# Optimal Protection Scheme for Enhancing AC Microgrids Stability against Cascading Outages by Utilizing Events Scale Reduction Technique and Fuzzy Zero-Violation Clustering Algorithm

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- An innovative scale reduction technique called N-K-ESRT is utilized to decrease the scale of the N-2 contingencies.
- The F-ZVCA is proposed to eradicate the DOCR’s miscoordination and reduce the scope of the POSP.
- The distinguish MOAs are recommended for determining the best DSPs.
- The offered solving procedure is applied to three AC microgrids, including a real distribution system (named TESKO2 feeder), besides the IEEE Std. 399-1997 and IEEE 14 bus systems.

## 2. Problem Modeling of DOCRs

#### 2.1. Objective Function

#### 2.2. DOCRs Relations and Constraints

_{FC}). The values of DSPs are directly proportional to the DOCR’s operational time. In contrast, assuming the DSPs are fixed, (2) demonstrates that the operation time of DOCRs is inversely proportional to the fault current magnitude. Fault current is considered the near-end three-phase to ground faults.

## 3. Protection Optimization Setting Problem

#### 3.1. N-K Events Scale Reduction Technique

^{ESRT}equals two times the number of buses in the network under investigation). Rather, if all N-2 outages are considered, 36 occurrences (called OCC) will need to be investigated as (9) [46]. POSP is able to access the “maximum voltage violation study” for cascading events with the help of the Power Factory 15.1.7 DIgSILENT software. The result of this analysis reveals which of these 36 scenarios has the greatest and least noticeable impact on the network bus voltage. So, this method has led to a 75% decrease in the number of N-2 events in the sample network, which would help reduce the size of the problem and speed up the POSP. It should be emphasized that, with the rise of assuming equipment for N-2 events, this technique will be more beneficial than before.

#### 3.2. The Procedure of Achieving the CSP Practical Bound (PA-CSP-PB) for the POSP

_{M}(shown in Figure 2) according to (6) and (7), which can be applied to the rest of the DOCRs. First, the maximum network current passing through the R

_{M}is used to determine the least bound of (7) for the R

_{M}. This is accomplished by employing the Newton–Raphson load flow (NR-LF) to compute the current flowing through L1 (seen in part A).

_{M}’s maximum current. Additionally, (11) adds 20% to the ${I}_{\mathit{Loadmax}}^{{R}_{M}}$, named ${I}_{\mathit{Pickup}}^{{R}_{M}}$. This issue is due to the necessity of preventing a false trip caused by a maximum load current rather than a permanent fault (shown in part C). As seen in part D, (13) obtains the plug setting (${PS}_{}^{{R}_{M}}$) for the following approach, using (12) as an asset. The plug setting is the percent of R

_{M}’s CT winding, which varies from 50% to 200% in 25% increments. The ratio between the primary (CTP) and secondary (CTS) windings of a CT is denoted by (12) and written as CTR. In accordance with PA-CSP-PB, the plug setting is rounded up and ${I}_{\mathit{Pickup}}^{{R}_{M}}$ is recalculated by (13) as part E. Next, the current flowing through the secondary side of the CT (${I}_{CSP}^{{R}_{M}}$) is calculated using the formula (14) and is illustrated in part F. This current (${I}_{CSP}^{{R}_{M}}$) is the same current that should be deemed the lowest bound in (7). Particularly, the relation specified in (15) will suffice as the CSP bound of POSP. Accordingly, the lower limit of (15) is the greatest value between ${I}_{\mathit{CSP}}^{{R}_{M}}$ and ${\mathit{CSP}}_{\mathrm{min}}^{}$(seen in part G). Selecting the maximum value at the lower limit of (15) is intended to prevent network power interruptions. The upper limit of (15) also represents the least value between ${\mathit{CSP}}_{\mathit{max}}^{}$ and ${I}_{\mathit{FCmin}}^{{R}_{M}}$. Note that the minimal short circuit current (i.e., ${I}_{\mathit{FCmin}}^{{R}_{M}}$) employed in the case studies is equivalent to the single-phase ground fault current stipulated by standard IEC 60909-2001 [47] (part H). Similar to the preceding process that established the lower limit of the CSP, the short circuit current value used in the next part is the lowest short circuit current among all N-K-ESRT’s topologies based on (16) and depicted in part J. The fault current determined by (16) is the maximum bound of (7). Now, the upper limit of (15) is the minimum value between the ${I}_{\mathit{FCmin}}^{{R}_{M}}$ and ${\mathit{CSP}}_{\mathit{max}}^{}$ (part K). Considering that the L1 should be rendered inoperable in the event of a short circuit, the minimum value was set at the upper limit of (15). The PA-CSP-PB will perform all the described steps for each relay. The PA-CSP-PB relations can be defined as:

#### 3.3. Fuzzy Zero-Violation Clustering Algorithm

^{C}

^{1}, OT

^{C}

^{2}, OT

^{C}

^{3}, and OT

^{C}

^{4}). These center points indicate the total operating time (OT) of the network’s primary relays. For instance, OT

^{C}

^{1}is identified as the time center point for the “C1” cluster (i.e., cluster 1).

^{S}

^{1}, OT

^{S}

^{2}… etc.) with the help of (1) and the default TSMP = 1, and CSP = I

_{CSP}. For example, OT

^{S}

^{3}signifies the total operation time of the main DOCRs for the “S3” topology.

^{S}

^{1}from all time center points (i.e., OT

^{C}

^{1}, OT

^{C}

^{2}… etc.) is determined and designated as DOT

^{S}

^{1-C1}, DOT

^{S}

^{1-C2}, … This procedure is done for each resultant topology (i.e., DOT

^{S}

^{2-C1}… DOT

^{S}

^{3-C1}…).

^{S}

^{1-C1}, $D\omega $

^{S}

^{1-C2}, $\dots ,$ topology ‘S1’ is allocated to the cluster with the smallest $D\omega $

^{S-C}value. Lastly, steps 1 through 6 are repeated until the clusters’ constituents are no longer altered.

#### 3.4. Meta-Heuristic Optimization Algorithms

## 4. POSP Setup

#### 4.1. The Assumption about the POSP

_{CSP}is always higher than the CSP

_{min}and lower than the I

_{FCmin}in all evaluated cases. Nevertheless, as examined and validated by Noghabi et al. [34], including both decision variables of DOCRs in the cycle of optimization algorithms merely slows down the convergence process of the problem. Therefore, the CSP is equivalent to the I

_{CSP}, which will be produced by using PA-CSP-PB. As a result, the CSPs are the same across all clusters and are not cluster-dependent. The end criteria for POSP are OF’s tolerance and MOA’s execution time (MET). The OF’s tolerance is presumed to be 1 × 10

^{−16}, and the maximum limit of MET is set to 100 s, resulting in more accurate findings [50]. This section additionally provides the average tripping time (ATT), the ATT for one relay (ATTO), the maximum tripping time (MTT), the overall TSMP (O-TSMP), and the iteration of MOAs (IMA) to aid comprehension of the POSP. Furthermore, logarithmic indices have been utilized on numerous vertical and horizontal axes of the figure obtained from POSP in order to enhance the distance portrayal and coherence of the paper’s figures.

#### 4.2. N-K-ESRT and F-ZVCA Results: IEEE Std. 399-1997 System

#### 4.3. Simulation Results: IEEE Std. 399-1997 System

#### 4.4. Simulation Results: TESKO2 System

_{a}, DG

_{b}, and DG

_{c}) with a capacity of 2.2 MVA, five lines (L1, …, L5), three loads (Load

_{a}, Load

_{b}, and Load

_{c}), and ten DOCRs (R

_{a}, …, R

_{X}). In the TESKO2 network, the presumed equipment for N-2 events consists of 12 components, including all loads, synchronous machines, and lines, of which only five topologies are analyzed as N-K-ESRT. The repercussions of N-K-ESRT have involved Load

_{a}-Load

_{b}outages, L1-L2 outages, DG

_{a}-DG

_{c}outages, DG

_{a}-DG

_{b}outages, and FT. If the F-ZVCA is employed, it is expected that all NU

^{ESRT}occurrences are kept within a single cluster with zero miscoordination.

#### 4.5. Simulation Results: IEEE 14 Bus System

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

µ | Set of main/backup DOCRs pairs | OT^{S} | Overall tripping time of main DOCRs (s) |

M | Mth main DOCR; M ∈ {1, 2,…,Q} | ${\lambda}_{}^{S}$ | Average ratio of the fault current of main DOCR to their backup relays (A) |

JB | Jth backup DOCR (each main DOCR can have j backup relays) | ${DOT}_{}^{S-C}$ | Difference between OT^{S} and OT^{C} |

S | The network structure (topology) | $\delta {T}_{}^{MJB,S}$ | Difference between the tripping times of main and its backup DOCRs (s) |

N | Number of equipment assumed for outage | OCC | Number of permutations resulting from N-2 events |

K | Number of previously failed equipment | ${I}_{FC}^{\mathsf{\mu},\mathit{S}}$ | Fault current of main/backup DOCRs (A) |

NB | Number of network buses | ${I}_{FC}^{\mathit{M},\mathit{S}}$ | Fault current of main DOCR (A) |

$TSM{P}^{\mathrm{\mu},S}$ | Time setting multiplier parameter of DOCR (Seconds (s)) | ${I}_{FC}^{\mathit{JB},\mathit{S}}$ | Fault current of backup DOCRs (A) |

${CSP}_{}^{\mathsf{\mu},\mathit{S}}$ | Current setting parameter of DOCR (Ampere (A)) | ${I}_{FCmin}^{\mathsf{\mu},\mathit{S}}$ | Minimum fault current of main/backup DOCRs (A) |

${T}^{\mathrm{\mu},S}$ | Tripping time of DOCR (s) | ${CTR}_{}^{M}$ | Current transformer ratio of main DOCR |

${T}_{}^{JB,S}$ | Tripping time of backup DOCR/DOCRs (s) | ${CTP}_{}^{M}$ | Number of primary winding turns of current transformer (CT) for main DOCR |

${T}_{}^{M,S}$ | Tripping time of main DOCR (s) | ${CTS}_{}^{M}$ | Number of secondary winding turns of CT for main DOCR |

${NU}_{}^{ESRT}$ | Number of ‘N-2 events’ resulting from the ESRT | ${I}_{Pickup}^{M}$ | Maximum network current of main DOCR assumed for the procedure of achieving the CSP practical bound (A) |

${I}_{Loadmax}^{\mathsf{\mu},\mathrm{S}}$ | Maximum network current of main DOCR (A) | OT^{C} | Time center points of F-ZVCA (s) |

${I}_{CSP}^{M}$ | Current passing through the secondary winding of CT for main DOCR (A) | ${\lambda}_{}^{C}$ | Fault current center locations of F-ZVCA |

${PS}_{}^{M}$ | Percentage of CT winding turns for main DOCR | $\omega {\lambda}_{}^{S-C}$ | Fuzzy parameter of F-ZVCA |

NAB | Number of all network buses | ${D\omega}_{}^{S-C}$ | Comparison index of F-ZVCA |

## Appendix A. (TESKO2 Network Data)

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

3.498 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | Gas-engine | Generator type |

0.2935 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | 2.2 MVA | Rated capacity |

0.274 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 20 kV | Rated voltage |

0.0419 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ | 50 Hz | Frequency |

0.1531 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.93 lag | Nominal Power factor |

Round-rotor | Rotor type | Directly grounded | Earthling type |

1200 rpm | Nominal speed | 0.9 lag–0.9 lead | Power factor range |

4-wire YN | Winding connection |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

50 Hz | Frequency | 20 Kv | Voltage |

0.0258 pu | $\mathrm{Impedance}\text{}\mathrm{ratio},\text{}\frac{{R}_{0}}{{X}_{0}}$ | PQ | Corresponding Bus type |

1 pu | $\mathrm{Impedance}\text{}\mathrm{ratio},\text{}\frac{{X}_{0}}{{X}_{1}}$ | 1 pu | $\mathrm{Impedance}\text{}\mathrm{ratio},\text{}\frac{{Z}_{2}}{{Z}_{1}}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

0.11 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | Cable | Cable/OHL |

0.13 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 20 kV | Rated voltage |

0.11 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.815 kA | Rated current |

0.13 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Aluminum | Conductor material | 0.268 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0.25 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

L5 | L4 | L3 | L2 | L1 | Line |
---|---|---|---|---|---|

0.32 | 0.277 | 0.268 | 0.731 | 0.856 | Length |

Feature/Value | Parameter |
---|---|

Balance | Balance/Unbalance |

2.125 MW | Active power |

1.733 Mvar | Reactive power |

Feature/Value | Parameter |
---|---|

Balance | Balance/Unbalance |

1.113 MW | Active power |

0.71 Mvar | Reactive power |

Feature/Value | Parameter |
---|---|

Balance | Balance/Unbalance |

0.325 MW | Active power |

0.21 Mvar | Reactive power |

## Appendix B. (IEEE Std. 399-1997 Network Data)

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

2 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | Gas-engine | Generator type |

0.3 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | 15.6 MVA | Rated capacity |

0.128 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 13.8 kV | Rated voltage |

0.057 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ | 60 Hz | Frequency |

0.112 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.8 lag | Power factor |

Round-rotor | Rotor type | Directly grounded | Earthling type |

1200 rpm | Nominal speed | 0.8 lag–0.8 lead | Power factor range |

4-wire YN | Winding connection |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

2 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | Gas-engine | Generator type |

0.3 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | 12.5 MVA | Rated capacity |

0.128 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 13.8 kV | Rated voltage |

0.058 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ | 60 Hz | Frequency |

0.128 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.8 lag | Nominal Power factor |

Round-rotor | Rotor type | Directly grounded | Earthling type |

1200 rpm | Nominal speed | 0.8 lag–0.8 lead | Power factor range |

4-wire YN | Winding connection |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

60 Hz | Frequency | 69 Kv | Voltage |

0.0454 pu | $\mathrm{Impedance}\text{}\mathrm{ratio},\text{}\frac{{R}_{0}}{{X}_{0}}$ | PV | Corresponding Bus type |

1 pu | $\mathrm{Impedance}\text{}\mathrm{ratio},\text{}\frac{{X}_{0}}{{X}_{1}}$ | 1 pu | $\mathrm{Impedance}\text{}\mathrm{ratio},\text{}\frac{{Z}_{2}}{{Z}_{1}}$ |

**Table A11.**Technical data of lines (i.e., L1, L2, L6… L20) (per km) for the IEEE Std. 399-1997 system.

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

0.12 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | Cable | Cable/OHL |

0.144 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 13.8 kV | Rated voltage |

0.12 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.315 kA | Rated current |

0.144 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 60 Hz | Frequency |

Aluminum | Conductor material | 0.265 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0.24 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

0.462 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | Overhead line (OHL) | Cable/OHL |

0.217 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 69 kV | Rated voltage |

0.462 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.251 kA | Rated current |

0.217 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 60 Hz | Frequency |

Aluminum | Conductor material | 0 | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

L20 | L19 | L18 | L17 | L16 | L15 | L14 | L13 | L12 | L11 | L10 | L9 | L8 | L7 | L6 | L5 | L4 | L3 | L2 | L1 | Line |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0.55 | 0.19 | 0.19 | 0.15 | 0.15 | 0.36 | 0.18 | 0.29 | 0.14 | 0.2 | 0.09 | 0.14 | 0.06 | 0.003 | 0.05 | 3.048 | 0.6 | 3.048 | 0.6 | 0.6 | Length |

## Appendix C. (IEEE 14 Bus Network Data)

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

3.498 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | Gas-engine | Generator type |

0.2935 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | 2.2 MVA | Rated capacity |

0.274 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 33 kV | Rated voltage |

0.0419 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ | 50 Hz | Frequency |

0.1531 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.93 lag | Nominal Power factor |

Round-rotor | Rotor type | Directly grounded | Earthling type |

1200 rpm | Nominal speed | 0.9 lag–0.9 lead | Power factor range |

4-wire YN | Winding connection |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

50 Hz | Frequency | 132 Kv | Voltage |

2 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | SL | Corresponding Bus type |

0.3 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | YN | Winding connection |

0.2 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 0.8 | Power factor |

0.2 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.1 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

50 Hz | Frequency | 132 Kv | Voltage |

2 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | PV | Corresponding Bus type |

0.3 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | YN | Winding connection |

0.2 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 0.8 | Power factor |

0.2 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.1 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

50 Hz | Frequency | 132 Kv | Voltage |

2 pu | $\mathrm{Synchronous}\text{}\mathrm{reactance},\text{}{X}_{d}$ | PV | Corresponding Bus type |

0.3 pu | $\mathrm{Transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime}$ | 23.4 Mvar | Reactive power |

0.2 pu | $\mathrm{Sub}-\mathrm{transient}\text{}\mathrm{reactance},\text{}{X}_{d}^{\prime \prime}$ | 0.8 | Power factor |

0.2 pu | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 0.1 pu | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

YN | Winding connection |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

2.785 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

1.338 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

2.785 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

1.338 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

1.418 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

0.72 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

1.418 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

0.72 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

2.176 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

2.405 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

2.176 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

2.405 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

3.789 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

1.861 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

3.789 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

1.861 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

2.166 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

1.034 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

2.166 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

1.034 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

2.091 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

0.893 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

2.091 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

0.893 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

0.92 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | OHL | Cable/OHL |

0.346 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{1}$ | 33 kV | Rated voltage |

0.92 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{2}$ | 1 kA | Rated current |

0.346 Ohm | $\mathrm{Negative}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{2}$ | 50 Hz | Frequency |

Copper | Conductor material | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{resistance},\text{}{R}_{0}$ |

80 °C | Max. Operational Temperature | 0 Ohm | $\mathrm{Zero}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{0}$ |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

0.252 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | YN/yn0 | Connection |

0.5 pu | Leakage reactance | 132 kV/33 kV | Rated voltage |

0.5 pu | Leakage resistance | 50 Hz | Frequency |

Feature/Value | Parameter | Feature/Value | Parameter |
---|---|---|---|

0.556 Ohm | $\mathrm{Positive}-\mathrm{sequence}\text{}\mathrm{reactance},\text{}{X}_{1}$ | YN/yn0 | Connection |

0.5 pu | Leakage reactance | 132 kV/33 kV | Rated voltage |

0.5 pu | Leakage resistance | 50 Hz | Frequency |

YN/yn0 | Connection | 50 Hz | Frequency |

Bus | EV | VFT | EN | |
---|---|---|---|---|

Bus 1 | UB | 1.314 | 1.104 | L1-L3 |

LB | 1.058 | L2-DG1 | ||

Bus 2 | UB | 1.177 | 1.070 | Generator1-T1 |

LB | 1.070 | FT | ||

Bus 3 | UB | 1.187 | 1.087 | Generator1-L8 |

LB | 1.087 | FT | ||

Bus 4 | UB | 1.269 | 1.092 | L1-L3 |

LB | 1.058 | DG1-DG2 | ||

Bus 5 | UB | 1.301 | 1.113 | L3-L6 |

LB | 1.051 | T1-T2 | ||

Bus 6 | UB | 1.151 | 1.075 | Generator1-T2 |

LB | 1 | T1-T2 | ||

Bus 7 | UB | 1.150 | 1.078 | Generator1-T2 |

LB | 1.078 | FT |

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Reference | Year | Dual-Setting | Double Inverse | MSGs | HDOCR | SCD | N-SCD | SSSCD | FT | N-1 Contingency | N-2 Contingencies | Islanded Mode | PCAC | MOOP | Optimization Algorithm |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

[1] | 2020 | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | - |

[2] | 2020 | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | - |

[3] | 2021 | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✔ | ✘ | - |

[5] | 2022 | ✘ | ✘ | ✔ | ✘ | ✔ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ | - |

[6] | 2018 | ✘ | ✘ | ✔ | ✘ | ✔ | ✘ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ | ✘ | GA |

[7] | 2021 | ✘ | ✘ | ✔ | ✘ | ✔ | ✘ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ | ✔ | - |

[9] | 2019 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | IFOA |

[10] | 2020 | ✘ | ✘ | ✘ | ✘ | ✔ | ✔ | ✔ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | IMFOA |

[11] | 2021 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | ICOA |

[12] | 2022 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | ISOA |

[13] | 2022 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | CSCTOA |

[14] | 2018 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | GA |

[16] | 2023 | ✔ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | GA |

[17] | 2022 | ✔ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | GA/GWOA |

[18] | 2023 | ✘ | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | PSO |

[19] | 2019 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | HWOA |

[20] | 2021 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ | GA-LP/PSO-LP |

[21] | 2019 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ | ✔ | GA-LP |

[22] | 2020 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | HSAOA-LP |

[23] | 2019 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | HACOA |

[24] | 2021 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | HGBO |

[25] | 2022 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | HGBO |

[26] | 2021 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | HOBL-FOCTOA |

[27] | 2019 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✔ | IPA |

[28] | 2021 | ✘ | ✘ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | FA-Target Remedy |

[29] | 2023 | ✘ | ✘ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | GA-Fuzzy Logic |

[30] | 2020 | ✘ | ✘ | ✘ | ✘ | ✔ | ✔ | ✔ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | GA-PSO-DE |

[31] | 2022 | ✘ | ✘ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ | ✘ | ✘ | ✘ | FA-LP |

[32] | 2022 | ✘ | ✘ | ✘ | ✘ | ✔ | ✘ | ✘ | ✔ | ✔ | ✘ | ✔ | ✘ | ✘ | HGA-LP |

Bus | B1 | B5 | B6 | B7 | B8 | B9 | B10 | B 11 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | |

EV | 0.95 | 1 | 0.94 | 1 | 0.94 | 0.99 | 0.94 | 1 | 0.94 | 0.99 | 0.94 | 1 | 0.94 | 0.99 | 0.94 | 1 |

VFT | 1 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | ||||||||

EN | L11-DG1 | FT | L11-DG1 | L13-L9 | L11-DG1 | FT | L11-DG1 | FT | L11-DG1 | FT | L11-DG1 | FT | L11-DG1 | FT | L11-DG1 | L9-Load5 |

Bus | B 12 | B13 | B14 | B15 | B 16 | B17 | B18 | B19 | ||||||||

LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | LB | UB | |

EV | 0.94 | 0.99 | 0.94 | 1 | 0.94 | 0.99 | 0.94 | 1 | 0.94 | 0.99 | 0.95 | 1 | 0.95 | 1 | 0.95 | 1 |

VFT | 0.99 | 0.99 | 1 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | ||||||||

EN | L11-DG1 | FT | L11-DG1 | L7-Load9 | L11-DG1 | FT | L11-DG1 | L1-Load10 | L11-DG1 | L20-Load11 | L6-DG2 | L1-Load12 | L6-DG2 | L1-Load13 | L6-DG2 | L1-Load14 |

Relay | R1 | R2 | R3 | R4 | R5 | R6 | R7 | R8 | R9 | R10 | R11 | R12 | R13 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CSP | 1.8 | 1.8 | 1.8 | 1.8 | 1.4 | 1.4 | 1.4 | 1.4 | 1.4 | 2 | 2 | 1.6 | 1.6 | |

TSMP | Cluster 1 | 0.39 | 0.427 | 0.399 | 0.427 | 0.691 | 0.381 | 0.49 | 0.847 | 0.49 | 0.876 | 0.509 | 0.595 | 0.529 |

Cluster 2 | 0.392 | 0.454 | 0.391 | 0.456 | 1 | 0.583 | 0.84 | 0.964 | 0.05 | 0.994 | 0.052 | 0.113 | 0.667 | |

Cluster 3 | 0.471 | 0.05 | 0.471 | 0.05 | 0.557 | 0.999 | 0.356 | 0.45 | 0.05 | 0.667 | 0.05 | 0.285 | 0.508 | |

Relay | R14 | R15 | R16 | R17 | R18 | R19 | R20 | R21 | R22 | R23 | R24 | R25 | R26 | |

CSP | 1.6 | 1.6 | 1.6 | 1.6 | 1.4 | 1 | 1 | 1.8 | 1.4 | 1.4 | 0.8 | 1.8 | 1.6 | |

TSMP | Cluster 1 | 0.645 | 0.973 | 0.429 | 0.516 | 0.178 | 0.491 | 0.492 | 0.462 | 0.978 | 0.354 | 0.475 | 0.475 | 0.475 |

Cluster 2 | 0.142 | 0.91 | 0.053 | 0.488 | 0.08 | 0.285 | 0.267 | 0.276 | 0.488 | 0.488 | 0.292 | 0.266 | 0.278 | |

Cluster 3 | 0.388 | 0.829 | 0.393 | 0.482 | 0.051 | 0.649 | 0.05 | 0.392 | 0.482 | 0.337 | 0.393 | 0.361 | 0.366 |

System | O-TSMP | MTT | ATT | ATTO | OF | MET | IMA | TOFE |
---|---|---|---|---|---|---|---|---|

Cluster 1 | 14.015 | 28.332 | 28.229 | 1.085 | 314 | 1.8 | 20 | 715 |

Cluster 2 | 11.281 | 25.892 | 25.892 | 1.078 | 240 | 8.1 | 85 | 3010 |

Cluster 3 | 10.147 | 21.22 | 21.22 | 0.884 | 184.5 | 1.8 | 19 | 687 |

Relay | R_{a} | R_{b} | R_{c} | R_{d} | R_{e} | R_{f} | R_{g} | R_{h} | R_{i} | R_{x} | All Relays | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CSP | 1.8 | 1.8 | 1.8 | 1.8 | 1.4 | 1.4 | 1.4 | 1.4 | 1.4 | 2 |
O-TSMP | ATT | MTT | ATTO | OF | MET | IMA | |

TSMP | IPA | 0.465 | 0.407 | 0.418 | 0.572 | 0.41 | 0.409 | 0.413 | 0.571 | 0.998 | 0.573 | 5.236 | 9.432 | 12.284 | 0.943 | 1300.8 | 1.1 | 11 |

SAOA | 0.128 | 0.067 | 0.389 | 0.486 | 0.216 | 0.067 | 0.266 | 0.259 | 0.547 | 0.366 | 2.796 | 6.915 | 11.198 | 0.691 | 555.9 | 100 | 1777 | |

PSOA | 0.05 | 0.146 | 0.185 | 1 | 0.15 | 0.05 | 0.214 | 0.17 | 0.311 | 0.246 | 2.522 | 4.562 | 5.863 | 0.456 | 262.9 | 25.5 | 263 |

**Table 6.**Time results of previous studies compared to the proposed method of this paper in the IEEE 14 bus system.

STATE | The Proposed Method of This Paper without N-K-ESRT | The Proposed Method of This Paper with N-K-ESRT | [1] | [5] | [6] | [12] |
---|---|---|---|---|---|---|

1 | TT = 7.765, O-TMSP = 2.013 | TT = 7.765, O-TMSP = 2.013 | TT = 8.366 | TT = 14.062 | - | TT = 11.058 |

2 | ATT = 15.125, O-TMSP = 4.321 | ATT = 12.598, O-TMSP = 3.487 | - | ATT = 19.969 | O-TMSP = 10.48 | - |

3 | ATT = 20.213, O-TMSP = 6.558 | ATT = 18.517, O-TMSP = 5.771 | ATT = 49.783 | - | - | - |

4 | - | ATT = 21.098, O-TMSP = 6.884 | - | - | - | - |

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**MDPI and ACS Style**

Zand, H.K.; Mazlumi, K.; Bagheri, A.; Hashemi-Dezaki, H.
Optimal Protection Scheme for Enhancing AC Microgrids Stability against Cascading Outages by Utilizing Events Scale Reduction Technique and Fuzzy Zero-Violation Clustering Algorithm. *Sustainability* **2023**, *15*, 15550.
https://doi.org/10.3390/su152115550

**AMA Style**

Zand HK, Mazlumi K, Bagheri A, Hashemi-Dezaki H.
Optimal Protection Scheme for Enhancing AC Microgrids Stability against Cascading Outages by Utilizing Events Scale Reduction Technique and Fuzzy Zero-Violation Clustering Algorithm. *Sustainability*. 2023; 15(21):15550.
https://doi.org/10.3390/su152115550

**Chicago/Turabian Style**

Zand, Hossein Karimkhan, Kazem Mazlumi, Amir Bagheri, and Hamed Hashemi-Dezaki.
2023. "Optimal Protection Scheme for Enhancing AC Microgrids Stability against Cascading Outages by Utilizing Events Scale Reduction Technique and Fuzzy Zero-Violation Clustering Algorithm" *Sustainability* 15, no. 21: 15550.
https://doi.org/10.3390/su152115550