Copula-Based Monte Carlo Scenarios Generation Method for STOPF Problem

This paper introduces a Monte Carlo scenario generation method based on copula theory for the stochastic optimal power flow （STOPF） problem with wind power. By using copula theory, the scenarios are simulated from multivariable joint distribution but only from their dependency matrix. Hence, the scenarios generated by proposed method can contain flail statistical information of multivariate. Here, the details of simu- lating scenarios for multi-wind-farm are explained with four steps： determine margin of one wind farm, fit the copulas, choose optimal copulas and simulate scenarios by Mote Carlo. Moreover, the producing process of scenarios is demonstrated by two adjacent actual wind farms in China. With the scenarios, the STOPF is con- verted into the same amount deterministic sub OPF models which can be solved by available technology per- fectly. Results using copula theory are compared against results from history samples based on two designs： IEEE 30-bus and IEEE 118-bus systems. The comparison results prove the accuracy of the proposed methodology.

Stochastic optimization based on a novel scenario generation method for midstream and downstream petrochemical supply chain

A two-stage mixed integer linear programming model(MILP)incorporating a novel method of stochastic scenario generation was proposed in order to optimize the economic performance of the synergistic combination of midstream and downstream petrochemical supply chain.The uncertainty nature of the problem intrigued the parameter estimation,which was conducted through discretizing the assumed probability distribution of the stochastic parameters.The modeling framework was adapted into a real-world scale of petrochemical enterprise and fed into optimization computations.Comparisons between the deterministic model and stochastic model were discussed,and the influences of the cost components on the overall profit were analyzed.The computational results demonstrated the rationality of using reasonable numbers of scenarios to approximate the stochastic optimization problem.

Distributed Robust Optimal Dispatch for the Microgrid Considering Output Correlation between Wind and Photovoltaic

As an effective carrier of integrated clean energy,the microgrid has attracted wide attention.The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids.This paper proposes an optimization scheme based on the distributionally robust optimization(DRO)model for a microgrid considering solar-wind correlation.Firstly,scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function;then the generated scenario results are reduced by K-means clustering;finally,the probability confidence interval of scenario distribution is constrained by 1-norm and∞-norm.The model is solved by a column-and-constraint generation algorithm.Experimental studies are conducted on a microgrid system in Jiangsu,China and the obtained scheduling solution turned out to be superior under wind and solar power uncertainties,which verifies the effectiveness of the proposed DRO model.

Optimal Operation Strategy Analysis with Scenario Generation Method Based on Principal Component Analysis,Density Canopy,and K-medoids for Integrated Energy Systems

The operation of integrated energy systems(IESs)is confronted with great challenges for increasing penetration rate of renewable energy and growing complexity of energy forms.Scenario generation is one of ordinary methods to alleviate the system uncertainties by extracting several typical scenarios to represent the original high-dimensional data.This paper proposes a novel representative scenario generation method based on the feature extraction of panel data.The original high-dimensional data are represented by an aggregated indicator matrix using principal component analysis to preserve temporal variation.Then,the aggregated indicator matrix is clustered by an algorithm combining density canopy and K-medoids.Together with the proposed scenario generation method,an optimal operation model of IES is established,where the objective is to minimize the annual operation costs considering carbon trading cost.Finally,case studies based on the data of Aachen,Germany in 2019 are performed.The results indicate that the adjusted rand index(ARI)and silhouette coefficient(SC)of the proposed method are 0.6153 and 0.6770,respectively,both higher than the traditional methods,namely K-medoids,K-means++,and density-based spatial clustering of applications with noise(DBSCAN),which means the proposed method has better accuracy.The error between optimal operation results of the IES obtained by the proposed method and all-year time series benchmark value is 0.1%,while the calculation time is reduced from 11029 s to 188 s,which verifies that the proposed method can be used to optimize operation strategy of IES with high efficiency without loss of accuracy.

SceGAN:A method for generating autonomous vehicle cut-in scenarios on highways based on deep learning

With the increasing level of automation of autonomous vehicles,it is important to conduct comprehensive and extensive testing before releasing autonomous vehicles into the market.Traditional public road and closed-field testing failed to meet the requirements of high testing efficiency and scenario coverage.Therefore,scenario-based autonomous vehicle simulation testing has emerged.Many scenarios form the basis of simulation testing.Generating additional scenarios from an existing scenario library is a significant problem.Taking the scenarios of a proceeding vehicle cutting into an adjacent lane on highways as an example,based on an autoencoder and a generative adversarial network(GAN),a method that combines Transformer to capture the features of a long-time series,called SceGAN,is proposed to model and generate scenarios of autonomous vehicles on highways.An evaluation system is established to analyze the reliability of SceGAN using discriminative and predictive scores and further evaluate the effect of scenario generation in terms of similarity and coverage.Experiments showed that compared with TimeGAN and AEGAN,SceGAN is superior in data fidelity and availability,and their similarity increased by 27.22%and 21.39%,respectively.The coverage increased from 79.84%to 93.98%as generated scenarios increased from 2,547 to 50,000,indicating that the proposed method has a strong generalization capability for generating multiple trajectories,providing a basis for generating test scenarios and promoting autonomous vehicle testing.

Renewable Scenario Generation Using Controllable Generative Adversarial Networks with Transparent Latent Space

With the growing penetration of renewable energysources in power systems, it becomes increasingly important tocharacterize their inherent variability and uncertainty. Scenariogeneration is a key approach to provide a series of possible powerscenarios in the future for the system planner and operator tomake decisions. In this paper, a data-driven method is presentedfor renewable scenario generation using stable and controllablegenerative adversarial networks with transparent latent space(ctrl-GANs). The machine learning based algorithm can capturethe nonlinear and dynamic renewable patterns without the needfor modeling assumptions and complicated sampling techniques.The orthogonal regularization and spectral normalization areadopted to improve the training stabilization of the GAN model.To control the generation process, a relationship is built betweenfeatures of the generated scenarios and latent vectors on themanifold. Moreover, several new metrics for GANs are used toevaluate the quality of the scenarios. The proposed approachis applied to generate realistic time series data of wind andphotovoltaic power. The results demonstrate that our methodhas a better performance on numerical stabilization and is ableto control the generation process with latent space.

Forecasting Scenario Generation for Multiple Wind Farms Considering Time-series Characteristics and Spatial-temporal Correlation

Scenario forecasting methods have been widely studied in recent years to cope with the wind power uncertainty problem. The main difficulty of this problem is to accurately and comprehensively reflect the time-series characteristics and spatial-temporal correlation of wind power generation. In this paper, the marginal distribution model and the dependence structure are combined to describe these complex characteristics. On this basis, a scenario generation method for multiple wind farms is proposed. For the marginal distribution model, the autoregressive integrated moving average-generalized autoregressive conditional heteroskedasticity-t (ARIMA-GARCH-t) model is proposed to capture the time-series characteristics of wind power generation. For the dependence structure, a time-varying regular vine mixed Copula (TRVMC) model is established to capture the spatial-temporal correlation of multiple wind farms. Based on the data from 8 wind farms in Northwest China, sufficient scenarios are generated. The effectiveness of the scenarios is evaluated in 3 aspects. The results show that the generated scenarios have similar fluctuation characteristics, autocorrelation, and crosscorrelation with the actual wind power sequences.

Scenario Generations for Renewable Energy Sources and Loads Based on Implicit Maximum Likelihood Estimations

Scenario generations for renewable energy sources and loads play an important role in the stable operation and risk assessment of integrated energy systems.This paper proposes a deep generative network based method to model time-series curves,e.g.,power generation curves and load curves,of renewable energy sources and loads based on implicit maximum likelihood estimations(IMLEs),which can generate realistic scenarios with similar patterns as real ones.After training the model,any number of new scenarios can be obtained by simply inputting Gaussian noises into the data generator of IMLEs.The proposed approach does not require any model assumptions or prior knowledge of the form in the likelihood function being made during the training process,which leads to stronger applicability than explicit density model based methods.The extensive experiments show that the IMLEs accurately capture the complex shapes,frequency-domain characteristics,probability distributions,and correlations of renewable energy sources and loads.Moreover,the proposed approach can be easily generalized to scenario generation tasks of various renewable energy sources and loads by fine-tuning parameters and structures.

Generation of a scenario library for testing driver-automation cooperation safety under cut-in working conditions

To improve the efficiency of safety tests of driver-automation cooperation,a method for generating a scenario library is proposed that considers the probability of scenario occurrence and driver-handling challenges in real driving situations.First,the original scenario data under cut-in conditions stored in a time series are extracted from the scenario data set.Then,a mathematical performance index is used to model the scenario and a significance function in terms of the occurrence frequency of the scenario,and the performance challenge between the driver and the vehicle is established.Next,the important scenario set is extracted from the original scenario set by constructing and optimizing a significance auxiliary function.Finally,the extracted important scenario sets are filtered by using the significance function values of the scenarios to generate a scenario library.Simulation results show that the proposed method for scenario library generation can effectively identify scenarios with potential adventure during driver-automation cooperation and thus accelerate safety tests compared with traditional methods.

Hybrid Scenario Generation Method for Stochastic Virtual Bidding in Electricity Market

Stochastic optimization can be used to generate optimal bidding strategies for virtual bidders in which the uncertain electricity prices are represented by using scenarios.This paper proposes a hybrid scenario generation method for electricity price using a seasonal autoregressive integrated moving average(SARIMA)model and historical data.The electricity price spikes are first identified by using an outlier detection method.Then,the historical data are decomposed into base and spike components.Next,the base and spike component scenarios are generated by using the SARIMA-and historical data-based methods,respectively.Finally,the electricity price scenarios are obtained by combining the base and spike component scenarios.Case studies are carried out for a virtual bidder in the PJM electricity market to validate the proposed method.The optimal bidding strategies of the virtual bidder are generated by solving a stochastic optimization problem using the electricity price scenarios generated by the proposed method,the SARIMA method,and a historical data-based method,respectively.Case study results show that the proposed method is better than the SARIMA method in preserving statistical properties of the electricity price in the generated scenarios and is better than the historical data-based method in predicting the future trend of the electricity price and,therefore,can help the virtual bidder earn more profit in the electricity market.

Scenario Generation for Cooling,Heating,and Power Loads Using Generative Moment Matching Networks

Scenario generations of cooling,heating,and power loads are of great significance for the economic operation and stability analysis of integrated energy systems.In this paper,a novel deep generative network is proposed to model cooling,heating,and power load curves based on generative moment matching networks(GMMNs)where an auto-encoder transforms highdimensional load curves into low-dimensional latent variables and the maximum mean discrepancy represents the similarity metrics between the generated samples and the real samples.After training the model,the new scenarios are generated by feeding Gaussian noises to the scenario generator of the GMMN.Unlike the explicit density models,the proposed GMMN does not need to artificially assume the probability distribution of the load curves,which leads to stronger universality.The simulation results show that the GMMN not only fits the probability distribution of multiclass load curves very well,but also accurately captures the shape(e.g.,large peaks,fast ramps,and fluctuation),frequency-domain characteristics,and temporal-spatial correlations of cooling,heating,and power loads.Furthermore,the energy consumption of generated samples closely resembles that of real samples.

Genetic Algorithm‑Based SOTIF Scenario Construction for Complex Traffic Flow

The Safety of The Intended Functionality(SOTIF)challenge represents the triggering condition by elements of a specific scenario and exposes the function limitation of an autonomous vehicle(AV),which leads to hazards.As for operationcontent-related features,the scenario is similar to AVs’SOTIF research and development.Therefore,scenario generation is a significant topic for SOTIF verification and validation procedure,especially in the simulation testing of AVs.Thus,in this paper,a well-designed scenario architecture is first defined,with comprehensive scenario elements,to present SOTIF trigger conditions.Then,considering complex traffic disturbance as trigger conditions,a novel SOTIF scenario generation method is developed.An indicator,also known as Scenario Potential Risk,is defined as the combination of the safety control intensity and the prior collision probability.This indicator helps identify critical scenarios in the proposed method.In addition,the corresponding vehicle motion models are established for general straight roads,curved roads,and safety assessment areas.As for the traffic participants’motion model,it is designed to construct the key dynamic events.To efficiently search for critical scenarios with the trigger of complex traffic flow,this scenario is encoded as genes and it is regenerated through selection,mutation,and crossover iteration processes,known as the Genetic Algorithm(GA).Experimental results show that the GA-based method could efficiently construct diverse and critical traffic scenarios,contributing to the construction of the SOTIF scenario library.

A Scenario-Based Robust Transmission Network Expansion Planning Method for Consideration of Wind Power Uncertainties

This paper uses a novel scenario generation method for tackling the uncertainties of wind power in the transmission network expansion planning(TNEP)problem.A heuristic moment matching(HMM)method is first applied to generate the typical scenarios for capturing the stochastic features of wind power,including expectation,standard deviation,skewness,kurtosis,and correlation of multiple wind farms.Then,based on the typical scenarios,a robust TNEP problem is presented and formulated.The solution of the problem is robust against all the scenarios that represent the stochastic features of wind power.Three test systems are used to verify the HMM method and is compared against Taguchi’s Orthogonal Array(OA)method.The simulation results show that the HMM method has better performance than the OA method in terms of the trade-off between robustness and economy.Additionally,the main factors influencing the planning scheme are studied,including the number of scenarios,wind farm capacity,and penalty factors,which provide a reference for system operators choosing parameters.

Economic benefit evaluation method for the micro-grid renewable energy system operation

The development of micro-grid renewable energy system in China has achieved rapid growth in recent years,and the micro-grid renewable energy system has been drawing more and more attention by its flexible operation.Due to the randomness,fluctuation,uncertainty of the wind and photovoltaic renewable generation,abundant flexibility is required to meet the needs of safe,reliable and independent operation of the micro-grid energy system.We need to connect large energy systems to accept outside assistance when the micro-grid renewable energy system is short of adjustment capability.Independent operation and network operation will affect the economic benefit of the micro-grid energy system,so it is practically meaningful to study on the economic benefit evaluation of the micro-grid renewable energy system.This paper proposes a micro-grid energy system operation simulation model about wind and photovoltaic generation,the uncertainty of which is tackled based on the scenario generation and extraction techniques.Based on the proposed indices,the economic benefit could be evaluated by simulating the micro-grid energy system operation.The proposed method is validated by a real micro-grid energy system.