Multicriteria analysis for optimal reconfiguration of a distribution network in case of failures

Abstract

This work presents a methodology for the optimal reconfiguration of a distribution network in the presence of a failure, through a multicriteria optimization algorithm. For this purpose, the optimal network reconfiguration alternative is verified in the IEEE 33 bus test system and 123 bus test system. The variables analyzed within the multicriteria decision matrix include the total interruption time per nominal kVA installed (TITK), mean frequency of interruption per nominal kVA installed (MFIK), reset time for reconfiguration, energy not supplied, total losses in the lines of the system and operation and maintenance costs. The result enables selecting the best scenario based on analyzing every decision criterion; the multicriteria decision algorithm is developed in the Matlab environment. Subsequently, the winning reconfiguration alternatives are validated through simulations in Cymdist for different failure scenarios. In the analysis of results, metrics are presented that enable us to observe a significant improvement in the typical problems that occur in an electric system.

1. Introduction

Electric distribution companies are responsible for supplying electric power to their residential, commercial, and industrial customers in a continuous manner, under the control of the corresponding regulation entities. Consequently, researchers have been forced to understand the different problems that appear in electric distribution networks due to the interruption of the electric service, with the purpose of making technological developments and innovations towards a smart distribution network that enables to increase in the reliability of the electric service through the estimation of quality indices of the electric supply such as SAIDI, SAIFI, AIT, ASAI, ENS, etc. [1]. Many research works about proposals for network reconfiguration are focused on reduced objectives and mathematical constraints that offer an acceptable solution. However, it is not considered the analysis of the variables that may cause conflict in the system for achieving the objective pursued. Many case studies are carried out in test distribution systems that are mainly validated in operating scenarios of maximum demand, many of which have balanced loads and do not consider data of other variables. This work analyzes a group of variables for making a decision about the reconfiguration of a network, using multiple criteria that have an influence on the reliability and quality of the electric service [2].

This work proposes an alternative for optimal reconfiguration of the distribution network that minimizes all decision criteria, whose objective is to analyze all network reconfigurations in the occurrence of a failure with the purpose of reducing the de-energized zones while maintaining maximum system reliability, through the operation of switching devices either remotely or automatically, for isolating the failure zone and thus search for an energizing path either from the same feeder or from other feeders. Various authors conclude that the reconfiguration analysis should be based on radial network topology and that such network should be operated automatically or manually to reduce the load points due to the occurrence of failures, minimization of losses, sustained interruptions, reduce the energy not supplied, reliability improvement, incorporation of distributed generation and its impact on the operation of protection devices, among others [[3], [4], [5], [6], [7], [8]]. The variables are identified through simulations in Cymdist utilizing power flows and a reliability evaluation in which it is considered global parameters of reliability of devices [9], times of operation, inspection, and momentaneous interruption considering all possible reconfigurations concerning the operation of tripping and switching devices. With the construction of the matrix of results, an algorithm is developed in Matlab in which each variable is weighted to reach a minimization criterion in which each reconfiguration (matrix columns) will have a unique solution.

This work is organized as follows. Section 2 presents the reconfiguration of distribution networks, its problems, and solution strategies. Section 3 presents the methodology statement. Section 4 presents the test system under analysis with its different scenarios of failure occurrence. Section 5 presents the analysis of results and, finally, section 6 describes the conclusions obtained from the research work.

2. Reconfiguration of the distribution network

2.1. Problem statement

Normally, a reconfiguration of the distribution network leads to a general model that may be solved using different optimization algorithms, guaranteeing convergence of the system under analysis. According to a new topology, it is solved an optimization problem that guarantees minimization of the accumulated cost of dispatched operation and load reduction through linear programming, as it is in the case studies of the IEEE systems [4], which consider the worst operation scenarios in the presence of failures in the feeders. An automatic reconfiguration is proposed in Ref. [10], in which the network is remotely divided into three smaller subnetworks with the purpose of increasing the reliability of the distribution system, thus decreasing the problems associated with failures due to de-energizing. Similarly, researchers evaluate real transient phenomena with the aim of contributing a complex analysis of the series of events that lead to failures of this equipment; in this case, it is sought to raise awareness about the use of modern software for transient analysis (similar to EMTP), where the reconfiguration enables reconstructing the transient events measured in a real distribution network [11,12].

A mathematical model is presented in Ref. [13] to obtain a decentralized optimization with the purpose of maximizing the benefit of independent systems; the algorithm coordinates the independent systems and identifies the optimal operating point. An optimal reconfiguration of the network is stated in Ref. [14] through an exploration of the topology structure and considerations of voltage regulators (VR, SVC, DSTATCOM). On the other hand [15], consider limitations with reconfiguration times, whereas [16] focus their problem on the diagnosis of failures for an automatic energy restoration through a framework of multiple agents, for which they consider an open ring distribution system due to the performance required by a protection scheme. For this reason, the protection coordination should be jointly analyzed for restoration through optimization algorithms, also addressing the problems associated with failures in the communications and physical malfunction of these devices.

2.2. Solution strategies and methodologies

To decide on the optimal reconfiguration of the distribution network, some strategies and methodologies employed by different authors are described; in turn, these remain hot research fields for new and future implementations. In Ref. [5] it is presented a discussion about automatic reconfiguration to reduce the load points in the presence of a failure, and thus improve the reliability of the system; this analysis is carried out based on a cost–benefit study. Using a method with binary descriptor matrices [17], calculate reliability indices that enable to contribute to collective, systematic, and effective modeling in relation to failure times, including the operation of distributed generation in island mode; the stated technique becomes efficient in planning and optimization of distribution networks, provided that constraints that imply thermal and voltage limits are fulfilled. An alternative to isolating the failure as soon as possible with the purpose of restoring the service is to identify hierarchical zones for centralized and decentralized consideration, as described in Ref. [18]. In Ref. [19], an artificial neural network model is used to forecast reliability considering failures in the distribution network.

In [6], the reconfiguration of the network implies a consideration to improve power losses in sub-transmission systems, improve voltage profiles and increase reliability. Its main restriction is due to the radial topology, where the variables should be within their allowable limits to enable this technology to be applied in real systems. This consideration may be complemented by taking into account the load curves for the different types of consumers, with the purpose of determining a reconfiguration according to the day and distinguishing a minimization of the energy not supplied [7]. Metaheuristic algorithms are employed in Ref. [3], and an evaluation by means of optimization methods showed that the Firefly Algorithm (FA) is better than evolutionary programming (EP). A fuzzy multicriteria decision algorithm is developed in Ref. [6], in which the Bellman-Zadeh method is used for a methodology that promotes final solutions to the objective space. This is different than [7], which considers a solution with a Genetic Algorithm (GA) to find configurable optimal solutions, and [20], which presents a reconfiguration to minimize losses using mixed-integer programming. Limitations in current flows and operation capacity are introduced in Ref. [1], so the model proposed is focused on the consideration of the protection devices to maintain a selectivity of protections, using an AMPL mathematical programming and solving problems with a CLPEX optimization in which it is of vital importance to define operating limits through protection devices under considerations of a network reconfiguration.

A stochastic methodology is proposed in Ref. [21] to model the effect of the PHEVs in the changes in network topology, which is solved with a modified K rill Herd optimization algorithm (SAMKHOA), in order to improve the performance of the KHOA algorithm. On the other hand [22], focus on load restoration using a discrete multiobjective optimization (PD-NSGA-II), which emphasizes on improving the efficiency of a solution whose further evaluation enables to conclude that the algorithm is constant for a reconfiguration of the network of real systems. Moreover [23], focus on an multiobjective optimization using the epsilon constraint method (EPC) to recognize an optimal reconfiguration through mathematical models. Authors in Ref. [24] focus on a deep reinforcement learning where the distribution network is modified by the flow when the re liability of the system is affected; this algorithm exhibits scalability and deals with the constraints due to distributed generation. This is similar to Ref. [25], whose aim is to use the network reconfiguration to mitigate the considerations of distributed generation due to the high penetration impact, and at the same time solve the problems associated to electronic devices such as Open Point (SOP). The reconfiguration of the network is carried out through ant colony optimization, and the SOP outputs through the Taxi-cab algorithm [26], where it is proposed a restoration using graph theory and the expansion tree search algorithm to restore to the maximum extent the critical loads using micro-networks. This work performs a simulation in a system with 1069 buses and proposes approaches to improve resiliency considering unique and multiple failures [[27], [28], [29]].

3. Methodology

This section describes the multicriteria decision algorithm employed for the optimal reconfiguration of the distribution system in the presence of failures. The multicriteria optimization is applied to the solutions obtained for each of the variables under analysis for the system being considered. The reconfiguration of distribution systems has been analyzed as an optimization problem with different methodologies that attempt to minimize or maximize a specific variable. The reconfiguration optimization problems in electric distribution systems have been mainly analyzed as a single objective problem, that searches for an “optimal” solution with a unique criterion for minimization of the energy not supplied or minimize losses in the system. However, in this problem there are multiple variables involved in the decision criteria to really propose a good general solution for reliability indices. The search for a solution focused on the improvement of a single variable might yield results with conflicts between the solution variables in the power flows [30].

Therefore, it is important to identify a unique solution that involves minimizing decision criteria such as the total interruption time per nominal kVA installed (TITK), mean frequency of interruption per nominal kVA installed (MFIK), reset time, energy not supplied, total losses in the lines of the system and operation and maintenance costs. A comparative analogical methodology is used for fulfilling the objectives, to obtain an optimal model under a multicriteria technique based on a decision theory.

The multicriteria decision algorithm makes reference to the analysis of a set of n decision variables in a distribution system with a set of objective functions with decision weight, and a set of constraints. The multicriteria optimization technique is applied to the set of solutions obtained for each analysis variable as optimal reconfigurations of the distribution system obtained in each scenario considered, based on the theory of decision makers. The algorithm assigns a particular reconfiguration in one of the scenarios that are candidates for the analysis [30].

To be able to obtain an optimal reconfiguration result, it is first necessary to establish the decision matrix (1) [30,31], where the n columns of this decision matrix represent the reconfiguration alternatives with their corresponding switching devices, and the m rows represent the decision criteria which are the variables under analysis that enable selecting the optimal reconfiguration option.

(1)

The winning solution for an optimal reconfiguration of the distribution network is obtained by developing a matrix constituted by the section where the failure occurs, in which it is considered the set of all possible reconfigurations that vary according to the section in which the failure will occur and the possible available transfers.

First, the criteria to be evaluated are defined, which for this case, are reliability indicators such as MFIK, TITK, and ENS, as well as reset time, active power losses, and operation costs. The solution space is defined considering all switching and protection devices as possible candidates for a transfer, also considering as constraints the analysis of the level of fulfillment of the electric variables that may cause a collapse in the distribution system, thus obtaining the decision matrix.

To determine the winning alternative in a re-configuration, the decision matrix should be normalized. Different statistical normalization methods are available for this purpose. In this case, it has been considered to carry out the normalization by means of ranges (minimum and maximum values) as indicated in (2) [30,31]:

$$X_{iNorm}=\frac{X_i-X_{\mathit{min}}}{X_{\mathit{max}}-X_{\mathit{min}}}$$ (2)

The critic method is used to determine the winning reconfiguration from the decision matrix, through weighting of the criteria. This is based on the normalized weighted sums of each of the criteria per available reconfiguration. The critic method presented in (3) defines the valuation with the purpose of establishing weights to each of the variables defined as decision criteria as [30,31]:

$$W_i=S_i\sum \left(1-r_{ij}\right)$$ (3)

where:

$W_i$ is the weight of criterion i.

$S_i$ is the standard deviation of the reconfigurations data to criterion i.

$r_{ij}$ is the correlation coefficient between row i and column j.

Finally, the decision vector results from the weighted sum of each of the reconfiguration alternatives, obtained as the total sum of the products of the result of each criterion times its corresponding weighting (4). Since all criteria are variables to be minimized, the winning alternative will be chosen as the one that results with the minimum value in the vector of the resulting weighted sum; this calculation is performed as [30,31]:

$${Pond}_i=\sum _{i=1}^m\sum _{j=1}^n{W}_i{X}_{ij}$$ (4)

Fig. 1 shows the multicriteria decision algorithm employed in the case studies under analysis; in order to apply this algorithm, the decision matrix should be constructed with the corresponding criteria being considered and the n possible reconfiguration alternatives, so that their evaluation enables to establish an optimal solution for a reconfiguration of the distribution system in the occurrence of a failure. The data of the decision matrix are processed in Matlab through the multicriteria algorithm, in which a resulting vector is obtained with the optimal reconfiguration that minimizes all decision criteria.

Fig. 1.

Multicriteria algorithm.

4. Test system with 33 buses

An analysis of the different zones in failure has been carried out in this work. Each section under analysis enables us to find the optimal result for reconfiguring the network. The test system corresponds to the IEEE 33 bus model, which is generally used to evaluate reconfiguration problems of the distribution system. This is a system of 12.66 kV constituted by 33 buses, 32 lines, and 5 link points; the system data have been obtained from Refs. [9,26]. In the initial topology of the system, lines 33, 34, 35, 36, and 37 are disconnected employing the switching equipment that has been incorporated.

Fig. 2 shows the one-line diagram of the test system, showing the 33 buses and the protection and switching devices incorporated with the help of the Cymdist software for the corresponding location of the devices. These devices are configured with their associated operation mode, either automated or remotely operated, with a switching time defined as 1 min for the automated devices and 3 min for the remotely operated devices. Similarly, Fig. 2 shows the sections in which possible failures may occur, and likewise the scenarios in which there will be no option for a reconfiguration will be indicated in the analysis of results.

Fig. 2.

Test system with 33 buses.

Table 1 shows the switching and protection devices incorporated in the test system, identifying the type and operation mode configured.

Table 1.

Switching and protection devices.

Device	Type	Operation Mode
R1	Protection	Remotely operated
R2	Protection	Automated
R3	Protection	Automated
R5	Protection	Automated
R6	Protection	Remotely operated
R8	Protection	Remotely operated
R11	Protection	Remotely operated
R14	Protection	Remotely operated
R16	Protection	Remotely operated
R17	Protection	Automated
R18	Protection	Remotely operated
R19	Protection	Remotely operated
R22	Protection	Automated
R25	Protection	Remotely operated
R28	Protection	Remotely operated
R30	Protection	Remotely operated
R33	Switching	Automated
R34	Switching	Remotely operated
R35	Switching	Remotely operated
R36	Switching	Remotely operated
R37	Switching	Remotely operated

Once the operation mode of the switching and protection devices has been identified, the parameters of the 33-bus test system that are shown in Table 2 are entered, with the purpose of obtaining the power flow solution. Similarly, the data required for a system reliability evaluation analysis, such as the failure rate, have been obtained from Ref. [9].

Table 2.

System parameters.

Line	N1	N2	R (pu)	X (pu)	Customers	P (kW)	Q (kVAr)
1	1	2	0.0058	0.0029	26	100	60
2	2	3	0.0308	0.0157	23	90	40
3	3	4	0.0228	0.0116	31	120	80
4	4	5	0.0238	0.0121	16	60	30
5	5	6	0.0511	0.0441	16	60	20
6	6	7	0.0117	0.0386	52	200	100
7	7	8	0.0444	0.0147	52	200	100
8	8	9	0.064	0.0462	15	60	20
9	9	10	0.0651	0.0462	15	60	20
10	10	11	0.0123	0.0041	12	45	30
11	11	12	0.0234	0.0077	16	60	35
12	12	13	0.0916	0.0721	16	60	35
13	13	14	0.0338	0.0445	31	120	80
14	14	15	0.0369	0.0328	16	60	10
15	15	16	0.0466	0.0340	16	60	10
16	16	17	0.0804	0.1074	16	60	20
17	17	18	0.0457	0.0358	23	60	20
18	2	19	0.0102	0.0098	23	90	40
19	19	20	0.0939	0.0846	23	90	40
20	20	21	0.0255	0.0298	23	90	40
21	21	22	0.0442	0.0585	23	90	40
22	3	23	0.0282	0.0192	23	90	50
23	23	24	0.0560	0.0442	109	420	200
24	24	25	0.0559	0.0437	109	420	200
25	6	26	0.0127	0.0065	16	60	25
26	26	27	0.0177	0.0090	16	60	25
27	27	28	0.0661	0.0583	16	60	25
28	28	29	0.0502	0.0437	31	120	70
29	29	30	0.0317	0.0161	25	200	600
30	30	31	0.0608	0.0601	39	150	70
31	31	32	0.0194	0.0226	35	210	100
32	32	33	0.0213	0.0331	16	60	40
33	8	21	0.1248	0.1248	33	–	–
34	9	15	0.1248	0.1248	33	–	–
35	12	22	0.1248	0.1248	33	–	–
36	18	33	0.0312	0.0312	33	–	–
37	25	29	0.0312	0.0312	33	–	–

The parameters that have been entered enable obtaining a power flow solution in normal operating conditions of the system, in which its electric variables are not affected, and its minimum value of voltage occurs in nodes 17 and 18, with a value of 0.914 p.u. Table 3 presents the power flow solution obtained under the initial operating conditions, showing the powers and the magnitude and angle of the voltages in the buses.

Table 3.

Load flow solution.

Node	V (pu)	Pg (kW)	Qg (kVAr)
1	1	3912	2371
2	0.997	3800	2305
3	0.983	3298	2078
4	0.976	2219	1531
5	0.968	2141	1492
6	0.95	2044	1440
7	0.947	893	422
8	0.942	688	320
9	0.936	624	297
10	0.93	561	274
11	0.929	515	244
12	0.928	454	209
13	0.921	392	172
14	0.919	271	91
15	0.918	211	81
16	0.916	150	60
17	0.914	90	40
18	0.914	0	0
19	0.997	271	121
20	0.993	180	80
21	0.992	90	40
22	0.992	0	0
23	0.979	846	405
24	0.973	421	201
25	0.969	0	0
26	0.948	886	886
27	0.946	823	859
28	0.935	753	830
29	0.927	626	814
30	0.923	422	212
31	0.919	270	140
32	0.918	60	40
33	0.918	0	0

5. Analysis of results

5.1. Evaluation of the multicriteria algorithm

For the IEEE 33 bus test system, each of the sections in Fig. 1 in which a failure may occur is analyzed, with the purpose of determining the winning alternative for an optimal reconfiguration of the distribution network.

Fig. 3 indicate the normalized unit performances of the variables (criteria) for each of the reconfiguration alternatives, according to the section where the failure is located, through a normalized matrix. In these failure scenarios, it may be observed that the behavior of each decision variable differs significantly, according to the reconfiguration in which they are. On the other hand, Fig. 4 indicate the results of the vector of weighted sums, which enables to visualize the winning reconfiguration alternative. The results are presented below.

Fig. 3.

Normalized criteria for the reconfiguration scenarios in the case of a failure in sections C, D, F, G, H, I, J, K, L, N, O.

Fig. 4.

Weighted sums for each reconfiguration scenario for a failure in sections C, D, F, G, H, I, J, K, L, N, O.

5.1.1. Failure in section A

For this scenario, no reconfiguration alternative is available because the failure occurs at the substation, and in this case, no other source is available for its reconfiguration.

5.1.2. Failure in section B

For this scenario, the failure is cleared by the operation of R1. Still, there is no reconfiguration alternative available because there is no link point with the source without the reconfiguration causing the failure transfer.

5.1.3. Failure in section C

For this scenario, the failure is cleared by the operation of R2, and the failure is isolated with the operation of R3 and R22. Under this context, there are 16 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to the alternative one, which is defined with the closure of R33 and R37 once the failure zone has been isolated.

5.1.4. Failure in section D

For this scenario, the failure is cleared by the operation of R18, and the failure is isolated with the operation of R19; in this context, there are 2 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario one, which is defined with the closure of device R33 once the failure zone has been isolated.

5.1.5. Failure in section E

For this scenario, the failure is cleared by the operation of R19, and there is no reconfiguration alternative.

5.1.6. Failure in section F

For this scenario, the failure is cleared by the operation of R3, and the failure zone is isolated with the operation of R5; in this context, there are 38 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario three, which is defined with the closure of device R37 once the failure zone has been isolated.

5.1.7. Failure in section G

For this scenario, the failure is cleared by the operation of R5, and the failure zone is isolated through the operation of R6 and R25; in this context, there are 15 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario one, which is defined with the closure of devices R33 and R37 once the failure zone has been isolated.

5.1.8. Failure in section H

For this scenario, the failure is cleared by the operation of R6, and the failure zone is isolated with the operation of R8; in this context, there are 12 reconfiguration alternatives.

5.1.9. Failure in section I

For this scenario, the failure is cleared by the operation of R8, and the failure zone is isolated with the operation of R11; in this context, there are 10 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario one, which is defined with the closure of device R35 once the failure zone has been isolated.

5.1.10. Failure in section J

For this scenario, the failure is cleared by the operation of R11, and the failure zone is isolated with the operation of R14; in this context, there are 10 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario one, which is defined with the closure of device R36 once the failure zone has been isolated.

5.1.11. Failure in section K

For this scenario, the failure is cleared by the operation of R14, and the failure zone is isolated with the operation of R16; in this context there are 10 reconfiguration alternatives.

5.1.12. Failure in section L

For this scenario the failure is cleared by the operation of R16, and the failure zone is isolated with the operation of R17. In this context there are 10 reconfiguration alternatives.

5.1.13. Failure in section M

For this scenario, the failure is cleared by the operation of R17; however, in this scenario, there is no reconfiguration alternative available.

5.1.14. Failure in section N

For this scenario the failure is cleared by the operation of R25, and the failure zone is isolated with the operation of R28. In this context, there are 8 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario two, which is defined with the closure of device R37 once the failure zone has been isolated.

5.1.15. Failure in section O

For this scenario, the failure is cleared by the operation of R28, and the failure zone is isolated with the operation of R30. In this context, there are 7 reconfiguration alternatives. In this case, the winning reconfiguration corresponds to scenario one, which is defined with the closure of device R36 once the failure zone has been isolated.

Table 4 presents a summary of the winning reconfiguration alternatives according to the section where the failure occurs, with its corresponding normalized value of the vector of weighted sum, and the closing maneuver of the protection devices that should be operated to carry out the reconfiguration.

Table 4.

Summary of reconfiguration alternatives.

Section with failure	Winning Alternative	Value	Maneuver
Failure C	Alternative 1	0.083033	33 and 37
Failure D	Alternative 1	0	33
Failure F	Alternative 3	0.2061	37
Failure G	Alternative 1	0.020633	33 and 37
Failure H	Alternative 1	0	35
Failure I	Alternative 1	0	35
Failure J	Alternative 1	0.1268	36
Failure K	Alternative 1	0.1211	36
Failure L	Alternative 1	0.1165	36
Failure N	Alternative 2	0	37
Failure O	Alternative 1	0.1552	36

5.2. Analysis of results in the presence of reconfigurations

Once the algorithm has chosen the winning alternative of network reconfiguration in the occurrence of a failure, this alternative is verified with power flow simulations and reliability analysis, obtaining a minimization of all the criteria under consideration. The results obtained are presented below.

5.2.1. Mean frequency of interruption per kVA

Fig. 5 shows the result obtained regarding the mean frequency of interruption (FMIK) of each of the winning reconfiguration alternatives. In this figure it is possible to visualize that the reliability indicator is minimized, with the failure in section D being slightly larger after the reconfiguration; this increment is negligible because it occurs with the purpose of not altering the remaining variables of the system.

Fig. 5.

MFIK reliability index in the failure and reconfigured cases.

5.2.2. Total interruption time per kVA

Fig. 6 presents the result obtained regarding the total interruption time (TITK) of each of the winning reconfiguration alternatives. In this figure, it is possible to visualize that this indicator is minimized in the sections where a failure has occurred. Similar to Fig. 5, the failure in section D is slightly larger after the reconfiguration with the purpose of not altering the remaining variables of the system.

Fig. 6.

TTIK reliability index in the failure and reconfigured cases.

5.2.3. Energy not supplied

Fig. 7 presents the result corresponding to the energy not supplied (ENS) of the winning reconfiguration alternatives. It may be observed that, after the reconfiguration, this indicator is minimized in all sections with failures that are under analysis, without alterations in the remaining variables of the system.

Fig. 7.

Energy not supplied in the failure and reconfigured cases.

5.2.4. Voltage profile

The voltage profiles are verified in this test system to validate that the reliability of the system is maintained, and that there are no voltage drops smaller than the ones that occurred under normal operating conditions, as shown in Fig. 8.

Fig. 8.

Voltage profile in the failure and reconfigured cases.

6. Test system with 123 buses

IEEE Node Test Feeder operates at a nominal voltage of 4.16 kV. This circuit is characterized by overhead and underground lines, unbalanced loading with constant current, impedance, and power, four voltage regulators, shunt capacitor banks, and multiple switches [32].

In this system, maneuver and protection devices were added to identify the sections in failure, having 6 sections in which a fault can occur. In this case of analysis, section B has been chosen with all the reconfiguration alternatives, in Fig. 9, the test system is presented with the identification of its possible sections in failure.

Fig. 9.

Test system with 123 buses.

6.1. Evaluation of the multicriteria algorithm

For the IEEE 123 bus test system, section B in Fig. 9 in which a failure may occur is analyzed, with the purpose of determining the winning alternative for an optimal reconfiguration of the distribution network.

Fig. 10 indicate the normalized unit performances of the variables (criteria) for the reconfiguration alternatives, according to section B where the failure occurs, by means of a normalized matrix. In this failure scenario, it may be observed that the behavior of each decision variable differs significantly, according to the reconfiguration in which they are. On the other hand, Fig. 11 indicate the results of the vector of weighted sums, which enables to visualization of the winning reconfiguration alternative. The results are presented below.

Fig. 10.

Normalized criteria for the reconfiguration scenarios in the case of a failure in section B.

Fig. 11.

Weighted sums for each reconfiguration scenario for a failure in section B.

6.1.1. Failure in section B

For this scenario the failure is cleared by the operation of R2, and the failure zone is isolated with the operation of R6; in this context there are 13 reconfiguration alternatives.

In this case, the winning reconfiguration corresponds to scenario five, which is defined with the closure of device R11 once the failure zone has been isolated.

6.2. Analysis of results in the presence of reconfigurations

Once the algorithm has chosen the winning alternative of network reconfiguration in the occurrence of a failure, this alternative is verified with power flow simulations and reliability analysis, obtaining a minimization of all the criteria under consideration. The results obtained are presented below.

6.2.1. Mean frequency of interruption per kVA

Fig. 12 shows the result obtained regarding the mean frequency of interruption (FMIK) of two of the winning reconfiguration alternatives. In this figure, it is possible to visualize that the reliability indicator is minimized.

Fig. 12.

MFIK reliability index in the failure and reconfigured cases.

6.2.2. Total interruption per kVA

Fig. 13 presents the result obtained regarding the total interruption time (TITK) of two winning reconfiguration alternatives. In this figure, it is possible to visualize that this indicator is minimized in the section where a failure has occurred.

Fig. 13.

TTIK reliability index in the failure and reconfigured cases.

6.2.3. Energy not supplied

Fig. 14 presents the result corresponding to the energy not supplied (ENS) of the two winning reconfiguration alternatives. It may be observed that, after the reconfiguration, this indicator is minimized in all sections with failures that are under analysis, without alterations in the remaining variables of the system.

Fig. 14.

Energy not supplied in the failure and reconfigured cases.

6.2.4. Voltage profile

The voltage profiles are verified in this test system to validate that the system's reliability is maintained, and that there are no voltage drops smaller than the ones that occurred under normal operating conditions, as shown in Fig. 15.

Fig. 15.

Voltage profile in the failure and reconfigured cases.

The proposed methodology has many advantages over approximate or heuristic algorithms since these seek solutions close to the optimum with a lower computational cost, but without guaranteeing optimality. The main limitation of the proposed methodology is time and computational capacity, since depending on the size of the case study and the criteria (objectives) to be considered, it is possible that the search for the optimal solution takes more or less computational time. However, the multi-criteria algorithm with the exploration of all feasible scenarios guarantees to find the optimal solution. Moreover, this algorithm is very flexible and allows mathematical manipulation of the criteria through weightings that can be mathematically assigned by the standard deviation of the particular results of each scenario or by human intervention according to specific interests. The computational time limitation that increases with the size of the case study and the number of criteria may not be very important if this algorithm is applied to decision-making problems for planning and not for dynamic analysis or requiring real-time solutions [30].

It is important to emphasize, due to a large number of alternatives in the IEE 123 system for making a decision, it is not practical to make a comparison of all the alternatives for the evaluation, since the model would be too heavy and would lose practicality. However, analyzed test systems are practical and provide the minimization of the criteria considered. The approach of the multicriteria algorithm aims to obtain efficient solutions even within the programming, which consists of obtaining the set of feasible and efficient solutions, without affecting its analysis in the restrictions and weightings for the robustness of the analyzed system.

7. Conclusions

A multicriteria decision algorithm was presented to determine the best alternative for reconfiguring the system in the presence of a failure, considering reliability indices, power active losses in the system, operation costs, and reset times.

In this work, the possible reconfiguration options are determined through the decision matrix, which varies according to the scenario in which the failure occurs. This algorithm enables the determination of the reconfiguration solution that minimizes all the criteria that were analyzed after they have been normalized and weighted.

The algorithm's performance was validated with the winning reconfiguration alternatives according to the failure scenario, through an individual comparison.

Based on the proposed methodology, it may be assured that the solution of the winning reconfiguration alternative guarantees the minimization of the criteria under consideration, without altering the remaining operating variables of the system.

It is stated that the optimal reconfiguration of the distribution network in the presence of failures, using the multi-criteria decision algorithm, impacts directly on the criteria analyzed, as opposed to other studies carried out that have formulated the reconfiguration of the distribution network using a unique objective function to be minimized, which implies the alteration of the remaining variables, affecting the power quality of the system. As a complement to this study, voltage profiles are presented in each of the nodes which it is guaranteed the reliability of the system with a reconfiguration of the network in the presence of a failure.

The Multicriteria algorithm attempts to determine an efficient solution, closest to the ideal solution; that is, that hypothetical solution that would allow the best result to be obtained for each criterion. According to this principle, it is considered that a problem with multiple criteria is 90% efficient since no other possible optimal solution is found that provides an improvement in one criterion without producing a worsening in at least one other criterion, this is in relation to multi-objective algorithms or heuristic methods.

Author contribution statement

Edison Guanochanga, Alexander Aguila Téllez: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Leony Ortiz: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

Data included in article/supp. material/referenced in article.

Declaration of interest's statement

The authors declare no conflict of interest.