Output Uncertainty Research Articles

Probabilistic photovoltaic generation and load demand uncertainties modelling for active distribution networks hosting capacity calculations

With the increasing integration of photovoltaic (PV) systems in active distribution networks (ADNs), accurate modelling of PV power generation and the network demand has become essential, especially for system operators (SO). However, existing studies have focused on deterministic representations of hourly profiles for PV generation and load consumption, which cannot thoroughly evaluate the existing uncertainties of PV power output and load demands. In this study, uncertain parameters load demand and PV power output profile will be modelled with forecasted values, and their profile will be obtained over probability density functions (PDFs). Firstly, a vast quantity of realistic load and PV generation profiles are produced over a day with 15-minute resolution, with a scenario generation method using the Monte Carlo methodology. Afterward, the generated scenarios are reduced to a set of scenarios to represent the span of all generated scenarios. A fully local reactive power regulation strategy is used in this study to evaluate the hosting capacity of the ADN. This proposed method is tested on modified 33-bus and 69-bus distribution test systems by using practical solar generation and load data. The proposed methodology results in the hosting capacity improvement by 20% besides the existing Q-Voltage and PF-Power local voltage control methods, where it has the flexibility to be implemented to any distribution feeder.

Bidirectional machine learning-assisted sensitivity-based stochastic searching approach for groundwater DNAPL source characterization.

In this study, we designed a machine learning-based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input-output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input-output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD-PSO-MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD-PSO-MC inversion outputs was more precise than that obtained using the multichain MCMC approach.

Video velocity measurement: a two-stage flow velocity prediction method based on deep learning

Abstract Due to the uncertainty in output caused by environmental changes, significant discrepancies are expected between the surface flow velocities predicted using deep learning methods and the instantaneous flow velocities. In this paper, a two-stage deep learning flow velocity measurement algorithm is proposed. During the external calibration process, the upper and lower frames of the recorded water flow video are cyclically traversed to acquire predicted flow velocity values using the deep learning velocity measurement algorithm. Meanwhile, the pixel displacement is obtained using the sparse optical flow tracking method and then post-processed to derive the velocity calibration value and pixel calibration value. During the detection process, the deep learning-predicted flow velocity is internally calibrated using the velocity calibration value and the pixel calibration value to adapt to changes in water flows. Compared with the pre-improved algorithm, the method achieves the minimum root mean square error in five different flow velocity videos and maintains high accuracy when the flow velocity changes rapidly. The obtained results are very promising and can help improve the reliability of video flow rate assessment algorithms.

Towards low-carbon power networks: Optimal location and sizing of renewable energy sources and hydrogen storage

This paper proposes a systematic optimization framework to jointly determine the optimal location and sizing decisions of renewables and hydrogen storage in a power network to achieve the transition to low-carbon networks efficiently. We obtain these strategic decisions based on the multi-period alternating current optimal power flow (AC MOPF) problem that jointly analyzes power network, renewable, and hydrogen storage interactions at the operational level by considering the uncertainty of renewable output, seasonality of electricity demand, and electricity prices. We develop a tailored solution approach based on second-order cone programming within a Benders decomposition framework to provide globally optimal solutions. In a test case, we show that the joint integration of renewable sources and hydrogen storage and consideration of the AC MOPF model significantly reduces the operational cost of the power network. In turn, our findings can provide quantitative insights to decision-makers on how to integrate renewable sources and hydrogen storage under different settings of the hydrogen selling price, renewable curtailment cost, emission tax price, and conversion efficiency.

Robust Fractional-Order PI/PD Controllers for a Cascade Control Structure of Servo Systems

In this paper, a cascade control structure is suggested to control servo systems that normally include a servo motor in coupling with two kinds of mechanism elements, a translational or rotational movement. These kinds of systems have high demands for performance in terms of fastest response and no overshoot/oscillation to a ramp function input. The fractional-order proportional integral (FOPI) and proportional derivative (FOPD) controllers are addressed to deal with those control problems due to their flexibility in tuning rules and robustness. The tuning rules are designed in the frequency domain based on the concept of the direct synthesis method and also ensure the robust stability of controlled systems by using the maximum sensitivity function. The M-Δ structure, using multiplicative output uncertainties for both control loops simultaneously, is addressed to justify the robustness of the controlled systems. Simulation studies are considered for two kinds of plants that prove the effectiveness of the proposed method, with good tracking of the ramp function input under the effects of the disturbances. In addition, the robustness of the controlled system is illustrated by a structured singular value (µ) plot in which its value is less than 1 over the frequency range.

Geospatial optimisation of wind and solar energy generation: A framework for optimised resource allocation

Wind and solar power generation profiles exhibit a high degree of power output variability and uncertainty compared to conventional fossil fuel generation plants. However, it is generally accepted that this variability and uncertainty can be mitigated by geographic siting and dispersion of the renewable energy plants, particularly with the view to leverage aggregation effects. In this context, this paper proposes a framework for the geospatial optimisation of wind and solar PV generation for scenarios with a high penetration of wind and solar renewable energy. The proposed optimisation framework represents a probabilistic risk-based approach that seeks to minimise the number of events where high residual load values require ancillary service interventions to maintain power balance. In this approach, the wind and solar resources are categorised in terms of the statistical properties of the associated spatiotemporal wind and solar power profiles for a given set of daily and seasonal Time of Use periods. It is thereby recognised that the resource characteristics and grid impact of wind and solar generation profiles can be interpreted with reference to the daily and seasonal cycles exhibited by the demand profiles, wherein some Time of Use periods are more important than others. The proposed framework is implemented for a number of baseline case studies and optimisation case studies, using wind and solar resource data sets covering South Africa. Overall, it is concluded that this approach can leverage geospatial site optimisation to substantially reduce the risks associated with high residual load events. Furthermore, the proposed framework is highly flexible in that the formulation of the minimum and maximum allocation constraints allows application for real-world scenarios whereby stringent capacity allocation constraints can be applied.

Using Median Point in Keeling Plot to Reduce the Uncertainty of the Isotopic Composition of Evapotranspiration

Abstract The isotopic composition of evapotranspiration δET is a crucial parameter in isotope-based evapotranspiration (ET) partitioning and moisture recycling studies. The Keeling plot method is the most prevalent method to calculate δET, though it contains large extrapolated uncertainties from the least squares regression. Traditional Keeling regression uses the mean point of individual measurements. Here, a modified Keeling plot framework was proposed using the median point of individual measurements. We tested the δET uncertainty using the mean point [σET (mean)] and median point [σET (median)]. Multiple resolutions of input and output data from six independent sites were used to test the performance of the two methods. The σET (mean) would be greater than σET (median) when the mean value of inverse vapor concentration () is greater than the median value of inverse vapor concentration []. When applying the filter of r2 > 0.8, around 70% of σET (mean) was greater than σET (median). This phenomenon might be due to the normality of the vapor concentration Cυ producing the asymmetric distribution of 1/Cυ. The median method could perform significantly better than the mean method when inputting high-resolution measurements (e.g., 1 Hz) and when the water vapor concentration Cυ is relatively low. Compared to the mean method, applying the median method could on average reduce 6.88% of ET partitioning uncertainties and could on average reduce 9.00% of moisture recycling uncertainties. This study provided a new insight of the Keeling plot method and emphasized handling model output uncertainty from multiple perspectives instead of only from input parameters.

Quantitative assessment method of new energy output uncertainty based on the prediction error

With a high percentage of distributed new energy sources connected to the power system, the power grid needs to reserve a larger margin to deal with the uncertainty of renewable energy outputs, leading to an increase in the cost of controlling the margins for the safe operation of the power grid. In order to reduce costs and increase efficiency, a quantitative assessment of new energy output uncertainty is needed. In this paper, a quantitative assessment method of new energy output uncertainty based on the prediction error is proposed, which makes use of a graph database to efficiently obtain massive new energy historical data, uses the clustering in quest (CLIQUE) algorithm to cluster the new energy historical data, and calculates the renewable energy real power confidence interval based on a given new energy power prediction, taking account of the impact of prediction errors caused by the new energy uncertainty and realizing the quantitative description of new energy output uncertainty. Finally, the method is calculated and analyzed together with the actual example data to verify the practical effect of the method.

Piecewise Linear Transformation – Propagating Aleatoric Uncertainty in Neural Networks

Real-world data typically exhibit aleatoric uncertainty which has to be considered during data-driven decision-making to assess the confidence of the decision provided by machine learning models. To propagate aleatoric uncertainty represented by probability distributions (PDs) through neural networks (NNs), both sampling-based and function approximation-based methods have been proposed. However, these methods suffer from significant approximation errors and are not able to accurately represent predictive uncertainty in the NN output. In this paper, we present a novel method, Piecewise Linear Transformation (PLT), for propagating PDs through NNs with piecewise linear activation functions (e.g., ReLU NNs). PLT does not require sampling or specific assumptions about the PDs. Instead, it harnesses the piecewise linear structure of such NNs to determine the propagated PD in the output space. In this way, PLT supports the accurate quantification of predictive uncertainty based on the criterion exactness of the propagated PD. We assess this exactness in theory by showing error bounds for our propagated PD. Further, our experimental evaluation validates that PLT outperforms competing methods on publicly available real-world classification and regression datasets regarding exactness. Thus, the PDs propagated by PLT allow to assess the uncertainty of the provided decisions, offering valuable support.

A dynamic optimal decoupling controller design for a multi-variable system with stability analysis: an algebraic approach

ABSTRACT This study describes the design and implementation of an algebraic approach for a dynamic optimal decoupling controller in a multi-variable liquid-level system. This method aligns with model-matching criteria and the frequency-matching technique. The prime objective of the proposed approach is to create a closed-loop feedback system using a PID controller that aligns with a user-defined linear system model in terms of both system dynamics and static behavioral response. To illustrate robust stability, the study incorporates multiplicative input and output uncertainty. Simulation results verify the efficacy of the proposed decentralized controller, presenting its effectiveness in achieving both set-point accuracy and disturbance attenuation. Furthermore, the study employs disk margin analysis to ascertain safe ranges for gain and phase margin.

Real-time dynamic analysis of EEG Response for Live Indian Classical Vocal Stimulus with Therapeutic Indications

Numerous studies have been conducted on the connection between music and the brain, and it has been established that listening to music directly affects brain activity and stimulation. The potential benefits of music therapy, which uses music as a tool for healing and fostering well-being, have come to light in a number of circumstances. However, there is a gap in understanding the effects of Indian classical music (ICM) on the brain and its therapeutic applications. Yaman and Puria Dhanashree were the two chosen ragas, which share same notes (swaras) and differs in two of their counter notes. The brain responses are captured from five volunteers through 24 channel Electroencephalogram (EEG) cap using a smartphone, which is utilized to allocate electrodes to different regions of the brain. In this work, different automated approaches for identifying brain regions evoked to live ICM stimuli are proposed, considering input and output uncertainties. These approaches are based on automated energy and Mahalanobis distance measurements, and, a region-specific real-time algorithm based on eigen perturbation, which provides a measure to capture the time evolution of brain activity. This identification is relevant in understanding dynamic changes in brain responses during musical experiences providing a more comprehensive perception and processing of ICM in the human brain. Also, significant change in beta band power reduction was observed after music. These approaches can help integrate it into evidence-based music therapy for cognitive, emotional, and psychological conditions. The findings of this study provide evidence indicating ragas activate different brain regions based on listener’s musical knowledge and is a first step for mhealth based applications.

Multi-objective optimization scheduling method considering flexible load integration for distribution network

In response to a series of issues in the distribution network, such as inadequate and inflexible utilization of flexible loads, delayed response to demand participation, and the uncertainty of new energy source output, a differentiated objective-based method for optimizing distribution network operations is proposed. Firstly, flexible loads are categorized, and corresponding mathematical models are established. Secondly, by employing chance-constrained programming to account for the uncertainty in new energy source output, a multi-objective optimization model is developed to reduce distribution network economic costs, decrease network losses, and enhance power supply reliability. Subsequently, an improved NSGA-III algorithm is introduced to address the multi-objective model. Finally, an 11-node distribution network is used as a case study, and three different algorithms are comprehensively compared. This confirms the rationality of the optimized scheduling scheme proposed in this paper.

Document-Level Relation Extraction with Uncertainty Pseudo-Label Selection and Hard-Sample Focal Loss

Relation extraction is a fundamental task in natural language processing that aims to identify structured triple relationships from unstructured text. In recent years, research on relation extraction has gradually advanced from the sentence level to the document level. Most existing document-level relation extraction (DocRE) models are fully supervised and their performance is limited by the dataset quality. However, existing DocRE datasets suffer from annotation omission, making fully supervised models unsuitable for real-world scenarios. To address this issue, we propose the DocRE method based on uncertainty pseudo-label selection. This method first trains a teacher model to annotate pseudo-labels for a dataset with incomplete annotations, trains a student model on the dataset with annotated pseudo-labels, and uses the trained student model to predict relations on the test set. To mitigate the confirmation bias problem in pseudo-label methods, we performed adversarial training on the teacher model and calculated the uncertainty of the model output to supervise the generation of pseudo-labels. In addition, to address the hard-easy sample imbalance problem, we propose an adaptive hard-sample focal loss. This loss can guide the model to reduce attention to easy-to-classify samples and outliers and to pay more attention to hard-to-classify samples. We conducted experiments on two public datasets, and the results proved the effectiveness of our method.

Multi-scenario flexibility assessment of power systems considering renewable energy output uncertainty

The widespread adoption of renewable energy sources presents a significant challenge to the flexibility of power system. To assess the flexibility of the power system in scenarios with uncertain renewable energy output, it is crucial to quantify it quantitatively. This evaluation plays a vital role in planning flexible regulatory resources and dispatching resources for both the energy source and load. This study introduces a novel flexibility assessment model tailored for power grids with high renewable energy penetration, specifically addressing uncertainty associated with wind and PV. By analyzing the impact of wind and PV uncertainty on system flexibility, the paper proposes an improved cohesive hierarchical cluster analysis method, incorporating reliability considerations based on the Davies-Bouldin classification reliability index. Additionally, the study develops models for flexibility resources and demands within high renewable energy power systems, along with quantitative assessment indicators across three key aspects. Through a structured flexibility assessment process accounting for wind and PV uncertainty, the effectiveness of the proposed approach is validated using real-world data from a renewable energy power grid in Shandong province. A set of typical renewable energy output scenarios with uncertainty is constructed using the improved hierarchical cluster analysis method. The study then analyses the impact of different wind and PV penetration rates and the proportion of energy storage units on system flexibility by the flexibility assessment model to validate the proposed method's effectiveness.

MELCOR – DAKOTA coupling for uncertainty analyses in the SNAP environment/architecture

Uncertainty estimation to assess figures of merit characterizing evolution of a severe accident transient is a topic of current investigation in development of best-estimate plus uncertainty methodology. The probabilistic method to propagate input uncertainty is one of the methodologies used to develop Uncertainty Analyses (UAs). Using this methodology, UAs are performed by sampling probability distributions that describe the range of possible values that computer simulation model inputs can have. For each sample (or realization) of a set of uncertain input parameters, a computer simulation is performed. From the range of code simulation results obtained for each input realization, a distribution of code results is obtained. In this process, the distribution of input uncertainties is propagated to obtain a distribution of possible code results (i.e., the code output uncertainty). This probabilistic methodology is facilitated using Uncertainty Tools (UTs), which can be coupled with the accident analysis computer code to perform an UA. One of the UTs currently available is DAKOTA, developed by Sandia National Laboratories. DAKOTA is also provided as a SNAP plug-in. SNAP is a graphical user interface designed to support the use of USNRC codes (MELCOR, TRACE, etc). This paper is entirely derived from the NUREG/IA-532 issued by USNRC in April 2023 (Mascari et al., 2023) and has as a major target to summarize the main needs of UA in severe accident, the main element of the probabilistic method to propagate input uncertainty, and the workflow within SNAP to assist other interested analysts with their applications given they are members of the USNRC Cooperative Severe Accident Research Program (CSARP).

Available Transfer Capability Assessment of Multiarea Power Systems with Conditional Generative Adversarial Network

Available transfer capability (ATC) is an important measurement index to evaluate the security margin of interconnected power grids and serve as a reference for the transmission right transaction. In modern power systems, ATC is affected by the transmission network topology, renewable power output uncertainty, and load demand uncertainty. Traditional works usually model the power source-load uncertainty by using robust optimization, interval optimization, or chance-constraint optimization, which cannot fully reflect the probabilistic distribution of the daily source-load uncertainty. This paper proposes an ATC assessment methodology based on the typical stochastic scenarios of renewable output and load demand of multiarea power systems. Furthermore, the conditional generative adversarial network (CGAN) algorithm is adopted to generate and select representative scenario sets based on historical raw data, which can fully reflect the usual operating condition of a system with high renewable energy penetration. The scenario set that is fed into the ATC assessment model can fully characterize the impact of source-load uncertainty on daily ATC. Finally, the proposed method is verified by a modified three-area IEEE 9-bus system and a real-world provincial power system.

Multi-objective calibration and uncertainty analysis for the event-based modelling of flash floods

ABSTRACT This study investigates the best approach to calibrate an event-based conceptual Hydrologiska Byråns Vattenbalansavdelning (HBV) model, comparing different trials of single-objective, single-event multi-objective (SEMO), and multi-event-multi-objective (MEMO) model calibrations using root mean squared error (RMSE), Nash-Sutcliffe model efficiency coefficient (NSE), and Bias as objective functions. Model performance was validated for several peak events via 90% confidence interval (CI)-based output uncertainty quantification of relative error of discharges. Multi-objective optimization yielded more accurate and robust solutions compared to single-objective calibrations. Ensembles of Pareto solutions from the multi-objective calibrations better characterized the flood peaks within the uncertainty intervals. MEMO calibration exhibited lower uncertainties and better prediction of peak events versus SEMO calibration. Moreover, the MEMO_6D (six-dimensional) approach outperformed the SEMO_3D and MEMO_3D in capturing the larger peak events. This study suggests that the MEMO_6D is the best approach for predicting large flood events with lower model output uncertainties when the calibration is performed with a better combination of peak events.

Global sensitivity analysis for degraded braided composite with interval process

Global sensitivity analysis has predominantly focused on examining the effect of time-invariant parameters on the mechanical properties of fiber-reinforced composites, while ignoring degradation. However, fiber-reinforced composites are subject to degradation, which means that the physical system is dynamic. It is important to consider this dynamic behavior in sensitivity analysis. This paper presents a set of sensitivity indices based on the interval method to measure the influence of the time-invariant and time-variant parameters on the synthetic uncertainty of output in global sensitivity analysis for 2D triaxially braided composites (2DTBCs) considering degradation. To achieve this purpose, we represent time-variant uncertain parameter using an interval process and describe them with multiple uncorrelated interval variables using the interval Karhunen-Loève explansion method. We then introduce a two-dimensional interval process and similarity degree to define a new sensitivity index for time-invariant uncertain parameters. For time-variant uncertain parameter, a novel sensitivity index combining multi-dimensional interval process and similarity degree is proposed which considers the synthetic influence of the group of multiple uncorrelated interval variables. Additionally, an efficient sampling-based method is presented to estimate the global sensitivity analysis indices using the Monte Carlo method and Newton-Cotes formula. Finally, the feasibility and potential benefits of the proposed sensitivity indices are demonstrated by applying them to a 2DTBC made of carbon fiber reinforced polyether ether ketone with thermal ageing consideration.

Interactive scheduling optimization of regional multi-agent integrated energy systems considering uncertainties based on game theory

With the increasing number of integrated energy system (IES) construction, a multi-agent system group composed of multiple IESs would be formed in a certain region. Moreover, complex uncertainties gradually existed in the IES which affect the system optimal situation and optimization results. In order to take full use of each agent's advantages and improve the performance of the whole region under uncertainty, this paper focuses on the multiple energy types' interaction of multi-agent IESs within the region to realize the stable operation, economic and environmental improvement of each agent and the whole region. To this aim, a multi-objective multiple energy types' multi-agent interactive optimization model considering energy demand and renewable energy output uncertainties was built. The model was based on Nash bargaining cooperative game theory and took economy, flexibility and carbon emission as objectives. Moreover, energy interaction scheduling and its corresponding price can be optimized through the model. The results of non-cooperative operation mode without interaction and cooperative operation mode with interaction were compared to analyze the superiority of interaction from the cost, carbon emission and flexibility aspects. The overall regional carbon emission and the economic cost has been reduced by 13.84% and 9.94%, for each IES, the carbon emission and economic cost could reduce by up to 41.5% and 44.5%. Moreover, the flexibility of the IES was correspondingly increased by nearly 47%. These results denoted that after multi-agent interaction, not only the overall region's energy, economic and environmental performance are improved, but also that of each agent are significantly improved. In addition, different energy types among multiple agents could be effectively used and regional joint energy storage is realized, improving the region flexibility level and resilience.

Capacity sizing method of virtual power plants based on game theory

AbstractIn the context of a low‐carbon economy, considering the output uncertainties of the renewable energy sources and the fluctuation of electrical price, the cost–benefit analysis is proposed for multi‐investor virtual power plant (VPP) under different risk preferences, and multi‐investor VPP capacity sizing problem is researched. First, the structural organization and flexible regulation characteristics of multi‐investor VPPs are analyzed. Second, integrated model and cost–benefit analysis indexes of VPP are built. Third, an optimal capacity sizing model of multi‐investor VPP is established, aiming at income maximization. Game theory is used to configure the distributed generators in the VPP under various cooperative modes and noncooperative modes of multiple investors. Fourth, according to the installed proportion of each distributed generator and the risk preference coefficient of each investor, the income allocation correction model based on the improved Shapley value method is proposed to stabilize the optimal VPP alliance. Finally, the demonstration project in the animation industry park of Sino‐Singapore Tianjin Eco‐City is employed as representative scenarios, which is used to validate the effectiveness of the proposed model. The results prove that the method proposed in this paper can guide knowledge for the investors with different risk preferences when planning the optimal capacity of multiple distributed generators in the VPP.