This talk concentrates on the scaling of approximative solution due to aggregation of linear energy system models. The scaling is performed both on the temporal scale as well as the regional scale

Cao, Karl-Kien

von Krbek, Kai

Wetzel, Manuel

Institute of Transport Research:Publications

Methods to reduce computation times of linear optimising Energy System Models >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 1 Kai von Krbek, Karl-Kiên Cao, Manuel Wetzel  DLR, Department of Energy Systems Analysis WeatherAggReOpt, Essen (online) 2020-04-03 • Motivation • What systems were investigated and their characteristics  and dimensions • Model based speed up methods • Downscaling (temporal and spatial) • Rolling Horizon and heuristics • Conclusion Content >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 2 • Highly temporal and spatial resolved models are computationally intensive. • How can we reduce computation times? • If we simplify the models, how much accuracy do we lose? • What are the best speed-up methods and how much faster do we get? Motivation >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 3 • Efficient coding • Solver parameterisation tuning • Buy a bigger/better computer • Reduce the size of the ESM How can we speed-up energy system models (ESM) >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 4 • linear optimising energy system models • computing times > 12h (dominated by solver) • storage and transmission as characteristic components of the ESM • dispatch and investment models • shared memory hardware • usage of standard solvers (e.g. CPLEX) • formulated in GAMS What systems were investigated  >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 5 • temporal dimensions • typical-days / typical periods • hours in year (8760h) • spatial dimensions • NUTS 0/1/2/3 • extra high voltage transmission network • technological dimension • power plants • conventional power plants • VRE plants (hourly feed-in time series) • transmission • storage  Main dimensions of ESM >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 6 Evaluated system >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 7 Model name REMix Author (Institution) German Aerospace Center (DLR) Model type Linear programing minimization of total costs for system operation  economic dispatch / optimal dc power flow with expansion of storage and transmission capacities Sectoral focus Electricity Geographical focus Germany Spatial resolution > 450 nodes (reference model) Analyzed year (scenario) 2030 Temporal resolution 8760 time steps (hourly) Solver Commercial Algorithm Barrier  Cross-over Disabled Max. parallel barrier threads 16 Scaling Aggressive • Reduce the accuracy of the result • i.e. reduce the solver tolerance • don’t do crossover, if it is not necessary • this leads to results that is very close to the optimum (solver tolerance) • you will not  get the basic feasible solution • caveat: there might be negative numbers in results of positive variable • additional effort with analysis of the results • if results are used for a “warm-start” of another solve, this might lead to infeasibilities Recapture: solver based improvements and general improvements >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 8 • pure model reduction (downscaling) • temporal (averaging time-steps) • spatial • rolling horizon and temporal zooming heuristics Model based speed up methods >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 9 • the parameterisations will be investigated with and without expansion of transmission and storage • spatial aggregation • aggregation through hierarchical clustering of the nodes • the transmission lines will be summed accordingly • within one region, a copper plate is assumed • at full aggregation, Germany is one big copper plate • temporal aggregation • temporal averaging of feed-in time series and demand  Spatial and temporal scaling   >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 10 Spatial scaling without expansion CPLEX ticks 16.3 Mio. Total memory 79 GB GAMS time 0.6 h Total wall-clock time 3.6 h   Objective 21.9 Bio € Wind 162 TWh Gas 174 TWh; Coal 105 TWh Storage 4.1 TWh Transmission 434 TWh    >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 11 Spatial scaling with expansion CPLEX ticks 381.3 Mio. Total memory <256 GB GAMS time 6.6 h Total wall clock time 50.9 h    Objective 23.2 Bio € Wind 175 TWh Gas153 TWh; Coal 115 TWh Storage expansion 123 GWh; Transmission expansion 28.8 GW    >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 12 Temporal scaling without expansion CPLEX ticks 16.3 Mio. Total memory 79 GB GAMS time 0.6 h Total wall-clock time 3.6 h   Objective 21.9 Bio € Wind 162 TWh Gas 174 TWh; Coal 105 TWh Storage 4.1 TWh Transmission 434 TWh   >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 13 Temporal scaling with expansion CPLEX ticks 16.3 Mio. Total memory 79 GB GAMS time 0.6 h Total wall-clock time 3.6 h   Objective 21.9 Bio € Wind 162 TWh Gas 174 TWh; Coal 105 TWh Storage 4.1 TWh Transmission 434 TWh   >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 14 Speed up spatial temporal • transmission has a strong deviation • without expansion • speed-up 4. accuracy ~70-95% • with expansion • speed-up 8. accuracy ~70-95%  • storage has a strong deviation • without expansion • speed-up 6. accuracy ~80-95% • with expansion • speed-up 10. accuracy ~85-95%   >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 15  - The larger the system is, the greater the speed-up will be.  - For small systems the speed-up might be negligible. • Implemented on the temporal scale • Pure rolling horizon • only dispatch, no expansion planning • variable overlap of the intervals for more realistic boundary conditions • with higher number of interval the accuracy gets worse • Temporal zooming heuristics • low resolution (8 hourly) initial run to fix the boundary conditions (b.c.) • sub-intervalls in the year will be calculated with 8h-run as b.c. • expansion possible Rolling horizon >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 16 >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 17 Rolling horizon >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 18 Temporal zooming heuristics • Speed-up of factor five • Less accurate than full model (up to 30%) • storage usage is more accurate than simple down-sampling • bigger memory usage • better representation of actual operation => full year optimisation is not realistic Rolling Horizon - Summary >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 19 • Temporal or spatial scaling work best • use appropriate scaling for the chosen question • temporal reduction works well for transmission (expansion) • spatial clustering works well for storage (expansion) • Rolling horizon can improve the result performance, but uses more RAM • First steps should be the improvement of lean formulation of the ESM Key take-aways >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 22 Thank you for your attention >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 23 a project byKai von Krbek Kai.Krbek@dlr.de https://www.dlr.de/tt/  • input data should not differ much in order of magnitude • use adequate precission of input data • use of „option kill“, e.g. for long time-series input data, saves memory • abundant use of contraints (dolar condition) over domain of defintion • avoidance of consideration of technologies providing power at same costs • i.e. no decisions of equal options  • Helpful reference for GAMS: “Speeding up GAMS Execution Time” by Bruce A. McCarl https://www.gams.com/mccarl/speed.pdf  Recapture: source code improvement (example GAMS) >Methods to reduce computation times > Kai von Krbek > 2020-04-03 DLR.de  •  Chart 24 

Methods to reduce computation times of linear optimising Energy System Models

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Methods to reduce computation times of linear optimising Energy System Models

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