Efficient Reallocation of BESS in Monopolar DC Networks for Annual Operating Costs Minimization: A Combinatorial-Convex Approach

Abstract

This article deals with the solution of a mixed-integer nonlinear programming (MINLP) problem related to the efficient reallocation of battery energy storage systems (BESS) in monopolar direct current (DC) grids through a master–slave optimization approach. The master stage solves the integer nature of the MINLP model, which is related to the nodes where the BESS will be located. In this stage, the discrete version of the vortex search algorithm is implemented. To determine the objective function value, a recursive convex approximation is implemented to solve the nonlinear component of the MINLP model (multi-period optimal power flow problem) in the slave stage. Two objective functions are considered performance indicators regarding the efficient reallocation of BESS in monopolar DC systems. The first objective function corresponds to the expected costs of the annual energy losses, and the second is associated with the annual expected energy generation costs. Numerical results for the DC version of the IEEE 33 bus grid confirm the effectiveness and robustness of the proposed master–slave optimization approach in comparison with the solution of the exact MINLP model in the General Algebraic Modeling System (GAMS) software. The proposed master–slave optimizer was programmed in the MATLAB software. The recursive convex solution of the multi-period optimal power flow problem was implemented in the convex discipline tool (CVX) with the SDPT3 and SEDUMI solvers. The numerical reductions achieved with respect to the benchmark case in terms of energy loss costs and energy purchasing costs were 7.2091% and 3.2105%, which surpassed the results reached by the GAMS software, with reductions of about 6.0316% and 1.5736%.

Solving the Power Flow Problem in Bipolar DC Asymmetric Distribution Networks Using Broyden’s Method

“…Note that, in (20), if x = x t is defined while considering the definition in (17) and making some algebraic manipulations, the following result is reached:…”

“…The information regarding branches and monopolar and bipolar power consumptions is presented in Table 2 [ 20 ].…”

“…The main characteristics of this distribution network are the following: (i) the substation bus is located at bus 1, and the voltage outputs in the positive and negative poles are ±12.66 kV with respect to the neutral point, which is solidly grounded; and (ii) the total monopolar consumption is 2615 kW in the positive pole and 2185 kW in the negative pole, while the bipolar power consumption is 2350 kW. The information regarding branches and monopolar and bipolar power consumptions is presented in Table 2 [20].…”