Investigation on New Metaheuristic Algorithms for Solving Dynamic Combined Economic Environmental Dispatch Problems

: In this paper, the dynamic combined economic environmental dispatch problems (DCEED) with variable real transmission losses are tackled using four metaheuristics techniques. Due to the consideration of the valve-point loading effects (VPE), DCEED have become a non-smooth and more complex optimization problem. The seagull optimization algorithm (SOA), crow search algorithm (CSA), tunicate swarm algorithm (TSA), and firefly algorithm (FFA), as both na-ture and biologic phenomena-based algorithms, are investigated to solve DCEED problems. Our proposed algorithms, SOA, TSA, and FFA, were evaluated and applied on the IEEE five-unit test system, and the effectiveness of the proposed CSA approach was applied on two-unit, five-unit, and ten-unit systems by considering VPE. We defined CSA for different objective functions, such as cost of production, emission, and CEED, by considering VPE. The obtained results reveal the effi-ciency and robustness of the CSA compared to SOA, TSA, FFA, and to other optimization algorithms reported recently in the literature. In addition, Matlab simulation results show the ad-vantages of the proposed approaches for solving DCEED problems.


Introduction
A competitive electricity generation market necessitates high concentration to solve the economic load dispatch (ELD) problem of power generation. The essential objective of the ELD is to distribute the production of the available production units in such a way that the load demand is covered with a minimum total cost of fuel, taking into account the physical and operational limitations of the electrical system [1].
Due to these physical and operational limitations, the ELD problem is a non-linear optimization problem [1]. As a result, the conventional mathematical methods fall somewhat short in solving such a problem. On the other hand, with the growing concern about polluting emissions and the total cost of fuel, finding a solution to emissions has become a critical issue for the power generation systems around the world. However, the functions of pollutant emission and operating cost are incompatible; reducing emissions increases operating costs and vice versa [2]. Therefore, a grid operator allocates generation units to the tradeoff between the total operation cost reduction and/or reducing emissions under the newest generations, such as prohibited operating zones [3] and ramp rate limits [4], which have a high order of nonlinearities, discontinuities, dimensions, and valve loading points that determine the characteristics of the ELD problem [5]. Therefore, considering more non-convex and multiple local minima increases the complexity of obtaining the optimal fuel cost function. In contrast, metaheuristic optimization techniques have become common to find the best solution to the EED problem. Such algorithms include a colony optimizer [6], multi-verse optimizer [7], particle swarm optimization [8], gray wolf optimizer [9], biogeography-based optimization [10], enhanced exploratory whale optimization algorithm (EEWOA) [7], and hybrid bat-crow search algorithm (HBACSA); they are used exceptionally, in a unique, improved, or hybrid form with others approaches.
Thermal power plants release toxic gases into the atmosphere, endangering human health. Environmental pollution caused by these chemicals has the potential to harm not only humans but also animals and birds. It also has a negative impact on visibility, material quality, and contributes to global warming. DEED provides a solution to these problems by scheduling a renewable energy source and backup power generation based on the predicted load demand to decrease the operational generator's cost and emissions [2].

Literature Review
According to the importance of DEED, researchers have adapted and proposed these new algorithms to address the DEED problem. In [11], the authors proposed a method based on improved sailfish algorithm to solve the hybrid dynamic economic emission dispatch (HDEED). In addition, the paper in [12] presented a novel multi-objective optimization based on enhanced moth-flame optimization approach to locate the optimal solution of the hybrid DEED, including renewable energy generation. Ref. [13] proposed an improved tunicate swarm method to explore the search space for DEED. The proposed ITSA in [13] was applied to the 5, 10, and 15-unit systems, respectively. Ref. [14] proposed a novel approach, namely a multi-objective differential evolution algorithm, to deal with the constraints in DEED problems by considering the difference in the power generation range of the units. Authors in [15] suggested a multi-objective virus colony search algorithm (MOVCS) for solving the DEED problem in the power system integrated electric vehicle and wind units over a 24h period. Ref. [16] formulated DEED as a third-order polynomial fitting curve method to balance between emissions gas and fuel cost by utilizing renewable energy and PEVs. In [17], the authors proposed an enhanced exploratory whale optimization algorithm (EEWOA) to solve the dynamic economic dispatch (DED), which coordinates the behavior of whales, random exploration, and local random search. The feasibility of EEWOA is validated on 5, 10, and 15 units considering VPE and power loss constraints.
In the last two years, various research works have focused on solving the DEED problems by using novels metaheuristic techniques. The research in [18] developed a new model of the multi-objective DCEED using a hybridized flower pollination algorithm (FPA) with sequential quadratic programming (SQP). The FPA-SQP is tested on 5 and 10unit systems for a 24h period. Ref. [19] suggested a novel multi-objective hybrid optimization-algorithm-based equilibrium optimizer (EO) and differential evolution (DE) to solve the DEED. The proposed algorithm is validated and verified on the test system containing ten thermal power generators and one wind farm. The study showed that the hybrid EO-DE method with a constraint management system is able to counter balance the tasks of exploitation and exploration. The results obtained in [20] show that the new chaotic artificial bee colony (IABC) rides the local trap and improves the convergence of the solution in terms of solving the CEED with different constraints. A 10-unit system without and with a wind farm and a 40-unit system were investigated to prove the effectiveness and accuracy of the suggested IABC for tackling the CEED problem. In [21], the improved slime mold algorithm (ISMA) is developed and applied to optimize the single-and bi-objective economic emission dispatch (EED) problems considering VPE. Five test systems (6-unit, 10-unit, 11-unit, 40-unit, and 110-unit) are used to validate the proposed ISMA. Additionally, [22] presented an optimal allocation of the power system for the combined economic emission dispatch problem using a moth swarm algorithm (MSA). The method was tested on two different systems. The first system is a combination of six thermal generators and thirteen solar plants, and the second test system comprises three thermal units combined with thirteen photovoltaic plants.
This paper proposes, presents, and applies more effective methods, such as, TSA, SOA, CSA, and FFA, for solving the DCEED problem, including VPE. The most important contributions of this article can be summarized as follows: • Improvement of some optimization methods, such as TSA, SOA, CSA, and FFA.

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Application of the proposed algorithms to solve single-and bi-objective DEED problems.

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The four techniques are validated and tested by applying them on the IEEE standard five-unit test system to demonstrate their robustness and accuracy.
The rest of the article is organized as follows. The DEED problem with the mathematical model is presented in Section 3. Section 4 demonstrates the four metaheuristic approaches: TSA, SOA, CSA, and FA. The investigation of the simulation results and discussion are shown in Section 5. Finally, we conclude this paper in Section 6.

DCEED Problem Formulation Including VPE
Due to the dynamic behavior of the electrical network and the prodigious variations in load demand on the consumer side, the DCEED problem can be described as a multiobjective mathematical optimization problem, which is non-linear and dynamic. DCEED is a constraint optimization problem that minimizes simultaneously the fuel cost and emission effects in order to meet a power system's load demand over some appropriate periods while meeting certain equality and inequality constraints [23].

Objective Function
DCEELDP's objective is to minimize total fuel costs while also reducing the level of emissions emitted by generating units. Thus, the objective function is mathematically defined as the weighted summation of the production cost of generating units and emissions caused by fossil fuel thermal plants, which is shown below [16]: (1) where F indicates the single objective to be minimized; , ( , )denotes the fuel cost of generators in the ℎ (t =1, 2, …, T) time interval in USD/h; , ( , ) stands for the emissions generated by the generation stations over T dispatch intervals in kg/h; , denotes the dynamic dispatch power in MW.
is the price penalty factor determined by the ratio of ( )and ( ) in USD/kg.

Dynamic Economic Load Dispatch Model (DED)
The objective of the DED problem is to minimize the overall economic cost of fossil fuel during a 24-h period. In some large generators, their cost functions are also non-linear, due to the effect of the valve opening [24]. Consequently, the valve dynamics increase several local minimum points in the cost function, hence complicating the problem. The DED problem involved with VPE is expressed as minimization of the production cost of power dispatch in the following way [25]: where , , and are the coefficients of the fuel cost corresponding to the generator i; , and stand for the fuel cost coefficients of the ℎ generator due to VPE; and denotes the minimum real power of the ℎ (i = 1, 2, …, Ng) generating unit.

Dynamic Environmental Dispatch Model (DEnD)
Global warming and increased movements to protect the environment have forced producers to reduce gas emissions caused by the combustion of fossil fuels in various power plants mainly due to sulfur dioxide (SO2) and nitrate oxide (NOx) [26,27].
Each thermal power plant will produce its power according to a dynamic nonsmooth emission function given by the following quadratic form [28]: where , , ,  , and are the emission curve coefficients.

Constraints Functions
The minimization of the DCEED problem is subject to the following constraints and limits:

Power Balance Constraint
The sum of total power generated by all generators at each time interval t should be matched with the load demand PD and the total transmission losses in the corresponding time period, which is given as follows [29]: The power losses incurred in the transmission lines can be computed by using Kron's loss coefficients formula given below [30]: where , denotes the transmission loss coefficients. Wood et al.in [31] provide detailed procedures for calculating the B coefficients.

Power Output Limits
The dispatch active power outputs of each generator must be between the capacities of each specific generating unit at each time interval t [32]: Where and indicate, respectively, the minimum and the maximum power limits of , .

Seagull Optimization Algorithm (SOA)
The seagull optimization algorithm (SOA) [33] is a recently proposed metaheuristic technique inspired by the natural behaviors of seagulls. The seagull optimization algorithm is a metaheuristic algorithm that mimics gull behavior. Seagulls live in colonies. Seagulls are omnivorous, eating reptiles, earthworms, insects, fish, and other animals.
Seagulls are highly intelligent birds. This aids the seagull in its hunt for prey. The migratory and hunting habits of seagulls are well known. Seagulls migrate in search of a new plentiful food source. After arriving at a new home, seagulls attack their prey (Figure 1 [33]). The most important thing about seagulls is their migrating and attacking behavior [34]. Thus, the SOA focuses on these two natural behaviors. This behavior is clarified as follows:

Migration (Exploration)
During migration, the members of a seagull swarm should avoid colliding with each other (see Figure 2a). To achieve this purpose, an additional variable A is employed [35]: where ⃗⃗⃗ indicates the position of each agent, ⃗⃗⃗ ( ) denotes the current position of seagulls in the jth iteration (j = 1, 2,…, Maxiteration), and A depicts the movement behavior of seagulls.
where a is a constant and responsible for controlling the frequency of employing variable A, which linearly decreases from a to 0. To find the richest food resources, seagulls move toward the best search agent as shown in Figure 2b.
where ⃗⃗⃗⃗⃗ indicates seagull position ⃗⃗⃗ ( ) toward the best search agent ⃗⃗⃗⃗⃗ ( ). The coefficient B is a random value responsible for making a tradeoff between exploitation and exploration and is expressed as follows: where rd is a random number that lies in the interval (0,1). As seagulls move toward the fittest search agent, they might remain close to each other (see Figure 2c). Thus, seagulls can update their position according to the following rule [33]: where ⃗⃗⃗⃗ stands for the distance between seagulls and the best search agent.

Attacking (Exploitation)
Seagulls attack their prey in a spiral shape after arriving at a new place, as presented in Figure 2d. Their attacking behavior in the x, y, and z planes is explained as follows [33]: where r denotes the radius of each turn of the spiral; k is a random number with [0 ≤ k ≤ 2π]; u and v are constants to define the spiral shape [33,36]. The updated position of the search agent ⃗⃗⃗ ( ) is determined by using Equations (11)(12)(13) [36].

Crow Search Algorithm (CSA)
Crow search algorithm (CSA) is a nature-inspired algorithm suggested by A. Askarzadeh in 2016 [37]. This evolutionary computation technique based-population algorithm imitates crow birds' conduct and social interaction [38].
One of the best indications of their cleverness is hiding food and remembering its location. Moreover, the mechanism of exploration and exploitation of CSA can be learned from Figure 3 [39]. As shown in Figure 3a, small values of fl (<1) result in a solution to an optimum local; otherwise, if fl of more than 1is selected, the optimal solution leads in the global search, as shown in Figure 3b. Overall, the pseudo code of CSA can be explained as shown in Algorithm 1.
The CSA process is discussed in this subsection [39]: Step 1:Initializing crow swarm in the d-dimension randomly.
Step 2: A fitness function is used to evaluate each crow, and its value is put as an initial memory value. Each crow stores its hiding place in its memory variable Pi.
Step 3: The crow updates its position by selecting another random crow, (i.e, Mj) and generating a random value. If this value is greater than the awareness probability "AP", then crow Pi will follow Pj to know Mj. Step 4: The crow updates its position by selecting another random crow (i.e., Pj) and following it to know Mj. Then new Pj is calculated as follows: where t refers to iteration number; and refer to random numbers; is the crow i flight length to denote crow j memory.
Step 5: Updating memory The crows' memory is updated as follows: Step 6: Check termination criterion. Steps 3-5 are repeated until tmax is reached.

Tunicate Swarm Algorithm (TSA)
The standard tunicate swarm algorithm is a very simple bio-inspired metaheuristic optimization technique, which was first proposed by S. Kaur et al. in 2020 [40]. Its inspiration and performance were proven over the seventy-four benchmark problems compared to several other optimization approaches. Its efficacy and unpretentious structure draw the attention to employ and improve this algorithm for the considered problem. The swarm behavior of TSA is given in Figure 4 [40]. TSA main limitates the swarming behaviors of the marine tunicates and their jet propulsions during its navigation and foraging procedure [41]. In TSA, a population of tunicates (PT) is swarming to search for the best source of food (SF), representing the fitness function. In this swarming, the tunicates update their positions related to the first best tunicates stored and upgraded in each iteration. The TSA begins where the tunicate population is initialized randomly, considering the permissible bounds of the control variables. The dimension of the control variables composes each tunicate (T), which can be initially created as [40] where T(m) stands for the position of each tunicate (m); n refers to each control variable in dimension Dim; r is a random number within the range (0:1); and indicates the number of tunicates in the population.
The update process of the tunicates position is executed by the following formula [41]: where * denotes the updated position of the ℎ tunicate based on Equation (18); T(m−1)refers to the neighbor tunicate; 1 is a random number, uniformly distributed between 0 and 1.
where SF is the source of food, which is represented by the best tunicate position in the whole population; A is a randomized vector to avoid any conflicts between tunicates and each other, which is expressed as: [40] where 2 and 3 are random numbers within the range (0:1); and represent the initial and subordinate speeds to produce social interaction.
The TSA method's key steps can be described as [42]: Step 1: Create the initial tunicate population.
Step 2: Determine the control units of TSA and stopping criteria.
Step 3: Compute the fitness values of the initial population.
Step 4: Select the position of the tunicate with the best fitness value.
Step 5: Create the new position for each tunicate by using Equation (18).
Step 6: Update the position of the tunicates that are out of the search space.
Step 7: Compute the fitness values for the new positions of tunicates.
Step 9: After stopping criteria is satisfied, save the best tunicate position.

Overview of the Firefly Algorithm (FFA)
The firefly algorithm developed by X-S. Yang in 2007 [43] is one of the swarm-based optimization algorithms, which works based on the sparkling performance of all the fireflies. Fireflies use their flashing property to communicate. There are three rules in the firefly algorithm, which are based on the idealized behavior of the flashing characteristics of fireflies [44].

Attractiveness
All fireflies are unisex, and they will move toward more attractive and brighter ones regardless of their sex. In the firefly algorithm, the form of attractiveness function of a firefly is the following monotonically decreasing function [44]: where r is the distance between any two fireflies 0  is the initial attractiveness at r = 0, and γ is an absorption coefficient which controls the decrease in light intensity.

Distance
The degree of attractiveness of a firefly is proportional to its brightness, which decreases as the distance from the other firefly increases because the air absorbs light. If there is no brighter or more attractive firefly than a particular one, it will move randomly [45].
The distance between any two fireflies i and j, at positions xi and xj, respectively, can be defined as a Cartesian or Euclidean distance as follows [46]: where , is the ℎ component of the spatial coordinate of the ℎ firefly. In the dimensions 2-d, we have:

Movement
The movement of a firefly i, which is attracted by a more attractive (brighter) firefly j, is calculated by [46] where the second term is due to the attraction, while the third term is randomization with α being the randomization parameter, and rand is a random number within the range (0:1).

Simulation Results and Discussion
In order to solve the dynamic combined economic environmental dispatch problem, we developed and executed the CSA, SOA, TSA, and FFA algorithms in MATLAB 2017, and they were run on a personal computer with an Intel Core(TM) i5 with a processor of 2.60 GHz and a Ram of 8.0 GB under MS Windows 8.1. In the first part, the four proposed techniques were tested on the five-unit test system by considering VPE for three case studies, and in the second part, the CSA method was applied on the IEEE ten-unit system, including VPE, for three cases. The constraints involved in all cases were power balance limit with consideration of transmission losses and generator operating limits constraints.
The obtained results were compared with the optimization approaches recently published in the literature.

IEEE Five-Unit Test System
The five-unit test system was derived from [47,48]. Tables 2 and 3 include the generation data. In this subsection, the dynamic load dispatch (DLD) cases through the application of the four metaheuristics techniques include:      The dynamic economic dispatch (DED) considering VPE with variables power losses is studied in this subsection (for total load = 14,577 MW).
The optimal schedule for a five-thermal-generator test system considering VPE and transmission losses, using the crow search algorithm (CSA), is presented in Table 4. The best results are highlighted in bold font. The comparison results of the optimization techniques (CSA, SOA, TSA, and FFA) and the statistical analysis of the optimal results of Case 1 are given in Table 5. The best values, the robustness and effectiveness of the proposed CSA in finding optimal solutions to the DED problem with a reasonable number of iterations are compared and the constraints verified.
The results shown in Table 4 present the total cost found by the CSA algorithm, which is equal to 42,425.455 USD/h, is lower compared to that found by the SOA, TSA, and FFA algorithms, which is estimated at 48,609.77 USD/h, 46,672.4787 USD/h and 45,474.198 USD/h respectively.
The CSA algorithm, which offers the best production cost, on the other hand, offers a relatively higher amount of transmission losses compared to FFA, i.e., 193  It is also worth mentioning that in Table 5, the total emissions found by the CSA algorithm, which amount to 21,960.553 lb/h are more reduced compared to those found by the SOA, TSA, and FFA algorithms, which are estimated at 32,652.86 lb/h, 27,641.23 lb/h, and 24,862.338 lb/h respectively. Figure 5, shows the graphical depiction of the convergence of the DED problem with time (iterations) obtained by applying our proposed methods corresponding to the peak hour (PD =740 MW). In comparison to SOA, TSA, and FFA, we can see that CSA has an incredibly fast convergence ability. In addition, CSA was trapped into the local optimum at around 230 iterations.

Case 2
The dynamic environmental dispatch (DEnD) considering the valve-point loading effect and transmission losses as given in Equation (3) are discussed in this case. Table 6 shows the results of the optimum power dispatch for the five-unit system over 24 h obtained by CSA. The optimal results of the pollutant power generation, fuel cost, and active power loss obtained by the CSA are depicted in Table 6.
The total losses, total fuel cost, and total emissions computed by our proposed approaches are illustrated in Table 7.We compared them with those determined by other algorithms recently applied in the literature. By analyzing the results given in Table 7, we infer that the total emissions found by the CSA algorithm, which amount to 17,733.6 lb/h, are lower, compared to those found by the SOA TSA, and FFA algorithms, which are estimated at 18 From the results shown in Table 7, we notice that the total cost determined by the CSA algorithm, which amounts to 51,149.5 USD/h, is lower compared to that found by the SOA, TSA, and FFA algorithms, which is estimated at 51,385.3 USD/h, 51,878.7 USD/h, and 51,263.5 USD/h, respectively.
In addition, when compared to CSA, SOA, and TSA, FFA has a relatively low amount of active power losses. The CS algorithm, which offers the minimum pollutant power generation, in return offers relatively higher transmission losses than FFA, and lower than SOA and TSA, i.e., 187.901 MW, 204.66MW, 188.825 MW, and, 187.07 MW for CSA, SOA, TSA, and FFA, respectively. Figure 6 represents the convergence curves of our proposed approaches for the DEnD problem. It describes the stable convergence of the objective function of the problem given in Equation (3). The convergence characteristics shown in Figure 6 prove that CSA has better qualities than SOA, TSA, and FFA. We conclude that CSA is favorable for largescale power systems.

Case 3
In this case, we deal with the dynamic combined economic environmental dispatching (DCEED) with the variable losses by applying the price penalty factor under the impact of the valve-point. Electrical losses are variable depending on the power generated. Table 8 summarizes the best solutions achieved for DCEED for a given load. We can deduce from the same table that CSA and our three competitive algorithms adjust the value of the output power ( 1 − 5 ) such that load demand and the constraint limits are satisfied, and the best fuel cost and pollutants emission results are achieved.  Table 9 shows the values of the active power losses, the best cost, the best emission, and the total cost objectives against 0.5 weight for the test system. The results displayed in the mentioned table are obtained from NEHS, MHS, HS-NPSA, PSO-GSA, DE-SQO, PSO, and our proposed approaches. Column five of Table 9 depicts the value of the single-objective function of the problem, as specified in Equation (1). The effectiveness of the suggested CSA is demonstrated by the percentage change of some algorithms listed in the same table.
According to Table 9, we infer that minimizing the cost of generation and minimizing emissions are contradictory goals. Emissions are highest when the cost of production is minimized. Figure 7 shows the convergence curves of the total cost with iterations, obtained by applying CSA, SOA, TSA, and FFA methods corresponding to the power demand equal to 740 MW. We infer that CSA and FFA reach the optimum solution more quickly than SOA and TSA, which is shown in Figure 7.  Figure 8 presents a graphical comparison of the total fuel cost, the total emissions, and the total cost of our proposed methods and other algorithms for a five-unit test system. This clearly demonstrates that CSA has the lowest total cost when compared to other algorithms. Percentage enhancement of the suggested CSA over other algorithms is shown in Figure 9. From this figure, the positive bars show the largest values of the total cost compared to those obtained by CSA, and negative bars represent smaller values of the total cost compared to those obtained by CSA.
The statistical summary of 50 runs for each study case performed (i.e., Case 1 to Case 3) using CSA, SOA, TSA, and FFA approaches is depicted in Table 10.
The columns display the min, average, worst, and standard deviation values for the objective function in each case. According to Table 10, it is clear the CSA method delivers the best fitness, best mean, and best standard deviation values in all the cases.

IEEE 10-Unit Test System
In this case study, the then-unit generating system is utilized to evaluate the performance of the proposed CSA by considering the valve-point loading effect. In this experiment, a 24-h scheduling period with 1-h intervals is used. The original data of the 10-unit system are shown in Table 11, which are available in the literature [53]. Tables 12 and 13 are the 10-unit generator loads demand and the B matrix, respectively, which are derived from [53]. In this research, the weighting function approach (w.f.a) is used to converts multi-objective functions into a single problem [56]. Hence, by the usage of the w. f. a, Equation (1) can be reformulated as: (n: number of problems). Dynamic load dispatch (DLD) cases in this subsection include:  Table 11. IEEE 10-unit generator coefficients.  The dynamic economic dispatch (DED) considering VPE with variables power losses is studied in this subsection (for total load = 39.848 MW).
Hourly generation (MW) schedule obtained from DED using CSA for a 10-unit system by considering VPE and transmission losses are presented in Table 14. The best results are highlighted in bold font. Total fuel cost and total emission results obtained from the CSA algorithm are compared with other methods in Table 15. As can be seen from Table 15, the proposed CSA algorithm produces fewer fuel cost value by 2.487512 × 10 6 USD than other algorithms. CSA was able to achieve an enhanced in total fuel cost in rang 10 6 of 0.01659 USD, 0.013315 USD and 0.029288 USD, respectively as compared to MHS [49], SA [57], and NSGAII [58]. IBFA [59], GCABC [60], and TLBO [61] gives a best solutions (less than this obtained by our proposed approach of 5,812 USD, 13,039 USD, and 15,396 USD, respectively).
To elaborate the transition of CSA for different phases of the search convergence characteristics for the 10-unit test system under a fixed hour (PD = 2150 MW) for 1000 iterations is shown in Figure 11. From the figure, we can be seen that CSA has an incredibly fast convergence ability it has been quickly trapped the optimal values.  [49] 2.504106 NA SA [57] 2.537200 NA NSGAII [58] 2.516800 3.17400 IBFA [59] 2.481700 3.27500 GCABC [60] 2.474473 NA TLBO [61] 2.472116 3.30411 Figure 11. Convergence curve for10-unit test system for a fixed hour (PD = 2150 MW).

Case 5
The dynamic environmental dispatch (DEnD) considering the valve-point loading effect and transmission losses as given in Equation (3) is discussed in this case. Table 16 shows the results of the optimum power dispatch for the 10-unit system over 24 h obtained by CSA. The optimal results of the pollutant power generation and fuel cost obtained by the CSA are depicted in Table 16. The total fuel cost and total emissions computed by the CSA method are illustrated in Table 17. We compared the obtained solutions with those determined by other algorithms recently published in the literature.
Method GCABC in [60] obtains the less total emission values of 293,416 lb compared with those values obtained by the methods cited in Table 17.
According to Table 17, we notice that the total cost determined by the CSA algorithm which is equal to 2.62594 × 10 6 USD is lower compared to that found by the NSGA-II [58] algorithm, which is estimated at 2.6563 × 10 6 USD.  Figure 12 represents the convergence curves of our proposed approach for the DEnD problem. It describes the stable convergence of the objective function of the problem given in (3) (Case 5). The convergence characteristics shown in Figure 12 prove that CSA has good qualities. We conclude that CSA is favorable for large-scale power systems.

Case 6
In this case, we deal with the dynamic combined economic environmental dispatching (DCEED) by considering the power losses and the valve point-effect loading. Table 18 summarizes the best compromise solutions achieved for DCEED for a given load. According to Table 18, we can deduce that CSA adjust the value of the output power ( 1 − 10 ) such that load demand and the constraint limits are satisfied, and the best fuel cost and pollutants emission results are achieved. However, the statistical comparative results of CSA method along with various other methods for both cost and emission objective functions are provided in Table 19. The minimum cost obtained by the proposed CSA approach is 2,492,050 USD among 50 trials in the economic dispatch problem and considered as the ever best solution. It is also clear from the simulation results that the proposed approach provides better statistical results as compared with many other available methods given in Table 19.   Figure 13 shows the convergence curves of the CEED with time (iterations) obtained by applying the CSA method corresponding to a fixed hour with a power demand of 2150 MW. It is observed from the convergence curve that a better reduction in combined cost and emission can be obtained with less number of iterations using the proposed CSA.

Conclusions and Future Work
In this paper, new optimization approaches were proposed, presented and applied to solve the problem of the dynamic economic emissions dispatch of generator units considering the valve-point loading effects. The main inspiration of these optimization techniques are the fact that metaheuristic algorithms are easy to implement and can be used for a variety of other problems.
The proposed strategies are validated by simulating MATLAB and testing on the two standard IEEE power systems, 5-unit and 10-unit systems. The numerical results of this system are presented to show the capabilities of the proposal algorithms to establish an optimal solution of the dynamics problem of combined economic emissions dispatch in several passages. From Tables 4,6,8,14,16,and 18, it is obviously clear that the optimal generation schedule of a 5-units and 10-unit system obtained by CSA satisfy power balance constraint with considering power losses and generator operating limits constraint. The proposed CSA gives better performance compared to methods cited in the literature.
In all cases, our proposed algorithms can reach the optimum solution more quickly which. In future works, we intend to combine CSA with TSA, and introduce it to other kinds of optimization issues, such as large-scale economic load dispatch problems, integrated renewable energy sources, multi-objective ED problems with many complex constraints.

Conflicts of Interest:
The authors declare no conflict of interest.