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 Three-Phase Unbalanced Optimal Power Flow Using Holomorphic Embedding Load Flow Method

2019 ◽  
Vol 11 (6) ◽  
pp. 1774 ◽  
Author(s):  
Bharath Rao ◽  
Friederich Kupzog ◽  
Martin Kozek
Keyword(s):  
Power Flow ◽  
Optimal Power Flow ◽  
Low Voltage ◽  
Distribution Networks ◽  
Optimization Method ◽  
Load Flow ◽  
Flow Method ◽  
Optimal Power ◽  
Three Phase ◽  
Holomorphic Embedding

Distribution networks are typically unbalanced due to loads being unevenly distributed over the three phases and untransposed lines. Additionally, unbalance is further increased with high penetration of single-phased distributed generators. Load and optimal power flows, when applied to distribution networks, use models developed for transmission grids with limited modification. The performance of optimal power flow depends on external factors such as ambient temperature and irradiation, since they have strong influence on loads and distributed energy resources such as photo voltaic systems. To help mitigate the issues mentioned above, the authors present a novel class of optimal power flow algorithm which is applied to low-voltage distribution networks. It involves the use of a novel three-phase unbalanced holomorphic embedding load flow method in conjunction with a non-convex optimization method to obtain the optimal set-points based on a suitable objective function. This novel three-phase load flow method is benchmarked against the well-known power factory Newton-Raphson algorithm for various test networks. Mann-Whitney U test is performed for the voltage magnitude data generated by both methods and null hypothesis is accepted. A use case involving a real network in Austria and a method to generate optimal schedules for various controllable buses is provided.

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.

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 Time-Series Temperature-Dependent Power Flow Considering Unbalanced Thermoelectric Equivalent Circuits for Underground LV and MV Cables

2021 ◽  
Author(s):  
Evangelos Pompodakis ◽  
Andreas I. Chrysochos ◽  
Arif Ahmed ◽  
Minas C. Alexiadis
Keyword(s):  
Time Series ◽  
Power Flow ◽  
Low Voltage ◽  
Distribution Networks ◽  
Temperature Dependent ◽  
Underground Cables ◽  
Thermal Circuit ◽  
Three Phase ◽  
Homogeneous Soil ◽  
Conductor Temperature

<p>This manuscript proposes a time-series temperature-dependent power flow method for unbalanced distribution networks consisting of underground cables. A thermal circuit model for unbalanced three-phase multi-core cables is developed to estimate the conductor temperature and resistance of Medium and Low Voltage distribution networks. More specifically, a novel approach is proposed to model and estimate the parameters of the three-phase thermal circuit of 3/4-core cables, using the results of Finite Element Method and Particle Swarm Optimization. The proposed approach is generic and can be accurately applied to any kind of 3- or 4-core cables buried in homogeneous or non-homogeneous soil. Furthermore, it is applicable in cases where one or more adjacent cables exist. Using the proposed approach, the conductor temperature of each phase can be individually and precisely calculated even in networks with highly unbalanced loads. The proposed approach is expected to be an important tool for simulating the steady state of unbalanced distribution networks and estimating the conductor temperatures. The proposed thermal circuit is validated using two 4-core LV and one 3-core MV cables buried in different depths in homogeneous or non-homogeneous soil. Time-series power flow for a whole year is performed in a 25-bus unbalanced LV network consisting of multicore underground cables.</p>

scholarly journals Impact of Network Reconfiguration: Case Study of Port-Harcourt Town 132/33kV Sub-transmission Substation and Its 33/11kV Injection Substation Distribution Networks

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
Chinweike Innocent Amesi ◽  
Tekena Kashmony Bala ◽  
Anthony O. Ibe
Keyword(s):  
Power Flow ◽  
Low Voltage ◽  
Distribution Networks ◽  
Total Power ◽  
Base Case ◽  
Network Reconfiguration ◽  
Voltage Profile ◽  
Distribution Transformers ◽  
Port Harcourt ◽  
Bus Voltage

This paper examined the power flow status of the Port Harcourt Town (Zone 4) distribution networks to improve the performance. The network consists of 18 injection substations fed from 4 different sizes of transformers with a total power rating of 165 MVA, 132/33kV at the Port Harcourt Town sub-transmission substation. Gauss-seidel power flow algorithm was used to analyse the network in Electrical Transient Analyzer Program software (ETAP 12.6) to determine the various bus operating voltages, power flow, and over or under-loaded Transformers’ units. From the base-case simulation results obtained, it shows that these injection distribution transformers (PH Town 106.3%, RSU 90.5%, Marine Base 86.5%, UTC 87.9%, Nzimiro 89.5%, and Borokiri 88.7%) were overloaded on the network and the operating voltages observed for (PH Town 95.1%, RSU 83.0%, Marine Base 83.4%, UTC 82.8%, Nzimiro 85.2%, and Borokiri 82.1%) indicates low voltage profile. However, using network reconfiguration technique as proposed in this paper; there was reduction in the percentage loading of the said Transformers as it was upgraded to affect positively on its lifespan with (PH Town 44.1%, RSU 65.3%, Marine Base 60.7%, UTC 47.3%, Nzimiro 61.3%, and Borokiri 52.0%) loading,  and the bus voltage profiles was improved for (PH Town 100%, RSU 98.4%, Marine Base 98.8%, UTC 98.2%, Nzimiro 98.6%, and Borokiri 99.1%) with additional facilities. It is recommended that the power infrastructure facilities in Port Harcourt Town distribution network be immediately upgraded to reduce losses and improve the electricity supply to consumers. Also, in regard to these analyses, the sub-transmission substation requires 240 MW of power for effective power delivery.

scholarly journals Black hole optimizer for the optimal power injection in distribution networks using DG

2021 ◽  
Vol 2135 (1) ◽  
pp. 012010
Author(s):  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez ◽  
Luis Fernando Grisales-Noreña
Keyword(s):  
Black Hole ◽  
Power Distribution ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Distribution Networks ◽  
Test System ◽  
Load Flow ◽  
Optimization Strategy ◽  
Optimal Power ◽  
Distribution Company

Abstract The optimal sizing of Distributed Generators (DG) in electric power distribution networks is carried out through a metaheuristic optimization strategy. To size DG it is proposed an optimal power flow model is formulated by considering that the location of these sources has been previously defined by the distribution company. The solution of the optimal power flow is reached with the Black Hole Optimizer (BHO). A methodology is used master-slave optimization methodology, where the BHO (i.e., master stage) defines the sizes of the DG and the slave stage evaluates the objective function with a load flow algorithm, this work using the triangular-based power flow method. Numerical results in the 33-node and the 69-node test system demonstrates the effectiveness and robustness of the proposed approach when compared with literature results.

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