Distribution network topology planning and optimization: a brief review

. This article investigates distribution network topologies, with an emphasis on Mesh, Radial, and Ring designs, within the context of smart grids. With the primary goal of decreasing power losses using optimization techniques. The ZIP model is used to precisely capture load behaviour in load flow. This research adds to our understanding of topology selection, optimization approaches, and load behaviour modelling, improving in this way increases the efficiency and reliability of electrical distribution networks.


Introduction
In the course of the evolution of distribution networks since the early 20th century, various network architectures have been designed to meet different requirements[1] [2] .These architectures are distinguished by their topology, layout and mode of operation.The topology of an electrical network encompasses all its elements, components and connections within the network.For distributors, defining a topology involves choosing a specific number of physical elements according to criteria linked to objectives and/or technical constraints.The literature lists several effective algorithms for solving the challenge of load flow management in electrical distribution networks with radial topologies [3] [4] .However, these methods are not suitable for mesh networks.Instead, numerous load flow management algorithms have been developed specifically for mesh distribution networks, and information about them is available in the literature [5] [6] .A nonlinear mixed-integer programming approach for the reconfiguration of radial power systems presented in [ 7 ] , including capacitor allocation, with the aim of minimizing energy losses while taking into account various load levels.A new efficient method for optimal capacitor placement in radial distribution systems is proposed in [8] .The method determines ideal capacitor locations and sizes to improve voltage profiles and reduce energy losses.Moreover, a methodology that enables the simultaneous allocation of capacitors and voltage regulators in distribution networks using genetic algorithms and an optimal power flow approach is discussed in [9].The use of particle swarm optimization to determine the optimal size and location of capacitors reported in [10] [11] .Finally, a modified discrete particle swarm optimization strategy to identify the optimal size and location of fixed and switched capacitors El berkaoui Ayoub: ayoub.elberkaoui@ced.uca.ma* * E3S Web of Conferences 469, 00054 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/202346900054 in distribution networks introduced in [12] [13].When designing configurations for electrical distribution networks, three main optimization problems are usually addressed.Considering a specific load scenario.Firstly, it is essential to size the network infrastructure in order to satisfy throughput and reliability constraints [14] [15] [16].The aim here is to minimize the costs associated with investments in power lines and switches.Secondly, in the event of network failure, reconfiguration is necessary, and generally, two objectives are subject to optimization [17] [18].These are to maximize the restored load and to minimize the sequence of operations required to achieve the desired reconfiguration, including switch activation (these two objectives can be addressed jointly [19] [20]).Finally, planning schedules [21] [22] [23] involve establishing a sequence of successive configurations for consecutive load demand scenarios.A new method for estimating actual energy losses resulting from load variations between feeders in a distribution system presented in [24] .A heuristic algorithm using the power flow method is advanced with the aim of finding the optimal configuration for a radial distribution system while minimizing losses is developed in [25] .However, it should be noted that one of the limitations of this approach is that the search strategy employed may prove inefficient, implying that an overall optimal solution is not guaranteed.An heuristic algorithm based on power flow minimization, designed to maintain the radial structure of the system by rearranging switches, turning them on and off, in order to reconfigure the network is mentioned in [26].However, it is essential to note that this method, although suitable for systems, requires a large amount of computing resources, particularly when implemented on a large scale.Other methods based on branch exchange can be found in the work of [27] [28].Numerous publications have sought to increase the reliability of radial distribution network planning in [29] [30], the focus is on improving system reliability by optimizing the location of manual and remote-controlled turnouts, as well as connecting lines [31] [32].Opt for the co-location of distributed generation and connecting lines using an algorithm combining learning (TLBO) and second-order conic programming (SOCP) to enhance reliability.However, distribution lines remain invariant and are not part of the optimization challenge.This article highlights the importance of carefully selecting distribution network topologies and exploiting advanced optimization techniques, such as the ZIP model, to analyze load flows and minimize losses [29] [32].Integrating these tools is crucial to making better decisions.It should be noted that other topologies also exist, such as multi-branch networks, feeder break networks and loop or daisy chain networks [33] [34].
The rest of the paper is organized as follows.Section 1 presents an overview of the different distribution network topologies focusing on Radial, Mesh and ring.Some study cases of load flow analysis also some optimization tools are presented in section 2. The results of simulation and discussion are presented in section 3.

Different distribution network topologies
In this section, several distribution network topologies and their morphologies will be explored with their advantages, disadvantages, applications scopes and cost of each topology.The main network topologies are as follows: mesh, radial and ring.A lot may be learned about how the robustness is affected by these various network topologies, dependability, and effectiveness of contemporary infrastructure systems by comprehending their subtleties.Each topology's properties and uses will be examined throughout this section.

Radial topology
Radial topology is shown in fig. 2. In the early days of the electrical power distribution system, various feeders ran in a radial configuration from the substation to the primary distribution transformer.However, this configuration of the electrical distribution system had a significant drawback: in the event of a feeder failure, the devices connected to that feeder were susceptible to damage.The advantages of this topology are simplicity, easy maintenance and clear direction of power flow.As disadvantages, there is single point of failure, limited redundancy, voltage drop and scalability challenges.This topology can be applied in residential area, small commercial areas, rural regions and Localized Networks.Moving to the cost, radial topology is among the most cost-effective distribution network designs.The straightforward nature of the design, the absence of extensive interconnections, and the use of a single source contribute to lower implementation and maintenance costs.

Ring topology
Ring topology design is shown in fig. 3.This topology in distribution network systems is a network configuration where each node (or substation) is interconnected with precisely two other nodes, forming a closed loop or ring.This arrangement offers redundancy and multiple paths for energy flow.In the event of failure or breakdown at one point in the ring, electricity can still flow in the opposite direction, thus maintaining continuity of supply to connected loads.The advantages of this topology are redundancy, high reliability, Scalability and efficient data transfer.Coming to disadvantages there is, complexity and Maintenance Challenges.This topology can be applied in industrial facilities, corporate networks, transportation systems and localized critical infrastructure.The cost of a ring topology is generally medium compared to radial and mesh topology.

Topologies comparison and discussion
Radial topology is a simple and cost-effective alternative for small networks with few interconnection requirements.Because of its simplicity, it is excellent for home or small office contexts, as well as for easy setup and maintenance.However, it has a key disadvantage: it is dependent on a central hub.If the central hub fails, the entire network goes down.This single point of failure might be a major issue for sensitive applications.But mesh topology, on the other hand, is highly dependable due to its great redundancy and fault tolerance.Its capacity to connect many devices means that data can travel various channels, lowering the chance of network failure.Mesh topology is appropriate for applications requiring data integrity and continuous connectivity, such as hospital or military communication networks.The complexity and cost of building and maintaining a large-scale mesh network, on the other hand, might pose substantial obstacles, making it less practicable for smaller networks with less strict dependability requirements.In the other side ring, topology is ideal for medium-sized configurations with predictable data flow.It is useful for token-ring networks and certain types of LANs because it provides efficient data transmission with no collisions.However, the ring topology, like the radial E3S Web of Conferences 469, 00054 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/202346900054topology, is susceptible to a single point of failure.If any device or connection in the ring fails, the entire network can be disrupted.Adding and removing devices in a ring topology can also be more difficult than in a radial topology.When the cost of each topology is considered, the radial topology is the most cost-effective due to its simplicity and lower number of required wires.The mesh topology, on the other hand, is the most expensive choice due to the large number of connections necessary for redundancy.As it finds a compromise between the simplicity of the radial topology and the redundancy of the mesh topology, the ring topology falls in the middle, at a modest cost.To summarize, the network architecture chosen is determined by the application's individual requirements and needs.Radial topology is appropriate for tiny, low-cost networks with low complexity requirements.Mesh topology is appropriate for important applications that require great reliability and fault tolerance, but it is more complex and expensive.Ring topology is useful in medium-sized settings with predictable data flows, but it must be carefully planned to avoid single points of failure.Understanding the trade-offs between each topology is critical for making informed network design and implementation decisions.

An overview of some studied cases
In this section, the findings from three study scenarios that examined the Radial, Mesh, and Ring topologies are given in order to optimize distribution network topologies.These study cases' primary goal is to use a variety of optimization algorithms to find the optimal solution that minimize losses for each topology.Improving the distribution networks' efficiency, dependability, and cost-effectiveness is desired by using these algorithms.

Radial
The first study case was the same simple radial distribution system was worked on in [35] , [36], [37] and [38] as shown in fig. 4 Fig. 4: simple radial distribution system.
After replacing the distributed generators, two series of tests were carried out, the first on the IEEE-33 node radial distribution system, and the second on the IEEE-69 bus radial distribution system.
Furthermore, in [39] two case studies were conducted using the IEEE-33 node radial distribution system, with an additional test conducted on the IEEE-69 bus radial distribution system.With the aim of reducing losses, various optimization methods were applied, including particle swarm optimization (PSO), binary particle swarm optimization (BPSO) and selective particle swarm optimization (SPSO).

Mesh
Similarly, in [35], [36] and [37] for the simple mesh distribution system with three loops addition to make the network as a mesh network is shown in fig. 5.In the presence of tie lines, the effective power at receiving end of each branch is recalculated as: P(1) ′ + jQ (1) ′ = P(1) + jQ(2) (7) P( 2 The calculation of loop impedance matrix is KVL equations for a simple meshed distribution system can be represented in matrix form as follows: ( Elements on the diagonal of the loop impedance matrix: (, ) =   (, ) + ((, )) *   () ( For i = 1: links and for j = 1: Components outside the diagonal of the loop impedance matrix,   (, ) =   (, ) + (, ) * (, ) *   () (15)   (, ) =   (, ) The process of scanning backwards to add up the real and reactive power loads starts with the last branch and works backwards to the root node.The actual real and reactive power load demands are then as follows: However in [40] he major contributions are articulated as follows: (i) Allocation of distributed generation in mesh networks using a sensitivity approach.(ii) Introduction of an innovative modified method for calculating the allocation and sizing of distributed generators (DGs) in mesh distribution systems, considering load fluctuations.(iii) Comparison of the results obtained by placing one or two DGs in the context of load variations.(iv) Evaluation of the losses and overall annual savings associated with the installation of one or two DGs in a load fluctuation situation.

Ring
The challenge examined by the authors of [41] concerns the identification of a valid directed acyclic graph (DAG) that maintains a balance between the amount of electricity generated and the maximum generation capacity for each source.It is shown that this minimization problem is classified as NP-complete in the general case, but becomes polynomial for ring network topologies, fig.6 illustrates an example demonstrating the equivalence between instances of ring structures and instances of caterpillar structures.But in [42] an optimal routing approach for ring power distribution systems is presented.The problem is fully formulated as a mixed integer linear programming (MILP) model.A new modeling technique is introduced to take into account the return of cables in the same trenches and the load connection possibilities for network paths and nodes.Symmetry breaking constraints are included to eliminate symmetry in solutions.The proposed approach optimally determines the allocation of loads to rings, the routing of cables, the order of load buses, the non-powered parts in each ring and the allocation of renewable energy sources for annualized investment, maintenance, losses and energy cost minimization.The approach takes into account multiple load levels, renewable energy generation uncertainty, cable capacity and voltage drop constraints.In addition, an algorithm is suggested to determine the optimal E3S Web of Conferences 469, 00054 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/202346900054number of rings.The optimization framework is applied to a multi-station medium-voltage network, a real single-station distribution network with transfer bus, and a 54-bus network, fig.7 illustrates a straightforward ring distribution system with two rings.Solid lines depict energized sections, while dashed lines indicate un-energized sections.
In conclusion, this section has covered the outcomes of the three research cases offered insightful information on the advantages of distribution network topology optimization.When put through several optimization techniques, each topology Radial, Mesh, and Ring displayed unique advantages.The Mesh topology displayed improved fault tolerance and scalability while the Radial topology excelled in decreasing energy losses and addressing demand fluctuations.
The Ring topology optimization, on the other side, placed an emphasis on lowered latency and increased transmission speed.These results underline how crucial it is to customize the distribution network to particular needs by taking both the topology type and the right optimization algorithm into account.We pave the path for more effective, dependable, and economical distribution networks in numerous sectors and applications by determining the optimal options for each topology.

Discussion
The authors of [35] compared, existing and proposed load flow analysis methods that applied to both radial and meshed distribution systems.The results are then compared in terms of voltage profile, total real power loss (TPL) in kW, total reactive power loss (TQL) in kVAR, iterations (ITER) and CPU time in seconds.The proposed load flow method is evaluated on two IEEE reference distribution systems, and results are presented for IEEE 33-bus test systems.The analysis of balanced distribution systems, whether radial or meshed, is carried out using two IEEE 33-bus test systems.However, this thesis [36] proposes a new and efficient method for solving the load flow problem of a distribution system using the ZIP model.This proposed method is compared with existing methods and found to perform better in terms of number of iterations, computational efficiency and convergence robustness, while maintaining solution accuracy.The ZIP load flow approach shows strong agreement with existing methods.Nevertheless, the paper referred to in [37] presents an innovative and highly efficient method for solving the load flow problem in distribution systems.This method is subjected to a comparison with already existing methods, and it is clearly demonstrated that it outperforms them in terms of iterations, computational efficiency and convergence robustness, while maintaining a high level of accuracy in the solutions obtained.In addition, the proposed load flow approach aligns significantly with conventional methods.The performance of the proposed method is evaluated on two IEEE reference distribution systems, covering a wide range of load conditions, various R/X ratios, and taking into account various static load models, as well as the evolution of electricity demand.Furthermore, the integration of distributed generators (DGs) and the reconfiguration system into radial distribution networks results in a significant reduction in energy losses in [38].A key observation highlights a substantial reduction in losses, particularly in scenario -4, with smaller DGs.This load balance is achieved by reducing both real and reactive power losses, thus improving the system's power factor.It should be noted that the reduction in reactive power losses is largely dependent on the system voltage profile, as demonstrated by the two test cases presented in this paper.In addition, in the paper [39], presents a method for reconfiguring distribution networks to minimize active power losses.This method is based on an evolutionary algorithm based on BPSO, called IS-BPSO.The proposed method modifies the BPSO sigmoid function to regulate the rate of change of the particle vector, leading to better exploration of the search space and improved population convergence.Simulation results testify to the remarkable efficiency of this method, guaranteeing global optimization.However, the paper listed in [40] presents an innovative method for allocating distributed generation within a meshed network, using sensitivity-based techniques.This method relies on unique energy-loss sensitivity expressions, allowing the identification of optimal distributed generation sizes for unit or staggered power factors.In addition, this approach is extended to optimally determine the location of multiple DG units within the distribution system.The effectiveness of this approach is evaluated on a practical test system consisting of 38 buses, incorporating a time-varying ZIP load model, with consideration of both radial and meshed network configurations.The study covers different scenarios of unitary and shifted power factors, while calculating the costs associated with energy loss, the power generated by distributed generation units and the savings achieved through loss reduction, for both types of network.However, with regard to [41], to create an efficient configuration for a switched power network, the researchers formulated two algorithmic problems related to the graphical structure of this network.The first problem aims to identify a feasible configuration by activating switches and orienting edges, while the second problem aims to optimize the balance between the utilization rates of different sources to guarantee the resilience of the network in the event of a failure.Interestingly, the researchers demonstrated that when switches are organized in a ring topology, these problems become solvable in polynomial time.Furthermore, in the context of [42], the study developed an optimal routing strategy for a medium-voltage distribution network organized in rings.Within a mixed-integer linear programming framework, the optimization encompassed the specific routing of each ring, the assignment of loads to each ring, as well as the identification of nonpowered areas of each ring, all with the aim of minimizing the costs associated with investments, including costs related to cables, cable trenches, renewable energy sources, maintenance operations, energy expenses and losses.It was suggested that a new modelling technique be adopted for network optimization, making it possible to manage routing within the same cable trenches, the connection order of load buses and transfer nodes.In addition, the impact of restricting each ring to a single feeder was examined, and a method for determining the optimum number of rings was presented.

Conclusion
The research and studies done on distribution network topologies have shown the significance of this field in the effective and dependable delivery of electricity to end users.It is clear that much more research and development may be done.As a result of the variety of distribution network topologies available, including radial, ring, and mesh systems, it is possible to experiment with various configurations to meet various operational needs.Additionally, the combination of optimization algorithms, opens up intriguing new directions for loss minimization and load flow analysis.It is crucial to understand that distribution network design is not a one-size-fits-all strategy and that the ideal answer may change depending on the particular situation and available options.As a result, ongoing research into and evaluation of alternative topologies and optimization approaches should be done.Joint advancement may be made distribution network topologies and optimization methods as researchers and engineers.Time-varying ZIP load models will be used in rigorous experimentation and simulations on real test systems to better understand how various configurations work in the real world.The ultimate objective is to create an ideal distribution system that not only guarantees low economic costs but also reduces power losses, and solid against disturbance.

E3S
Web of Conferences 469, 00054 (2023) ICEGC'2023 https://doi.org/10.1051/e3sconf/2023469000541.1 Mesh topology Mesh structure is depicted in fig.1.The mesh or grid structure represents a variation of the branch circuit architecture.It is characterized by the presence of a considerable number of loops formed by cables linking high-voltage source substations (EHV/HV), loads and intermediate interconnections.This configuration operates radially, which is made possible by the strategic arrangement of multiple switching devices, generally open throughout the network.Some advantages of this topology are high reliability, fault Tolerance, high Resilience, flexible expansion and reduced voltage drop.The disadvantages are complexity, maintenance challenge and limited scalability.It can be applied in critical infrastructures, data centres, industrial complexes and smart grids.The implementation cost of a mesh topology is generally higher compared to simpler topologies like radial or ring.

Fig. 6 :
Fig.6: Example of equivalence between ring instances (on the left) and caterpillar instances.