An Approximate Mixed-Integer Convex Model to Reduce Annual Operating Costs in Radial Distribution Networks Using STATCOMs

The problem of optimal siting and sizing of distribution static compensators (STATCOMs) is addressed in this research from the point of view of exact mathematical optimization. The exact mixed-integer nonlinear programming model (MINLP) is decoupled into two convex optimization sub-problems, named the location problem and the sizing problem. The location problem is addressed by relaxing the exact MINLP model, assuming that all the voltages are equal to 1∠0∘, which allows obtaining a mixed-integer quadratic programming model as a function of the active and reactive power flows. The solution of this model provides the best set of nodes to locate all the STATCOMs. When all the nodes are selected, it solves the optimal reactive power problem through a second-order cone programming relaxation of the exact optimal power flow problem; the solution of the SOCP model provides the optimal sizes of the STATCOMs. Finally, it refines the exact objective function value due to the intrinsic non-convexities associated with the costs of the STATCOMs that were relaxed through the application of Taylor’s series expansion in the location and sizing stages. The numerical results in the IEEE 33- and 69-bus systems demonstrate the effectiveness and robustness of the proposed optimization problem when compared with large-scale MINLP solvers in GAMS and the discrete-continuous version of the vortex search algorithm (DCVSA) recently reported in the current literature. With respect to the benchmark cases of the test feeders, the proposed approach reaches the best reductions with 14.17% and 15.79% in the annual operative costs, which improves the solutions of the DCVSA, which are 13.71% and 15.30%, respectively.

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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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A Multistage Solution Approach for Dynamic Reactive Power Optimization Based on Interval Uncertainty

Mathematical Problems in Engineering ◽

10.1155/2018/3854812 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Xiaodong Shen ◽

Yang Liu ◽

Yan Liu

Keyword(s):

Large Scale ◽

Reactive Power ◽

Power Optimization ◽

Programming Model ◽

Nonconvex Programming ◽

Interval Uncertainty ◽

Mixed Integer ◽

Reactive Power Optimization ◽

Renewable Energy Resources ◽

Integer Quadratic Programming

In order to solve the uncertainty and randomness of the output of the renewable energy resources and the load fluctuations in the reactive power optimization, this paper presents a novel approach focusing on dealing with the issues aforementioned in dynamic reactive power optimization (DRPO). The DRPO with large amounts of renewable resources can be presented by two determinate large-scale mixed integer nonlinear nonconvex programming problems using the theory of direct interval matching and the selection of the extreme value intervals. However, it has been admitted that the large-scale mixed integer nonlinear nonconvex programming is quite difficult to solve. Therefore, in order to simplify the solution, the heuristic search and variable correction approaches are employed to relax the nonconvex power flow equations to obtain a mixed integer quadratic programming model which can be solved using software packages such as CPLEX and GUROBI. The ultimate solution and the performance of the presented approach are compared to the traditional methods based on the evaluations using IEEE 14-, 118-, and 300-bus systems. The experimental results show the effectiveness of the presented approach, which potentially can be a significant tool in DRPO research.

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Genetic-Convex Model for Dynamic Reactive Power Compensation in Distribution Networks Using D-STATCOMs

Applied Sciences ◽

10.3390/app11083353 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3353

Author(s):

Oscar Danilo Montoya ◽

Harold R. Chamorro ◽

Lazaro Alvarado-Barrios ◽

Walter Gil-González ◽

César Orozco-Henao

Keyword(s):

Objective Function ◽

Optimal Power Flow ◽

Reactive Power ◽

Programming Model ◽

Distribution Networks ◽

Optimal Placement ◽

Mixed Integer ◽

Energy Losses ◽

Optimization Approach ◽

Operative Costs

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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Optimal Operation of Soft Open Points-Based Energy Storage in Active Distribution Networks by Considering the Battery Lifetime

Frontiers in Energy Research ◽

10.3389/fenrg.2020.633401 ◽

2021 ◽

Vol 8 ◽

Author(s):

Jian Wang ◽

Niancheng Zhou ◽

Anqi Tao ◽

Qianggang Wang

Keyword(s):

Energy Storage ◽

Reactive Power ◽

Programming Model ◽

Distribution Networks ◽

Optimal Operation ◽

Mixed Integer ◽

Operation Model ◽

Battery Lifetime ◽

Battery Degradation ◽

Active Distribution Networks

Soft open point-based energy storage (SOP-based ES) can transfer power in time and space and also regulate reactive power. These characteristics help promote the integration of distributed generations (DGs) and reduce the operating cost of active distribution networks (ADNs). Therefore, this work proposed an optimal operation model for SOP-based ES in ADNs by considering the battery lifetime. First, the active and reactive power equations of SOP-based ES and battery degradation cost were modeled. Then, the optimal operation model that includes the operation cost of ADNs, loss cost, and battery degradation cost was established. The mixed integer nonlinear programming model was transformed to a mixed integer linear programming model derived through linearization treatment. Finally, the feasibility and effectiveness of the proposed optimization model are verified by the IEEE33 node system.

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Convex Model for Estimation of Single-Phase Photovoltaic Impact on Existing Voltage Unbalance in Distribution Networks

Applied Sciences ◽

10.3390/app10248884 ◽

2020 ◽

Vol 10 (24) ◽

pp. 8884

Author(s):

Verner Püvi ◽

Matti Lehtonen

Keyword(s):

Single Phase ◽

Low Voltage ◽

Distribution Networks ◽

Mixed Integer ◽

Convex Model ◽

Phase Selection ◽

Voltage Unbalance ◽

Integer Quadratic Programming ◽

Mixed Integer Quadratic Programming ◽

Photovoltaic Plants

Due to the increasing adoption of solar power generation, voltage unbalance estimation gets more attention in sparsely populated rural networks. This paper presents a Monte Carlo simulation augmented with convex mixed-integer quadratic programming to estimate voltage unbalance and maximum photovoltaic penetration. Additionally, voltage unbalance attenuation by proper phase allocation of photovoltaic plants is analysed. Single-phase plants are simulated in low-voltage distribution networks and voltage unbalance is evaluated as a contribution of measured background and photovoltaic-caused unbalance. Voltage unbalance is calculated in accordance with EN 50160 and takes into account 10-minute average values with 5% tolerance condition. Results of the optimization revealed substantial unbalance attenuation with optimal phase selection and increased potential of local generation hosting capacity in case of higher background unbalance.

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Approximated Mixed-Integer Convex Model for Phase Balancing in Three-Phase Electric Networks

Computers ◽

10.3390/computers10090109 ◽

2021 ◽

Vol 10 (9) ◽

pp. 109

Author(s):

Oscar Danilo Montoya ◽

Luis Fernando Grisales-Noreña ◽

Edwin Rivas-Trujillo

Keyword(s):

Power Flow ◽

Reactive Power ◽

Search Algorithm ◽

Triangular Matrix ◽

Mixed Integer ◽

Decision Variable ◽

Convex Model ◽

Electric Networks ◽

Three Phase ◽

Final Steady State

With this study, we address the optimal phase balancing problem in three-phase networks with asymmetric loads in reference to a mixed-integer quadratic convex (MIQC) model. The objective function considers the minimization of the sum of the square currents through the distribution lines multiplied by the average resistance value of the line. As constraints are considered for the active and reactive power redistribution in all the nodes considering a 3×3 binary decision variable having six possible combinations, the branch and nodal current relations are related to an extended upper-triangular matrix. The solution offered by the proposed MIQC model is evaluated using the triangular-based three-phase power flow method in order to determine the final steady state of the network with respect to the number of power loss upon the application of the phase balancing approach. The numerical results in three radial test feeders composed of 8, 15, and 25 nodes demonstrated the effectiveness of the proposed MIQC model as compared to metaheuristic optimizers such as the genetic algorithm, black hole optimizer, sine–cosine algorithm, and vortex search algorithm. All simulations were carried out in MATLAB 2020a using the CVX tool and the Gurobi solver.

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Optimal Capacity Allocation of Energy Storage in Distribution Networks Considering Active/Reactive Coordination

Energies ◽

10.3390/en14061611 ◽

2021 ◽

Vol 14 (6) ◽

pp. 1611

Author(s):

Tao Xu ◽

He Meng ◽

Jie Zhu ◽

Wei Wei ◽

He Zhao ◽

...

Keyword(s):

Energy Storage ◽

Life Cycle Cost ◽

Large Scale ◽

Reactive Power ◽

Supply And Demand ◽

Distribution Networks ◽

Capacity Allocation ◽

Mixed Integer ◽

Optimal Capacity ◽

Network Losses

Energy storage system (ESS) has been advocated as one of the key elements for the future energy system by the fast power regulation and energy transfer capabilities. In particular, for distribution networks with high penetration of renewables, ESS plays an important role in bridging the gap between the supply and demand, maximizing the benefits of renewables and providing various types of ancillary services to cope the intermittences and fluctuations, consequently improving the resilience, reliability and flexibility. To solve the voltage fluctuations caused by the high permeability of renewables in distribution networks, an optimal capacity allocation strategy of ESS is proposed in this paper. Taking the life cycle cost, arbitrage income and the benefit of reducing network losses into consideration, a bilevel optimization model of ESS capacity allocation is established, the coordination between active/reactive power of associate power conversion system is considered, and the large scale nonlinear programming problem is solved using genetic algorithm, simulated annealing and mixed integer second-order cone programming method. The feasibility and effectiveness of the proposed algorithm have been verified.

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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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