Distributionally Robust Optimal Dispatch of Offshore Wind Farm Cluster Connected by VSC-MTDC Considering Wind Speed Correlation

Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.

A novel method for reliability and risk evaluation of wind energy conversion systems considering wind speed correlation

This paper investigates an analytical approach for the reliability modeling of doubly fed induction generator （DFIG） wind turbines. At present, to the best of the authors＇ knowledge, wind speed and wind turbine generator outage have not been addressed simultaneously. In this paper, a novel methodology based on the Weibull- Markov method is proposed for evaluating the probabil- istic reliability of the bulk electric power systems, including DFIG wind turbines, considering wind speed and wind turbine generator outage. The proposed model is presented in terms of appropriate wind speed modeling as well as capacity outage probability table （COPT）, considering component failures of the wind turbine generators. Based on the proposed method, the COPT of the wind farm has been developed and utilized on the IEEE RBTS to estimate the well-known reliability and sensitive indices. The simulation results reveal the importance of inclusion of wind turbine generator outage as well as wind speed in the reliability assessment of the wind farms. Moreover, the proposed method reduces the complexity of using analytical methods and provides an accurate reliability model for the wind turbines. Furthermore, several case studies are considered to demonstrate the effectiveness of the proposed method in practical applications.

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.