Abstract
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.
Highlights
Direct current (DC) distribution networks have attracted much attention in recent years in specialized literature [1], since these networks have better voltage profiles [2] and low energy losses [3]
As for the comparison of the proposed MI-second-order cone programming (SOCP) with the results reported in [3] and [8], where convex optimization methods based on semidefinite and sequential quadratic programming models were combined with a heuristic algorithm based on hyperplanes, we can affirm that our mixed-integer second-order cone programming (MI-SOCP) approach allows for the reaching of the global optimum
This research paper proposed an MI-SOCP reformulation for the optimal siting and dimensioning of constant power sources in DC grids that allows for the reaching of global optimal solutions, which is not possible with the exact mixed-integer nonlinear programming (MINLP) model
Summary
Direct current (DC) distribution networks have attracted much attention in recent years in specialized literature [1], since these networks have better voltage profiles [2] and low energy losses [3]. The authors in [3] performed a semidefinite programming relaxation for the optimal locating and dimensioning of distributed generators (DGs) in DC grids, combined with a heuristic method based on random hyperplanes This approach demonstrated the possibility of finding better solutions than the different metaheuristic approaches. The authors of [10] proposed a mixed-integer quadratic transformation of the original MINLP model by solving both models in the GAMS software; they observed that the quadratic approximation was easier to solve and took tens of seconds, while the exact MINLP model took hundreds of seconds The former had the best numerical results for the minimization of the total grid losses. Integer optimization based on the branch and bound (B&B) method is used to solve the problem of the optimal placement and sizing of constant power sources in DC grids
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