Large-Scale Network Layout Optimization for Radial Distribution Networks by Parallel Computing: Implementation and Numerical Results

Distribution network design is one of the most essential strategic decisions in logistics systems and supply chains, as it structures the network by determining the number of echelons and specifying the types, quantities, and locations of various facilities. This chapter presents decision-support models for distribution and logistics network design, covering both continuous location models (gravity location models) and discrete network design models (capacitated/uncapacitated and their relevant variants). Comprehensive numerical experiments based on the same case study offer a direct comparison of these different network design approaches. Furthermore, as one of the most disruptive technologies in Industry 5.0, the impact of generative AI (GenAI) and large language models (LLMs) on the research and education of distribution network design is thoroughly analyzed. Our experiments demonstrate that GenAI and LLMs are powerful tools in providing structured introductions to existing problems, guiding model selection and explanation, assisting with coding and code clarification, facilitating model comparison, and generating initial ideas for new research questions in distribution and logistics network design. However, they also face reliability and accuracy challenges, exhibit limited critical thinking capabilities, and struggle to address emerging research questions. Our findings offer valuable guidance for incorporating GenAI tools and LLMs into research and educational processes in distribution and logistics network design.

This paper undertakes the problem of optimal capacitor placement, replacement and control in large-scale unbalanced, radial or loop distribution networks. The problem is how to optimally determine the locations to install (or replace, or remove) capacitors, the types and sizes of capacitors to be installed (or replaced) and, during each load level, the control schemes for each capacitor in the nodes of a general three-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints (e.g. the voltage profile) at different load levels are satisfied. The objective function considered consists of two terms: cost for energy loss and cost related to capacitor purchase, capacitor installation, capacitor replacement and capacitor removal. Comprehensive modelings of different components are presented which include primary power networks, three-phase transformers (different winding connections, off-nominal tap ratio, core and copper losses), co-generators, voltage sensitive load models for single-phase, two-phase and three-phase loads, shunt capacitors and reactors. The new problem is formulated as a combinatorial optimization problem with a nondifferentiable objective function. The configuration space essential in the design of an annealing-based solution methodology for the new problem is derived. >

The purpose of this paper is to establish algorithms in the design of rural low-voltage (LV) distribution networks. Planning of rural LV distribution networks involves the optimal design of radial configuration and location of MV/LV substations considering cost functions. In this work both goals are considered by taking into account different conductors, voltage drop constraints, power losses in lines and deterministic loads. The algorithms developed in this paper are based on dynamic programming; and were implemented on large-scale rural LV distribution networks, but they could also be used for other network optimization.

A Hybrid Jaya Algorithm for Design Optimisation of Large-Scale Water Distribution Networks

This paper presents a mathematical stochastic methodology for transit route network optimization. The goal is to provide an effective computational tool for the optimization of a large-scale transit route network to minimize transfers with reasonable route directness while maximizing service coverage. The methodology includes representation of transit route network solution search spaces, representation of transit route and network constraints, and a stochastic search scheme based on an integrated simulated annealing and genetic algorithm solution search method. The methodology has been implemented as a computer program, tested using previously published results, and applied to a large-scale realistic network optimization problem.

The large scale of real distribution systems makes difficult the development of computational tools for real-time monitoring of these systems. Thus, the decomposition of distribution networks into smaller sub-networks emerges as an alternative for this development, embracing the use of smaller models, instead of a single large-scale model, parallel computing and decentralized processing architectures.This chapter introduces decomposition methods to perform state estimation in large-scale distribution networks, employing the concepts of multiarea state estimation (MASE). A brief contextualization of scalability and decentralization is presented to emphasize the need of such architectures. Then, the main ideas of MASE are discussed. Two multiarea state estimation algorithms are presented, both make use of specialized methods for distribution system state estimation. However, one based on the traditional approach of the nodal voltage state estimation and the other on current-based model. Finally, numerical examples with both estimators illustrate the accuracy and computational aspects.

This study introduces the Spanning-Tree Matrix Approach, a novel computational method for modeling large-scale, tree-shaped water distribution networks. The method focuses on minimizing network cost while satisfying hydraulic design constraints. A case study demonstrated the integration of this approach with the Honey-Bee Mating Optimization algorithm to determine the optimal combination of pipe diameters. Results confirm the model’s effectiveness and scalability for tree-shaped network configurations. The Spanning-Tree Matrix Approach is also versatile—it can accommodate various governing equations and design criteria, and can be easily embedded in modern stochastic optimization algorithms such as Genetic Algorithms, Simulated Annealing, and Ant-Colony Optimization. Due to its adaptability and simplicity, further research is encouraged to apply this approach to other spanning-tree hydraulic systems, including waster water networks, river or groundwater networks.

This study proposes a new optimisation framework based on Monte Carlo embedded hybrid variant mean–variance mapping (MVMO-SH) optimisation​ for planning Photovoltaic Distributed Generation (PVDG) in the urban Radial Distribution Network (RDN). The Active Power Loss (APL) index was calculated considering the risk of uncertain photovoltaic generation and urban load distributions. The Monte Carlo Probability Density Function method was initially used to manage uncertainties. The Monte Carlo-embedded MVMO-SH was then used to optimise PVDG in the urban RDN. Simulations were run for several scenarios in three load cases based on 288 segments: residential, commercial, and industrial urban loads. The MVMO-SH had the lowest APL index compared to genetic algorithm and particle swarm optimisation when the probabilistic power flow with PVDG was optimised under uncertainty. The APL indexes with three PVDG installations in the 33-bus RDN for residential, commercial, and industrial urban load models were 0.4094, 0.4811, and 0.4655, respectively. In the 69-bus RDN, the APL indexes with three PVDG installations for residential, commercial, and industrial urban load models were 0.3403, 0.3570, and 0.3504, respectively. For all load models examined, there was a significant reduction in the APL index for the case of three PVDGs compared to the system without PVDG. The findings showed that uncertainty significantly impacted the optimal location and size of PVDG in the RDN.

Dynamic reconfiguration is an effective method to improve the unbalanced distribution of load demand. The traditional global dynamic reconfiguration based on the centralized cloud service system may lead to large-scale power flow regulation and increase the computational burden in large-scale distribution networks. In this letter, a time-segmented multi-level method preferring local reconfiguration is proposed to minimize the photovoltaic power generation curtailment and load shedding. Furthermore, a novel cloud-edge collaboration framework is devised to alleviate the huge pressure bought by excessive concentration of computational tasks. Numerical results on a 445-node system are presented to demonstrate the effectiveness of the proposed method.

Multiobjective shortest path problem (MSPP) is one of the most critical issues in network optimization, aimed at identifying all efficient paths across conflicting objectives. Nowadays, existing methods face substantial bottlenecks in addressing the diverse preferences of decision makers and high spatiotemporal overhead caused by the calculation process, particularly in cases with large-scale networks. To overcome these obstacles, a generalized MSPP in large-scale networks is investigated with the aim of solving it with diverse preferences of decision makers satisfied and low spatiotemporal overhead. Toward this end, with a novel concept, the generalized dominance relation is introduced, and the generalized multiobjective shortest path algorithm via the generalized dynamic programming approach is developed. Moreover, the H-reducible technique is further employed to accelerate the convergence of the proposed algorithm. Additionally, several rigorous proofs are provided for the conclusions that all efficient paths could be found within a tolerable time by the developed algorithm and the algorithm could be implemented in a distributed manner under mild assumptions. Finally, numerous routing experiments are conducted on large-scale communication networks for demonstrating the effectiveness and competitiveness of our approach.

This paper presents an optimal way to control steady-state voltage in distribution feeders using reactive power ancillary service that is provided by synchronous distributed generators (DGs). Based on load forecasts provided one day in advance, DG reactive power is dispatched on the hour in coordination with the switching operations of an on-load tap changer (OLTC) and shunt capacitors (SCs). This aims to reduce not only distribution line power losses but also the number of switching operations of the OLTC and the SCs, which affect the feeder voltage quality and switching device lifetime. For the reactive power dispatch, a mixed-integer nonlinear optimization problem is formulated using a multiobjective function and solved using a particle swarm optimization (PSO) algorithm. Modules using evolutionary and dynamic programming are incorporated into the PSO algorithm to be less susceptible to becoming trapped in local optima and have a better chance of reaching global optimum. Simulation case studies using small- and large-scale distribution networks were performed using MATLAB to demonstrate that the coordinated reactive power support of the DGs, OLTC, and SCs can achieve the objective effectively, resulting in improved voltage quality.

The design of water distribution networks (WDNs) is addressed by using a variant of the particle swarm optimization (PSO) algorithm. This variant, which makes use of a discrete version of PSO already considered by the authors, overcomes one of the PSO's main drawbacks, namely its difficulty in maintaining acceptable levels of population diversity and in balancing local and global searches. The performance of the variant proposed here is investigated by applying the model to solve two standard benchmark problems: the Hanoi new water distribution network and the New York Tunnel water supply system. The results obtained show considerable improvements in both convergence characteristics and the quality of the final solutions, and near-optimal results are consistently achieved at reduced computational cost.

The paper addresses the optimal design of distribution networks (DNs). Considering a distributed system composed of stages connected by material links labelled with suitable performance indices, a procedure employing multi-objective genetic algorithms (MOGAs) is presented to select the optimal DN configuration. The paper enhances a deterministic procedure for DN strategic configuration by employing MOGACOP, a real-valued chromosome MOGA that can be applied to the case of constrained nonlinear function. The main MOGA characteristics are the presence of three populations: two reference sets of individuals satisfying all constraints, namely, a set of Pareto optimal individuals (frontier population) and a set of individuals covering the previous population (archive population), together with a search set which, on the contrary, includes individuals that are allowed to not satisfy all constraints (laboratory population). MOGACOP allows solving the DN design nonlinear problem, which exhibits a multi-objective function that varies linearly only with some variables and nonlinearly with the remaining variables. The proposed MOGA application allows finding a Pareto frontier of optimal solutions, which is compared with the frontier obtained by solving the same problem with Integer Linear Programming (ILP), where piecewise constant contributions are linearly approximated. The two found curves represent, respectively, the upper and the lower limit of the region including the real Pareto curve. Both the genetic optimisation and the ILP models are applied under structural constraints to a case study describing the distribution chain of a large enterprise of southern Italy producing consumer goods.

Distributed energy resources (DERs) can improve the performance of radial distribution systems. The nonlinear power flow constraints, multi-objective trade-offs, and network reconfiguration scenarios for DER placement and sizing call for the formulation of optimization problems. Most of the times optimization algorithms suffer from premature convergence and poor exploration-exploitation balance. These problems exhibit an inherent internal structural symmetry. In order to overcome the above problem, this study uses the Multi-Objective Archimedes Optimization Algorithm (MAOA) to optimally allocate DERs in the Radial Distribution Networks (RDNs), moreover the performance of the proposed MAOA is compared with the other well established algorithms including Particel Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Shuffled Frog Leaping Algorithm (SFLA), Atom Search Optimization (ASO), and Butterfly Optimization Algorithm (BOA) on the IEEE-33 RDN. The comparison is made for the four cases (S1: DER Only), (S2—Network Reconfiguration Only), (S3—DER Followed by Reconfiguration), and (S4—Reconfiguration Followed by DER) considering factors like voltage profile, network reconfiguration, active and reactive power loss reduction, carbon emission DER utilization and Cost reduction. The MAOA is observed to provide better results among all the other benchmark algorithms. In S3, the active power loss is reduced by 68.41%, whereas the reactive power loss is reduced by 57.44% and the MAOA algorithm improves the voltage by 3.98%. The minimum voltage of the network is also improved by 6.28%. The algorithm improves convergence with a percentage of 18.50% enhancing the system’s operational symmetry and stability, while satisfying all constraints. At Bus 3 and Bus 6 of IEEE-33 bus radial distribution network (Baran–Wu test system), DG capacity is allocated to be 3.8 MW and 2.1 MW, respectively.

“We get by with a little help from our friends”: Small-scale informal and large-scale formal peer distribution networks of sterile injecting equipment in Australia