RESUMO
This research addresses the power flow analysis in bipolar asymmetric direct current (DC) networks by applying Broyden's numerical method. This general successive approximations method allows for a simple Newton-based recursive formula to reach the roots of multiple nonlinear equations. The main advantage of Broyden's approach is its simple but efficient structure which can be applied to real complex nonlinear equations.The power flow problem in bipolar DC networks is still challenging, as multiple operating options must be considered, e.g., the possibility of having a solidly grounded or floating neutral wire. The main goal of this research is to contribute with a generalization of Broyden's method for the power flow solution in bipolar DC networks, with the main advantage that, under well-defined conditions, this is a numerical method equivalent to the matricial backward/forward power flow, which is equivalent to the successive approximations power flow method. Numerical results in the 21-, 33-, and 85-bus grids while considering two connections for the neutral wire (i.e., solidly grounded at any node or floating) show the effectiveness of Broyden's method in the power flow solution for bipolar asymmetric DC networks. All numerical simulations were carried out in the MATLAB programming environment.
RESUMO
This paper deals with the problem regarding the optimal siting and sizing of distribution static compensators (D-STATCOMs) in electrical distribution networks to minimize the expected total annual operating costs. These costs are associated with the investments made in D-STATCOMs and expected energy losses costs. To represent the electrical behavior of the distribution networks, a power flow formulation is used which includes voltages, currents, and power as variables via incidence matrix representation. This formulation generates a mixed-integer nonlinear programming (MINLP) model that accurately represents the studied problem. However, in light of the complexities involved in solving this MINLP model efficiently, this research proposes a mixed-integer convex reformulation. Numerical results regarding the final annual operating costs of the network demonstrate that the proposed mixed-integer convex model is efficient for selecting and locating D-STATCOMs in distribution networks, with the main advantage that it is applicable to radial and meshed distribution grid configurations. A comparative analysis with respect to metaheuristic optimizers and convex approximations confirms the robustness of the proposed formulation. All numerical validations were conducted in the MATLAB programming environment with our own scripts (in the case of metaheuristics) and the CVX convex disciplined tool via the Gurobi solver. In addition, the exact MINLP model is solved using the GAMS software.
RESUMO
This paper analyzes the power flow solution in bipolar direct current networks with radial structures considering multiple monopolar and bipolar constant power loads. The electrical configuration of the bipolar DC grid considers that the reference pole is non-grounded along the feeder, which produces important neutral currents and voltage imbalances along the DC grid. The power flow problem is formulated through the triangular-based representation of the grid topology, which generates a recursive formulation that allows determining the voltage values in the demand nodes through an iterative procedure. The linear convergence of the triangular-based power flow method is tested through multiple load variations with respect to the nominal grid operative condition. Numerical results in the 21- and the 85-bus grids reveal the relevant variations in the voltage profiles and total grid power losses when the neutral cable is solidly grounded or not.
