Combined Economic and Emission Dispatch (CEED) task forms multi-objective optimization problems to be resolved to minimize emission and fuel costs. The disadvantage of the conventional method is its incapability to avoid falling in local optimal, particularly when handling nonlinear and complex systems. Metaheuristics have recently received considerable attention due to their enhanced capacity to prevent local optimal solutions in addressing all the optimization problems as a black box. Therefore, this paper focuses on the design of an improved sand cat optimization algorithm based CEED (ISCOA-CEED) technique. The ISCOA-CEED technique majorly concentrates on reducing fuel costs and the emission of generation units. Moreover, the presented ISCOA-CEED technique transforms the equality constraints of the CEED issue into inequality constraints. Besides, the improved sand cat optimization algorithm (ISCOA) is derived from the integration of traditional SCOA with the Levy Flight (LF) concept. At last, the ISCOA-CEED technique is applied to solve a series of 6 and 11 generators in the CEED issue. The experimental validation of the ISCOA-CEED technique ensured the enhanced performance of the presented ISCOA-CEED technique over other recent approaches.

Smart grids can be defined as a set of technologies, approaches, and concepts, permitting the integration of distribution, generation, and transmission, employing them into one internet by using information technology, advanced sensor measurement technologies, communications technologies, new energy technologies, computer technology, control technology [

The conventional ED issue was to determine the best active power allotment from every involved unit for reducing the whole working cost irrespective of emissions formed while fulfilling every unit and system limitation [

Recently, as a replacement to the conventional optimized techniques, many population-related nature-inspired heuristic approaches were widely presented to solve several complicated optimization issues in the real world like electric power system planning, feature selection, image processing, neural networks training, and robotic path planning. Certain heuristic techniques were reported in the literature for solving CEED issues [

This paper focuses on the design of an improved sand cat optimization algorithm based CEED (ISCOA-CEED) technique. The presented ISCOA-CEED technique majorly concentrates on the reduction of fuel cost and emission of generation units. Moreover, the presented ISCOA-CEED technique transforms the equality constraints of the CEED issue into inequality constraints. Besides, the improved sand cat optimization algorithm (ISCOA) is derived from the integration of traditional SCOA with the Levy Flight (LF) concept. At last, the ISCOA-CEED technique is applied to solve a series of 6 generators as well as 11 generators in the CEED issue. The experimental validation of the ISCOA-CEED technique ensured the enhanced performance of the presented ISCOA-CEED technique over other recent approaches. In short, the key contributions of the study are given as follows.

Develop a new ISCOA-CEED technique for reducing fuel cost and emission of generation units

Converts the equality constraints of the CEED issue into the inequality constraints

Propose an ISCOA by the integration of the conventional SCOA with the LF concept

Validate the proposed model on a series of 6 generators as well as 11 generators in the CEED issue

The author in [

Deb et al. [

The author in [

In this study, a new ISCOA-CEED technique has been developed for CEED. The presented ISCOA-CEED technique aims at the effectual reduction of fuel costs and the emission of generation units. Following, the presented ISCOA-CEED technique transforms the equality constraint of the CEED issues into an inequality constraint.

The solution to CEED problems can be accomplished by minimalizing the objective function (OF) incorporated with weighted sum methodology under the system constraint [

From the expression, the fuel cost rate ($/h) can be demonstrated with

The fuel cost function of every generator in the system might be characterized by the quadratic function of real power production:

Fossil-fuelled thermal unit causes atmospheric waste emission made up of gases and particles namely nitrogen oxide

In the minimization method, inequality and equality constraints should be fulfilled. In the presented model, inequality constraints are named generation capacity constraints and equality constraints are termed power balance.

The overall power production should cover the real power loss in transmission line

The communication loss of the system is denoted as loss coefficients

In

The real power output of all the generators is constrained using minimal

The SCOA technique is called based on a special feature of sand cat (SC) performance in the environment which is the size to classify lower-frequency sound [

The dimensional of the candidate matrix to a

The

For escaping the local optimal trap, all the SCs have a distinct sensitivity range

Therefore,

In which

At last, the

Once

In

Moreover, the ISCOA is derived from the integration of traditional SCOA with the LF concept. LF is a type of chaotic system where the leap magnitude can be defined using the likelihood function [

In

Now,

In

For the provided number of search iterations,

During this phase, the CSBO algorithm derives a fitness function to resolve the CEED problems. The fitness function for CEED is the total costs of the estimated system and the fitness function for effective EED is the total emitted emission evaluated as follows:

In

In

The proposed model is simulated using the MATLAB tool. The performance validation of the ISCOA-CEED model has been validated through two scenarios a test system with 11 generators and a test system with 6 generators. The test system with eleven generators involves emission level and quadratic cost functions. The power demand ranges from 1000 to 2500 MW. As well, the test system with six generators involves emission level and quadratic cost functions. The power demand ranges from 500 to 1100 MW.

Load | Fuel cost ($) | ||||
---|---|---|---|---|---|

Recursive | Improved recursive | PSO | Differential evaluation | ISCOA-CEED | |

500 | 30890 | 28432 | 26949 | 26408 | 25312 |

600 | 32873 | 30155 | 30099 | 29997 | 27422 |

700 | 38985 | 36879 | 34944 | 34926 | 30947 |

800 | 43977 | 42426 | 41891 | 37242 | 31406 |

900 | 45728 | 43945 | 42667 | 42554 | 40923 |

1000 | 54124 | 52384 | 51734 | 49996 | 48364 |

1100 | 59962 | 59116 | 58999 | 58033 | 54314 |

Load | Fuel emission (kg) | ||||
---|---|---|---|---|---|

Recursive | Improved recursive | PSO | Differential evaluation | ISCOA-CEED | |

500 | 154.57 | 152.37 | 140.88 | 124.09 | 94.45 |

600 | 189.03 | 177.40 | 175.28 | 169.99 | 158.19 |

700 | 228.00 | 195.48 | 193.71 | 186.58 | 185.56 |

800 | 271.48 | 264.61 | 256.60 | 253.96 | 228.77 |

900 | 325.00 | 321.63 | 307.84 | 285.79 | 274.74 |

1000 | 417.81 | 386.24 | 383.93 | 346.65 | 339.75 |

1100 | 479.49 | 478.27 | 473.56 | 442.58 | 421.34 |

In

Load | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 |
---|---|---|---|---|---|---|---|

P1 | 9.94 | 17.84 | 80.01 | 104.74 | 143.45 | 147.29 | 159.71 |

P2 | 37.57 | 43.14 | 109.05 | 148.42 | 202.16 | 219.65 | 237.14 |

P3 | 25.43 | 40.62 | 105.58 | 125.61 | 195.61 | 203.8 | 225.68 |

P4 | 17.38 | 38.58 | 86.06 | 112.26 | 165.71 | 198.41 | 207.25 |

P5 | 82.37 | 90.28 | 141.16 | 156.68 | 221.94 | 243.33 | 282.46 |

P6 | 82.91 | 95.33 | 146.99 | 198.22 | 243.74 | 256.62 | 289.57 |

Load | Fuel cost ($) | ||||
---|---|---|---|---|---|

Recursive | Improved recursive | PSO | Differential evaluation | ISCOA-CEED | |

1000 | 7560.54 | 6072.59 | 5467.60 | 5363.81 | 3633.09 |

1250 | 8738.53 | 7223.51 | 7011.49 | 6673.60 | 6606.49 |

1500 | 12178.87 | 10733.49 | 7731.90 | 7110.32 | 6724.36 |

1750 | 13053.54 | 12188.72 | 10852.45 | 10454.39 | 7466.58 |

2000 | 14288.96 | 12595.19 | 11449.69 | 11403.29 | 10770.98 |

2250 | 15401.53 | 14410.58 | 13171.69 | 12896.60 | 12116.40 |

2500 | 17614.45 | 16871.59 | 14823.51 | 13401.53 | 13270.60 |

Load | Fuel emission (kg) | ||||
---|---|---|---|---|---|

Recursive | Improved recursive | PSO | Differential evaluation | ISCOA-CEED | |

1000 | 120.04 | 113.09 | 106.20 | 97.53 | 61.68 |

1250 | 188.64 | 168.10 | 160.73 | 160.64 | 127.79 |

1500 | 287.49 | 242.61 | 227.08 | 221.83 | 189.3 |

1750 | 398.44 | 391.14 | 361.17 | 360.97 | 309.63 |

2000 | 545.40 | 517.83 | 490.54 | 487.10 | 439.78 |

2250 | 695.35 | 691.92 | 682.22 | 681.25 | 629.33 |

2500 | 951.13 | 937.76 | 933.35 | 930.19 | 877.67 |

In

Load | 1000 | 1250 | 1500 | 1750 | 2000 | 2250 | 2500 |
---|---|---|---|---|---|---|---|

P1 | 54.50 | 70.57 | 94.87 | 103.18 | 97.92 | 148.79 | 136.25 |

P2 | 47.72 | 54.89 | 80.07 | 83.88 | 87.34 | 101.78 | 136.02 |

P3 | 98.20 | 101.29 | 115.64 | 122.98 | 150.28 | 180.84 | 163.56 |

P4 | 61.55 | 85.26 | 100.49 | 109.45 | 102.08 | 152.09 | 139.42 |

P5 | 77.23 | 95.64 | 103.89 | 117.19 | 111.39 | 158.10 | 147.00 |

P6 | 105.79 | 147.83 | 167.36 | 200.31 | 226.04 | 256.97 | 304.37 |

P7 | 100.00 | 103.47 | 122.00 | 141.85 | 151.58 | 189.20 | 194.00 |

P8 | 100.45 | 112.15 | 141.44 | 175.29 | 162.92 | 200.91 | 213.41 |

P9 | 119.65 | 154.60 | 185.24 | 221.02 | 263.54 | 303.68 | 346.65 |

P10 | 107.05 | 151.54 | 182.72 | 206.79 | 235.35 | 289.87 | 345.35 |

P11 | 164.09 | 158.72 | 212.30 | 227.46 | 291.78 | 335.35 | 376.80 |

The computation time (CT) analysis of the ISCOA-CEED model under varying loads of six generators is given in

Load | Six generator time–(s) |
---|---|

500 | 6.62 |

600 | 7.00 |

700 | 8.93 |

800 | 10.02 |

900 | 10.57 |

1000 | 11.86 |

1100 | 12.03 |

The CT examination of the ISCOA-CEED approach under varying loads of eleven generators is demonstrated in

Load | Eleven generator time–(s) |
---|---|

1000 | 10.29 |

1250 | 10.98 |

1500 | 11.18 |

1750 | 13.85 |

2000 | 15.11 |

2250 | 16.80 |

2500 | 18.28 |

In this study, a new ISCOA-CEED technique has been developed for CEED. The presented ISCOA-CEED technique aims at the effectual reduction of fuel cost and emission of generation units. Following, the presented ISCOA-CEED technique transforms the equality constraint of the CEED issues into the inequality constraint. Moreover, the ISCOA is derived from the integration of traditional SCOA with the LF concept. Finally, the ISCOA-CEED technique is applied to solve a series of 6 generators as well as 11 generators in the CEED issue. The experimental validation of the ISCOA-CEED technique ensured the enhanced performance of the presented ISCOA-CEED technique over other recent approaches. Therefore, the ISCOA-CEED technique can resolve the CEED in a real-time environment. In the future, the presented ISCOA-CEED technique can be extended by the use of deep learning (DL) models.

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R77), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444). The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4340237DSR65.

The authors declare that they have no conflicts of interest to report regarding the present study.