Hybrid ga-socp approach for placement and sizing of distributed generators in DC networks

This research addresses the problem of the optimal location and sizing distributed generators (DGs) in direct current (DC) distribution networks from the combinatorial optimization. It is proposed a master–slave optimization approach in order to solve the problems of placement and location of DGs, respectively. The master stage applies to the classical Chu & Beasley genetic algorithm (GA), while the slave stage resolves a second-order cone programming reformulation of the optimal power flow problem for DC grids. This master–slave approach generates a hybrid optimization approach, named GA-SOCP. The main advantage of optimal dimensioning of DGs via SOCP is that this method makes part of the exact mathematical optimization that guarantees the possibility of finding the global optimal solution due to the solution space’s convex structure, which is a clear improvement regarding classical metaheuristic optimization methodologies. Numerical comparisons with hybrid and exact optimization approaches reported in the literature demonstrate the proposed hybrid GA-SOCP approach’s effectiveness and robustness to achieve the global optimal solution. Two test feeders compose of 21 and 69 nodes that can locate three distributed generators are considered. All of the computational validations have been carried out in the MATLAB software and the CVX tool for convex optimization

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

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

An mi-sdp model for optimal location and sizing of distributed generators in dc grids that guarantees the global optimum

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

Optimal Location and Sizing of Distributed Generators in DC Networks Using a Hybrid Method Based on Parallel PBIL and PSO

This paper addresses the problem of the locating and sizing of distributed generators (DGs) in direct current (DC) grids and proposes a hybrid methodology based on a parallel version of the Population-Based Incremental Learning (PPBIL) algorithm and the Particle Swarm Optimization (PSO) method. The objective function of the method is based on the reduction of the power loss by using a master-slave structure and the consideration of the set of restrictions associated with DC grids in a distributed generation environment. In such a structure, the master stage (PPBIL) finds the location of the generators and the slave stage (PSO) finds the corresponding sizes. For the purpose of comparison, eight additional hybrid methods were formed by using two additional location methods and two additional sizing methods, and this helped in the evaluation of the effectiveness of the proposed solution. Such an evaluation is illustrated with the electrical test systems composed of 10, 21 and 69 buses and simulated on the software, MATLAB. Finally, the results of the simulation demonstrated that the PPBIL–PSO method obtains the best balance between the reduction of power loss and the processing time

Integration of PV Distributed Generators into Electrical Networks for Investment and Energy Purchase Costs Reduction by Using a Discrete–Continuous Parallel PSO

The problem of optimally integrating PV DGs into electrical networks to reduce annual costs (which include energy purchase and investment costs) was addressed in this research by presenting a new solution methodology. For such purpose, we used a Discrete–Continuous Parallel Particle Swarm Optimization method (DCPPSO), which considers both the discrete and continuous variables associated with the location and sizing of DGs in an electrical network and employs a parallel processing tool to reduce processing times. The optimization parameters of the proposed solution methodology were tuned using an external optimization algorithm. To validate the performance of DCPPSO, we employed the 33- and 69-bus test systems and compared it with five other solution methods: the BONMIN solver of the General Algebraic Modeling System (GAMS) and other four discrete–continuous methodologies that have been recently proposed. According to the findings, the DCPPSO produced the best results in terms of quality of the solution, processing time, and repeatability in electrical networks of any size, since it showed a better performance as the size of the electrical system increased. © 2022 by the authors

Optimal Location and Operation of PV Sources in DC Grids to Reduce Annual Operating Costs While Considering Variable Power Demand and Generation

Due to the need to include renewable energy resources in electrical grids as well as the development and high implementation of PV generation and DC grids worldwide, it is necessary to propose effective optimization methodologies that guarantee that PV generators are located and sized on the DC electrical network. This will reduce the operation costs and cover the investment and maintenance cost related to the new technologies (PV distributed generators), thus satisfying all technical and operative constraints of the distribution grid. It is important to propose solution methodologies that require short processing times, with the aim of exploring a large number of scenarios while planning energy projects that are to be presented in public and private contracts, as well as offering solutions to technical problems of electrical distribution companies within short periods of time. Based on these needs, this paper proposes the implementation of a Discrete–Continuous Parallel version of the Particle Swarm Optimization algorithm (DCPPSO) to solve the problem regarding the integration of photovoltaic (PV) distributed generators (DGs) in Direct Current (DC) grids, with the purpose of reducing the annual costs related to energy purchasing as well as the investment and maintenance cost associated with PV sources in a scenario of variable power demand and generation. In order to evaluate the effectiveness, repeatability, and robustness of the proposed methodology, four comparison methods were employed, i.e., a commercial software and three discrete–continuous methodologies, as well as two test systems of 33 and 69 buses. In analyzing the results obtained in terms of solution quality, it was possible to identify that the DCPPSO proposed obtained the best performance in relation to the comparison methods used, with excellent results in relation to the processing times and standard deviation. The main contribution of the proposed methodology is the implementation of a discrete–continuous codification with a parallel processing tool for the evaluation of the fitness function. The results obtained and the reports in the literature for alternating current networks demonstrate that the DCPPSO is the optimization methodology with the best performance in solving the problem of the optimal integration of PV sources in economic terms and for any kind of electrical system and size. © 2022 by the authors

Integration of PV Distributed Generators into Electrical Networks for Investment and Energy Purchase Costs Reduction by Using a Discrete–Continuous Parallel PSO

The problem of optimally integrating PV DGs into electrical networks to reduce annual costs (which include energy purchase and investment costs) was addressed in this research by presenting a new solution methodology. For such purpose, we used a Discrete–Continuous Parallel Particle Swarm Optimization method (DCPPSO), which considers both the discrete and continuous variables associated with the location and sizing of DGs in an electrical network and employs a parallel processing tool to reduce processing times. The optimization parameters of the proposed solution methodology were tuned using an external optimization algorithm. To validate the performance of DCPPSO, we employed the 33- and 69-bus test systems and compared it with five other solution methods: the BONMIN solver of the General Algebraic Modeling System (GAMS) and other four discrete–continuous methodologies that have been recently proposed. According to the findings, the DCPPSO produced the best results in terms of quality of the solution, processing time, and repeatability in electrical networks of any size, since it showed a better performance as the size of the electrical system increased

A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks

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

Solar-Based DG Allocation Using Harris Hawks Optimization While Considering Practical Aspects

The restructuring of power systems and the ever-increasing demand for electricity have given rise to congestion in power networks. The use of distributed generators (DGs) may play a significant role in tackling such issues. DGs may be integrated with electrical power networks to regulate the drift of power in the transmission lines, thereby increasing the power transfer capabilities of lines and improving the overall performance of electrical networks. In this article, an effective method based on the Harris hawks optimization (HHO) algorithm is used to select the optimum capacity, number, and site of solar-based DGs to reduce real power losses and voltage deviation. The proposed HHO has been tested with a complex benchmark function then applied to the IEEE 33 and IEEE 69 bus radial distribution systems. The single and multiple solar-based DGs are optimized for the optimum size and site with a unity power factor. It is observed that the overall performance of the systems is enhanced when additional DGs are installed. Moreover, considering the stochastic and sporadic nature of solar irradiance, the practical size of DG has been suggested based on analysis that may be adopted while designing the actual photovoltaic (PV) plant for usage. The obtained simulation outcomes are compared with the latest state-of-the-art literature and suggest that the proposed HHO is capable of processing complex high dimensional benchmark functions and has capability to handle problems pertaining to electrical distribution in an effective manner.publishedVersio