A Review on Time Series Aggregation Methods for Energy System Models
Abstract
:1. Introduction
1.1. Drivers of Model Complexity
1.2. Motivation and Scope of the Review
2. Methodology and Structure of the Review
2.1. Methodology of the Literature Research
2.2. Structure of the Review
3. Time Series Aggregation
3.1. Resolution Variation
3.1.1. Downsampling
3.1.2. Segmentation
3.1.3. Multiple Time Grids
3.2. Typical Periods
3.2.1. Time-Based Merging
3.2.1.1. Averaging
3.2.1.2. Time Slices
3.2.1.3. Time Slices/Averaging + Downsampling/Segmentation
3.2.2. Feature-Based Merging
- A normalization (and sometimes a dimensionality reduction).
- A distance metric.
- A clustering algorithm.
- A method to choose representatives [59].
- A rescaling step in the case of non-centroid based clustering algorithms.
3.2.2.1. Preprocessing and Normalization
3.2.2.2. Algorithms, Distance Metrics, Representation
3.2.2.3. Rescaling
3.2.3. Modified Feature-Based Merging
3.2.4. Linking Typical Periods
3.3. Random Sampling
3.3.1. Unsupervised
3.3.2. Supervised
3.4. Miscellaneous Methods
3.5. Overview and Trends in Aggregation
4. Preserving Additional Information
- Values of the original time series which could be especially important for the ESM are usually not preserved.
- A reliable estimation of the deviation of the optimization result based on aggregated time series from the one based on full time series can usually not be given.
4.1. A Priori Methods
4.1.1. Adding Extreme Periods
4.1.2. Inclusion of Extreme Values or Additional Features
4.1.3. Additional Constraints in Feature-Based Merging
4.2. A Posteriori Methods
4.2.1. Non-Iterative
4.2.2. Iterative
- Separating complicating binary variables from the vast majority of continuous variables.
- Separating the design problem from the operational problem.
- Obtaining feasible but suboptimal solutions instead of optimal but infeasible solutions for the fully resolved input data.
- Deriving implications for a meaningful TSA from the system itself instead of the input data only.
- Determining a more robust energy system by exposing the once optimized energy systems to different input data scenarios.
4.3. Overview and Trends in the Integration of Additional Information
5. Conclusions
- The question of the most important statistical features of the time series to be kept, i.e., whether the clustering of statistical features in a lower dimensional space is superior to the traditional TSA methods.
- A way to measure the accuracy of different aggregation methods a priori by defining bounds that are also valid for the computationally intractable problem.
- Enhancing the convergence rate of iterative methods in order to compete with the branch-and-bound or decomposition methods of commercial solvers
- Developing an approach that is capable of identifying the most critical situations in input time series in a non-empirical manner. This could lead to robust optimizations not based on MonteCarlo-like approaches.
Author Contributions
Funding
Conflicts of Interest
Abbreviations
Abbreviation | Meaning |
DTW | Dynamic Time Warping |
ESM | Energy System Model |
GEP | Generation Expansion Planning |
MILP | Mixed Integer Linear Program |
RES | Renewable Energy Sources |
TR | Temporal Resolution |
TD | Typical Day |
TTS | Typical Time Step |
TS | Time Slice |
TSA | Time Series Aggregation |
UC | Unit Commitment |
Appendix A
Year | Author | ESM for Case Study, (Framework) | Normalization | Distance Metric | Clustering/Grouping | Representative | Extreme Periods | Linking Periods | Duration Curve |
---|---|---|---|---|---|---|---|---|---|
1999 | Balachandra et al. [53] | None (just approach) | No | No | Multiple discriminant analysis | Mean | No | Yes | No |
2002 | Yokoyama et al. [66] | Building or district model, no storage technologies, but multiple commodities | No | No | Season-based (summer, mid-season, winter) with 4-, 2-, or 1- h resolution | (probably) Mean | No | No | No |
2007 | Lee et al. [183] | UC problem for 48 unit power system (not further specified) | No | No | No | No | No | Yes | No |
2007 | Swider et al. [122] | Single-node model for electricity production in Germany with wind and pumped hydro storage | No | No | Every two months, one weekday and one weekend day with 2-h resolution | (probably) Mean | No | No | No |
2008 | Marton et al. [98] | None (just approach) | No | Integral of absolute error (L1 norm) | Clustering by comparing each new day to clusters of preceding days | Mean | Yes, if outlier surpass a certain threshold of the IAE and the following day is close to the preceding cluster | Yes | No, although curve was called the duration curve |
2008 | Mavrotas et al. [54] | Building model for a hospital, no storage technologies, but multiple commodities | No | No | Monthly average | Mean | No | No | No |
2008 | Mavrotas et al. [54] | Building model for a hospital, no storage technologies, but multiple commodities | No/not mentioned | No/not mentioned | Seasonal rescaled average further segmented | Rescaled mean | Peak demand value of each cluster is kept for each attribute | No | No |
2009 | Alzate et al. [195] | Customer or unit partitioning/none (just approach) | Z-normalization | No (Hamming distance for out-of-sample extension) | Spectral clustering | None (just grouped) | No | No | No |
2009 | Casisi et al. [114] | District model, no storage technologies, but multiple commodities | No | No | Season-based (3 seasons for energy demand and 24 for sold energy to the grid) | (probably) Mean | No | No | No |
2009 | Lozano et al. [111] | Building model for a hospital, no storage technologies, but multiple commodities | No | No | Monthly average with distinction between weekday and weekend | (probably) Mean | No | No | No |
2010 | Lozano et al. [99] | District model, thermal storage units, multiple commodities | No | No | Monthly average | (probably) Mean | No | No | No |
2010 | Nicolosi et al. [104] | Single-node electricity dispatch model for Texas (ERCOT), no storage, technologies mentioned, (THEA) | No | No | Full resolution, 4 seasons, Wednesday, Saturday and Sunday with hourly resolution, 16 time slices | Means | No | No | No |
2011 | Domínguez-Muñoz et al. [55] | None (just approach) | Yes, but not mentioned which | Euclidean | k-medoids | Medoids | Peak heating and peak cooling day | No | No |
2011 | Haydt et al. [105] | Island electricity model for Flores (Azores), no explicitly modeled storage technologies (only via availability), (TIMES, LEAP, EnergyPlan) | No | No | LEAP: 9 time slices from the duration curve TIMES: 4 seasons, Wednesday, Saturday, and Sunday with hourly resolution EnergyPLAN: full hourly resolution | Means | No | Yes | LEAP: Yes TIMES: No |
2011 | Ortiga et al. [179] | Building model, thermal storage units, multiple commodities | No/not mentioned | No/not mentioned | Graphical method | Existing days | Peak heating and peak cooling day | No | Yes |
2011 | Pina et al. [124] | Island electricity model for São Miguel (Azores), no explicitly modeled storage technologies (only via availability), no storage technologies, (TIMES) | No | No | 4 seasons, weekday, Saturday and Sunday with hourly resolution | (probably) Mean | No | Yes | No |
2011 | Weber et al. [112] | Multi-node district model, daily heat and electricity storages, multiple commodities | No | No | 3 seasons further segmented into 6 irregular periods | (probably) Mean | No | No | No |
2012 | Buoro et al. [89] | Building model, thermal storage units, multiple commodities | No | No | Monthly average, typical weeks with 168 h | (probably) Mean | No | No | No |
2012 | Devogelaer et al. [125] | Multi-node model for Belgium, multiple storage technologies, multiple commodities, (JRC-EU-TIMES) | No | No | 26 2-week periods with three daily levels | (probably) Mean | Peak demand slice | Yes | No |
2012 | Mehleri et al. [129] | District model, no storage technologies, multiple commodities | No | No | 3 seasons further segmented into 6 irregular periods | (probably) Mean | No | No | No |
2012 | Van der Weijde et al. [180] | Multi-node electricity model for Great Britain, no explicitly modeled storage technologies (only as source/sink) | No | No | N hourly samples | Existing hours | No | No | No |
2012 | Welsch et al. [106] | Single-node electricity model for a town, battery storages, demand shifting, (OSeMOSYS) | No | No | In Proposal: 4 seasons, work days and weekends, 3 daily intervals. In example: Just one day in hourly resolution | (probably) Mean | No | Yes | No |
2013 | De Sisternes et al. [93] | Single-node electricity model, no storage technologies, but minimum up- and down-times | Min-max normalization for NLDC | Euclidean | Exhaustive search or heuristic | Existing weeks | Including peak week or peak day | No | Yes |
2013 | Kannan et al. [126] | Single-node electricity model for Switzerland and pumped hydro storage, (TIMES) | No | No | Season-based (four seasons and to diurnal time slices), or weekdays, Saturdays, Sundays in hourly resolution | Average | No | Yes | No |
2013 | Mehleri et al. [130] | District model, thermal storage units, multiple commodities | No | No | 3 seasons with hourly resolution | (probably) Mean | No | No | No |
2013 | Pina et al. [115] | Electricity model for Portugal, storage technologies considered, but modeling not explained, number of regions not mentioned, (TIMES and EnergyPLAN) | No | None | One weekday, one Saturday and one Sunday, 4 seasons | Not mentioned | No | No | No |
2013 | Simões et al. [127] | Multi-node model for Europe, multiple storage technologies, multiple commodities, (TIMES) | No | No | Season-based (four seasons, day, night and peak time slice) | Average | Average peak demand during each season | Yes | No |
2013 | Spiecker et al. [116] | Multi-node electricity model for Europe, hydro storage units, cogeneration units on regional scale | No/not mentioned | None | One weekday and one weekend day for every two months with 2 h resolution | Not mentioned | Yes, with stochastic approach | Yes | No |
2013 | Voll et al. [103] | District model, no storage technologies, multiple commodities | No | No | Monthly average | Mean | Two more time steps for summer and winter peak loads | No | No |
2014 | Adhau et al. [153] | Stochastic single-node electricity model, no storage technologies | No/not mentioned | Euclidean | k-means | Centroids | No | No | No |
2014 | Benítez et al. [196] | Customer or unit partitioning/none (just approach) | No/not mentioned (only one attribute) | Euclidean | Dynamic k-means | Centroids | No | Yes (yearly trajectory) | No |
2014 | Deane et al. [64] | UC of the Irish electricity system, pumped hydro storage, (PLEXOS) | No | No | Downsampling (5, 15, 30 and 60 min) | Average | No | Yes | No |
2014 | Fazlollahi et al. [138] | District heating model, no storage technologies | Min-max normalization | Euclidean | k-means | Centroids | Attribute peaks | No | No |
2014 | Fazlollahi et al. [69] | Two single-node district models with fixed capacities, no storage technologies, multiple commodities, UC (minimizing operating costs) | Min-max normalization | Euclidean | k-means and segmentation | Centroids | Attribute peaks | No | No |
2014 | Green et al. [154] | Electric dispatch model for UK, pumped hydro storage simulated, number of regions not mentioned | No (just two attributes of same scale clustered) | Euclidean | k-means | Centroids | Dominant ramp integration | No | No |
2014 | Poncelet et al. [36] | Island electricity model for Belgium, no storage technologies or transmissions, re-evaluation with UC model, (TIMES) | No | No | Season-based (four seasons, night, day and peak slice) | (probably) Mean | By choosing peak slice | No | No |
2014 | Stadler et al. [113] | Building model, multiple storage technologies, multiple commodities (DER-CAM) | No | No | (seven typical days or one typical weekday, one typical weekend day and one peak day) | (probably) Mean | Peak demand day in case of typical weekday and typical weekend day | No | No |
2014 | Wakui et al. [110] | Building model, thermal storage units, multiple commodities | No | No | Season-based | (probably) Mean | Peak summer day and peak winter day | No | No |
2014 | Wogrin et al. [85] | Single-node electricity model, no storage technologies | No (attributes of the same unit) | Euclidean | k-means, hourly, 6 system states | Centroids | No | No | No |
2014 | Xiao et al. [186] | Island electricity model for, no storage technologies | No | No | No | No | No | Yes | No |
2015 | Agapoff et al. [63] | Multi-node electricity model for GEP, no storage technologies | No/not mentioned | Euclidean | k-means, typical hours (snapshots) | Medoids | Included as clustered features (min, max, std., local difference and avg.) | No | No |
2015 | Brodrick et al. [155] | Single-node model of a coal-plant with alternative natural gas and solar thermal heat sources and carbon capture and storage, CO2 solvent storage unit, multiple commodities | Normalization by dividing by the average | Euclidean | k-means | Centroids | No | No | No |
2015 | Bungener et al. [70] | UC of a chemical cluster, multiple commodities | Normalized by average values and multiplied by weight | None, but variance indicator and zero flowrate indicator | Evolutionary mechanisms (segmentation) | Means | No | Yes (adjacent time steps are merged) | No |
2015 | Deml et al. [71] | Single-node electric dispatch model, pumped hydro storage | No | No | Progressive downsampling | Means | No | Yes | No |
2015 | Fitiwi et al. [142] | IEEE 24-bus Reliability Test System [197], multi-node electricity model, no storage technologies | Normalized by maximum line length and base load | Euclidean | k-means, typical hours (snapshots) | Medoids closest to the clusters’ centroids | No | No | No |
2015 | Harb et al. [101] | Building model and district model, thermal storage units, multiple commodities | No | No | Monthly average, also 15 min. and hourly resolution | Mean | No | No | No |
2015 | Harb et al. [90] | District model, thermal and battery storage units, multiple commodities | No | No | Cluster by sums of weeks (sensitivity analysis also for different day numbers), typical weeks | Means | No | No | No |
2015 | Marquant et al. [149] | District heating model, no storage technologies, multiple commodities | No/not mentioned | Euclidean | k-medoids | Medoids | Peak electricity and peak heating days | No | Yes |
2015 | Merkel et al. [91] | District model, thermal storage units, multiple commodities | No | No | Season based (three weeks from spring/autumn, summer and winter), 15 min. resolution | (probably) Existing weeks | No | No | No |
2015 | Munoz et al. [181] | IEEE Reliability Test System [188], multi-node electricity model, no storage technologies | No/not mentioned | Euclidean | Daily moment-matching, k-means for hours, typical hours (snapshots) | Centroids | Top 10 peak load hours included | No | No |
2015 | Poncelet et al. [177] | None (just approach) | No/not mentioned | L1-Norm | Using so-called “bins” | Existing days | No | No | Yes |
2015 | Samsatli et al. [16] | Multi-node island model, multiple hydrogen storage technologies, multiple commodities | No | No | Season-based (four seasons, weekdays and weekend days) | (probably) Mean | No | Yes | No |
2015 | Schiefelbein et al. [163] | District model, thermal storage units, multiple commodities | No/not mentioned | Euclidean | k-medoids | Medoids | No | No | |
2015 | Wakui et al. [109] | Building model, thermal and battery storage units, multiple commodities | No | No | Season based | (probably) Mean | Peak summer day and peak winter day | No | No |
2015 | Wouters et al. [117] | District model, heat, cold and battery storage technologies, multiple commodities | No | No | Season-based (spring/autumn, summer and winter) | (probably) Mean | Sensitivity analysis by adding variability to PV input data | No | No |
2015 | Yang et al. [118] | District model, heat and cold storage technologies, multiple commodities | No | No | Season-based (spring/autumn, summer and winter), 2 h resolution | (probably) Mean | No | No | No |
2015 | Yokoyama et al. [67] | Building model for a hotel, no storage technologies, but multiple commodities | No | No | Season-based (summer, mid-season, winter) with 8, 4, or 2 h resolution and for commercial solver 1 h | (probably) Mean | No | No | No |
2016 | Ameri et al. [119] | District model no storage technologies, multiple commodities | No | No | Season-based (summer and winter) | (probably) Mean | No | No | No |
2016 | Beck et al. [65] | Electric building model, battery storage | No | No | Single day downsampled (10, 30, 60, 300, 900, 3600 s), analyzed single days | Mean | No | Yes | No |
2016 | Bracco et al. [120] | District model, thermal and battery storage technologies, multiple commodities, (DESOD) | No/not mentioned | No | Season-based (summer, winter, mid-season) | (probably) Mean | No | No, initial conditions at each day, e.g., | No |
2016 | De Sisternes et al. [92] | Single-node electricity model, battery storage and minimum up- and down-times | Min-max normalization for NLDC | Euclidean | Exhaustive search or heuristic (refers to [93], but with additional cycled power error), typical weeks | Existing weeks | Including peak week or peak day | No | Yes |
2016 | Frew et al. [182] | Multi-node electric model of the US, pumped hydro, thermal and battery storage technologies, (POWER) | Yes, but not mentioned is which, but averaged across all potential developable sites | None | Random days | Existing days, weights calculated with least squares method | Extreme days containing the peak value for each of the eight attributes | No (net storage values of each day must be zero or SOC at start of each day equals that at the end) | Yes |
2016 | Haikarainen et al. [198] | Customer or unit partitioning/district model, thermal storage units, multiple commodities | No | Euclidean | k-means | Means | No | No | No |
2016 | Kools et al. [102] | District electricity model, battery storage units, heat demand driven CHP units considered | No | No | Averaging of eight consecutive weeks in each season to one typical day | Mean | Normal distributions added for 1 min, 15 min and 1 h resolution (stochastic impact) | Control policy for the storage (not across days) | No |
2016 | Lin et al. [156] | Multiple building models, thermal and battery storage units, multiple commodities | No/not mentioned (attributes of the same unit) | Euclidean | k-means | Existing day which is closest to the centroid | No | No (periodic SOC) | No |
2016 | Lythcke-Jørgensen et al. [88] | CHP-plant model, no storage technologies, multiple commodities | Heat demand normed by maximum value | No/not mentioned | So-called “CHOP” aggregation (graphical method) for five years of hourly data | Means | No | No | No |
2016 | Merrick et al. [40] | Single-node electricity model, no storage technologies | No | None | Monthly median and peak electricity demand day with 4 h resolution and only one averaged period | Medoids | Peak electricity demand days | No | No |
2016 | Nahmmacher et al. [143] | Multi-node electricity model LIMES-EU [199] with intraday storage technologies, (LIMES-EU) | Demand: region-specific divided by maximum value VRE: divided by maximum value across all regions | Euclidean | hierarchical | Medoids | No | No | No |
2016 | Oluleye et al. [123] | Single-node district model, thermal storage units, multiple commodities | None | None | One weekday and one weekend day for winter, summer and transition with 7 (6) time bands (slices) | Not mentioned | No | No | No |
2016 | Patteeuw et al. [94] | Building heating model of nine buildings, thermal storage units, multiple commodities | No/not mentioned, Demand: region-specific divided by maximum value | L1-Norm | Using so-called “bins”, heuristic, hierarchical clustering according to Nahmmacher et al. [143] for the years of 2013–2016 | Existing weeks (6) | Coldest week and week with highest e-demand (same week) | No | Yes |
2016 | Ploussard et al. [87] | IEEE 24-bus Reliability Test System [197], multi-node electricity model, no storage technologies | No/not mentioned | Euclidean | k-means, typical hours (snapshots) | Existing snapshot closest to the centroids | No | No | No |
2016 | Poncelet et al. [128] | Island electricity model for Belgium, no storage technologies or transmissions, re-evaluation with UC model, (TIMES) | No | None | For each of the four seasons one night, day and peak electricity time slice | Mean | Peak electricity time slice | No | No |
2016 | Poncelet et al. [144] | Single-node electricity model based on [200], no storage technologies, (LUSYM) | No/not mentioned, Demand: region-specific divided by maximum value | L1-Norm, Euclidean | Using so-called “bins”, heuristic, hierarchical clustering according to Nahmmacher et al. [143] | Existing days, medoids | No, for heuristics days with highest and lowest value for e-demand and highest and lowest average for wind and PV | No | Yes |
2016 | Samsatli et al. [17] | Multi-node hydrogen-electricity model for Great Britain, multiple hydrogen storage units, multiple commodities | No | No | Season-based (four seasons, work days and weekend days) | (Probably) Mean | No | Yes | No |
2016 | Schütz et al. [139] | Building model, thermal and battery storage units, multiple commodities | Min-max normalization | Euclidean | k-means k-medians k-medoids k-centers | Centroids Medians Medoids Centers | No | No | No |
2016 | Stenzel et al. [38] | UC of building electricity model with battery storage | No | None | downsampling | Means | No | Yes | No |
2016 | Wakui et al. [108] | Building model, thermal and battery storage units, multiple commodities | No | No | Season based | (probably) Mean | Peak summer day and peak winter day | No | No |
2016 | Wogrin et al. [83] | Single-node electricity model, pumped hydro and battery storage | No/not mentioned | Euclidean | k-means (98 system states (typical hours)) | Centroids | No, but the first and last hour of the time horizon were manually added | Yes | No |
2017 | Bahl et al. [157] | District model from Voll et al. [103], no storage technologies, multiple commodities | No/not mentioned (attributes of same scale clustered) | (probably) Euclidean | k-means, typical hours (snapshots) | Centroids | Feasibility time steps (peak values) and operation optimization for full time series | No | No |
2017 | Brodrick et al. [146] | UC of an integrated solar combined cycle, no storage technologies, multiple commodities | Z-normalization | Euclidean | k-means | Centroids | No | No | No |
2017 | Härtel et al. [86] | Multi-node transmission expansion planning model, no storage technologies | Either normed by highest value per market or highest value across all markets | Euclidean | k-means, k-medoids, hierarchical, systematic sampling, moment-matching, typical hours (snapshots) | Centroids, medoids, sample points | Heurisitc defining new cluster centers if 95% of a cluster’s data points are below or above a 6 h moving average, with the lowest or highest chosen as the new cluster center | No | No |
2017 | Heuberger et al. [158] | Single-node electricity model with carbon capture and storage and grid-level storage | Yes, but not mentioned which | Euclidean | k-means | Means | Day with annual electricity peak demand | No | No |
2017 | Marquant et al. [150] | District heating model, thermal and battery storage units, multiple commodities | No/not mentioned | Euclidean | k-medoids | Medoids | Peak electricity and peak heating days | No | Yes |
2017 | Moradi et al. [121] | Single-node model of an energy hub, thermal and battery storage, multiple commodities | No | No | Season-based (one work day and one weekend day per spring, summer, autumn and winter) | (probably) Mean | No | No | No |
2017 | Pfenninger et al. [37] | Multi-node electricity model for Great Britain, pumped hydro and battery storage units | Normalized by the maximum value across all time steps and model zones | Euclidean | k-means, hierarchical, downsampling, heuristics | Centroids, medoids | Min/max solar and wind days, wind and PV weeks and wind-demand weeks | No | No |
2017 | Renaldi et al. [61] | Single-node district heating system, long- and short-term thermal storage units, multiple commodities | No | None | Multiple time grids for different storage technologies | Downsampled 3 h steps for long-term storage | No | Yes | No |
2017 | Timmerman et al. [107] | Two business park models (one based on the model of Voll et al. [103]), thermal and electrical storage units, multiple commodities, (Syn-E-Sys) | No | No | Season and weekday-based (4 × 2 × 4 6 h intervals) | (probably) Mean | No | Yes | No |
2017 | Schütz et al. [100] | Building model, thermal and battery storage units, multiple commodities | No | No | Monthly average (one typical day per month and weighted) | (probably) Mean | No | No | No |
2017 | Sun et al. [136] | Customer or unit partitioning/none (just approach) | Time steps wise (in period) average s divided by maximum value of each customer | Likelihood-function | Vine-copula mixture model | None | No | No | No |
2017 | Teichgräber et al. [147] | Oxyfuel natural gas plant, liquid oxygen storage, multiple commodities | Z-Normalization | Euclidean | k-means | Centroids | No | No | No |
2017 | vom Stein et al. [79] | Multi-node electricity dispatch model for Europe, pumped hydro storage | No | L1-Norm | Clustering of consecutive time steps with objective to minimize gradients within clusters | Mean | No | Yes (clustering of consecutive time steps) | No |
2017 | Yang et al. [201] | Customer or unit partitioning/none (just approach) | Z-normalization | Shape-based distance | k-shape | None | No | No | No |
2017 | Zhu et al. [164] (refers to [55]) | Building model for an airport in China optimizing economics or CO2 emissions, no storage technologies, but start-up and shut-down costs | Yes, but not mentioned which | Euclidean | k-medoids (only three season-specific typical days) | Medoids | No | No | No |
2018 | Almaimouni et al. [137] | Single-node GEP for electricity, validated with rolling horizon UC, no storage technologies | Normalize by with m as number of days, principal components | Euclidean | k-means | Centroids | No | No | Only as error estimator |
2018 | Bahl et al. [192] | District model from Voll et al. [103] and a single-node pump system, no storage technologies, multiple commodities | No/not mentioned (attributes of same scale clustered) | Euclidean | k-means, typical hours (snapshots) | Undersestimators from minimum values of each cluster | Feasibility time steps (peak values) and operation optimization for full time series | No | No |
2018 | Bahl et al. [74] | District model from Voll et al. [103] with additional heat and cold storage units, multiple commodities | Yes, but not mentioned which | Euclidean | k-medoids (daily clustering and segmentation) | Medoids further segmented | Feasibility time steps (peak values) and operation optimization for full time series | No | No |
2018 | Brodrick et al. [97] refers to [146] | UC of an integrated solar combined cycle, no storage technologies, multiple commodities | Z-normalization | Euclidean | k-means (6 representative days) further reduced to three extreme hours | Centroids | Three extreme hours | No | No |
2018 | Gabrielli et al. [15] | Single-node district model, thermal, battery and hydrogen storage, multiple commodities | No/not mentioned | Not mentioned (probably Euclidean/default for Matlab k-means) | k-means | Centroids | Maximum and minimum values of the demand profiles | Yes | No |
2018 | Kotzur et al. [57] | Three single-node models (CHP system, residential building, island system), thermal, battery and hydrogen storage, multiple commodities | Min-max normalization | Euclidean | k-means, averaging, k-medoids, hierarchical, typical days and typical weeks | Centroids medoids | Peak periods heat and electricity demand, minimum PV feed-in | No | No |
2018 | Kotzur et al. [14] | Three single-node models (CHP system, residential building, island system), thermal, battery and hydrogen storage, multiple commodities | Min-max normalization | Euclidean | Exact k-medoids | Medoids | No | Yes | No |
2018 | Lara et al. [24] | Multi-node electricity model for Texas, multiple storage units (e.g., lithium-ion, lead-acid, and flow batteries) | Mentioned, but not which one | Euclidean | k-means for the years of 2004–2010 | Centroids | No | No, 50% SOC heuristic | No |
2018 | Liu et al. [148] | Multi-node electricity model for Texas (greenfield GEP), storage units and ramping constraints considered | Z-Normalization | DTW distance, Euclidean as benchmark | (k-means initially), hierarchical, k-means as benchmark | Medoids, centroids for k-means-benchmark | No | No | No |
2018 | Mallapragada et al. [39] (2004–2010) | Electricity GEP model for Texas, no storage or transmission units, ramping in production cost simulation considered | Min-max normalization between 0 and 2 | Euclidean and L1-Norm (as benchmark) | 4 seasons and 4 daily segments vs. k-means | Medoids | No | No, refers to [24], 50% heuristic | No |
2018 | Neniškis et al. [51] | Electricity and district heat model of Lithuania, pumped hydro storage, multiple commodities, (MESSAGE) | No | None | Workday and weekend day either for four seasons or for twelve months | Mean | No (but synthesized wind time series) | No | No |
2018 | Pineda et al. [72] | Multi-node electricity model of Europe, intraday, interday storage and ramping constraints considered | Mentioned, but not which one | Euclidean | Hierarchical | Medoids | No | Yes, by clustering adjacent periods | No |
2018 | Schütz et al. [58] | Building model, thermal and battery storage units, multiple commodities | Min-max normalization | Euclidean | k-means k-medians k-medoids k-centers | Centroids medians medoids centers | No | No | No |
2018 | Stadler et al. [165] | Building model, thermal and battery storage units, multiple commodities | No/not mentioned | (probably) Euclidean | k-medoids | Medoids | No | No | No |
2018 | Teichgräber et al. [159] | Two minimal UC problems: An electricity storage model and a gas turbine dispatch model | Element-wise Z-Normalization | Euclidean, Dynamic Time Warping, Shape-based Distance | k-means k-medoids Barycenter Averaging k-shape hierarchical | Centroid, medoids | No | No | No |
2018 | Tejada-Arango et al. [19] | UC of the Spanish electricity system, battery and pumped hydro storage | Yes, but not mentioned what kind of normalization | (probably) Euclidean | k-medoids for RP, k-means for SS | Medoids, centroids | No | Yes | No |
2018 | Tejada-Arango et al. [84] | UC of the IEEE 14 bus electricity model, battery and pumped hydro storage | No/not mentioned (attributes of same scale clustered) | Euclidean | k-means (for typical hours) | Centroids | No | No | No |
2018 | Tupper et al. [167] | UC of the IEEE 30 bus electricity model with wind generation, no storage technologies | No/not mentioned | Euclidean, band distance | k-medoids | Medoids | No | No | No |
2018 | Van der Heijde et al. [95] | Single-node district heating model, thermal storage | No/not mentioned | L1-Norm | Using so-called “bins” and four seasons | Existing weeks | No, but each season needs to contain at least one typical week | Yes | Yes |
2018 | Voulis et al. [145] | Customer or unit partitioning/none (just approach) | Normalization by maximum e-demand | Euclidean | k-means (spatio-temporal differentiation between workdays, weekends, neighborhoods, districts and municipalities) | Centroids | No | No | No |
2018 | Welder et al. [18] | Multi-node model for power-to- hydrogen in Germany, hydrogen storage technologies, multiple commodities | Min-max normalization | Euclidean | hierarchical | Medoids | No | Yes | Yes |
2019 | Baumgärtner et al. [78] | District model from Voll et al. [103] with additional heat and cold storage units and a single-node pump system, multiple commodities | No/not mentioned | Euclidean | k-medoids | Segmented under- and overestimators | Feasibility time steps (peak values) and operation optimization for full time series | No | No |
2019 | Baumgärtner et al. [77] | Single-node model for industrial site based on Baumgärtner et al. [202] with heat, cold and battery storage, Multi-node model for Germany with battery and hydrogen storage, multiple commodities | No/not mentioned | Euclidean | k-means | Centroids, segmented under- and overestimators | Feasibility time steps (peak values) and operation optimization for full time series | Yes | No |
2019 | Gabrielli et al. [160] | Single-node district model, thermal, battery and hydrogen storage, multiple commodities | No/not mentioned | Not mentioned (probably Euclidean/default for Matlab k-means) | k-means | Centroids | Maximum and minimum values of the demand profiles | Yes | No |
2019 | Hilbers et al. [166] | Single-node electricity model of Great Britain, no storage technologies | Yes, but not mentioned which | Euclidean | Samples (hourly). As benchmark: k-medoids (days) | Existing hours. As benchmark: medoids (days) | Yes with the method of subsampling and keeping the most expensive days | No | No |
2019 | Kannengießer et al. [140] | Multi-node district model and single-node island model, thermal, battery and hydrogen storage, multiple commodities | Min-max normalization | Euclidean | hierarchical | Medoids | No, but operation optimization for full time series | No | Yes |
2019 | Motlagh et al. [203] | Customer or unit partitioning/none (just approach) | No/not mentioned | Adjacency metric, in mapping parameter space: Euclidean d | Feature-based clustering or dynamic load-clustering | None | No | No | No |
2019 | Pavičević et al. [204] | Customer or unit partitioning/multi-node electricity model of the western Balkan, pumped hydro storage and CHP with thermal storage, (Dispa-SET) | No | None | By technology and location | Mean | No | No | No |
2019 | Pöstges et al. [187] | Single-node electricity model, no storage technologies, analytically solved as peak-load-pricing model | Yes, cap-specific costs | None | Segments in the duration curve implying use of different technologies (hours) | Sorted existing hours | Yes, by determining the capacity of each component from the merit order | No | Yes |
2019 | Savvidis et al. [80] | UC of dispatch electricity model for Germany, pumped hydro storage, (E2M2) | No | No | No | No | Certain time series qualities define intervals in which can be downsampled | Yes, by clustering adjacent periods | No |
2019 | Sun et al. [135] | Multi-node electricity model of Great Britain with intraday storage | Min-max normalization, dimensionality reduction applied | Euclidean | hierarchical | Medoids | No | No | No |
2019 | Teichgräber et al. [41] | Two minimal UC problems: An electricity storage model and a gas turbine dispatch model | Element-wise Z-Normalization | Euclidean, Dynamic Time Warping, Shape-based Distance | k-means k-medoids Barycenter Averaging k-shape hierarchical | Centroid, medoids | No | No | No |
2019 | Van der Heijde et al. [20] | Multi-node district heating model, thermal storage | No/not mentioned | L1-Norm | Using so-called “bins” | Existing days | No, but rearranging the typical days to the original sequence using a MIP | Yes | Yes |
2019 | Yokoyama et al. [68] | Building model for two hotels and four office buildings, no storage technologies, but multiple commodities | No | None | downsampling | Means | No | No | No |
2019 | Zatti et al. [141] | District model of Parma university campus and building model, thermal and battery storage, multiple commodities | Min-max normalization | Euclidean | (k-means, k-medoids) k-MILP (modification of k-medoids) | (Centroids), medoids | Automatically integrating atypical days | No | No |
2019 | Zhang et al. [161] | Single-node electricity model consisting of hydro, PV and wind power plants with reservoir storage | No/not mentioned | Euclidean | k-means | Means | No, but used Vine-Copula, ARMA-model and latin hypercube sampling to generate scenarios | No | No |
Appendix B
Customer and Unit Partitioning
Appendix C
Calculation Example for Time Series Normalization
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Term | Synonym (Term in This Review) | Definition | Keywords Used for Literature Research |
---|---|---|---|
Clustering (of Time Series) | Grouping, (Clustering) | “Given a dataset of n time series data , the process of unsupervised partitioning of into in such a way that homogeneous time series data are grouped together based on a certain similarity measure” [59] | Clustering |
Complexity Reduction | None, (Complexity Reduction) | Different techniques to increase the computational tractability of ESMs [35] | Complexity Reduction |
Energy System Model | Energy System Optimization Model, (Energy System Model) | A model “the analysis of existing national energy systems, as well as the prediction of potential future scenarios, is usually performed with” [9] | Energy System Optimization Model, Energy System Model |
Period | None, (Period) | A group of consecutive time steps describing a regular amount of time (e.g., 24 h) | Typical Period |
Representative | Typical, (Typical) | A single time step or a period representing a group of time steps or periods determined by clustering | Representative Day, Representative Week |
Sample | None, (Sample) | A single time step or period taken from the original time series | Sampling, Random Sampling, Subsampling |
Snapshot | System State, Time Step, (Time Step, If subset of TS: Typical Time Step) | A term used in the literature for typical time steps (TTS) | Snapshot |
System State | Snapshot, Time Step, (Time Step, If subset of TS: Typical Time Step) | A term misleadingly used in the literature for typical time steps (TTS). It actually describes the state of a system under both external conditions (e.g., capacity factors) and internal state variables (e.g., storage levels) at a specific time step | System State |
Temporal Resolution | None, (Temporal Resolution) | The resolution of a discretized time series given by the length of its time steps | Temporal Resolution |
Time Series Aggregation | Temporal Aggregation, (Time Series Aggregation | In the narrow sense: The reduction of time steps in time series In a broader sense: The reduction of the number of time steps or time series | Time Series Aggregation, Temporal Aggregation |
Time Slice | Time Slot, (Time Slice) | Hierarchically merged time steps appearing in a systematic order as used by the TIMES framework | Time Slice |
Time Step | Snapshot System State (Time Step) | The smallest possible time interval of a discrete time series represented by a single value for each attribute | Time Step Typical Time Step |
Typical | Representative (Typical) | Periods or single time steps considered to capture the basic characteristics of the external operating conditions of an energy system are named “typical” | Typical Day Typical Week |
Sets & Indices | |
---|---|
Set | |
Set/Index of Attributes | , |
Set/Index of Time Steps | , |
Set/Index of Periods | , |
Set/Index of Inner-Period Time Steps | , |
Set/Index of Cluster Members | , |
Cluster Center (as Defined) | |
Discrete Value of Time Series (Normed) | |
Number of Items in a Set | |
Matrix Path for Dynamic Time Warping | |
Minkowski Exponent |
Period Merging Type | Resolution Variation | Typical Periods |
---|---|---|
Time-based | Downsampling | Time Slices and Averaging |
Feature-based | Segmentation | Clustering |
Period Merging Type | Resolution Variation | Typical Periods |
---|---|---|
Time-Based | Downsampling - Does not exploit repeating time series patterns - Does not differentiate between more and less variant sections of the time series | Time Slices and Averaging + Exploits repeating time series patterns - Based on the modeler’s experience - Does not merge similar adjacent time steps |
Feature-Based | Segmentation - Does not exploit repeating time series patterns + Differentiates between more and less variant sections of the time series | Clustering + Exploits repeating time series patterns + Automatic identification of similar patterns - Does not merge similar adjacent time steps |
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Hoffmann, M.; Kotzur, L.; Stolten, D.; Robinius, M. A Review on Time Series Aggregation Methods for Energy System Models. Energies 2020, 13, 641. https://doi.org/10.3390/en13030641
Hoffmann M, Kotzur L, Stolten D, Robinius M. A Review on Time Series Aggregation Methods for Energy System Models. Energies. 2020; 13(3):641. https://doi.org/10.3390/en13030641
Chicago/Turabian StyleHoffmann, Maximilian, Leander Kotzur, Detlef Stolten, and Martin Robinius. 2020. "A Review on Time Series Aggregation Methods for Energy System Models" Energies 13, no. 3: 641. https://doi.org/10.3390/en13030641