scholarly journals A Novel Linear Optimal Power Flow Model for Three-Phase Electrical Distribution Systems

2020 ◽  
Author(s):  
Juan Sebastian Giraldo ◽  
Pedro Pablo Vergara ◽  
Juan Camilo Lopez ◽  
Phuong Nguyen ◽  
Nikolaos Paterakis
Keyword(s):  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Optimal Power Flow ◽  
Flow Model ◽  
Mixed Integer ◽  
Electrical Distribution Systems ◽  
Optimal Power ◽  
Electrical Distribution ◽  
Three Phase

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes; while the bus voltage magnitude approximation uses a linear combination of the L1 and the L∞ norm. Results were obtained for an unbalanced distribution system, in order to assess the accuracy of the linear formulation when compared to a nonlinear power flow with fixed power injections, showing errors of less than 4\% for currents and 0.005\% for voltages.

scholarly journals A Novel Linear Optimal Power Flow Model for Three-Phase Electrical Distribution Systems

2020 ◽  
Author(s):  
Juan Sebastian Giraldo ◽  
Pedro Pablo Vergara ◽  
Juan Camilo Lopez ◽  
Phuong Nguyen ◽  
Nikolaos Paterakis
Keyword(s):  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Optimal Power Flow ◽  
Flow Model ◽  
Mixed Integer ◽  
Electrical Distribution Systems ◽  
Optimal Power ◽  
Electrical Distribution ◽  
Three Phase

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes; while the bus voltage magnitude approximation uses a linear combination of the L1 and the L∞ norm. Results were obtained for an unbalanced distribution system, in order to assess the accuracy of the linear formulation when compared to a nonlinear power flow with fixed power injections, showing errors of less than 4\% for currents and 0.005\% for voltages.

scholarly journals Distribution Optimal Power Flow With Energy Sharing Via a Peer-To-Peer Transactive Market

2021 ◽  
Vol 9 ◽  
Author(s):  
Boshen Zheng ◽  
Yue Fan ◽  
Wei Wei ◽  
Yourui Xu ◽  
Shaowei Huang ◽  
...  
Keyword(s):  
Equilibrium Condition ◽  
Power Flow ◽  
Distribution Systems ◽  
Optimal Power Flow ◽  
Distribution Network ◽  
Market Equilibrium ◽  
Peer To Peer ◽  
Mixed Integer ◽  
Optimal Power ◽  
Transactive Energy

The technology advancement and cost decline of renewable and sustainable energy increase the penetration of distributed energy resources (DERs) in distribution systems. Transactive energy helps balance the local generation and demand. Peer-to-peer (P2P) energy trading is a promising business model for transactive energy. Such a market scheme can increase the revenue of DER owners and reduce the waste of renewable energy. This article proposes an equilibrium model of a P2P transactive energy market. Every participant seeks the maximum personal interest, with the options of importing or providing energy from/to any other peer across different buses of the distribution network. The market equilibrium condition is obtained by combining the Karush–Kuhn–Tucker conditions of all problems of individual participants together. The energy transaction price is endogenously determined from the market equilibrium condition, which is cast as a mixed-integer linear program and solved by a commercial solver. The transactive energy flow is further embedded in the optimal power flow problem to ensure operating constraints of the distribution network. We propose a remedy to recover a near optimal solution when the second-order cone relaxation is inexact. Finally, a case study demonstrates that the proposed P2P market benefits all participants.

scholarly journals Robust Stochastic Dynamic Optimal Power Flow Model of Electricity-Gas Integrated Energy System considering Wind Power Uncertainty

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhengfeng Qin ◽  
Xiaoqing Bai ◽  
Xiangyang Su
Keyword(s):  
Stochastic Optimization ◽  
Wind Power ◽  
Power Output ◽  
Gas Turbines ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Flow Model ◽  
Mixed Integer ◽  
Stochastic Dynamic ◽  
Optimal Power

The application of gas turbines and power to gas equipment deepens the coupling relationship between power systems and natural gas systems and provides a new way to absorb the uncertain wind power as well. The traditional stochastic optimization and robust optimization algorithms have some limitations and deficiencies in dealing with the uncertainty of wind power output. Therefore, we propose a robust stochastic optimization (RSO) model to solve the dynamic optimal power flow model for electricity-gas integrated energy systems (IES) considering wind power uncertainty, where the ambiguity set of wind power output is constructed based on Wasserstein distance. Then, the Wasserstein ambiguity set is affined to the eventwise ambiguity set, and the proposed RSO model is transformed into a mixed-integer programming model, which can be solved rapidly and accurately using commercial solvers. Numerical results for EG-4 and EG-118 systems verify the rationality and effectiveness of the proposed model.

scholarly journals Calculation of Maximum Total Supply Capacity of Three-Phase Unbalance Distribution Network Based on Mixed Integer Second-Order Cone

2019 ◽  
Author(s):  
Jieyun Zheng ◽  
Shiyuan Ni ◽  
Pengjia Shi ◽  
Guilian Wu ◽  
Ri’an Wang ◽  
...  
Keyword(s):  
Power Supply ◽  
Distribution System ◽  
Power Flow ◽  
Flow Model ◽  
Distribution Network ◽  
Second Order ◽  
Mixed Integer ◽  
Power Distribution System ◽  
Second Order Cone ◽  
Three Phase

Considering the fault "N-1" checksum and the power flow, the single-phase power flow model is further transformed into a three-phase power flow model, and the asymmetry of the three-phase power flow is measured by the three-phase unbalance factor. The calculation model is linearized by the second-order cone relaxation and the Big-M method. At the same time, the load response and distribution network reconstruction are used to improve the reliability of the power supply network to cope with the power failure. The relationship between power supply capability and power flow constraints, main transformer capacity and distributed power parameters is analyzed by IEEE 33-node three-phase power distribution system. The feasibility of the proposed model and the accuracy of the second-order cone relaxation are verified by numerical examples, which provides a technical reference for distribution network planning.

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