Load Uncertainty Research Articles

Renewable Energy Community Sizing Based on Stochastic Optimization and Unsupervised Clustering

Renewable Energy Communities (RECs) are emerging as significant in the global paradigm shift towards a smart and sustainable energy environment. By empowering energy consumers to actively participate in local energy generation, and sharing, using renewable energy sources, energy storage, and flexible loads, REC participants can reduce costs, and also contribute to low-carbon objectives, providing the flexibility needed to address modern smart grid challenges. This article presents a mixed integer linear programming model for optimal sizing of the solar PVs and battery energy storage systems (BESS) of REC participants who engage in P2P energy exchange. The model is formulated using a two-stage stochastic optimization to address load and PV uncertainty, and unsupervised clustering to structure the data for the stochastic optimization process. The model enables sizing solar PVs for different rooftop geometries and the objective function includes comprehensively defined electricity, operational, and scaled investment costs for solar PV and BESS, where economic fairness constraints are analyzed and implemented. The model is validated on real solar and atmospheric measured data from Zagreb, Croatia, and publicly available household consumption data from Northern Germany. The article also analyzes how tariff models, and electricity prices affect PV and BESS sizes, cost reductions, and P2P energy exchange for different REC participants with varying consumption and production profiles.

An online loop closing current calculation method for complex distribution networks considering source and load uncertainties

AbstractTo address the challenges posed by frequent source and load fluctuations in existing loop closing current calculation methods, this paper proposes an online loop closing current calculation method that considers source and load uncertainties. First, a dual‐stack dynamic monitoring system is utilized to obtain real‐time voltage and current variations before and after disturbances. Second, Thevenin's theorem is employed to build an equivalent model of the distribution network, simplifying the complex network into a combination of an independent voltage source and a series impedance. Then, the steady‐state loop closing current is calculated based on the open‐circuit voltage and equivalent impedance at both sides of the loop closing point. Next, the optimal frequency method is applied to determine the equivalent impedance and attenuation time constant at a specific frequency, achieving accurate calculation of the transient loop closing current. Finally, simulations are conducted to model the fluctuations in distributed generation and load, analysing the steady‐state and transient loop closing currents. The simulation results demonstrate that the proposed method accurately captures the effects of source and load fluctuations on the loop closing current in dynamic environments, with minimal calculation error, indicating its high practicality.

Appraising annual post-maintenance functional performance of asphalt roadway based on causal inference approach

ABSTRACT To maintain good functional pavement performance and extend the service life of asphalt pavements, the long-term performance of pavements under maintenance policies needs to be evaluated and favourable options need to be chosen based on the condition of the pavement. A major challenge in evaluating maintenance policies is to produce valid treatments for the outcome assessment under the control of uncertainty of vehicle loads and the disturbance of freeze-thaw cycles in the climatic environment. In this study, a novel causal inference approach, combining a classical causal structural model and a potential outcome model framework, is proposed to appraise the annual post-maintenance performance of four preventive preservation treatments of pavements for longitudinal cracking over a 5-year period of upkeep. Three fundamental issues were brought to our attention: detection of causal relationships prior to variables under environmental loading (identification of causal structure); obtaining direct causal effects of treatment on outcomes excluding covariates (identification of causal effects) and sensitivity analysis of causal relationships. The results show that the method can accurately evaluate the effect of preventive maintenance treatments, assess the maintenance time to cater well for the functional performance of different preventive maintenance approaches and develop appropriate maintenance strategies for pavements.

A Novel Graph Reinforcement Learning-Based Approach for Dynamic Reconfiguration of Active Distribution Networks with Integrated Renewable Energy

The dynamic reconfiguration of active distribution networks (ADNDR) essentially belongs to a complex high-dimensional mixed-integer nonlinear stochastic optimization problem. Traditional mathematical optimization algorithms tend to encounter issues like slow computational speed and difficulties in solving large-scale models, while heuristic algorithms are prone to fall into local optima. Furthermore, few scholars in the existing research on distribution network (DN) reconfiguration have considered the graph structure information, resulting in the loss of critical topological information and limiting the effect of optimization. Therefore, this paper proposes an ADNDR approach based on the graph convolutional network deep deterministic policy gradient (GCNDDPG). Firstly, a nonlinear stochastic optimization mathematical model for the ADNDR is constructed, taking into account the uncertainty of sources and loads. Secondly, a loop-based encoding method is employed to reduce the action space and complexity of the ADNDR. Then, based on graph theory, the DN structure is transformed into a dynamic network graph model, and a GCNDDPG-based ADNDR approach is proposed for the solution. In this method, graph convolutional networks are used to extract features from the graph structure information, and the state of the DN, and the deep deterministic policy gradient is utilized to optimize the ADNDR decision-making process to achieve the safe, stable, and economic operation of the DN. Finally, the effectiveness of the proposed approach is verified on an improved IEEE 33-bus power system. The simulation results demonstrate that the method can effectively enhance the economy and stability of the DN, thus validating the effectiveness of the proposed approach.

Dispatch model of park-level integrated energy system with photovoltaic/thermal hydrogen generation equipment: A scenario analysis method based on improved K-means clustering

As the carbon emission problem brought by the traditional energy consumption pattern is becoming more and more prominent, it has become a common strategic choice for all countries to realize the carbon-neutral goal and to drive energy conversion to clean and renewable energy. Meanwhile, the significant uncertainty of renewable energy sources and their large-scale access to the grid poses new challenges to power system operation and dispatch. Therefore, this paper proposes a dispatch model for the park-level integrated energy system (PIES) with photovoltaic/thermal (PV/T) hydrogen generation equipments based on improved stepped carbon trading and adopts a scenario analysis method based on improved K-means clustering to cope with the uncertainties of the multi-energy loads and PV/T output. First, the PV/T model is constructed through five energy balance equations of the glass protection screen, solar panel, heat pipe, water inside the heat pipe, and heat storage tank, which is further combined with the hydrogen ion exchange membrane electrolyzer (HIEME) to analyze the energy flow conversion in the process of hydrogen production by the coupled equipment. Second, an improved stepped carbon trading price model is proposed by constructing a continuously monotonically increasing trading price function. Finally, based on the improved stepped carbon trading mechanism, the day-ahead dispatching model aims to optimize the sum of PIES operation cost and carbon trading cost, and the example simulation is carried out by the scenario analysis method based on improved K-means clustering. The simulation results show that the proposed model has certain significance in hydrogen production efficiency and carbon emission reduction.

System reliability analysis of cold-formed steel structures for serviceability limit states

The adoption of numerical analyses in structural design practice has ensured greater control over the actual behavior of structures. Design-by-analysis approaches deviate from traditional methods by directly considering the load-bearing capacity of the entire system rather than individual element checks. These approaches can even incorporate inherent nonlinearities into the analysis, such as second-order effects, material inelasticity, geometric imperfections, and semi-rigid connections. These advanced analysis models may produce results closer to the actual behavior of the structure in service, enabling the safe utilization of lighter structural systems. In this context, the evaluation of serviceability limit states becomes relevant, particularly for cold-formed steel structures, which are typically assembled using slender elements. This paper presents the application of a reliability-based procedure to assess the compliance of cold-formed steel frames with serviceability limit state criteria for excessive lateral displacement. Considering two groups of cold-formed steel structures based on their functions: single-story building frames and industrial storage rack frames, the lateral drift limits are extracted from the AISI S100, ASCE/SEI 7, ANSI MH 16.1, and Brazilian NBR 14762 and NBR 15524-2 standards, along with the target reliability indices for the corresponding limit state. The subsequent step involves evaluating system reliability, considering typical load cases for these structures (dead and wind loads for single-story frames and dead and product loads for racks) selected from the mentioned specifications, accounting for the uncertainties in loads and in the material and geometric parameters of the steel members. For this purpose, a MATLAB reliability framework is presented, coupling the First Order Reliability Method (FORM) to the MASTAN2 finite-element package, in order to apply the structural analysis results in each evaluation of the limit state functions. Conclusions regarding reliability indices and the potential adequacy of resistance factors are presented.

Operational Influence Line Identification of High-Speed Railway Bridge Considering Uncertainty of Train Load

Operational Influence Line Identification of High-Speed Railway Bridge Considering Uncertainty of Train Load

A multi-objective improved horse herd optimizer based on convex lens imaging for stochastic optimization of wind energy resources in distribution networks considering reliability and uncertainty

In this study, stochastic multi-objective allocation of wind turbines (WTs) in radial distribution networks is performed using a new multi-objective improved horse herd optimizer (MOIHHO) and an unscented transformation (UT) method for modeling the uncertainties of WTs power and network load. The objective function aims to minimize power loss, improve reliability, and reduce the costs associated with wind turbines (WTs), presenting these goals as a three-dimensional function. The Multi-Objective Improved Horse Herd Optimizer (MOIHHO) is derived from an enhanced version of the traditional horse herd optimizer. This enhancement utilizes mirror imaging based on convex lens principles to address issues of premature convergence. Additionally, the decision-making process is designed to identify the final fuzzy solution among the non-dominant solutions within the Pareto front set. The simulation results are presented with and without considering uncertainty in two scenarios of deterministic and stochastic WT allocation on 33- and 69-bus distribution networks and different objectives are compared. Also, the effect of incorporating uncertainties are evaluated on power loss and reliability using the MOIHHO. Moreover, the superiority of the MOIHHO is investigated in achieving better objective function value compared with conventional MOHHO, multi-objective particle swarm optimization (MOSPO), multi-objective gray wolf optimizer (MOGWO), and multi-objective gazelle optimization algorithm (MOGOA). The obtained results demonstrated that considering the UT-based stochastic scenario, the power losses cost is increased, and the reliability is weakened for 33- and 69-bus networks in comparison with the deterministic scenario.

Distributionally robust optimal configuration of battery energy storage system considering nodal RoCoF security constraints

The large-scale integration of renewable energy source (RES) exacerbates net load fluctuations, reduces system inertia, limits frequency response capabilities, and leads to uneven spatial distribution of inertia resources. To ensure the economic and safe operation of the system, we propose a distributionally robust optimal configuration scheme of battery energy storage system (BESS) considering nodal RoCoF security constraints to address these issues. First, we describe and model the dynamic frequency response characteristics after disturbances, derive the expressions for the system frequency nadir and maximum nodal RoCoF (MN-RoCoF). Second, we address net load uncertainty using the distributionally robust chance constrained (DRCC) approach and incorporate frequency security constraints into the BESS configuration optimization model, embedding the short-term system operation model into the long-term BESS planning. Then, to tackle the highly nonlinear MN-RoCoF constraint, we propose a divide and conquer-based support vector machine (D&C-SVM), to extract the linear relationship between the BESS virtual inertia constant and MN-RoCoF, reformulating the proposed scheme into a mixed-integer second-order cone programming (MISOCP). Finally, we conducted case studies on the IEEE 39-bus and 118-bus test systems. The results verify that the proposed configuration scheme can ensure that the RoCoF at all nodes remains below 1 Hz/s under the preset disturbances. The proposed D&C-SVM demonstrate 99 % accuracy in managing the nonlinear MN-RoCoF constraint. Moreover, the uncertainty in net load is well managed, with all chance constraints satisfied with a confidence level of over 95 %.

Real-Time Short-Circuit Current Calculation in Electrical Distribution Systems Considering the Uncertainty of Renewable Resources and Electricity Loads

Existing short-circuit calculation methods for distribution networks with renewable energy sources ignore the fluctuation of renewable sources and cannot reflect the impact of renewable sources and load changes on short-circuit current in real time at all times of the day and in extreme scenarios. A real-time short-circuit current calculation method is proposed to take into account the stochastic nature of distributed generators (DGs) and electricity loads. Firstly, the continuous power flow of distribution networks is calculated based on the real-time renewable energy output and electricity loads. And then, equivalent DG models with low-voltage ride through (LVRT) strategies are substituted into the iterative calculation method to obtain the short-circuit currents of all main branches in real time. The effects of different renewable energy output curves on distribution network short-circuit currents are quantitatively analyzed during the fluctuation in distributed power output, which can provide an important basis for the setting calculation of distribution network relay protection and the study of new principles of protection.

Two-stage distributionally robust optimization operation of virtual power plant considering the virtual energy storage of electric vehicles

Virtual Power Plant (VPP) is a key to aggregate various distributed energy sources. With the vigorous rise of various distributed energy sources, the direct access of large-scale electric vehicle load will increase the complexity of VPP coordinated operation. Hence, this paper proposes a VPP optimization method for Electric Vehicle Virtual Energy Storage (EV-VES). Firstly, the travel characteristics of electric vehicles are analyzed, and EV-VES model is established to coordinate and manage the charge-discharge behavior of EV. Secondly, the “carbon charge rate” model of energy storage (ES) is introduced to establish the relationship between carbon emission and electricity price, and the VPP operation model considering the “carbon charge rate” of energy storage is established. Finally, the two-stage robust optimization operation model of VPP is constructed, Wasserstein distance is used to describe the confidence set of uncertain probability distribution of wind power generation and load, and the uncertainty of system source and load are described by the confidence set. The Column and Constraint Generation (C&CG) algorithm was used to determine the optimal operational benefit solution. The effectiveness of the proposed VPP optimal operation model was validated through case study.

Optimization Dispatch of Distribution Network–Prosumer Group–Prosumer Considering Flexible Reserve Resources of Prosumer

The bidirectional uncertainty of source and load creates scarcity in the reserve resources of the distribution network. Therefore, it is highly significant for the safe and economic operation of the system to harness spare energy storage capacity from prosumers to provide reserves. This paper proposes a bi-layer optimal scheduling model of “distribution network–prosumer group–prosumer” that considers the flexible reserve resources of a prosumer. The upper layer is the “distribution network–prosumer group” optimization model, in which the distribution network sets the electricity price and reserve price according to its own economic benefit and sends it to the prosumer group and guides it to participate in the scheduling of the resources of the prosumer. The lower layer is the “prosumer group–prosumer” optimization model, where the prosumer group incentivizes the prosumer to adjust its energy storage charging and discharging plans through prices and mobilize its own resources to provide flexible reserve resources. The results show that the optimal method proposed in this paper can fully utilize flexible reserve resources from prosumers, improve the economy of distribution network operations, and reduce the pressure of providing reserves using the upper grid.

Enhancing the motion performance of 3-DOF micro/nano-manipulators facing thermo-piezoelectric-mechanical coupling effects

Achieving ultra-high accuracy manipulation with piezoelectric micro/nano-manipulators is significantly hindered by thermal loads uncertainties in the digital control diagram. To address the problem, we propose a sampled-data fixed-time extended state observer based control strategy to enhance the manipulation performance. Initially, we delve into the dynamical model of the micro/nano-manipulator, examining the thermo-piezoelectric-mechanical coupling effects. Following the kinematics decoupling of the 3-DOF model, sampled-data fixed-time extended state observer based control strategy is designed to estimate the system states and total disturbances including thermal impacts and system uncertainties in the sampled-data control architecture, where an output predictor is integrated to forecast system output between consecutive sampling instances, while the observation gains are meticulously crafted to ensure a fixed-time convergence in estimation. Leveraging this estimation framework, a fixed-time feedback controller is designed to compensate the total disturbance and control the system, enabling the system to achieve a tracking convergence, irrespective of the inconsistent initial values stemming from thermal effects disparities. Finally, experimental validation on a piezoelectric thin-sheet-actuated 3-DOF flexible micro/nano-manipulator verifies the effectiveness of the proposed control strategy. Notably, we have observed a minimum enhancement of 26% in spatial trajectory positioning and scanning accuracy in the context of varying thermal loads.

Design optimization of continuous fiber composites with thermo-mechanical coupling and load uncertainties

This paper introduces a theoretical framework for the design optimization of continuous fiber composites reinforced with continuous fiber trajectories subject to thermo-mechanical coupling and load uncertainties. Different uniform temperature variations are applied in the structure to investigate the influence of ambient temperature change on the structural performance. To consider the external load uncertainties, a robust design optimization model is proposed where the loads are modeled as hybrid variables, namely magnitudes as random variables and directions as interval variables, with the robust objective determined through a hybrid orthogonal polynomial expansion method. Furthermore, we use a level-set function to represent the structural boundary, with its evolution driven by shape derivatives calculated based on uncertainty analysis. The continuous fiber paths are subsequently determined by the level-set isoline extracted from the structural boundary, which in turn influences the structural mechanical performance due to the material anisotropy of composites. The continuity of continuous fiber and the equal space between adjacent trajectories largely ensure the additive manufacturability of the composites. Three numerical examples are presented to demonstrate the effectiveness of the developed framework. The results show that the ambient temperature variations and load uncertainties largely impact the optimized topology and fiber infill patterns of composites, thus are important to be considered in the design stage. Moreover, the optimized structure can have a 5-fold stiffness per unit mass compared with the initial design thus largely increasing the material efficiency in carrying external uncertain loads.

Optimization of emergency frequency control strategy for power systems considering both source and load uncertainties

With the increasing integration of renewable energy sources and the presence of numerous controllable loads such as electric vehicles and energy storage in the modern power system, higher nonlinearities and uncertainty both sources and loads are introduced. These factors pose challenges in achieving fast and accurate emergency frequency control. Therefore, this paper addresses the issue of dual source-load uncertainties in power system and presents an optimization strategy based on the Soft Actor Critic (SAC) algorithm that involves the participation of controllable loads in emergency frequency control. Firstly, the spatio-temporal uncertainties of wind farm power output on power supply side and power demand on the load side are described using Weibull and normal probability distributions, respectively. Secondly, an improved Markov Decision Process (MDP) model for emergency frequency control is established, which considers the characteristics of the dual source-load uncertainties. Finally, an optimization of the SAC algorithm is conducted based on Deep Reinforcement Learning (DRL), aiming to achieve rapid system frequency recovery and minimize the cost of removing controllable loads. The presented approach in the paper enhances the emergency frequency control strategy for uncertain power systems and effectively addresses the issue of source-load uncertainty compounded by fault power shortages.

Hybrid energy system optimization integrated with battery storage in radial distribution networks considering reliability and a robust framework

This research presents a robust optimization of a hybrid photovoltaic-wind-battery (PV/WT/Batt) system in distribution networks to reduce active losses and voltage deviation while also enhancing network customer reliability considering production and network load uncertainties. The best installation position and capacity of the hybrid system (HS) are found via an improved crow search algorithm with an inertia weight technique. The robust optimization issue, taking into account the risk of uncertainty, is described using the gap information decision theory method. The proposed approach is used with 33- and 69-bus networks. The results reveal that the HS optimization in the network reduces active losses and voltage variations, while improving network customer reliability. The robust optimization results show that in the 33-bus network, the system remains resilient to prediction errors under the worst-case uncertainty scenario, with a 44.53% reduction in production and a 22.18% increase in network demand for a 30% uncertainty budget. Similarly, in the 69-bus network, the system withstands a 36.22% reduction in production and a 16.97% increase in load for a 25% uncertainty budget. When comparing stochastic and robust methods, it was found that the stochastic Monte Carlo method could not consistently provide a reliable solution for all objectives under uncertainty, whereas the robust approach successfully managed the maximum uncertainty related to renewable generation and network demand across different uncertainty budgets.

Improved binary quantum-based Elk Herd optimizer for optimal location and sizing of hybrid system in micro grid with electric vehicle charging station

In recent times, there has been increasing interest in renewable power generation and electric vehicles within the domain of smart grids. The integration of electric vehicles with hybrid systems presents several critical challenges, including increased power loss, power quality issues, and voltage deviations. To tackle these challenges, researchers have proposed various techniques. Effective management of energy systems is essential for maximizing the benefits of integrating a hybrid system with a microgrid at an electric vehicle charging station. This research specifically aims to optimize the location and sizing of such a hybrid system within the microgrid. Additionally, an improved binary quantum-based Elk Herd optimizer approach is proposed. This approach addresses for optimally managing renewable energy sources and load uncertainty. The proposed system also considers the stochastic nature of electric vehicles and operational restrictions, encompassing diverse charging control modes. The proposed technique performance is implemented in MATLAB platform and compared against existing approaches. The analysis demonstrates the effectiveness in achieving optimal location and sizing for a hybrid system with an electric vehicle charging station. Additionally, the proposed approach contributes to minimizing power loss, electricity costs, and average waiting time. Furthermore, the proposed approach reduces computing time, net present cost, and emissions are 12.5 s, 1.1×106 dollar, 2.21×108 g year−1, respectively.

Optimization model for distributed energy trading based on a market value allocation mechanism in the electricity spot market

This study proposes a novel distributed energy trading market model with a value distribution mechanism to optimize the allocation and transactions of distributed energy resources (DERs). The framework incorporates a direct load management approach via an electricity aggregator agent, simplifying market processes and reducing transaction costs. A Nash bargaining model is employed to design a fair and efficient value distribution mechanism, promoting equitable benefit allocation among participants. The model integrates stochastic programming to account for uncertainties in real-time load and DER output, enhancing its robustness and applicability in real-world scenarios. The proposed mechanism quantifies each DER’s contribution using a market value contribution rate, serving as a foundation for the Nash bargaining model. This approach ensures individual rationality for both the aggregator and DERs while maximizing overall system benefits. Case studies validate the model’s effectiveness, demonstrating improvements in resource utilization and fair benefit allocation. This research contributes to the advancement of distributed energy markets, offering valuable insights for designing efficient and equitable market structures, ultimately promoting grid stability, renewable energy adoption, and the development of more sustainable and flexible energy systems.

Optimal scheduling of park-level integrated energy system considering multiple uncertainties: A comprehensive risk strategy-information gap decision theory method

Multiple uncertainties in the park-level integrated energy system (PIES) can affect the optimal operation of system. Information gap decision theory (IGDT) is a commonly used method of dealing with uncertainty by developing risky strategies to avoid risks or seek risky returns. However, there is no unified method or process for the selection of risk strategies and the setting of related parameters, leading to a certain blindness in the application of IGDT method. A comprehensive risk strategy (CRS)- IGDT approach is proposed for scheduling of PIES considering uncertainties of heat load, photovoltaic output and electric load. Risk averse strategy (RAS) and Risk seek strategy (RSS) scheduling models are constructed. Then an optimized solution method based on adaptive steps ratio (ASR) is proposed to solve the above two models. The CRS and comprehensive risk cost function are proposed from a risk equalization perspective. The target deviation coefficient and steps ratio in the IGDT model are automatically optimized with the objective of minimizing the comprehensive risk cost. Combining the two cases, the average cost reduction is 6.6 % compared to Risk-neutral (RN), 11 % compared to RAS-IGDT, and 4.1 % compared to RSS-IGDT. Moreover, the average costs of CRS-IGDT are lower compared to stochastic programming and robust optimization methods. The experiments verify the generalization and superiority of the proposed method in coping with different information gap situations caused by uncertainty. CRS-IGDT provides new research ideas for dealing with uncertainty problems in PIES and other fields.

Reliability-constrained configuration optimization for integrated power and natural gas energy systems: A stochastic approach

With the escalating dependence on electricity and natural gas infrastructure, ensuring both reliability and economic efficiency becomes paramount. It necessitates reliability centric measures to mitigate disruptions that could cascade between these interconnected systems. To address this challenges, this paper introduces a reliability-constrained two-stage stochastic model to optimize power-to-gas (P2 G) and gas-to-power (G2P) unit placement and sizing, aiming to enhance the reliability of both systems under stochastic scenarios. The proposed model, employing Sequential Monte Carlo (SMC) within its optimization framework, seeks to minimize investment, operation, and reliability costs. By addressing temporal uncertainties in component outages for both systems and considering uncertainties in power and gas system loads with a high temporal resolution and annual load growth, the model provides a comprehensive reliability perspective. Furthermore, sensitivity analysis is conducted to explore the impact of varying Values of Lost Load (VOLL) on the planning results. Numerical evaluation, using two integrated energy systems including IEEE 14-bus-10-gas node, and large-scale energy systems including IEEE 118-bus-85-gas node integrated power-gas system (IPGS), demonstrates a significant 12.53 % improvement in overall system reliability. Furthermore, a 2.81 % reduction in operation costs and a substantial 26.3 % reduction in reliability costs, validating the effectiveness of the proposed model.