Search

This study addresses the problem of cost-optimal expansion planning for rural radial distribution networks via a mixed-integer nonlinear programming (MINLP) formulation that jointly determines feeder routing and conductor type selection. The developed method was evaluated using standard 9-node and 25-node test networks, with performance benchmarked against minimum spanning tree (MST)-based procedures and two metaheuristic techniques (sine-cosine algorithm and tabu search). The application of the MINLP approach led to significant reductions in overall expenditure. In the 9-node test case, the total cost was reduced from USD 131,819.33 (obtained via MST-TSA) to USD 77,129.34, resulting in savings of USD 54,689.99, equivalent to 41.48%. Energy loss costs alone decreased from USD 111,746.73 to USD 63,764.12, a drop of USD 47,982.61 or 42.94%. In the 25-node network, overall costs fell by more than 65%, from USD 371,516.59 to USD 128,974.72, while energy loss expenses decreased by USD 210,057.16 (61.06%). Although conductor-related capital expenditure increased under the MINLP solution, the strategy generated significant long-run economic benefits by markedly reducing operating expenses. In contrast to conventional strategies that address topology definition and conductor sizing in separate stages, the proposed framework integrates these decisions, thereby ensuring globally optimal configurations. These outcomes highlight the method’s ability to scale and its practical value for strategic, long-horizon planning in sophisticated distribution grids. All numerical experiments were conducted in Julia (v1.10.2), leveraging JuMP (v1.21.1) together with the BONMIN solver.

This study introduces a coordinated control approach to address the challenge of volt-var optimization (VVO), incorporating load tap-changing transformers, step-voltage regulators, and switched-capacitor banks, along with a photovoltaic (PV)-integrated microgrid. The harmony search (HS) metaheuristic algorithm was applied to efficiently compute the globally optimal operating parameters for these devices, ensuring robust performance across fluctuating operating conditions. The key aims of the volt-var control strategy were to achieve substantial reductions in active power losses, peak demand, and voltage deviations throughout the distribution system, while simultaneously maintaining bus voltages within acceptable regulatory limits under all possible load scenarios. The optimization problem is a mixed-integer nonlinear program with discrete decision variables, binary variables representing capacitor bank switching states (on/off), integer variables for voltage regulator tap positions, continuous variables for the microgrid’s injected current, and nonlinear network power-flow constraints. The proposed methodology was tested and validated on the standard IEEE 13-node distribution test feeder. Time-series simulations used realistic daily load profiles from the main grid, along with the microgrid’s PV output, both resolved at 15-minute intervals. All power flow computations were carried out with OpenDSS (version 9.5.1.1, released in 2022), an established open-source distribution system analysis tool. The developed control framework supports both real-time operation and long-term planning studies. Simulation results showed that the integrated volt-var coordination significantly reduced total active power losses, lowered peak demand, and effectively mitigated voltage variations across the network.