This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for exam...This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.展开更多
Process optimization in equation-oriented(EO)modeling environments favors the gradient-based optimization algorithms by their abilities to provide accurate Jacobian matrices via automatic or symbolic differentiation.H...Process optimization in equation-oriented(EO)modeling environments favors the gradient-based optimization algorithms by their abilities to provide accurate Jacobian matrices via automatic or symbolic differentiation.However,computational inefficiencies including that in initial-point-finding for Newton type methods have significantly limited its application.Recently,progress has been made in using a pseudo-transient(PT)modeling method to address these difficulties,providing a fresh way forward in EO-based optimization.Nevertheless,research in this area remains open,and challenges need to be addressed.Therefore,understanding the state-of-the-art research on the PT method,its principle,and the strategies in composing effective methodologies using the PT modeling method is necessary for further developing EO-based methods for process optimization.For this purpose,the basic concepts for the PT modeling and the optimization framework based on the PT model are reviewed in this paper.Several typical applications,e.g.,complex distillation processes,cryogenic processes,and optimizations under uncertainty,are presented as well.Finally,we identify several main challenges and give prospects for the development of the PT based optimization methods.展开更多
Nonequilibrium stage model is a significant improvement in multicomponent separation process simulation,but more equations are involved and the solution of the model equations,which relies on an adequate initial guess...Nonequilibrium stage model is a significant improvement in multicomponent separation process simulation,but more equations are involved and the solution of the model equations,which relies on an adequate initial guess for convergence of the Newton method,is difficult.In this work,based on the concept of pseudo-transient continuation approach,we proposed a new pseudo-transient(PT)nonequilibrium method.The proposed method decouples the strongly coupled model equations by introducing dynamic equations for material and energy conservation,as well as transition equations.Thus,the steady-state solution of the nonequilibrium stage model can be obtained through a robust and fast integration process,and the initial guess issue in Newton method can be effectively avoided.Two simulation cases were used to demonstrate the advantages and applicability of the proposed PT nonequilibrium method.展开更多
The liquid hold-up in a reactive distillation(RD)column not only has a significant impact on the extent of reactions,but also affects the pressure drop and hydraulic conditions in the column.Therefore,the liquid hold-...The liquid hold-up in a reactive distillation(RD)column not only has a significant impact on the extent of reactions,but also affects the pressure drop and hydraulic conditions in the column.Therefore,the liquid hold-up would be a critical design factor for RD columns.However,the existing design methods for RD columns typically neglect the influence of considerable amount of liquid hold-up in downcomers owing to the difficulties of solving a large-scale nonlinear model system by considering downcomer hydraulics,resulting in significant deviations from actual situation and even operation infeasibility of the designed column.In this paper,a pseudo-transient(PT)RD model based on equilibrium model considering tray hydraulics was established for rigorous simulation and optimization of RD plate columns considering the liquid hold-up both in downcomers and column trays,and a steady-state optimization algorithm assisted by the PT model was adopted to robustly solve the optimization problem.The optimization results of either ethylene glycol RD or methyl acetate RD demonstrated that assuming all the liquid hold-up of a stage belonged to the tray will cause significant deviations in the column diameter,weir height,and the number of stages,which leads to not meeting the separation requirements and even operation hydraulic infeasibility.The rigorous model proposed in this study which considers the liquid hold-up both on trays and in downcomers as well as hydraulic constraints can be applied to systematically design industrial RD plate columns to simultaneously obtain optimal operating variables and equipment structure variables.展开更多
文摘This paper is a further study of two papers [1] and [2], which were related to Ill-Conditioned Load Flow Problems and were published by IEEE Trans. PAS. The authors of this paper have some different opinions, for example, the 11-bus system is not an ill-conditioned system. In addition, a new approach to solve Load Flow Problems, E-ψtc, is introduced. It is an explicit method;solving linear equations is not needed. It can handle very tough and very large systems. The advantage of this method has been fully proved by two examples. The authors give this new method a detailed description of how to use it to solve Load Flow Problems and successfully apply it to the 43-bus and the 11-bus systems. The authors also propose a strategy to test the reliability, and by solving gradient equations, this new method can answer if the solution exists or not.
基金supported by the National Natural Science Foundation of China(21978203,21676183).
文摘Process optimization in equation-oriented(EO)modeling environments favors the gradient-based optimization algorithms by their abilities to provide accurate Jacobian matrices via automatic or symbolic differentiation.However,computational inefficiencies including that in initial-point-finding for Newton type methods have significantly limited its application.Recently,progress has been made in using a pseudo-transient(PT)modeling method to address these difficulties,providing a fresh way forward in EO-based optimization.Nevertheless,research in this area remains open,and challenges need to be addressed.Therefore,understanding the state-of-the-art research on the PT method,its principle,and the strategies in composing effective methodologies using the PT modeling method is necessary for further developing EO-based methods for process optimization.For this purpose,the basic concepts for the PT modeling and the optimization framework based on the PT model are reviewed in this paper.Several typical applications,e.g.,complex distillation processes,cryogenic processes,and optimizations under uncertainty,are presented as well.Finally,we identify several main challenges and give prospects for the development of the PT based optimization methods.
基金supported by the National Natural Science Foundation of China(21978203).
文摘Nonequilibrium stage model is a significant improvement in multicomponent separation process simulation,but more equations are involved and the solution of the model equations,which relies on an adequate initial guess for convergence of the Newton method,is difficult.In this work,based on the concept of pseudo-transient continuation approach,we proposed a new pseudo-transient(PT)nonequilibrium method.The proposed method decouples the strongly coupled model equations by introducing dynamic equations for material and energy conservation,as well as transition equations.Thus,the steady-state solution of the nonequilibrium stage model can be obtained through a robust and fast integration process,and the initial guess issue in Newton method can be effectively avoided.Two simulation cases were used to demonstrate the advantages and applicability of the proposed PT nonequilibrium method.
基金supported by the National Natural Science Foundation of China(22378304).
文摘The liquid hold-up in a reactive distillation(RD)column not only has a significant impact on the extent of reactions,but also affects the pressure drop and hydraulic conditions in the column.Therefore,the liquid hold-up would be a critical design factor for RD columns.However,the existing design methods for RD columns typically neglect the influence of considerable amount of liquid hold-up in downcomers owing to the difficulties of solving a large-scale nonlinear model system by considering downcomer hydraulics,resulting in significant deviations from actual situation and even operation infeasibility of the designed column.In this paper,a pseudo-transient(PT)RD model based on equilibrium model considering tray hydraulics was established for rigorous simulation and optimization of RD plate columns considering the liquid hold-up both in downcomers and column trays,and a steady-state optimization algorithm assisted by the PT model was adopted to robustly solve the optimization problem.The optimization results of either ethylene glycol RD or methyl acetate RD demonstrated that assuming all the liquid hold-up of a stage belonged to the tray will cause significant deviations in the column diameter,weir height,and the number of stages,which leads to not meeting the separation requirements and even operation hydraulic infeasibility.The rigorous model proposed in this study which considers the liquid hold-up both on trays and in downcomers as well as hydraulic constraints can be applied to systematically design industrial RD plate columns to simultaneously obtain optimal operating variables and equipment structure variables.
