Energy Uncertainty Research Articles

Simplified Approach for Wind Uncertainty Cost Functions using a Mixture of Uniform Probability Distribution

Wind energy generation is an individual source of energy considered in renewable energy resources. It is completely dependent on the natural process of air blown in the area or past forecasting of air blown data. It is considered an uncertain source of energy and less reliable in the context of real-time energy provisions. To make this wind energy more reliable and consistent, we are introducing a simplified approach for wind uncertainty cost functions based on uniform probability distributions and its evaluation for usage. We have developed analytical mathematics cost functions based on several assumptions and they are constructed using Weibull and Rayleigh probability distributions. The proposed method produces the required results to make this energy reliable and consistent with the distribution networks. Computing time and complexity are less as compared to the other methods to minimize the uncertainty of wind energy.

Chance-constrained co-optimization of peer-to-peer energy trading and distribution network operations

Peer-to-Peer (P2P) energy markets enable participants to trade locally produced electrical energy at a mutually agreed-upon price. Distributed Energy Resources (DERs) and flexible loads are fundamental components of P2P energy markets, facilitating the market participants to supply or consume energy in accordance with trading agreements. Consequently, it is vital to account for the stochastic nature of DERs and load demand while designing the P2P energy trading model in order to attain optimal operation of P2P energy markets and secure operation of the distribution network. The scenario-based and robust optimization techniques commonly used to characterize uncertainty suffer from data requirement, computational burden, and solution conservatism standpoints. This paper, therefore, proposes a chance-constrained model for P2P energy trading considering renewable energy uncertainty and distribution network constraints. The uncertain behaviour of renewable generation resources is modelled using chance constraints and integrated with the decision-making process of the P2P energy market and distribution network operation. The chance-constrained P2P energy trading problem is reformulated as a deterministic equivalent problem that can be solved by readily available commercial solvers. The ex-ante and ex-post-performance of the proposed chance-constrained formulation is evaluated on a 15-bus radial distribution network, while the scalability of the proposed formulation is demonstrated on modified IEEE 33-bus and 69-bus test networks. The results showcase the effectiveness of the proposed chance-constrained model in handling the uncertainty and respecting the network constraints while deriving the P2P energy trading outcomes.

A novel design strategy of track‐based asymmetric nonlinear energy sink for seismic response mitigation of structures

AbstractMass dampers, whether linear or nonlinear, rely on resonance with the structure to achieve optimal control performance. However, linear mass dampers require frequency tuning, while nonlinear mass dampers are sensitive to input energy levels, rendering both inadequate for control problems that involve frequency and energy uncertainties. To address this issue, the track asymmetric nonlinear energy sink (TANES) has been developed as a robust mass damper against frequency and energy changes. In this study, a novel design strategy consisting of physical and parameter design was proposed for TANESs. First, TANESs with inverted tracks as the auxiliary mass were proposed, resulting in a significant reduction in the dimensions and weight of the device. The new physical design was then realized, and the mathematical descriptions of the TANES system were validated through experiments on a two‐story frame structure. Subsequently, a parameter design method was proposed to match the frequency variation pattern of the TANES with the given structural and load conditions. Following the design procedure, three TANESs with markedly different track shapes were obtained and compared with existing mass dampers under different types of excitations. Results showed that the frequency responses of the TANES systems subjected to harmonic ground excitations shared great similarity with those of a well‐tuned TMD system at small‐to‐moderate energy levels. As the energy level increased, nonlinear responses such as strongly modulated responses were observed in the TANES systems with decrease structural frequencies, which significantly reduced the resonant peak in the frequency responses. The frequency responses of the TANES systems were consistent with the design objective and could be used to quantitatively predict the robustness performance of the devices under impulsive and seismic excitations. With the reduced dimensions and weight resulting from the inverted‐track configuration and the robustness performance in line with common structural and load conditions, the proposed design strategy of TANESs demonstrated great potential in the seismic response mitigation of engineering structures.

A Distributionally Robust Optimization Strategy for a Wind–Photovoltaic Thermal Storage Power System Considering Deep Peak Load Balancing of Thermal Power Units

With the continuous expansion of grid-connected wind, photovoltaic, and other renewable energy sources, their volatility and uncertainty pose significant challenges to system peak regulation. To enhance the system’s peak-load management and the integration of wind (WD) and photovoltaic (PV) power, this paper introduces a distributionally robust optimization scheduling strategy for a WD–PV thermal storage power system incorporating deep peak shaving. Firstly, a detailed peak shaving process model is developed for thermal power units, alongside a multi-energy coupling model for WD–PV thermal storage that accounts for carbon emissions. Secondly, to address the variability and uncertainty of WD–PV outputs, a data-driven, distributionally robust optimization scheduling model is formulated utilizing 1-norm and ∞-norm constrained scenario probability distribution fuzzy sets. Lastly, the model is solved iteratively through the column and constraint generation algorithm (C&CG). The outcomes demonstrate that the proposed strategy not only enhances the system’s peak-load handling and WD–PV integration but also boosts its economic efficiency and reduces the carbon emissions of the system, achieving a balance between model economy and system robustness.

Energy management of multi-microgrid system with renewable energy using data-driven distributionally robust optimization

ABSTRACT By clustering multiple microgrids (MGs), a multi-microgrid (MMG) system plays a significant role in integrating a large amount of renewable generation. However, the large-scale utilization of renewable energy also brings uncertainties to MMG energy management. In this work, a novel comprehensive bi-level MMG energy management model considering uncertainties of renewable energy is first developed which includes unit commitment (UC) problem and other models in the lower MG level. Then considering the non-convexity of the bi-level problem, a decomposition method called analytical target cascading (ATC) is employed to deal with it by decentralization. With regard to the energy management of each individual MG, a two-stage distributionally robust model is developed which describes the uncertainties from probability distribution of renewable generation with a metric-based ambiguity set. Moreover, an efficient solution scheme based on column and constraint generation (CCG) algorithm and a decomposition method without duality is designed to handle the MG energy management problem. Finally, we implement extensive experiments to corroborate the effectiveness of the proposed approach. Particularly, the optimal solution from the proposed method can attain 2.98% less cost compared with that from robust optimization (RO) method and achieve 86.17% less energy trading amount than that in independent mode.

Metal and energy price uncertainties and the global economy

We construct novel monthly measures of energy and metal price uncertainty based on the one-year-ahead price forecast dispersion for twenty commodities. Using a simple VAR model, we show both metal and energy price uncertainty shocks are contractionary for the world economy, and these results are largely robust to a battery of alternative specifications. However, our results highlight the differences between metal and energy price uncertainties, both in terms of their propagation channels, as well as the driving forces behind them. Counterfactual analysis reveals that metal price uncertainty has a mainly direct impact on global economic activity while the impact of energy price uncertainty is indirectly mediated through global financial and economic uncertainties. Variance decomposition shows fluctuations of both metal and energy price uncertainties are mainly self-driven, however global financial uncertainty plays a significant role in driving metal price uncertainty in the short run while global economic activity uncertainty plays a significant role in driving energy price uncertainty in the medium to long run.

Robust generation expansion planning in power grids under renewable energy penetration via honey badger algorithm

Robust reliability Generation Expansion Planning (GEP) turns out to be a crucial step for an efficient energy management system in a modern power grid, especially under renewable energy employment. The integration of all such components in a GEP model makes it a large-scale, nonlinear, and mixed-variable mathematical modeling problem. In this paper, the presence of wind energy uncertainty is analyzed. Both long and short-term uncertainties are incorporated into the proposed GEP model. The first step concerns the impact of long-term wind uncertainties through the annual variations of the capacity credit of two real sites in Egypt at Zafaranh and Shark El-ouinate. The second step deals with the short-term uncertainties of each wind site. The wind speed uncertainty of each wind site is modeled by probability distribution function. Then, wind power is estimated from the wind power curve for each wind site and Monte-Carlo Simulation is performed. Fast Gas Turbine and/or Pump Hydro Storage are incorporated to cope with short-term uncertainties. Sensitivity analysis is implemented for 3, 6, and 12 stages as short and long planning horizons to minimize the total costs with wind energy penetration and emission reduction over planning horizons. Also, a novel Honey Badger Algorithm (HBA) with model modifications such as Virtual Mapping Procedure, Penalty Factor Approach, and the Modified of Intelligent Initial Population Generation is utilized for solving the proposed GEP problem. The obtained results are compared with other algorithms to ensure the superior performance of the proposed HBA. According to the results of the applicable test systems, the proposed HBA performs better than the others, with percentage reductions over CSA, AO, BES, and PSO ranging up to 4.2, 2.72, 2.7, and 3.4%, respectively.

Two-stage robust optimization of unified power quality conditioner (UPQC) siting and sizing in active distribution networks considering uncertainty of loads and renewable generators

This paper proposes a robust optimization siting and sizing strategy for the unified power quality conditioner (UPQC) in the active distribution network (ADN) integrated with renewable energy generators. The optimization objectives including investment cost, line loss, and voltage deviation are integrated into an overall cost for both the planning and operating stages. A novel UPQC equivalent power injection model is proposed based on the auxiliary branch method. A set of linear and second-order conic (SOC) constraints are employed to accurately describe the steady-state operation of UPQC. An improved branch current flow model is developed to incorporate radial distribution networks with UPQCs. The UPQC siting and sizing planning is formulated as a mixed integer second-order conic programming (MISOCP) problem. Accounting for the uncertainty in loads and distributed generators, a two-stage robust optimization model is established to address worst-case operational scenarios. A solving strategy is developed based on the strong duality theory and the column-and-constraint generation (C&CG) algorithm, and then commercial solvers can solve the problem accurately and efficiently. Case studies on an IEEE 33-node distribution network demonstrate this strategy's robustness in dealing with loads and renewable energy uncertainties, making it applicable across different UPQC topologies and operation modes. The proposed method has superior performance over the representative meta-heuristic approaches in terms of global optimality as well as an over 7.5 times faster computation speed. This work has significance in enhancing the quality and efficiency of modern power systems highly integrated with renewable energy.

How does trade policy uncertainty affect firms’ pollution emissions? Theory and evidence from China

AbstractThe literature investigates trade-environment relationship at the firm level, but does not focus on the environmental effect of trade policy uncertainty. In the context of de-globalization and Sino-US trade friction, trade policy uncertainty significantly increases. How does trade policy uncertainty affect firms’ pollution emissions? In this study, we incorporate energy, pollution, and trade policy uncertainty into Melitz’s (2003) framework and construct a theoretical model to reveal the relationship between trade policy uncertainty and pollution emissions. Then, we employ the event that the USA granted permanent normal trade relationship to China as a quasi natural experiment. We use difference-in-difference-in-difference model and the data of Chinese manufacturing firms for empirical analysis. Our results indicate that the decrease in trade policy uncertainty reduces emission intensity of exporting firms, but has no significant impact on emission levels. Given that these firms do not aggravate emission levels under the condition of expanding output scale, we conclude that the decrease in trade policy uncertainty can improve environmental performance. Mechanism analysis shows an interesting finding that the decrease in trade policy uncertainty reduces emission intensity mainly by improving energy efficiency rather than improving abatement technology and optimizing energy structure. In addition, pollution reductions mainly occur in pollution-intensive and capital-intensive industries as well as coastal regions. Altogether, this study contributes to the literature on trade-environment relationship and trade policy uncertainty.

Integrated energy system model with multi-time scale optimal dispatch method based on a demand response mechanism

A flexible integrated energy system (IES) can curb the supply–demand imbalances caused by renewable energy and load uncertainty. This study proposes an IES model based on a demand response mechanism and a multi-time-scale optimization scheduling method with the aim of fully utilizing its flexibility. Specifically, the demand response strategy of electric heating/cold complementary substitution and horizontal time shifting was introduced at different stages of dispatch to enhance the flexible dispatching capability of the IES. Furthermore, the contribution of thermal inertia of pipes in resisting supply and demand uncertainties and reducing thermoelectric coupling was considered. On this basis, the time resolution was determined according to the adjustment rates of the different components, and a multi-timescale optimal scheduling method was developed. The quantum sparrow search algorithm was applied to solve the proposed model, and the optimal scheduling strategy of the system was obtained. Results revealed that, from an environmental perspective, the amount of wind and light abandonment was reduced by 89.71%, thereby increasing the penetration of renewable energy and promoting carbon neutrality. From an economic perspective, the daily operating cost decreased by 1380 yuan/day, effectively improving the operational costs of the IES. From a reliability perspective, thermal inertia of networks reduced the intensity of thermoelectric coupling and increased the flexibility of IES dispatching, curbing the uncertainties in renewable energy and loads during system operation.

Multi-Indicator Fused Resilience Assessment of Power Grids Considering Wind-Photovoltaic Output Uncertainty during Typhoon Disasters

Extreme weather events such as typhoons pose a serious threat to the safe operation of power grids. In the field of power system resilience assessment during typhoon disasters, a parametric typhoon wind field model combined with actual historical meteorological data has not been well adopted, and the conventional renewable energy uncertainty modeling methods are not suitable for typhoon disaster periods. In this paper, a multi-indicator fused resilience assessment strategy considering wind-photovoltaic uncertainty and component failure during typhoon disasters is proposed. Firstly, based on the actual historical meteorological data of typhoons, an uncertainty model of typhoon wind speed is established by a rolling non-parametric Dirichlet process Gaussian mixture model. Then, a spatial–temporal contingency set is constructed by considering the best-fit wind field model and stress–strength interference model for failure probability of transmission lines. On this basis, a holistic resilience assessment framework is established from the perspectives of priority, robustness, rapidity, and sustainability, and the entropy weight method combined with the technology for order preference by similarity to an ideal solution is leveraged to obtain the comprehensive resilience indicator. Finally, numerical studies are performed on the IEEE-30 bus test system to identify vulnerable lines and improve system resilience during typhoon disasters.

Stochastic programming based coordinated expansion planning of generation, transmission, demand side resources, and energy storage considering the DC transmission system

With the increasing penetration of wind and solar energies, the accompanying uncertainty that propagates in the system places higher requirements on the expansion planning of power systems. A source-grid-load-storage coordinated expansion planning model based on stochastic programming was proposed to suppress the impact of wind and solar energy fluctuations. Multiple types of system components, including demand response service entities, converter stations, DC transmission systems, cascade hydropower stations, and other traditional components, have been extensively modeled. Moreover, energy storage systems are considered to improve the accommodation level of renewable energy and alleviate the influence of intermittence. Demand-response service entities from the load side are used to reduce and move the demand during peak load periods. The uncertainties in wind, solar energy, and loads were simulated using stochastic programming. Finally, the effectiveness of the proposed model is verified through numerical simulations.

Where Did the Amaterasu Particle Come From?

The Telescope Array Collaboration recently reported the detection of a cosmic-ray particle, “Amaterasu,” with an extremely high energy of 2.4 × 1020 eV. Here we investigate its probable charge and the locus of its production. Interpreted as a primary iron nucleus or slightly stripped fragment, the event fits well within the existing paradigm for UHECR composition and spectrum. Using the most up-to-date modeling of the Galactic magnetic field strength and structure, and taking into account uncertainties, we identify the likely volume from which it originated. We estimate a localization uncertainty on the source direction of 6.6% of 4π or 2726 deg2. The uncertainty of magnetic deflections and the experimental energy uncertainties contribute about equally to the localization uncertainty. The maximum source distance is 8–50 Mpc, with the range reflecting the uncertainty on the energy assignment. We provide sky maps showing the localization region of the event and superimpose the location of galaxies of different types. There are no candidate sources among powerful radio galaxies. An origin in active galactic nuclei or star-forming galaxies is unlikely but cannot be completely ruled out without a more precise energy determination. The most straightforward option is that Amaterasu was created in a transient event in an otherwise undistinguished galaxy.

The energy management strategy of a loop microgrid with wind energy prediction and energy storage system day-ahead optimization

Microgrid has been extensively applied in the modern power system as a supplementary mode for the distributed energy resources. The microgrid with wind energy is usually vulnerable to the intermittence and uncertainty of the wind energy. To increase the robustness of the microgrid, the energy storage system (ESS) is necessary to compensate the power imbalance between the power supply and the load. To further maximize the economic efficiency of the system, the system level control for the microgrid is desired to be optimized when it is integrated with the utility grid. Aiming at the aforementioned problem, this paper comprehensively analyzes the power flow of a typical loop microgrid. A transformer-based wind power prediction (WPP) algorithm is proposed and compared with recurrent neural networks algorithm. With the historical weather data, it can accurately predict the 24 h average wind energy. Based on the predicted wind energy and the time-of-use (TOU) electricity price, a day-ahead daily cycling profile of the ESS with particle swarm optimization algorithm is introduced. It comprehensively considers the system capacity constraints and the battery degree of health. The functionality of the proposed energy management strategy is validated from three levels. First, WPP is conducted with the proposed algorithm and the true historical weather data. It has validated the accuracy of the transformer algorithm in prediction of the hourly level wind energy. Second, with the predicted wind energy, a case study is given to validate the day-ahead daily cycling profile. A typical 1 MVA microgrid is utilized as the simulation model to validate performance of the daily cycling optimization algorithm. The case study results show that the ESS daily cycling can effectively reduce the daily energy expense and help to shave the peak power demand in the grid.

A novel power control scheme for distributed DFIG based on cooperation of hybrid energy storage system and grid-side converter

Due to the uncertainty of wind energy, the wind power is difficult to be dispatched and may cause the voltage fluctuations for distributed network. Therefore, a novel power control scheme is proposed to manage the output power of the distributed doubly-fed induction generator (DFIG) by cooperating the hybrid energy storage system (HESS). In the proposed scheme, the grid-side converter of DFIG is controlled to manage overall output power of the DFIG/HESS hybrid system in accordance to the power dispatching command. The HESS is utilized to deal with the power difference between DFIG generation power and the power dispatching command. The HESS is embedded in the DC-link bus of DFIG and is composed of superconducting magnetic energy storage and batteries. Additionally, in order to avoid HESS from overcharging and over-discharging, the pitch angle control and power dispatching command are adjusted by considering the state of charge (SOC) of HESS. Finally, the simulation model of distributed DFIG and HESS is built on the real-time digital simulation (RTDS) platform, and the simulation results validate the effectiveness and reliability of the proposed power control scheme.

Analysis of Extreme Random Uncertainty in Energy and Environment Systems for Coal-Dependent City by a Copula-Based Interval Cost–Benefit Stochastic Approach

Extreme random events will interfere with the inversion analysis of energy and environment systems (EES) and make the planning schemes unreliable. A Copula-based interval cost–benefit stochastic programming (CICS) is proposed to deal with extreme random uncertainties. Taking Yulin city as an example, there are nine constraint-violation scenarios and six coal-reduction scenarios are designed. The results disclose that (i) both system cost and pollutant emission would decrease as the industrial energy supply constraint-violation level increases; (ii) when the primary and secondary energy output increases by 9% and 13%, respectively, and industrial coal supply decreases by 40%, the coal-dependent index of the system would be the lowest, and the corresponding system profitability could reach [29.3, 53.0] %; (iii) compared with the traditional chance-constrained programming, Copula-based stochastic programming can reflect more uncertain information and achieve a higher marginal net present value rate. Overall, the CICS-EES model offers a novel approach to gain insight into the tradeoff between system reliability and profitability.

Time–Energy Uncertainty Relation in Nonrelativistic Quantum Mechanics

The time–energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm and by Margolus and Levitin and evaluate their validity using a minimal quantum toy model composed of a single qubit inside an external magnetic field. We show that the ℓ1 norm of energy coherence C is invariant with respect to the unitary evolution of the quantum state. Thus, the ℓ1 norm of energy coherence C of an initial quantum state is useful for the classification of the ability of quantum observables to change in time or the ability of the quantum state to evolve into an orthogonal state. In the single-qubit toy model, for quantum states with the submaximal ℓ1 norm of energy coherence, C<1, the Mandelstam–Tamm and Margolus–Levitin relations generate instances of infinite “time uncertainty” that is devoid of physical meaning. Only for quantum states with the maximal ℓ1 norm of energy coherence, C=1, the Mandelstam–Tamm and Margolus–Levitin relations avoid infinite “time uncertainty”, but they both reduce to a strict equality that expresses the Einstein–Planck relation between energy and frequency. The presented results elucidate the fact that the time in the Schrödinger equation is a scalar variable that commutes with the quantum Hamiltonian and is not subject to statistical variance.

Multi-objective station-network synergy planning for regional integrated energy system considering energy cascade utilization and uncertainty

Regional integrated energy system (RIES) is conductive to integrating distributed renewable energy and represent a crucial form for constructing low-carbon energy systems in future cities. Addressing key issues in RIES planning such as station-network synergy optimization, uncertainty optimization, and multi-objective optimization, this paper proposes a synergy planning framework for RIES considering energy cascading utilization and uncertainty. Firstly, a dual-layer synergy planning model is established. In the upper layer, it resolves the station-network layout optimization problem considering user distribution and load complementarity. An improved P-median model is introduced to optimize the site selection and network layout of energy stations. In the lower layer, a two-stage stochastic programming model is proposed to address the configuration optimization problem for energy stations considering uncertainty. To enhance the energy utilization efficiency of RIES, exergy efficiency is incorporated into the multi-objective optimization model. A combination of ε-constrant methods and the TOPSIS method is employed for multi-objective solving and decision-making. The proposed models and methods are validated through a case study. The analysis of seven comparative experiments indicates that there is an optimal number of energy stations for the overall economic efficiency in RIES station-network layout optimization. Compared to single-objective optimization, multi-objective optimization considering both economic and exergy efficiency has advantages in improving energy utilization efficiency and reducing carbon emissions. When the load complementarity between multiple regions is higher, the interconnection gains between energy stations are greater. The research framework proposed in this study can provide essential references for designers of urban RIES.

Spillover Effects between Crude Oil Returns and Uncertainty: New Evidence from Time-Frequency Domain Approaches

This paper examines the extent to which uncertainty in the energy market, the financial market, the commodity market, the economic policy, and the geopolitical events affect crude oil returns. To consider the complex properties of time series, such as nonlinearity, temporal variability, and unit roots, we adopt a two-instrument technique in the time–frequency domain that employs the DCC-GARCH (1.1) model and the Granger causality test in the frequency domain. This allows us to estimate the dynamic transmission of uncertainty from various sources to the oil market in the time and frequency domains. Significant dynamic conditional correlations over time are found between oil returns—commodity uncertainty, oil returns—equity market uncertainty, and oil returns—energy uncertainty. Furthermore, at each frequency, the empirical results demonstrate a significant spillover effect from the commodity, energy, and financial markets to the oil market. Additionally, we discover that sources with high persistence volatility (such as commodities, energy, and financial markets) have more interactions with the oil market than sources with low persistence volatility (economic policy and geopolitical risk events). Our findings have significant ramifications for boosting investor trust in risky energy assets.

Verification labels for rovibronic quantum-state energy uncertainties

Transition wavenumbers contained in line-by-line rovibronic databases can be compromised by errors of various nature. When left undetected, these errors may result in incorrect quantum-state energies, potentially compromising a large number of derived spectroscopic data. Spectroscopic networks treat the complete set of line-by-line spectroscopic data as a large graph, and through a least-squares refinement the measured line positions are converted into empirical quantum-state energies. Spectroscopic networks also offer a highly useful framework to develop mathematical tools helping to identify possible errors and conflicts within the dataset. For example, wavenumber errors can be detected by checking for violations of the law of energy conservation. This paper describes a new graph-theory tool, which results in so-called verification labels for the quantum states. Verification labels help to express the vulnerability of a calculated empirical energy value and its uncertainty against possible wavenumber errors, providing complementary information to simple statistical uncertainties.