A Mixed-Integer Conic Formulation for Optimal Placement and Dimensioning of DGs in DC Distribution Networks

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.

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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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A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks

Applied Sciences ◽

10.3390/app11020627 ◽

2021 ◽

Vol 11 (2) ◽

pp. 627

Author(s):

Walter Gil-González ◽

Alejandro Garces ◽

Oscar Danilo Montoya ◽

Jesus C. Hernández

Keyword(s):

Power Distribution ◽

Power Flow ◽

Distribution Networks ◽

Global Optimum ◽

Optimal Placement ◽

Mixed Integer ◽

Power Distribution Networks ◽

Distributed Generators ◽

Second Order Cone ◽

Proposed Model

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.

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An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum

Applied Sciences ◽

10.3390/app10217681 ◽

2020 ◽

Vol 10 (21) ◽

pp. 7681 ◽

Cited By ~ 1

Author(s):

Walter Gil-González ◽

Alexander Molina-Cabrera ◽

Oscar Danilo Montoya ◽

Luis Fernando Grisales-Noreña

Keyword(s):

Nonlinear Programming ◽

Optimization Problem ◽

System Analysis ◽

Programming Model ◽

Classical Problem ◽

Distribution Networks ◽

Global Optimum ◽

Optimal Location ◽

Mixed Integer ◽

Distributed Generators

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.

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Adaptive Volt–Var Control in Smart PV Inverter for Mitigating Voltage Unbalance at PCC Using Multiagent Deep Reinforcement Learning

Applied Sciences ◽

10.3390/app11198979 ◽

2021 ◽

Vol 11 (19) ◽

pp. 8979

Author(s):

Yoongun Jung ◽

Changhee Han ◽

Dongwon Lee ◽

Sungyoon Song ◽

Gilsoo Jang

Keyword(s):

Reinforcement Learning ◽

Optimal Solution ◽

Distribution Networks ◽

Voltage Unbalance ◽

Pv Inverter ◽

Distributed Generators ◽

Modern Distribution ◽

Point Of Common Coupling ◽

Time Required ◽

Policy Optimization

Modern distribution networks face an increasing number of challenges in maintaining balanced grid voltages because of the rapid increase in single-phase distributed generators. Because of the proliferation of inverter-based resources, such as photovoltaic (PV) resources, in distribution networks, a novel method is proposed for mitigating voltage unbalance at the point of common coupling by tuning the volt–var curve of each PV inverter through a day-ahead deep reinforcement learning training platform with forecast data in a digital twin grid. The proposed strategy uses proximal policy optimization, which can effectively search for a global optimal solution. Deep reinforcement learning has a major advantage in that the calculation time required to derive an optimal action in the smart inverter can be significantly reduced. In the proposed framework, multiple agents with multiple inverters require information on the load consumption and active power output of each PV inverter. The results demonstrate the effectiveness of the proposed control strategy on the modified IEEE 13 standard bus systems with time-varying load and PV profiles. A comparison of the effect on voltage unbalance mitigation shows that the proposed inverter can address voltage unbalance issues more efficiently than a fixed droop inverter.

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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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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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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 Placement of Social Digital Twins in Edge IoT Networks

Sensors ◽

10.3390/s20216181 ◽

2020 ◽

Vol 20 (21) ◽

pp. 6181

Author(s):

Olga Chukhno ◽

Nadezhda Chukhno ◽

Giuseppe Araniti ◽

Claudia Campolo ◽

Antonio Iera ◽

...

Keyword(s):

Internet Of Things ◽

Social Relationships ◽

Data Exchange ◽

Service Discovery ◽

Programming Model ◽

Optimal Solution ◽

Optimal Placement ◽

Mixed Integer ◽

Digital Twins ◽

The Social

In next-generation Internet of Things (IoT) deployments, every object such as a wearable device, a smartphone, a vehicle, and even a sensor or an actuator will be provided with a digital counterpart (twin) with the aim of augmenting the physical object’s capabilities and acting on its behalf when interacting with third parties. Moreover, such objects can be able to interact and autonomously establish social relationships according to the Social Internet of Things (SIoT) paradigm. In such a context, the goal of this work is to provide an optimal solution for the social-aware placement of IoT digital twins (DTs) at the network edge, with the twofold aim of reducing the latency (i) between physical devices and corresponding DTs for efficient data exchange, and (ii) among DTs of friend devices to speed-up the service discovery and chaining procedures across the SIoT network. To this aim, we formulate the problem as a mixed-integer linear programming model taking into account limited computing resources in the edge cloud and social relationships among IoT devices.

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Hybrid GA-SOCP Approach for Placement and Sizing of Distributed Generators in DC Networks

Applied Sciences ◽

10.3390/app10238616 ◽

2020 ◽

Vol 10 (23) ◽

pp. 8616 ◽

Cited By ~ 1

Author(s):

Oscar Danilo Montoya ◽

Walter Gil-González ◽

Luis Fernando Grisales-Noreña

Keyword(s):

Power Flow ◽

Optimal Power Flow ◽

Mathematical Optimization ◽

Optimal Solution ◽

Distribution Networks ◽

Optimization Approach ◽

Global Optimal Solution ◽

Distributed Generators ◽

Second Order Cone ◽

Global Optimal

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.

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