The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curv...The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.展开更多
Coordinated charging of electric vehicles(EVs)is critical to provide safe and cost effective operation of distribution systems where household single phase charging of EV could contribute to imbalance of the distribut...Coordinated charging of electric vehicles(EVs)is critical to provide safe and cost effective operation of distribution systems where household single phase charging of EV could contribute to imbalance of the distribution system.To date,reported researches on optimization methods for coordinated charging aiming at minimizing power losses have the disadvantages of low calculation efficiency when applied to large systems or have not taken the voltage constraints into account.The phase component and polar coordinates power flow equations of an unbalanced distribution system are derived.Primal dual interior point dynamic programming is introduced for coordinated charging of EVs to minimize distribution system losses where charging demand,voltage and current constraints have been taken into account.The proposed optimization is evaluated using an actual 423-bus case as the test system.Results are promisingwith the proposed method having good convergence under time-efficient calculations while providing optimization of power losses,lower load variance,and improvement of voltage profile versus uncoordinated scenarios.展开更多
This paper indicates the possible difficulties for applying the interior point method to NPcomplete problems,transforms an NP-complete problem into a nonconvex quadratic program and then develops some convexity theori...This paper indicates the possible difficulties for applying the interior point method to NPcomplete problems,transforms an NP-complete problem into a nonconvex quadratic program and then develops some convexity theories for it. Lastly it proposes an algorithm which uses Karmarkar's algorithm as a subroutine. The finite convergence of this algorithm is also proved.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51275067)
文摘The position synthesis of planar linkages is to locate the center point of the moving joint on a rigid link, whose trajectory is a circle or a straight line. Utilizing the min-max optimization scheme, the fitting curve needs to minimize the maximum fitting error to acquire the dimension of a planar binary P-R link. Based on the saddle point programming, the fitting straight line is determined to the planar discrete point-path traced by the point of the rigid body in planar motion. The property and evolution of the defined saddle line error can be revealed from three given separate points. A quartic algebraic equation relating the fitting error and the coordinates is derived, which agrees with the classical theory. The effect of the fourth point is discussed in three cases through the constraint equations. The multi-position saddle line error is obtained by combination and comparison from the saddle point programming. Several examples are presented to illustrate the solution process for the saddle line error of the moving plane. The saddle line error surface and the contour map presented to show the variations of the fitting error in the fixed frame. The discrete kinematic geometry is then set up to disclose the relations of the separate positions of the rigid body, the location of the tracing point on the moving body, and the position and orientation of the saddle line to the point-path. This paper presents a new analytic geometry method for saddle line fitting and provides a theoretical foundation for position synthesis.
基金supported by the National Natural Science Fundation of China(No.51577046,No.5160070415)the National Defense Advanced Research Project(No.C1120110004,No.9140A27020211DZ5102)+1 种基金the Key Grant Project of Chinese Ministry of Education(No.313018)Anhui Provincial Science and Technology Foundation of China(No.1301022036)
文摘Coordinated charging of electric vehicles(EVs)is critical to provide safe and cost effective operation of distribution systems where household single phase charging of EV could contribute to imbalance of the distribution system.To date,reported researches on optimization methods for coordinated charging aiming at minimizing power losses have the disadvantages of low calculation efficiency when applied to large systems or have not taken the voltage constraints into account.The phase component and polar coordinates power flow equations of an unbalanced distribution system are derived.Primal dual interior point dynamic programming is introduced for coordinated charging of EVs to minimize distribution system losses where charging demand,voltage and current constraints have been taken into account.The proposed optimization is evaluated using an actual 423-bus case as the test system.Results are promisingwith the proposed method having good convergence under time-efficient calculations while providing optimization of power losses,lower load variance,and improvement of voltage profile versus uncoordinated scenarios.
文摘This paper indicates the possible difficulties for applying the interior point method to NPcomplete problems,transforms an NP-complete problem into a nonconvex quadratic program and then develops some convexity theories for it. Lastly it proposes an algorithm which uses Karmarkar's algorithm as a subroutine. The finite convergence of this algorithm is also proved.
