Research On Available Transfer Capability Calculation Considering Wind Power Uncertainty

In the electricity market,the available transfer capability(ATC)is a quantitative measure of the security and reliability of power systems,as well as an essential signal for guiding the market transactions.It is of technical and economic value for the power system operation and planning.In the context of clean,low-carbon and diversified energy revolutions,the high proportion of integrated renewable energy generation,represented by wind power,is the development trend of the power system in China nowadays,and the inherent characteristic of it in the future.The significant uncertainty of wind power makes the operation features of the power system with wind power integration become more complicated and diverse,as well as presents the probabilistic characteristics in the balance of electric power.With no doubt,the integration of wind power puts forward new requirements and challenges for the ATC computation.When assessing the ATC,the ongoing researches are focused on how to reasonably take the wind power uncertainties into account in the computation model.Moreover,the computation method,which gives consideration to both the computation accuracy and cost,would be a promising one.Therefore,this paper is focused on the ATC calculation methods for the power system with wind power Integration.The research works are listed below.Based on the generalized polynomial chaos,a new probabilistic load flow calculation method is proposed.In the proposed method,optimal orthogonal polynomials are selected as the basis at first,according to the probability density functions of the input random variables.The generalized polynomial chaos expansion is subsequently built up with the basis.And then,given a small number of deterministic load flow solutions,the sparse expansion coefficients are solved using the stochastic collocation methods with the compressive sensing.Finally,the sparse polynomial chaos expansion is used as the surrogate model,with which sufficient samples of the load flow responses can be efficiently generated in an algebraic way.The case studies indicate that the proposed method is able to produce the probabilistic load flow results of the same precision to the Monte Carlo simulation,but saves the computational effort.A new probabilistic load flow calculation method is proposed using the improved stochastic response surface method(SRSM).The singular value decomposition technique is deployed to transform the high-dimensional correlated random variables to a group of independent random variables in the lower dimension so that SRSM is able to handle the correlation issue.Besides,the number of required solutions on the load flow equation is also reduced,by which the efficiency of SRSM is much improved for high-dimensional probabilistic load flow calculations.On the other hand,after further combining with the sensitivity-based load flow analysis and the total probability theory,SRSM can be applied in calculating the probabilistic load flow efficiently,under N-1 conditions that are caused by the stochastic outages of branches.The case studies indicate that the proposed method can report the load flow distributions affected by the correlated and discrete random variables,efficiently and accurately.A computationally accurate and efficient approach based on the low-rank approximation for probabilistic ATC assessment is proposed.The statistically-equivalent surrogate model for the probabilistic ATC solutions is built up through a small number of simulations on the original ATC computation model,which is generally complicated and time-consuming for solving.The statistics and the probability distribution functions of the ATC can be efficiently evaluated with the obtained surrogate model.The tensor-product structure of the univariate polynomial basis makes the total number of unknown coefficients in the surrogate model,as well as the number of original model simulations needed,are linear to the number of input random variables.This feature makes the proposed method is particularly promising for the probabilistic ATC with a large of random inputs.The performance of the proposed method is tested in case studies.It demonstrates that the computational effort is less in the proposed method for high-dimensional problems,compared to the methods based on Monte Carlo simulation or generalized polynomial chaos.Besides the probabilistic ATC calculation,the global sensitivity analysis(GSA)for ATC is also performed with an efficient scheme.In the proposed GSA scheme,a set of samples in small-scale are firstly generated according to the joint probability distributions of the input random variables.The ATC is calculated for each sample,and the sparse polynomial chaos expansion or low-rank approximation is subsequently built up as the surrogate model.Then,the global sensitivity indices are calculated by the algebraic operations based on the coefficients of the surrogate model,if the input random variables are independent.Otherwise,sufficient ATC samples are generated through the surrogate model,and the global sensitivity indices are calculated using the numerical integration formulation in subsequence.The effectiveness of the proposed GSA scheme is verified in the case studies,which also indicate that the influences of the individual input random variables on the ATC variance are reasonably quantified by the global sensitivity indices.Chance-Constrained programming(CCP)based ATC assessment model is proposed.The Gaussian mixture model is employed to model the non-independent and non-Gaussian features of multiple wind power outputs.Based on the DC load flow equations,the analytical expressions of the inverse cumulative distribution function of the branch active power is derived.Consequently,the chance constraints are transformed to the equivalent deterministic inequality constraints,and the chance-constrained programming model can be solved as a linear programming model using existing methods.In the case studies,the effectiveness of the proposed method on handling the chance constraints is demonstrated.Moreover,it also indicates that the CCP based ATC computation model can give the ATC results accounting for both the operational security and economy.