Search Results (7)

In the unmanned aerial vehicle (UAV) assisted non-orthogonal multiple access (NOMA) networks, the practical hardware impairments (HIs) and resource allocation is still a challenging problem. Most existing research on resource allocation algorithms for UAV communication is considered with the ideal hardware condition. However, the impact of HIs on system performance cannot be ignored, especially in the case of high bit rates. Considering the HIs, most studies are from the perspective of performance analysis. The resource allocation of UAV relay-assisted NOMA systems is investigated in this paper with HIs. We aim to maximize the sum rate by jointly optimizing the deployment of UAV and transmit power. To address this problem, we first transformed the mixed integer programming problem (MIPP) into a standard convex optimization problem based on successive convex approximation (SCA) technology. Then, we introduced the Lagrangian dual transformation and quadratic transform methods to solve the power allocation problem. Finally, we propose an effective iterative algorithm to achieve an approximate optimal solution. Numerical results demonstrate that the proposed algorithm achieved better performance in terms of the sum rate compared with other benchmark schemes. Full article

The problem regarding the optimal location and sizing of fixed-step capacitor banks in distribution networks with radial configuration is studied in this research by applying a two-stage optimization approach. The first stage consists of determining the nodes where the capacitor banks will be placed. In this stage, the exact mixed-integer nonlinear programming (MINLP) model that represents the studied problem is transformed into a mixed-integer quadratic convex (MIQC) model. The solution of the MIQC model ensures that the global optimum is reached given the convexity of the solution space for each combination of nodes where the capacitor banks will be installed. With the solution of the MIQC, the suitable nodes for the installation of the fixed-step capacitors are fixed, and their sizes are recursively evaluated in a power flow methodology that allows for determining the optimal sizes. In the second stage, the successive approximation power flow method is applied to determine the optimal sizes assigned to these compensation devices. Numerical results in three test feeders with 33, 69, and 85 buses demonstrate the effectiveness of the proposed two-stage solution method for two operation scenarios: (i) operation of the distribution system under peak load conditions throughout the year, and (ii) operation considering daily demand variations and renewable generation penetration. Comparative results with the GAMS software confirm the excellent results reached using the proposed optimization approach. All the simulations were carried out in the MATLAB programming environment, version 2021b, as well as using the Gurobi solver in the convex programming tool known as CVX. Full article

The minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select the nodes where the capacitor banks must be installed. In the second stage, a recursive power flow method is employed to make an exhaustive evaluation of the solution space. The main contribution of this research is the use of the expected load curve to estimate the equivalent annual grid operating costs. Numerical simulations in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness of the proposed methodology in comparison with the solution of the exact optimization model in the General Algebraic Modeling System software. Reductions of $33.04\%$ and $34.29\%$ with respect to the benchmark case are obtained with the proposed two-stage approach, with minimum investments in capacitor banks. All numerical implementations are performed in the MATLAB software using the convex tool known as CVX and the Gurobi solver. The main advantage of the proposed hybrid optimization method lies in the possibility of dealing with radial and meshed distribution system topologies without any modification on the MIQC model and the recursive power flow approach. Full article

This paper contributes with a new two-stage optimization methodology to solve the problem of the optimal placement and sizing of solar photovoltaic (PV) generation units in medium-voltage distribution networks. The optimization problem is formulated with a mixed-integer nonlinear programming (MINLP) model, where it combines binary variables regarding the nodes where the PV generators will be located and continuous variables associated with the power flow solution. To solve the MINLP model a decoupled methodology is used where the binary problem is firstly solved with mixed-integer quadratic approximation; and once the nodes where the PV sources will be located are known, the dimensioning problem of the PV generators is secondly solved through an interior point method applied to the classical multi-period power flow formulation. Numerical results in the IEEE 33-bus and IEEE 85-bus systems demonstrate that the proposed approach improves the current literature results reached with combinatorial methods such as the Chu and Beasley genetic algorithm, the vortex search algorithm, the Newton-metaheuristic algorithm as well as the exact solution of the MINLP model with the GAMS software and the BONMIN solver. All the numerical simulations are implemented in the MATLAB programming environment and the convex equivalent models are solved with the CVX tool. Full article

This paper deals with the problem of the optimal selection and location of batteries in DC distribution grids by proposing a new mixed-integer convex model. The exact mixed-integer nonlinear model is transformed into a mixed-integer quadratic convex model (MIQC) by approximating the product among voltages in the power balance equations as a hyperplane. The most important characteristic of our proposal is that the MIQC formulations ensure the global optimum reaching via branch & bound methods and quadratic programming since each combination of the binary variables generates a node with a convex optimization subproblem. The formulation of the objective function is associated with the minimization of the energy losses for a daily operation scenario considering high renewable energy penetration. Numerical simulations show the effectiveness of the proposed MIQC model to reach the global optimum of the optimization model when compared with the exact optimization model in a 21-node test feeder. All the validations are carried out in the GAMS optimization software. Full article

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 $3\times 3$ 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. Full article

In a transactive energy market, distributed energy resources (DERs) such as dispatchable distributed generators (DGs), electrical energy storages (EESs), distribution-scale load aggregators (LAs), and renewable energy sources (RESs) have to earn their share of supply or demand through a bidding process. In such a market, the distribution system operator (DSO) may optimally schedule these resources, first in a forward market, i.e., day-ahead, and in a real-time market later on, while maintaining a reliable and economic distribution grid. In this paper, an efficient day-ahead scheduling of these resources, in the presence of interaction with wholesale market at the locational marginal price (LMP), is studied. Due to inclusion of EES units with integer constraints, a detailed mixed integer linear programming (MILP) formulation that incorporates simplified DistFlow equations to account for grid constraints is proposed. Convex quadratic line and transformer apparent power flow constraints have been linearized using an outer approximation. The proposed model schedules DERs based on distribution locational marginal price (DLMP), which is obtained as the Lagrange multiplier of the real power balance constraint at each distribution bus while maintaining physical grid constraints such as line limits, transformer limits, and bus voltage magnitudes. Case studies are performed on a modified IEEE 13-bus system with high DER penetration. Simulation results show the validity and efficiency of the proposed model. Full article