Recursive convex approximations for optimal power flow solution in direct current networks

The optimal power flow problem in direct current (DC) networks considering dispersal generation is addressed in this paper from the recursive programming point of view. The nonlinear programming model is transformed into two quadratic programming approximations that are convex since the power balance constraint is approximated between affine equivalents. These models are recursively (iteratively) solved from the initial point vt equal to 1.0 pu with t equal to 0, until that the error between both consecutive voltage iterations reaches the desired convergence criteria. The main advantage of the proposed quadratic programming models is that the global optimum finding is ensured due to the convexity of the solution space around vt. Numerical results in the DC version of the IEEE 69-bus system demonstrate the effectiveness and robustness of both proposals when compared with classical metaheuristic approaches such as particle swarm and antlion optimizers, among others. All the numerical validations are carried out in the MATLAB programming environment version 2021b with the software for disciplined convex programming known as CVX tool in conjuction with the Gurobi solver version 9.0; while the metaheuristic optimizers are directly implemented in the MATLAB scripts

An Energy Management System for PV Sources in Standalone and Connected DC Networks Considering Economic, Technical, and Environmental Indices

This research proposes an efficient energy management system for standalone and grid-connected direct current (DC) distribution networks that consider photovoltaic (PV) generation sources. A complete nonlinear programming model is formulated to represent the efficient PV dispatch problem while taking three different objective functions into account. The first objective function corresponds to the minimization of the operational costs with respect to the energy purchasing costs at terminals of the substation, including the maintenance costs of the PV sources. The second objective function is the reduction of the expected daily energy losses regarding all resistive effects of the distribution lines. The third objective function concerns the minimization of the total emissions of CO (Formula presented.) into the atmosphere by the substation bus or its equivalent (diesel generator). These objective functions are minimized using a single-objective optimization approach through the application of the Salp Swarm Algorithm (SSA), which is combined with a matrix hourly power flow formulation that works by using a leader–follower operation scheme. Two test feeders composed of 27 and 33 nodes set for standalone and grid-connected operation are used in the numerical validations. The standalone grid corresponds to an adaptation of the generation and demand curves for the municipality of Capurganá, and the grid-connected system is adapted to the operating conditions in the metropolitan area of Medellín, i.e., a rural area and a major city in Colombia. A numerical comparison with three additional combinatorial optimizers (i.e., particle swarm optimization (PSO), the multiverse optimizer (MVO), and the crow search algorithm (CSA)) demonstrates the effectiveness and robustness of the proposed leader–follower optimization approach to the optimal management of PV generation sources in DC grids while considering different objective function indices. © 2022 by the authors

Metaheuristic Optimization Methods for Optimal Power Flow Analysis in DC Distribution Networks

In this paper is addressed the optimal power flow problem in direct current grids, by using solution methods based on metaheuristics techniques and numerical methods. For which was proposed a mixed integer nonlinear programming problem, that describes the optimal power flow problem in direct current grids. As solution methodology was proposed a master–slave strategy, which used in master stage three continuous solution methods for solving the optimal power flow problem: a particle swarm optimization algorithm, a continuous version of the genetic algorithm and the black hole optimization method. In the slave stages was used a methods based on successive approximations for solving the power flow problem, entrusted for calculates the objective function associated to each solution proposed by the master stage. As objective function was used the reduction of power loss on the electrical grid, associated to the energy transport. To validate the solution methodologies proposed were used the test systems of 21 and 69 buses, by implementing three levels of maximum distributed power penetration: 20%, 40% and 60% of the power supplied by the slack bus, without considering distributed generators installed on the electrical grid. The simulations were carried out in the software Matlab, by demonstrating that the methods with the best performance was the BH/SA, due to that show the best trade-off between the reduction of the power loss and processing time, for solving the optimal power flow problem in direct current networks

Optimal power dispatch in direct current microgrids considering variation in wind and solar generation and energy demand behavior

El incremento del consumo energético mundial, los problemas asociados a la generación de electricidad en grandes centrales, el agotamiento de combustibles no renovables, pérdidas de energía y el alto impacto ambiental, han motivado el uso de generadores distribuidos basados en energías renovables e integrados a microrredes DC, las cuales ofrecen ventajas frente a las microrredes AC tales como: la facilidad de integración con dispositivos de almacenamiento de energía y con fuentes de energía renovable que generan en DC, el aumento de la capacidad de las líneas eléctricas, así como la reducción en la complejidad matemática del modelo que representa la microrred, debido a la ausencia de frecuencia y de potencia reactiva, entre otras ventajas. Para satisfacer las necesidades técnicas, operativas y económicas de este tipo de sistemas y de su operador y/o propietario, es necesario realizar un adecuado despacho de la potencia de los generadores distribuidos dentro de la microrred, lo cual se conoce como problema de despacho óptimo de potencia. La solución a este tipo de despacho requiere resolver modelos matemáticos no lineales y no convexos que cumplan con la demanda de energía y las restricciones del sistema, para lo cual se desarrollan estrategias computacionales que determinen en el menor tiempo posible, la mejor configuración de potencias a inyectar en el sistema. Este trabajo propone una estrategia para el despacho óptimo de potencia en microrredes de DC considerando la variación en generación eólica y solar, y en la demanda de potencia en un horizonte de 24 horas que permita mejorar las condiciones técnico-económicas. Para el trabajo se definieron las componentes de la microrred DC, el modelo matemático que representa el problema, los sistemas de prueba, y las técnicas de solución a implementar para los problemas de flujo de potencia y de flujo óptimo de potencia en microrredes DC. Para la programación de los algoritmos propuestos se utilizó el software especializado Matlab. Finalmente, se obtuvo una técnica o metodología de solución computacionalmente eficiente aplicable al problema de despacho óptimo de potencia considerando un periodo de análisis de 24 horas, la cual es aplicable en cualquier topología de microrred DC, que cuente con generación distribuida a base de energía solar y eólica.The increase in world energy consumption, the problems associated with the generation of electricity in large power plants, the depletion of non-renewable fuels, energy losses and the high environmental impact, have motivated the use of distributed generators based on renewable energies and integrated into DC microgrids, which offer advantages over AC microgrids such as: the ease of integration with energy storage devices and renewable energy sources that generate in DC, the increase in the capacity of the power lines, as well as the reduction in the mathematical complexity of the model that represents the microgrid, due to the absence of frequency and reactive power, among other advantages. To satisfy the technical, operational and economic needs of this type of system and its operator and / or owner, it is necessary to adequately dispatch the power of the generators distributed within the microgrid, which is known as the optimal power dispatch problem. The solution to this type of dispatch requires solving non-linear and non-convex mathematical models that meet the energy demand and system constraints, for which computational strategies are developed that determine in the shortest possible time, the best configuration of powers at inject into the system. This work proposes a strategy for the optimal power dispatch in DC microgrids considering the variation in wind and solar generation, and in the demand for power in a 24-hour horizon that allows improving the technical-economic conditions. For this work, the components of the DC microgrid, the mathematical model representing the problem, the test systems, and the solution techniques to be implemented for the problems of power flow and optimal power flow in DC microgrids were defined. Matlab specialized software was used to program the proposed algorithms. Finally, an efficient computational solution technique or methodology applicable to the optimal power dispatch problem was obtained considering a 24-hour analysis period, which is applicable in any DC microgrid topology, which has distributed generation based on solar and wind energy

An Energy Management System for PV Sources in Standalone and Connected DC Networks Considering Economic, Technical, and Environmental Indices

This research proposes an efficient energy management system for standalone and grid-connected direct current (DC) distribution networks that consider photovoltaic (PV) generation sources. A complete nonlinear programming model is formulated to represent the efficient PV dispatch problem while taking three different objective functions into account. The first objective function corresponds to the minimization of the operational costs with respect to the energy purchasing costs at terminals of the substation, including the maintenance costs of the PV sources. The second objective function is the reduction of the expected daily energy losses regarding all resistive effects of the distribution lines. The third objective function concerns the minimization of the total emissions of CO2 into the atmosphere by the substation bus or its equivalent (diesel generator). These objective functions are minimized using a single-objective optimization approach through the application of the Salp Swarm Algorithm (SSA), which is combined with a matrix hourly power flow formulation that works by using a leader–follower operation scheme. Two test feeders composed of 27 and 33 nodes set for standalone and grid-connected operation are used in the numerical validations. The standalone grid corresponds to an adaptation of the generation and demand curves for the municipality of Capurganá, and the grid-connected system is adapted to the operating conditions in the metropolitan area of Medellín, i.e., a rural area and a major city in Colombia. A numerical comparison with three additional combinatorial optimizers (i.e., particle swarm optimization (PSO), the multiverse optimizer (MVO), and the crow search algorithm (CSA)) demonstrates the effectiveness and robustness of the proposed leader–follower optimization approach to the optimal management of PV generation sources in DC grids while considering different objective function indices