An Efficient Method for Estimating Capability Curve of Virtual Power Plant

To incorporate the operating constraints of a virtual power plant(VPP)in transmission-level operation and market clearing,the concept of the VPP capability curve(VPP-CC)is proposed which explicitly characterizes the allowable range of active and reactive power outputs of a VPP.A two-step projection-based calculation framework is proposed to approximate the VPP-CC by the convex hull of critical points on its perimeter.The output of the proposed algorithm is concise and can be easily incorporated in the existing system operation and market clearing.Case studies based on the IEEE 33 and 123 test feeders show the computational efficiency of the proposed method outperforms existing methods by 4~7 times.Additionally,many fewer inequalities are needed to depict the VPP-CC while achieving the comparative approximation accuracy compared to sampling-based methods,which will relieve the communication and computation burden.

Robust spline-line energy management guidance algorithm with multiple constraints and uncertainties for solid rocket ascending

For the solid rocket with depletion shutdown system,effective energy management is significant to meet terminal constraints by exhausting excess energy.Several traditional energy management algorithms cannot satisfy the altitude constraint and path constraints are not sufficiently considered.The velocity adjustment capability of these algorithms is limited and the uncertainties are not considered.Based on the on-line programming of velocity capability curve,Spline-Line Energy Management(SLEM)guidance algorithm is proposed.It introduces lateral maneuvers to further consume the available velocity on the basis of longitudinal energy management.After expressing the constraints as several algebraic equations,the closed-loop guidance problem is converted to solving a system of nonlinear equations about the curve parameters in real time.The advantage is that the altitude constraint can be satisfied theoretically.The overload and control variable change rate and amplitude constraints are also considered during the flight by constructing the feasible boundary of velocity capability curve.To improve the robustness,it is further extended by estimating the actual uncertainties.The effectiveness and advantages of SLEM are demonstrated by simulations and comparisons with other energy management algorithms.Simulation results show that the proposed approach can satisfy multiple constraints with high precision under the condition of uncertainties.