1 Introduction
2 Problem formulation
2.1 Boundaries on DOCRs characteristics and operating time of zone-2
2.2 Coordination constraints
3 Proposed optimization algorithm
3.1 Particle swarm optimization (PSO)
3.2 Genetic algorithm (GA)
3.3 GWO grey wolf optimizer (GWO)
3.4 Teaching learning-based optimization (TLBO)
3.5 Marine predators algorithm (MPA)
3.6 Flow direction algorithm (FDA)
3.7 African vultures optimization algorithm (AVOA)
3.8 Gorilla troops optimizer (GTO)
4 Results and discussion
4.1 8-bus network
Relay no. | PSO | GA | ||||||
---|---|---|---|---|---|---|---|---|
Ip (A) | TDS | Tp(s) | Tzone-2 (s) | Ip (A) | TDS | Tp(s) | TZ2 (s) | |
1 | 247.13 | 0.13 | 0.37 | 0.72 | 232.34 | 0.14 | 0.40 | 0.79 |
2 | 466.18 | 0.19 | 0.52 | 0.80 | 306.83 | 0.25 | 0.59 | 0.87 |
3 | 292.21 | 0.16 | 0.44 | 0.70 | 214.50 | 0.20 | 0.50 | 0.76 |
4 | 266.73 | 0.10 | 0.33 | 0.59 | 203.00 | 0.14 | 0.38 | 0.65 |
5 | 236.57 | 0.06 | 0.23 | 0.70 | 187.03 | 0.08 | 0.29 | 0.72 |
6 | 271.34 | 0.19 | 0.45 | 0.72 | 314.72 | 0.19 | 0.47 | 0.75 |
7 | 130.59 | 0.26 | 0.50 | 0.82 | 207.53 | 0.23 | 0.52 | 0.85 |
8 | 205.26 | 0.18 | 0.38 | 0.65 | 212.59 | 0.23 | 0.50 | 0.79 |
9 | 197.90 | 0.07 | 0.24 | 0.69 | 157.22 | 0.10 | 0.32 | 0.74 |
10 | 351.85 | 0.09 | 0.33 | 0.60 | 291.92 | 0.12 | 0.40 | 0.67 |
11 | 207.79 | 0.19 | 0.45 | 0.70 | 222.36 | 0.21 | 0.51 | 0.77 |
12 | 328.68 | 0.23 | 0.56 | 0.82 | 357.73 | 0.24 | 0.60 | 0.88 |
13 | 438.96 | 0.07 | 0.27 | 0.76 | 211.02 | 0.16 | 0.44 | 0.80 |
14 | 230.46 | 0.21 | 0.49 | 0.83 | 189.69 | 0.25 | 0.54 | 0.88 |
Objective function | 15.67 | 17.37 |
Relay no. | TLBO | GWO | ||||||
---|---|---|---|---|---|---|---|---|
Ip (A) | TDS | Tp(s) | Tzone-2 (s) | Ip (A) | TDS | Tp(s) | TZ2 (s) | |
1 | 449.46 | 0.06 | 0.23 | 0.74 | 229.43 | 0.14 | 0.40 | 0.82 |
2 | 473.11 | 0.19 | 0.54 | 0.83 | 180.81 | 0.30 | 0.60 | 0.87 |
3 | 314.77 | 0.16 | 0.47 | 0.90 | 89.96 | 0.27 | 0.50 | 0.74 |
4 | 477.75 | 0.08 | 0.36 | 0.66 | 296.06 | 0.10 | 0.35 | 0.62 |
5 | 126.52 | 0.12 | 0.33 | 0.65 | 192.54 | 0.08 | 0.27 | 0.68 |
6 | 479.37 | 0.11 | 0.32 | 0.58 | 410.84 | 0.17 | 0.47 | 0.76 |
7 | 314.16 | 0.17 | 0.44 | 0.79 | 310.84 | 0.18 | 0.48 | 0.83 |
8 | 479.93 | 0.10 | 0.30 | 0.58 | 287.85 | 0.16 | 0.38 | 0.66 |
9 | 230.42 | 0.06 | 0.21 | 0.72 | 199.65 | 0.07 | 0.24 | 0.72 |
10 | 478.28 | 0.07 | 0.29 | 0.56 | 425.52 | 0.08 | 0.31 | 0.59 |
11 | 313.48 | 0.14 | 0.41 | 0.66 | 436.15 | 0.13 | 0.41 | 0.68 |
12 | 450.80 | 0.18 | 0.51 | 0.77 | 137.86 | 0.30 | 0.55 | 0.80 |
13 | 479.99 | 0.06 | 0.23 | 0.71 | 410.15 | 0.08 | 0.30 | 0.75 |
14 | 80.25 | 0.31 | 0.52 | 0.82 | 249.63 | 0.20 | 0.48 | 0.82 |
Objective function | 15.13 | 16.08 |
Relay no. | MPA | AVOA | ||||||
---|---|---|---|---|---|---|---|---|
Ip (A) | TDS | Tp(s) | Tzone-2 (s) | Ip (A) | TDS | Tp(s) | TZ2 (s) | |
1 | 429.15 | 0.09 | 0.34 | 0.79 | 191.18 | 0.17 | 0.44 | 0.81 |
2 | 325.01 | 0.24 | 0.59 | 0.88 | 303.74 | 0.25 | 0.61 | 0.88 |
3 | 276.21 | 0.19 | 0.51 | 0.77 | 318.10 | 0.18 | 0.52 | 0.79 |
4 | 315.14 | 0.12 | 0.40 | 0.76 | 275.69 | 0.13 | 0.42 | 0.72 |
5 | 184.30 | 0.10 | 0.32 | 0.76 | 126.65 | 0.12 | 0.35 | 0.68 |
6 | 478.81 | 0.15 | 0.46 | 0.75 | 441.79 | 0.17 | 0.48 | 0.78 |
7 | 175.39 | 0.25 | 0.53 | 0.87 | 318.64 | 0.18 | 0.48 | 0.84 |
8 | 126.05 | 0.27 | 0.49 | 0.77 | 462.06 | 0.14 | 0.41 | 0.78 |
9 | 161.81 | 0.10 | 0.31 | 0.83 | 110.14 | 0.15 | 0.40 | 0.75 |
10 | 281.23 | 0.12 | 0.40 | 0.67 | 327.16 | 0.13 | 0.45 | 0.74 |
11 | 121.27 | 0.26 | 0.52 | 0.77 | 479.89 | 0.15 | 0.52 | 0.81 |
12 | 410.34 | 0.23 | 0.61 | 0.90 | 405.77 | 0.23 | 0.61 | 0.88 |
13 | 417.29 | 0.09 | 0.33 | 0.82 | 304.47 | 0.12 | 0.38 | 0.81 |
14 | 223.89 | 0.23 | 0.53 | 0.88 | 316.73 | 0.19 | 0.49 | 0.85 |
Objective function | 17.55 | 17.65 |
Relay no. | FDA | GTO | ||||||
---|---|---|---|---|---|---|---|---|
Ip (A) | TDS | Tp(s) | Tzone-2 (s) | Ip (A) | TDS | Tp(s) | TZ2 (s) | |
1 | 303.79 | 0.11 | 0.34 | 0.77 | 392.35 | 0.08 | 0.28 | 0.78 |
2 | 473.42 | 0.20 | 0.57 | 0.86 | 470.48 | 0.21 | 0.58 | 0.87 |
3 | 161.84 | 0.22 | 0.50 | 0.75 | 225.43 | 0.21 | 0.52 | 0.78 |
4 | 217.14 | 0.13 | 0.38 | 0.64 | 210.70 | 0.14 | 0.41 | 0.67 |
5 | 186.73 | 0.08 | 0.27 | 0.67 | 215.05 | 0.09 | 0.32 | 0.71 |
6 | 422.27 | 0.14 | 0.40 | 0.90 | 169.39 | 0.25 | 0.51 | 0.79 |
7 | 289.45 | 0.18 | 0.47 | 0.90 | 242.10 | 0.21 | 0.50 | 0.84 |
8 | 436.93 | 0.16 | 0.46 | 0.88 | 465.82 | 0.14 | 0.41 | 0.71 |
9 | 188.05 | 0.07 | 0.25 | 0.72 | 144.83 | 0.11 | 0.33 | 0.67 |
10 | 328.20 | 0.10 | 0.34 | 0.61 | 474.71 | 0.09 | 0.37 | 0.66 |
11 | 475.32 | 0.13 | 0.43 | 0.70 | 468.62 | 0.13 | 0.46 | 0.73 |
12 | 255.93 | 0.24 | 0.55 | 0.90 | 474.55 | 0.19 | 0.54 | 0.82 |
13 | 248.38 | 0.13 | 0.38 | 0.75 | 252.58 | 0.13 | 0.38 | 0.83 |
14 | 320.00 | 0.17 | 0.46 | 0.85 | 280.86 | 0.19 | 0.47 | 0.81 |
Objective function | 16.68 | 16.72 |
Relay pairs | PSO | GA | TLBO | GWO | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Tp(s) | Tb (s) | CTI | Tp(s) | Tb (s) | CTI | Tp(s) | Tb (s) | CTI | Tp(s) | Tb (s) | CTI | ||
1 | 6 | 0.37 | 0.57 | 0.20 | 0.40 | 0.60 | 0.20 | 0.23 | 0.43 | 0.20 | 0.40 | 0.62 | 0.22 |
2 | 1 | 0.52 | 0.77 | 0.25 | 0.59 | 0.82 | 0.23 | 0.54 | 0.74 | 0.20 | 0.60 | 0.81 | 0.20 |
2 | 7 | 0.52 | 0.72 | 0.20 | 0.59 | 0.79 | 0.20 | 0.54 | 0.74 | 0.20 | 0.60 | 0.80 | 0.20 |
3 | 2 | 0.44 | 0.64 | 0.20 | 0.50 | 0.70 | 0.20 | 0.47 | 0.67 | 0.20 | 0.50 | 0.70 | 0.20 |
4 | 3 | 0.33 | 0.53 | 0.20 | 0.38 | 0.59 | 0.20 | 0.36 | 0.56 | 0.20 | 0.35 | 0.56 | 0.21 |
5 | 4 | 0.23 | 0.43 | 0.20 | 0.29 | 0.49 | 0.20 | 0.33 | 0.53 | 0.20 | 0.27 | 0.47 | 0.20 |
6 | 5 | 0.45 | 0.70 | 0.26 | 0.47 | 0.71 | 0.25 | 0.32 | 0.66 | 0.34 | 0.47 | 0.68 | 0.21 |
6 | 14 | 0.45 | 0.76 | 0.31 | 0.47 | 0.80 | 0.34 | 0.32 | 0.71 | 0.39 | 0.47 | 0.75 | 0.28 |
7 | 5 | 0.50 | 0.70 | 0.20 | 0.52 | 0.72 | 0.20 | 0.44 | 0.66 | 0.22 | 0.48 | 0.68 | 0.20 |
7 | 13 | 0.50 | 0.76 | 0.26 | 0.52 | 0.81 | 0.29 | 0.44 | 0.71 | 0.27 | 0.48 | 0.80 | 0.32 |
8 | 7 | 0.38 | 0.72 | 0.34 | 0.50 | 0.79 | 0.29 | 0.30 | 0.74 | 0.44 | 0.38 | 0.80 | 0.42 |
8 | 9 | 0.38 | 0.69 | 0.31 | 0.50 | 0.78 | 0.28 | 0.30 | 0.73 | 0.42 | 0.38 | 0.68 | 0.30 |
9 | 10 | 0.24 | 0.44 | 0.20 | 0.32 | 0.52 | 0.20 | 0.21 | 0.41 | 0.20 | 0.24 | 0.44 | 0.20 |
10 | 11 | 0.33 | 0.53 | 0.20 | 0.40 | 0.60 | 0.20 | 0.29 | 0.49 | 0.20 | 0.31 | 0.51 | 0.20 |
11 | 12 | 0.45 | 0.65 | 0.20 | 0.51 | 0.71 | 0.20 | 0.41 | 0.61 | 0.20 | 0.41 | 0.62 | 0.21 |
12 | 13 | 0.56 | 0.76 | 0.20 | 0.60 | 0.80 | 0.20 | 0.51 | 0.71 | 0.20 | 0.55 | 0.80 | 0.25 |
12 | 14 | 0.56 | 0.76 | 0.20 | 0.60 | 0.80 | 0.20 | 0.51 | 0.71 | 0.20 | 0.55 | 0.75 | 0.20 |
13 | 8 | 0.27 | 0.49 | 0.22 | 0.44 | 0.64 | 0.20 | 0.23 | 0.43 | 0.20 | 0.30 | 0.50 | 0.20 |
14 | 1 | 0.49 | 0.77 | 0.28 | 0.54 | 0.82 | 0.28 | 0.52 | 0.75 | 0.22 | 0.48 | 0.81 | 0.33 |
14 | 9 | 0.49 | 0.69 | 0.20 | 0.54 | 0.78 | 0.24 | 0.52 | 0.73 | 0.20 | 0.48 | 0.68 | 0.20 |
Relay pairs | MPA | AVOA | FDA | GTO | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Tp(s) | Tb (s) | CTI | Tp(s) | Tb (s) | CTI | Tp(s) | Tb (s) | CTI | Tp(s) | Tb (s) | CTI | ||
1 | 6 | 0.34 | 0.62 | 0.28 | 0.44 | 0.64 | 0.20 | 0.34 | 0.54 | 0.20 | 0.28 | 0.63 | 0.35 |
2 | 1 | 0.59 | 1.05 | 0.46 | 0.61 | 0.83 | 0.22 | 0.57 | 0.79 | 0.22 | 0.58 | 0.78 | 0.20 |
2 | 7 | 0.59 | 0.80 | 0.20 | 0.61 | 0.81 | 0.20 | 0.57 | 0.77 | 0.20 | 0.58 | 0.78 | 0.20 |
3 | 2 | 0.51 | 0.71 | 0.20 | 0.52 | 0.72 | 0.20 | 0.50 | 0.70 | 0.20 | 0.52 | 0.72 | 0.20 |
4 | 3 | 0.40 | 0.60 | 0.20 | 0.42 | 0.62 | 0.20 | 0.38 | 0.58 | 0.20 | 0.41 | 0.61 | 0.20 |
5 | 4 | 0.32 | 0.54 | 0.21 | 0.35 | 0.56 | 0.21 | 0.27 | 0.48 | 0.21 | 0.32 | 0.52 | 0.20 |
6 | 5 | 0.46 | 0.80 | 0.34 | 0.48 | 0.71 | 0.23 | 0.40 | 0.67 | 0.26 | 0.51 | 0.88 | 0.37 |
6 | 14 | 0.46 | 0.81 | 0.35 | 0.48 | 0.81 | 0.33 | 0.40 | 0.75 | 0.34 | 0.51 | 0.74 | 0.23 |
7 | 5 | 0.53 | 0.80 | 0.27 | 0.48 | 0.71 | 0.23 | 0.47 | 0.67 | 0.20 | 0.50 | 0.88 | 0.39 |
7 | 13 | 0.53 | 0.88 | 0.35 | 0.48 | 0.81 | 0.33 | 0.47 | 0.75 | 0.28 | 0.50 | 0.74 | 0.25 |
8 | 7 | 0.49 | 0.80 | 0.30 | 0.41 | 0.81 | 0.39 | 0.46 | 0.77 | 0.31 | 0.41 | 0.78 | 0.37 |
8 | 9 | 0.49 | 0.77 | 0.28 | 0.41 | 0.81 | 0.40 | 0.46 | 0.69 | 0.23 | 0.41 | 0.76 | 0.34 |
9 | 10 | 0.31 | 0.51 | 0.20 | 0.40 | 0.60 | 0.20 | 0.25 | 0.45 | 0.20 | 0.33 | 0.53 | 0.20 |
10 | 11 | 0.40 | 0.60 | 0.20 | 0.45 | 0.65 | 0.20 | 0.34 | 0.54 | 0.20 | 0.37 | 0.57 | 0.20 |
11 | 12 | 0.52 | 0.72 | 0.20 | 0.52 | 0.72 | 0.20 | 0.43 | 0.63 | 0.20 | 0.46 | 0.66 | 0.20 |
12 | 13 | 0.61 | 0.88 | 0.27 | 0.61 | 0.81 | 0.20 | 0.55 | 0.75 | 0.20 | 0.54 | 0.74 | 0.20 |
12 | 14 | 0.61 | 0.81 | 0.20 | 0.61 | 0.81 | 0.20 | 0.55 | 0.75 | 0.20 | 0.54 | 0.74 | 0.20 |
13 | 8 | 0.33 | 0.61 | 0.28 | 0.38 | 0.58 | 0.20 | 0.38 | 0.64 | 0.25 | 0.38 | 0.58 | 0.20 |
14 | 1 | 0.53 | 1.05 | 0.52 | 0.49 | 0.83 | 0.34 | 0.46 | 0.79 | 0.33 | 0.47 | 0.78 | 0.32 |
14 | 9 | 0.53 | 0.78 | 0.24 | 0.49 | 0.81 | 0.32 | 0.46 | 0.69 | 0.23 | 0.47 | 0.76 | 0.29 |
Relay pairs | PSO | GA | |||||||
---|---|---|---|---|---|---|---|---|---|
Fault1 | Fault 2 | Fault 3 | Fault1 | Fault 2 | Fault 3 | ||||
CTI1 | CTI2 | CTI3 | CTI4 | CTI1 | CTI2 | CTI3 | CTI4 | ||
1 | 6 | 0.20 | 0.36 | 0.51 | 0.24 | 0.20 | 0.35 | 0.55 | 0.25 |
2 | 1 | 0.25 | 0.20 | 0.79 | 0.51 | 0.23 | 0.20 | 0.84 | 0.49 |
2 | 7 | 0.20 | 0.29 | 0.67 | 0.27 | 0.20 | 0.26 | 0.76 | 0.32 |
3 | 2 | 0.20 | 0.36 | 0.54 | 0.22 | 0.20 | 0.36 | 0.60 | 0.22 |
4 | 3 | 0.20 | 0.37 | 0.45 | 0.22 | 0.20 | 0.37 | 0.51 | 0.22 |
5 | 4 | 0.20 | 0.36 | 0.37 | 0.25 | 0.20 | 0.36 | 0.43 | 0.24 |
6 | 5 | 0.26 | 0.26 | 1.07 | 5.27 | 0.25 | 0.25 | 0.90 | 1.40 |
6 | 14 | 0.31 | 0.38 | 0.76 | 0.55 | 0.34 | 0.41 | 0.81 | 0.56 |
7 | 5 | 0.20 | 0.20 | 5.53 | 20.00 | 0.20 | 0.20 | 1.80 | 20.00 |
7 | 13 | 0.26 | 0.25 | 3.83 | 20.00 | 0.29 | 0.29 | 1.19 | 20.00 |
8 | 7 | 0.34 | 0.43 | 0.72 | 0.56 | 0.29 | 0.35 | 0.82 | 0.62 |
8 | 9 | 0.31 | 0.31 | 1.04 | 5.83 | 0.28 | 0.24 | 1.01 | 1.82 |
9 | 10 | 0.20 | 0.35 | 0.39 | 0.28 | 0.20 | 0.35 | 0.47 | 0.28 |
10 | 11 | 0.20 | 0.37 | 0.45 | 0.21 | 0.20 | 0.37 | 0.52 | 0.21 |
11 | 12 | 0.20 | 0.37 | 0.58 | 0.22 | 0.20 | 0.36 | 0.64 | 0.22 |
12 | 13 | 0.20 | 0.20 | 0.87 | 0.78 | 0.20 | 0.20 | 0.80 | 0.37 |
12 | 14 | 0.20 | 0.27 | 0.72 | 0.30 | 0.20 | 0.27 | 0.76 | 0.29 |
13 | 8 | 0.22 | 0.38 | 0.42 | 0.23 | 0.20 | 0.35 | 0.58 | 0.23 |
14 | 1 | 0.28 | 0.23 | 1.38 | 20.00 | 0.28 | 0.25 | 1.40 | 20.00 |
14 | 9 | 0.20 | 0.20 | 3.08 | 20.00 | 0.24 | 0.20 | 1.80 | 20.00 |
Relay pairs | TLBO | GWO | |||||||
---|---|---|---|---|---|---|---|---|---|
Fault1 | Fault 2 | Fault 3 | Fault1 | Fault 2 | Fault 3 | ||||
CTI1 | CTI2 | CTI3 | CTI4 | CTI1 | CTI2 | CTI3 | CTI4 | ||
1 | 6 | 0.20 | 0.36 | 0.37 | 0.25 | 0.22 | 0.37 | 0.57 | 0.29 |
2 | 1 | 0.20 | 0.20 | 0.95 | 1.25 | 0.20 | 0.22 | 0.83 | 0.47 |
2 | 7 | 0.20 | 0.24 | 0.73 | 0.36 | 0.20 | 0.23 | 0.79 | 0.38 |
3 | 2 | 0.20 | 0.36 | 0.57 | 0.23 | 0.20 | 0.37 | 0.60 | 0.22 |
4 | 3 | 0.20 | 0.54 | 0.49 | 0.21 | 0.21 | 0.39 | 0.47 | 0.21 |
5 | 4 | 0.20 | 0.33 | 0.51 | 0.36 | 0.20 | 0.35 | 0.41 | 0.27 |
6 | 5 | 0.34 | 0.33 | 0.72 | 0.80 | 0.21 | 0.22 | 0.87 | 1.43 |
6 | 14 | 0.39 | 0.51 | 0.67 | 0.51 | 0.28 | 0.35 | 0.76 | 0.53 |
7 | 5 | 0.22 | 0.21 | 1.04 | 20.00 | 0.20 | 0.20 | 1.83 | 20.00 |
7 | 13 | 0.27 | 0.26 | 11.48 | 20.00 | 0.32 | 0.27 | 2.86 | 20.00 |
8 | 7 | 0.44 | 0.48 | 0.81 | 0.91 | 0.42 | 0.45 | 0.88 | 0.93 |
8 | 9 | 0.42 | 0.42 | 1.36 | 20.00 | 0.30 | 0.34 | 1.03 | 6.41 |
9 | 10 | 0.20 | 0.35 | 0.38 | 0.32 | 0.20 | 0.35 | 0.39 | 0.31 |
10 | 11 | 0.20 | 0.37 | 0.41 | 0.21 | 0.20 | 0.37 | 0.44 | 0.22 |
11 | 12 | 0.20 | 0.37 | 0.53 | 0.22 | 0.21 | 0.39 | 0.54 | 0.21 |
12 | 13 | 0.20 | 0.20 | 0.85 | 0.93 | 0.25 | 0.20 | 0.90 | 0.76 |
12 | 14 | 0.20 | 0.32 | 0.64 | 0.24 | 0.20 | 0.27 | 0.71 | 0.31 |
13 | 8 | 0.20 | 0.35 | 0.37 | 0.25 | 0.20 | 0.35 | 0.44 | 0.22 |
14 | 1 | 0.22 | 0.22 | 20.00 | 20.00 | 0.33 | 0.34 | 1.37 | 20.00 |
14 | 9 | 0.20 | 0.20 | 20.00 | 20.00 | 0.20 | 0.24 | 3.17 | 20.00 |
Primary (DOCR) | Backup zone-2 | PSO | GA | TLBO | GWO |
---|---|---|---|---|---|
Fault 4 | Fault 4 | Fault 4 | Fault 4 | ||
CTI 5 | CTI 5 | CTI 5 | CTI 5 | ||
1 | 1 | 0.20 | 0.20 | 0.37 | 0.27 |
2 | 2 | 0.20 | 0.20 | 0.20 | 0.20 |
3 | 3 | 0.20 | 0.29 | 0.37 | 0.20 |
4 | 4 | 0.35 | 0.20 | 0.21 | 0.20 |
5 | 5 | 0.20 | 0.20 | 0.20 | 0.29 |
6 | 6 | 0.20 | 0.21 | 0.20 | 0.20 |
7 | 7 | 0.20 | 0.28 | 0.20 | 0.20 |
8 | 8 | 0.33 | 0.20 | 0.20 | 0.20 |
9 | 9 | 0.20 | 0.20 | 0.39 | 0.37 |
10 | 10 | 0.20 | 0.20 | 0.20 | 0.21 |
11 | 11 | 0.20 | 0.21 | 0.20 | 0.20 |
12 | 12 | 0.33 | 0.20 | 0.20 | 0.20 |
13 | 13 | 0.20 | 0.20 | 0.34 | 0.28 |
14 | 14 | 0.20 | 0.20 | 0.20 | 0.20 |
Relay pairs | MPA | AVOA | |||||||
---|---|---|---|---|---|---|---|---|---|
Fault1 | Fault 2 | Fault 3 | Fault1 | Fault 2 | Fault 3 | ||||
CTI1 | CTI2 | CTI3 | CTI4 | CTI1 | CTI2 | CTI3 | CTI4 | ||
1 | 6 | 0.28 | 0.42 | 0.58 | 0.35 | 0.20 | 0.34 | 0.60 | 0.28 |
2 | 1 | 0.46 | 0.20 | 1.33 | 1.71 | 0.22 | 0.20 | 0.84 | 0.44 |
2 | 7 | 0.20 | 0.27 | 0.76 | 0.31 | 0.20 | 0.23 | 0.80 | 0.38 |
3 | 2 | 0.20 | 0.37 | 0.61 | 0.22 | 0.20 | 0.36 | 0.62 | 0.21 |
4 | 3 | 0.20 | 0.37 | 0.53 | 0.22 | 0.20 | 0.36 | 0.55 | 0.22 |
5 | 4 | 0.21 | 0.44 | 0.49 | 0.30 | 0.21 | 0.37 | 0.51 | 0.29 |
6 | 5 | 0.34 | 0.30 | 1.01 | 1.57 | 0.23 | 0.20 | 0.78 | 0.70 |
6 | 14 | 0.35 | 0.42 | 0.82 | 0.60 | 0.33 | 0.37 | 0.85 | 0.66 |
7 | 5 | 0.27 | 0.22 | 1.97 | 20.00 | 0.23 | 0.20 | 1.13 | 20.00 |
7 | 13 | 0.35 | 0.28 | 3.38 | 20.00 | 0.33 | 0.33 | 1.56 | 20.00 |
8 | 7 | 0.30 | 0.37 | 0.82 | 0.60 | 0.39 | 0.42 | 0.89 | 0.91 |
8 | 9 | 0.28 | 0.34 | 1.02 | 1.99 | 0.40 | 0.33 | 0.94 | 1.13 |
9 | 10 | 0.20 | 0.35 | 0.46 | 0.27 | 0.20 | 0.34 | 0.57 | 0.31 |
10 | 11 | 0.20 | 0.38 | 0.51 | 0.20 | 0.20 | 0.35 | 0.59 | 0.24 |
11 | 12 | 0.20 | 0.37 | 0.65 | 0.23 | 0.20 | 0.36 | 0.65 | 0.21 |
12 | 13 | 0.27 | 0.21 | 1.00 | 0.85 | 0.20 | 0.20 | 0.84 | 0.48 |
12 | 14 | 0.20 | 0.27 | 0.77 | 0.30 | 0.20 | 0.24 | 0.78 | 0.33 |
13 | 8 | 0.28 | 0.44 | 0.54 | 0.28 | 0.20 | 0.40 | 0.53 | 0.27 |
14 | 1 | 0.52 | 0.26 | 13.03 | 20.00 | 0.34 | 0.31 | 1.27 | 20.00 |
14 | 9 | 0.24 | 0.30 | 1.88 | 20.00 | 0.32 | 0.25 | 1.33 | 20.00 |
Relay pairs | FDA | GTO | |||||||
---|---|---|---|---|---|---|---|---|---|
Fault1 | Fault 2 | Fault 3 | Fault1 | Fault 2 | Fault 3 | ||||
CTI1 | CTI2 | CTI3 | CTI4 | CTI1 | CTI2 | CTI3 | CTI4 | ||
1 | 6 | 0.20 | 0.56 | 0.49 | 0.26 | 0.35 | 0.51 | 0.56 | 0.38 |
2 | 1 | 0.22 | 0.20 | 0.85 | 0.59 | 0.20 | 0.20 | 0.92 | 0.87 |
2 | 7 | 0.20 | 0.33 | 0.75 | 0.35 | 0.20 | 0.26 | 0.76 | 0.33 |
3 | 2 | 0.20 | 0.36 | 0.60 | 0.23 | 0.20 | 0.36 | 0.62 | 0.23 |
4 | 3 | 0.20 | 0.37 | 0.50 | 0.21 | 0.20 | 0.37 | 0.53 | 0.22 |
5 | 4 | 0.21 | 0.37 | 0.42 | 0.26 | 0.20 | 0.36 | 0.46 | 0.24 |
6 | 5 | 0.26 | 0.26 | 0.83 | 1.34 | 0.37 | 0.20 | 1.24 | 3.04 |
6 | 14 | 0.34 | 0.45 | 0.78 | 0.66 | 0.23 | 0.29 | 0.76 | 0.51 |
7 | 5 | 0.20 | 0.20 | 1.68 | 20.00 | 0.39 | 0.22 | 3.46 | 20.00 |
7 | 13 | 0.28 | 0.28 | 1.20 | 20.00 | 0.25 | 0.33 | 1.21 | 20.00 |
8 | 7 | 0.31 | 0.44 | 0.83 | 0.75 | 0.37 | 0.43 | 0.83 | 0.74 |
8 | 9 | 0.23 | 0.26 | 0.99 | 3.51 | 0.34 | 0.26 | 0.94 | 1.52 |
9 | 10 | 0.20 | 0.36 | 0.40 | 0.28 | 0.20 | 0.33 | 0.51 | 0.36 |
10 | 11 | 0.20 | 0.36 | 0.47 | 0.23 | 0.20 | 0.36 | 0.50 | 0.22 |
11 | 12 | 0.20 | 0.46 | 0.55 | 0.20 | 0.20 | 0.36 | 0.58 | 0.22 |
12 | 13 | 0.20 | 0.20 | 0.74 | 0.40 | 0.20 | 0.28 | 0.74 | 0.39 |
12 | 14 | 0.20 | 0.31 | 0.72 | 0.33 | 0.20 | 0.26 | 0.71 | 0.31 |
13 | 8 | 0.25 | 0.50 | 0.59 | 0.33 | 0.20 | 0.33 | 0.53 | 0.27 |
14 | 1 | 0.33 | 0.31 | 1.80 | 20.00 | 0.32 | 0.32 | 3.83 | 20.00 |
14 | 9 | 0.23 | 0.26 | 2.44 | 20.00 | 0.29 | 0.20 | 1.56 | 20.00 |
Primary (DOCR) | Backup Zone-2 | MPA | AVOA | FDA | GTO |
---|---|---|---|---|---|
Fault 4 | Fault 4 | Fault 4 | Fault 4 | ||
CTI 5 | CTI 5 | CTI 5 | CTI 5 | ||
1 | 1 | 0.25 | 0.21 | 0.28 | 0.35 |
2 | 2 | 0.21 | 0.20 | 0.20 | 0.20 |
3 | 3 | 0.20 | 0.20 | 0.20 | 0.20 |
4 | 4 | 0.28 | 0.22 | 0.20 | 0.20 |
5 | 5 | 0.28 | 0.20 | 0.27 | 0.23 |
6 | 6 | 0.20 | 0.20 | 0.41 | 0.20 |
7 | 7 | 0.20 | 0.20 | 0.28 | 0.20 |
8 | 8 | 0.20 | 0.27 | 0.32 | 0.20 |
9 | 9 | 0.38 | 0.20 | 0.35 | 0.20 |
10 | 10 | 0.20 | 0.20 | 0.20 | 0.20 |
11 | 11 | 0.20 | 0.20 | 0.20 | 0.20 |
12 | 12 | 0.21 | 0.20 | 0.29 | 0.20 |
13 | 13 | 0.31 | 0.27 | 0.22 | 0.30 |
14 | 14 | 0.21 | 0.20 | 0.25 | 0.20 |
Methods | Objective function (s) |
---|---|
PSO | 15.67 |
GA | 17.37 |
TLBO | 15.13 |
GWO | 16.08 |
MPA | 17.55 |
AVOA | 17.65 |
FDA | 16.68 |
GTO | 16.71 |