This research proposes a more advanced way to address Combined Economic Emission Dispatch (CEED) concerns. Economic Load Dispatch (ELD) and Economic Emission Dispatch (EED) have been implemented to reduce generating unit fuel costs and emissions. When both economics and emission targets are taken into account, the dispatch of an aggregate cost-effective emission challenge emerges. This research affords a mathematical modeling-based analytical technique for solving economic, emission, and collaborative economic and emission dispatch problems with only one goal. This study takes into account both the fuel cost target and the environmental impact of emissions. This bi-intention CEED problem is converted to a solitary goal function using a price penalty factor technique. In this case, a metaheuristic and an environment-inspired, intelligent Spider Monkey Optimization technique (SMO) are used to address the CEED dilemma. By following the generator’s scheduling process, the SMO method is used to regulate the output from the power generation system in terms of pollution and fuel cost. The Fission-Fusion social (FFS) structure of spider monkeys promotes them to utilize a global optimization method known as SMO during foraging behaviour. The emphasis is mostly on lowering the cost of generation and pollution in order to improve the efficiency of the power system and handle dispatch problems with constraints. The economic dispatch has been remedied, and the improved result demonstrates that the system’s performance is stable and flexible in real time. Finally, the system’s output demonstrates that the system has improved in resolving CEED difficulties. When compared to earlier investigations, the proposed model’s findings have improved. As the generating units, wind and solar are used to explore the CEED crisis in the IEEE 30 bus system.

The economic dispatch (ED) problem has become a critical mission in terms of power system operational and strategic planning. Because the power supplier’s primary aim is to provide the finest economic strategy capable of convincing and fulfilling the demand for loads. Due to the consumption of fossil fuels during power generation, a thermal power station emits poisonous gases that pollute the environment. The thermal power station releases poisonous gases and damages the environment. Hence, it is important to minimize the use of these gases and the cost of fuel as much as possible for the welfare of society.

Over the last few decades, there have been numerous studies and techniques geared toward solving ELD issues. ELD problems are solved using techniques that have been around for a while, such as the gradient method, the lambda iteration method [

Optimum power flow (OPF) provides the economic operation and balance of power and load flow situations were considered. While actual load flows for implementation and cost-effective power operation are examined in the OPF, social wellbeing is not given attention in this method [

A substitute strategy is to make use of Evolutionary Algorithms (EA). EA is regarded as highly successful in dealing with the ELD problem since it can process non-linear objective functions. A Genetic Algorithm [

The literature illustrates Simulated Annealing (SA) [

The cost efficiency transmit was resolved by means of differential evolution (DE) and has proven to be successful in finding the best answer globally [

The Firefly algorithm (FA) replicates the clever technique of the firefly to solve engineering issues in the best way possible. A Flashing light based on an objective function is designed for optimization. This algorithm can be used to optimize or reduce difficulties. The Flower pollen algorithm (FPA) is a smart algorithm with an easy optimization procedure [

SMO is a modern population-based flock intelligence method. When used to address universal optimization problems, it performs admirably. Hence, a new optimization strategy using spider monkeys was employed to resolve CEED problems. The functions and limits help to improve the system source. As a result, the system results are examined, and an optimum output is achieved with reduced processing time and costs.

Renewable energy systems with CEED problem mitigation have been studied in a number of reviews. Wind turbine generation is a function of wind speed. Different wind flows in this research are evaluated during the 24 h and this electricity is directly injected into the new generation power system. Solar power production is dependent on sunlight and is available throughout the day. Solar energy is estimated on the basis of the projected irradiation and directly introduced into the power system during its availability [

The CEED’s twin goals are to reduce generation fuel costs while also reducing emissions of poisonous gases such as sulphur oxides (SOx), carbon oxides (COx), and nitrogen oxides (NOx). To integrate these bi-intentions into one target, a price penalty factor is employed. For generation cost, quadratic cost equations are considered, and the VPL (valve point loading) effect is employed. The typical quadratic function of genuine power is observed and presented in the following equations for emissions.

where F is the total fuel cost in $/hr, F1 is the total cost of generation in $/hr, F2 is the total emission cost in ton/hr, h is the price penalty factor used to transform the bi intention into a single intention in $/ton, NG is the total number of generators used. The actual price performance coefficients are α, β, γ. The real power coefficients a, b, c, d and e are employed in the emission function.

To merge both objectives into one aim, the price penalty factor is applied. Emissions are assessed in ton/hr and converted into dollars/hr by increasing their price penalty factor. The final goal is therefore measured in dollars/hr. The price penalty factor of the ith generator is the highest quantity of production and the highest emission rate in the ith generation.

Subject to Inequality boundary conditions:

Equality load flow constraint:

where NT is the total number of transformers, NB–maximum number of buses allowed; MVAi–the i-th transmission line’s MVA flow; Vi–the voltage level of the i-th bus; Ti–i-th transformer’s tap position; PL and QL denote real and reactive power loss, respectively. The real and reactive power demand for load is denoted by PD and QD. Pgi, Qgi: real and reactive power generation of the generator.

α, β, γ are the fuel cost coefficients and ζ, λ are the valve point effect coefficients in the objective functions. The coefficients α, β, γ, ζ and λ are expressed in dollar/h, dollar/MWh, dollar/MW2 h, dollar/h and dollar/MWh, respectively. t/h, t/MWh, t/MW2 h, t/h and t/MWh are the respective units of emission coefficients a, b, c, d and e.

The objective of swarm intelligence is to solve optimization disputes using a metaheuristic approach that is based on social species’ collective behavior. Social animals use their abilities to learn socially to tackle complex tasks. Earlier research has revealed that Swarm Intelligence algorithms have a strong potential to tackle the genuine difficulty in optimization. Over the last few years, the algorithms have included Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO), Firefly Algorithm (FA), Flower Pollination Algorithm (FPA), and so on.

SMO is a population based algorithm with the following important phases. A Detailed description of SMOIA is delineated here.

Initially, a population of N spider monkeys is represented by a D-dimensional series SMi where i = 1, 2,…, N and i symbolises the ith spider monkey. Each Spider Monkey (SM) symbolizes a possible outcome of the crisis under consideration. Each SMi is set up as follows:

In this case, SMminj and SMmaxj are the limits of SMi in the jth vector, and U (0, 1) is a random number in the range (0, 1).

The spider Monkey renews its present location in this phase, providing a fitness value based on the observations of the local leader and group mates. If the current location’s fitness measure is higher than the prior location’s, SM replaces it with the most recent one. As a result, the ith SM in the kth local group modifies its position.

Here, SMij defines ith SM in jth dimension, whereas LLkj shows a relationship to the kth leader of the local assembly location in jth dimension. SMrj characterizes rth SM which is indiscriminately picked from kth group such that r ≠ i in j th dimension.

The Global Leader (GLP) segment starts on following the completion of the Local Leader phase. In GLP, the entire SM updates its position using the awareness of the global leader, the skills of neighbouring SM, and its own individual determination. The location renewal equation is as follows for this phase:

Which GLj is a global leader’s jth dimension, and j ∈ {1, 2,…, D} is the random index chosen. The position of SMi is updated in this phase on the basis of a probability probi which is determined using its fitness. The superior candidate has more opportunities to improve itself. Probability probi can be evaluated using the equation

where fitness_{i} is the ith SM’s fitness value. In addition, it calculates and compares the suitability of the recently formed location of the SM with the old one and takes the better one.

The location of the global leader is reorganized in this phase by using greedy choices in the population, i.e., the updated location of the global leader is the SM with the best fitness in the population. Furthermore, the location of the global leader is ensured to see if it is updated, and if it isn’t, the global limit count is increased by one.

The location of the local leader is restructured in this phase by using greedy choices in that group, i.e., the updated location of the local leader is the SM with the finest fitness in that group. The local leader’s new location is then compared to the old one, and if the local leader has not been reorganized, the local limit count is increased by one.

If the local leader location is not modified up to a pre-calculated limit known as the Local Leader Limit through an equation based on perturbation rate, the local leader location is updated in one of two ways: by random initialization or by blending information gained via global and local leaders (pr).

Evidently, the modified dimension of this SM is mesmerised by the global leader and opposes the local leader, as seen in

The location of the global leader is examined in this phase, and if no adjustment is made to the prearranged iteration limit, known as the Global Leader Limit, the population is separated into tiny crowds by the local leader. Initially, the population is divided into two classes, then three, four, and so on until the higher bounce, known as the group of greatest number (GN), is reached. In the intervening time, for freshly generated subclasses, local leaders are chosen using the LL approach. As a result, the suggested algorithm is modelled after the spider monkeys’ fission-fusion structure.

Maximum Group (MG)

Local Leader Limit (LLL) must be D × N

Global Leader Limit (GLL) must be ɛ [N/2, 2 × N]

Perturbation rate (pr) ɛ [0.1, 0.8] where N is the group size.

The SMO mathematical model is simulated using MATLAB. The typical IEEE 30 bus test case was utilized to optimize the spider monkey algorithm. It has 6 steam generators, 4 transformers and 41 transmission lines. The system base MVA is 100 MVA. There are 15 control variables: 4 for tap positions, 6 for bus voltages and 5 for real power generations. The challenge of CEED is to reduce the cost of fuel and emissions.

Gen. no | P limit (MW) | Cost coefficients | Emission coefficients | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

min | max | a | b | c | d | e | α | β | γ | ||||

1 | 50 | 200 | 0 | 2.0 | 0.00375 | 18 | 0.037 | 4.091 | −5.554 | 6.490 | 2e−4 | 2.857 | |

2 | 20 | 80 | 0 | 1.75 | 0.01750 | 16 | 0.038 | 2.543 | −6.047 | 5.638 | 5e−4 | 3.333 | |

3 | 15 | 50 | 0 | 1.0 | 0.06250 | 14 | 0.040 | 4.258 | −5.094 | 4.586 | 1e−6 | 8.000 | |

4 | 10 | 35 | 0 | 3.25 | 0.00834 | 12 | 0.045 | 5.426 | −3.550 | 3.380 | 2e−3 | 2.000 | |

5 | 10 | 30 | 0 | 3.0 | 0.02500 | 13 | 0.042 | 4.258 | −5.094 | 4.586 | 1e−6 | 8.000 | |

6 | 12 | 40 | 0 | 3.0 | 0.02500 | 13.25 | 0.041 | 6.131 | −5.555 | 5.151 | 1e−5 | 6.667 |

The six generator buses should have at least one slack bus for the reference location. The decision variables are the P and V of the generator buses, as well as the transformer tap locations. These decision variables must fall inside the boundaries of the test case. The generator’s dependent variable Q must be checked and kept within the limitations specified. The fuel cost for generating plants is calculated in $/hr using generation cost coefficients, while the emissions of generating plants are calculated in tonnes per hour using emission coefficients.

The results are addressed in terms of valve point loading and without valve point loading. The input-output characteristics of generating units are affected by valve point loading, making fuel prices nonlinear and unpredictable. This has been considered while addressing load dispatch challenges, but not when arranging unit committment. The info yield attributes are viable without valve point loading, bringing about a direct and steady fuel cost.

For the specified set of decision factors, the power flow of the power system with the standard NR load flow is calculated. This power flow re-estimates the decision variable. The population size of 20 spider monkeys, LLL, GLL, and pr is first assumed. The fitness of the spider monkey is computed based on an estimation of the individual spider monkey’s distance from food sources.

Methods | Total emissions (ton/h) | |
---|---|---|

Without valve point loading | With valve point loading | |

SFLA | 0.2063 | 0.2265 |

GA | 0.2117 | 0.2271 |

PSO | 0.2096 | 0.2269 |

FFA-mGA | 0.2067 | 0.2213 |

SMO | 0.2058 | 0.2119 |

Gen. (MW) | Without valve point loading | With valve point loading | |||||||
---|---|---|---|---|---|---|---|---|---|

GA-OPF | SFLA | Hybrid MPSO-SFLA | PSO | FFA-mGA | SMO | PSO | FFA-mGA | SMO | |

PG1 | 174.83 | 181.06 | 180.53 | 180.23 | 179.16 | 176.61 | 162.31 | 148.03 | 177.27 |

PG2 | 48.88 | 52.17 | 52.09 | 52.09 | 47.18 | 49.19 | 43.21 | 60.95 | 49.22 |

PG3 | 23.78 | 22.47 | 22.78 | 22.81 | 23.06 | 21.50 | 30.55 | 27.39 | 21.52 |

PG4 | 20.2 | 15.35 | 15.49 | 15.62 | 18.29 | 22.64 | 12.74 | 19.25 | 22.66 |

PG5 | 13.14 | 10 | 10 | 10 | 12.36 | 10.40 | 22.65 | 17.25 | 10.42 |

PG6 | 12.22 | 12.07 | 12.05 | 12.21 | 12.50 | 12.03 | 20.54 | 18.61 | 12.01 |

Loss (MW) | 11.65 | 11.72 | 11.54 | 10.56 | 10.16 | 9.66 | 11.24 | 10.09 | 9.71 |

Fuel Cost in $/hr | 803.92 | 802.21 | 801.75 | 801.89 | 801.11 | 800.52 | 886.88 | 884.14 | 873.54 |

The combined minimization of generating cost and emission is shown in

Gen. (MW) | Excluding valve point loading | Including valve point loading | |||||||
---|---|---|---|---|---|---|---|---|---|

PSO | DE-OPF | MDE-OPF | GSA | FFA-mGA | SMO | PSO | FFA-mGA | SMO | |

PG1 | 25.555 | 28.242 | 24.439 | 22.019 | 19.930 | 24.148 | 8.421 | 7.193 | 5.971 |

PG2 | 36.931 | 35.291 | 34.922 | 34.362 | 32.634 | 36.960 | 37.844 | 34.331 | 38.609 |

PG3 | 61.019 | 52.798 | 56.287 | 59.433 | 55.042 | 57.312 | 68.132 | 68.562 | 48.349 |

PG4 | 68.561 | 73.278 | 75.815 | 74.744 | 75.335 | 75.925 | 64.899 | 80.494 | 87.359 |

PG5 | 54.623 | 55.859 | 55.277 | 52.551 | 60.236 | 51.921 | 53.571 | 54.415 | 66.428 |

PG6 | 39.002 | 40.358 | 39.180 | 42.636 | 42.594 | 39.413 | 52.527 | 40.890 | 39.004 |

Emission (ton/hr) | 0.224 | 0.213 | 0.212 | 0.209 | 0.206 | 0.204 | 0.2213 | 0.2185 | 0.2164 |

Fuel Cost in $/hr | 614.88 | 613.87 | 612.85 | 612.74 | 612.11 | 611.67 | 628.08 | 620.15 | 618.31 |

The influence of wind and solar on CEED-SMO with and without VPL is shown in

Gen. (MW) | Excluding valve point loading | Including valve point loading | ||
---|---|---|---|---|

Without wind and solar | With wind and solar | Without wind and solar | With wind and solar | |

PG1 | 24.148 | 31.754 | 5.971 | 30.349 |

PG2 | 36.960 | 34.221 | 38.609 | 36.056 |

PG3 | 57.312 | 34.246 | 48.349 | 26.362 |

PG4 | 75.925 | 26.642 | 87.359 | 19.961 |

PG5 | 51.921 | 42.380 | 66.428 | 30.256 |

PG6 | 39.413 | 40.138 | 39.004 | 38.367 |

Wind power injection (MW) | - | 60 | - | 60 |

Solar power injection (MW) | - | 50 | - | 50 |

Emission (ton/hr) | 0.204 | 0.201 | 0.2164 | 0.2061 |

Fuel cost in $/hr | 611.67 | 475.99 | 618.31 | 442.15 |

The emission in ton/hr in CEED-SMO is shown in

Solar irradiation and wind power are also used in this study, which is available 24 h a day. In

Hours | PG1 (MW) | PG2 (MW) | PG3 (MW) | PG4 (MW) | PG5 (MW) | PG6 (MW) | Wind (MW) | Solar (MW) | Loss (MW) | Gen. cost ($/h) | Emission (ton/hr) |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 28.09 | 20.35 | 15.00 | 10.48 | 10.00 | 12.00 | 100.00 | 0 | 32.12 | 245.14 | 0.2300 |

2 | 80.26 | 20.93 | 15.00 | 10.00 | 10.00 | 12.00 | 30.00 | 0 | 24.87 | 370.47 | 0.2392 |

3 | 49.93 | 20.00 | 15.00 | 10.00 | 10.00 | 12.00 | 57.60 | 0 | 16.84 | 292.69 | 0.2296 |

4 | 35.67 | 20.00 | 15.00 | 10.00 | 10.00 | 12.00 | 63.00 | 0 | 13.20 | 259.59 | 0.2293 |

5 | 56.41 | 21.45 | 17.07 | 10.00 | 11.42 | 12.21 | 44.00 | 0 | 25.22 | 323.82 | 0.2287 |

6 | 72.59 | 21.05 | 16.96 | 10.00 | 10.00 | 12.08 | 34.00 | 0 | 38.12 | 357.20 | 0.2347 |

7 | 55.28 | 20.00 | 15.00 | 10.00 | 10.05 | 12.13 | 60.00 | 0 | 39.17 | 306.14 | 0.2303 |

8 | 82.48 | 22.55 | 16.10 | 10.00 | 11.75 | 12.00 | 34.00 | 6.99 | 31.67 | 417.76 | 0.2388 |

9 | 78.92 | 24.38 | 19.28 | 13.47 | 10.56 | 12.52 | 16.00 | 31.47 | 32.25 | 544.89 | 0.2346 |

10 | 70.14 | 30.92 | 15.21 | 12.49 | 11.13 | 12.49 | 42.00 | 33.57 | 39.67 | 553.84 | 0.2304 |

11 | 132.55 | 36.28 | 18.43 | 11.35 | 11.79 | 12.61 | 2.00 | 48.96 | 75.79 | 778.60 | 0.2830 |

12 | 126.29 | 28.69 | 21.34 | 10.00 | 13.25 | 12.25 | 11.00 | 55.95 | 67.29 | 775.60 | 0.2749 |

13 | 124.63 | 34.21 | 17.90 | 10.00 | 10.00 | 12.00 | 15.00 | 48.96 | 63.03 | 734.05 | 0.2742 |

14 | 111.49 | 34.03 | 15.00 | 10.00 | 10.00 | 12.00 | 26.00 | 47.56 | 53.70 | 681.17 | 0.2602 |

15 | 117.34 | 35.00 | 21.54 | 11.26 | 10.00 | 13.61 | 27.20 | 41.97 | 58.60 | 710.03 | 0.2632 |

16 | 164.43 | 39.47 | 23.97 | 16.52 | 11.29 | 12.28 | 16.00 | 8.39 | 89.60 | 760.65 | 0.3370 |

17 | 158.23 | 39.70 | 23.02 | 10.13 | 10.00 | 12.25 | 24.00 | 0 | 81.37 | 677.30 | 0.3261 |

18 | 154.34 | 47.05 | 23.80 | 10.49 | 14.57 | 12.85 | 46.00 | 0 | 87.07 | 711.99 | 0.3157 |

19 | 79.90 | 32.05 | 15.22 | 10.07 | 10.56 | 12.00 | 150.00 | 0 | 65.89 | 402.12 | 0.2357 |

20 | 144.22 | 32.31 | 15.00 | 11.56 | 10.00 | 12.00 | 86.00 | 0 | 78.57 | 588.09 | 0.3038 |

21 | 133.86 | 34.45 | 15.00 | 10.00 | 10.00 | 12.00 | 72.00 | 0 | 67.75 | 557.47 | 0.2877 |

22 | 57.71 | 20.98 | 15.00 | 10.00 | 10.00 | 12.00 | 124.00 | 0 | 31.70 | 313.82 | 0.2306 |

23 | 18.75 | 20.00 | 15.00 | 10.00 | 10.00 | 12.00 | 156.20 | 0 | 24.84 | 222.31 | 0.2325 |

24 | 32.02 | 20.00 | 15.00 | 10.00 | 10.00 | 12.00 | 130.00 | 0 | 23.34 | 251.37 | 0.2297 |

The solar power perforation in the power system is depicted in

The estimated voltage magnitudes of all 30 buses, are within the minimum (0.95 per unit) and maximum limitations (1.05 per unit). The voltage limit equation is thus met. The IEEE 30 bus standard test scenario employs four transformers. Within the limits of the provided objective function, the smart SMO algorithm determined the best transformer tap point.

In this paper, the spider monkey optimization algorithm is used to unravel CEED with and without valve point loading. A single objective function is created by combining the cost of generation with the reduction of emissions. An IEEE standard test scenario is used to validate the proposed algorithm. When constraints are taken into account, the results show that the proposed SMO method is preferable in terms of achieving optimal results. The spider monkey optimization algorithm has produced excellent convergence properties when compared to other methods. Wind power and solar power are being recognized as renewable energies. Solar and wind power are used when they are available, and dedicated thermal generators are used to meet the remaining net demand. After the wind and solar power is included along with the thermal generating unit, 22.19% of generating cost is reduced without valve point loading and 28.49% of cost is reduced with valve point loading. Similarly 1.47% of emission is reduced without valve point loading and 4.76% of emission is reduced with valve point loading. This method reduces the cost and emissions of the power system’s generation. The initial population selection is crucial for the most optimal solution, which is one of SMOIA’s drawbacks. The mutation process isn’t available, and there are only a few search alternatives. Although a larger population demands more time to find the ideal solution, the recommended SMO approach handles the CEED problem better and produces superior results when compared to previous algorithms. In future, hybrid metaheuristics can be designed to improve performance.