Abstract
This paper addresses the optimal power flow problem in direct current (DC) networks employing a master–slave solution methodology that combines an optimization algorithm based on the multiverse theory (master stage) and the numerical method of successive approximation (slave stage). The master stage proposes power levels to be injected by each distributed generator in the DC network, and the slave stage evaluates the impact of each power configuration (proposed by the master stage) on the objective function and the set of constraints that compose the problem. In this study, the objective function is the reduction of electrical power losses associated with energy transmission. In addition, the constraints are the global power balance, nodal voltage limits, current limits, and a maximum level of penetration of distributed generators. In order to validate the robustness and repeatability of the solution, this study used four other optimization methods that have been reported in the specialized literature to solve the problem addressed here: ant lion optimization, particle swarm optimization, continuous genetic algorithm, and black hole optimization algorithm. All of them employed the method based on successive approximation to solve the load flow problem (slave stage). The 21- and 69-node test systems were used for this purpose, enabling the distributed generators to inject 20%, 40%, and 60% of the power provided by the slack node in a scenario without distributed generation. The results revealed that the multiverse optimizer offers the best solution quality and repeatability in networks of different sizes with several penetration levels of distributed power generation.
Highlights
Due to the importance of the optimal power flow problem in Direct Current (DC) networks and the need to propose new solution methodologies that are more efficient in terms of solution quality and repeatability, this study proposes a new methodology based on a master–slave strategy to solve the Optimal Power Flow (OPF) problem in DC networks
Said table specifies the proposed solution method; the nodes where the Distributed Generators (DGs) are located and the power each one of them injects into the network in; the minimum power losses (Ploss ) in and the percentage of reduction compared to the base case (%); the average value of Ploss in and the average reduction with respect to the base case (%); the standard deviation in percentage, which was obtained after each solution method was executed 100 times; the worst voltage; and the maximum current in the DC grid employing the distributed power injection proposed by each solution methodology
The multiverse optimizer (MVO) determines the electrical power to be injected by each DG located in the DC network
Summary
DC offers technical-operational advantages; for instance, as most loads used by people are DC, generating and distributing DC eliminates the need for converting electrical energy from AC to DC This type of electric current promotes the use Sustainability 2021, 13, 8703. DC electrical networks, i.e., (slack and distributed) loads and power generators, solution methodologies should be used to identify the operating points of these devices, mainly the generators, in order to guarantee the technical conditions of the network (power balance, power and voltage limits, penetration levels of the distributed generators, etc.) Such methodologies should enable network operators or owners to meet the objective functions they have established in order to improve the technical conditions of the system (power losses, voltage stability, loadability of the lines, etc.), as well as its environmental characteristics, or to reduce operating costs (buying electricity from the grid) [3]. This problem, known as Optimal Power Flow (OPF), is about finding the reference points for the power of the Distributed Generators (DGs) in a network in order to meet the objective functions that have been defined
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