Simon H. Tindemans
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Transmission System Operators routinely use transmission switching as a tool to manage congestion and ensure system security. Motivated by sub-transmission operations at RTE, this paper considers the Optimal Transmission Switching with De-energization (OTSD), which captures potential loss of connectivity (and therefore localized blackout) following loss of transmission elements. While directly relevant to real-life operations, this problem has received very little attention in the literature. The paper proposes a new mixed-integer linear programming formulation for OTSD that represents post-contingency loss of connectivity without requiring additional binary variables. This new formulation provides the foundation for a fast, iterative heuristic algorithm. Computational experiments confirms that state-of-the-art optimization solvers struggle to solve the extensive formulation of OTSD, often failing to find even trivial solutions within reasonable time. In contrast, numerical results demonstrate the efficiency of the proposed heuristic, which finds high-quality feasible solutions 100–1000x faster than using Gurobi.
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Transmission System Operators routinely use transmission switching as a tool to manage congestion and ensure system security. Motivated by sub-transmission operations at RTE, this paper considers the Optimal Transmission Switching with De-energization (OTSD), which captures potential loss of connectivity (and therefore localized blackout) following loss of transmission elements. While directly relevant to real-life operations, this problem has received very little attention in the literature. The paper proposes a new mixed-integer linear programming formulation for OTSD that represents post-contingency loss of connectivity without requiring additional binary variables. This new formulation provides the foundation for a fast, iterative heuristic algorithm. Computational experiments confirms that state-of-the-art optimization solvers struggle to solve the extensive formulation of OTSD, often failing to find even trivial solutions within reasonable time. In contrast, numerical results demonstrate the efficiency of the proposed heuristic, which finds high-quality feasible solutions 100–1000x faster than using Gurobi.
The living forecast
Evolving day-ahead predictions into intraday reality
Accurate intraday forecasts are essential for power system operations, complementing day-ahead forecasts that gradually lose relevance as new information becomes available. This paper introduces a Bayesian updating mechanism that converts fully probabilistic day-ahead forecasts into intraday forecasts without retraining or re-inference. The approach conditions the Gaussian mixture output of a conditional variational autoencoder-based forecaster on observed measurements, yielding an updated distribution for the remaining horizon that preserves its probabilistic structure. This enables consistent point, quantile, and ensemble forecasts while remaining computationally efficient and suitable for real-time applications. Experiments on household electricity consumption and photovoltaic generation datasets demonstrate that the proposed method improves forecast accuracy up to 25% across likelihood-, sample-, quantile-, and point-based metrics. The largest gains occur in time steps with strong temporal correlation to observed data, and the use of pattern dictionary-based covariance structures further enhances performance. The results highlight a theoretically grounded framework for intraday forecasting in modern power systems.
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Accurate intraday forecasts are essential for power system operations, complementing day-ahead forecasts that gradually lose relevance as new information becomes available. This paper introduces a Bayesian updating mechanism that converts fully probabilistic day-ahead forecasts into intraday forecasts without retraining or re-inference. The approach conditions the Gaussian mixture output of a conditional variational autoencoder-based forecaster on observed measurements, yielding an updated distribution for the remaining horizon that preserves its probabilistic structure. This enables consistent point, quantile, and ensemble forecasts while remaining computationally efficient and suitable for real-time applications. Experiments on household electricity consumption and photovoltaic generation datasets demonstrate that the proposed method improves forecast accuracy up to 25% across likelihood-, sample-, quantile-, and point-based metrics. The largest gains occur in time steps with strong temporal correlation to observed data, and the use of pattern dictionary-based covariance structures further enhances performance. The results highlight a theoretically grounded framework for intraday forecasting in modern power systems.
Probabilistic forecasting in power systems often involves multi-entity datasets like households, feeders, and wind turbines, where generating reliable entity-specific forecasts presents significant challenges. Traditional approaches require training individual models for each entity, making them inefficient and hard to scale. This study addresses this problem using GUIDE-VAE, a conditional variational autoencoder that allows entity-specific probabilistic forecasting using a single model. GUIDE-VAE provides flexible outputs, ranging from interpretable point estimates to full probability distributions, thanks to its advanced covariance composition structure. These distributions capture uncertainty and temporal dependencies, offering richer insights than traditional methods. To evaluate our GUIDE-VAE-based forecaster, we use household electricity consumption data as a case study due to its multi-entity and highly stochastic nature. Experimental results demonstrate that GUIDE-VAE outperforms conventional quantile regression techniques across key metrics while ensuring scalability and versatility. These features make GUIDE-VAE a powerful and generalizable tool for probabilistic forecasting tasks, with potential applications beyond household electricity consumption.
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Probabilistic forecasting in power systems often involves multi-entity datasets like households, feeders, and wind turbines, where generating reliable entity-specific forecasts presents significant challenges. Traditional approaches require training individual models for each entity, making them inefficient and hard to scale. This study addresses this problem using GUIDE-VAE, a conditional variational autoencoder that allows entity-specific probabilistic forecasting using a single model. GUIDE-VAE provides flexible outputs, ranging from interpretable point estimates to full probability distributions, thanks to its advanced covariance composition structure. These distributions capture uncertainty and temporal dependencies, offering richer insights than traditional methods. To evaluate our GUIDE-VAE-based forecaster, we use household electricity consumption data as a case study due to its multi-entity and highly stochastic nature. Experimental results demonstrate that GUIDE-VAE outperforms conventional quantile regression techniques across key metrics while ensuring scalability and versatility. These features make GUIDE-VAE a powerful and generalizable tool for probabilistic forecasting tasks, with potential applications beyond household electricity consumption.
EnergySHR
A platform for energy dataset sharing and communications
Conference paper
(2025)
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Zaman Ziabakhshganji, Mathijs de Weerdt, Sreeparna Deb, Caroline Duterloo, Yashar Ghiassi-Farrokhfal, Doron Gollnast, Jhon Jairo Quinones-Cortes, Alicia Julia Wilson Takaoka, Simon Tindemans, More authors...
Because the energy transition is a critical and urgent issue that is increasingly reliant on data, the Center for Energy System Intelligence (CESI), a Convergence collaboration between TU Delft and Erasmus University Rotterdam, has developed a platform where researchers on the energy transition can share, publish, and/or find energy-related datasets and algorithms: EnergySHR. This platform aims to accelerate energy transition research into intelligent, data-driven algorithms. In this demonstration, we present the EnergySHR platform as both a platform for storing, accessing, managing, and archiving datasets as well as a tool to conduct empirical research about platformization and data-driven decision-making about the energy transition.
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Because the energy transition is a critical and urgent issue that is increasingly reliant on data, the Center for Energy System Intelligence (CESI), a Convergence collaboration between TU Delft and Erasmus University Rotterdam, has developed a platform where researchers on the energy transition can share, publish, and/or find energy-related datasets and algorithms: EnergySHR. This platform aims to accelerate energy transition research into intelligent, data-driven algorithms. In this demonstration, we present the EnergySHR platform as both a platform for storing, accessing, managing, and archiving datasets as well as a tool to conduct empirical research about platformization and data-driven decision-making about the energy transition.
The sudden proliferation of Electric Vehicles (EVs), batteries and photovoltaic cells in power networks can lead to congested distribution networks. A substitute for upgrading network capacity is a redispatch market that enables the Distribution System Operators (DSOs) to mitigate congested networks by requesting the energy consumers to modify their consumption schedules. However, energy consumers are able to strategically modify their day-ahead market bids in anticipation of the redispatch market outcomes. This behaviour, which is known as increase-decrease gaming, can exacerbate congestion and give arbitrage opportunities to the energy consumers for gaining windfall profits from the DSO. In this paper, we propose an algorithm based on mean-field Stackelberg game to mitigate the increase-decrease game for large populations of energy consumers. In this game, the energy consumers (followers) maximize their individual welfare on the day-ahead market with anticipation of the redispatch market outcomes while the leader maximizes the social welfare of all agents and minimizes the costs of DSO on the redispatch market. We show the convergence of this algorithm to the mean-field leader-follower εN-Nash equilibrium.
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The sudden proliferation of Electric Vehicles (EVs), batteries and photovoltaic cells in power networks can lead to congested distribution networks. A substitute for upgrading network capacity is a redispatch market that enables the Distribution System Operators (DSOs) to mitigate congested networks by requesting the energy consumers to modify their consumption schedules. However, energy consumers are able to strategically modify their day-ahead market bids in anticipation of the redispatch market outcomes. This behaviour, which is known as increase-decrease gaming, can exacerbate congestion and give arbitrage opportunities to the energy consumers for gaining windfall profits from the DSO. In this paper, we propose an algorithm based on mean-field Stackelberg game to mitigate the increase-decrease game for large populations of energy consumers. In this game, the energy consumers (followers) maximize their individual welfare on the day-ahead market with anticipation of the redispatch market outcomes while the leader maximizes the social welfare of all agents and minimizes the costs of DSO on the redispatch market. We show the convergence of this algorithm to the mean-field leader-follower εN-Nash equilibrium.
operators are required to monitor and analyze these systems, raising the challenge of integration and management of large, spatially distributed time-series data that are both high-dimensional and affected by missing values. In this work, a probabilistic entity embedding-based clustering framework is proposed to address these problems. This method encodes each PV system’s characteristic power generation patterns and uncertainty as a probability distribution, then groups systems by their statistical distances and agglomerative clustering. Applied to a multi-year residential PV dataset, it produces concise, uncertainty-aware cluster profiles that outperform a physics-based baseline in representativeness and robustness, and support reliable missing-value imputation. A systematic hyperparameter study further offers practical guidance for balancing model performance and robustness.
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operators are required to monitor and analyze these systems, raising the challenge of integration and management of large, spatially distributed time-series data that are both high-dimensional and affected by missing values. In this work, a probabilistic entity embedding-based clustering framework is proposed to address these problems. This method encodes each PV system’s characteristic power generation patterns and uncertainty as a probability distribution, then groups systems by their statistical distances and agglomerative clustering. Applied to a multi-year residential PV dataset, it produces concise, uncertainty-aware cluster profiles that outperform a physics-based baseline in representativeness and robustness, and support reliable missing-value imputation. A systematic hyperparameter study further offers practical guidance for balancing model performance and robustness.
This paper deals with the secure Optimal Transmission Switching (OTS) problem in situations where the TSO is forced to accept the risk that some contingencies may result in the de-energization of parts of the grid to avoid the violation of operational limits. This operational policy, which mainly applies to subtransmission systems, is first discussed. Then, a model of that policy is proposed that complements the classical MILP model of the N-1 secure OTS problem. It comprises a connectivity and notably a partial grid loss analysis for branch outage contingencies. Finally, its application to the IEEE 14- bus system is presented. Solutions similar to those observed in operation are reached by the algorithm, notably revealing the preventive-openings-cascade phenomenon.
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This paper deals with the secure Optimal Transmission Switching (OTS) problem in situations where the TSO is forced to accept the risk that some contingencies may result in the de-energization of parts of the grid to avoid the violation of operational limits. This operational policy, which mainly applies to subtransmission systems, is first discussed. Then, a model of that policy is proposed that complements the classical MILP model of the N-1 secure OTS problem. It comprises a connectivity and notably a partial grid loss analysis for branch outage contingencies. Finally, its application to the IEEE 14- bus system is presented. Solutions similar to those observed in operation are reached by the algorithm, notably revealing the preventive-openings-cascade phenomenon.
Electrical grid congestion has emerged as an immense challenge in Europe, making the forecasting of load and its associated metrics increasingly crucial. Among these metrics, peak load is fundamental. Non-time-resolved models of peak load have their advantages of being simple and compact, and among them Velander’s formula (VF) is widely used in distribution network planning. However, several aspects of VF remain inadequately addressed, including year-ahead prediction, scaling of customers, aggregation, and, most importantly, the lack of probabilistic elements. The present paper proposes a quantile interpretation of VF that enables VF to learn truncated cumulative distribution functions of peak loads with multiple quantile regression under non-crossing constraints. The evaluations on non-residential customer data confirmed its ability to predict peak load year ahead, to fit customers with a wide range of electricity consumptions, and to model aggregations of customers. A noteworthy finding is that for a given electricity consumption, aggregations of customers have statistically larger peak loads than a single customer.
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Electrical grid congestion has emerged as an immense challenge in Europe, making the forecasting of load and its associated metrics increasingly crucial. Among these metrics, peak load is fundamental. Non-time-resolved models of peak load have their advantages of being simple and compact, and among them Velander’s formula (VF) is widely used in distribution network planning. However, several aspects of VF remain inadequately addressed, including year-ahead prediction, scaling of customers, aggregation, and, most importantly, the lack of probabilistic elements. The present paper proposes a quantile interpretation of VF that enables VF to learn truncated cumulative distribution functions of peak loads with multiple quantile regression under non-crossing constraints. The evaluations on non-residential customer data confirmed its ability to predict peak load year ahead, to fit customers with a wide range of electricity consumptions, and to model aggregations of customers. A noteworthy finding is that for a given electricity consumption, aggregations of customers have statistically larger peak loads than a single customer.
Increased electrification of energy end-usage can lead to network congestion during periods of high consumption. Flexibility of loads, such as aggregate smart charging of Electric Vehicles (EVs), is increasingly leveraged to manage grid congestion through various market-based mechanisms. Under such an arrangement, this paper quantifies the effect of lead time on the aggregate flexibility of EV fleets. Simulations using realworld charging transactions spanning over different categories of charging stations are performed for two flexibility products (redispatch and capacity limitations) when offered along with different business-as-usual (BAU) schedules. Results show that the variation of tradable flexibility depends mainly on the BAU schedules, the duration of the requested flexibility, and its start time. Further, the implication of these flexibility products on the average energy costs and emissions is also studied for different cases. Simulations show that bidirectional (V2G) charging outperforms unidirectional smart charging in all cases.
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Increased electrification of energy end-usage can lead to network congestion during periods of high consumption. Flexibility of loads, such as aggregate smart charging of Electric Vehicles (EVs), is increasingly leveraged to manage grid congestion through various market-based mechanisms. Under such an arrangement, this paper quantifies the effect of lead time on the aggregate flexibility of EV fleets. Simulations using realworld charging transactions spanning over different categories of charging stations are performed for two flexibility products (redispatch and capacity limitations) when offered along with different business-as-usual (BAU) schedules. Results show that the variation of tradable flexibility depends mainly on the BAU schedules, the duration of the requested flexibility, and its start time. Further, the implication of these flexibility products on the average energy costs and emissions is also studied for different cases. Simulations show that bidirectional (V2G) charging outperforms unidirectional smart charging in all cases.
To optimize the dispatch of batteries, a model is required that can predict the state of energy (SOE) trajectory for a chosen open-loop power schedule to ensure admissibility (i.e., that schedule can be realized). However, battery dispatch optimization is inherently challenging when batteries cannot simultaneously charge and discharge, which begets a non-convex complementarity constraint. In this letter, we develop a novel composition of energy storage elements that can charge or discharge independently and provide a sufficient linear energy storage model of the composite battery. This permits convex optimization of the composite battery dispatch while ensuring the admissibility of the resulting (aggregated) power schedule and its disaggregation to the individual elements.
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To optimize the dispatch of batteries, a model is required that can predict the state of energy (SOE) trajectory for a chosen open-loop power schedule to ensure admissibility (i.e., that schedule can be realized). However, battery dispatch optimization is inherently challenging when batteries cannot simultaneously charge and discharge, which begets a non-convex complementarity constraint. In this letter, we develop a novel composition of energy storage elements that can charge or discharge independently and provide a sufficient linear energy storage model of the composite battery. This permits convex optimization of the composite battery dispatch while ensuring the admissibility of the resulting (aggregated) power schedule and its disaggregation to the individual elements.
Multilevel Monte Carlo (MLMC) is a flexible and effective variance reduction technique for accelerating reliability assessments of complex power system. Recently, data-driven surrogate models have been proposed as lower-level models in the MLMC framework due to their high correlation and negligible execution time once trained. However, in resource adequacy assessments, pre-labeled datasets are typically unavailable. For large-scale systems, the efficiency gains from surrogate models are often offset by the substantial time required for labeling training data. Therefore, this paper introduces a speed metric that accounts for training time in evaluating MLMC efficiency. Considering the total time budget is limited, a vote-by-committee active learning approach is proposed to reduce the required labeling calls. A case study demonstrates that, within a given computational budget, active learning in combination with MLMC can result in a substantial reduction variance.
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Multilevel Monte Carlo (MLMC) is a flexible and effective variance reduction technique for accelerating reliability assessments of complex power system. Recently, data-driven surrogate models have been proposed as lower-level models in the MLMC framework due to their high correlation and negligible execution time once trained. However, in resource adequacy assessments, pre-labeled datasets are typically unavailable. For large-scale systems, the efficiency gains from surrogate models are often offset by the substantial time required for labeling training data. Therefore, this paper introduces a speed metric that accounts for training time in evaluating MLMC efficiency. Considering the total time budget is limited, a vote-by-committee active learning approach is proposed to reduce the required labeling calls. A case study demonstrates that, within a given computational budget, active learning in combination with MLMC can result in a substantial reduction variance.
Congestion management in the day-ahead timeframe
Lessons from The Netherlands
The decarbonisation of electricity supply through variable renewable energy (VRE) is causing increasing congestion in electricity transmission and distribution grids. Redispatching after the closure of the day ahead market has been the most common congestion management instrument. A key challenge for congestion management via redispatching is the growing scarcity of upward reserves for counter activation, as synchronously connected assets are often out of merit order during periods of high VRE output. To proactively manage congestion before the day-ahead market closes, the Netherlands introduced the dispatch limitation product (DLP) in 2022. Since its introduction, the DLP has been widely contracted and used. Furthermore, starting in 2025, Flexible Connection Agreements (FCA) will be introduced, providing additional mechanisms for congestion management. This paper presents key lessons from the Dutch experience with congestion management in the day-ahead timeframe, analysing the effectiveness of these new instruments and their impact on grid flexibility and market efficiency.
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The decarbonisation of electricity supply through variable renewable energy (VRE) is causing increasing congestion in electricity transmission and distribution grids. Redispatching after the closure of the day ahead market has been the most common congestion management instrument. A key challenge for congestion management via redispatching is the growing scarcity of upward reserves for counter activation, as synchronously connected assets are often out of merit order during periods of high VRE output. To proactively manage congestion before the day-ahead market closes, the Netherlands introduced the dispatch limitation product (DLP) in 2022. Since its introduction, the DLP has been widely contracted and used. Furthermore, starting in 2025, Flexible Connection Agreements (FCA) will be introduced, providing additional mechanisms for congestion management. This paper presents key lessons from the Dutch experience with congestion management in the day-ahead timeframe, analysing the effectiveness of these new instruments and their impact on grid flexibility and market efficiency.
Electric vehicles (EVs) play a crucial role in the transition towards sustainable modes of transportation and thus are critical to the energy transition. As their number grows, managing the aggregate power of EV charging is crucial to maintain grid stability and mitigate congestion. This study analyses more than 500 thousand real charging transactions in the Netherlands to explore the challenge and opportunity for the energy system presented by EV growth and smart charging flexibility. Specifically, it analyses the collective ability to provide congestion management services according to the specifications of those services in the Netherlands. In this study, a data-driven model of charging behaviour is created to explore the implications of delivering dependable congestion management services at various aggregation levels and types of service. The probability of offering specific grid services by different categories of charging stations (CS) is analysed. These probabilities can help EV aggregators, such as charging point operators, make informed decisions about offering congestion mitigation products per relevant regulations and distribution system operators to assess their potential. The ability to offer different flexibility products, namely redispatch and capacity limitation, for congestion management, is assessed using various dispatch strategies. Next, machine learning models are used to predict the probability of CSs being able to deliver these products, accounting for uncertainties. Results indicate that residential charging locations have significant potential to provide both products during evening peak hours. While shared EVs offer better certainty regarding arrival and departure times, their small fleet size currently restricts their ability to meet the minimum order size of flexible products. The findings demonstrate that the timing of EV arrivals, departures, and connections plays a crucial role in determining the feasibility of product offerings, and dependable services can generally be delivered using a sufficiently large number of CSs.
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Electric vehicles (EVs) play a crucial role in the transition towards sustainable modes of transportation and thus are critical to the energy transition. As their number grows, managing the aggregate power of EV charging is crucial to maintain grid stability and mitigate congestion. This study analyses more than 500 thousand real charging transactions in the Netherlands to explore the challenge and opportunity for the energy system presented by EV growth and smart charging flexibility. Specifically, it analyses the collective ability to provide congestion management services according to the specifications of those services in the Netherlands. In this study, a data-driven model of charging behaviour is created to explore the implications of delivering dependable congestion management services at various aggregation levels and types of service. The probability of offering specific grid services by different categories of charging stations (CS) is analysed. These probabilities can help EV aggregators, such as charging point operators, make informed decisions about offering congestion mitigation products per relevant regulations and distribution system operators to assess their potential. The ability to offer different flexibility products, namely redispatch and capacity limitation, for congestion management, is assessed using various dispatch strategies. Next, machine learning models are used to predict the probability of CSs being able to deliver these products, accounting for uncertainties. Results indicate that residential charging locations have significant potential to provide both products during evening peak hours. While shared EVs offer better certainty regarding arrival and departure times, their small fleet size currently restricts their ability to meet the minimum order size of flexible products. The findings demonstrate that the timing of EV arrivals, departures, and connections plays a crucial role in determining the feasibility of product offerings, and dependable services can generally be delivered using a sufficiently large number of CSs.
Aggregation is crucial to the effective use of flexibility, especially in the case of electric vehicles (EVs) because of their limited individual battery sizes and large aggregate impact. This research proposes a novel method to quantify and represent the aggregate charging flexibility of EV fleets within a fixed flexibility request window. These windows can be chosen based on relevant network operator needs, such as evening congestion periods. The proposed representation is independent of the number of assets but scales only with the number of discrete time steps in the chosen window. The representation involves 2T parameters, with T being the number of consecutive time steps in the window. The feasibility of aggregate power signals can be checked using 2T constraints and optimized using 2(2T−1) constraints, both exactly capturing the flexibility region. Using a request window eliminates uncertainty related to EV arrival and departure times outside the window. We present the necessary theoretical framework for our proposed methods and outline steps for transitioning between representations. Additionally, we compare the computational efficiency of the proposed method with the common direct aggregation method, where individual EV constraints are concatenated.
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Aggregation is crucial to the effective use of flexibility, especially in the case of electric vehicles (EVs) because of their limited individual battery sizes and large aggregate impact. This research proposes a novel method to quantify and represent the aggregate charging flexibility of EV fleets within a fixed flexibility request window. These windows can be chosen based on relevant network operator needs, such as evening congestion periods. The proposed representation is independent of the number of assets but scales only with the number of discrete time steps in the chosen window. The representation involves 2T parameters, with T being the number of consecutive time steps in the window. The feasibility of aggregate power signals can be checked using 2T constraints and optimized using 2(2T−1) constraints, both exactly capturing the flexibility region. Using a request window eliminates uncertainty related to EV arrival and departure times outside the window. We present the necessary theoretical framework for our proposed methods and outline steps for transitioning between representations. Additionally, we compare the computational efficiency of the proposed method with the common direct aggregation method, where individual EV constraints are concatenated.
Journal article
(2024)
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Nico Brinkel, Thijs van Wijk, Anoeska Buijze, Nanda Kishor Panda, Jelle Meersmans, Peter Markotić, Bart van der Ree, Henk Fidder, Simon Tindemans, More authors...
Smart charging of electric vehicles can alleviate grid congestion and reduce charging costs. However, various electric vehicle models currently lack the technical capabilities to effectively implement smart charging since they cannot handle charging pauses or delays. These models enter sleep mode when charging is interrupted, preventing resumption afterwards. To avoid this, they should be continuously charged with their minimum charging power, even when a charging pause would be desirable, for instance with high electricity prices. This research examines this problem to inform various stakeholders, including policymakers and manufacturers, and stimulates the adoption of proactive measures that address this problem. Here, we demonstrate through technical charging tests that around one-third of tested car models suffer from this issue. Through model simulations we indicate that eliminating paused and delayed charging problems would double the smart charging potential for all applications. Lastly, we propose concrete legal and practical solutions to eliminate these problems.
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Smart charging of electric vehicles can alleviate grid congestion and reduce charging costs. However, various electric vehicle models currently lack the technical capabilities to effectively implement smart charging since they cannot handle charging pauses or delays. These models enter sleep mode when charging is interrupted, preventing resumption afterwards. To avoid this, they should be continuously charged with their minimum charging power, even when a charging pause would be desirable, for instance with high electricity prices. This research examines this problem to inform various stakeholders, including policymakers and manufacturers, and stimulates the adoption of proactive measures that address this problem. Here, we demonstrate through technical charging tests that around one-third of tested car models suffer from this issue. Through model simulations we indicate that eliminating paused and delayed charging problems would double the smart charging potential for all applications. Lastly, we propose concrete legal and practical solutions to eliminate these problems.
The electrification of end-energy use and the increasing integration of distributed energy resources (DERs) are significantly reshaping the landscape of low voltage (LV) distribution grids. However, many LV networks were originally designed without considering these transformative factors, potentially leading to congestion and overloads. Assessing the hosting capacity of these networks has become crucial, as it quantifies the ability of the distribution network to accommodate additional DERs while maintaining stable and reliable operations. In this context, we introduce the concept of remaining hosting capacity as a metric to evaluate LV distribution networks' capacity to absorb additional DERs, considering the existing DER deployment. We present two simulation methodologies: Gaussian mixture model-based stochastic power flow simulations that deliver a detailed network analysis, including specific current and voltage data but require substantial computational resources, and a data resampling simulation methodology that employs detailed load and DER profiles to rapidly approximate load demands at the transformer level. Furthermore, we conduct a sensitivity analysis for different levels of DER penetration to calculate the networks' capability to accommodate more DERs. The results obtained illustrate the effectiveness of GM models and the data resampling simulation methodology proposed in this work. The remaining hosting capacity concept provides essential insights into the networks' capabilities to accommodate additional DERs in the future, facilitating informed decisions for both Distribution System Operators (DSOs) and DER developers regarding grid operation, necessary upgrades, and sustainable DER expansion.
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The electrification of end-energy use and the increasing integration of distributed energy resources (DERs) are significantly reshaping the landscape of low voltage (LV) distribution grids. However, many LV networks were originally designed without considering these transformative factors, potentially leading to congestion and overloads. Assessing the hosting capacity of these networks has become crucial, as it quantifies the ability of the distribution network to accommodate additional DERs while maintaining stable and reliable operations. In this context, we introduce the concept of remaining hosting capacity as a metric to evaluate LV distribution networks' capacity to absorb additional DERs, considering the existing DER deployment. We present two simulation methodologies: Gaussian mixture model-based stochastic power flow simulations that deliver a detailed network analysis, including specific current and voltage data but require substantial computational resources, and a data resampling simulation methodology that employs detailed load and DER profiles to rapidly approximate load demands at the transformer level. Furthermore, we conduct a sensitivity analysis for different levels of DER penetration to calculate the networks' capability to accommodate more DERs. The results obtained illustrate the effectiveness of GM models and the data resampling simulation methodology proposed in this work. The remaining hosting capacity concept provides essential insights into the networks' capabilities to accommodate additional DERs in the future, facilitating informed decisions for both Distribution System Operators (DSOs) and DER developers regarding grid operation, necessary upgrades, and sustainable DER expansion.
Electric demand and renewable power are highly variable, and the solution of a planning model relies on capturing this variability. This paper proposes a hybrid multi-area method that effectively captures both the intraday and interday chronology of real data considering extreme values, using a limited number of representative days, and time points within each day. An optimization-based representative extraction method is proposed to improve intraday chronology capturing. It ensures higher precision in preserving data chronology and extreme values than hierarchical clustering methods. The proposed method is based on a piecewise linear demand and supply representation, which reduces approximation errors compared to the traditional piecewise constant formulation. Additionally, sequentially linked day blocks with identical representatives, created through a mapping process, are employed for interday chronology capturing. To evaluate the efficiency of the proposed method, a comprehensive expansion co-planning model is developed, including transmission lines, energy storage systems, and wind farms.
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Electric demand and renewable power are highly variable, and the solution of a planning model relies on capturing this variability. This paper proposes a hybrid multi-area method that effectively captures both the intraday and interday chronology of real data considering extreme values, using a limited number of representative days, and time points within each day. An optimization-based representative extraction method is proposed to improve intraday chronology capturing. It ensures higher precision in preserving data chronology and extreme values than hierarchical clustering methods. The proposed method is based on a piecewise linear demand and supply representation, which reduces approximation errors compared to the traditional piecewise constant formulation. Additionally, sequentially linked day blocks with identical representatives, created through a mapping process, are employed for interday chronology capturing. To evaluate the efficiency of the proposed method, a comprehensive expansion co-planning model is developed, including transmission lines, energy storage systems, and wind farms.
Quantitative risk analysis is essential for power system planning and operation. Monte Carlo methods are frequently employed for this purpose, but their inherent sampling uncertainty means that accurate estimation of this uncertainty is essential. Basic Monte Carlo procedures are unbiased and, in the limit of large sample counts, have a well-characterised error distribution. However, for small time budgets and ill-behaved distributions (such as those for rare event risks), we may not always operate in this limit. Moreover, multilevel Monte Carlo was recently proposed as a computationally efficient alternative to regular Monte Carlo. In this approach, great asymptotic speedups are achieved by reducing the number of full model evaluations. This further challenges the assumption that normally distributed errors can be used. This paper investigates the sampling error distributions for a practical resource adequacy case study, in combination with the Multilevel Monte Carlo method. It further proposes a practical test for validating error estimates, based on a bootstrap approach.
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Quantitative risk analysis is essential for power system planning and operation. Monte Carlo methods are frequently employed for this purpose, but their inherent sampling uncertainty means that accurate estimation of this uncertainty is essential. Basic Monte Carlo procedures are unbiased and, in the limit of large sample counts, have a well-characterised error distribution. However, for small time budgets and ill-behaved distributions (such as those for rare event risks), we may not always operate in this limit. Moreover, multilevel Monte Carlo was recently proposed as a computationally efficient alternative to regular Monte Carlo. In this approach, great asymptotic speedups are achieved by reducing the number of full model evaluations. This further challenges the assumption that normally distributed errors can be used. This paper investigates the sampling error distributions for a practical resource adequacy case study, in combination with the Multilevel Monte Carlo method. It further proposes a practical test for validating error estimates, based on a bootstrap approach.
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation mechanism as a probability distribution to assess the data quality and generate more data, if needed. Kernel density estimation (KDE) based models are popular choices for this task, but they fail to adapt to data regions with varying densities. In this paper, an adaptive KDE model is employed to circumvent this, where each kernel in the model has an individual bandwidth. The leave-one-out maximum log-likelihood (LOO-MLL) criterion is proposed to prevent the singular solutions that the regular MLL criterion gives rise to, and it is proven that LOO-MLL prevents these. Relying on this guaranteed robustness, the model is extended by adjustable weights for the kernels. In addition, a modified expectation–maximization algorithm is employed to accelerate the optimization speed reliably. The performance of the proposed method and models are exhibited on two power systems datasets using different statistical tests and by comparison with Gaussian mixture models. Results show that the proposed models have promising performance, in addition to their singularity prevention guarantees.
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Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation mechanism as a probability distribution to assess the data quality and generate more data, if needed. Kernel density estimation (KDE) based models are popular choices for this task, but they fail to adapt to data regions with varying densities. In this paper, an adaptive KDE model is employed to circumvent this, where each kernel in the model has an individual bandwidth. The leave-one-out maximum log-likelihood (LOO-MLL) criterion is proposed to prevent the singular solutions that the regular MLL criterion gives rise to, and it is proven that LOO-MLL prevents these. Relying on this guaranteed robustness, the model is extended by adjustable weights for the kernels. In addition, a modified expectation–maximization algorithm is employed to accelerate the optimization speed reliably. The performance of the proposed method and models are exhibited on two power systems datasets using different statistical tests and by comparison with Gaussian mixture models. Results show that the proposed models have promising performance, in addition to their singularity prevention guarantees.