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Special Issue "Optimization Methods Applied to Power Systems"

A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "Electrical Power and Energy System".

Deadline for manuscript submissions: 28 February 2019

Special Issue Editors

Guest Editor
Dr. Francisco G. Montoya

Department of Engineering, University of Almeria, Carretera de Sacramento s/n, E-04120, Almeria (Spain)
Website | E-Mail
Interests: power quality; smart metering; smart grids; renewable energy
Guest Editor
Dr. Raúl Baños Navarro

Department of Engineering, University of Almeria, Carretera de Sacramento s/n, E-04120, Almeria (Spain)
Website | E-Mail
Interests: power systems; renewable energy; engineering economics; network optimization; multiobjective optimization; ICT in education

Special Issue Information

Dear Colleagues,

We are inviting submissions to a Special Issue of Energies Journal on the subject area of “Optimization Methods Applied to Power Systems”. Power systems are made up of extensive complex networks governed by physical laws in which unexpected and uncontrolled events can occur. This complexity has increased considerably in recent years due to the increase in distributed generation associated with increased generation capacity from renewable energy sources. Therefore, the analysis, design and operation of current and future electrical systems require an efficient approach to different problems (like load flow, parameters and position finding, filter designing, fault location, contingency analysis, system restoration after blackout, islanding detection of distributed generations, economic dispatch, unit commitment, etc.). Given the complexity of these problems, the efficient management of electrical systems requires the application of advanced optimization methods that take advantage of the advances of current computers.

The topics of interest in this Special Issue include different optimization methods applied to any field related to power systems, such as conventional and renewable energy generation, distributed generation, transport and distribution of electrical energy, electrical machines and power electronics, intelligent systems, advances in electric mobility, etc. The optimization methods of interest for publication include, but are not limited to:

  • Expert Systems
  • Artificial Neural Networks
  • Fuzzy Logic
  • Genetic Algorithms
  • Evolutionary Algorithms
  • Simulated Annealing
  • Tabu Search
  • Ant Colony Optimization
  • Particle Swarm Optimization
  • Multi-objective Optimization
  • Parallel Computing
  • Linear and Nonlinear Programming
  • Integer and Mixed-Integer Programming
  • Dynamic Programming
  • Interior Point Methods
  • Lagrangian Relaxation and Benders Decomposition-based Methods
  • General Stochastic Techniques

Prof. Dr. Francisco G. Montoya
Dr. Raúl Baños
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Energies is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • power systems
  • electrical systems
  • optimization techniques
  • heuristic techniques
  • artificial intelligence techniques

Published Papers (15 papers)

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Research

Open AccessArticle Demand Bidding Optimization for an Aggregator with a Genetic Algorithm
Energies 2018, 11(10), 2498; https://doi.org/10.3390/en11102498
Received: 8 August 2018 / Revised: 11 September 2018 / Accepted: 18 September 2018 / Published: 20 September 2018
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Abstract
Demand response (DR) is an effective solution used to maintain the reliability of power systems. Although numerous demand bidding models were designed to balance the demand and supply of electricity, these works focused on optimizing the DR supply curve of aggregator and the
[...] Read more.
Demand response (DR) is an effective solution used to maintain the reliability of power systems. Although numerous demand bidding models were designed to balance the demand and supply of electricity, these works focused on optimizing the DR supply curve of aggregator and the associated clearing prices. Limited researches were done to investigate the interaction between each aggregator and its customers to ensure the delivery of promised load curtailments. In this paper, a closed demand bidding model is envisioned to bridge the aforementioned gap by facilitating the internal DR trading between the aggregator and its large contract customers. The customers can submit their own bid as a pairs of bidding price and quantity of load curtailment in hourly basis when demand bidding is needed. A purchase optimization scheme is then designed to minimize the total bidding purchase cost. Given the presence of various load curtailment constraints, the demand bidding model considered is highly nonlinear. A modified genetic algorithm incorporated with efficient encoding scheme and adaptive bid declination strategy is therefore proposed to solve this problem effectively. Extensive simulation shows that the proposed purchase optimization scheme can minimize the total cost of demand bidding and it is computationally feasible for real applications. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Using Piecewise Linearization Method to PCS Input/Output-Efficiency Curve for a Stand-Alone Microgrid Unit Commitment
Energies 2018, 11(9), 2468; https://doi.org/10.3390/en11092468
Received: 7 September 2018 / Revised: 12 September 2018 / Accepted: 13 September 2018 / Published: 17 September 2018
PDF Full-text (2295 KB) | HTML Full-text | XML Full-text
Abstract
When operating a stand-alone micro grid, the battery energy storage system (BESS) and a diesel generator are key components needed in order to maintain demand-supply balance. Using Unit Commitment (UC) to calculate the optimal operation schedule of a BESS and diesel generator helps
[...] Read more.
When operating a stand-alone micro grid, the battery energy storage system (BESS) and a diesel generator are key components needed in order to maintain demand-supply balance. Using Unit Commitment (UC) to calculate the optimal operation schedule of a BESS and diesel generator helps minimize the operation cost of the micro grid. While calculating the optimal operation schedule for the microgrid, it is important that it reflects the actual characteristics of the implanted devices, in order to increase the schedule result accuracy. In this paper, a piecewise linearization, on the actual power conditioning system (PCS) input/output-efficiency characteristic curve, has been considered while calculating the optimal operation schedule using UC. The optimal schedule result calculated by the proposed method has been examined by comparing the schedule calculated by a fixed input/output-efficiency case, which is conventionally used while solving UC for a stand-alone microgrid. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Dynamic Optimization of Combined Cooling, Heating, and Power Systems with Energy Storage Units
Energies 2018, 11(9), 2288; https://doi.org/10.3390/en11092288
Received: 4 August 2018 / Revised: 28 August 2018 / Accepted: 29 August 2018 / Published: 30 August 2018
PDF Full-text (3735 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, a combined cooling, heating, and power (CCHP) system with thermal storage tanks is introduced. Considering the plants’ off-design performance, an efficient methodology is introduced to determine the most economical operation schedule. The complex CCHP system’s state transition equation is extracted
[...] Read more.
In this paper, a combined cooling, heating, and power (CCHP) system with thermal storage tanks is introduced. Considering the plants’ off-design performance, an efficient methodology is introduced to determine the most economical operation schedule. The complex CCHP system’s state transition equation is extracted by selecting the stored cooling and heating energy as the discretized state variables. Referring to the concept of variable cost and constant cost, repeated computations are saved in phase operating cost calculations. Therefore, the most economical operation schedule is obtained by employing a dynamic solving framework in an extremely short time. The simulation results indicated that the optimized operating cost is reduced by 40.8% compared to the traditional energy supply system. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle A Hybrid DA-PSO Optimization Algorithm for Multiobjective Optimal Power Flow Problems
Energies 2018, 11(9), 2270; https://doi.org/10.3390/en11092270
Received: 3 August 2018 / Revised: 20 August 2018 / Accepted: 27 August 2018 / Published: 29 August 2018
PDF Full-text (6217 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
In this paper, a hybrid optimization algorithm is proposed to solve multiobjective optimal power flow problems (MO-OPF) in a power system. The hybrid algorithm, named DA-PSO, combines the frameworks of the dragonfly algorithm (DA) and particle swarm optimization (PSO) to find the optimized
[...] Read more.
In this paper, a hybrid optimization algorithm is proposed to solve multiobjective optimal power flow problems (MO-OPF) in a power system. The hybrid algorithm, named DA-PSO, combines the frameworks of the dragonfly algorithm (DA) and particle swarm optimization (PSO) to find the optimized solutions for the power system. The hybrid algorithm adopts the exploration and exploitation phases of the DA and PSO algorithms, respectively, and was implemented to solve the MO-OPF problem. The objective functions of the OPF were minimization of fuel cost, emissions, and transmission losses. The standard IEEE 30-bus and 57-bus systems were employed to investigate the performance of the proposed algorithm. The simulation results were compared with those in the literature to show the superiority of the proposed algorithm over several other algorithms; however, the time computation of DA-PSO is slower than DA and PSO due to the sequential computation of DA and PSO. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Adaptive Consensus Algorithm for Distributed Heat-Electricity Energy Management of an Islanded Microgrid
Energies 2018, 11(9), 2236; https://doi.org/10.3390/en11092236
Received: 10 July 2018 / Revised: 18 August 2018 / Accepted: 19 August 2018 / Published: 26 August 2018
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Abstract
This paper proposes a novel adaptive consensus algorithm (ACA) for distributed heat-electricity energy management (HEEM) of an islanded microgrid. In order to simultaneously satisfy the heat-electricity energy balance constraints, ACA is implemented with a switch between unified consensus and independent consensus according to
[...] Read more.
This paper proposes a novel adaptive consensus algorithm (ACA) for distributed heat-electricity energy management (HEEM) of an islanded microgrid. In order to simultaneously satisfy the heat-electricity energy balance constraints, ACA is implemented with a switch between unified consensus and independent consensus according to the dynamic energy mismatches. The feasible operation region of a combined heat and power (CHP) unit is decomposed into eight searching sub-regions, thus its electricity and heat energy outputs can simultaneously match the incremental cost consensus requirement and the heat-electricity energy balance constraints. Case studies are thoroughly carried out to verify the performance of ACA for distributed HEEM of an islanded microgrid. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Using Generalized Generation Distribution Factors in a MILP Model to Solve the Transmission-Constrained Unit Commitment Problem
Energies 2018, 11(9), 2232; https://doi.org/10.3390/en11092232
Received: 9 August 2018 / Revised: 20 August 2018 / Accepted: 24 August 2018 / Published: 26 August 2018
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Abstract
This study proposes a mixed-integer linear programming (MILP) model to figure out the transmission-constrained direct current (DC)-based unit commitment (UC) problem using the generalized generation distribution factors (GGDF) for modeling the transmission network constraints. The UC problem has been reformulated using these linear
[...] Read more.
This study proposes a mixed-integer linear programming (MILP) model to figure out the transmission-constrained direct current (DC)-based unit commitment (UC) problem using the generalized generation distribution factors (GGDF) for modeling the transmission network constraints. The UC problem has been reformulated using these linear distribution factors without sacrificing optimality. Several test power systems (PJM 5-bus, IEEE-24, and 118-bus) have been used to validate the introduced formulation. Results demonstrate that the proposed approach is more compact and less computationally burdensome than the classical DC-based formulation, which is commonly employed in the technical literature to carry out the transmission network constraints. Therefore, there is a potential applicability of the accomplished methodology to carry out the UC problem applied to medium and large-scale electrical power systems. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Maintenance Factor Identification in Outdoor Lighting Installations Using Simulation and Optimization Techniques
Energies 2018, 11(8), 2169; https://doi.org/10.3390/en11082169
Received: 20 July 2018 / Revised: 8 August 2018 / Accepted: 14 August 2018 / Published: 20 August 2018
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Abstract
This document addresses the development of a novel methodology to identify the actual maintenance factor of the luminaires of an outdoor lighting installation in order to assess their lighting performance. The method is based on the combined use of Radiance, a free and
[...] Read more.
This document addresses the development of a novel methodology to identify the actual maintenance factor of the luminaires of an outdoor lighting installation in order to assess their lighting performance. The method is based on the combined use of Radiance, a free and open-source tool, for the modeling and simulation of lighting scenes, and GenOpt, a generic optimization program, for the calibration of the model. The application of this methodology allows the quantification of the deterioration of the road lighting system and the identification of luminaires that show irregularities in their operation. Values lower than 9% for the error confirm that this research can contribute to the management of street lighting by assessing real road conditions. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Reactive Power Dispatch Optimization with Voltage Profile Improvement Using an Efficient Hybrid Algorithm
Energies 2018, 11(8), 2134; https://doi.org/10.3390/en11082134
Received: 12 July 2018 / Revised: 12 August 2018 / Accepted: 13 August 2018 / Published: 16 August 2018
PDF Full-text (5558 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents an efficient approach for solving the optimal reactive power dispatch problem. It is a non-linear constrained optimization problem where two distinct objective functions are considered. The proposed approach is based on the hybridization of the particle swarm optimization method and
[...] Read more.
This paper presents an efficient approach for solving the optimal reactive power dispatch problem. It is a non-linear constrained optimization problem where two distinct objective functions are considered. The proposed approach is based on the hybridization of the particle swarm optimization method and the tabu-search technique. This hybrid approach is used to find control variable settings (i.e., generation bus voltages, transformer taps and shunt capacitor sizes) which minimize transmission active power losses and load bus voltage deviations. To validate the proposed hybrid method, the IEEE 30-bus system is considered for 12 and 19 control variables. The obtained results are compared with those obtained by particle swarm optimization and a tabu-search without hybridization and with other evolutionary algorithms reported in the literature. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessFeature PaperArticle Parameter Estimation of Electromechanical Oscillation Based on a Constrained EKF with C&I-PSO
Energies 2018, 11(8), 2059; https://doi.org/10.3390/en11082059
Received: 18 July 2018 / Revised: 3 August 2018 / Accepted: 6 August 2018 / Published: 8 August 2018
PDF Full-text (2175 KB) | HTML Full-text | XML Full-text
Abstract
By combining together the extended Kalman filter with a newly developed C&I particle swarm optimization algorithm (C&I-PSO), a novel estimation method is proposed for parameter estimation of electromechanical oscillation, in which critical physical constraints on the parameters are taken into account. Based on
[...] Read more.
By combining together the extended Kalman filter with a newly developed C&I particle swarm optimization algorithm (C&I-PSO), a novel estimation method is proposed for parameter estimation of electromechanical oscillation, in which critical physical constraints on the parameters are taken into account. Based on the extended Kalman filtering algorithm, the constrained parameter estimation problem is formulated via the projection method. Then, by utilizing the penalty function method, the obtained constrained optimization problem could be converted into an equivalent unconstrained optimization problem; finally, the C&I-PSO algorithm is developed to address the unconstrained optimization problem. Therefore, the parameters of electromechanical oscillation with physical constraints can be successfully estimated and better performed. Finally, the effectiveness of the obtained results has been illustrated by several test systems. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessFeature PaperArticle A Novel Multi-Population Based Chaotic JAYA Algorithm with Application in Solving Economic Load Dispatch Problems
Energies 2018, 11(8), 1946; https://doi.org/10.3390/en11081946
Received: 1 July 2018 / Revised: 20 July 2018 / Accepted: 22 July 2018 / Published: 26 July 2018
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Abstract
The economic load dispatch (ELD) problem is an optimization problem of minimizing the total fuel cost of generators while satisfying power balance constraints, operating capacity limits, ramp-rate limits and prohibited operating zones. In this paper, a novel multi-population based chaotic JAYA algorithm (MP-CJAYA)
[...] Read more.
The economic load dispatch (ELD) problem is an optimization problem of minimizing the total fuel cost of generators while satisfying power balance constraints, operating capacity limits, ramp-rate limits and prohibited operating zones. In this paper, a novel multi-population based chaotic JAYA algorithm (MP-CJAYA) is proposed to solve the ELD problem by applying the multi-population method (MP) and chaotic optimization algorithm (COA) on the original JAYA algorithm to guarantee the best solution of the problem. MP-CJAYA is a modified version where the total population is divided into a certain number of sub-populations to control the exploration and exploitation rates, at the same time a chaos perturbation is implemented on each sub-population during every iteration to keep on searching for the global optima. The proposed MP-CJAYA has been adopted to ELD cases and the results obtained have been compared with other well-known algorithms reported in the literature. The comparisons have indicated that MP-CJAYA outperforms all the other algorithms, achieving the best performance in all the cases, which indicates that MP-CJAYA is a promising alternative approach for solving ELD problems. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Optimal Micro-PMU Placement Using Mutual Information Theory in Distribution Networks
Energies 2018, 11(7), 1917; https://doi.org/10.3390/en11071917
Received: 28 June 2018 / Revised: 17 July 2018 / Accepted: 19 July 2018 / Published: 23 July 2018
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Abstract
Micro-phasor measurement unit (μPMU) is under fast development and becoming more and more important for application in future distribution networks. It is unrealistic and unaffordable to place all buses with μPMUs because of the high costs, leading to the necessity of determining optimal
[...] Read more.
Micro-phasor measurement unit (μPMU) is under fast development and becoming more and more important for application in future distribution networks. It is unrealistic and unaffordable to place all buses with μPMUs because of the high costs, leading to the necessity of determining optimal placement with minimal numbers of μPMUs in the distribution system. An optimal μPMU placement (OPP) based on the information entropy evaluation and node selection strategy (IENS) using greedy algorithm is presented in this paper. The uncertainties of distributed generations (DGs) and pseudo measurements are taken into consideration, and the two-point estimation method (2PEM) is utilized for solving stochastic state estimation problems. The set of buses selected by improved IENS, which can minimize the uncertainties of network and obtain system observability is considered as the optimal deployment of μPMUs. The proposed method utilizes the measurements of smart meters and pseudo measurements of load powers in the distribution systems to reduce the number of μPMUs and enhance the observability of the network. The results of the simulations prove the effectiveness of the proposed algorithm with the comparison of traditional topological methods for the OPP problem. The improved IENS method can obtain the optimal complete and incomplete μPMU placement in the distribution systems. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Modular Predictor for Day-Ahead Load Forecasting and Feature Selection for Different Hours
Energies 2018, 11(7), 1899; https://doi.org/10.3390/en11071899
Received: 25 June 2018 / Revised: 10 July 2018 / Accepted: 12 July 2018 / Published: 20 July 2018
PDF Full-text (3375 KB) | HTML Full-text | XML Full-text
Abstract
To improve the accuracy of the day-ahead load forecasting predictions of a single model, a novel modular parallel forecasting model with feature selection was proposed. First, load features were extracted from a historic load with a horizon from the previous 24 h to
[...] Read more.
To improve the accuracy of the day-ahead load forecasting predictions of a single model, a novel modular parallel forecasting model with feature selection was proposed. First, load features were extracted from a historic load with a horizon from the previous 24 h to the previous 168 h considering the calendar feature. Second, a feature selection combined with a predictor process was carried out to select the optimal feature for building a reliable predictor with respect to each hour. The final modular model consisted of 24 predictors with a respective optimal feature subset for day-ahead load forecasting. New England and Singapore load data were used to evaluate the effectiveness of the proposed method. The results indicated that the accuracy of the proposed modular model was higher than that of the traditional method. Furthermore, conducting a feature selection step when building a predictor improved the accuracy of load forecasting. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Distributed Energy Sharing for PVT-HP Prosumers in Community Energy Internet: A Consensus Approach
Energies 2018, 11(7), 1891; https://doi.org/10.3390/en11071891
Received: 27 June 2017 / Revised: 15 July 2018 / Accepted: 17 July 2018 / Published: 20 July 2018
PDF Full-text (719 KB) | HTML Full-text | XML Full-text
Abstract
Community Energy Internet (CEI) integrates electric network and thermal network based on combined heat and power (CHP) to improve the economy of energy system in Smart Community. In the CEI, an energy sharing framework for prosumers equipped with photovoltaic-thermal (PVT) system and heat
[...] Read more.
Community Energy Internet (CEI) integrates electric network and thermal network based on combined heat and power (CHP) to improve the economy of energy system in Smart Community. In the CEI, an energy sharing framework for prosumers equipped with photovoltaic-thermal (PVT) system and heat pump (HP) is introduced. Supporting by the PVT and HP, the prosumer has four role attributes with either heat or electricity producer/consumer. A social welfare maximization model is built for the CEI, including PVT-HP prosumers, CHP system, and utility grid. Considering there are multiply participants in the local market of CEI, the social welfare maximization problem is decoupled by using Lagrange multiplier method. Moreover, a consensus-based fully distributed algorithm is designed to solve the problem. Finally, six residential buildings are selected as the case study to validate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle Solving Non-Smooth Optimal Power Flow Problems Using a Developed Grey Wolf Optimizer
Energies 2018, 11(7), 1692; https://doi.org/10.3390/en11071692
Received: 13 June 2018 / Revised: 25 June 2018 / Accepted: 26 June 2018 / Published: 28 June 2018
PDF Full-text (1124 KB) | HTML Full-text | XML Full-text
Abstract
The optimal power flow (OPF) problem is a non-linear and non-smooth optimization problem. OPF problem is a complicated optimization problem, especially when considering the system constraints. This paper proposes a new enhanced version for the grey wolf optimization technique called Developed Grey Wolf
[...] Read more.
The optimal power flow (OPF) problem is a non-linear and non-smooth optimization problem. OPF problem is a complicated optimization problem, especially when considering the system constraints. This paper proposes a new enhanced version for the grey wolf optimization technique called Developed Grey Wolf Optimizer (DGWO) to solve the optimal power flow (OPF) problem by an efficient way. Although the GWO is an efficient technique, it may be prone to stagnate at local optima for some cases due to the insufficient diversity of wolves, hence the DGWO algorithm is proposed for improving the search capabilities of this optimizer. The DGWO is based on enhancing the exploration process by applying a random mutation to increase the diversity of population, while an exploitation process is enhanced by updating the position of populations in spiral path around the best solution. An adaptive operator is employed in DGWO to find a balance between the exploration and exploitation phases during the iterative process. The considered objective functions are quadratic fuel cost minimization, piecewise quadratic cost minimization, and quadratic fuel cost minimization considering the valve point effect. The DGWO is validated using the standard IEEE 30-bus test system. The obtained results showed the effectiveness and superiority of DGWO for solving the OPF problem compared with the other well-known meta-heuristic techniques. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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Open AccessArticle A Thermal Probability Density–Based Method to Detect the Internal Defects of Power Cable Joints
Energies 2018, 11(7), 1674; https://doi.org/10.3390/en11071674
Received: 22 May 2018 / Revised: 21 June 2018 / Accepted: 22 June 2018 / Published: 27 June 2018
PDF Full-text (7106 KB) | HTML Full-text | XML Full-text
Abstract
Internal defects inside power cable joints due to unqualified construction is the main issue of power cable failures, hence in this paper a method based on thermal probability density function to detect the internal defects of power cable joints is presented. First, the
[...] Read more.
Internal defects inside power cable joints due to unqualified construction is the main issue of power cable failures, hence in this paper a method based on thermal probability density function to detect the internal defects of power cable joints is presented. First, the model to calculate the thermal distribution of power cable joints is set up and the thermal distribution is calculated. Then a thermal probability density (TPD)-based method that gives the statistics of isothermal points is presented. The TPD characteristics of normal power cable joints and those with internal defects, including insulation eccentricity and unqualified connection of conductors, are analyzed. The results indicate that TPD differs with the internal state of cable joints. Finally, experiments were conducted in which surface thermal distribution was measured by FLIR SC7000, and the corresponding TPDs are discussed. Full article
(This article belongs to the Special Issue Optimization Methods Applied to Power Systems)
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