Comparing Power Flow Equations on a Local Basis for Distribution Networks

2007 ◽  
Author(s):  
C. M. S. C. de Jesus ◽  
L. A. F. M. Ferreira
Keyword(s):  
Power Flow ◽  
Distribution Networks ◽  
Flow Equations ◽  
Local Basis

scholarly journals Stochastic Expansion Planning of Various Energy Storage Technologies in Active Power Distribution Networks

2021 ◽  
Vol 13 (10) ◽  
pp. 5752
Author(s):  
Reza Sabzehgar ◽  
Diba Zia Amirhosseini ◽  
Saeed D. Manshadi ◽  
Poria Fajri
Keyword(s):  
Energy Storage ◽  
Power Distribution ◽  
Power Flow ◽  
Lithium Ion ◽  
Distribution Networks ◽  
Renewable Energy Resources ◽  
Flow Equations ◽  
Second Order Cone ◽  
Li Ion ◽  
The Cost

This work aims to minimize the cost of installing renewable energy resources (photovoltaic systems) as well as energy storage systems (batteries), in addition to the cost of operation over a period of 20 years, which will include the cost of operating the power grid and the charging and discharging of the batteries. To this end, we propose a long-term planning optimization and expansion framework for a smart distribution network. A second order cone programming (SOCP) algorithm is utilized in this work to model the power flow equations. The minimization is computed in accordance to the years (y), seasons (s), days of the week (d), time of the day (t), and different scenarios based on the usage of energy and its production (c). An IEEE 33-bus balanced distribution test bench is utilized to evaluate the performance, effectiveness, and reliability of the proposed optimization and forecasting model. The numerical studies are conducted on two of the highest performing batteries in the current market, i.e., Lithium-ion (Li-ion) and redox flow batteries (RFBs). In addition, the pros and cons of distributed Li-ion batteries are compared with centralized RFBs. The results are presented to showcase the economic profits of utilizing these battery technologies.

scholarly journals Laplacian Matrix-Based Power Flow Formulation for LVDC Grids with Radial and Meshed Configurations

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1866
Author(s):  
Zahid Javid ◽  
Ulas Karaagac ◽  
Ilhan Kocar ◽  
Ka Wing Chan
Keyword(s):  
Fixed Point ◽  
Power Flow ◽  
Low Voltage ◽  
Mathematical Formulation ◽  
Distribution Networks ◽  
Load Flow ◽  
Banach Fixed Point Theorem ◽  
Loading Conditions ◽  
Flow Equations ◽  
Uniqueness Of The Solution

There is an increasing interest in low voltage direct current (LVDC) distribution grids due to advancements in power electronics enabling efficient and economical electrical networks in the DC paradigm. Power flow equations in LVDC grids are non-linear and non-convex due to the presence of constant power nodes. Depending on the implementation, power flow equations may lead to more than one solution and unrealistic solutions; therefore, the uniqueness of the solution should not be taken for granted. This paper proposes a new power flow solver based on a graph theory for LVDC grids having radial or meshed configurations. The solver provides a unique solution. Two test feeders composed of 33 nodes and 69 nodes are considered to validate the effectiveness of the proposed method. The proposed method is compared with a fixed-point methodology called direct load flow (DLF) having a mathematical formulation equivalent to a backward forward sweep (BFS) class of solvers in the case of radial distribution networks but that can handle meshed networks more easily thanks to the use of connectivity matrices. In addition, the convergence and uniqueness of the solution is demonstrated using a Banach fixed-point theorem. The performance of the proposed method is tested for different loading conditions. The results show that the proposed method is robust and has fast convergence characteristics even with high loading conditions. All simulations are carried out in MATLAB 2020b software.

scholarly journals A Mixed-Integer Quadratic Formulation of the Phase-Balancing Problem in Residential Microgrids

2021 ◽  
Vol 11 (5) ◽  
pp. 1972
Author(s):  
Alejandro Garces ◽  
Walter Gil-González ◽  
Oscar Danilo Montoya ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios
Keyword(s):  
Power Distribution ◽  
Power Flow ◽  
Heuristic Algorithms ◽  
Low Voltage ◽  
Distribution Networks ◽  
Test System ◽  
Mixed Integer ◽  
Flow Equations ◽  
Distribution Grids ◽  
Selection Of

Phase balancing is a classical optimization problem in power distribution grids that involve phase swapping of the loads and generators to reduce power loss. The problem is a non-linear integer and, hence, it is usually solved using heuristic algorithms. This paper proposes a mathematical reformulation that transforms the phase-balancing problem in low-voltage distribution networks into a mixed-integer convex quadratic optimization model. To consider both conventional secondary feeders and microgrids, renewable energies and their subsequent stochastic nature are included in the model. The power flow equations are linearized, and the combinatorial part is represented using a Birkhoff polytope B3 that allows the selection of phase swapping in each node. The numerical experiments on the CIGRE low-voltage test system demonstrate the use of the proposed formulation.

Mathematical modeling of electric vehicles contributions in voltage security of smart distribution networks

SIMULATION ◽  
2018 ◽  
Vol 95 (5) ◽  
pp. 429-439 ◽  
Author(s):  
Sasan Pirouzi ◽  
Jamshid Aghaei
Keyword(s):  
Electric Vehicle ◽  
Electric Vehicles ◽  
Power Flow ◽  
Reactive Power ◽  
Distribution Networks ◽  
Operational Cost ◽  
Objective Functions ◽  
Voltage Security ◽  
Flow Equations ◽  
Operating Limits

This paper evaluates the voltage security of the distribution networks in the presence of electric vehicles in the optimization framework. Accordingly, the main objective functions of this optimization problem include maximization of voltage security margin and minimization of operational cost. Also, it is supposed that the electric vehicles are equipped with bidirectional chargers to control active and reactive power in smart distribution networks, simultaneously. The objective functions are subject to the constraints of power flow equations, system operating limits and electric vehicle constraints. The proposed model is implemented on the 33-bus distribution network to evaluate the performance of the proposed optimization scheme for the management of the smart distribution networks in the presence of electric vehicles. The results show that the operational cost and network voltage security margin are reduced in the case of the higher electric vehicle penetration rate when electric vehicles are used for charging active power and reactive power control capability, with respect to the case that does not include electric vehicles.

scholarly journals Optimal Integration of Photovoltaic Sources in Distribution Networks for Daily Energy Losses Minimization Using the Vortex Search Algorithm

2021 ◽  
Vol 11 (10) ◽  
pp. 4418
Author(s):  
Alejandra Paz-Rodríguez ◽  
Juan Felipe Castro-Ordoñez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Search Algorithm ◽  
Peak Load ◽  
Distribution Networks ◽  
Energy Losses ◽  
Continuous Version ◽  
Continuous Section ◽  
Daily Energy ◽  
Discrete Part

This paper deals with the optimal siting and sizing problem of photovoltaic (PV) generators in electrical distribution networks considering daily load and generation profiles. It proposes the discrete-continuous version of the vortex search algorithm (DCVSA) to locate and size the PV sources where the discrete part of the codification defines the nodes. Renewable generators are installed in these nodes, and the continuous section determines their optimal sizes. In addition, through the successive approximation power flow method, the objective function of the optimization model is obtained. This objective function is related to the minimization of the daily energy losses. This method allows determining the power losses in each period for each renewable generation input provided by the DCVSA (i.e., location and sizing of the PV sources). Numerical validations in the IEEE 33- and IEEE 69-bus systems demonstrate that: (i) the proposed DCVSA finds the optimal global solution for both test feeders when the location and size of the PV generators are explored, considering the peak load scenario. (ii) In the case of the daily operative scenario, the total reduction of energy losses for both test feeders are 23.3643% and 24.3863%, respectively; and (iii) the DCVSA presents a better numerical performance regarding the objective function value when compared with the BONMIN solver in the GAMS software, which demonstrates the effectiveness and robustness of the proposed master-slave optimization algorithm.

scholarly journals Optimal Selection of Conductors in Three-Phase Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 80
Author(s):  
John Fernando Martínez-Gil ◽  
Nicolas Alejandro Moyano-García ◽  
Oscar Danilo Montoya ◽  
Jorge Alexander Alarcon-Villamil
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Phase Distribution ◽  
Search Algorithm ◽  
Distribution Networks ◽  
Discrete Version ◽  
Optimal Selection ◽  
Flow Method ◽  
Three Phase ◽  
Selection Of

In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ− and Y−connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.

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