Optimal Operational Reliability and Reconﬁguration of Electrical Distribution Network Based on Jellyﬁsh Search Algorithm

: In this paper, the electricity network automation based on Power Network Reconﬁguration (PNR) is implemented to improve the operational reliability of distribution systems using jellyﬁsh search algorithm. For this purpose, system average interruption frequency index (SAIFI), system average interruption unavailability index (SAIUI) and total energy not supplied (TENS) are critical measures. In this paper, a new optimization technique of jellyﬁsh search (JFS) algorithm is employed for distribution network reconﬁguration for reliability improvement. It is concerned with the moving patterns of jellyﬁsh. They are divided into three categories. The jellyﬁsh could ﬂow towards the ocean current or between its own swarm. Meanwhile, whenever the food supply is adequate, the jellyﬁshes are attracted to its location. It is formulated considering the three reliability indices of SAIFI, SAIUI and TENS, simultaneously in a multi-objective model based on the weight factors. The proposed methodology based on the JFS optimizer is implemented on an IEEE 33-node distribution network. According to the numerical results, the SAIFI, SAIUI and TENS is improved by 36.44%, 34.11% and 33.35%, compared to the initial condition. For comparison purposes, tuna swarm optimizer and tunicate swarm algorithm, besides the JFS algorithm, are implemented as well. The simulation results declare the signiﬁcant outperformance of the JFS algorithm compared to TUNA and TSA in terms of the obtained improvements and the regarding convergence properties.


Introduction
Power outages are irregular in developed countries; notwithstanding, they have severe consequences. A power system's reliability is characterized by two parameters: the frequency of outages and the duration of power outages [1]. A substantial amount of research has been conducted to reduce the frequency of power outages. However, more methods for reducing the duration of power outages by improving the distribution system performance must be identified [2,3]. Additionally, it is critical to employ distribution network reconfiguration to discover the optimum solutions according to the regulations and limits given by the operators in an attempt to provide a safe and economically optimal energy supply.
The Power Network Reconfiguration (PNR) is a method which helps mitigate the impacts of the power outages and enhance the reliability parameters in distribution networks [4]. In latest years, operational research has grown progressively in identifying the best PNR while considering a variety of objectives into care [5]. To reduce losses, the PNR issue was explored in [6] that used a harmony search method for radial balanced distribution networks. In [2], the PNR process was created by closing and opening switches using thermore, the numeric fitness function reveals the volume of food. The JFS was recently applied in effective manner for several engineering problems such as selective harmonic elimination in multilevel inverters [27], combined heat and power dispatching [28], maximum power point tracking (MPPT) of solar PV systems [29], design of a solar-powered thermoelectric air-conditioning system [30], control of superconducting magnetic energy storage system [31], PV parameter estimation [32], integration of renewable energy sources in power systems [33].
Hence, in this paper, the JFS algorithm is employed for distribution network reconfiguration for reliability improvement. In [14], the JFS algorithm was employed for addressing the PNR in the distribution networks considering the dispatching of distributed generation units and static Var compensators. The study in [14] was dedicated to the dynamic operation of distribution networks for the sake of minimizing the distribution losses and the emissions. On the other side, the operational reliability indices in distribution networks were not considered while its great importance of high impacts to guarantee the feeding continuity to consumers. In this paper, the JFS algorithm is formulated considering three reliability indices, simultaneously in a multi-objective model based on the weight factors. In this model, the system average interruption frequency index (SAIFI), the system average interruption unavailability index (SAIUI) and the total energy not supplied (TENS) are comprised. The proposed methodology based on the JFS optimizer is implemented on IEEE 33-node distribution network. According to the numerical results, the SAIFI, SAIUI and TENS is improved compared to the initial condition. For comparison purposes, Tuna swarm optimizer (TUNA) and tunicate swarm algorithm (TSA) besides the JFS algorithm are implemented as well. The simulation results declare the significant outperformance of the JFS algorithm compared to TUNA and TSA in terms of the obtained improvements and the regarding convergence properties

Distribution Network (DN) Reliability Indices
The reliability indices approved by Chilean law for a DN with multiple laterals and multi-feeding nodes are specified by the Inter-American Committee of Regional Electricity-CIER and are stated as follow [2]: U n = τ n × r n n =1, 2, . . . .., N n where SAIFI is the DN's average interruption frequency index, SAIUI is the DN's average interruption unavailability index, SAIDI is the DN's average interruption duration index and TENS is the total energy not supplied in the DN. ENSI n is the ENS related to each distribution node (n) to be not supplied. S n and P n are the apparent and active load demand of the DN at the distribution node (n) to be not supplied; N n is the number of DN nodes; τ n and r n are the failure rate and the repair time of each DN node (n). U n is the unavailability of each distribution node (n).

Problem Formulation
Based on the three reliability indices of SAIFI, SAIUI and TENS, the problem formulation of reliability improvement in DNs is formulated to solve a multi-objective optimization function (MOF) as follows: where, ω 1 , ω 2 and ω 3 are weighting factors to be specified by the DN operator according to their preference. In Equation (6), the parameters weighting factors are considered similar to each other and equivalent to (1/3) which represents the same priority for all indices. The superscript "max" indicates the maximum value to be specified.
The multi-objective model presented in Equation (6)  The open tie links must always be assigned an integer value that is limited by the total number of DN lines, as shown below: The voltage at all DN nodes must be bounded by the permissible bounds related to the distribution code as follows: where, V n is the voltage magnitude at each DN node (n); N n is the number of the DN nodes. The superscripts "min" and "max" refer to the minimum and maximum of each variable.
The current flow at all DN lines must be bounded by the permissible bounds related to the current capacity of each one as follows: |I br | ≤ I max br br = 1, 2, . . .. N br (10) where, I br is the current flow in the branch (br) which is limited by the regarding thermal capacity (I max ). The power balance constraints at each distribution node must be maintained as equality constraints which guarantee the convergence of the load flow as follows: where, P j and Q j are the real and reactive power at each DN node (j); V j and I j is the voltage magnitude and the current injected at each DN node (j). Furthermore, the DN's radial structure is kept in operating service, with a branch-bus incidence matrix generated as regards: This matrix has the dimensions of N n × N br . The DN configuration is radial in form if their determinant is −1 or 1, but the DN is not radial if the is zero [34].

JFS Optimizer
The JFS algorithm is a new optimization technique which is fascinated by the moving patterns of jellyfish. They are divided into three categories. To begin, the jellyfish could flow towards to the ocean current or between its own swarm. Meanwhile, whenever the food supply is adequate, the jellyfishes are attracted to their locations. Furthermore, the numeric fitness function reveals the volume of food [35,36]. The initial population could be arithmetically represented as follows [26]: where X i (t + 1) indicates the ith jellyfish chaotic counterpart, and P 0 is a randomized value within range [0, 1] and does not equal to {0.0, 0.25, 0.75, 0.5, 1.0}. The value of the time control function CF(t) is evaluated as described in Equation (14) which is changed from 0 to 1 over time [37]: where, t refers to the iteration number; T max is the maximum number of iterations; r 1 is a randomized value within range [0, 1]. If the CF value is greater than 0.5, the fresh place of each jellyfish could be developed, as shown in Equation (15) [26]: where µ symbolizes the mean of the jellyfishes; X * is the best position of the jellyfishes in the population; R is a number chosen at random from the range [0, 1]. The best position of the jellyfishes of the population is extracted based on the minimum fitness value. Over all the jellyfishes of the population, the volume of food is evaluated, which is defined as the fitness function. They are sorted in an ascending order, and the first one is extracted as the best position. The considered fitness function of the PNR problem is formulated in Equation (6), comprising the three reliability indices of SAIFI, SAIUI and TENS as an MOF model. If the CF value is lower than 0.5, the fresh place of each jellyfish could be developed, depending on the moving inside the swarm, via either Equation (16) representing the passive type or Equation (17) following the active type as shown [26]: where U b and L b signify the upper and lower limits of the control parameters, which are in between; and f symbolizes the quantity of food in aspects of the qualitative function associated with each jellyfish location. The upper and lower limits of the control parameters are related to the open links for reconfiguration which is formulated in Equation (7). Thus, the possibilities are regarding to the distribution lines which ranges from the first line to the maximum number of the lines as formulated in Equation (8). Also, Equation (18) describes the checking model of each jellyfish location to be restored in the nearest boundary.
where X i,d indicates the ith jellyfish place in dth dimension. The dimension for jellyfish place is the number of the control parameters which is defined as the open links for reconfiguration as in Equation (7). Figure 1 depicts the major stages of the JFS.

Simulation Results
The proposed methodology based on the JFS optimizer is implemented on a 33-node DN with 32 sectionalizing links and 5 open sections. Its single network diagram is depicted in Figure 2, where 12.66 kV is the base voltage of the 69-node DN [11]. For the nominal condition of this DN, the total apparent, active, and reactive power demands are, respectively, 4.6602 MVA, 3.802 MW and 2.6946 MVAr [38]. The test DN is expected to perform under balanced load circumstances. All loads are expected to have constant power in nature. The DN reliability data, comprising failure rates and lines repair time, is derived from [2].

Simulation Results
The proposed methodology based on the JFS optimizer is implemented on a 33-node DN with 32 sectionalizing links and 5 open sections. Its single network diagram is depicted in Figure 2, where 12.66 kV is the base voltage of the 69-node DN [11]. For the nominal condition of this DN, the total apparent, active, and reactive power demands are, respectively, 4.6602 MVA, 3.802 MW and 2.6946 MVAr [38]. The test DN is expected to perform under balanced load circumstances. All loads are expected to have constant power in nature. The DN reliability data, comprising failure rates and lines repair time, is derived from [2].  By applying the JFS algorithm on the four cases studied, Table 1 displays the must open tie lines which is optimally selected. Table 2 illustrates the related reliability measures.  By applying the JFS algorithm on the four cases studied, Table 1 displays the must open tie lines which is optimally selected. Table 2 illustrates the related reliability measures.

Comparative Assessment for Solving the Cases Studied
In this sub-section, a comparative assessment is carried out for the three cases studied using three recent advanced algorithms. Tuna swarm optimizer (TUNA) [39] and tunicate swarm algorithm (TSA) [40], besides the JFS algorithm, are implemented as well. The three techniques are applied with population size of 30 individual and maximum number of 60 iterations. TUNA, TSA and JFS algorithms are implemented for 10 separate runs. The listing of technical details of the essential parameter settings in all techniques, i.e., TSA, TUNA, and JFS are shown in the Appendix A, Table A1.
For the four cases studied, the related average convergence curves are displayed in Figures 3-6, respectively, for minimizing the SAIFI, SAIUI, TENS and MOF. Added to that, Table 3 displays the related average objectives in terms of the SAIFI, SAIUI, TENS and MOF, respectively.      In the third case, for minimizing the TENS, the JFS algorithm declares significant superiority over TUNA and TSA algorithms. It obtains the least average TENS with 4.7304 MWh/year, where TUNA and TSA algorithms obtains counterparts of 4.8049 and 5.04028 MWh/year. Also, the SNS algorithm obtains the least standard deviation with 9.36 × 10 −16 where TUNA and TSA algorithms obtains counterparts of 0.0969 and 0.328. In the first case, for minimizing the SAIFI, the JFS algorithm declares significant superiority over TUNA and TSA algorithms. It obtains the least average SAIFI with 3.9682 times/year, where TUNA and TSA algorithms obtains counterparts of 3.9981 and 4.0487 times/year. Also, the JFS algorithm obtains the least standard deviation with 9.36 × 10 −16 , where TUNA and TSA algorithms obtains counterparts of 0.0464 and 0.0998.
In the second case, for minimizing the SAIUI, the JFS algorithm declares significant superiority over TUNA and TSA algorithms. It obtains the least average SAIUI with 1.22744 h/year, where TUNA and TSA algorithms obtains counterparts of 1.30744 and 1.3179 h/year. Also, the JFS algorithm obtains the least standard deviation with 0.00, where TUNA and TSA algorithms obtains counterparts of 0.0558 and 0.03412.        To investigate the sensitivity analysis of the setting parameters for critical variables of different setting scenarios for the proposed jellyfish algorithm, different number of search agents and maximum number of iterations are considered, and the proposed jellyfish algorithm is applied for each scenario several times and the regarding indices are recorded in Table 5. As shown, great improvement is provided with higher reduction in the mean, maximum, standard deviation (Std), and standard error (Ste) with the increasing the number of search agents and maximum number of iterations. On the other side, the required computing time is increased. For that reason, the best settings are achieved at 30 search agents and 60 maximum number of iterations.

Conclusions
This paper presents an innovative application of the jellyfish search (JFS) algorithm to enhance the operational reliability of distribution systems. This application aims at improving the electricity networks automation via optimizing the Power Network Reconfiguration (PNR). In this regard, the system average interruption frequency index (SAIFI), system average interruption unavailability index (SAIUI) and total energy not supplied (TENS) are formulated, being considered simultaneously in a multi-objective model based on the weight factors. The proposed methodology based on the JFS optimizer is implemented on the IEEE 33-node distribution network. According to the numerical results, the SAIFI, SAIUI and TENS are improved by 36.44%, 34.11% and 33.35% compared to the initial condition. For comparison purposes, Tuna swarm optimizer and tunicate swarm algorithmm besides the proposed JFS algorithm, are implemented as well. The simulation results declare the significant outperformance of the JFS algorithm compared to TUNA and TSA in terms of the obtained improvements and the regarding convergence properties. A comparative analysis based on sensitivity analysis at different parameters of population size and iteration number is carried out. Great improvement is provided with higher reduction in the mean fitness function, maximum fitness function, standard deviation (Std), and standard error (Ste) with increasing the number of search agents and maximum number of iterations.
In the future studies, as the mixed integer linear programming (MILP) can get an effective mathematical modelling to solve complex optimization problems. These points will be added future approach for solving the target problem for single and multi-objective frameworks.

Conflicts of Interest:
The authors declare no conflict of interest. Table A1 describes the listing of technical details of the essential parameter settings in all techniques, i.e., TSA, TUNA, and JFS. Table A1. Essential parameter settings in all techniques, i.e., TSA, TUNA, and JFS.

Algorithms Proposed Time Parameters Settings Reference
Tuna swarm optimizer (TUNA) 2021 • Number of tuna population = 30 • Probability to regenerate the position in the space according to z = 0.05 • Constant to determine the extent to which the tuna follow the optimal individual and the previous individual in the initial phase a = 0.7 [39] Tunicate swarm algorithm (TSA) 2020 • Jet propulsion behavior with number of search agents = 30 • Social forces between search agents are based on initial and subordinate speeds to make social interaction which are Pmax = 4, Pmin = 1 [40] JFS 2020 • Number of search agents in population = 30 • maximum number of iterations = 60 [26]