Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an...Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.展开更多
Electromagnetic transient simulation for large-scale power system is a time-consuming problem.A new frequency-dependent equivalence method is presented in the paper,which might significantly accelerate power system el...Electromagnetic transient simulation for large-scale power system is a time-consuming problem.A new frequency-dependent equivalence method is presented in the paper,which might significantly accelerate power system electromagnetic transient simulation.In the method,an effective algorithm is designed to directly transfer the port admittance determinant of external system's mixing matrix into admittance rational function;and the step-by-step strategy for the equivalence of actual large system is put forward,which further reduces the calculation quantities needed.Moreover,the study of multiple real root pole characteristics of admittance transfer function of two-port network is performed and a proposition is achieved.Based on the proposition and residue theorem,the equivalence system for external system corresponding to the admittance rational function is obtained.The computation complexity of the step-by-step equivalence method is about o(┌n/np×T┐)(┌┐ is upper integral operation,n is the total buses number of external system,N P is the total buses number of single step equivalence network,T is single step equivalence time),which indicates that the computation complexity of the method proposed has nearly linear relationship with the buses number of external system,and the method proposed has satisfactory computation speed.Since the mixing matrix of external system includes all the information of external system,therefore,port admittance rational function derived from it can reflect its full frequency characteristic and the equivalence network achieved has high equivalence precision.Moreover,since the port rational function is gained at the condition of the external system without source,which equals stable passive network,it could not show any unstable pole and need not extra measure to make the equivalence system stable.The test results of the samples and comparison with other methods demonstrate that the new method proposed is valid and effective.展开更多
基金Supported by the National Natural Science Foundation of China(No.61772031)the Special Energy Saving Foundation of Changsha,Hunan Province in 2017
文摘Granular computing is a very hot research field in recent years. In our previous work an algebraic quotient space model was proposed,where the quotient structure could not be deduced if the granulation was based on an equivalence relation. In this paper,definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure. Then the accuracy and roughness were defined to measure the quotient structure in quantification. Finally,a numerical example was given to demonstrate that the rough representation and measuring methods are efficient and applicable. The work has greatly enriched the algebraic quotient space model and granular computing theory.
基金supported by the National Natural Science Foundation ofChina (Grant No. 51177107)
文摘Electromagnetic transient simulation for large-scale power system is a time-consuming problem.A new frequency-dependent equivalence method is presented in the paper,which might significantly accelerate power system electromagnetic transient simulation.In the method,an effective algorithm is designed to directly transfer the port admittance determinant of external system's mixing matrix into admittance rational function;and the step-by-step strategy for the equivalence of actual large system is put forward,which further reduces the calculation quantities needed.Moreover,the study of multiple real root pole characteristics of admittance transfer function of two-port network is performed and a proposition is achieved.Based on the proposition and residue theorem,the equivalence system for external system corresponding to the admittance rational function is obtained.The computation complexity of the step-by-step equivalence method is about o(┌n/np×T┐)(┌┐ is upper integral operation,n is the total buses number of external system,N P is the total buses number of single step equivalence network,T is single step equivalence time),which indicates that the computation complexity of the method proposed has nearly linear relationship with the buses number of external system,and the method proposed has satisfactory computation speed.Since the mixing matrix of external system includes all the information of external system,therefore,port admittance rational function derived from it can reflect its full frequency characteristic and the equivalence network achieved has high equivalence precision.Moreover,since the port rational function is gained at the condition of the external system without source,which equals stable passive network,it could not show any unstable pole and need not extra measure to make the equivalence system stable.The test results of the samples and comparison with other methods demonstrate that the new method proposed is valid and effective.
