基于Copula函数的风-电-热相关性及其潜在不确定性分析

Wind-power-heat Correlation and Its Underlying Uncertainty Analysis Based on Copula Function

在电力系统经济调度中,考虑热负荷、电负荷和风电出力之间的相关性对节省发电成本和实现风电合理消纳是必要且有效的.为此,基于Copula相关性分析理论,提出多元Copula分析工具箱(Multivariate Copula analysis toolbox,MvCAT),它包含各种复杂程度不同的Copula族,采用基于残差高斯似然函数的贝叶斯框架来推断Copula参数和估计潜在的不确定性.在贝叶斯框架内进行模型的推断,并利用混合进化马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法进行后验分布的数值估计和Copula参数的生成.根据模拟的双变量概率与其经验观测值的接近程度来评价Copula的性能,选取最优Copula模型.最后,以某省的数据为样本进行分析,结果表明提出的方法可以很好地反映变量间的秩相关性,并且能定量地评估与数据长度相关的不确定性.

In economic dispatch of power system,it is necessary and effective to consider the correlation between heat load,electric load and wind power output to save power generation costs and achieve reasonable wind power consumption.Therefore,based on the theory of Copula correlation analysis,a multivariate Copula analysis toolbox(MvCAT)is proposed,which contains various Copula families with different degrees of complexity.The Bayesian framework based on residual Gaussian likelihood function is used to infer Copula parameters and estimates potential uncertainty.First,the model is inferred in the Bayesian framework,and the hybrid evolutionary Markov chain Monte Carlo(MCMC)method is used to estimate the posterior distribution and generate the Copula parameters.Then the performance of Copula is evaluated based on how close the simulated bivariate probability is to its empirical observations,and the optimal Copula model is selected.Finally,the data from a certain province is used as a sample for analysis.The results show that the proposed method can well reflect the rank correlation between variables,and the uncertainty associated with data length can be assessed quantitatively.