Contemporarily, the development of distributed generations (DGs) technologies is fetching more, and their deployment in power systems is becoming broad and diverse. Consequently, several glitches are found in the recent studies due to the inappropriate/inadequate penetrations. This work aims to improve the reliable operation of the power system employing reliability indices using a metaheuristic-based algorithm before and after DGs penetration with feeder system. The assessment procedure is carried out using MATLAB software and Modified Salp Swarm Algorithm (MSSA) that helps assess the Reliability indices of the proposed integrated IEEE RTS79 system for seven different configurations. This algorithm modifies two control parameters of the actual SSA algorithm and offers a perfect balance between the exploration and exploitation. Further, the effectiveness of the proposed schemes is assessed using various reliability indices. Also, the available capacity of the extended system is computed for the best configuration of the considered system. The results confirm the level of reliable operation of the extended DGs along with the standard RTS system. Specifically, the overall reliability of the system displays superior performance when the tie lines 1 and 2 of the DG connected with buses 9 and 10, respectively. The reliability indices of this case namely SAIFI, SAIDI, CAIDI, ASAI, AUSI, EUE, and AEUE shows enhancement about 12.5%, 4.32%, 7.28%, 1.09%, 4.53%, 12.00%, and 0.19%, respectively. Also, a probability of available capacity at the low voltage bus side is accomplished a good scale about 212.07 times/year.

The primary function of any electric power system network is to supply energy to its consumers at optimum operational costs by warranting superior quality and continuity at all eras [

Generally, two approaches are adapted for reliability assessment of a power network, such as simulation and analytical [

The distribution system (DS) contributes the highest proportion of power outages at the customer load points due to the radial nature of the network [

Ref. no | Year | Methods | Indices | Inferences |
---|---|---|---|---|

[ |
2016 | Fish Electro- location Optimization (FEO) | SAIFI, SAIDI, ASUI, ASAI, AENS and CBRI | -Optimal distributed generations (DG), and capacitor placement was performed to improve reliability indices economically. |

[ |
2017 | Markov model | SAIFI, SAIDI, CAIDI, AENS, IEAR, and EENS, | -Presented a wide-ranging reliability evaluation of the DS that fulfills the customer load demand penetrating WT, PV, and electric storage system (ESS). |

[ |
2017 | Hierarchical decoupling optimization framework | EENS, and, |
-Study was performed on IEEE 14 bus system extended with a 14 node gas system and IEEE 118 bus system with a Belgian natural gas system. |

[ |
2018 | Analytical Methodology | SAIFI, SAIDI, CAIDAI, |
-Reliability assessment and failure analysis was performed for an existing power system network. |

[ |
2018 | Monte Carlo | SAIFI, SAIDI, CAIDI, ASAI, ENS, and AENS. | -Developed a Monte Carlo model for the assessment of closed-ring grids by integrating total loss of continuity. |

[ |
2015 | Analytical Methodology | SAIFI, SAIDI, CAIDI, ASAI, ASUI, EENS, and AENS | -Demonstrated the influence of DG on the reliability of the distribution system. |

[ |
2018 | Reliability bock diagram (RBD) and Monte Carlo | SAIDI, SAIFI, CAIDI, ASAI, and ASUI. | -Presented an approach to assess the reliability of a micro-grid integrated into a central grid and renewable energy resources. |

[ |
2015 | Fuzzy based analytical hierarchy process (AHP) | SAIFI, SAIDI, CAIDI, ASAI, AUSI, |
-Input factors were demonstrated using suitable membership tasks with the fuzzy triangular set of rules. |

[ |
2017 | Automatic circuit reclosers (ACRs) | SAIFI, SAIDI, CAIDI, MAIFI, |
-Reliability index evaluation was analyzed in the existing system before and after the presentation of ACRs. |

[ |
2018 | Virus Colony Search Algorithm (VCSA) | SAIFI, SAIDI, and AENS. | -VCSA was engaged to find the optimal location and magnitude of DGs subject to increase the reliability indices of the test system. |

[ |
2020 | Fault tree with cyber system | EENS, SAIDI, and SAIFI. | -Two indices were suggested to assess the cyber impression on the dispatch capacity of DGs. |

[ |
2017 | Cyber-physical |
ASAI, SAIFI, SAIDI, and EENS | -The author treated the circuit breakers and DERs as the coupling elements between the physical and cyber systems. |

[ |
2020 | Binary hybrid PSO and GSA algorithms | SAIFI, SAIDI, ASIDI, and ASAI. | -Proposed a long-term strategy considering a cost-benefit to state the optimum automation level of DS constrained with limits of reliability indices. |

Based on the inferences from the intensive literature study, it is found that there are research gaps that need to be carried forward to find or enhance the solution further. Some of them are as follows,

Optimized reliability evaluation metrics are not significantly demonstrated.

Analytical approaches are adapted by several authors that lead to severe computation time.

Meta-heuristic approaches are not employed prominently for extended/integrated power networks.

Limited works are found that evaluate the reliability indices after integrating with renewable energy resources.

Most of the authors derived the reliability indices by segregating the whole system into several feeders.

There is evidence of limited consideration of reliability indices for integrated distributed systems.

Considering the research gaps mentioned-above, this work targets to derive the following objectives,

To evaluate the reliability of the extended power network integrated with Photovoltaic (PV), Wind turbine (WT), and Gas turbine (GT).

To compute the most optimized reliability indices using meta-heuristic algorithm i.e., Modified Salp Swarm algorithm.

To demonstrate various case studies considering the tie line operation of the extended system with the existing system.

To evaluate the penetration of distributed generations into the existing system using optimized reliability indices.

To assess the overall indices without classifying the feeder in the existing system.

The rest of the work is organized as follows: Section 2 demonstrated the problem formulation, proposed methodology, and case study used for the study. Subsequently, Section 3 illustrates the detailed results and discussions from the proposed model. Then, a comparative analysis is carried out between various cases and several existing methodologies in Section 4 that can validate the effectiveness of the proposed method. Finally, conclusions are made in Section 5 based on the observed results.

The main three technical objective functions considered are minimizing the active power losses (PL) and Voltage Deviation (VD), and maximizing the Voltage Stability (VS) as detailed below [

✓ The feeder system power losses (PL) can be minimized using

where I_{m} is the m^{th} branch current magnitude, R_{m} is the resistance of m^{th} branch, and nb is the total number of branches in the feeder system.

✓ The voltage deviation (VD) can be minimized by

where N_{L} is the total number of load buses, V_{r} is the rated voltage, V_{m} is the actual voltage magnitude at m^{th} node.

✓ Maximization of voltage stability (VS) can be expressed as

where V_{a} denotes magnitude of the voltage at a^{th} node, P_{b} and Q_{b} are active and reactive power of the load at b^{th} node, respectively, and R_{ab} and X_{ab} are the resistance and reactance of the line between the nodes a and b, respectively.

The objective functions are subjected to the following operating constraints [

In a feeder system, the power balance constraints are as follows:

where P_{sb} and Q_{sb} are active and reactive powers of the slack bus, respectively, P_{DGp} and Q_{DGp} are the DG active and reactive power capacities at p^{th} bus, respectively, P_{Lossq} and Q_{Lossq} are the feeder active and reactive power losses of q^{th} bus, respectively, P_{dq} and Q_{dq} are the demanded active and reactive powers at q^{th} bus, respectively, and ‘n’ is the total number of buses in the feeder system.

✓ Generator performance constraints:

where P_{DGm}^{min} and P_{DGm}^{max} are minimum and maximum active power capacities of the DG at m^{th} bus, and Q_{DGm}^{min} and Q_{DGm}^{max} are minimum and maximum reactive power capacities of the DG at m^{th} bus, respectively.

✓ Capacity of DGs:

where P_{DGm} is real power fed by the DGs at the m^{th} node, N^{DG} is total number of DG units, and P_{TD} is the total active power demand.

✓ Feeder voltage:

The feeder voltage constraints are stated as

where V_{m}^{min} and V_{m}^{max} are lowest and highest acceptable values of voltage at m^{th} bus, respectively, V_{m} is load bus RMS voltage at m^{th} bus, N_{L} is the total number of load buses.

Modified Salp Swarm Algorithm (MSSA) mimics the swarming behavior of salps, and it is similar to jellyfishes that survive in the ocean as impelled through the body as propulsion to shift forward often appears as a flock called salp chain. These salp chains are classified into two groups such as leader and follower. Here the leader in the salp is present in front of the chain, and the remaining all salps are followers of the salp chain. A mathematical model for the position of the salp is defined in an m-dimensional exploration space where m is the number of variables in a given problem. Positions of all the salps are stored in a two-dimensional matrix called k. it is also assumed that there is a food source called f in the search space as the swarm’s target. In order to leader update the position of the leader, the following equation is expressed as:

where ^{th} dimension.

^{th} dimension.

^{th} dimension.

^{th} dimension.

To update the position of the followers (Newton’s law of motion) is utilized, and it is expressed as follows:

where i ≥ 2, ^{th} follower in n^{th} dimension.

t is time.

The Modified Salp Swarm Algorithm (MSSA) algorithm modifies two control parameters of the actual SSA algorithm (

(1) In the actual SSA technique, the leader movement depends on the coefficient (

where l and L represents the current iteration and the maximum no. of iteration, respectively. In the actual SSA algorithm,

(2) Also in SSA algorithm, the location of the follower salp is updated from its previous location as well as neighbourhood salp’s location as follows.

where ^{th} and (i − 1)^{th} salps in m^{th} dimension. This eventually necessitates storing the position of i^{th} and (i − 1)^{th} salp after each iteration for calculating the next position of i^{th} salp. It leads to extra computational time as well as additional memory requirement. It is to be noted that the location of any follower salp relies only on its previous location not on its neighbouring salp location. It has a direct impact on the exploitation ability of the algorithm. Consequently,

As the neighborhood follower salp’s location needs not to be saved, the modified equation reduces the execution time with minimum memory requirement. This in turn enhances the exploitation capability of the algorithm.

Though the global optimal of the optimization delinquent is unidentified, it can be presumed that the most satisfactory solution can be achieved through leader observation that travels towards the food source. Owing to this, the followers follow the assigned leader effectively. Consequently, as explained in the flowchart below, the salp chain attained supremacy to travel towards the global optimal circumstances but varying against diverse iterations [

Parameters | Definitions | Values |
---|---|---|

p_{s} |
Population size | 30 |

Constant of leader salp movement towards the food source | 0.1 | |

Random numbers | (−1, 1) | |

n_{max} |
Maximum iterations | 50 |

Considering the proposed methodology, this work targets the reliability assessment of the selected power system case studies, as illustrated in the following section.

To evaluate the effectives of the proposed metaheuristic algorithm, the modified IEEERTS 79 test system extended with three feeder line IEEE 6 bus system shown in

MSSA is a simulation procedure to consider the time sequence of the test system. This procedure dramatically reflects the randomness and uncertainty of the entire network [

The test system is modeled as a composite system designed with the help of MATPOWER tool, which includes the generation and transmission section. The composite section and distribution section are connected through the substation as a low voltage busbar. From the low voltage bus bar side, feeders are extended to connect the IEEE 6 bus system. From the original test system, IEEERTS 79 bus is now extended with IEEE 6 bus system; therefore, the size and level of complexity are increased. In this situation, the reliability assessment of a modified power network is calculated for with and without distributed generating units. After extending the system, the probability of every layer and the capacity is framed. The potential buses for extended integration can be identified using the least sensitivity factor (LSF).

Firstly, every component of the power network is sampled. Assuming the load demand (X) of the respective test system is the expected value (E(ζ)) of a haphazard variable (ζ). The number of sampling is carried out to confer the probability distribution function (ζ). The arithmetic mean value of the distribution function is expressed as,

when the value of (N_{k}) is the maximum number, it can get by the following expression.

Due to the law of large numbers, we can prove that _{1}, P_{2}, P_{3} ….., P_{Nk,} and its respective frequency is represented as f_{1}, f_{2}, f_{3} ….., f_{Nk}. The time duration and capacity state can be obtained using the statistical method. The probability and the frequency of the (Z) states are expressed as,

where

In the sampling, the computer generates the haphazard number order and can’t be distributed evenly, so the dual sampling method is used to produce a negative association with each haphazard number as the succeeding sampling value to achieve a more accurate value. Let F(Z) be a test of the state z, the probable importance of the test results are as follows:

where Nk represents the number of sampling represent the state value of (i) times.

The distribution section includes the main and lateral line section, distributed transformers, isolators, fuses, breakers with relay, and alternate power supplies (distributed generating units). Here line section and transformers can generally be represented by a 2-state model that is shown in

The period when the component remains in the UP state is the Time to Failure (TTF) rate. The time, when the component remains in a downstate is the Time to Repair (TTR) rate. The transition process from upstate to downstate is the failure process, and the down state to up state is the Restoration process. These TTR and TTF are the random variables which are different probability distributions of parameters. The basic three load point reliability indices are average failure rate (λ), average outage period (r), and average annual unavailability or average annual outage time (U).

where _{u.}

_{d.}

The reliability index such as System Average Interruption Frequency Index (SAIFI), System Average Interruption Duration Index (SAIDI), Customer Average Interruption Duration Index (CAIDI), Average Service Availability Index (ASAI), Average Service Un-served Index (ASUI), Expected Un-served Energy (EUE) and Average Expected Un-served Energy (AEUE) of the load and the system could be obtained.

The elementary reliability indices at a load point are calculated with the help of three parameters, namely average failure rate (

System Average Interruption Frequency Index (SAIFI)

System Average Interruption Duration Index (SAIDI)

Customer Average Interruption Duration Index (CAIDI)

Average Service Availability Index (ASAI)

Average Service Unavailability Index (ASUI)

Expected Unserved Energy (EUE)

Average Expected Unserved Energy (AEUE)

where

Here,

The effectiveness of the developed model is evaluated using IEEE RTS79 [

Further, the Expected Energy Not Supplied or Expected Unserved Energy (EENS or EUE) is calculated using the Variance coefficient. The time setting interval of the substation at low voltage bus bar maintained up to 5%, and the ranked capacity table comprises 21 statuses. Also, the simulation time for the assessment program is 1000000 h, and the variance coefficient of EENS is 0.0011093. The complete evaluation is carried out using 7 cases as illustrated below,

Case 1: Base case (no tie line with extended DG system)

Case 2: Combination: Tie line 1- bus no 9 and Tie line 2 – bus no 10.

Case 3: Combination: Tie line 1- bus no 9 and Tie line 3 – bus no 10.

Case 4: Combination: Tie line 2- bus no 9 and Tie line 1 – bus no 10.

Case 5: Combination: Tie line 2- bus no 9 and Tie line 3 – bus no 10.

Case 6: Combination: Tie line 3- bus no 9 and Tie line 1 – bus no 10.

Case 7: Combination: Tie line 3- bus no 9 and Tie line 2 – bus no 10.

In this case, a base case is simulated to identify the reliability indices of the existing system without the penetration of DGs into the system. The overall assessment is evaluated using MATLAB and the pictorial illustration of the results obtained from MATLAB is given in

The penetration of DGs, i.e., PV, WT, and GT, is analysed in this case. As stated earlier, the potential location for DG penetrations is computed as bus 9 and bus 10. Therefore, Tie lines 1 and 2 are connected to bus no 9 and bus no 10, respectively. Further, the reliability assessment is carried out using indices after DG penetration, and the detailed values are illustrated in

Similar to case 2, the DGs penetration is performed with two buses. Tie line 1 and Tie line 3 are connected to bus no 9 and bus no 10, respectively. Again, the reliability assessment is carried out using indices, and the detailed scales are represented in

In this case, the penetration of DGs, i.e., Tie line 2 and Tie line 1 are connected to bus no 9 and bus no 10, respectively. The reliability assessment indices display improved value compared with the existing system and case 3 but show less performance than case 2, as illustrated in

The integration of DGs is performed using the same nodes as mentioned in previous cases but using different Tie lines, i.e., Tie line 2 and Tie line 3 are connected to bus no 9 and bus no 10, respectively. Owing to the indirect penetration of higher capacity through Tie line 2 and Tie line 3, the reliability assessment indices display some declined values compared with other cases discussed above except base system, as illustrated in

This case analyzed the indices, similar configuration of case 3 but with interchanged Tie line connection. While comparing the observed results, it is found that the system indices are significantly greater than case 3, case 4, and case 5, but closer results with case 2: nonetheless, not higher than case 6 (

In this case, Tie line 3 and Tie line 2 are connected with bus 9 and bus 10, respectively, replicating the configuration of case 5 but with interchanged tie line arrangements. Comparing with base system and case 5, this configuration shows improved indices, but not great with other cases, as illustrated in

The assessment of hierarchical capacity on low voltage bus bar can attain the same precision to reflect a characteristic of the test system veritably, and the corresponding calculated results are illustrated in

Status | Available Capacity (MW) | Probability (%) | Frequency (time/year) |
---|---|---|---|

1 | 370 | 82.47 | 212.076015 |

2 | 351.5 | 10.32 | 26.5396945 |

3 | 333 | 4.04 | 10.3900646 |

4 | 314.5 | 2.001 | 5.14641301 |

5 | 296 | 1.03 | 2.64920421 |

6 | 277.5 | 0.05 | 0.12860827 |

7 | 259 | 0.04 | 0.10289151 |

8 | 240.5 | 0.002 | 0.00514482 |

9 | 222 | 0.0003 | 0.00077176 |

10 | 203.5 | 0.00005 | 0.00012863 |

11 | 185 | 0 | 0 |

12 | 166.5 | 0 | 0 |

13 | 148 | 0 | 0 |

14 | 129.5 | 0 | 0 |

15 | 111 | 0 | 0 |

16 | 92.5 | 0 | 0 |

17 | 74 | 0 | 0 |

18 | 55.5 | 0 | 0 |

19 | 37 | 0 | 0 |

20 | 18.5 | 0 | 0 |

21 | 0 | 0.0386 | 0.2875 |

The probability of the 21^{st} status is not zero because the trouble due to un-reasonable maintenance leads to the failure of the substation on the low voltage bus bar section.

A detailed comparative study between all the cases is performed and illustrated in

Similarly, the other indices such as CAIDI, ASAI, AUSI, EUE, and AEUE display a superior enhancement scale of about 7.28%, 1.09%, 4.53%, 12.00%, and 0.19%, respectively for case 2, as illustrated in

Further, the effectiveness of the MSSA is compared with the conventional SSA for the best case attained in this work. It is noted that the proposed modifications in the MSSA helps to obtain better a reliability of the considered system using evaluation indices (_{1} as 0.1, and avoids the local optima. Modified SSA technique reduces the execution time compared with SSA technique, in turn improves the exploitation ability of the algorithm.

In a nutshell, the meta-heuristic algorithm effectively evaluates the reliability indices for all the considered cases that comprise different DGs penetration schemes through available tie-line possibilities. Also, the total run time of the algorithm is small, about 4.01 s for the existing case, and 5.02 s for integrated configurations, i.e., after DGs penetration. Also, run time of the system depends on system configuration and optimization level, it can be reduced by altering the weightage of the parameters. Consequently, this algorithm can be adapted for a large-scale system that could generate commendable results.

A reliability assessment and available capacity of extended system is studied in this work using modified salp swarm algorithm (MSSA). The wok procedure and their simulation results display some notable effects, as described follows: The proposed MSSA algorithm facilitated to assess the distribution section’s reliability indices considering the influence DGs penetration with existing system. There were seven different configurations considered to assess the superior Tie-line integration. Among these, case 2 that connects the Tie line 1 and Tie line 2 with bus 9 and bus 10, respectively displayed superior results in terms of indices and availability capacity. Further, the reliability indices of best case such as SAIFI, SAIDI, CAIDI, ASAI, AUSI, EUE, and AEUE exhibited better enhancement about 12.5%, 4.32%, 7.28%, 1.09%, 4.53%, 12.00%, and 0.19%, respectively. Also, the probable availability capacity at the low voltage bus side was found to be 82.47%. Furthermore, the frequency of the availability was measured to be 212.07 times/year. The total computation time of the algorithm was found to be small about 5.02 s after DGs penetration.

The above results warrant the effectiveness of the proposed meta-heuristic algorithm for extended system particularly for DGs integration. This proposed scheme can be adapted for any standard or real-time system, comprises large system dimensions. However, the computation time of the algorithm may increase accordingly that may cause a complexity in the computation process and this can be addressed in the future works.