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

2021 ◽  
Vol 11 (23) ◽  
pp. 11525
Author(s):  
Oscar Danilo Montoya ◽  
Luis Fernando Grisales-Noreña ◽  
Lázaro Alvarado-Barrios ◽  
Andres Arias-Londoño ◽  
Cesar Álvarez-Arroyo

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.

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 61
Author(s):  
Oscar Danilo Montoya ◽  
Juan S. Giraldo ◽  
Luis Fernando Grisales-Noreña ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios

The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including Δ- and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures.


2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández

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.


Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4078 ◽  
Author(s):  
Baljinnyam Sereeter ◽  
Werner van Westering ◽  
Cornelis Vuik ◽  
Cees Witteveen

In this paper, we propose a fast linear power flow method using a constant impedance load model to simulate both the entire Low Voltage (LV) and Medium Voltage (MV) networks in a single simulation. Accuracy and efficiency of this linear approach are validated by comparing it with the Newton power flow algorithm and a commercial network design tool Vision on various distribution networks including real network data. Results show that our method can be as accurate as classical Nonlinear Power Flow (NPF) methods using a constant power load model and additionally, it is much faster than NPF computations. In our research, it is shown that voltage problems can be identified more efficiently when MV and LV are integrally evaluated. Moreover, Numerical Analysis (NA) techniques are applied to the Large Linear Power Flow (LLPF) problem with 27 million nonzeros in order to improve the computation time by studying the properties of the linear system. Finally, the original computation times of LLPF problems with real and complex components are reduced by 2.8 times and 5.7 times, respectively.


2021 ◽  
Vol 11 (2) ◽  
pp. 627
Author(s):  
Walter Gil-González ◽  
Alejandro Garces ◽  
Oscar Danilo Montoya ◽  
Jesus C. Hernández

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.


2021 ◽  
Vol 11 (8) ◽  
pp. 3353
Author(s):  
Oscar Danilo Montoya ◽  
Harold R. Chamorro ◽  
Lazaro Alvarado-Barrios ◽  
Walter Gil-González ◽  
César Orozco-Henao

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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