# Online implementation of time augmentation of over current relay coordination using water cycle algorithm

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## Abstract

In the present paper, a technique is presented for new investigations for the constrained type optimal coordination of over current relay problem using the water cycle algorithm (WCA). It is shown that the operating time of relay mainly depends upon the time dial setting (TDS) and plug settings. The paper introduces a novel metaheuristic optimizer algorithm, WCA, encouraged by the water sequence process and movements of rivers and flows on the way to the sea. Results are presented for the application of the methodology on a distribution system of single-end one loop system, Single-end multi-loop system and single-end multi-parallel feeder distribution system. Subsequently, the results find the minimal operating time of relay with optimized TDS for over current relay. The result reveals the effectiveness and superiority of the proposed WCA over the other techniques presented in the literature in terms of accuracy, input parameter and iterations.

## Keywords

Relay coordination Time dial setting (TDS) Water cycle algorithm (WCA)## 1 Introduction

A continuous and uninterrupted power supply needs to be delivered safely to the consumers in order to assure that more revenue is generated and that the financial activities of the utility provider remain functioning smoothly. Power system protection plays a very vital role in making and maintaining such types of power transactions smooth and efficient. Proper installation and operation of power system protection devices leads to curtailment of harm to the network and helps sustain a more secure connection for power delivery. In a distribution network, over current (OC) relays are mainly employed for primary protection besides being employed for backup protection, whereas in transmission systems, it is applied for backup protection [1]. Due to its ease of use, sensitivity, selectivity, and consistency, OC relays are one of the most widespread relays in use today.

When an electrical network experiences a fault condition, the fault is sensed by both the primary and secondary relays. The primary relay is expected to execute the necessary action of activating the corresponding circuit breakers (CBs) and detach and isolate the faulty section of the network in order to limit the propagation of the fault and prevent any severe damages to the system. However, if for any reason the primary relay setup fails to activate, then after a set user-defined coordination time interval (CTI) from the instant of initial detection of the fault, the backup relay should activate and trip the required CBs and isolate the faulty section to effectively prevent any further damage. In order to avoid incorrect operation of the primary and backup relays such as the backup relay taking action before the primary relay or the backup relay failing to trigger after CTI has elapsed [1, 2], appropriate relay coordination procedures should be implemented.

Relays have to be coordinated appropriately to avoid any malfunction and unnecessary downtime in other elements of the network. In the earlier days, relay coordination was executed manually and was thus a labor and time intensive process. But with the growth of the electricity network involving multiple sources and load points and the ever growing network complexity, the applicability of the straightforward old conventional methods proved to be a challenging task. Due to the difficulties involved and the lack of techniques in formulating an optimal solution for the coordination problem, power system operators had no choice but to accept the non-optimal coordination that met the protection system requirements at that time.

In order to achieve fast fault clearing time, an optimal coordination procedure is a necessity. This is more so for cases involving highly complex networks. In recent years, great efforts have been taken in the OC relay coordination problem to obtain the optimal relay setting. In [3] the authors have briefly discussed on the topological methods (graph theory) and optimization methods. Initially the trial and error method was applied in topological methods [4] but due to the requirements of a large number of iterations the rate of convergence is slow in the trial and error method. To achieve a faster rate of convergence at reduced iterations, techniques such as curve fitting method [5], graph theoretical method [6, 7] and analytical approach [8] were considered by different authors.

In 1988, Urdanta et al. [9] suggested the gauss–seidel iterative technique. The coordination of OC relay is a nonlinear problem since it involves simultaneous adjustment of the time dial setting (TDS) and plug setting (PS) values, however by considering a fixed plug setting (PS) value it can be treated and solved as a linear problem. The advantage of treating OC relay coordination as a linear problem lies in making the problem easier to solve and with less CPU time. Linear programming (LP) techniques including simplex [2, 10], dual simplex [11] and two-phase simplex [12] have been considered for solving the relay coordination problem when treating it as a linear problem. Although LP is simple, it still suffers from the possibility of being stuck in local optima. The major drawback in solving relay coordination by considering it as a linear problem is that only the TDS values can be calculated for fixed PS values. Though non-linear programming (NLP) approach is more complicated and takes more CPU time when compared to LP approaches, with OC relay coordination being a nonlinear problem at the roots, applying a nonlinear approach to solve it to obtain the optimal values for both the TDS and PS is a much preferred choice. Since the NLP approach also suffers from the possibility of being stuck at local optima, some researchers proposed a mixed-integer linear program (MINLP) to solve the coordination problem [13, 14, 15]. Both NLP and MINLP approaches struggle with the selection of initial guess value.

In the past few years, to solve the relay coordination problem, many heuristic and evolutionary algorithms have been proposed by many researchers such as genetic algorithm (GA) [16], particle swarm optimization (PSO) [17], teaching learning-based optimization (TLBO) [18], ant colony optimization (ACO) [19], and differential evolution (DE) [20]. Some researchers further improved the GA approaches as continuous GA [21] and hybrid GA [22], which greatly reduced relay operating time. Further, researchers and scholars have also modified and improved the techniques mentioned in the literature, some of the modified versions of which are, adaptive DE [23], modified adaptive TLBO [24], and modified PSO [25].

Optimization techniques recently in use for solving the relay coordination problem include firefly algorithm (FA) [1], chaotic firefly algorithm (CFA) [26], harmony search algorithm (HAS) [27], symbiotic organism search (SOS) [28], root tree algorithm (RTA) [29], grey wolf optimization (GWO) [30] and most valuable player algorithm (MVPA) [31]. However, the drawback with most of these heuristic approaches in computing an optimal relay setting is that there is always a risk of convergence to local minima, requires a large population, have a slow rate of convergence and takes more computational time. Thus, there still exist possibilities for further improvement in finding an optimal relay setting that can help achieve reduced operating time and thereby minimize the fault clearing time.

The main objective of this paper is to find out the optimized TDS and minimize the overall operating time of relays installed on the system. The objective function is formulated by a linear equation considering TDS is a decision variable. The main contribution of this article is the application of novel metaheuristic WCA techniques for optimal OC relay coordination problems. WCA was first proposed and presented by Eskander et al. [33] as a new evolutionary algorithm (EA), and has been proven to be very competitive and fast compare to other EA techniques. The competency of the proposed WCA is evaluated with three case studies, and the comparison of the proposed method with GA, SM, FA, CFA, CGA, and RTA is presented. The rest of this article is organized as follows: Sect. 2 provides a detailed procedure for problem formulation of relay coordination. Water cycle algorithm is explained in brief in Sect. 3. Section 4 consists of the implementation of WCA on the relay coordination problem. The three case studies along with their computational results, comparison, and discussion with the existing algorithm are provided in Sect. 5. Section 6 concluded the article.

## 2 Problem formulation

_{2}acts first to take over this fault because R

_{2}is the adjacent relay to this fault. If, due to any reason R

_{2}fails to operate, R

_{1}comes in action after a predefined time delay. Hence, the relay R

_{1}performs a duty of backup protection. If the operating time of R

_{2}is set at 0.1 s, then the operating time of R

_{1}is set with the addition of time delay, which includes 0.1 s in addition to the operating time of CB at bus A and the overshoot time of R

_{1}.

*z*denotes the objective function of this paper problem statement.

*n*is the number of relays, \(T_{{i_{k } }}\) represents the operating time of relay

*i*at fault location k. \(\varvec{W}_{{\varvec{j }}}\) is the weighting factor. The possible approach to using the weighting factor is to achieve the minimum system shock due to the faults would be to reduce a weighted the total operating time of all primary relays would be close to the minimum individual operating times that could be feasible. A fault may occur anywhere across the line since there are short lines in the distribution system and they have almost equal length and equal weights. \(\varvec{W}_{{\varvec{j }}}\) is therefore considered to be 1 (\(\varvec{W}_{{\varvec{j }}} = 1\)) for all relays. It is also a coefficient indicating the likelihood of fault occurrence. Therefore, since the length and weight of the lines are identical, the probability that the fault will occur on each line is equal. Because of this equal probability, usually \(\varvec{W}_{{\varvec{j }}}\) is set to 1 [2, 12, 18, 26, 35].

### 2.1 Constraint criterion

Following constraints have to take into considerations which are as:

#### 2.1.1 Operating time constraints

The load continuously varies at the distribution end. Due to these small disturbances which frequently come on the system, a relay has to wait for a few cycles and also not to take too long time to identify and register a fault condition.

Typical values for \(T_{ikmin} = 0.1\;{\text{s}}\) and \(T_{ikmax} = 1.1\;{\text{s}}\) [28].

Sometimes \(T_{ikmax}\) may vary upon network configuration. This constraint indicate that lower the operating time constraints faster will be the relay response and hence lower will be the TDS.

#### 2.1.2 TDS constraints

In this paper, typical values for \(TDS_{imin} = 0.025\) and \(TDS_{\text{i max}} = 1.2\) are considered [2].

#### 2.1.3 Coordination constraint

When a fault arises in the system both primary and backup relay sense this fault and may act simultaneously. Hence to avoid this false tripping, the backup relay should operate subsequently to predefined time interval known as CTI only when the primary relay fails.

### 2.2 Relay characteristics

Values for α and β of different over current relay characteristics [28]

Relay type | \(\varvec{\beta}\) | α |
---|---|---|

Inverse definite minimum time | 0.14 | 0.02 |

Very inverse | 13.5 | 1 |

Extremely inverse | 80 | 2 |

Instantaneous | Fixed operating time | |

Definite time | Predefined and fixed operating time |

## 3 Water cycle algorithm

Inspired by the natural water cycle process, Eskander et al. [33]. proposed the meta-heuristic water cycle algorithm (WCA). WCA can find the best minimum or maximum value of a given function with higher accuracy in less time. The author in [37] applied the WCA technique to solve an optimal reactive power dispatch problem considering the standard IEEE 30 bus test system and obtained encouraging results. Jabbar et al. [38] also used WCA to the rough set theory for attribute reduction problems. Based on their findings, the WCA performed just as well or even better than other methods to detect optimal selection of attributes. The optimal relay coordination problem is a constrained type of optimization problem that cannot be addressed effectively using traditional approaches. Therefore, the motivation is developed to use the WCA to solve the over current relay coordination problem for the various distribution network.

Mathematical Model for water cycle algorithm is described below in the following stages as:

### 3.1 Initial Population

In this algorithm, the population is called raindrops. For each raindrop is an array of 1 × N_{var}.

_{var}is the number of variables. For optimization, the array is represented in a matrix form

_{pop}is the number of population for raindrops as an initialization.

### 3.2 Streamflow to the river or river flow to the sea

*rand*is the random number evenly distributed between 0 and 1. C is the number between 1 and 2. If the updated stream location gives the solution, then no need to connect it to the river. The location of stream and river interchange (i.e. streams becomes the river and vice versa). Perhaps, such an interchange can occur for the river and the sea.

### 3.3 Condition for evaporation and raining

*iter.max*is the maximum iterations.

*lb*and

*ub*are lower and upper bounds assigned for the given problem.

*randn*is the normally distributed random number. The suitable value of

*µ*is taken as 0.1 because the larger value of

*µ*increases the probability to escape from the feasible region. Hence, the smaller value is considered which leads to exploring in the smaller region near to the sea. The term \(\sqrt {\varvec{\mu}}\) represent the standard deviation.

### 3.4 End of loop

The most exceptional result is computed when the termination condition comes with the maximum number of iterations. The end of the loop in WCA is continued till the convergence criterion is satisfied.

## 4 Implementation of WCA for Relay Coordination

- Stage 1:
Select the initialization parameters such as N

_{pop}, N_{sr}, d_{max}, and maximum iterations.Where N

_{sr}is the number of streams and rivers- Stage 2:
Create random initialization population matrix by Eq. (10)

- Stage 3:
Calculate the cost function of relay coordination for each raindrop by Eq. (11)

- Stage 4:
Determine the streams and river flow by using Eqs. (12) and (13)

- Stage 5:
Interchange the location of the river with stream and vice versa for the best solution

- Stage 7:
Decrease the defined d

_{max}value by Eq. (15)- Stage 8:
Check for convergence criterion using Eq. (17) If it is satisfied and reached up to the maximum iteration algorithm will stop otherwise, go to stage 4 and repeat the above procedure

## 5 Result and discussion

The proposed WCA program has been developed in MATLAB software to find the optimal TDS value of OC relay in a single and multi-loop distribution network. The execution of WCA is implemented on three different network configurations and it was observed that the proposed WCA gives a better solution in all the contextual analysis. The detailed system descriptions of all three cases can be found in [2, 26, 29]. The purpose behind considering a single loop and multi-loop network is that depending upon different networks, the number of constraints, CTI and complexity varies. Therefore, the viability of the proposed WCA must be reviewed and evaluated with the simple as well as complicated network to evaluate its computational time and number of iterations. Besides the reason behind choosing the three case studies presented in the paper is that these case studies are already discussed in the literature. So, the results obtained from the proposed WCA results can be compared and validated with the other existing technique.

### 5.1 Case study I

CT ratios and plug settings of seven relays [2]

Relay | CT ratios (A: A) | Plug settings |
---|---|---|

1 | 1000:1 | 0.8 |

2 | 1000:1 | 0.8 |

3 | 500:1 | 0.8 |

4 | 500:1 | 0.8 |

5 | 1000:1 | 0.8 |

6 | 1000:1 | 0.8 |

7 | 500:1 | 0.5 |

Primary/backup relationship and fault current through relay [2]

Fault location | Primary relay | Backup relay | Fault current (A) |
---|---|---|---|

K | 5 | – | 3289 |

6 | 3 | 1096.5 | |

L | 7 | 3 | 1315.8 through relay 3 and 5 |

– | 5 | 2631.6 through relay 7 | |

M | 3 | 1 | 2193 |

4 | 5 | 1315.5 | |

N | 1 | – | 6579 |

2 | 4 | 939 |

\(a_{i}\) constant and relay current (A) for case study I [2]

Fault location | Relay | |||||||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | ||

K | Relay current | – | – | 2.741 | – | 4.111 | 1.370- | – |

\(a_{i}\) | – | – | 6.872 | – | 4.881 | 22.165 | – | |

L | Relay current | – | – | 3.289 | – | 3.289 | – | 5.263 |

\(a_{i}\) | – | – | 5.809 | – | 5.809 | – | 4.145 | |

M | Relay current | 8.223 | 1.1737 | – | 2.347 | – | – | – |

\(a_{i}\) | 3.252 | 43.776 | – | 8.159 | – | – | – | |

N | Relay current | 2.741 | – | 5.482 | 3.288 | 1.644 | – | – |

\(a_{i}\) | 6.872 | – | 4.044 | 5.811 | 14.01 | – | – |

In this case study, twelve constraints are taken into consideration. Seven constraints are taken for minimum operating time, and five constraints are due to the coordination criterion. CTI is considered as 0.2 s. The TDS of seven OC relays are represented by x_{1} to x_{7} in Eq. (25). (x_{1},…x_{7} subscripts indicates the relay numbers).

The following calculations are useful to model the objective function for case study I. In the following Eqs. (18)–(24), the value of \(a_{i}\) constant is taken from Table 4.

#### 5.1.1 Application of WCA

Optimized TDS and total operating time for case study I

Time dial settings | Simplex method [2] | Root tree algorithm [29] | Proposed water cycle algorithm |
---|---|---|---|

TDS 1 | 0.238 | 0.085 | 0.059 |

TDS 2 | 0.12 | 0.025 | 0.025 |

TDS 3 | 0.36 | 0.095 | 0.052 |

TDS 4 | 0.031 | 0.025 | 0.025 |

TDS 5 | 0.027 | 0.025 | 0.025 |

TDS 6 | 0.025 | 0.025 | 0.025 |

TDS 7 | 0.08 | 0.025 | 0.025 |

Total operating time(z) in second | 15.70 | 5.17 | 4.20 |

Net time gain in seconds with WCA | 11.50 | 0.97 |

#### 5.1.2 Comparison of WCA with simplex method and root tree algorithm

The results obtained with the proposed WCA show the better quality performances of the suggested algorithm. It reduces minimum operating time by 11.50 s and 0.97 s in comparison with the simplex method and root tree algorithm, respectively. It is found that WCA provides slightly improved net time gain relative to RTA, but as oppose to RTA, WCA takes fewer iterations [29]. The WCA gave less operating time and improved the performance of seven OC relay with optimized TDS. It can be seen from Fig. 4 if carefully observed that the convergence has been started only before 10^{th} iterations, even though 100 iterations are taken. Even though 100 iterations are taken. This shows the superiority of WCA in terms of smoothness and fast convergence in relay coordination problems.

### 5.2 Case study II

_{1}to x

_{8}in Eq. (44).

Primary/backup relation of relay and maximum fault current for case study 3 [29]

Fault location | Primary relay | Backup relay | Maximum fault current (A) |
---|---|---|---|

K | 3, 7 | –, 4 | 2330 |

L | 3, 4 | –, 1, 2 | 1200 |

M | 4, 8 | 1, 2, 3 | 1400 |

N | 1, 5 | –, 8 | 2800 |

O | 2, 6 | –, 8 | 2800 |

P | 1, 2, 8 | –, –, 3 | 2330 |

\(a_{i}\) constants and relay currents (A) for case study II [29]

Fault location | Relay | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||

K | Relay current | 2 | 2 | 10 | 4 | – | – | 4 | – |

\(a_{i}\) | 10.035 | 10.035 | 2.971 | 4.9804 | – | – | 4.9804 | – | |

L | Relay current | 3.45 | 3.45 | 5.1 | 6.9 | – | – | – | – |

\(a_{i}\) | 5.584 | 5.584 | 4.227 | 3.551 | – | – | – | – | |

M | Relay current | 5 | 5 | 4 | 10 | – | – | – | 4 |

\(a_{i}\) | 4.281 | 4.281 | 4.9804 | 2.971 | – | – | – | 4.9804 | |

N | Relay current | 20 | 6 | 2 | – | 8 | – | – | 2 |

\(a_{i}\) | 2.267 | 3.837 | 10.035 | – | 3.297 | – | – | 10.035 | |

O | Relay current | 6 | 20 | 2 | – | – | 8 | – | 2 |

\(a_{i}\) | 3.837 | 2.267 | 10.035 | – | – | 3.297 | – | 10.035 | |

P | Relay current | 10 | 10 | 3.3 | – | – | – | – | 3.3 |

\(a_{i}\) | 2.971 | 2.971 | 5.749 | – | – | – | – | 5.749 |

#### 5.2.1 Application of WCA

Optimized TDS and total operating time for case study II

Time dial setting | Genetic algorithm [34] | Root tree algorithm [29] | Water cycle algorithm |
---|---|---|---|

TDS 1 | 0.297 | 0.252 | 0.194 |

TDS 2 | 0.297 | 0.252 | 0.145 |

TDS 3 | 0.227 | 0.20 | 0.030 |

TDS 4 | 0.173 | 0.151 | 0.145 |

TDS 5 | 0.06 | 0.03 | 0.030 |

TDS 6 | 0.06 | 0.03 | 0.030 |

TDS 7 | 0.04 | 0.025 | 0.025 |

TDS 8 | 0.113 | 0.08 | 0.069 |

Total operating time(z) in seconds | 31.883 | 26.681 | 24.141 |

Net time gain in seconds with WCA | 9.742 | 2.5 |

#### 5.2.2 Comparison of the WCA with exiting algorithms

The results obtained by the proposed WCA is compared with GA and RTA are given in Table 8. This shows from Table 8 that the TDS value of all relay optimally improved. The performance of the WCA gives the advantage of net time gain with a large margin of 9.742 s over the genetic algorithm. The advantage of net time gain shows the improvement in overall minimum operating time for all relays. Also, it gives the advantage of 2.5 s over the recently introduced root tree algorithm. The best part of the proposed WCA is that it takes fewer iterations compared to both techniques GA and RTA as cited in the paper. It can be observed from Fig. 6 that the convergence towards minimum operating time has been started only between 40th and 45th iterations. The results achieved by the WCA must meet the coordination constraints for all relays. Besides, no violation of the coordination constraint has been found.

### 5.3 Case study III

_{1}to x

_{6}in Eq. (65).

Line data for case study III [26]

Line | Impedance (Ω) |
---|---|

1–2 | 0.08 + j1 |

1–3 | 0.16 + j2 |

2–3 | 0.08 + j1 |

Primary/backup relay pair [26]

Fault location | Primary relay | Backup relay |
---|---|---|

K | 5 | – |

6 | 3 | |

L | 3 | 1 |

5 | – | |

M | 3 | 1 |

4 | 5 | |

N | 1 | – |

2 | 4 |

CT ratios and plug settings of relay for case study III [26]

Relay | CT ratio (A) | Plug setting |
---|---|---|

2 | 300:1 | 1 |

4 | 600:1 | 1 |

3 | 600:1 | 1 |

6 | 600:1 | 1 |

1 | 1000:1 | 1 |

3 | 1000:1 | 1 |

\(a_{i}\) constant and relay current (A) for case study III [26]

Fault location | Relay | ||||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | ||

K | Relay current | 1.096 | – | 1.096 | – | 5.482 | 1.827 |

\(a_{i}\) | 75.91 | – | 75.91 | – | 4.044 | 11.539 | |

L | Relay current | 1.644 | – | 1.644 | – | 2.741 | – |

\(a_{i}\) | 13.99 | – | 13.99 | – | 6.872 | – | |

M | Relay current | 2.193 | – | 2.193 | 2.193 | 2.193 | – |

\(a_{i}\) | 8.844 | – | 8.844 | 8.844 | 8.844 | – | |

N | Relay current | 6.579 | 3.13 | – | 1.565 | 1.565 | – |

\(a_{i}\) | 3.646 | 6.065 | – | 15.55 | 15.558 | – |

#### 5.3.1 Application of WCA

Optimized TDS and total operating time for case study III

Time dial settings | Firefly algorithm [1] | Continuous genetic algorithm [23] | Chaotic firefly algorithm [26] | Root tree algorithm [29] | Proposed water cycle algorithm |
---|---|---|---|---|---|

TDS1 | 0.027 | 0.0765 | 30.027 | 0.059 | 0.0589 |

TDS2 | 0.13 | 0.034 | 0.221 | 0.025 | 0.025 |

TDS3 | 0.025 | 0.0339 | 0.025 | 0.025 | 0.025 |

TDS4 | 0.025 | 0.036 | 0.025 | 0.029 | 0.029 |

TDS5 | 0.025 | 0.0711 | 0.029 | 0.065 | 0.0626 |

TDS6 | 0.489 | 0.0294 | 0.363 | 0.025 | 0.025 |

Total operating time (z) in seconds | 16.25 | 15.58 | 14.39 | 11.93 | 11.86 |

Net time gain in seconds with WCA | 4.39 | 3.72 | 2.53 | 0.07 |

#### 5.3.2 Comparison of the proposed WCA with the existing algorithms

To analyze the execution of the proposed WCA, this method has been contrasted with other metaheuristic techniques such as FA, CGA, CFA, and RTA techniques as demonstrated in Table 13. In terms of the total net time gain, the WCA outstripped the FA, CGA, CFA, RTA and provides the advantages of 4.39, 3.72, 2.53, and 0.07 s respectively over this process. In the case of RTA, however, the difference is less just 0.07 s but for the convergence, the RTA technique requires to adjust more input parameters, also it takes more computational effort. RTA takes 200 iterations to converge [29] but for the same WCA takes only 100 iterations. Instead, for convergence towards optimal TDS value, WCA requires to adjust only the initial population and it takes less number of iterations compared to RTA and other techniques. The advantage of even 0.07 s makes the protective system fast and reliable under abnormal conditions. It can be observed from Fig. 7 that convergence towards the optimal solution has been started from only between 10th to 20th iterations. So, it is revealed from Table 13 and above discussion, the proposed WCA technique shows the faster response over the trending evolutionary algorithms with improved TDS and total operating time with fewer iteration.

## 6 Conclusion

Water cycle algorithm has been recommended to investigate the coordination problem of over current relays in mesh type power distribution network to calculate the time dial setting (TDS) for a certain pickup current. The study exposes that the suggested method can convey the overall operating time of the over current relay using the present technique is reduced. The proposed idea has been adequately examined and contrasted with other up to date techniques on three different test systems, and it has been observed that the overall operating time of the Over current relay using the present method is reduced, and the algorithm could successfully work for over current relay coordination.

## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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