scholarly journals An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum

2020 ◽  
Vol 10 (21) ◽  
pp. 7681 ◽  
Author(s):  
Walter Gil-González ◽  
Alexander Molina-Cabrera ◽  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problem ◽  
System Analysis ◽  
Programming Model ◽  
Classical Problem ◽  
Distribution Networks ◽  
Global Optimum ◽  
Optimal Location ◽  
Mixed Integer ◽  
Distributed Generators

This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

scholarly journals A Mixed-Integer Conic Formulation for Optimal Placement and Dimensioning of DGs in DC Distribution Networks

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 176
Author(s):  
Federico Molina-Martin ◽  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Jesus C. Hernández
Keyword(s):  
Optimal Solution ◽  
Distribution Networks ◽  
Global Optimum ◽  
Point Of View ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Sources ◽  
Distributed Generators ◽  
Dc Distribution ◽  
Time Required

The problem of the optimal placement and dimensioning of constant power sources (i.e., distributed generators) in electrical direct current (DC) distribution networks has been addressed in this research from the point of view of convex optimization. The original mixed-integer nonlinear programming (MINLP) model has been transformed into a mixed-integer conic equivalent via second-order cone programming, which produces a MI-SOCP approximation. The main advantage of the proposed MI-SOCP model is the possibility of ensuring global optimum finding using a combination of the branch and bound method to address the integer part of the problem (i.e., the location of the power sources) and the interior-point method to solve the dimensioning problem. Numerical results in the 21- and 69-node test feeders demonstrated its efficiency and robustness compared to an exact MINLP method available in GAMS: in the case of the 69-node test feeders, the exact MINLP solvers are stuck in local optimal solutions, while the proposed MI-SOCP model enables the finding of the global optimal solution. Additional simulations with daily load curves and photovoltaic sources confirmed the effectiveness of the proposed MI-SOCP methodology in locating and sizing distributed generators in DC grids; it also had low processing times since the location of three photovoltaic sources only requires 233.16s, which is 3.7 times faster than the time required by the SOCP model in the absence of power sources.

scholarly journals A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 627
Author(s):  
Walter Gil-González ◽  
Alejandro Garces ◽  
Oscar Danilo Montoya ◽  
Jesus C. Hernández
Keyword(s):  
Power Distribution ◽  
Power Flow ◽  
Distribution Networks ◽  
Global Optimum ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Distribution Networks ◽  
Distributed Generators ◽  
Second Order Cone ◽  
Proposed Model

The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and Gurobi solver.

scholarly journals Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1452
Author(s):  
Cristian Mateo Castiblanco-Pérez ◽  
David Esteban Toro-Rodríguez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimization Method ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Balance ◽  
Continuous Version ◽  
Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

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.

A Genetic Algorithm Approach for Multi-Product Multi-Machine CONWIP Production System

2011 ◽  
Vol 110-116 ◽  
pp. 3624-3630
Author(s):  
Saeede Ajorlou ◽  
Issac Shams ◽  
Mirbahador G. Aryanezhad
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Programming ◽  
Programming Model ◽  
Search Algorithms ◽  
Mixed Integer ◽  
Simplified Model ◽  
Mathematical Programming Model ◽  
Production Lines ◽  
Work In Process ◽  
Genetic Algorithm Approach

In this paper, a new mathematical programming model is developed to address common issues relating to single-stage CONstant-Work-In-Process based production lines. A Ge-netic Algorithm (GA) approach is then proposed to directly solve the model in order to simultaneously determines the optimal job sequence and WIP level. Unlike many existing approaches, which are based on deterministic search algorithms such as nonlinear programming and mixed integer programming, our proposed method does not rely on a linearized or simplified model of the system. results from a comprehensive numerical example indicate computational efficiency and validation of our method.

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