Electricity-heat-gas integrated demand response dependency assessment based on BOXCOX-Pair Copula model

With the continuous development of Regional Integrated Energy System (RIES), demand response (DR) is composed of diversified loads including electric load, heat load and gas load. Their cross-dependencies reflecting the nonlinear coupling complementary relationship between each load type are one of the key factors to improve multi-energy flow optimisation modelling and utilisation efficiency on the demand side. Accordingly, this paper proposes a DR dependency assessment method considering electricity-heat-gas loads based on the BOXCOX-Pair Copula model. BOXCOX transformation is introduced to convert various probability distribution statistics of electricity-heat-gas loads into Gaussian distributed variables. C-vine Pair Copula is used to characterise an ensemble-of-trees of high-dimensional dependency structure among multi-energy demand modalities. Then the combined model of BOXCOX transformation and C-vine Pair Copula can be employed to determine the complex coupling dependency among electricity-heat-gas loads according to different DR statistics. Some metrics between the original empirical distribution and BOXCOX-Pair Copula distribution are introduced to assess the dependency evaluation precision of the proposed model. Finally, the novel dependency assessment model is numerically tested utilising the electricity load, heat load and gas load data sequences in a real RIES. The results illustrate that the cross-dependency of electricity-heat-gas integrated DR based on the BOXCOX-C-vine copula model is closer to that of actual sample data, which verify the effectiveness and superiority of the proposed approach.