Optimal Selection of Conductors in Distribution System Designs Using Multi-Criteria Decision

Abstract

The growth in the demand for electrical energy, which is driven by the constant growth of the metropolises and the expansion of the productive capacities of the industrial sector, entails the inevitable development of the electrical system to satisfy all the required demands in a convenient, efficient, and reliable manner. In this scenario, power distribution companies will continue to need to expand their electrical systems in the short and medium term to obtain the lowest investment and operating prices for the period considered in the analysis horizon. The expansion of the system can be projected statically or dynamically, which depends on the criteria that each distributor, in turn, applies in their expansion projects. Multi-criteria decision making can provide deeper analysis perspectives considering infinite possibilities for optimal network sizing and the technical, operational, quality of service, and even system reliability factors. This research proposes a multi-criteria decision technique based on the CRITIC method to determine the optimal design of an electrical distribution system. For this purpose, several design scenarios are defined with different types of electrical conductors, and the power flows are calculated in each. From these simulations, the results obtained in voltage profiles, namely active and reactive power losses, current levels, and the costs associated with the conductors used, are recorded. With the multi-criteria technique, the winning alternative is the design scenario containing the best joint solutions for the analysis variables. The proposed methodology is validated in an IEEE 34-bar test system. The Matpower tool, available through Matlab, generates power flows for each proposed design case. The results obtained in the analysis variables are generated and stored in a decision matrix of 210 alternatives. The proposed method represents a novel and powerful alternative for design proposals of distribution systems considering quality, efficiency, and cost criteria.

1. Introduction

Demand growth is one of the primary challenges electricity distribution companies face worldwide. This growth not only implies the urgent need to expand the capacity of the distribution systems but also generates problems related to the adequate implementation of the infrastructure due to unfavorable geographical conditions or difficulties in accessing transmission or sub-transmission networks. Electricity distribution companies must develop effective strategies and innovative solutions to face these challenges [1].

While it is true that planning is most often used in designing new infrastructure, there are also cases where a design approach is necessary to improve or optimize an existing network. The purpose of this is to reduce power losses, improve the voltage profile, or replace the infrastructure when it has reached the end of its useful life. Planning and strategic design are fundamental in creating new networks and improving existing ones, thus allowing for the efficient and reliable operation of electrical systems [2].

Distribution companies generally prioritize aspects related to the costs of deploying distribution networks, including transformation and conduction stages. In this sense, the conductor is an essential part of such a deployment, representing a significant portion of the implementation costs. It is crucial that companies carefully consider these costs and seek efficient and cost-effective solutions to optimize the deployment of distribution networks, thus maximizing benefits and minimizing expenses [2].

Distribution companies recognize the importance of planning tasks and seek strategies to make optimal operational and economic decisions. Both factors must be considered holistically during the decision-making process. In general, experts in this area generally resort to heuristic algorithms, combinational techniques, genetic algorithms, evolutionary strategies, and linear and non-linear modeling. These techniques are applied through specialized software to achieve effective optimization in planning distribution operations. The objective is to maximize efficiency, minimize costs, and make informed decisions that drive the company’s overall performance [1,3,4,5,6,7,8].

In [8], an optimization method that uses mixed integer nonlinear programming for modeling the electrical network is presented. This method uses a single ground return conductor and considers fixed and variable costs, which are minimized as an objective function. The research proposes a comprehensive solution that addresses network configuration and associated cost optimization. This approach seeks to find an optimal solution that maximizes efficiency and minimizes expenses in the operation of the electrical network.

Article [4] proposes a constraint alternative considering the radial topology common in electrical distribution systems. These radiality constraints are tested in deployment and reconfiguration problems to validate their functionality and adaptability in various optimization models. The research seeks to demonstrate the effectiveness of these restrictions when applied in real scenarios, evaluating their ability to guarantee a reliable and efficient network structure. When considering the radial topology, it seeks to simplify and speed up the design and operation processes of the electrical network.

On the other hand, in [5], the use of a heuristic model based on an evolutionary strategy for the optimal selection of conductors for each primary that is part of a distribution system is tested, and the methodology contemplates biological type structures for decision-making inspired by recombination, mutation, and other similar forms.

Furthermore, in [6], an electrical network, in which non-uniform charges are distributed throughout the primary circuits, is analyzed. The optimization problem is approached from a simplified perspective proposed by the authors, which combines an economical method based on current density and an index-directed heuristic method. This combination of approaches seeks to find an optimal solution considering both economic efficiency and optimization of network performance. The authors propose a technique that considers unbalanced loads and uses heuristic indices to make informed decisions in the planning and design of the electrical network. The objective is to find a balance between load distribution and the global efficiency of the system.

In [7], a mixed integer linear model is proposed for optimal conductor selection in a distribution network. This model uses two objective functions accompanied by linear expressions that represent the steady-state operation of the network. In addition, a heuristic technique is introduced to obtain the Pareto front, meaning the resolution of the problem is addressed. Using a mathematical model and the proposed heuristic method, it seeks to provide an integrated solution that maximizes the performance and efficiency of the system.

Finally, ref. [3] focuses on optimal conductor selection using a metaheuristic technique known as Taboo search. In this method, a single mixed integer nonlinear-type objective function model is used. The study analyzes the costs of implementation and operation over one year. Power flows in single-phase radial systems are analyzed to evaluate the system’s results. The main objective is to find an optimal solution that minimizes the total costs, considering the operational and economic aspects.

The current research addresses a multi-criteria selection method for choosing conductors by using a predefined set of options and correctly identifying decision variables. The purpose is to develop a systematic approach that considers multiple criteria and allows for informed and optimal decisions when selecting electrical conductors, analyzing the different options, and evaluating keyable aims to find the most appropriate combination that satisfies the electrical distribution system’s technical, operational, and economic requirements.

2. Materials and Methods

2.1. Radial Distribution Systems

A radial distribution system presents a tree-shaped configuration, where the tree’s root starts from the power supply point, which generally corresponds to the substations in electric power systems. The typical structure of a radial distribution system implies the presence of distribution lines, feeders, transformers, protection devices, and disconnectors. Figure 1 provides a visual representation of a possible classification of distribution systems, showing different categories according to their characteristics.

The inherently unidirectional nature of power flow in radial distribution systems poses numerous challenges for operators of these networks. Its objective is to provide a reliable and quality electrical service that meets the demand of residential and commercial users connected to its networks. In addition, they must ensure that they are effectively connected to the available transmission and sub-transmission systems. It is important to note that the power feed from the substation to the user must follow a single path, which adds additional complexity to grid planning and operation. Compliance with these requirements ensures efficient and safe power distribution [1,4,9,10].

As mentioned above, the quality of service and the availability of energy resources to meet demands and reduce technical losses are important issues that must be addressed. Numerous techniques are available to improve service quality, among which are the optimal installation of distributed generation systems; the use of compensation systems, such as FACTS (Flexible AC Transmission Systems); and the implementation of storage systems standout, such as BESS (Battery Energy Storage Systems), among others. These techniques are focused on optimizing and improving the efficiency of the electrical network, allowing for better demand management, more excellent stability, and a reduction in technical losses. [5,11,12,13,14].

Despite their benefits, these devices are especially useful in ring topologies or systems requiring frequent reconfiguration, which poses additional challenges and may imply higher investment costs. However, building and sizing the network right from the start is crucial to ensure that the distribution infrastructure is correct. By carefully planning and considering factors such as expected load, grid topology, and responsiveness, a solid foundation can be laid for deploying electrical infrastructure. This ensures that the network can meet demand efficiently and minimizes the need for costly and complex reconfigurations in the future [12,15,16].

2.2. Optimum Conductor Selection

The optimal selection of conductors is essential to reduce technical losses in a conventional distribution system. Loss reduction is typically achieved by using higher voltage levels or conductors with lower resistance. However, both techniques are often expensive in practice. Therefore, having a minimization method, even a modest one, can be a necessary tool to make deployment decisions that help mitigate these losses. Radial distribution systems face the challenge of providing reliable and quality service capable of satisfying current and future loads as planned. This need is because network failures are reduced, increasing the system’s reliability. This can be quantified using system reliability indices related to downtime and the number of users affected by system outages.

In summary, the excellent selection of conductors and improved system reliability are crucial in radial distribution systems to reduce technical losses and guarantee a reliable and quality electrical service for users [7,10,11,17,18].

In [17], it is mentioned that two broad groups of techniques can be used to achieve optimal driver selection. These groups include conventional analysis methods and metaheuristic techniques.

Ref. [19] introduces a technique that uses power flows in radial systems as an analysis tool combined with an optimization model. This approach considers power flow data, conductor capital costs, and costs associated with system losses to minimize total costs.

On the other hand, Ref. [20] proposes an alternative that uses the Whale Optimization (WO) method, using a catalog of 20 types of conductors for their selection. This technique considers various aspects, such as market availability, demand growth, payback times, and technical considerations, such as voltage limits and conductor operating limits.

In [17], the optimal selection of conductors and the placement of capacitors in the network are also discussed as an integrated approach. The voltage profile, loss reduction, and economic impact are considered. Particle Swarm Optimization (PSO) is used to obtain the optimal parameters. This strategy allows us to find the ideal values for conductors and capacitors efficiently, thus maximizing the benefits of voltage profile and loss reduction with an economical approach [2,7,16,21].

2.3. Power Flow in Radial Systems

This section presents the formulation to calculate the power flow in radial distribution systems. The following expressions detail this formulation with greater precision, while Figure 2 illustrates the basic scheme of a typical radial network.

In Figure 2:

$m1$ and $m2$ are the sending and receiving nodes;

$P_{m2}$ is the sum of the real powers that follow the receiving node, the real load power of the node, and the real power losses;

$Q_{m2}$ is the sum of the active powers that follow the receiving node, the active power of the node load, and the active power losses;

$I_{jj}$ is the current flowing through the link jj;

$V_{\left(i\right)}$ is the voltage present on each bar I;

$d_{\left(m1\right)}$ is the voltage angle of node $m1$;

$d_{\left(m2\right)}$ is the voltage angle of node $m2$;

$R_{jj}$ is the resistance of the link jj;

$X_{jj}$ is the reactance of the link jj.

The current flowing through a link between two network nodes is expressed using the expression (1).

$$I_{jj}=\frac{(P_{\left(m2\right)}-{jQ}_{\left(m2\right)})}{{V^{\mathrm{*}}}_{\left(m2\right)}}=\frac{(V_{\left(m1\right)}-V_{\left(m2\right)})}{(r_{\left(jj\right)}-{jx}_{\left(jj\right)})}$$

(1)

An analysis of the terms involved indicates that the voltage value in the receiving bus can be calculated using the following expression (2):

$$\left|V_{\left(m2\right)}\right|={\left[\frac{1}{2}\left[b_{\left(jj\right)}+{\left\{b_{\left(jj\right)}^2-4c_{jj}\right\}}^{1/2}\right]\right]}^{1/2}$$

(2)

where $c_{jj}$ is represented by Equation (3).

$$c_{jj}=\left\{P_{\left(m2\right)}^2+Q_{\left(m2\right)}^2\right\}\left\{r_{\left(jj\right)}^2+x_{\left(jj\right)}^2\right\}$$

(3)

On the other hand, the system losses can be calculated with the expressions (4) and (5).

$${LP}_{\left(jj\right)}=\frac{r_{\left(jj\right)}\left\{P_{\left(m2\right)}^2+Q_{\left(m2\right)}^2\right\}}{{\left|V_{\left(m2\right)}\right|}^2}$$

(4)

$${LQ}_{\left(jj\right)}=\frac{x_{\left(jj\right)}\left\{P_{\left(m2\right)}^2+Q_{\left(m2\right)}^2\right\}}{{\left|V_{\left(m2\right)}\right|}^2}$$

(5)

Since information on the output voltage of the substation is generally available, it is possible to theoretically determine the values of $V_{\left(m1\right)}$ as long as the load values in each one of the nodes are available.

The computation can proceed for all links jj, and sets of sending and receiving nodes, $m1={IS}_{\left(jj\right)}$ and $m2={IR}_{\left(jj\right)}$. Therefore, at each computation iteration that is performed, the value of $\left|V_{\left(m2\right)}\right|$, $P_{\left(m2\right)}$, and $Q_{\left(m2\right)}$can be determined.

The loads will be updated by increasing the values of losses in each node in an iterative way to achieve results with a tolerance as low as 0.0001 p.u. The formulation proposed in this study is based on the authors’ research in [22] and uses fuzzy arithmetic and fuzzy logic techniques to solve power flows effectively.

Finally, the equations must be rewritten to calculate the parameters with k possible elements for the existing conductors. Expressions (6)–(9) are the equations that consider the above.

$$\left|V_{(m2,k)}\right|={\left[\frac{1}{2}\left[b_{(jj,k)}+{\left\{b_{(jj,k)}^2-4c_{(jj,k)}\right\}}^{1/2}\right]\right]}^{1/2}$$

(6)

$$I_{(jj,k)}=\frac{(P_{\left(m2\right)}-{jQ}_{\left(m2\right)})}{{V^{*}}_{(m2,k)}}$$

(7)

$${LP}_{(jj,k)}=\frac{r_{\left(jj,k\right)}\left\{P_{\left(m2\right)}^2+Q_{\left(m2\right)}^2\right\}}{{\left|V_{(m2,k)}\right|}^2}$$

(8)

$${LQ}_{(jj,k)}=\frac{x_{\left(jj,k\right)}\left\{P_{\left(m2\right)}^2+Q_{\left(m2\right)}^2\right\}}{{\left|V_{(m2,k)}\right|}^2}$$

(9)

The total active power losses are those shown in (10).

$$TLP=\sum _{jj=1}^{LN1}{LP}_{(jj,k)}$$

(10)

where:

${LP}_{(jj,k)}$ is the active power losses of the lines;

${LQ}_{(jj,k)}$ is the reactive power losses of the system lines;

$TLP$ is the total active power losses of the system.

The restrictions to be considered in the optimal driver selection model are derived from the above.

$$F_{(jj,k)}={CL}_{(jj,k)}+{CC}_{(jj,k)}$$

(11)

where:

$F_{(jj,k)}$ is the cost for each link for each of the conductor types;

$CL$ represents the costs of lost energy for each type of conductor possible;

${CL}_{(jj,k)}={Perd. Pico }_{(jj,k)}\left[Kp+Ke\times Lsf\times T\right]$;

$CC$ represents the annual investment capital for each conductor on each link;

$CC=\propto \left[{cost}_{\left(k\right)}{len}_{\left(jj\right)}\right]$.

On the other hand, it is possible to establish two restrictions related to operational aspects that address the minimum required voltages and conductor current limits, as shown in Equations (12) and (13).

$$\left|V_{(m2,k)}\right|>V_{min}$$

(12)

$$\left|I_{(jj,k)}\right|<I_{max}$$

(13)

2.4. CRITIC Method

The CRITIC method uses a set of matrix calculations to analyze a data set that covers the different cases under analysis and all the decision criteria to be considered. The objective is to minimize the criteria values and select the best alternative in a weighted manner [11,23,24,25,26].

The first step will be to define the decision criteria (output variables) to calculate and analyze. A decision matrix can be built with the results of these output variables for each analysis scenario. This matrix will have n columns representing the number of alternatives (scenarios) to be analyzed and m rows representing the calculated decision criteria.

The second step considers normalizing the values associated with the decision matrix. For this purpose, a normalization method defined by the ranges of the results will be used, and its calculation is based on the use of minimum and maximum values.

After, the third step contemplates the weighting of the decision criteria. The calculation of the weight that will be assigned to each variable will depend on the dispersion that the results may present. This dispersion must be defined by statistical values associated with the standard deviation of the results and the correlation coefficient that may exist between rows and columns of the decision matrix.

The decision vector will comprise the weighted sum of the driver selection alternatives and correspond to the sum of the resulting products between each criterion and its weighting. The sum that delivers the lowest totalized value will be selected as the winning alternative, with which the criteria will be minimized.

Algorithm 1 shows the algorithm that describes those mentioned above, considering that this algorithm does not contemplate the construction of the decision matrix since it must be built beforehand based on the results obtained in each analysis scenario.

Algorithm 1. CRITIC Method.

M = Decision matrix Obtaining minimum values Minimum = diag(min(M′)) × ones(size(M)) Obtaining maximum valuesMaximum = diag(max(M′)) × ones(size(M)) Normalization of values Mp = (M − Minimum)/(Maximum − Minimum) Obtaining standard deviation d = std(Mp′) Obtaining correlation coefficients R = corrcoef(Mp′) Weighing Weight = d × sum(1 − R) A = sum(weight) Weighted Matrix Normalization Normp = (weight/A)′ matrix weight for all i:n For everything j:m V = normp(i) × Mp(j,i) Weighted Matrix(j,i) = [v] end to all end to all weighted summation for all i:n V3 = 0 For everything j:m V3 = V3 + weighted matrix(j,i) Weighted Sums(i) = [V3] end to all end to all Best case selection Best case = find(weighted sums == min(weighted sums))

3. Results

3.1. Problem Determination

The problem is approached from a multi-criteria perspective in which the development of an algorithm that allows for the excellent selection of the conductors to be used in a distribution system defined by an IEEE 34-bar case study is proposed based on a 33-bar system.

The algorithm aims to determine the best driver alternative to achieve optimal operation, considering both driver costs and distribution network deployment. The Parameters to be considered include busbar voltages, system currents, active and reactive power losses, and costs associated with conductors.

3.2. Conductor Characteristics

The conductors used in distribution or transmission systems are widely known, which allows us to obtain data from various literary sources. To calculate the proposed scenarios, simulations are used as they cover all the possibilities involved with evaluating 31 different types of electrical conductors. These conductors define the different study scenarios in which the power flow is calculated using the Matpower tool. This tool allows you to perform various types of power flow analysis, including calculating optimal power flows. The results obtained from these simulations will be used later in the proposed methodology for creating the decision matrix.

3.3. Test System

The power system to be studied is a 34-bar radial distribution system in which loads are distributed along all the bars, considering bar 1 as the main reference since it represents the substation from which it originates the distribution network. It is important to note that in this test system, there are several reconfiguration options. However, these options have yet to be considered since they are disconnected. Therefore, the system is considered entirely radial for design purposes. In addition, it is established that the main sections of each branch use the same specific conductor gauge. In contrast, the segments derived from these areas use a second type of conductor defined by a smaller gauge than the one existing in the main primary.

3.4. Criteria and Cases

For the development of this research work, the use of a total of 31 driver alternatives is proposed. They will be segmented into two groups of drivers, i.e., one of 10 drivers and another group of 21 drivers, that will be combined in the network, which will obtain a total of 210 cases of analysis or selection alternatives.

The criteria to be selected include the voltage deviation of each of the system bars, the active and reactive power flows in each of the links, and the generation power that will be demanded from the system, which implies it explicitly reduces the number of system losses since it seeks to minimize the power necessary to meet the demand. Finally, a monetary criterion resulting from implementing the different drivers in the system is added.

The aforementioned supposes the use of a total of 210 selection alternatives, while a total of 102 criteria are selected under analysis.

In the case of costs, penalties are placed on the use of each conductor, categorizing the selection of each one of the cases so that the use of conductors of a more excellent caliber for the links or main sections is more expensive. Each increase in caliber considerably increases the cost of the service, while the selection of the conductors of the smaller section does not significantly affect the selection of the conductor. The aforementioned is shown in expression (14).

$$Costo=opc1+30\times opc2$$

(14)

3.5. Analysis of Results

The Matpower tool, available through Matlab, is used to generate power flows for each of the cases proposed. These cases are caused and stored, totaling 210 options, as previously mentioned.

A decision matrix comprising 102 selection criteria includes the most relevant parameters. The calculations are made on a computer with a sixth generation Core i7 processor (version Matlab R2021b), 16 GB of RAM, and a 2 GB dedicated video card. The generation of the cases takes approximately 6 s, while the multi-criteria decision-making algorithm returns results in 12.3 s.

The results indicate the selection of case 210, corresponding to option 10 for smaller gauge conductors and option 21 for more prominent section conductors. This results in an option cost of 640, as shown in expression 14 in the previous section.

Figure 3 shows the voltage profiles for the different analysis cases. In it, you can see areas where the voltage profiles are high, corresponding to points where there are derivations of the primaries. In these zones, the voltage level originates in areas closer to bus 1, which represents the substation with primary control. It is essential to point out that the figure above represents the voltage deviations in each bus concerning the substation voltage, which is considered as 1 p.u.

In addition, Figure 4 represents an enlargement of the power flow around bar 18, where it can be seen that the differences between the cases are minimal. However, it is essential to highlight that these differences become more relevant during the normalization process, which is carried out using the CRITIC method selected for this study. At first glance, the differences between the cases may seem insignificant. However, applying the CRITIC method’s normalization process will reveal more significant differences, allowing for a more accurate and objective evaluation of the cases. This figure shows the differences in powers around bar 18 for the scenarios analyzed.

Similarly, Figure 5 illustrates the reactive power flow obtained through the line shown in Figure 4. In this graphical representation, it can be seen again that there are minimal changes or fluctuations between each one of the cases studied. It is essential to highlight that to analyze the results more precisely, the values must be normalized. This will allow for a better comparison and evaluation of the cases regarding reactive power flow.

Figure 5 shows how the system’s reactive power flow is distributed throughout each evaluated case. Although the differences may seem subtle at first glance, applying normalization will make it possible to more accurately identify the cases that present a better performance in terms of power flow. This graphic representation is a valuable tool for understanding the behavior of the reactive power flow in each case and supporting the analysis and conclusions presented in the study. In addition, it provides a visual perspective that facilitates the interpretation of the results and making informed decisions.

On the other hand, Figure 6 presents the scores obtained for each case after applying the CRITIC method, from which the results above have been extracted. Each case has been evaluated considering multiple criteria and the weights assigned to each of them. The CRITIC method has made it possible to conduct an exhaustive and weighted evaluation of the different design alternatives, providing a numerical rating that reflects the relative performance of each case.

Figure 7 allows you to identify the differences in scores between the different cases quickly. It is possible to observe significant variations in the ratings, indicating that some instances perform significantly better than others in terms of the criteria considered. This visual representation is valuable for intuitively understanding and comparing scores for each case, making it easier to identify standout cases and make informed decisions. In addition, Figure 7 provides a visual reference to support the results and conclusions presented in the analysis of the evaluated cases.

Figure 7 illustrates the method’s sensitivity by allowing for a detailed analysis of similar cases, such as cases 209 and 210. Although the difference in the weighted sum is minimal, it is significant enough to select the alternative that presents the least as the winner. The Weighted sum among the 210 configuration options was evaluated. This finding highlights the ability of the method to detect even slight variations in the results and use them as criteria for selecting the best alternative. Although cases 209 and 210 may seem very similar in many respects, the method identifies the crucial difference in the weighted sum, ultimately determining the winning alternative’s choice. This meticulous and sensitive approach to the technique ensures that the best possible decision is made by considering multiple criteria and evaluating all configuration alternatives. In this case, the selected option stands out for having the lowest weighted sum, implying a better overall performance than the other alternatives considered.

A significant difference in the profiles can be seen when comparing the bus voltages between cases 209 and 210 (Figure 8). Case 210 exhibits a remarkably better voltage profile than case 209, which is the closest in rating. This difference in voltage profiles between the two cases highlights the importance of adequately selecting conductors in a distribution system.

These results emphasize the relevance of choosing the best conductor alternative to guarantee an optimum and stable voltage profile in the distribution system. Case 210 is the most favorable option since it offers better performance regarding voltage profiles, which is essential to ensure a reliable and quality electrical supply to the users connected to the system.

Regarding the analysis of the active power losses, variations are observed in the evaluated cases, particularly between case 190 and case 210. It can be noted that the active power losses fluctuate, presenting increases and decreases in relation to the previous cases. However, when considering the performance in terms of losses, case 210 stands out as the clear winner by exhibiting the minimum possible value. This is reflected in Figure 9, where the downward trend of losses is visualized as we move toward case 210. This implies greater efficiency in the energy distribution system and reduced costs associated with energy losses. These findings support the choice of case 210 as the best alternative in terms of minimizing active power losses.

Significant differences are evident between the cases considered when analyzing the reactive power absorbed in each study scenario. However, once again, case 210 stands out by obtaining the minimum value in this metric, as seen in Figure 10. These results indicate that case 210 minimizes reactive power losses effectively compared to the other cases evaluated. This information is relevant for decision making since it seeks to optimize efficiency and reduce losses in the energy distribution system.

Like what was previously reviewed, it is essential to highlight that when analyzing the average voltage deviation about its unit value in all the cases considered, it is observed that case 210 exhibits the lowest voltage deviation. This can be seen in Figure 11, where the comparison of the different cases and their respective voltage deviation is shown graphically. These results support the selection of case 210 as an outstanding option regarding the voltage profile in the analyzed system.

When analyzing cases 147, 168, 189, and 210, which are visually the ones that could have the slightest deviation, it can be observed, as shown in Figure 12, that they are different.

The information presented above is summarized in

Table 1. Analysis of the results of the criteria for the design alternatives that showed better values in the study of weighted sums. Case of 33 bars.

Calculated Scenario	Voltage Deviation (kV)	Active Losses (kW)	Reactive Losses (kVA)	Cost
147	0.0314	3.2375	14.7975	637
168	0.0313	3.2242	14.7208	638
189	0.0307	2.9701	14.7190	639
210	0.0305	2.9603	14.6563	640

, where cases 147, 168, 189, and 210 are shown, corresponding to the best results obtained when modifying a network segment. However, when considering the economic aspect, it is observed that case 210 is the most expensive in terms of implementation, surpassing case 189 in one unit.

To validate the proposed methodology, a test of the algorithm is carried out in another radial system of 13 bars. This new calculation uses the same cabling alternatives, with eight sections of the larger gauge cable and four sections of the smaller gauge cable. The results of this test are presented in

Table 2. Analysis of the results of the criteria for the design alternatives that showed better values in the study of weighted sums. Case of 13 bars.

Calculated Scenario	Voltage Deviation (kV)	Active Losses (kW)	Reactive Losses (kVA)	Cost
190	0.0183	0.9261	2.0622	10.000
198	0.0157	0.5771	1.9485	78.5714
210	0.0120	0.2429	1.6564	181.42

, where it is observed that, once again, case 210 shows the best performance in terms of voltage and losses. It should be noted that this case also offers an advantage in terms of price difference compared to the previous case, considering that it is a more minor system than the one previously studied.

In addition, the voltage profile obtained in the 13-bar system is presented, where the radial topology indicates that each bar is after the previous one, which implies that the voltage drop should be more significant in the more distant bars. This phenomenon can be seen in Figure 13.

It is important to note that the 13-bar system, compared to what was seen in the 34-bar system, only considers 39 selection criteria, which shows that the method can perform under different conditions in different designs, obtaining results in approximately 9.5 s.

The voltage deviation resulting from three different cases, including the winning case, can be seen in Figure 14.

4. Conclusions

The CRITIC method can match the values analysis even though different criteria are compared at the level of units and parameters. Thus, other criteria, both technical and economic, can be placed in the same analysis.

This document offers a different and broader perspective compared to similar documents since it proposes the analysis with different types of drivers, which provides more versatility to the method and guarantees an optimal solution. Most studies on this subject consider a single section for the entire primary, which may need to be more optimal and necessary.

Even though the current study analyzes more than 200 cases and contemplates nearly 100 criteria, it develops quickly since it is based on mathematical and statistical parameters for its operation. However, as it is a planning and design problem, the consumption of machine time does not represent a significant variable in the analysis of the performance of the proposed method.

Conducting a deep analysis of costs with accurate information is recommended since the present method contemplates only a penalty for using high calibers but not an economic analysis of current resources. However, for the optimization study, the cost variable is correctly represented.

The winning alternative achieved is defined by scenario (case) number 210. In this scenario, the minimum values of voltage deviation, losses, and costs were found together. In this scenario, the best results were obtained at a technical level, achieving the best performance of the study electrical network. From this winning alternative, it can be concluded that the highest cost of the evaluated options is presented in this scenario. However, the achievements in improving quality and efficiency validate the alternative as optimal in a multi-criteria manner.

It is worth noting that the weights defined by the CRITIC method can be manipulated based on the user’s interest. For example, the weighting for the cost variable could be increased, and the winning alternative would be another.