Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.

Location of Asymmetric Ground Fault Using Virtual Injected Current Ratio and Two-stage Recovery Strategy in Distribution Networks

Sparse measurements challenge fault location in distribution networks.This paper proposes a method for asymmetric ground fault location in distribution networks with limited measurements.A virtual injected current vector is formulated to estimate the fault line,which can be reconstructed from voltage sags measured at a few buses using compressive sensing(CS).The relationship between the virtual injected current ratio(VICR)and fault position is deduced from circuit analysis to pinpoint the fault.Furthermore,a two-stage recovery strategy is proposed for improving reconstruction accuracy of the current vector,where two different sensing matrixes are utilized to improve the incoherence.The proposed method is validated in IEEE 34 node test feeder.Simulation results show asymmetric ground fault type,resistance,fault position and access of distributed generators(DGs)do not significantly influence performance of our method.In addition,it works effectively under various scenarios of noisy measurement and line parameter error.Validations on 134 node test feeders prove the proposed method is also suitable for systems with more complex structure.

Risk-averse Robust Interval Economic Dispatch for Power Systems with Large-scale Wind Power Integration

This paper presents a robust interval economic dispatch(RIED)model for power systems with large-scale wind power integration.Differing from existing interval optimization(IO)approaches that merely rely on the upper and lower boundaries of random variables,the distribution information retained in the historical data is introduced to the IO method in this paper.Based on the available probability distribution function(PDF),wind power curtailment and load shedding are quantified as the operational risk and incorporated into the decision-making process.In this model,we need not rely on the forecasted value of wind power,which is randomly fluctuating and quite unpredictable.Furthermore,when the PDFs of wind power are taken into account,the resulting dispatch solution makes a good tradeoff between the generation cost and the operational risk.Finally,the RIED model yields an optimal dispatch solution for thermal units and the allowable intervals of wind power for the wind farms,which efficiently mitigates the uncertainty in wind power generation and provides more practical suggestions for system operators.Simulation studies are conducted on a modified IEEE-118 bus system and the results verify the effectiveness of the proposed RIED model.

Short-term local prediction of wind speed and wind power based on singular spectrum analysis and locality-sensitive hashing

With the growing penetration of wind power in power systems, more accurate prediction of wind speed and wind power is required for real-time scheduling and operation. In this paper, a novel forecast model for shortterm prediction of wind speed and wind power is proposed,which is based on singular spectrum analysis(SSA) and locality-sensitive hashing(LSH). To deal with the impact of high volatility of the original time series, SSA is applied to decompose it into two components: the mean trend,which represents the mean tendency of the original time series, and the fluctuation component, which reveals the stochastic characteristics. Both components are reconstructed in a phase space to obtain mean trend segments and fluctuation component segments. After that, LSH is utilized to select similar segments of the mean trend segments, which are then employed in local forecasting, so that the accuracy and efficiency of prediction can be enhanced. Finally, support vector regression is adopted forprediction, where the training input is the synthesis of the similar mean trend segments and the corresponding fluctuation component segments. Simulation studies are conducted on wind speed and wind power time series from four databases, and the final results demonstrate that the proposed model is more accurate and stable in comparison with other models.

Application of Morphological Max-Lifting Scheme for Identification of Induction Motor Stator Inter-turn Short Circuit

The harmonic components of stator winding current in induction motor will change under the condition of stator inter-turn short circuit.According to these characteristics,in this paper,a novel technique based on morphological maxlifting scheme is proposed for identification of induction motor stator inter-turn short circuit.A max-lifting scheme is applied to process stator winding currents to extract these characteristics.An indicator,r,is computed to identify the short circuit.The transient model of induction motor is employed to simulate oneturn to six-turn stator inter-turn short circuits in an induction motor.Extensive simulation work has been conducted under normal conditions,abnormal conditions(voltage imbalance and varying load),stator inter-turn short circuit conditions,and conditions of any combinations of the above.The results have shown that the scheme proposed in this paper has a high identification rate for induction motor stator inter-turn short circuit.

Stochastic optimization of cost-risk for integrated energy system considering wind and solar power correlated

Due to the growing penetration of renewable energies(REs)in integrated energy system(IES),it is imperative to assess and reduce the negative impacts caused by the uncertain REs.In this paper,an unscented transformation-based mean-standard(UT-MS)deviation model is proposed for the stochastic optimization of cost-risk for IES operation considering wind and solar power correlated.The unscented transformation(UT)sampling method is adopted to characterize the uncertainties of wind and solar power considering the correlated relationship between them.Based on the UT,a mean-standard(MS)deviation model is formulated to depict the trade-off between the cost and risk of stochastic optimization for the IES optimal operation problem.Then the UT-MS model is tackled by a multi-objective group search optimizer with adaptive covariance and Levy flights embedded with a multiple constraints handling technique(MGSO-ACL-CHT)to ensure the feasibility of Peratooptimal solutions.Furthermore,a decision-making method,improved entropy weight(IEW),is developed to select a final operation point from the set of Perato-optimal solutions.In order to verify the feasibility and efficiency of the proposed UT-MS model in dealing with the uncertainties of correlative wind and solar power,simulation studies are conducted on a test IES.Simulation results show that the UT-MS model is capable of handling the uncertainties of correlative wind and solar power within much less samples and less computational burden.Moreover,the MGSOACL-CHT and IEW are also demonstrated to be effective in solving the multi-objective UT-MS model of the IES optimal operation problem.

Optimal Operation of Integrated Energy Systems Subject to Coupled Demand Constraints of Electricity and Natural Gas

This paper proposes a hybrid multi-objective optimization and game-theoretic approach(HMOGTA)to achieve the optimal operation of integrated energy systems(IESs)consisting of electricity and natural gas(E&G)utility networks,multiple distributed energy stations(DESs),and multiple energy users(EUs).The HMOGTA aims to solve the coordinated operation strategy of the electricity and natural gas networks considering the demand characteristics of DESs and EUs.In the HMOGTA,a hierarchical Stackelberg game model is developed for generating equilibrium strategies of DESs and EUs in each district energy network(DEN).Based on the game results,we obtain the coupling demand constraints of electricity and natural gas(CDCENs)which reflect the relationship between the amounts and prices of electricity and cooling(E&C)that DESs purchase from utility networks.Furthermore,the minimization of conflicting costs of E&G networks considering the CDCENs are solved by a multi-objective optimization method.A case study is conducted on a test IES composed of a 20-node natural gas network,a modified IEEE 30-bus system,and 3 DENs,which verifies the effectiveness of the proposed HMOGTA to realize fair treatment for all participants in the IES.

Optimal reactive power dispatch with wind power integrated using group search optimizer with intraspecific competition and le´vy walk

This paper presents the mean–variance(MV)model to solve power system reactive power dispatch problems with wind power integrated.The MV model considers the profit and risk simultaneously under the uncertain wind power(speed)environment.To describe this uncertain environment,the Latin hypercube sampling with Cholesky decomposition simulation method is used to sample uncertain wind speeds.An improved optimization algorithm,group search optimizer with intraspecific competition and le´vy walk,is then used to optimize the MV model by introducing the risk tolerance parameter.The simulation is conducted based on the IEEE 30-bus power system,and the results demonstrate the effectiveness and validity of the proposed model and the optimization algorithm.

Fault Identification in Power Network Based on Deep Reinforcement Learning

With the integration of alternative energy and renewables,the issue of stability and resilience of the power network has received considerable attention.The basic necessity for fault diagnosis and isolation is fault identification and location.The conventional intelligent fault identification method needs supervision,manual labelling of characteristics,and requires large amounts of labelled data.To enhance the ability of intelligent methods and get rid of the dependence on a large amount of labelled data,a novel fault identification method based on deep reinforcement learning(DRL),which has not received enough attention in the field of fault identification,is investigated in this paper.The proposed method uses different faults as parameters of the model to expand the scope of fault identification.In addition,the DRL algorithm can intelligently modify the fault parameters according to the observations obtained from the power network environment,rather than requiring manual and mechanical tuning of parameters.The methodology was tested on the IEEE 14 bus for several scenarios and the performance of the proposed method was compared with that of population-based optimization methods and supervised learning methods.The obtained results have confirmed the feasibility and effectiveness of the proposed method.

Ultra-short Term Wind Speed Prediction Using Mathematical Morphology Decomposition and Long Short-term Memory

This paper proposes a new model,which consists of a mathematical morphology(MM)decomposer and two long short term memory(LSTM)networks,to perform ultra-short term wind speed forecast.The MM decomposer is developed in order to improve the forecast accuracy,which separates the wind speed into two parts:a stationary long-term baseline and a nonstationary short-term residue.Afterwards,two LSTM networks are implemented to forecast the baseline and residue,respectively.Besides,this paper makes an integrated forecast that takes into account multiple climate factors,such as temperature and air pressure.The baseline,temperature and air pressure are used as the inputs of baseline network for training and prediction,and the baseline,residue,temperature and air pressure are used as the inputs of residue network for training and prediction.The performance of the proposed model has been validated using data collected from the Australian Meteorological Station,which is compared with least squares-support vector machine(LS-SVM),back-propagation artificial neural network(BPNN),LSTM,MM-LS-SVM,and MM-BPNN.The results demonstrate that the proposed model is more suitable to solve non-stationary time-series forecast,and achieves higher accuracy than the other models under various conditions.

On the State-dependent Switched Energy Functions of DFIG-based Wind Power Generation Systems

This paper proposes a novel state-dependent switched energy function(SdSEF)for general nonlinear autonomous systems,and constructs an SdSEF for doubly-fed induction generator(DFIG)-based wind power generation systems(WPGSs).Different from the conventional energy function,SdSEF is a piece-wise continuous function,and it satisfies the conditions of conventional energy functions on each of its continuous segments.SdSEF is designed to bridge the gap between the well-developed energy function theory and the description of system energy of complex nonlinear systems,such as power electronics converter systems.The stability criterion of nonlinear autonomous systems is investigated with SdSEF,and mathematical proof is presented.The SdSEF of a typical DFIGbased WPGS is simulated in the whole processes of a grid fault and fault recovery.Simulation results verify the negativeness of the derivative of each continuous segment of the SdSEF.

Fault Location in Distribution System Using Convolutional Neural Network Based on Domain Transformation

Distribution lines are integral parts of the modern power system,which can affect the security and stability of power supply directly.An effective power system protection scheme should be able to detect all occurring faults as soon as possible.There are two tasks in fault diagnosis.One is the fault classification,where high accuracy rates have already achieved.Thus,this paper focuses on the other task,i.e.fault location.Enlightened by Fourier transform,this paper proposes an online data-driven method,which transforms signals from time domain to image domain through signal-to-image(SIG)algorithm and then process the transformed images with framework based on convolutional neural network(CNN).On the one hand,we can extract more crucial characteristic and information from image domain.On the other hand,the CNN-based structure is much smaller than others.It needs less memory space and would be easier to be transplanted to hardware platform.Moreover,the proposed algorithm does not require synchronous devices.The numerical comparison shows that the proposed SIG-CNN fault location model achieves robust and accurate results compared with other data-driven algorithms.

Comparison and Error Analysis of Off-design and Design Models of Energy Hubs

The accuracy of the simulation model has a pro-found impact on the optimal operation of the energy hubs(EHs).However,in many articles,the constant model of the efficiency of equipment is adopted to formulate the operation system,which would probably lead to a simplification of the simulation models.But,EHs are typically operated under off-design condition due to the fluctuations in cooling,heating,electricity requirement.More-over,even though the off-design characteristics are considered,few studies have suggested comparing the differences between those two models by considering the operation cost.In order to assess the effect of the off-design characteristics of EH on the optimal operation accuracy in this paper,two test cases are performed on the fixed and variable load conditions,respectively.In addition,the individual effect of off-design characteristics of each equipment on the optimal operation cost of the EH is also investigated through four optimization runs.It is worth mentioning that the optimal operation problem of the EH considering the off-design characteristics and on-off status of the equipment is a mixed integer non-linear programming problem(MINLP).By testing the design and off-design models on the two cases,the results of simulation demonstrate that the optimal operation cost for the off-design model is larger than that for the design model.Nonetheless,in the aspect of the authenticity of the system operation strategy,the off-design model performs better than the design model.Furthermore,a larger relative error of the system operation cost between the two models can be observed when the EH is operated under a relatively lower load condition,revealing that the influence of off-design characteristic on the optimal operation of EHs is too significant to be neglected.

A Hybrid Signal Processing Method Combining Mathematical Morphology and Walsh Theory for Power Quality Disturbance Detection and Classification

In this paper, a novel signal processing method combining mathematical morphology (MM) and Walsh theory is proposed, which uses Walsh functions to control the structuring element (SE) and MM operators. Based on the Walsh-MM method, a scheme for power quality disturbances detection and classification is developed, which involves three steps: denoising, feature extraction and morphological clustering. First, various evolution rules of Walsh function are used to generate groups of SEs for the multiscale Walsh-ordered morphological operation, so the original signal can be denoised. Next, the fundamental wave of the denoised signal is suppressed by Hadamard matrix;thus, disturbances can be extracted. Finally, the Walsh power spectrum of the waveform extracted in the previous step is calculated, and the parameters of which are taken by morphological clustering to classify the disturbances. Simulation results reveal the proposed scheme can effectively detect and classify disturbances, and the Walsh-MM method is less affected by noise and only involves simple calculation, which has a potential to be implemented in hardware and more suitable for real-time application.

Detection of false data injection attacks on power systems using graph edge-conditioned convolutional networks

State estimation plays a vital role in the stable operation of modern power systems,but it is vulnerable to cyber attacks.False data injection attacks(FDIA),one of the most common cyber attacks,can tamper with measure-ment data and bypass the bad data detection(BDD)mechanism,leading to incorrect results of power system state estimation(PSSE).This paper presents a detection framework of FDIA for PSSE based on graph edge-conditioned convolutional networks(GECCN),which use topology information,node features and edge features.Through deep graph architecture,the correlation of sample data is effectively mined to establish the mapping relationship between the estimated values of measurements and the actual states of power systems.In addition,the edge-conditioned convolution operation allows processing data sets with different graph structures.Case studies are undertaken on the IEEE 14-bus system under different attack intensities and degrees to evaluate the performance of GECCN.Simulation results show that GECCN has better detection performance than convolutional neural networks,deep neural net-works and support vector machine.Moreover,the satisfactory detection performance obtained with the data sets of the IEEE 14-bus,30-bus and 118-bus systems verifies the effective scalability of GECCN.