scholarly journals Optimal Demand Reconfiguration in Three-Phase Distribution Grids Using an MI-Convex Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1124
Author(s):  
Oscar Danilo Montoya ◽  
Andres Arias-Londoño ◽  
Luis Fernando Grisales-Noreña ◽  
José Ángel Barrios ◽  
Harold R. Chamorro
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Phase Distribution ◽  
Mathematical Formulation ◽  
Mixed Integer ◽  
Decision Variable ◽  
Convex Model ◽  
Load Redistribution ◽  
Three Phase ◽  
The Ideal

The problem of the optimal load redistribution in electrical three-phase medium-voltage grids is addressed in this research from the point of view of mixed-integer convex optimization. The mathematical formulation of the load redistribution problem is developed in terminals of the distribution node by accumulating all active and reactive power loads per phase. These loads are used to propose an objective function in terms of minimization of the average unbalanced (asymmetry) grade of the network with respect to the ideal mean consumption per-phase. The objective function is defined as the l1-norm which is a convex function. As the constraints consider the binary nature of the decision variable, each node is conformed by a 3×3 matrix where each row and column have to sum 1, and two equations associated with the load redistribution at each phase for each of the network nodes. Numerical results demonstrate the efficiency of the proposed mixed-integer convex model to equilibrate the power consumption per phase in regards with the ideal value in three different test feeders, which are composed of 4, 15, and 37 buses, respectively.

scholarly journals Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks

Computers ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 109
Author(s):  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Edwin Rivas-Trujillo
Keyword(s):  
Power Flow ◽  
Reactive Power ◽  
Search Algorithm ◽  
Triangular Matrix ◽  
Mixed Integer ◽  
Decision Variable ◽  
Convex Model ◽  
Electric Networks ◽  
Three Phase ◽  
Final Steady State

With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a 3×3 binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020a using the CVX tool and the Gurobi solver.

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.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

scholarly journals Three-Phase Distribution Locational Marginal Pricing to Manage Unbalanced Variable Renewable Energy

2020 ◽  
Author(s):  
Lawryn Edmonds ◽  
M. Nazif Faqiry ◽  
Hongyu Wu ◽  
Ananth Palani
Keyword(s):  
Renewable Energy ◽  
Case Studies ◽  
Reactive Power ◽  
Phase Distribution ◽  
Phase Component ◽  
Locational Marginal Pricing ◽  
Marginal Pricing ◽  
Three Phase ◽  
Economic Price ◽  
Pricing Schemes

This paper investigates three-phase, component-wise real and reactive distribution locational marginal pricing (DLMP). Through the use of case studies, mixtures of positive and negative, as well as real and reactive, DLMP components are explored in detail. A modified three-phase unbalanced 69-node PG&E system is used to demonstrate the validity of the three-phase real and reactive DLMP model. Results emphasize the importance of three-phase pricing schemes and reactive power pricing. The results also indicate the DLMP mechanism can potentially assist in balancing power across phases. DLMP can serve as an economic price signal to efficiently operate the system while minimizing losses, voltage violations, congestion, and imbalances across all phases.

scholarly journals From the Balancing Reactive Compensator to the Balancing Capacitive Compensator

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 1979 ◽  
Author(s):  
Adrian Pană ◽  
Alexandru Băloi ◽  
Florin Molnar-Matei
Keyword(s):  
Mathematical Model ◽  
Distribution System ◽  
Reactive Power ◽  
Phase Distribution ◽  
Software Tool ◽  
Industrial Applications ◽  
Numerical Application ◽  
Three Phase ◽  
Specialized Equipment ◽  
The Mathematical Model

Nowadays, improving the power quality at the Point of Common Coupling (PCC) between the consumers’ installations and the distribution system operators’ installations depends more and more on the use of specialized equipment, able to intervene in the network to eliminate or diminish the disturbances. The reactive power compensators remain valid solutions for applications in consumer and electricity distribution, in those situations when the criterion regarding the costs of installing and operating the equipment is more important than the ones related to the reaction speed or the control accuracy. This is also the case of the equipment for power factor improvement and load balancing in a three-phase distribution network. The two functions can be achieved simultaneously by using an unbalanced static var compensator, known as an adaptive balancing compensator, achieved by adjusting the equivalent parameters of circuits containing single-phase coils and capacitor banks. The paper presents the mathematical model for the sizing and operation of a balancing reactive compensator for a three-phase four-wire network and then presents some resizing methods to convert it into a balancing capacitive compensator, having the same functions. The mathematical model is then validated by a numerical application, modelling with a specialized software tool, and by experimental laboratory determinations. The paper contains strong arguments to support the idea that a balancing capacitive compensator becomes a very advantageous solution in many industrial applications.

scholarly journals Three-Phase Distribution Locational Marginal Pricing to Manage Unbalanced Variable Renewable Energy

2020 ◽  
Author(s):  
Lawryn Edmonds ◽  
M. Nazif Faqiry ◽  
Hongyu Wu ◽  
Ananth Palani
Keyword(s):  
Renewable Energy ◽  
Case Studies ◽  
Reactive Power ◽  
Phase Distribution ◽  
Phase Component ◽  
Locational Marginal Pricing ◽  
Marginal Pricing ◽  
Three Phase ◽  
Economic Price ◽  
Pricing Schemes

This paper investigates three-phase, component-wise real and reactive distribution locational marginal pricing (DLMP). Through the use of case studies, mixtures of positive and negative, as well as real and reactive, DLMP components are explored in detail. A modified three-phase unbalanced 69-node PG&E system is used to demonstrate the validity of the three-phase real and reactive DLMP model. Results emphasize the importance of three-phase pricing schemes and reactive power pricing. The results also indicate the DLMP mechanism can potentially assist in balancing power across phases. DLMP can serve as an economic price signal to efficiently operate the system while minimizing losses, voltage violations, congestion, and imbalances across all phases.

scholarly journals Iterative Method for Determining the Values of the Susceptances of a Balancing Capacitive Compensator

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2742
Author(s):  
Adrian Pană ◽  
Alexandru Băloi ◽  
Florin Molnar-Matei
Keyword(s):  
Load Balancing ◽  
Distribution System ◽  
High Performance ◽  
Reactive Power ◽  
Phase Distribution ◽  
Electrical Power ◽  
Power Converter ◽  
Problem Solution ◽  
Three Phase ◽  
Wide Range

To increase the electrical power quality, in the last decades, an intense development in the last decades of high-performance equipment built as advanced power electronics applications, such as the compensators from Switching Power Converter category, has taken place. For all that, Reactive Power Compensators (RPC) based on passive circuit elements, such as Static var Compensators (SVCs), still occupy a wide range of applications in customer and installations of the distribution system installations. The functions of power factor (PF) improvement and load balancing in a three-phase distribution network can be achieved with an unbalanced SVC, known as the Adaptive Balancing Reactive Compensator (ABRC). Presenting first the mathematical model of the initial sizing and the working mechanism of a Balancing Reactive Compensator (BRC) for a three-phase four-wire network, this article develops a compensator resizing algorithm through an iterative change of the initial sizing to transform the compensator into a Balancing Capacitive Compensator (BCC), which keeps the same functions. By using two computational and modeling software tools, a case study on the application of the method was carried out, demonstrating the availability of the sizing problem solution and validating the unbalanced capacitive compensation as an efficient way to PF improving and load balancing in a PCC (Point of Common Coupling).

Modeling and Simulation of Three Phase D-SVC for Load Compensation

2017 ◽  
Vol 8 (1) ◽  
pp. 262
Author(s):  
Ashwin Kumar Sahoo ◽  
Sarat Kumar Sahoo ◽  
Nalinikanta Mohanty
Keyword(s):  
Distribution System ◽  
Dynamic Capabilities ◽  
Reactive Power ◽  
Phase Distribution ◽  
Open Loop ◽  
Voltage Profile ◽  
Load Compensation ◽  
Three Phase ◽  
Shunt Capacitors ◽  
Shunt Compensation

The transmission of electric power has to take place in the most efficient way in addition to providing flexibility in the process. Flexible A.C. Transmission System (FACTS) promotes the use of static controllers to enhance the controllability and increase the power transfer capability. Providing reactive shunt compensation with shunt-connected capacitors and reactors is a well-established technique to get a better voltage profile in a power system. Shunt Capacitors are inexpensive but lack dynamic capabilities, thus some form of dynamically controlled reactive power compensation becomes essential.  In this paper, three phase Distribution Static Var Compensator (D-SVC) has been developed and studied under different conditions. Open loop mode and closed loop mode of operation of D-SVC is simulated and studied. The work presented here is very much useful for distribution system, for effective reactive power management and better Voltage control.

scholarly journals Exact minimization of the energy losses and the CO2 emissions in isolated DC distribution networks using PV sources

DYNA ◽  
2021 ◽  
Vol 88 (217) ◽  
pp. 178-184
Author(s):  
Alexander Molina ◽  
Oscar Danilo Montoya ◽  
Walter Gil-González
Keyword(s):  
Mathematical Formulation ◽  
Main Idea ◽  
Distribution Networks ◽  
Global Optimum ◽  
Mixed Integer ◽  
Energy Losses ◽  
Electrical Networks ◽  
Convex Model ◽  
Daily Energy ◽  
Minlp Model

This paper addresses the optimal location and sizing of photovoltaic (PV) sources in isolated direct current (DC) electrical networks, considering time-varying load and renewable generation curves. The mathematical formulation of this problem corresponds to mixed-integer nonlinear programming (MINLP), which is reformulated via mixed-integer convex optimization: This ensures the global optimum solving the resulting optimization model via branch & bound and interior-point methods. The main idea of including PV sources in the DC grid is to minimize the daily energy losses and greenhouse emissions produced by diesel generators in isolated areas. The GAMS package is employed to solve the MINLP model, using mixed and integer variables; also, the CVX and MOSEK solvers are used to obtain solutions from the proposed mixed-integer convex model in the MATLAB. Numerical results demonstrate important reductions in the daily energy losses and the harmful gas emissions when PV sources are optimally integrated into DC grid.

scholarly journals Genetic-Convex Model for Dynamic Reactive Power Compensation in Distribution Networks Using D-STATCOMs

2021 ◽  
Vol 11 (8) ◽  
pp. 3353
Author(s):  
Oscar Danilo Montoya ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios ◽  
Walter Gil-González ◽  
César Orozco-Henao
Keyword(s):  
Objective Function ◽  
Optimal Power Flow ◽  
Reactive Power ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Energy Losses ◽  
Optimization Approach ◽  
Operative Costs

This paper proposes a new hybrid master–slave optimization approach to address the problem of the optimal placement and sizing of distribution static compensators (D-STATCOMs) in electrical distribution grids. The optimal location of the D-STATCOMs is identified by implementing the classical and well-known Chu and Beasley genetic algorithm, which employs an integer codification to select the nodes where these will be installed. To determine the optimal sizes of the D-STATCOMs, a second-order cone programming reformulation of the optimal power flow problem is employed with the aim of minimizing the total costs of the daily energy losses. The objective function considered in this study is the minimization of the annual operative costs associated with energy losses and installation investments in D-STATCOMs. This objective function is subject to classical power balance constraints and device capabilities, which generates a mixed-integer nonlinear programming model that is solved with the proposed genetic-convex strategy. Numerical validations in the 33-node test feeder with radial configuration show the proposed genetic-convex model’s effectiveness to minimize the annual operative costs of the grid when compared with the optimization solvers available in GAMS software.

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