Browsing by Author "Montoya, Oscar Danilo"

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A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation
(2021-10-21) Montoya, Oscar Danilo; Molina-Cabrera, Alexander; Hernández, Jesus C.
This paper presents a comparative analysis of six different iterative power flow methods applied to AC distribution networks, which have been recently reported in the scientific literature. These power flow methods are (i) successive approximations, (ii) matricial backward/forward method, (iii) triangular-based approach, (iv) product linearization method, (v) hyperbolic linearization method, and (vi) diagonal approximation method. The first three methods and the last one are formulated without recurring derivatives, and they can be directly formulated in the complex domain; the fourth and fifth methods are based on the linear approximation of the power balance equations that are also formulated in the complex domain. The numerical comparison involves three main aspects: the convergence rate, processing time, and the number of iterations calculated using the classical Newton–Raphson method as the reference case. Numerical results from two test feeders composed of 34 and 85 nodes demonstrate that the derivative-free methods have linear convergence, and the methods that use derivatives in their formulation have quadratic convergence
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors
(2020-12-03) Grisales-Noreña, Luis Fernando; Montoya, Oscar Danilo; Gil-González, Walter; Perea-Moreno, Alberto-Jesus; Perea-Moreno, Miguel-Angel
This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures.
A Discrete-Continuous PSO for the Optimal Integration of D-STATCOMs into Electrical Distribution Systems by Considering Annual Power Loss and Investment Costs
(2022-07-14) Grisales-Noreña, Luis Fernando; Montoya, Oscar Danilo; Hernández, Jesus C.; Ramos-Paja, Carlos Andres; Perea-Moreno, Alberto-Jesus
Currently, with the quick increase in global population, the energetic crisis, the environmental problematic, and the development of the power electronic devices generated the need to include new technologies for supporting and potentiating electrical distributions systems; Distribution Static Compensators (D-STATCOMs) are highly used for this task due to the advantages that this technology presents: reduction in power loss, operation costs, and chargeability of branches, among others. The possibility to include this kind of technology within the electrical system has shown the need to develop efficient methodologies from the point of view of quality solution, repeatability and processing times by considering operation and investment costs as well as the technical conditions of the electrical grids under a scenario of variable power demand and then representing the real operation of the electrical grid. With the aim to propose a solution for this requirement, this paper presents a new Discrete-Continuous Particle Swarm Optimization (DCPSO) algorithm to solve the problem of the optimal integration of D-STATCOMs into Electrical Distribution Systems (EDSs). In this case, the objective function is the minimization of annual operating costs by using a weighted mono-objective function composed of the annual power loss and the investment cost and by including all constraints associated with the operation of an EDS in a distributed reactive compensation environmentinside the mathematical formulation. In order to evaluate the effectiveness and robustness of the proposed solution method, this study implemented two tests systems (i.e., 33- and 69-bus), as well as four comparison methods, and different considerations related to the inclusion of D-STATCOMs in the EDSs. Furthermore, for evaluating the repeatability of the solution obtained by each solution methods used, each algorithm was executed 100 times in Matlab software. The results obtained demonstrated that the proposed DCPSO/HSA methodology achieved the best trade-off between solution quality and processing time, with low standard deviation values for EDSs of any size
A fixed-point current injection power flow for electric distribution systems using Laurent series
(2022-07-02) Giraldo, Juan S; Montoya, Oscar Danilo; Vergara, Pedro P.; Milano, Federico
his paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newtonlike iterative procedure and a fixed-point iteration based on the successive approximation method (SAM). The convergence analysis of the SAM is proven via the Banach fixed-point theorem, ensuring numerical stability, the uniqueness of the solution, and independence on the initializing point. Numerical results are obtained for both proposed algorithms and compared to well-known PF formulations considering their rate of convergence, computational time, and numerical stability. Tests are performed for different branch 𝑅��∕𝑋�� ratios, loading conditions, and initialization points in balanced and unbalanced networks with radial and weakly-meshed topologies. Results show that the SAM is computationally more efficient than the compared PFs, being more than ten times faster than the backward–forward sweep algorithm.
A Global Tracking Sensorless Adaptive PI-PBC Design for Output Voltage Regulation in a Boost Converter Feeding a DC Microgrid
(2023-01-19) Gil-González, Walter; Montoya, Oscar Danilo; Riffo, Sebastián; Restrepo, Carlos; Muñoz, Javier
The problem of the output voltage regulation in a DC-DC boost converter feeding a DC microgrid is addressed in this research via the passivity-based control theory with a proportional–integral action (PI-PBC). Two external input estimators were implemented in conjunction with the proposed controller to make it sensorless and adaptive. The first estimator corresponds to the immersion & invariance (I&I) approach applied to calculate the expected value of the DC load, which is modeled as an unknown DC current. The second estimator is based on the disturbance–observer (DO) approach, which reaches the value of the voltage input. The main advantage of both estimators is that these ensure exponential convergence under steady-state operating conditions, and their parametrization only requires the definition of an integral gain. A comparative analysis with simulations demonstrates that the proposed PI-PBC approach is effective in regulating/controlling the voltage profile in unknown DC loads as compared to the adaptive sliding mode controller. Experimental validations have demonstrated that the proposed PI-PBC approach, in conjunction with the I&I and the DO estimators, allowed regulation of the voltage output profile in the terminals of the DC load with asymptotic stability properties and fast convergence times (1.87 ms) and acceptably overshoots (6.1%) when the voltage input varies its magnitude (from 10 to 12 V and from 10 to 8 V) considering that the DC load changed with a square waveform between 1 and 2 A with 100 Hz.
A hybrid approach based on socp and the discrete version of the sca for optimal placement and sizing dgs in ac distribution networks
(2020-12-27) Montoya, Oscar Danilo; Molina-Cabrera, Alexander; Chamorro, Harold R.; Alvarado-Barrios, Lázaro; Rivas-Trujillo, Edwin
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.
A linearized approach for the electric light commercial vehicle routing problem combined with charging station siting and power distribution network assessment
(2021-05-21) Arias-Londoño, Andrés; Gil-González, Walter; Montoya, Oscar Danilo
Transportation electrification has demonstrated a significant position on power utilities and logistic companies, in terms of assets operation and management. Under this context, this paper presents the problem of seeking feasible and good quality routes for electric light commercial vehicles considering battery capacity and charging station siting on the power distribution system. Different transportation patterns for goods delivery are included, such as the capacitated vehicle routing problem and the shortest path problem for the last mile delivery. To solve the problem framed within a mixed integer linear mathematical model, the GAMS software is used and validated on a test instance conformed by a 19-customer transportation network, spatially combined with the IEEE 34 nodes power distribution system. The sensitivity analysis, performed during the computational experiments, show the behavior of the variables involved in the logistics operation, i.e., routing cost for each transport pattern. The trade-off between the battery capacity, the cost of the charging station installation, and energy losses on the power distribution system is also shown, including the energy consumption cost created by the charging operation.
A MIQP model for optimal location and sizing of dispatchable DGs in DC networks
(2020-08-27) Montoya, Oscar Danilo; Gil-González, Walter
The allocation and dimensioning of distributed generators (DGs) in direct current (DC) power grids were addressed in this study by using a mixed-integer quadratic programming (MIQP) formulation. The MIQP model corresponded to an approximation of the mixed-integer nonlinear programming (MINLP) model that represents this problem correctly. The proposed MIQP had, for its objective function, the minimization of the power losses; as constraints, it had power balance, voltage regulation, distributed generation capacity, and the number of DGs available, among others. The general algebraic modeling system (GAMS) was employed for solving the proposed MIQP as well as the MINLP formulation. Simulation results for one DC network with 21 nodes and another with 69 revealed that the proposed MIQP model obtains high-quality results regarding the locations of the generators, the objective function, and the power dispatch in comparison to the exact MINLP model and metaheuristic techniques recently reported in specialized literature.
A mixed-integer conic formulation for optimal placement and dimensioning of DGs in DC distribution networks
(2021-01-14) Molina-Martin, Federico; Montoya, Oscar Danilo; Grisales-Noreña, Luis Fernando; Hernández, Jesus C.
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.
A mixed-integer convex approximation for optimal load redistribution in bipolar DC networks with multiple constant power terminals
(2022) Montoya, Oscar Danilo; Molina-Cabrera, Alexander; Gil-González, Walter
This paper proposes a mixed-integer convex model for optimal load-balancing in bipolar DC networks while considering multiple constant power terminals. The proposed convex model combines the Branch and Cut method with interior point optimization to solve the problem of optimal load balancing in bipolar DC networks. Additionally, the proposed convex model guarantees that global optimum of the problem is found, which ensures minimal power losses in the bipolar DC distribution grid branches, as the total monopolar load consumption has been balanced at the substation's terminals. In addition, an optimal load balancing improves the voltage profiles due to current redistribution between the positive and negative poles. Numerical results in the 21- and 85-bus test feeders and a comparison with three metaheuristic techniques show the effectiveness of the proposed convex model in reducing the total grid imbalance while minimizing the power losses and improving the voltage profiles.
A mixed-integer convex model for the optimal placement and sizing of distributed generators in power distribution networks
(2021-01-11) Gil-González, Walter; Garcés, Alejandro; Montoya, Oscar Danilo; Hernández, Jesus C.
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.
A mixed-integer second-order cone model for optimal siting and sizing of dynamic reactive power compensators in distribution grids
(2022-06-20) Gil González, Walter Julián; Montoya, Oscar Danilo; Grisales-Noreña, Luis Fernando; Leonardo Trujillo, Cesar; Giral-Ramírez, Diego Armando
The problem of the optimal placement and sizing of dynamic reactive power compensators in AC distribution networks is addressed in this paper from convex optimization. The exact mixed-integer nonlinear programming (MINLP) model is transformed into a mixed-integer second-order cone programming (MISOCP) model. The main advantage of the MISOCP formulation is the possibility of finding a global optimum with branch & cut combined with interior-point method due to the convex structure of the continuous part of the problem, i.e., the multi-period branch optimal power flow. The dynamic reactive power compensators are sized and dimensioned considering daily load curves and variable reactive power injections. Numerical validations are tested in the 33- and 69-bus test feeders using the CVX tool available for MATLAB with the MOSEK solver. These simulations demonstrate the effectiveness and robustness of the MISOCP approach when compared with the solution of the exact MINLP obtained in the GAMS software.
A New Iterative Power Flow Method for AC Distribution Grids with Radial and Mesh Topologies
(2020-11-25) Bocanegra, Sara Yulieth; Gil-González, Walter; Montoya, Oscar Danilo
This brief discusses the classical problem of power flow analysis in alternating current (ac) distribution networks through Taylor series expansion. The main advantage of this approach is that it can work with radial and mesh configurations without modifications in its formulation. This method can deal with the hyperbolic relation between voltages and currents at k node, i.e., Ik = Sk/Vk , by transforming this into a linear approximation. To minimize the error in this linear transformation, an iterative procedure is implemented by updating the linearizing point, which allows reaching the same solution of the classical power flow methods for distribution systems in less processing time. Numerical results confirm the effectiveness of the proposed approach when compared to classical Gauss-Seidel, Newton-Raphson, and Backward/forward methods that can work with radial and mesh distribution network structures. All the numerical validations are conducted in MATLAB software.
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks
(2021-11-07) Montoya, Oscar Danilo; Arias‑Londoño, Andrés; Garrido Arévalo, Víctor Manuel; Gil-González, Walter; Grisales-Noreña, Luis Fernando
This paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage variables in the power balance equations into a linear combination of them. Numerical simulations in the general algebraic modeling system (GAMS) for both models show small diferences in the daily energy losses, which are lower than 3.00%. The main advantage of the proposed quadratic model is that its optimal solution is achievable with interior point methods guaranteeing its uniqueness (convexity properties of the solution space and objective function), which is not possible to guarantee with the exact nonlinear non-convex model. The 30-bus DC test feeder with four distributed generators (with power generation forecast via artifcial neural networks with errors lower than 1% between real and predicted generation curves) and three batteries is used to validate the proposed convex and exact models. Numerical results obtained by GAMS show the efectiveness of the proposed quadratic convex model for diferent simulation scenarios tested, which was confrmed by the CVX tool for convex optimization in MATLAB
A second-order cone programming reformulation of the economic dispatch problem of bess for apparent power compensation in ac distribution networks
(2020-10-14) Montoya, Oscar Danilo; Gil-González, Walter; Martin Serra, Federico; Hernández, Jesus C.; Molina-Cabrera, Alexander
The problem associated with economic dispatch of battery energy storage systems (BESSs) in alternating current (AC) distribution networks is addressed in this paper through convex optimization. The exact nonlinear programming model that represents the economic dispatch problem is transformed into a second-order cone programming (SOCP) model, thereby guaranteeing the global optimal solution-finding due to the conic (i.e., convex) structure of the solution space. The proposed economic dispatch model of the BESS considers the possibility of injecting/absorbing active and reactive power, in turn, enabling the dynamical apparent power compensation in the distribution network. A basic control design based on passivity-based control theory is introduced in order to show the possibility of independently controlling both powers (i.e., active and reactive). The computational validation of the proposed SOCP model in a medium-voltage test feeder composed of 33 nodes demonstrates the efficiency of convex optimization for solving nonlinear programming models via conic approximations. All numerical validations have been carried out in the general algebraic modeling system.
A successive approximations method for power flow analysis in bipolar DC networks with asymmetric constant power terminals
(2022-07-02) Montoya, Oscar Danilo; Gil-González, Walter; Garcés, Alejandro
This paper deals with the power flow problem in bipolar direct current distribution networks with unbalanced constant power loads. The effect of the neutral wire is considered in two prominent cases: (i) when the system is solidly grounded at each load point and (ii) when the neutral terminal is only grounded at the substation bus. The problem is solved using the successive approximation power flow method. Numerical results in two test feeders composed of 4 and 25 nodes demonstrate that the successive approximation power flow approach is adequate to solve the problem. It is also demonstrated that it is equivalent to the backward/forward power flow in matrix form. The main advantage of both power flow approaches is that they can work with radial and meshed distribution networks. Additionally, they do not require inverting matrices at each iteration, making them efficient in terms of computational processing times requirements. All the simulations are carried out in the MATLAB programming environment.
Accurate and efficient derivative-free three-phase power flow method for unbalanced distribution networks
(2021-05-27) Montoya, Oscar Danilo; Giraldo, Juan S.; Grisales-Noreña, Luis Fernando; Chamorro, Harold R.; Alvarado-Barrios, Lázaro
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 ∆- 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.
Adaptive control for second-order DC-DC converters: PBC approach
(2021) Gil-González, Walter; Montoya, Oscar Danilo; Espinosa-Perez, Gerardo
This chapter deals with the design of a passivity-based controller for DC-DC converters by using a general representation for second-order converters, that is, buck, boost, buck-boost, and noninverting buck-boost converters. The main idea is to propose a dynamic structure for representing these converters by introducing some constants that allow compressing them into a unique representation. The general model obtained for these converters is a bilinear port-controlled Hamiltonian (PCH) representation, whose control input is multiplied by some state variables. This PCH structure allows designing a general proportional-integral controller with passive output that ensures the asymptotic stability for closed-loop operation in the Lyapunov sense. Numerical results demonstrate that the general proposed control scheme allows regulating the voltage output of all the converters with minimum errors and adequate responses during step changes in the reference signal. © 2021 Elsevier Inc. All rights reserved.
Adaptive Sensorless PI+Passivity-Based Control of a Boost Converter Supplying an Unknown CPL
(2022) Riffo, Sebastián; Gil-González, Walter; Montoya, Oscar Danilo; Restrepo, Carlos; Muñoz, Javier
This paper presents an adaptive control to stabilize the output voltage of a DC–DC boost converter that feeds an unknown constant power load (CPL). The proposed controller employs passivity-based control (PBC), which assigns a desired system energy to compensate for the negative impedance that may be generated by a CPL. A proportional-integral (PI) action that maintains a passive output is added to the PBC to impose the desired damping and enhance disturbance rejection behavior, thus forming a PI+PBC control. In addition, the proposed controller includes two estimators, i.e., immersion and invariance (I&I), and disturbance observer (DO), in order to estimate CPL and supply voltage for the converter, respectively. These observers become the proposed controller for an adaptive, sensorless PI+PBC control. Phase portrait analysis and experimental results have validated the robustness and effectiveness of the adaptive proposed control approach. These results show that the proposed controller adequately regulates the output voltage of the DC–DC boost converter under variations of the input voltage and CPL simultaneously. © 2022 by the authors.
Allocation of Renewable Energy Resources in Distribution Systems While considering the Uncertainty of Wind and Solar Resources via the Multi-Objective Salp Swarm Algorithm
(2023) Zishan, Farhad; Mansouri, Saeedeh; Abdollahpour; Grisales-Noreña, Luis Fernando; Montoya, Oscar Danilo
Given the importance of renewable energy sources in distribution systems, this article addresses the problem of locating and determining the capacity of these sources, namely, wind turbines and solar panels. To solve this optimization problem, a new algorithm based on the behavior of salp is used. The objective functions include reducing losses, improving voltage profiles, and reducing the costs of renewable energy sources. In this method, the allocation of renewable resources is considered for different load models in distribution systems and different load levels using smart meters. Due to the fact that these objective functions are multi-objective, the fuzzy decision-making method is used to select the optimal solution from the set of Pareto solutions. The considered objective functions lead to loss reduction, voltage profile improvement, and RES cost reduction (A allocating RES resources optimally without resource limitations; B: allocating RES resources optimally with resource limitations). In addition, daily wind, solar radiation, and temperature data are taken into account. The proposed method is applied to the IEEE standard 33-bus system. The simulation results show the better performance of the multi-objective salp swarm algorithm (MSSA) at improving voltage profiles and reducing losses in distribution systems. Lastly, the optimal results of the MSSA algorithm are compared with the PSO and GA algorithms. © 2023 by the authors.