Time Series Aggregation Research Articles

Typical daily scenario extraction method based on key features to promote building renewable energy system optimization efficiency

Given its intrinsic volatility and randomness, the effective design of a building renewable energy system (BRES) necessitates long-period, short-step boundaries. Nevertheless, this poses computational burdens. In this context, time-series aggregation (TSA) emerges as a valuable approach, which involves obtaining a set of typical scenarios to substitute original time series. Numerous studies have focused on mathematical algorithms to minimize the deviation between typical scenarios and original time series. However, the premise of enhancing model-solving efficiency by extracting typical scenarios is to ensure the optimality of planning. Henceforth, identifying and quantifying key features in the original time series that significantly influence the planning, and further extracting need to be addressed. This paper proposes a typical day extraction method based on key features, named the feature-based method. Key features are summarized through an extensive literature review and then quantitatively expressed through different indicator models. Finally, a feature-based mixed integer linear programming (MILP) model is established for extraction. To evaluate the effectiveness of the feature-based method, it is applied to design a BRES and compared with traditional TSA methods such as Averaging Method (AM) and k-means. Results indicate that the feature-based method can effectively retain key features, thereby achieving more efficient and accurate designs.

Extraction of typical operating scenarios of new power system based on deep time series aggregation

Extraction of typical operating scenarios of new power system based on deep time series aggregation

The first step is the hardest: pitfalls of representing and tokenizing temporal data for large language models.

Large language models (LLMs) have demonstrated remarkable generalization and across diverse tasks, leading individuals to increasingly use them as personal assistants due to their emerging reasoning capabilities. Nevertheless, a notable obstacle emerges when including numerical/temporal data into these prompts, such as data sourced from wearables or electronic health records. LLMs employ tokenizers in their input that break down text into smaller units. However, tokenizers are not designed to represent numerical values and might struggle to understand repetitive patterns and context, treating consecutive values as separate tokens and disregarding their temporal relationships. This article discusses the challenges of representing and tokenizing temporal data. It argues that naively passing timeseries to LLMs can be ineffective due to the modality gap between numbers and text. We conduct a case study by tokenizing a sample mobile sensing dataset using the OpenAI tokenizer. We also review recent works that feed timeseries data into LLMs for human-centric tasks, outlining common experimental setups like zero-shot prompting and few-shot learning. The case study shows that popular LLMs split timestamps and sensor values into multiple nonmeaningful tokens, indicating they struggle with temporal data. We find that preliminary works rely heavily on prompt engineering and timeseries aggregation to "ground" LLMs, hinting that the "modality gap" hampers progress. The literature was critically analyzed through the lens of models optimizing for expressiveness versus parameter efficiency. On one end of the spectrum, training large domain-specific models from scratch is expressive but not parameter-efficient. On the other end, zero-shot prompting of LLMs is parameter-efficient but lacks expressiveness for temporal data. We argue tokenizers are not optimized for numerical data, while the scarcity of timeseries examples in training corpora exacerbates difficulties. We advocate balancing model expressiveness and computational efficiency when integrating temporal data. Prompt tuning, model grafting, and improved tokenizers are highlighted as promising directions. We underscore that despite promising capabilities, LLMs cannot meaningfully process temporal data unless the input representation is addressed. We argue that this paradigm shift in how we leverage pretrained models will particularly affect the area of biomedical signals, given the lack of modality-specific foundation models.

Real Time Hotel Booking Demand Optimization

The significance of having proper revenue management and convenient operations in hotels rely on accurate daily demand. The main challenges that are being tackled conventionally are the forecasting of the number of cancellations and the calculation of the Average Daily Rate (ADR). One of the distinct characteristics of the hotel industry being so unstable is to adopt proactive strategies by dealing with a lot of external changes such as pandemics, disasters caused by nature, and economic fluctuations around the world. Booking cancellations are instrumental in helping hotel managers to optimise resources and inventory while ADR forecasting offers them equally essential projections concerning anticipated profit or loss margins. This research relies on several data modelling steps, including time series aggregation and decision merging, which are later followed by decomposition and model selection. SARIMAX and LSTM models are adopted for future traffic flow modelling, which demonstrates better forecasting performances. Binary classification is employed for feature engineering techniques together with model selection methods. Binary Classification is performed with a number of experiments with machine learning algorithms, AdaBoost turned out to be the best model which surpassed CART , KNN , Random Forest, Gradient boosting algorithms , and Light Gradient Boosting algorithms. The results of this are of great help to the hotel management for taking better decisions which are connected to the changing situations of the market

Enhancing time series aggregation for power system optimization models: Incorporating network and ramping constraints

In this paper, we extend a recently developed Basis-Oriented time series aggregation approach for aggregating input-data in power system optimization models which has proven to be exact in simple economic dispatch problems. We extend this methodology to include network and ramping constraints, for the latter, to handle temporal linking, we developed a heuristic that, in its current version, relies on the dual solution to find a partition of the input data, which is then aggregated. Our numerical results, for a 3-bus system, show that with network constraints only, we reduced the number of hours needed for an exact approximation by a factor of 1747, and a factor of 12 with network and ramping constraints. Moreover, our findings suggest that in the presence of temporal linking, aggregations of variable length must be employed to obtain an exact result (i.e., the same objective function value in the aggregated model) while maintaining the computational tractability. Our findings also imply that better performing aggregations do not necessarily correspond to commonly used lengths like days or weeks; additionally, we also prove that this input-data partition, based on the dual information, is always possible for these models independent of their size.

Techno-economic comparison of different energy storage configurations for renewable energy combined cooling heating and power system

Amidst the growing imperative to address carbon emissions, renewable energy combined cooling heating and power (RCCHP) systems have emerged as a transformative alternative to their fossil fuel-driven counterparts. Given the intermittent and volatile nature of renewable energy, the integration of energy storage technology has taken center stage in the exploration of RCCHP systems. This paper presents a quantitative techno-economic assessment of seven prominent energy storage configurations, including battery (BAT), thermal energy storage (TES), hydrogen storage (HS), and their combinations within the context of RCCHP systems. To avoid potential deviations caused by the rule-based energy dispatch strategy, the optimization problem is solved by a deterministic tool named mixed integer linear programming (MILP). Meanwhile, an accuracy assessment is performed on various time series aggregation methods to ensure the reliability of optimization outcomes. The key results revealed that the optimal storage configuration varies with different self-sufficiency rate (SSR) requirements. The BAT+HS+TES emerges as the most cost-effective configuration to implement 100% SSR requirements. The annualized total cost (ATC) of BAT+HS+TES configuration is 11% ∼ 39.5% lower than other single or combined energy storage configurations. In addition, HS stands as a more economical technology for countering the off-grid effect than BAT or TES. The underestimated ATC for the RCCHP system enlarges with escalating SSR requirements when using inappropriate aggregation methods. The maximum underestimation of ATC reaches −34.8% under the 100% SSR requirement when only using one typical day from each season.

A hybrid meteorological data simulation framework based on time-series generative adversarial network for global daily solar radiation estimation

Solar energy has received considerable attention worldwide because of its clean, safe and easily accessible characteristics. Accurate global solar radiation estimation is crucial for local energy potential assessments and deployment of photovoltaic power generation systems. However, the distribution of metrological data varies considerably between regions, and its quality considerably affects the accuracy of the estimation model. Motivated by these concerns, a metrological data estimation framework based on the time-series generative adversarial network (TimeGAN) and deep belief network (DBN) was proposed. First, the metrological data collected from 30 urban meteorological stations in China were analyzed through time-series aggregation. Next, a novel metrological data simulation model based on TimeGAN was proposed to enrich the quality of training samples. Furthermore, a generalized estimation model of daily solar radiation based on DBN was constructed. In the case study in China, TimeGAN outperforms other conventional generative adversarial networks in terms of data generation performance. The simulation results reveal that the TimeGAN-based simulation model can capture the inherent temporal characteristics of the original data, generate high-quality simulation data to reasonably improve the distribution of training data in various cities. In addition, the estimation results indicate that the proposed hybrid framework improve the accuracy of daily solar radiation estimation.

Time series aggregation, disaggregation and long memory

Large-scale aggregation and its inverse, disaggregation, problems are important in many fields of studies like macroeconomics, astronomy, hydrology and sociology. It was shown in Granger (1980) that a certain aggregation of random coefficient AR(1) models can lead to long memory output. Dacunha-Castelle and Oppenheim (2001) explored the topic further, answering when and if a predefined long memory process could be obtained as the result of aggregation of a specific class of individual processes. In this paper, the disaggregation scheme of Leipus et al. (2006) is briefly discussed. Then disaggregation into AR(1) is analyzed further, resulting in a theorem that helps, under corresponding assumptions, to construct a mixture density for a given aggregated by AR(1) scheme process. Finally the theorem is illustrated by FARUMA mixture densityÆs example.

A Multi-Objective Time – Series Optimization for Optimum Planning Design of Integrative Power System with the Effects of Multi-Dimensional Sources of Uncertainty

Time series aggregation (TSA) procedures are used to simplify data entry and enhance solution efficiency. This study suggested a two-step multi-objective optimization framework for TSA strategy determination. TSA methodologies for optimum MES design and operation were used to create the multi-energy system’s preliminary design. In the second step, the system’s total annual cost, as well as loss of load probability (LSLP), were used as objectives, or the optimal combination of the several objectives was found optimal TSA strategy for the MES’s structure and performance. The ideal energy-storage MES design proved the method’s efficacy. TSA techniques were compared and analyzed for architectural schemes & system performance variations. The findings show that the initial full-time series data may be used to verify the viability of the best MES design schemes and quantify the departure of outcomes from alternative TSA procedures. LSLP decrease raises expenses. The TAC of the framework improves from $9.79 × 107 to $1.56 × 108 when the LSLP reduces to 7.90% to zero in the numerous grids method (TG1) with 730-time steps (TS). To fulfill energy system demand, the minimal LSLP approach must be chosen. The best TSA tactics for MES design may be chosen based on unique needs.

An effective approach for deriving and evaluating approximate optimal design solutions of energy supply systems by time series aggregation

It is important to design multi-energy supply systems optimally in consideration of their operations for variations in energy demands. An approach for efficiently solving such an optimal design problem with a large number of periods for variations in energy demands is to derive an approximate optimal design solution by time series aggregation. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. In this paper, an effective approach for time series aggregation is proposed to derive an approximate optimal design solution and evaluate a proper gap between the upper and lower bounds for the optimal value of the objective function based on a mixed-integer linear model. In accordance with aggregation, energy demands are relaxed to uncertain parameters and the problem for deriving an approximate optimal design solution and evaluating it is transformed to a three-level optimization problem, and it is solved by applying both the robust and hierarchical optimization methods. A case study is conducted on a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to derive much smaller gaps as compared with those obtained by a conventional approach.

An Optimized Fed-Batch Culture Strategy Based on Multidimensional Time Series Aggregation

An optimized feeding strategy for the fed-batch fermentation of 2-keto-L-gulonic acid (2-KGA) is proposed to enhance the total profit of a workshop. Instead of assigning the same quantity of substrate to each batch in the empirical scheduling, the online feeding strategy offers a practical approach that allows for the precise management of substrate feeding to maximize economic performance. The forecasting of the profit function has been achieved through the proposed similarity measurement and multidimensional time series aggregation method. This method solves the problem of predicting the total economic benefit at the end of fermentation, in the absence of fermentation substrate measurement data. Pseudo-online simulation has been conducted, utilizing data derived from ninety industrial batches. A 6% increase in total profit is observed, which indicates that the optimized strategy utilizes the substrate and other related resources more efficiently and leads to a higher overall profit.

Time Series Aggregation for Optimization: One-Size-Fits-All?

One of the fundamental problems of using optimization models that use different time series as data input, is the trade-off between model accuracy and computational tractability. To overcome computational intractability of these full optimization models, the dimension of input data and model size is commonly reduced through time series aggregation (TSA) methods. However, traditional TSA methods often apply a one-size-fits-all approach based on the common belief that the clusters that best approximate the input data also lead to the aggregated model that best approximates the full model, while the metric that really matters –the resulting output error in optimization results – is not well addressed. In this paper, we plan to challenge this belief and show that output-error based TSA methods with theoretical underpinnings have unprecedented potential of computational efficiency and accuracy.

Co-planning of transmission and energy storage by iteratively including extreme periods in time-series aggregation

The co-planning problem of transmission and energy storage system (ESS) requires a large amount of historical and forecasted input data to account for the volatility of renewable energy and loads. However, the large input data usually make the planning problem difficult to solve, so time series aggregation is often used to reduce the computational complexity. Nevertheless, it is difficult to guarantee the reliability of operation on the whole input data. Therefore, this paper proposes an iterative method to select extreme scenarios, and designs two indicators to select extreme scenarios, considering the system power balance and peak shaving capacity situation. Based on these two indicators, the periods of maximum load shedding and the periods of maximum renewable energy curtailment will be selected as extreme scenarios in the results of the operational optimization problem. We iteratively add extreme scenarios to the set of scenarios of the planning problem until the reliability of system operation can be adequately met. At the same time, in order to ensure the effectiveness of extreme scenarios, the operation statuses of thermal units in those periods are also taken into account. Our method is tested on an IEEE RTS-24 system with some modification. The results show that our method can guarantee the reliability of the whole system and is superior to the method that simply selects extreme scenarios. Meanwhile, we also perform a sensitivity analysis of the price of energy storage.

Reducing climate risk in energy system planning: A posteriori time series aggregation for models with storage

The growth in variable renewables such as solar and wind is increasing the impact of climate uncertainty in energy system planning. Addressing this ideally requires high-resolution time series spanning at least a few decades. However, solving capacity expansion planning models across such datasets often requires too much computing time or memory.To reduce computational cost, users often employ time series aggregation to compress demand and weather time series into a smaller number of time steps. Methods are usually a priori, employing information about the input time series only. Recent studies highlight the limitations of this approach, since reducing statistical error metrics on input time series does not in general lead to more accurate model outputs. Furthermore, many aggregation schemes are unsuitable for models with storage since they distort chronology.In this paper, we introduce a posteriori time series aggregation schemes that preserve chronology and hence allow modelling of storage technologies. Our methods adapt to the underlying energy system model; aggregation may differ in systems with different technologies or topologies even with the same time series inputs. They do this by using operational variables (generation, transmission and storage patterns) in addition to time series inputs when aggregating.We investigate a number of approaches. We find that a posteriori methods can perform better than a priori ones, primarily through a systematic identification and preservation of relevant extreme events. We hope that these tools render long demand and weather time series more manageable in capacity expansion planning studies. We make our models, data, and code publicly available.

Time series aggregation for energy system design: review and extension of modelling seasonal storages

Using optimization to design a renewable energy system has become a computationally demanding task as the high temporal fluctuations of demand and supply arise within the considered time series. The aggregation of typical operation periods has become a popular method to reduce effort. These operation periods are modelled independently and cannot interact in most cases. Consequently, seasonal storage is not reproducible. This inability can lead to a significant error, especially for energy systems with a high share of fluctuating renewable energy. The previous paper, “Time series aggregation for energy system design: Modeling seasonal storage”, has developed a seasonal storage model to address this issue. Simultaneously, the paper “Optimal design of multi-energy systems with seasonal storage” has developed a different approach. This paper aims to review these models and extend the first model. The extension is a mathematical reformulation to decrease the number of variables and constraints. Furthermore, it aims to reduce the calculation time while achieving the same results.

A multi-objective approach to determine time series aggregation strategies for optimal design of multi-energy systems

The optimal topology and operation of multi-energy systems (MES) can be determined by mathematical programming models, which are commonly difficult to solve due to the complex structures of the models and large-scale time-series data. The time series aggregation (TSA) strategies are usually adopted to reduce the complication of the data input and thus improve the solution efficiency. Nevertheless, for the optimal design of MES, significant differences exist in the structures and performances of the systems resulting from different TSA strategies. It is crucially important to determine appropriate TSA strategies in the optimal design of MES. In this work, a two-step method was proposed to determine TSA strategies based on a multi-objective optimization framework. In the first step, the preliminary design for the multi-energy system was obtained by different TSA strategies for the optimal design and operation of MES. In the second step, the total annual cost and loss of load probability (LSLP) of the system were taken as two objectives, and a multi-objective optimization approach was established to determine the appropriate TSA strategy for the optimal design of the MES, where the structure and performance of the system were considered simultaneously. The implementation and effectiveness of the proposed method were demonstrated by the optimal design of an MES with energy storage. The deviations of the design scheme and system performance obtained by different TSA strategies were comprehensively compared and analyzed. The results indicate that the feasibility of the optimal design schemes of the MES can be verified by using the original full-time series data, and the deviation of the results obtained by different TSA strategies can be quantified. The reduction of LSLP is at the expense of the increase of the costs. In the multiple time grids strategy (TG1) with the number of time steps (TS) 730, the TAC of the system increases from $9.79 × 107 to $1.56 × 108 when the LSLP of the system decreases from 7.90% to zero. The determination of the strategy based on the result of the minimum LSLP is critical to meet the demand in the energy system. The appropriate TSA strategies for the optimal design of MES can be selected and determined in compliance with specific requirements.

Corporate investment prediction using a weighted temporal graph neural network

AbstractCorporate investment is an important part of corporate financial decision‐making and affects the future profit and value of the corporation. Predicting corporate investment provides great significance for capital market investors to understand the future operation and development of a corporation. Many researchers have studied independent prediction methods. However, individual firms imitate each other's investment in the actual decision‐making process. This phenomenon of investment convergence indicates investment correlation among individual firms, which is ignored in these existing methods. In this article, we first identify key variables in multivariate sequences by our designed two‐way fixed effects model for precise corporate network construction. Then, we propose a weighted temporal graph neural network called weighted temporal graph neural network (WTGNN) for graph learning and investment prediction over the corporate network. WTGNN improves the graph convolution capability by weighted sampling with attention and multivariate time series aggregation. We conducted extensive experiments using real‐world financial reporting data. The results show that WTGNN can achieve excellent graph learning performance and outperforms existing methods in the investment prediction task.This article is categorized under: Technologies > Prediction Technologies > Machine Learning Application Areas > Business and Industry

Energy system modeling with aggregated time series: A profiling approach

Energy system models with a high technical, spatial and temporal resolution are not always feasible and therefore require a complexity reduction through, for example, time series aggregation. Modeling results of aggregated time series are not always reliable but may show large deviations depending on the energy system configuration, model and selected data. By analyzing the interaction between time series and modeling results, this study contributes to an improved understanding of these deviations and identifies relevant time series characteristics such as extreme values or parameters describing the relation between time series. The proposed profiling embeds these parameters and adapts already aggregated time series to the characteristics of original time series within three iterative steps. Results of an analysis including three scenarios, time series from eleven years and eight aggregation variants show that profiling can reduce systematic overestimation or underestimation of installed capacities by an average of 86% to a maximum of 0.4 GW and decrease the standard deviation of the modeling results by 71%. Profiling can be used to better represent time series characteristics and minimize deviations of the modeling results, thus providing a complement to existing aggregation methods. Despite these substantial improvements in comparison to aggregation methods, analyses suggest that there is further potential to improve time series aggregation using a profiling approach. Potential directions for future research are discussed.

Wind data introduce error in time-series reduction for capacity expansion modelling

Shares of renewable energy are rapidly increasing in many countries due to emissions policies and declining prices. Investment planning for future renewable deployment often relies on optimization models. Memory usage and solving time restrict these models, leading to tradeoffs in the treatment of temporal complexity, spatial complexity, and physical representation. A common approach is to reduce the temporal complexity of models. Reducing temporal complexity is often achieved by using time-series aggregating and modelling representative periods instead of a complete time series. But the impacts of such approaches are still poorly understood, especially for very low emissions systems with high shares of variable renewable energies. In this paper, the impacts of using time-series aggregation methods on optimal system design are investigated. It is found that the negative impact of time-series aggregation increases for lower emissions. It is also identified that modelling wind time-series data with representative days introduces this negative impact primarily and that representing wind time-series data with representative days decreases the reliability of supply defined as unserved load (0.05%–18.0%), introduces a bias in installed capacity (−31.15% to +12.2%), and underestimates total system cost (2.5%–44.9%). These effects are largest in cases with the strongest emission constraints. When designing low emissions systems with a high share of variable renewable energies, it is recommended not to use time-series aggregation to create representative days for wind power output. This paper contributes an Open Source analysis framework containing time-series aggregation and capacity expansion that should be applied when testing future time-series aggregation methods to reduce the identified negative impacts.

Co-optimizing transmission and active distribution grids to assess demand-side flexibilities of a carbon-neutral German energy system

In modern power system planning and operation, the relevance of distributed power generation units and demand-side flexibility options grows. As a consequence, smart planning and operation routines become necessary also in the distribution grid. We therefore develop a co-optimization framework to consider transmission and distribution system constraints and their interactions together. This enables bidirectional flows between both systems, supporting a consistent and cost-efficient overall energy system. The key feature of this paper is an automated coupling of two independently and modularly defined systems. It allows a bottom-up modelling approach of energy demands, conversion and storage technologies from both system levels. However, this approach increases the model size significantly. Thus, timeseries aggregation methods are applied to reduce the computational complexity. The results for the optimal planning of the coupled German energy system show that the electrification of heat and mobility sectors in the distribution grid is not only beneficial to achieve carbon neutrality in 2050, but also to particularly make use of additional flexibility potentials. Our results underline a significant positive correlation between a smart operation of heat pumps and charging stations with the maximum integrable capacities of low-cost rooftop photovoltaics in the distribution system.