors
Dipl.-Inf. Hasan Ümitcan Yilmaz is a Ph. D. candidate at the chair of Energy Economics of the Karlsruhe Institute of Technology (KIT). He holds a Diplom degree in Computer Science from KIT. His main research topics include energy system modeling and the decarbonization of the European energy system.
M. Sc. Edouard Fouché is a Ph. D. candidate in Data Mining at the Karlsruhe Institute of Technology (KIT), under the supervision of Prof. Dr.-Ing. Klemens Böhm. He holds a master’s degree in Computer Science from KIT and a master’s degree in Engineering from ESIEE Paris. His research focuses on Correlation Analysis, Bandit Algorithms, Outlier Detection and Clustering.
M. Sc. Thomas Dengiz is a Ph. D. candidate at the chair of Energy Economics of the Karlsruhe Institute of Technology (KIT). He holds a master’s degree in Industrial Engineering from KIT. His main research topics include the design of algorithms for smart grids and analyzing the flexibility of electric heating devices in buildings.
B. Sc. Lucas Krauß is a M. Sc. candidate in Computer Science at the Technische Universität Berlin. He is interested in scalable and online machine learning.
Dr. Dogan Keles graduated as industrial engineer from the Karlsruhe Institute of Technology (KIT) in 2006 and received his doctoral degree at the Economics Department of KIT in 2013 with summa cum laude. During his work at the KIT he analysed uncertainties in energy markets and developed methods to evaluate energy investments. During his research visit to University of California Berkeley in 2011, he worked on stochastic modeling. During his Senior Research Fellowship at Durham University in 2019, he carried out research on the effect of RES on electricity markets and designing systems with large shares of renewables. Currently, Dogan Keles is head of the research group “energy markets and energy system analysis” at the Institute of Industrial Production (IIP) at the KIT and works on different projects on the design of energy markets, evaluation of energy technologies (under uncertainty) and modelling of energy systems. His studies resulted in different publications in highly ranked journals and peer-reviewed conference proceedings.
Prof. Dr. Wolf Fichtner is Director of the Institute for Industrial Production (IIP) and the French-German Institute for Environmental Research (DFIU) of the Karlsruhe Institute of Technology (KIT). His main research topics include Energy Systems Analysis and Energy Modelling.
A.1 Exemplary ESM
PERSEUS-EU [20], [21], [22] is an optimization model for the electricity sector of 28 European countries with a multi-periodic linear optimization approach. PERSEUS-EU is used in particular for analyzing the impact of changing framework conditions caused by political or environmental reasons, with the objective to minimize total system costs under a set of technical, ecological and political constraints. Examples of important cost parameters are fuel costs for electricity generation, variable and fixed operating costs of power plants as well as fixed capital costs of new generation units.
The main decision variables of the optimization model are the production level of the existing and new capacities, investment in new capacities and energy exchanges between neighboring countries. In addition to future capacity and production mix, the model outputs – among others – details on primary energy mix, cross border exchanges, emissions in each country and marginal costs of electricity generation.
The model structure relies on a directed graph, where the nodes are connected to each other through energy flows. At the system nodes, several energy conversion technologies (e. g. power plants) are available. The source node provides fuel imports to the graph, while sink node contains the energy demand that is to be served through the inflows to this node. Exchange flows represent the electricity exchange between the system nodes (e. g. between European countries). A main restriction is the flow balance for each node.
To reduce the model complexity, generally, periods with duration of five years are selected and each 5 years is represented by a characteristic year. In addition, each characteristic year has an intra-year time resolution with several model time slices. The reduced intra-yearly time structure must represent the whole year.
For our experiments, we simplify the PERSEUS-EU model to limit the required computation time, since they involve the executions of hundreds of model instances. Still, we model the core restrictions of an ESM via the following equations:
A.1.1 Objective function
A.1.2 Energy balance restrictions
A.1.3 Capacity restriction
A.1.4 Load variation restriction
A.1.5 Expansion targets for RES
A.1.6 List of symbols
Energy carriers
Renewable energy carriers
Electricity
System Nodes
Production Processes
Production processes from RES
Sinks of the graph structure
Sources of the graph structure
Time slices
Units
Years
Electricity production target of RES in year y
Capacity expansion target of node n for energy carrier
Flow efficiency of the flow between n and
Efficiency of process
Share of produced or consumed energy carrier
Physical lifetime of unit u
Availability of u in y at time t
Fixed annual operation costs of unit u in year y
Fuel costs of
Annuitised investment expenditures for commissioning u in year y
Load variation costs of process
Variable operating costs of
Number of hours in time slice t
Initial capacity of unit u in year y
Discount rate of future cash flows
Secured capacity of unit u
Security factor for security of supply
Number of transitions between time slices
Flow level of energy carrier
Flow level between
Newly installed capacity of u in y
Capacity of unit u in year y
Load variation of process
Production level of
Production level of
A.2 Self-organizing maps
Self-Organising Maps (SOM) are a specific type of artificial neural networks traditionally used for dimensionality reduction and visualization of high-dimensional data [8]. It is a projection of a set of n-dimensional points to a two-dimensional neuron grid. The SOM is a
until the model has converged. Then, for our data reduction approach, we select as a representative the closest day to each neuron. We consider only square grids, i. e.,
Architecture of a Self-Organising Map.
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