Fully distributed multi-area dynamic economic dispatch method with second-order convergence for active distribution networks

2017 ◽  
Vol 11 (16) ◽  
pp. 3955-3965 ◽  
Author(s):  
Tong Xu ◽  
Wenchuan Wu ◽  
Hongbin Sun ◽  
Liming Wang
Keyword(s):  
Economic Dispatch ◽  
Distribution Networks ◽  
Second Order ◽  
Order Convergence ◽  
Second Order Convergence ◽  
Dynamic Economic Dispatch ◽  
Active Distribution Networks

scholarly journals Verification of Convergence Rates of Numerical Solutions for Parabolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Darae Jeong ◽  
Yibao Li ◽  
Chaeyoung Lee ◽  
Junxiang Yang ◽  
Yongho Choi ◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
Second Order ◽  
Order Convergence ◽  
Numerical Convergence ◽  
Verification Method ◽  
First Order ◽  
Convergence Test ◽  
Second Order Convergence

In this paper, we propose a verification method for the convergence rates of the numerical solutions for parabolic equations. Specifically, we consider the numerical convergence rates of the heat equation, the Allen–Cahn equation, and the Cahn–Hilliard equation. Convergence test results show that if we refine the spatial and temporal steps at the same time, then we have the second-order convergence rate for the second-order scheme. However, in the case of the first-order in time and the second-order in space scheme, we may have the first-order or the second-order convergence rates depending on starting spatial and temporal step sizes. Therefore, for a rigorous numerical convergence test, we need to perform the spatial and the temporal convergence tests separately.

scholarly journals Dynamic economic dispatch of wind-storage combined system based on conditional value-at-risk

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Yi Zheng ◽  
Xiaoqing Bai
Keyword(s):  
At Risk ◽  
Energy Storage ◽  
Value At Risk ◽  
Economic Dispatch ◽  
Second Order ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Combined System ◽  
Dynamic Economic Dispatch ◽  
Bus System

AbstractWind power's uncertainty is from the intermittency and fluctuation of wind speed, which brings a great challenge to solving the power system's dynamic economic dispatch problem. With the wind-storage combined system, this paper proposes a dynamic economic dispatch model considering AC optimal power flow based on Conditional Value-at-Risk ($$CVaR$$ CVaR ). Since the proposed model is hard to solve, we use the big-M method and second-order cone description technique to transform it into a trackable mixed-integer second-order conic programming (MISOCP) model. By comparing the dispatching cost of the IEEE 30-bus system and the IEEE 118-bus system at different confidence levels, it is indicated that $$CVaR$$ CVaR method can adequately estimate dispatching risk and assist decision-makers in making reasonable dispatching schedules according to their risk tolerance. Meanwhile, the optimal operational energy storage capacity and initial/final energy storage state can be determined by analyzing the dispatching cost risk under different storage capacities and initial/final states.

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