DOI:10.32604/iasc.2023.026546
| Intelligent Automation & Soft Computing DOI:10.32604/iasc.2023.026546 | |
| Article |
Combined Economic and Emission Power Dispatch Control Using Substantial Augmented Transformative Algorithm
Department of Electrical and Electronics Engineering, K. S. Rangasamy College of Technology, Tiruchengode, 637215, Tamilnadu, India
*Corresponding Author: T. R. Manikandan. Email: manikandan266@gmail.com
Received: 29 December 2021; Accepted: 16 February 2022
Abstract: The purpose of the Combined Economic Emission Dispatch (CEED) of electric power is to offer the most exceptional schedule for production units, which must run with both low fuel costs and emission levels concurrently, thereby meeting the lack of system equality and inequality constraints. Economic and emissions dispatching has become a primary and significant concern in power system networks. Consequences of using non-renewable fuels as input to exhaust power systems with toxic gas emissions and depleted resources for future generations. The optimal power allocation to generators serves as a solution to this problem. Emission dispatch reduces emissions while ignoring economic considerations. A collective strategy known as Combined Economic and Emission Dispatch is utilized to resolve the above-mentioned problems and investigate the trade-off relationship between fuel cost and emissions. Consequently, this work manages the Substantial Augmented Transformative Algorithm (SATA) to take care of the Combined Economic Emission Dispatch Problem (CEEDP) of warm units while fulfilling imperatives, for example, confines on generator limit, diminish the fuel cost, lessen the emission and decrease the force misfortune. SATA is a stochastic streamlining process that relies upon the development and knowledge of swarms. The goal is to minimize the total fuel cost of fossil-based thermal power generation units that generate and cause environmental pollution. The algorithm searches for solutions in the search space from the smallest to the largest in the case of forwarding search. The simulation of the proposed system is developed using MATLAB Simulink software. Simulation results show the effectiveness and practicability of this method in terms of economic and emission dispatching issues. The performance of the proposed system is compared with existing Artificial Bee Colony-Particle Swarm Optimization (ABC-PSO), Simulated Annealing (SA), and Differential Evolution (DE) methods. The fuel cost and gas emission of the proposed system are 128904 $/hr and 138094.4652$/hr.
Keywords: Economic emission; dispatch; fuel cost; substantial augmented transformative algorithm
The coefficient and the optimal economic activity of the force framework have constantly involved an unmistakable situation in the force industry. That process includes the allotment of all-out burden between the accessible units so that the complete expense has been followed to a minimum. In ongoing years, this issue has become a public worry that frequently turns into an ecological issue, so Economic Dispatch (ED) now contains the system shipments, minimizing pollutants and achieving the lowest cost in the right direction. Furthermore, there is a need to broaden the issue of financing optimization to remember the limitations for the working framework to forestall the disturbance of the program because of unanticipated conditions and to guarantee the security of the association. Economic dispatch and mechanical emissions booking have been applied to accomplish optimal fuel cost and optimal dispatch of the generator set, individually. The extreme natural impacts made by vaporous contaminations, for example, particulate and sulfur dioxide (SO2) and nitrogen (NOx) discharging oxides can be decreased by the satisfactory attack of the heap between plants in a power framework. Even so, as it is possible, this has inspired a significant increase in the cost of working in the power plant.
A few choices were talked about and proposed to decrease barometrical emissions [1,2]. This incorporates the establishment of contamination cleaning gear, for example, fuel-exchanging burners with a low-toxin cleaner on location, or dispatching power age to lessen contamination as a supplement to the financially savvy focus of ED. The initial three options required the establishment of new equipment and extra changes to existing ones including successful capital expenses, so they thought about the drawn-out alternative. The ED choices are an appealing momentary other option, where both emission and fuel costs have fallen. The valve point loading effect is considered where the fuel cost vs. power production curve is not linear but consists of ripples as a result of the sharp increase in losses due to the wire drawing effects which occur as each steam admission valve starts to open. In this case the cost function is obtained based on the ripple curve for more accurate modeling.
These days, this choice has gotten a lot of consideration since it is effortlessly executed and just a couple of minor changes are expected to the primary ED program to include contamination. The hurtful ecological impacts of gas contaminations, for example, particulate and sulfur dioxide (SO2) and nitrogen oxide (NOx) emissions, have been decreased by reasonable dissemination of burden between power plants. However, these plants demand a noticeable increase in job expense. Emissions shift to other operational requirements schedule skyline speaks for the level of limitation when the ED question is found and the ideal answer is fulfilled. The emission attributes of various toxins are unique and are generally very non-direct. It builds the non-monotonicity of the ED problem constrained by complex contamination control. Energy production is not enough to make even the minimum tariff, these requirements are taken out at the same time, sending out minimal pollution. The main objective of the Proposed Substantial Augmented Transformative Algorithm-based Combined Economic emission Dispatch system aims to generate minimum fuel costs and minimum pollution levels that generators operate, while simultaneously satisfying the energy, load requirements and implementation of power plants. Therefore in this work, a substantial augmented transformative technique has been used, three-Test Cases are discussed and compared in this work with ten unit generators for emission function are recognized, along with lack of generator capacity and power stability are discussed with and without energy loss. The algorithm developed MATLAB environment programming. The following objectives are motivated for this research work.
i. The main goal of this thesis is to study, understand, and implement one new algorithm to solve one of the complex real-world engineering problems.
ii. The major contribution made in this thesis is to find the optimum solution of combined economic and emission Dispatch using newly developed algorithms. The algorithm delivered optimum or near optimum solutions. Fuel cost and emission costs are considered together to get better results for economic dispatch.
The rest of this work has been organized as follows: Section 2 discusses the literature survey, the proposed materials and method has described in Section 3. Section 4 explains the Substantial Augmented Transformative Algorithm (SATA). Section-5 depicts the implementation of SATA for solving the Combined Economic and Emission Dispatch (CEED) problem. Section 6 presents the simulation results for different standard test cases. A comparative study has discussed in section 7. Finally, the conclusion has derived in Section 8.
The power system must determine the optimal coupling of power outputs to all generating units, which reduces the total fuel cost while satisfying the economic dispatch problem. The rate of temperature rise is the maximum rate specified by the time interval at which the unit’s power output can be (heating rate) or decrease (slope rate). Violation of the generation curve ratios should shorten the life of the rotor and therefore satisfy the operation of a practical system when changing with power generation requirements. Because of the significance of the ED of the power framework and its impact on the earth, there are numerous methodologies created by different specialists to balance out power systems. Many papers have concentrated on the transmission of coordinated modern emissions without considering valve point impact stacking [3–5]. As of late valve point impact, stacking has gotten extensive consideration [6,7]. The advancements used to tackle the problem of CEED have been isolated into two classifications.
The first is traditional optimization strategies, for example, Lagrangian relaxation gradients and dynamic programming techniques, number programming, Lambda-cycle and Newton-Raphson techniques [8]. These strategies gain target work data, yield unacceptable outcomes, and require complex computational time for complex non-direct problems. Direct programming procedures experience the ill effects of the limitation that it requires a piecewise straight installment estimate. Newton-based strategies battle with enormous scope imbalance controls. In outline, these strategies are influenced by the long-term convergence rate and can’t give a worldwide answer for the nonlinear ED problem [9–11].
The metaheuristic optimization algorithms are the second category [12]. Physics and biology often motivate these algorithms. Many metaheuristic algorithms have been used to solve ED problems such as Evolutionary Programming (EP) [13], Interior Search Algorithm [14], Genetic Algorithm (GA) [15], Simulated Annealing (SA) [16], Differential Evaluation (DE) [17],Particle Swarm Optimization (PSO) [18], and Artificial Neural Networks (ANNs) [19],. The disadvantage of EP is that it slowly converges to near-optimal for some problems [20]. The Tabu Search (TS) involves determining reliable memory [21]. GA in some cases doesn’t have a better capacity than producing the best posterity and prompted gradually amass close to the general burden, and in some cases must be adhered to a neighborhood ideal [22]. Differential assessment has been portrayed as an exceptionally powerful algorithm and it has the accompanying drawbacks, which is that the estimation procedure can be caught to the nearby ideal because of the eager update rule and essential distinction properties [23–25]. In literature, discussed various methods to solve the CEED problems but all methods have more drawbacks. Based on this literature following research gaps are identified.
i. Fuel cost and emission output could be minimized only when the problem is dealt with separately
ii. Fuel cost, emission output and convergence time were high for the solution of the Economic Emission Dispatch (EED) problem. Therefore in this work introduce a Substantial Augmented Transformative Technique to solve all issues. The SATA algorithm is developed by MATLAB environment programming. The results of the proposed algorithm are compared to those reported in a recent study. The results need to show effectiveness and consistency as a promising and proposed approach.
3 Substantial Augmented Transformative Control Method Based Combined Economic Emission Dispatch System
While the primary concern of generation economies in power systems is constantly respecting system constraints in an economic dispatch, the next generation of such a gap should define the output of each generating unit based on the composition of the current generation that has reduced the cost of production. Present-day thermal power plants have a few fuels added substance valves that are utilized to control the power yield on the premises. At the point when a turbine begins to open each steam embed valve, a rippling effect causes the curve of buildings to reflect the actual effect of steam inflow, adding to the fuel cost. This is also known as the valve point effect, which has been added by a quadratic approximation of the sinusoidal component to the fuel cost function. Therefore, the following two non-convex dispatching problems are considered for this work.
a. The non-convex generator power output curve
b. The non-convex arrangement of the feasible solution set because of transmission misfortunes denied working zones, and slope rate confines as the limitations of the power framework
The CEED problem is a single-objective optimization problem, therefore in this work to optimize the formulation of two different components of the system discussed. The calculation of the objective function and constraint development has been taken into account.
The objective of the general CEED problem is to explain it in the most proper portion of powers that a power framework makes. Power balance controllers and all units must fulfill the power limitations. As it were, the CEED problem lies in finding the optimal mix of power ages to decrease complete fuel costs while giving power balance fairness control and different imbalance control in the framework. Capacity partitioned by complete fuel cost is as per the following
where
f(Pg) = Total production cost dollar/hr.
f(Pgi) = Fuel cost function of unit I in dollar/hr;
Pgi = Real power output of unit I in MW
Due to its impact on the environment, it is considered to be the most significant emission of Sulfur Dioxide (SO2) and Nitrogen Oxides (NOx) in the power generation industry. These emissions have been produced by the associated power of functional modeling to produce emissions per unit. The emission of SO2 and NOx using a combination of polynomial and exponential terms.
where
αi, βi.γi, ϵi = emission coefficient parameters
The double objective combined economic emission booking problem has been changed over to a solitary optimization problem by presenting a value penalty factor f as follows.
Conditions are exposed to power stream constraints. The cost penalty factor is hourly mixes with fuel cost emission and F $/hour complete working expense. The value penalty factor is the greatest fuel cost proportion and most extreme tainting of the generator as follows.
The accompanying steps are utilized to discover the value of the penalty factor for SATA explicit burden prerequisites.
a. Finding the greatest fuel cost and the most extreme emissions rate for every generator.
b. Layer the value penalty factor esteems in climbing request
c. Include the most noteworthy limit of every unit
d. Include the most extreme potential for every unit at once
At this stage, the last piece of the Hi identified with the procedure in hourly penalty factor for a given burden. The above methodology gives the rough estimation of the cost trouble factor count for a similar burden prerequisite. In this manner, a modified Price Penalty Factor (hm) was acquainted in this work with giving the specific estimation of the predetermined burden request. The hourly figuring proceeds before the underlying two-phase balanced additional penalty factor is found. At that point it is determined by adding their heap request esteems into the relating conditions of the Hi.
Thermal arranging includes a mix of linear, non-linear and dynamic system power stream constraints and optimization because of the problem of non-direct target work. The goal is to diminish the absolute age cost of a power structure in some fitting period while the different constraints are fulfilled. The problem of ED is communicated as
Subject to following equality and inequality constraints
3.3.1 Power Balance Constraint
Each hour’s total generated power must be less than or equal to the corresponding hour’s load.
where
Pd = load order for the dispatch period t
Ploss = the transmission misfortune stream related to the power is resolved for the transportation time t.
Pi = Power of output unit with t (dispatch period)
3.3.2 Transmission Line Losses
The Power Losses In-Transmission (Ploss) can be determined utilizing a power stream estimation (DC or AC approach). Be that as it may, the problem is the estimation of complete transmission misfortunes as a two-dimensional capacity of power yield through a diminished straight recipe or units of creating or reparability, a typical practice. The Ploss can be calculated from the Newton-Raphson method, which gives all bus voltage magnitudes and angles is used only for this paper:
The g matrix coefficients are considered constant during the dispatch process. These coefficients should be calculated at both actual operating conditions and with significant accuracy when the case is enough to close. In addition, a power flow program must be reached in advance.
3.3.3 Generation Limit Constraints
For the free activity of generation limit constraints, the genuine power yield of every generator is restricted, and the upper limit is characterized as follows:
Expanding or diminishing the yield generated by every unit is restricted to the measure of power because of the physical constraints of each unit. Generate slope rate slice beyond reach to adjust viable genuine power working extents as follows
where
Pi(t-1) = Early dispatch output power generation.
3.3.5 Spinning Reserve Constraints
The spinning reserve is essentially spare generation capacity that has been set aside and is dispatchable in order to ensure the power system’s continuity and security of supply. Because solar energy is intermittent, the required spinning reserve capacity will be provided by the system’s thermal generators. For security reasons, if there should arise an occurrence of unforeseen blackouts, either due to over-burdening or over-burden transmission lines, the creating units are not completely stacked: 5% to 10% of the limit of each speed unit is accessible in the event of a crisis. The Prohibited Operating Zone (POZ) Controls the adaptability of the individual units in giving a turning store of control. The Spinning Reserve (SRi) constraints required for a particular load demand is represented as:
So the updated objective function considering SR is given by
SRi = Spinning reserve contribution
3.3.6 Prohibited Operating Zones (Poz)
Valve point loading Modern generators have several barriers to operating areas. Therefore, in practical operation, this work should avoid unit operation in restricted zones when tuning the unit generation output bag. A unit can be described as impossible operating zones as follows:
where
NPi = Quantity of forbidden zones of unit i.
The reason for emission dispatching is to limit all-out natural degradation or absolute toxin emissions because of burning of fuel for the creation of vitality to meet burden prerequisites. In this work, just NOx contamination is taken as it is more destructive than different toxins. NOx emissions are approximated as a two-dimensional capacity of the real power yield from producing units. The plan of emission dispatch is referenced in condition (18).
3.5 Combined Economic and Emission Dispatch (Ceed)
Economics and emissions dispatch is very unique. The Economic dispatch just limits exchanges for the aggregate sum of fuel costs that the framework abuses emissions constraints. Then again, the emission dispatch just diminishes the aggregate sum of NOx emissions from the framework and gets through economic constraints. Accordingly, to locate a working point, it is critical to simply feel the harmony among cost and emissions. CEED has accomplished this. The multi-objective CEED problem is an optimization problem that is changed over into solitary by presenting a value penalty factor H and it is detailed as
The cost penalty factor is the measure of contamination in hourly standard fuel costs, and the absolute working expense of the framework. When the estimation of the value penalty factor is resolved, the problem is decreased to a basic ED problem. Legitimate planning by the generator set diminishes the complete fuel cost and NOx emissions in like manner.
4 Combined Economic and Emission Power Dispatch () Using SATA Algorithm
This domain Economic Load Dispatch (ELD) and EED differ from each other. The ELD Reduces fuel costs by increasing field pollutants. EED reduces pollution of assets by expanding fuel costs whenever possible. Therefore, we need to find an operating point to make a balance between CEED operating cost and exit ratio and this. CEED’s primary purpose is to create functionality by combining the domain with EED with the help of a cost penalty factor.
The following formula is used to find out the penalty factor
4.1 SATA Algorithm of Ceed (Without Considering Loss)
a. Read data, namely cost coefficients Ai, Bi, Ci, Di, Ei, Fi B-coefficients Bij, Bio, Boo (i = 1, 2,…., NG).convergence tolerance,£, step size α and maximum iteration allowed, ITMAX, Pgimin, Pgimax, etc.
b. Find out hi by equation (vi) and see the modified cost coefficients ai, bi, ci
c. The formula can state the problem
The values μ and Pgi (i = 1, 2… NG) can be obtained directly using the formula
d. Consider any generator to be either a lower bound or a higher order of magnitude.
e. Check the boundaries of the generators, if any further violations such as the following step 3, if it goes to a different package
f. Repeat the steps from 3–6
g. Calculate the optimal total cost Vi
h. End
4.2 SATA Algorithm of CEED (with Considering Loss)
a. Read data, namely cost coefficients Ai, Bi, Ci, Di, Ei, Fi B-coefficients Bij, Bio, Boo (i = 1, 2,…., NG).convergence tolerance,£, step size α and maximum iteration allowed, ITMAX,Pgimin, Pgimax, etc.
b. Find the coefficients ai, b, and ci, which are the transformed charge coefficients to find the vector by equation (vi)
c. By assuming that the transmission loss is zero, the calculated Pgi (I = 1, 2, …, NG) and the initial value of γ., PL = 0. Then the problem can be formulated by
The values μ and Pgi (i = 1, 2… NG) can be obtained directly using the formula
d. Let’s assume that any generator is a constant or a minimum
e. Set iteration counter, IT = 1
f. Calculated Pgi (I = 1, …, R), which is not fixed at the upper or lower limit of the generator, using the following formula
g.
h. Check
i. Check
j. Update
k. IT = IT+1,
l. Check the limits of generators, if no more violations then g o to step 3, else fix as following
m. Go to step 5 Repeat the process
The proposed SATA algorithm has been applied for solving profit based unit commitment.
5 Simulation Results and Discussion
The proposed SATA algorithm and valve function are tested on 10 unit generator systems. The algorithm has implemented the i3 processor, 2.53 GHz, with a 4 GB RAM personal computer on the MATLAB software platform. The procedure is tested on a conventional test system that includes six thermal power production units and six photovoltaic plants. The PV Photo Voltaic Panel’s ratings were obtained from a Tamilnadu-based independent power producer. The ratings of the thermal unit are derived from [26]. The generator cost factor, emission factors, production limits, and the loss factor of the ten-unit system have been solved using SATA when the system demand is 2000 MW. For testing, the initial temperature was fixed at 20°C and the maximum attempt was 10000 for a final temperature of 1e–10C°.
In power system research and education, test systems are commonly employed. The following are the reasons for employing a test system rather than a practical system:
i. Information about power systems is usually kept private.
ii. The systems’ dynamic and static data are not sufficiently described.
iii. Due to the vast amount of data, calculating several scenarios is challenging.
iv. Inadequate software for handling vast amounts of data.
v. Results from an actual power system that is less general
The cases examined are as follows:
CASE I: Simultaneous optimization of emission.
CASE II: Simultaneous optimization of fuel costs.
5.1 CASE I: In this case, fuel cost and gas emissions are minimized as a single objective function, respectively. Minimize the functionality to be optimized by sufficient weight, ignoring each of the other objective functions that are performed smoothly.
The performance analysis of fuel cost of ten unit system is discussed in Tabs. 1 and 2 respectively with 2000 MW load conditions. The fuel cost output of the proposed system is 128904 $/hr and 4786 lb/hr respectively when the fuel cost is the optimized function.
Tab. 2 lists the results of environmental economic dispatching when objectively reducing only emissions (environmental solutions). The gas emission output of the proposed system is are138094.4652 $/hr and 3986.9769 $/hr respectively for when the gas emission is the optimized function. The electrical loss was 85.396 MW.
Fig. 1 presents the convergence curve for fuel cost minimization with 1200 iterations. Fig. 2 shows the convergence curve for emission output minimization with 1200 iterations
Figure 1: Fuel cost minimization
Figure 2: Convergence curve for emission output minimization
5.2 Case II. In this case, we deal with the problem, multi-target; the two goals are minimized by using the weighting coefficients w1 and w2. Multi-objective optimization problems have been converted to single-objective optimization problems by importing weighting factors.
Tab. 3 presents non-dominant techniques for cost and emission goals with the variation of weighted factors and Fig. 3 shows the optimal front for cost and gas emission objectives.
Figure 3: An optimal front for cost and gas emission objectives
Fig. 3 can show the optimal front for fuel cost and gas emission goals from the commercial solution to the environmental solution because we make an equivalence between the weighted factor of objectives (w1 = w2 = 0.5). In simulated annealing, the best accommodation solution can give 128157.5870 $ and 3985.0216 lb
Tab. 4 presents the dispatch of power output for each generator and the electrical energy losses with the variation of weighted factors. From Tab. 4, the power dispatch of the financial resolution is demonstrated by the first solution, the sixth resolution shows the power dispatch of the best compromise solution, and the power dispatch of the environmental solution is highest by the 11th solution.
Fig. 4 Shows total generation costs for different load demands graphically, and the burden shared by each generator for various test conditions.
Figure 4: Load demand vs. cost
The change in total production cost required by different load requirements for the load shared by the generators at different load requirements is shown in Fig. 5.
Figure 5: Load demand vs. generation of each generator
Fig. 6 demonstrates the presentation investigation between various algorithms, and it shows that the progressed substantial augmented transformative algorithm has made compelling than different methods.
Figure 6: Performance analysis
In this work, a SATA strategy for deciding the multilayer integrated economic contamination control power transmission problem. The problem has likewise been portrayed as a double reason optimization problem, to decrease creation cost and fumes rate. The substantial augmented transformative algorithm (SATA) is extremely productive for taking care of optimization problems with non-smooth and non-convex qualities. This procedure consolidates great development administrators, such transformation, hybrid, and choice into a single number juggling administrator. The essential idea driving SATA is an undertaking to make analytical preliminary vectors. Mutations are utilized to generate a freak vector by including a differential vector from the contrast between a few randomly chosen parameter vectors and the parent vector. In this examination work, the SATA procedure has been applied to explain CEED. The Simulation was created by utilizing MATLAB conditions. One framework is tried ten generator framework with valve-point impacts and transmission misfortunes. As compared with existing ABC_PSO, SA, and DE methods, the proposed method gives the best results against all working parameters, for example, the overall efficiency of the proposed system is around 96.0%. Other stochastic search methods in the literature may not be able to produce better results than the presented methodology. The comparison shows that the proposed method validates the effectiveness of a high-quality remedy for CEED issues.
Funding Statement: The authors received no specific funding for this study.
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.
1. N. A. Khan, G. A. S. Sidhu and F. Gao, “Optimizing combined emission economic dispatch for solar integrated power systems,” IEEE Access, vol. 4, pp. 3340–3348, 2016. [Google Scholar]
2. A. R. Bhowmik and A. K. Chakraborty, “NSMOOGSA for solving combined economic and emission dispatch problem,” in 2016 IEEE/PES Transmission and Distribution Conf. and Exposition (T&D), Dallas, TX, USA, pp. 1–5, 2016. [Google Scholar]
3. U. Guvenc, Y. Sonmez, S. Duman and N. Yorukeren, “Combined economic and emission dispatch solution using a gravitational search algorithm,” Scientia Iranica, vol. 19, no. 6, pp. 1754–1762, 2012. [Google Scholar]
4. S. Anbudasan, Mr. P. SundaraMallayan and S. S. Vignesh, “Economic and emission thermal power dispatch with practical constraints using firefly algorithm,” Middle-East Journal of Scientific Research, vol. 24, no. S1, pp. 177–183, 2016. [Google Scholar]
5. E. D. Manteaw and N. A. Odero, “Combined economic and emission dispatch solution using ABC_PSO hybrid algorithm with valve point loading effect,” International Journal Science Research Publications, vol. 2, no. 12, pp. 1–9, 2012. [Google Scholar]
6. H. Sita and P. U. Reddy, “A comprehensive study on combined economic and emission dispatch optimization problem,” IOSR Journal of Electrical and Electronics Engineering (IOSR JEEE), vol. 32, pp. 1–9, 2016. [Google Scholar]
7. D. Singla and S. Jain, “A review on combined economic and emission dispatch using evolutionary methods,” International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, vol. 2, no. 6, pp. 2581–2587, 2013. [Google Scholar]
8. H. Abdi, E. Dehnavi and F. Mohammadi, “Dynamic economic dispatch problem integrated with demand response (deddr) considering non-linear responsive load models,” IEEE Transactions on Smart Grid, vol. 7, no. 6, pp. 1–18, 2016. [Google Scholar]
9. J. Sun, V. Palade, X. J. Wu, F. Wei and Z. Wang, “Solving the power economic dispatch problem with generator constraints by random drift particle swarm optimization,” IEEE Transactions on Industrial Informatics, vol. 10, no. 1, pp. 1–14, 2014. [Google Scholar]
10. M. Kaedi, “Fractal-based algorithm: A new metaheuristic method for continuous optimization,” International Journal of Artificial Intelligence, vol. 15, no. 1, pp. 76–92, 2017. [Google Scholar]
11. B. Dey, S. K. Roy and B. Bhattacharyya, “Solving multi-objective economic emission dispatch of a renewable integrated microgrid using the latest bio-inspired algorithms,” Engineering Science and Technology, an International Journal, vol. 22, no. 1, pp. 1–12, 2019. [Google Scholar]
12. J. D. A. B. Júnior and M. V. A. Nunes, “Multi-objective optimization techniques to solve the economic emission load dispatch problem using various heuristic and metaheuristic algorithms,” Optimization and Control of Electrical Machines, vol. 13, pp. 1–14, 2018. [Google Scholar]
13. K. S. Me, “Combined economic emission dispatch using evolutionary programming technique,” International Journal of Computer Applications, vol. 2, pp. 62–66, 2010. [Google Scholar]
14. N. Karthik, A. K. Parvathy and R. Arul, “Multi-objective economic emission dispatch using interior search algorithm,” International Transactions on Electrical Energy Systems, vol. 29, no. 1, pp. 1–16, 2019. [Google Scholar]
15. O. A. Olakunle and K. A. Folly, “Economic load dispatch of power system using genetic algorithm with valve point effect,” in Proc. Int. Conference in Swarm Intelligence, Beiging, China, pp. 276–284, 2015. [Google Scholar]
16. D. He, L. Yang and Z. Wang, “Adaptive differential evolution based on simulated annealing for large-scale dynamic economic dispatch with valve-point effects,” Mathematical Problems in Engineering, vol. 2018, no. 4745192, pp. 1–20, 2018. [Google Scholar]
17. L. Jebaraj, C. Venkatesan, I. Soubache and C. C. A. Rajan, “Application of differential evolution algorithm in static and dynamic economic or emission dispatch problem: A review,” Renewable and Sustainable Energy Reviews, vol. 77, no. C, pp. 1206–1220, 2017. [Google Scholar]
18. X. Chen, B. Xu and W. Du, “An improved particle swarm optimization with biogeography-based learning strategy for economic dispatch problems,” Complexity, vol. 2018, no. 7289674, pp. 1–21, 2018. [Google Scholar]
19. T. Deng, X. He and Z. Zhigang, “Recurrent neural network for combined economic and emission dispatch,” Applied Intelligence, vol. 48, no. 8, pp. 2180–2198, 2018. [Google Scholar]
20. B. Taheri, G. Aghajani and M. Sedaghat, “Economic dispatch in a power system considering environmental pollution using a multi-objective particle swarm optimization algorithm based on the pareto criterion and fuzzy logic,” International Journal of Energy and Environmental Engineering, vol. 8, no. 2, pp. 99–107, 2017. [Google Scholar]
21. A. Gupta, K. K. Swarnkar and K. Wadhwani, “Combined economic emission dispatch problem using particle swarm optimization,” International Journal of Computer Applications, vol. 49, no. 6, pp. 1–14, 2012. [Google Scholar]
22. H. Sita and P. U. Reddy, “A comprehensive study on combined economic and emission dispatch optimization problem,” IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE), vol. 21, pp. 1–9, 2016. [Google Scholar]
23. P. Arumugam and R. C. Subramanain, “Power search algorithm (PSA) for combined economic-emission dispatch problems considering valve point effects in economic load dispatch,” Turkish Journal of Electrical Engineering & Computer Sciences, vol. 25, no. 6, pp. 4647–4656, 2017. [Google Scholar]
24. K. Mason, J. Duggan and E. A. Howley, “A Multi-objective neural network trained with differential evolution for dynamic economic emission dispatch,” International Journal of Electrical Power & Energy Systems, vol. 100, pp. 201–221, 2018. [Google Scholar]
25. H. Wu, Y. Zhou, Q. Luo and M. A. Basset, “Training feedforward neural networks using symbiotic organisms search algorithm,” Computational Intelligence and Neuroscience, vol. 2016, no. 9063065, pp. 1–14, 2016. [Google Scholar]
26. S. Y. Lim, M. Montakhab and H. Nouri, “Economic dispatch of power system using particle swarm optimization with constriction factor,” International Journal of Innovative Energy System Power, vol. 4, no. 2, pp. 29–34, 2009. [Google Scholar]
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