Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix d...Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.展开更多
Synchronous condensers(SCs)are generally used at the receiving-end stations of ultra-high-voltage direct current(UHVDC)transmission systems due to their strong reactive power support and flexible regulation of reactiv...Synchronous condensers(SCs)are generally used at the receiving-end stations of ultra-high-voltage direct current(UHVDC)transmission systems due to their strong reactive power support and flexible regulation of reactive power according to the interconnected grids operating conditions.In this paper,different starting control schemes of a SC integrated power grid are investigated providing four main contributions:1)The principle of reactive power support of the SC on the interconnected power grid is analytically studied,providing the establishment of mathematical models.2)Four different starting control schemes are developed for the initialization and SC integration,i.e.in Scheme 1,a preset initial falling speed is directly utilized without initialization;in Scheme 2,a black start sequential control approach with a static frequency converter(SFC)is proposed;in Scheme 3,PI/PD/PID controllers are respectively applied for the excitation device at the speed-falling stage;in Scheme 4,a pre-insertion approach of an energy absorption component with R/L/RL is utilized to suppress the surges at the SC integration instant.3)The dynamic behaviors of four different starting schemes at specific operating stages are evaluated.4)The success rate of SC integration is analyzed to evaluate starting control performance.Performance of the SC interconnected system with four different starting control schemes is evaluated in the timedomain simulation environment PSCAD/EMTDC^(TM).The results prove the superiority of the proposed starting control approach in Scheme 4.展开更多
In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solut...In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.展开更多
A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom （S...A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom （SDOF） system, and then is generalized for a multiple-degree of freedom （MDOF） system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.60273048and60174023).
文摘Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.
基金supported by the National Natural Science Foundation of China under Grant 51807091the Natural Science Foundation of Jiangsu Province BK20180478+2 种基金the China Postdoctoral Science Foundation under Grant 2019M661846the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources under Grant LAPS20016Engineering and Physical Sciences Research Council under Grant EP/N032888/1.
文摘Synchronous condensers(SCs)are generally used at the receiving-end stations of ultra-high-voltage direct current(UHVDC)transmission systems due to their strong reactive power support and flexible regulation of reactive power according to the interconnected grids operating conditions.In this paper,different starting control schemes of a SC integrated power grid are investigated providing four main contributions:1)The principle of reactive power support of the SC on the interconnected power grid is analytically studied,providing the establishment of mathematical models.2)Four different starting control schemes are developed for the initialization and SC integration,i.e.in Scheme 1,a preset initial falling speed is directly utilized without initialization;in Scheme 2,a black start sequential control approach with a static frequency converter(SFC)is proposed;in Scheme 3,PI/PD/PID controllers are respectively applied for the excitation device at the speed-falling stage;in Scheme 4,a pre-insertion approach of an energy absorption component with R/L/RL is utilized to suppress the surges at the SC integration instant.3)The dynamic behaviors of four different starting schemes at specific operating stages are evaluated.4)The success rate of SC integration is analyzed to evaluate starting control performance.Performance of the SC interconnected system with four different starting control schemes is evaluated in the timedomain simulation environment PSCAD/EMTDC^(TM).The results prove the superiority of the proposed starting control approach in Scheme 4.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.52008404,U1934217 and 11790283)Science and Technology Research and Development Program Project of China Railway Group Limited(Major Special Project,No.2020-Special-02)the National Natural Science Foundation of Hunan Province(Grant No.2021JJ30850).
文摘In this work,a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train-track-substructure(TTS)system.It is called implicit-explicit integration and multi-time-step solution method(abbreviated as mI-nE-MTS method).The TTS system is divided into train-track subsystem and substruc-ture subsystem.Considering that the root cause of low effi-ciency of obtaining TTS solution lies in solving the alge-braic equation of the substructures,the high-efficient Zhai method,an explicit integration scheme,can be introduced to avoid matrix inversion process.The train-track system is solved by implicitly Park method.Moreover,it is known that the requirement of time step size differs for different sub-systems,integration methods and structural frequency response characteristics.A multi-time-step solution is pro-posed,in which time step size for the train-track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand,namely the time spent for m implicit integral steps is equal to n explicit integral steps,i.e.,mI=nE as mentioned above.The numeri-cal examples show the accuracy,efficiency,and engineering practicality of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Nos.11602004 and11602081)the Fundamental Research Funds for the Central Universities(No.531107040934)
文摘A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom （SDOF） system, and then is generalized for a multiple-degree of freedom （MDOF） system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency.
