Study On Uncertainty Of Geomagnetically Induced Currents Based On Polynomial Chaos Expansion

Geomagnetically Induced Currents(GIC)can cause DC bias of the transformer,and its derivative effects may threaten the safety of power equipment and the grid.Most of the researches mainly focus on the analysis of GIC calculation under the determined parameters.In fact,there is great uncertainty in both the model itself and the parameters.Therefore,it is necessary to study GIC from the perspective of uncertainty and quantify the uncertainty of GIC caused by uncertain parameters.The main research contents and results are as follows:Firstly,the calculation model and method of electric field and GIC are introduced,and the parameters which may have uncertainties are derived,including the conductivity of each layer in the earth conductivity model and the DC resistance of the transmission line unit length in the grid,transformer DC resistance and substation grounding resistance.Based on their influencing factors,the types of distribution and the range of the distribution are determined.Secondly,based on the polynomial chaos expansion(PCE)method,only the conductivity is used as the input variable.Based on the original algorithm,the one-dimensional polynomial chaos expansion of the maximum of the electric field and GIC is constructed.Taking the typical three-layer earth conductivity model and Benchmark standard example model as an example,the constructed polynomial chaos expansion is used to quantify the maximum uncertainty of electric field and GIC caused by the earth conductivity.And the 95%confidence interval,mean and standard deviation are obtained.The validity of the PCE method is verified by comparison with the Monte Carlo method(MC),and the computational efficiency of the PCE method is much larger than that of the MC method.Thirdly,based on the one-dimensional expansion,the multi-dimensional expansion of the PCE method is constructed.The the expanded orthogonal polynomial base and its corresponding coefficients are solved.For the Xinjiang 750kV planning grid,let the three grid parameters obey the uniformly distributed.The uncertainty of the GIC of each substation in the power grid during the magnetic storm is carried out by using the projection method and the random response surface method.Then,for the 5D 9th-order GIC expansion,a hyperbolic truncation scheme and a sparse expansion method are proposed.The number of items of the expansion term is reduced from 2002 to 206,and finally to 25,which greatly simplifies polynomial chaos.Finally,on the basis of the multi-dimensional expansion,the variance decomposition method is used to calculate the Sobol sensitivity index,and the sensitivity of each substation GIC to different parameters is quantified.This paper provides an efficient method for quantifying the uncertainty of grid GIC.The analysis conclusion has important guiding significance for the comprehensive evaluation and defense of GIC.