On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks

Abstract

The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416kW and 145.397kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.

Impact of DGs on the Reactive Power-Supported Optimal EDN for Profit Maximisation

“…From Table I, it is also observed that the overall profit obtained in scenario 2 is $11727.012, which is 33.085 % compared to BC. The results achieved by LFM-SOA were compared with other methods in the literature and found that the performance of the proposed method is better compared to other methods discussed in [7]- [10], [15].…”

“…The purpose of OCS and AEDNS optimisation in the radial EDN is to maximise the net profit by minimising P Loss, lowering the capacitor investment cost and minimising the DG power purchase cost provided the power balancing and inequality limitations are satisfied. These issues are presented mathematically as stated in (1)- (10).…”

“…The conditions in ( 6) to (10) should be met at the beginning of each iteration. Ten particles exist for AEDNS alone in the standard 33-bus system, six for OCS alone, sixteen for optimising both AEDNS and OCS (one after the other), and six variables for IDG integration.…”

“…Capacitors installed on nonoptimal buses will reverse the objective. For the past four decades, many investigations based on OCS in EDNs have been focussed on [7]- [10].…”

Selection and Location of Fixed-Step Capacitor Banks in Distribution Grids for Minimization of Annual Operating Costs: A Two-Stage Approach

“…The authors of the ref. [21] proposed the application of the second-order cone programming with mixed-integer variables for siting and sizing fixed-step capacitor banks in radial distribution networks to reduce grid power losses under peak load conditions. Numerical simulations including annual grid operating costs under peak load conditions while considering investment costs in capacitor banks showed the effectiveness of the proposed methodology when compared to the exact solution in the GAMS software and some metaheuristic optimizers.…”