By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state v...By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.展开更多
The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the pen...The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the penalties by Beale and Small and the stronger penalties by Tomlin, describes the modifications of these penalties used for the method of bounded variables. The same examples from Petersen are taken and the satisfactory results are shown in comparison with those obtained by Tomlin.展开更多
The emergence of building condenser water systems with all-variable speed pumps and tower fans allows for increased efficiency and flexibility of chiller plants in partial load operation but also increases the control...The emergence of building condenser water systems with all-variable speed pumps and tower fans allows for increased efficiency and flexibility of chiller plants in partial load operation but also increases the control complexity of condenser water systems.This study aims to develop an integrated modeling technique for evaluating and optimizing the energy performance of such a condenser water system.The proposed system model is based on the semi-physical semi-empirical chiller,pump,and cooling tower models,with capabilities of fully considering the hydraulic and thermal interactions in the condenser water loop,being solved analytically and much faster than iterative solvers and supporting the explicit optimization of the pump and tower fan frequency.A mathematical approach,based on the system model and constrained optimization technique,is subsequently established to evaluate the energy performance of a typical dual setpoint-based variable speed strategy and find its energy-saving potential and most efficient operation by jointly optimizing pumps and tower fans.An all-variable speed chiller plant from Wuhan,China,is used for a case study to validate the system model’s accuracy and explore its applicability.The results showed that the system model can accurately simulate the condenser water system’s performance under various operating conditions.By optimizing the frequencies of pumps and tower fans,the total system energy consumption can be reduced by 12%–13%compared to the fixed dual setpoint-based strategy with range and approach setpoints of 4℃and 2℃.In contrast,the energy-saving potential of optimizing the cooling tower sequencing is insignificant.A simple joint speed control method for optimizing the pumps and tower fans emerged,i.e.,the optimal pump and fan frequency are linearly correlated(if both are non-extremes)and depend on the chiller part load ratio only,irrespective of the ambient wet-bulb temperature and chilled water supply temperature.It was also found that the oversizing issue has further limited the energy-saving space of the studied system and results in the range and approach setpoints being inaccessible.The study’s findings can serve as references to the operation optimization of all-variable speed condenser water systems in the future.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10632030,10902020,and 10721062)the Research Fund for the Doctoral Program of Higher Education of China(No.20070141067)+2 种基金the Doctoral Fund of Liaoning Province(No.20081091)the Key Laboratory Fund of Liaoning Province of China(No.2009S018)the Young Researcher Funds of Dalian University of Technology(No.SFDUT07002)
文摘By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.
文摘The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the penalties by Beale and Small and the stronger penalties by Tomlin, describes the modifications of these penalties used for the method of bounded variables. The same examples from Petersen are taken and the satisfactory results are shown in comparison with those obtained by Tomlin.
基金supported by the State Key Laboratory of Air-Conditioning Equipment and System Energy Conservation(No.ACSKL2019KT13)National Natural Science Foundation of China(No.51608297)+3 种基金Scientific Research Project of Beijing Municipal Education Commission(No.KM201910016009 and No.KZ202110016022)Beijing Advanced Innovation Center for Future Urban Design(No.UDC2019011121)Pyramid Talent Training Project(No.JDYC20220815)Post-Graduate Innovation Project(No.PG2024077)of Beijing University of Civil Engineering and Architecture.
文摘The emergence of building condenser water systems with all-variable speed pumps and tower fans allows for increased efficiency and flexibility of chiller plants in partial load operation but also increases the control complexity of condenser water systems.This study aims to develop an integrated modeling technique for evaluating and optimizing the energy performance of such a condenser water system.The proposed system model is based on the semi-physical semi-empirical chiller,pump,and cooling tower models,with capabilities of fully considering the hydraulic and thermal interactions in the condenser water loop,being solved analytically and much faster than iterative solvers and supporting the explicit optimization of the pump and tower fan frequency.A mathematical approach,based on the system model and constrained optimization technique,is subsequently established to evaluate the energy performance of a typical dual setpoint-based variable speed strategy and find its energy-saving potential and most efficient operation by jointly optimizing pumps and tower fans.An all-variable speed chiller plant from Wuhan,China,is used for a case study to validate the system model’s accuracy and explore its applicability.The results showed that the system model can accurately simulate the condenser water system’s performance under various operating conditions.By optimizing the frequencies of pumps and tower fans,the total system energy consumption can be reduced by 12%–13%compared to the fixed dual setpoint-based strategy with range and approach setpoints of 4℃and 2℃.In contrast,the energy-saving potential of optimizing the cooling tower sequencing is insignificant.A simple joint speed control method for optimizing the pumps and tower fans emerged,i.e.,the optimal pump and fan frequency are linearly correlated(if both are non-extremes)and depend on the chiller part load ratio only,irrespective of the ambient wet-bulb temperature and chilled water supply temperature.It was also found that the oversizing issue has further limited the energy-saving space of the studied system and results in the range and approach setpoints being inaccessible.The study’s findings can serve as references to the operation optimization of all-variable speed condenser water systems in the future.