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

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

Applied Sciences ◽

10.3390/app11052175 ◽

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.

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

Electronics ◽

10.3390/electronics10121452 ◽

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.

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An Approximate Mixed-Integer Convex Model to Reduce Annual Operating Costs in Radial Distribution Networks Using STATCOMs

Electronics ◽

10.3390/electronics10243102 ◽

2021 ◽

Vol 10 (24) ◽

pp. 3102

Author(s):

Oscar Danilo Montoya ◽

Lázaro Alvarado-Barrios ◽

Jesus C. Hernández

Keyword(s):

Optimal Power Flow ◽

Large Scale ◽

Location Problem ◽

Reactive Power ◽

Programming Model ◽

Search Algorithm ◽

Distribution Networks ◽

Mixed Integer ◽

Convex Model ◽

Integer Quadratic Programming

The problem of optimal siting and sizing of distribution static compensators (STATCOMs) is addressed in this research from the point of view of exact mathematical optimization. The exact mixed-integer nonlinear programming model (MINLP) is decoupled into two convex optimization sub-problems, named the location problem and the sizing problem. The location problem is addressed by relaxing the exact MINLP model, assuming that all the voltages are equal to 1∠0∘, which allows obtaining a mixed-integer quadratic programming model as a function of the active and reactive power flows. The solution of this model provides the best set of nodes to locate all the STATCOMs. When all the nodes are selected, it solves the optimal reactive power problem through a second-order cone programming relaxation of the exact optimal power flow problem; the solution of the SOCP model provides the optimal sizes of the STATCOMs. Finally, it refines the exact objective function value due to the intrinsic non-convexities associated with the costs of the STATCOMs that were relaxed through the application of Taylor’s series expansion in the location and sizing stages. The numerical results in the IEEE 33- and 69-bus systems demonstrate the effectiveness and robustness of the proposed optimization problem when compared with large-scale MINLP solvers in GAMS and the discrete-continuous version of the vortex search algorithm (DCVSA) recently reported in the current literature. With respect to the benchmark cases of the test feeders, the proposed approach reaches the best reductions with 14.17% and 15.79% in the annual operative costs, which improves the solutions of the DCVSA, which are 13.71% and 15.30%, respectively.

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Efficient Reduction in the Annual Investment Costs in AC Distribution Networks via Optimal Integration of Solar PV Sources Using the Newton Metaheuristic Algorithm

Applied Sciences ◽

10.3390/app112311525 ◽

2021 ◽

Vol 11 (23) ◽

pp. 11525

Author(s):

Oscar Danilo Montoya ◽

Luis Fernando Grisales-Noreña ◽

Lázaro Alvarado-Barrios ◽

Andres Arias-Londoño ◽

Cesar Álvarez-Arroyo

Keyword(s):

Power Flow ◽

Fitness Function ◽

Solution Space ◽

Distribution Networks ◽

Optimal Placement ◽

Mixed Integer ◽

Optimization Approach ◽

Solar Pv ◽

Flow Method ◽

Power Flow Method

This research addresses the problem of the optimal placement and sizing of (PV) sources in medium voltage distribution grids through the application of the recently developed Newton metaheuristic optimization algorithm (NMA). The studied problem is formulated through a mixed-integer nonlinear programming model where the binary variables regard the installation of a PV source in a particular node, and the continuous variables are associated with power generations as well as the voltage magnitudes and angles, among others. To improve the performance of the NMA, we propose the implementation of a discrete–continuous codification where the discrete component deals with the location problem and the continuous component works with the sizing problem of the PV sources. The main advantage of the NMA is that it works based on the first and second derivatives of the fitness function considering an evolution formula that contains its current solution (xit) and the best current solution (xbest), where the former one allows location exploitation and the latter allows the global exploration of the solution space. To evaluate the fitness function and its derivatives, the successive approximation power flow method was implemented, which became the proposed solution strategy in a master–slave optimizer, where the master stage is governed by the NMA and the slave stage corresponds to the power flow method. Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of 26.89% and 27.60% for each test feeder with respect to the benchmark cases.

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Optimal Operation of Soft Open Points-Based Energy Storage in Active Distribution Networks by Considering the Battery Lifetime

Frontiers in Energy Research ◽

10.3389/fenrg.2020.633401 ◽

2021 ◽

Vol 8 ◽

Author(s):

Jian Wang ◽

Niancheng Zhou ◽

Anqi Tao ◽

Qianggang Wang

Keyword(s):

Energy Storage ◽

Reactive Power ◽

Programming Model ◽

Distribution Networks ◽

Optimal Operation ◽

Mixed Integer ◽

Operation Model ◽

Battery Lifetime ◽

Battery Degradation ◽

Active Distribution Networks

Soft open point-based energy storage (SOP-based ES) can transfer power in time and space and also regulate reactive power. These characteristics help promote the integration of distributed generations (DGs) and reduce the operating cost of active distribution networks (ADNs). Therefore, this work proposed an optimal operation model for SOP-based ES in ADNs by considering the battery lifetime. First, the active and reactive power equations of SOP-based ES and battery degradation cost were modeled. Then, the optimal operation model that includes the operation cost of ADNs, loss cost, and battery degradation cost was established. The mixed integer nonlinear programming model was transformed to a mixed integer linear programming model derived through linearization treatment. Finally, the feasibility and effectiveness of the proposed optimization model are verified by the IEEE33 node system.

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Annual Cost and Loss Minimization in a Radial Distribution Network by Capacitor Allocation Using PSO

Applied Sciences ◽

10.3390/app112411840 ◽

2021 ◽

Vol 11 (24) ◽

pp. 11840

Author(s):

Muhammad Bilal ◽

Mohsin Shahzad ◽

Muhammad Arif ◽

Barkat Ullah ◽

Suhaila Badarol Hisham ◽

...

Keyword(s):

Objective Function ◽

Radial Distribution ◽

Annual Cost ◽

Reactive Power ◽

Optimal Solution ◽

Distribution Networks ◽

Optimal Placement ◽

Use Case ◽

Voltage Profile ◽

Sensitivity Indices

Increasing power demand from passive distribution networks has led to deteriorated voltage profiles and increased line flows. This has increased the annual operations and installation costs due to unavoidable reinforcement equipment. This work proposes the reduction in annual costs by optimal placement of capacitors used to alleviate power loss in radial distribution networks (RDNs). The optimization objective function is formulated for the reduction in operation costs by (i) reducing the active and reactive power losses, and (ii) the cost and installation of capacitors, necessary to provide the reactive power support and maintain the voltage profile. Initially, the network buses are ranked according to two loss sensitivity indices (LSIs), i.e., active loss sensitivity with respect to node voltage (LSI1) and reactive power injection (LSI2). The sorted bus list is then fed to the particle swarm optimization (PSO) for solving the objective function. The efficacy of the proposed work is tested on different IEEE standard networks (34 and 85 nodes) for different use cases and load conditions. In use case 1, the values finalized by the algorithm are selected without considering their market availability, whereas in use case 2, market-available capacitor sizes close to the optimal solution are selected. Furthermore, the static and seasonal load profiles are considered. The results are compared with recent methods and have shown significant improvement in terms of annual cost, losses and line flows reduction, and voltage profile.

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Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach

Computation ◽

10.3390/computation9060067 ◽

2021 ◽

Vol 9 (6) ◽

pp. 67

Author(s):

Oscar Danilo Montoya ◽

Alexander Molina-Cabrera ◽

Luis Fernando Grisales-Noreña ◽

Ricardo Alberto Hincapié ◽

Mauricio Granada

Keyword(s):

Genetic Algorithm ◽

Reactive Power ◽

Search Algorithm ◽

Peak Load ◽

Distribution Networks ◽

Numerical Results ◽

Optimization Approach ◽

Three Phase ◽

Operative Costs ◽

Power Curves

This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine–cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values.

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A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks

Electronics ◽

10.3390/electronics10010026 ◽

2020 ◽

Vol 10 (1) ◽

pp. 26 ◽

Cited By ~ 1

Author(s):

Oscar Danilo Montoya ◽

Alexander Molina-Cabrera ◽

Harold R. Chamorro ◽

Lazaro Alvarado-Barrios ◽

Edwin Rivas-Trujillo

Keyword(s):

Optimal Power Flow ◽

Hybrid Approach ◽

Optimal Solution ◽

Optimization Procedure ◽

Distribution Networks ◽

Optimal Placement ◽

Equivalent Model ◽

Mixed Integer ◽

Discrete Version ◽

Distributed Generators

This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool.

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Dynamic Reactive Power Compensation in Power Systems through the Optimal Siting and Sizing of Photovoltaic Sources

Resources ◽

10.3390/resources10050047 ◽

2021 ◽

Vol 10 (5) ◽

pp. 47

Author(s):

Andrés Felipe Buitrago-Velandia ◽

Oscar Danilo Montoya ◽

Walter Gil-González

Keyword(s):

Power Systems ◽

Optimization Model ◽

Power Plants ◽

Reactive Power ◽

Programming Model ◽

Power Converter ◽

Reactive Power Compensation ◽

Optimal Placement ◽

Mixed Integer ◽

Photovoltaic Generators

The problem of the optimal placement and sizing of photovoltaic power plants in electrical power systems from high- to medium-voltage levels is addressed in this research from the point of view of the exact mathematical optimization. To represent this problem, a mixed-integer nonlinear programming model considering the daily demand and solar radiation curves was developed. The main advantage of the proposed optimization model corresponds to the usage of the reactive power capabilities of the power electronic converter that interfaces the photovoltaic sources with the power systems, which can work with lagging or leading power factors. To model the dynamic reactive power compensation, the η-coefficient was used as a function of the nominal apparent power converter transference rate. The General Algebraic Modeling System software with the BONMIN optimization package was used as a computational tool to solve the proposed optimization model. Two simulation cases composed of 14 and 27 nodes in transmission and distribution levels were considered to validate the proposed optimization model, taking into account the possibility of installing from one to four photovoltaic sources in each system. The results show that energy losses are reduced between 13% and 56% as photovoltaic generators are added with direct effects on the voltage profile improvement.

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Flexible Genetic Algorithm Based Optimal Power Flow of Power Systems

Journal of Engineering ◽

10.31026/j.eng.2018.03.07 ◽

2018 ◽

Vol 24 (3) ◽

pp. 84

Author(s):

Hassan Abdullah Kubba ◽

Mounir Thamer Esmieel

Keyword(s):

Genetic Algorithm ◽

Objective Function ◽

Power Flow ◽

Optimal Power Flow ◽

Reactive Power ◽

Test System ◽

Multi Objective ◽

Optimal Power ◽

Blending Method ◽

Real Coded Genetic Algorithm

Nowadays, the power plant is changing the power industry from a centralized and vertically integrated form into regional, competitive and functionally separate units. This is done with the future aims of increasing efficiency by better management and better employment of existing equipment and lower price of electricity to all types of customers while retaining a reliable system. This research is aimed to solve the optimal power flow (OPF) problem. The OPF is used to minimize the total generations fuel cost function. Optimal power flow may be single objective or multi objective function. In this thesis, an attempt is made to minimize the objective function with keeping the voltages magnitudes of all load buses, real output power of each generator bus and reactive power of each generator bus within their limits. The proposed method in this thesis is the Flexible Continuous Genetic Algorithm or in other words the Flexible Real-Coded Genetic Algorithm (RCGA) using the efficient GA's operators such as Rank Assignment (Weighted) Roulette Wheel Selection, Blending Method Recombination operator and Mutation Operator as well as Multi-Objective Minimization technique (MOM). This method has been tested and checked on the IEEE 30 buses test system and implemented on the 35-bus Super Iraqi National Grid (SING) system (400 KV). The results of OPF problem using IEEE 30 buses typical system has been compared with other researches.

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