Combined Economic Emission Dispatch in Presence of Renewable Energy Resources Using CISSA in a Smart Grid Environment

Abstract

The geographically spatial and controlled distribution of fossil fuel resources, catastrophic global warming, and depletion of fossil fuel resources have forced us to integrate zero- or low-emissions energy resources, such as wind and solar, in the generation mix. These renewable energy resources are unexhausted, available around the globe, and free of cost. The advancement in wind and solar technologies has caused an appreciable decrease in installed the and global levelized costs of electricity via these sources. Therefore, the penetration of renewable energy resources in the generation mix can provide a promising solution to the above-mentioned problems. The aim of simultaneously reducing fuel consumption in terms of “Fuel Cost” and “Emission” in thermal power plants is called a combined economic emission dispatch problem. It is a combinatorial and multi-objective optimization problem. The solution of this problem is to allocate the load demand and losses on the committed units in such way that the overall costs of the generation and emission of thermal units are reduced, while the legal bounds (constraints) are met. It is a highly non-linear and complex optimization problem. The valve-point loading effect makes this problem non-convex. The addition of renewable energy resources (RERs) adds more complexities to this problem because they are intermittent. In this work, chaotic salp swarm algorithms (CISSA) are used to solve the combined economic emission dispatch problem. Chaos is used as an alternative to randomization for the tuning of the control variable to improve the trait of obtaining global extrema. Different test cases having different combinations of thermal, solar, and wind units are solved using the proposed algorithm. The results show the superiority of this study in comparison to the existent research results in terms of the cost of generation and emissions.

1. Introduction

Optimization has played a vital role in the field of engineering and technology. Many power system operation and control problems have been solved by optimization, including power system expansion planning, unit commitment, hydro-thermal coordination, optimal power flow, and economic load dispatch [1,2,3]. Economic dispatch holds a prominent position among various power system operation problems. In a conventional power system, fossil fuel power plants are the largest electric power producers [4,5,6]. Different thermal generating units have different fuel-cost curves, which means that they consume different amounts of fuel for producing the same amount of power. Basically, ED is a generation allocation problem; the solution of this problem is to distribute the system’s load demand among all the committed thermal generating units, so that the overall fuel cost is minimized while satisfying different operational constraints [7].

Climate change and global warming have attracted the attention of the modern world. Greenhouse gas emissions are the main cause of global warming [8]. Thermal power plants emit greenhouse gases into the environment. These pollutant gas emissions vary as a function of power produced by thermal units, which means that the power generation allocation problem should be solved so that both fuel costs and emissions are simultaneously minimized [9]. Interestingly, fuel costs and emissions are conflicting objectives in nature. Therefore, a trade-off is established between these two objectives and the problem is solved for a compromised solution. This combinatorial and bi-objective problem is called combined economic emission dispatch (CEED). It is a non-linear optimization problem and can be solved by the optimization theory [10].

Different combinatorial optimization problems are successfully solved by several swarm-based optimization algorithms [11,12,13]. The salp swarm algorithm (SSA) is a bio-inspired, swarm-based optimization algorithm that can provide a promising solution to the combined economic emission dispatch problem [14]. Renewable sources are low- or zero-emission sources. If they are integrated with fossil fuel power plants in the generation mix, a considerable reduction in both fuel costs and emissions can be achieved. However, this reduction in fuel consumption and emissions due to the inclusion of renewable energy resources results in the high levelized cost of electricity (LCOE) [15]. Therefore, by including large numbers of renewable sources, the overall generation cost is increased for the same demand for power [16]. Therefore, we only need to add a certain amount of renewable power to the system so that the overall power generation cost is minimized. This presents the CEED as a mixed integer, multi-objective optimization problem. In this study, the combined economic emission dispatch in the presence of renewable energy resources is solved using the chaotic salp swarm algorithm.

A brief literature review about the topics is presented as follows:

In Ref. [17], Y.S. Brar et al. formulated a multi-objective problem and applied a genetic algorithm for solving the economic load dispatch problem. In this research, the fuzzy set theory was applied for the evaluation of the fitness of potential solutions, and fuzzy-based penalties were imposed on unfeasible solutions. Equality and inequality constraints were included in the problem. The proposed method was applied to an eleven-node five-generator sample system. The authors in [18] co-optimized fuel and reserves with a consideration of the emissions and incorporated a wind-generation forecast in the dispatch decision. The dispatch model used was a self-commitment-based model for a deregulated market. The Ireland electricity system was used as the test case, and the wind-integration impact for fuel-saving and forecasted approaches for emission reductions were also studied. In Ref. [19], the authors proposed a novel approach for the optimum operation of the day-ahead electricity market while considering the market power. A non-dominated sorting genetic algorithm (NSGA-II) was used to solve a one-hour base optimal dispatch for minimizing fuel costs, emissions, and modified Herfindahl–Hirschman index for concentration values. This study assesses the effect of market sharks of firms on the diversity of non-dominated solutions.

In [20], the author used the E-constraint method for generating non-inferior solutions of conflicting objectives of CEEO problems for four different objectives defined for obtaining the best alternative among non-inferiority solutions. Similarly, the multi-objective stochastic search technique-II (EMOSST-II) was used for solving the combined economic dispatch problems technique to obtain divers multiple pareto-optimal solutions. In Ref. [21], the authors considered life cycle results for the calculation of CO₂ emissions from fossil fuel power plants in a combined economic emission dispatch problem of an off-grid power system in the presence of a renewable energy system. They compared the impact of photo-voltaic and wind turbines on economic and environmental costs. In Ref. [22], the authors proposed a hierarchal control strategy for an independent micro-grid for the combined economic emission dispatch problem. Low-and high-level control strategies were applied with the help of local controllers and combined control, respectively. A self-adaptive low–high evaluations evolutionary algorithm was used as the optimization algorithm.

In Ref. [23], the authors considered renewable energy resources in the combined economic emission dispatch and applied model predicative control (MPC) to handle the intermittent nature of renewable energy resources. They applied the model predicative control for the direct control of intermittent energy resources to compensate for rapid load fluctuations. For a renewable share less than 3% of the total generation, they considered renewable energy resources as negative loads. In [24], using the social foraging behavior bacterium for solving the CEED problem, the authors achieved a non-dominating solution and employed a fuzzy-based mechanism to extract the best compromised solution from the trade-off curve. The proposed algorithm was applied to the IEEE 30-bus standard test and Taiwan generating units power systems with value point effects, and the results were compared to the metaheuristic technique (MOSST), non-dominated sorting genetic algorithm (NSGA), linear programming (LP), strength pareto evolutionary algorithm (SPEA), nichel pareto algorithm (NPGA), fuzzy clustering-based particle swarm optimization (FCPSO), and differential evolution (DE).

In [25], security constraints and AC loads’ flow constraints in the multi-objective economic emission dispatch problem were included. To generate a pareto-optimal front, the multi-objective mathematical programming approach was proposed with ε-constraints. The best compromised solutions were achieved with the help of fuzzy decision-making processes. In [26], a local dispatch model for the minimization of NO_X emissions was developed. Thermal and wind units were considered. The impact of wind units were taken into account. The impact of wind energy was characterized through closed-form algorithms in incomplete function (IGF) terms. The authors derived the CDF of wind power. The model was successfully implemented on a power system consisting of six thermal and two wind units. In Ref. [27], the authors formulated the modified price penalty factor for solving the combined economic emission dispatch problem. The authors solved the CEED problem by the efficient particle swarm optimization technique and compared the results with DP, GA, EP, and MGSSA. In 2015, Bhattacharya et al. [16] proposed a hybrid cultural approach to solve the combined economic emission dispatch problem. Bi-objective optimization was converted into a single-objective problem using the price penalty factor. The results obtained were compared with the particle swarm optimization and genetic algorithm. In 2015, Hanenal Holttinen et al. [28] identified several issues that influenced the amount of wind power that can be added to a power system. The authors observed the different ways of minimizing the variability and forecast curves of wind power. They studied the wind integration level of 10–20% of the gross demand. The authors also recommended incorporating demand-side management in the economic operation of power systems.

In Ref. [29], an adaptive modified particle swarm optimization algorithm (APMSO) was presented for optimal and economic operations of a micro-grid with renewable energy resources. They considered the fuel cell, battery, and micro-turbine as back-ups to alternate energy resources for dealing with their intermittent nature search process, which was imposed by the hybrid PSO algorithm with a chaotic local search (CSS) mechanism and fuzzy self-adaptive (FSA) structure. They considered three scenarios as test cases. Non-dominated solution size was controlled by the fuzzy clustering-based approach. Pareto-optimal front was well-distributed. Similarly, U. Guvence et al. [30] proposed the gravitational search algorithm to solve the combined economic emission dispatch (CEED) problem. The bi-objective optimization problem was converted into a single-objective function by using a price penalty factor to solve it using the genetic search algorithm. The proposal approach was implemented on four test systems with different parameters and characteristics. In Ref. [31], the authors determined a optimal operation strategy, including a cost-minimization strategy and emission reductions in a micro-grid. The problem was considered a nonlinear constrained optimization problem. The micro-grid consisted of a micro-turbine, a wind turbine, a photovoltaic array, a diesel generator, battery storage, and a fuel cell. Security constraints were considered along with other physical constraints, and the cost function was minimized. The results of the proposed algorithm were compared with the MOSQPL multi-objective mesh adaptive direct search to show the quality of the result effects of different variables, such as weather conditions; purchased and sold tariffs and actual power demand on responses were also studied.

Rasoul Azizipanah et al. [32] incorporated wind power in the multi-objective economic emission dispatch problem to simultaneously handle generation costs and the emissions of fossil fuel fixed plants. They focused on the probabilistic nature of wind power and the stochastic algorithm based on the 2 m point estimation method. Considering the overestimation and underestimation of wind energy, the optimization algorithm used was a modified teaching learning algorithm, and a set of non-dominating optimal solutions were created. The fuzzy clustering-based technique was used to control the size of the optimal front repository, and a niching mechanism was employed to move the population towards smaller search space in the pareto optional front.

Chen et al. [33] introduced a prediction technique of a wind power and energy environmental efficiency concept in the economic emission dispatch problem of a wind power system. The prediction technique proposed was the time-series method for short-term predictions of wind speed. A hybrid PSO–SA algorithm was used with fuzzy optimization to solve the multi-objective problem. Low carbonization was emphasized by industry energy environmental efficiency in the modeling process of a combined economic emission dispatch. Bahman Firouzi et al. [34] presented a stochastic model to incorporate load and wind power uncertainties on an hourly basic. Probability distribution functions of wind power and load were used to implement the roulette wheel technique to generate different scenarios. For enhancing the performance of the particle swarm optimization, Q search, and fuzzy adaptive techniques, and for updating the velocity and turning inertia weight factor, a self-adaptive learning strategy was used, which helped the algorithm to avoid local entrapment. The nature of the search space was polar-coordinated, rather that Cartesian. The proposed algorithm was implemented in two different test systems. Constraints and other limitations included spinning reserve requirements, ramping limits, wind power constraints, and value point effects.

2. CEED Problem Formulation

The objective function for CEED in the presence of solar and wind units was solved to minimize the total cost of power generation as presented in Equation (1):

Minimize:

$${\mathrm{F}}_{\mathrm{T}}={\mathrm{w}}_1{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{x}}{\mathrm{H}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right) +{\mathrm{w}}_2{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{x}}{\mathrm{E}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right) +{\mathrm{w}}_3{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{F}}_{\mathrm{j}}\left({\mathrm{P}}_{\mathrm{j}}\right)+{\mathrm{w}}_4{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{U}}_{\mathrm{j}}\left({\mathrm{P}}_{\mathrm{j}}\right)+{\mathrm{w}}_5{{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{F}}_{\mathrm{w}}\left({\mathrm{P}}_{\mathrm{k}}\right)$$

(1)

where ${\mathrm{F}}_{\mathrm{T}}$ is the total cost of power generation.

$w_1$, $w_2$,$w_3$,$w_4$, and $w_5$ are the weights of thermal power production (fuel and emission costs), solar (production and unused solar power costs), and wind power costs, respectively. These weights are manually tuned and each of them represents the effect of their corresponding costs on the calculation of the overall power generation cost.

Additionally, $w_1$ + $w_2$ + $w_3$ + $w_4$ + $w_5$ = 1 is the necessary condition while tuning the weights.

${\mathrm{H}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$ is the fuel cost of the ${\mathrm{i}}_{\mathrm{th}}$ thermal unit. ${{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{x}}{\mathrm{H}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$ is the total fuel cost of x thermal units.

${\mathrm{E}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$ is the emission cost of the ${\mathrm{i}}_{\mathrm{th}}$ thermal unit. ${{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{x}}{\mathrm{E}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$ is the total emission cost of x thermal units.

Additionally, ${\mathrm{F}}_{\mathrm{j}}\left({\mathrm{P}}_{\mathrm{j}}\right)$ is the cost of the ${\mathrm{j}}_{\mathrm{th}}$ solar unit; ${{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{F}}_{\mathrm{j}}\left(\mathrm{j}\right)$ is the total cost of y solar units.

Additionally, ${\mathrm{U}}_{\mathrm{j}}\left({\mathrm{P}}_{\mathrm{j}}\right)$ is the penalty cost of the ${\mathrm{j}}_{\mathrm{th}}$ solar unit for not utilizing its available solar power; ${{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{F}}_{\mathrm{j}}\left(\mathrm{j}\right)$ is the total penalty cost of y solar units.

Additionally, ${\mathrm{F}}_{\mathrm{w}}\left({\mathrm{P}}_{\mathrm{k}}\right)$ is the cost of the ${\mathrm{w}}_{\mathrm{th}}$ wind unit; ${{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{F}}_{\mathrm{w}}$(${\mathrm{P}}_{\mathrm{k}}$) is the total cost of y wind units.

Each unit has its own cost associated with it. For thermal, solar, and wind units, this depends on thermal, solar, and wind unit cost coefficients of each unit, respectively.

2.1. Modeling of the Thermal Unit

The power dispatch of the thermal units is the minimization of both fuel and emission costs, which becomes a CEED problem [35]. The total cost of a thermal unit includes its fuel and emission costs. It is represented in Equation (2) as:

$${\mathrm{F}}_{\mathrm{i}}\left({\mathrm{P}}_{\mathrm{i}}\right)={\mathrm{H}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)+{\mathrm{E}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$$

(2)

where

${\mathrm{H}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$ is the fuel cost of the ${\mathrm{i}}_{\mathrm{th}}$ thermal unit.

${\mathrm{E}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)$ is the emission cost of the ${\mathrm{i}}_{\mathrm{th}}$ thermal unit.

The start-up and labor costs of a thermal unit are much lower than the fuel and emission costs; therefore, the considered total cost for a thermal unit is essentially the sum of fuel and emission costs only.

The fuel-cost equation of a thermal unit can be expressed either in convex (without considering the valve-point effect) or non-convex (considering the valve-point effect) forms. They are given as:

Convex Form:

$${\mathrm{H}}_{\mathrm{Th}} ({\mathrm{P}}_{\mathrm{i}})={\mathrm{a}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{b}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}+{\mathrm{c}}_{\mathrm{i}}$$

(3)

Non-Convex Form:

$${\mathrm{H}}_{\mathrm{Th}} ({\mathrm{P}}_{\mathrm{i}})={\mathrm{a}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{b}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}+{\mathrm{c}}_{\mathrm{i}}+\left|{\mathrm{e}}_{\mathrm{i}}\times \sin \left({\mathrm{f}}_{\mathrm{i}}\left({\mathrm{P}}_{\min ,\mathrm{i}}+{\mathrm{P}}_{\mathrm{i}}\right)\right)\right|$$

(4)

where ${\mathrm{a}}_{\mathrm{i}}$, ${\mathrm{b}}_{\mathrm{i}}$, ${\mathrm{c}}_{\mathrm{i}}$,${ \mathrm{e}}_{\mathrm{i}}$, and ${\mathrm{f}}_{\mathrm{i}}$ are the fuel-cost coefficients.

Similarly, the emission of each thermal unit is given as:

$$\mathrm{Emissions}={\mathrm{d}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{e}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}+{\mathrm{f}}_{\mathrm{i}}+{\mathsf{\mu }}_{\mathrm{g}}\ast \exp ({ \mathsf{\delta }}_{\mathrm{g}}.{ \mathrm{P}}_{\mathrm{g}})$$

(5)

where ${\mathrm{d}}_{\mathrm{i}}$, ${\mathrm{e}}_{\mathrm{i}}$, ${\mathrm{f}}_{\mathrm{i}}$, ${\mathsf{\mu }}_{\mathrm{g}}$, and ${\mathsf{\delta }}_{\mathrm{g}}$ are the emission coefficients of i-th thermal unit.

The emission cost of the i-th thermal unit is given as:

$${\mathrm{E}}_{\mathrm{Th}}\left({\mathrm{P}}_{\mathrm{i}}\right)={ \mathrm{v}}_{\mathrm{i}}({ \mathrm{d}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}^2+{\mathrm{e}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{i}}+{\mathrm{f}}_{\mathrm{i}}+{\mathsf{\mu }}_{\mathrm{i}}.\exp ({ \mathsf{\delta }}_{\mathrm{i}}.{ \mathrm{P}}_{\mathrm{i}}))$$

(6)

where ${ \mathrm{v}}_{\mathrm{i}}$ is the emission cost coefficient of the ${\mathrm{i}}_{\mathrm{th}}$ thermal generating unit.

2.2. Modeling of the Solar Unit

The power output by solar unit [36] is given by:

$${\mathrm{P}}_{\mathrm{j}}= \frac{{\mathrm{P}}_{\mathrm{rated}}}{1000}\{1+\mathsf{\beta }({\mathrm{T}}_{\mathrm{ref}}-{\mathrm{T}}_{\mathrm{amb}}\left)\right\}.{ \mathrm{S}}_{\mathrm{i}}$$

(7)

where ${\mathrm{P}}_{\mathrm{rated}}$ is the rated output power of the solar unit, ${\mathrm{T}}_{\mathrm{ref}}$ is the reference or fixed temperature of a region, and ${\mathrm{T}}_{\mathrm{amb}}$ is the ambient or variable temperature of the day. $\mathsf{{\rm B}}$ is the temperature coefficient and ${\mathrm{S}}_{\mathrm{i}}$ is incident solar radiation.

The solar share of m number of solar plants in the power system is given by:

$$\mathrm{Solar} \mathrm{Share}={{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{P}}_{\mathrm{j}}.{\mathrm{V}}_{\mathrm{j}}$$

(8)

where ${\mathrm{P}}_{\mathrm{j}}$ provides the power available in the ${\mathrm{j}}_{\mathrm{th}}$ solar plant and ${\mathrm{V}}_{\mathrm{j}}$ decides the working state of a solar unit, which is either 0 (OFF) or 1 (ON).

Since the power available at the output changes in accordance with the temperature and solar radiations, the output level for each solar unit varies with the temperature and radiance levels. Cost of operation of y solar unit to produce solar power is given as [37]:

$${\mathrm{F}}_{\mathrm{s}}({\mathrm{P}}_{\mathrm{j}})={{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{S}}_{\mathrm{j}}.{\mathrm{P}}_{\mathrm{j}}. {\mathrm{V}}_{\mathrm{j}}$$

(9)

where ${\mathrm{S}}_{\mathrm{j}}$ represents the per unit solar cost coefficient and is associated with each unit that produces solar power ${\mathrm{P}}_{\mathrm{j}}$.

Similarly, the penalty cost for unused solar power is given as:

$${\mathrm{U}}_{\mathrm{s}}({\mathrm{P}}_{\mathrm{j}})={{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{y}}{\mathrm{US}}_{\mathrm{j}}.{\mathrm{P}}_{\mathrm{j}}. (1-{\mathrm{V}}_{\mathrm{j}})$$

(10)

where ${\mathrm{US}}_{\mathrm{j}}$ represents the per unit unused solar cost coefficient and is different for each unit.

2.3. Modeling of the Wind Unit

The cost of the wind power unit [38] associated with schedule power ${\mathrm{P}}_{\mathrm{k}}$ is given in the following equation.

$${\mathrm{C}}_{\mathrm{w}}({\mathrm{P}}_{\mathrm{k}})={{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{z}}{\mathsf{\tau }}_{\mathrm{k}}. {\mathrm{P}}_{\mathrm{k}}$$

(11)

where ${\mathsf{\tau }}_{\mathrm{k}}$ is the wind power coefficient.

The velocity or speed of wind is a varying parameter and the power produced by the wind plant does not have a linear relationship with it. Wind value is given as input data for a certain hour of the day and the power output is computed. For wind power plants, power output depends on the speed of the wind, which is a variable parameter. As a result, the output power from wind plant also varies [39]. The probability density function of wind velocity is applied to calculate the scheduled wind power ${\mathrm{P}}_{\mathrm{k}}$ as a function of wind velocity [40]. Wind power is calculated from wind speed and is given as:

$${\mathrm{P}}_{\mathrm{k}}=\{\begin{array}{c}0 (\mathrm{v}<{\mathrm{v}}_{\mathrm{d}}, \mathrm{v} \ge {\mathrm{v}}_{\mathrm{m}})\\ {\mathrm{P}}_{\mathrm{i}}^{\mathrm{R}} \left({\mathrm{v}}_{\mathrm{n}}\le \mathrm{v}\le {\mathrm{v}}_{\mathrm{m}}\right)\\ \frac{\left(\mathrm{v}-{\mathrm{v}}_{\mathrm{in}}\right){\mathrm{P}}_{\mathrm{i}}^{\mathrm{R}}}{\left({\mathrm{v}}_{\mathrm{r}}-{\mathrm{v}}_{\mathrm{in}}\right)} ({\mathrm{v}}_{\mathrm{d}}\le \mathrm{v}<{\mathrm{v}}_{\mathrm{d}})\end{array}$$

(12)

Four zones of operation of a wind unit can be observed below in Figure 1:

The integration of the wind unit disturbs the security of the power system and affects its stability. It varies the spare capacity that accounts for the spare-capacity punishing cost. Spare capacity is the spare or extra power that occurs due to a difference in the scheduled wind power that is produced by the plant and actual wind power that is delivered to the load. Actual power delivered to the load is less than the scheduled power due to practical losses in the system. This difference in power accounts for a penalty cost that is called spare-capacity punishing or penalty cost. This cost is given by:

$${\mathrm{C}}_{\mathrm{RW},\mathrm{K}}={{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{z}}{\mathrm{r}}_{\mathrm{k}}\times ({\mathrm{P}}_{\mathrm{k}}- {\mathrm{P}}_{\mathrm{k},\mathrm{act}})$$

(13)

where ${\mathrm{r}}_{\mathrm{k}}$ is the spare capacity’s cost coefficient, ${\mathrm{P}}_{\mathrm{k}}$ is the schedule power generation, and ${\mathrm{P}}_{\mathrm{k},\mathrm{act}}$ is the actual wind power that is delivered to load. The spare-capacity punishing cost is added to the cost given in Equation (13) to present the total cost as:

$${\mathrm{F}}_{\mathrm{w}}({\mathrm{P}}_{\mathrm{k}})={{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{z}}{\mathsf{\tau }}_{\mathrm{k}}. {\mathrm{P}}_{\mathrm{k}}+{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{z}}{\mathrm{r}}_{\mathrm{k}}. ({\mathrm{P}}_{\mathrm{k}}- {\mathrm{P}}_{\mathrm{k},\mathrm{act}})$$

(14)

2.4. Power-Balance Constraint

This constraint must be fulfilled at any cost; if the total power generation is less than the load demand, then the target of the sustainable and reliable supply of electrical energy will not be achieved. On the other hand, if the total power generation is exceeded by the load demand, then the cost of this extra production rate has to be paid. Therefore, the total power produced by thermal, solar, and wind power plants must be equal to the load demand and transmission system losses. Mathematically,

$${{\displaystyle \sum }}_{i=1}^x{P}_i+{{\displaystyle \sum }}_{j=1}^y{P}_j+{{\displaystyle \sum }}_{k=1}^z{P}_k=P_D+P_{Loss}$$

(15)

where $P_{Loss}$ is the transmission system loss, which is presented by the Krons formula as:

$$P_{Loss}={{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^n{P}_i{B}_{ij}{P}_j+{{\displaystyle \sum }}_{i=1}^n{B}_{i0}{P}_i+B_{00}$$

(16)

where $B_{ij}$, $B_{i0}$, and $B_{00}$ are the loss coefficient of George’s formula, transmission loss constant of generating unit i, and Kron’s transmission loss constant, respectively.

2.5. Thermal Units’ Power Limits

For a stable operation of the power system, the total power generation of each generating unit must be within its maximum and minimum limits. It can be described as follows:

$$P_{min,i}\le P_i\le P_{max,i}$$

(17)

The maximum generation level of power is limited by the potential of a thermal unit to produce active power, and the minimum generation is limited by the flame instability of the furnace or boiler. If the output power of a generating unit is less than a pre-defined value $, P_{min,i}$, then this generator is not connected to the bus bar since it is not feasible to produce a small value of active power from that generator. Therefore, the power that is produced cannot violate the limits of the boundary.

2.6. Wind Units’ Power Limits

A solution is not feasible if the power limit constraint is not satisfied. Depending upon the capacity of the wind power plant, the maximum power that is produced from the wind speed is limited. Similarly, if the wind unit violates the lower limit of power, the unit will not be connected to the system. This is because a very-low power output value is not feasible for the system. The cost is minimized by the optimal scheduling of power within the generation limits. Power produced by wind plants must be in-between the lower and upper limits.

$${\mathrm{P}}_{\min ,\mathrm{k}}\le {\mathrm{P}}_{\mathrm{k}}\le {\mathrm{P}}_{\max ,\mathrm{k}}$$

(18)

2.7. Ramp Rate Constraint

All the generating units are practically restricted to operate in a certain operating range because of their ramp rate limits. Therefore, they must operate in two adjacent, specific operation zones. It is necessary to consider the generator ramp rate limit to accurately formulate the CEED value. Therefore, the power output of each generating unit considering the ramp rate limit can be formulated as below:

$$\mathrm{Max} ({\mathrm{P}}_{\mathrm{gi},\min }, {\mathrm{P}}_{\mathrm{gi}}^0-{\mathrm{DR}}_{\mathrm{i}}) \le {\mathrm{P}}_{\mathrm{gi}}\le \mathrm{Min} ({\mathrm{P}}_{\mathrm{gi},\max }, {\mathrm{P}}_{\mathrm{gi}}^0+{\mathrm{UR}}_{\mathrm{i}})$$

(19)

where ${\mathrm{P}}_{\mathrm{gi}}^0$ refers to the previous operating point of generating unit i $;{ \mathrm{DR}}_{\mathrm{i}}$ and ${\mathrm{UR}}_{\mathrm{i}}$ are the downrate and uprate limits of the generating unit i, respectively.

2.8. Prohibited Operating Zones

In a practical power generation system, the whole operating range of the generating unit is not always available for operation. Physical operational limitation can cause some units to have prohibited operating zones, and operating in these zones may lead to instabilities. For that reason, the generation output must avoid operation in the prohibited operating zones. Therefore, generating unit $\mathrm{i}$ should operate in the feasible operating zones described below:

$${\mathrm{P}}_{\mathrm{k}}=\{\begin{array}{c}{\mathrm{P}}_{\mathrm{gi},\min }\le {\mathrm{P}}_{\mathrm{gi}}\le {\mathrm{P}}_{\mathrm{gi},1,}^{\mathrm{L}}\\ {\mathrm{P}}_{\mathrm{gi},\mathrm{j}-1}^{\mathrm{U}}\le {\mathrm{P}}_{\mathrm{gi}}\le {\mathrm{P}}_{\mathrm{gi},\mathrm{j},}^{\mathrm{L}}\\ {\mathrm{P}}_{\mathrm{gi},\mathrm{Ki}}^{\mathrm{U}} \le {\mathrm{P}}_{\mathrm{gi}}\le {\mathrm{P}}_{\mathrm{gi}, \max }\end{array} \mathrm{j}=2,3\dots \dots ..\dots ,{ \mathrm{K}}_{\mathrm{i}}$$

(20)

where ${\mathrm{K}}_{\mathrm{i}}$ refers to the number of prohibited operating zones in the curve of the generating unit i, j represents the index of the prohibited operating zone of the generating unit i, and ${\mathrm{P}}_{\mathrm{gi},1,}^{\mathrm{L}}$ and ${\mathrm{P}}_{\mathrm{gi},\mathrm{j}-1}^{\mathrm{U}}$ are the lower limit of the jth prohibited zone and upper limit of the (j−1)-th prohibited operating zone of generating unit i, respectively.

3. Proposed Solution Methodology

Salp Swarm Algorithm

No free-luncheon theorem and few swarm-based algorithms motivated Mirjalili to propose a new swarm intelligence-based algorithm called the salp swarm algorithm in 2017. This algorithm is based upon the swarming behavior of salp. Salp is a marine specie with a translucent bucket-type body, and its shell composition and habits of movement resemble those of jellyfish. By letting the surrounding water flow through its barrel-like form, it creates a reverse-propulsive force when moving. The most interesting thing is that salp swarming varies from that of other social mammals; therefore, the SSA uses a special method for updating its swarm algorithm. The population is sequenced in each iteration, and each member closely follows a previous individual, instead of all salps only attaining the optimum value, thus making a chain with the whole population called a salp chain. Its individual shape and a salp chain are presented in Figure 2:

The proposed equation for updating the leader salp is as follows:

$$X_d^1=\{\begin{array}{c}{F}_d+c_1\left(\left(u{b}_d-l{b}_d\right)c_2+l{b}_d\right), c_3\ge 0.5\\ F_d-c_1\left(\left(u{b}_d-l{b}_d\right)c_2+l{b}_d\right), c_3<0.5\end{array}$$

(21)

$X_d^1$ is the position of the leader salp in the $d^{th}$ dimension; $F_d$ is the position of the target food source in the $d^{th}$ dimension. $u{b}_d$ presents the upper bound or limit of the $d^{th}$ dimension; similarly, $l{b}_d$ represents the lower bound of the $d^{th}$ dimension.

It is clear form Equation (21) that the leader salp only updates itself with respect to the target food source. This is an important quality of SSA because it ensures that the leader always follows the target food, no matter how diversified, non-smooth, and noisy the search space. $c_1$,$c_2$, and $c_3$ in Equation (21) are the control parameters. The pseudo-code of the SSA is shown in Figure 3. The most important control parameter is $c_1$, which stabilizes the exploration and exploitation phases during the search process in each iteration and is defined as follows:

$$c_1=2e^{-{\left(\frac{4l}{l_{max}}\right)}^2}$$

(22)

where $l$ and $l_{max}$ are the current and maximum numbers of iterations, respectively.

$c_2$ and $c_3$ are randomly generated numbers between [0, 1] used to boost the randomness of the leader’s movement and strengthen the exploratory capabilities of the search process. $c_2$ determines the step size of the leader’s movement and $c_3$ determines the leader’s movement direction in the $d^{th}$ dimension, either towards positive or negative infinities.

The movement of the followers accords with Newton’s second equation of motion.

Hence, the movement distance or step size R of follower salps is defined by Equation (23) as:

$$\mathrm{R}=\frac{1}{2}a{t}^2+V_{0}t$$

(23)

t is the difference between consecutive iterations. It is taken as 1. $V_0$ is the initial speed of the follower; it is taken as 0 at the beginning of each iteration and a is the acceleration of the follower.

$$\mathrm{a}=\frac{\left({\mathrm{V}}_{\mathrm{final}}-V_0\right)}{\mathrm{t}}$$

(24)

where

$${\mathrm{V}}_{\mathrm{final}}=\frac{\left({\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}-1}\right)-\left({\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}}\right)}{\mathrm{t}}$$

(25)

${\mathrm{V}}_{\mathrm{final}}$ is the speed of the follower salp following the previous salp located at the ${\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}-1}$ position in the $d^{th}$ dimension, and $X_d^m$ is the current position of the follower salp in the $d^{th}$ dimension.

For t = 1 and $V_0=0$:

$$\mathrm{R}=\frac{1}{2}(X_d^{m-1}-X_d^m)$$

(26)

Therefore, the follower salps update their positions as:

$${\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}\ast }={\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}}+\mathrm{R}$$

(27)

$${\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}\ast }=\frac{\left({\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}}+{\mathrm{X}}_{\mathrm{d}}^{\mathrm{m}-1}\right)}{2}$$

(28)

A novel, chaotic, improved salp swarm algorithm (CSSA) was proposed in this work where a chaotic map was utilized to replace random variables with chaotic variables. The original SSA has three control parameters that influence its performance. These parameters are $c_1$,$c_2$, and $c_3$. It is obvious from Equation (22) that $c_1$ is exponentially reduced over the path of iterations, whereas $c_3$ is responsible for determining whether the following position should be towards a positive or negative infinity value. As it is evident from Equation (21), $c_1$ and $c_2$ are both the main control parameters impacting the updated position of the salps. Therefore, they have a direct impact on the balance between diversification and intensification. Diversification deals with attaining new, improved solutions by exploring the search space on a relatively larger scale, whereas intensification deals with exploiting the search points in a local region [7]. An algorithm must appropriately balance these two search phases to obtain the near-global optima. In this work, a chaotic map was employed to adjust the $c_2$ parameter of SSA. Equation (29) shows the updating of the $c_2$ parameter according to the selected chaotic map. Equation (30) shows the updated position of the leader salp according to the chaotic map, where $o^t$ is the obtained value of the selected chaotic map at the t–th iteration.

$$c_2=o_s$$

(29)

For a logistic chaotic map, chaotic variable $c_2$ is generated and updated as:

$$o_s={\mathrm{c}}_{2\mathrm{l}+1}=\mathsf{\mu }{\mathrm{c}}_{2\mathrm{l}}(1-{\mathrm{c}}_{2\mathrm{l}})$$

(30)

where µ is the chaotic adjustment factor. When µ is equal to 4, the logistic map is completely chaotic. ${\mathrm{c}}_{2\mathrm{l}+1}$ is the subsequent value of the chaotic variable and ${\mathrm{c}}_{2\mathrm{l}}$ is the current value.

$$X_d^1=\{\begin{array}{c}{F}_d+c_1\left(\left(u{b}_d-l{b}_d\right)o^t+l{b}_d\right), c_3\ge 0.5\\ F_d-c_1\left(\left(u{b}_d-l{b}_d\right)o^t+l{b}_d\right), c_3<0.5\end{array}$$

(31)

Embedding the chaotic maps in the updated position of the leader salp enhances the convergence rate and performance of SSA. The process of updating the position of the follower salps is the same as previously mentioned.

For the cases in which the amount of renewable shares included in the dispatch process is controlled instead of dispatching all the generated renewable power, the generating units are controlled as on or off in the decision-making process. Therefore, a binary version of the algorithm is mandatory to select the generating units form the available pool of renewable generating units as per decision.

A pool of random generating units is created by a random function defined by Equation (32):

$${\mathrm{X}}_{\mathrm{i}}^{\mathrm{k}}\left(\mathrm{t}\right)=\{\begin{array}{c}0, \mathrm{if} \mathrm{rand}<0.5 \\ 1, \mathrm{if} \mathrm{rand} \ge 0.5\end{array}$$

(32)

One of the most efficient ways to update the binary positions is to utilize transfer functions (TFs). The purpose of a TF is to define a probability for updating an element in the calculated solution subset to be 1 (selected) or 0 (not selected), as in Equation (32), which was proposed by Kennedy and Eberhart [36] to covert the original PSO to a binary version.

$$T(X_j^i\left(t\right))=\frac{1}{1+ex{p}^{-X_j^i\left(t\right)}}$$

(33)

where $X_j^i$ is the j-th element in X solution in the $i_{th}$ dimension, and t is the current iteration.

An element of the solution in the subsequent iteration can be updated by Equation (34) as:

$$X_j^i\left(t+1\right)=\{\begin{array}{c}0, if rand<T(X_j^i\left(t\right)) \\ 1, if rand \ge T(X_j^i\left(t\right))\end{array}$$

(34)

where $X_i^k(t+1)$ is the $j^{th}$ element in the X solution in the $i_{th}$ dimension and $T(X_j^i\left(t\right))$ is the probability that can be calculated via Equation (33).

In Figure 4, the flowchart of the CISSA algorithm is presented.

4. Results and Discussion

In this section, the proposed algorithm is tested on different test cases having different scenarios and combinations of thermal, solar, and wind units. These case studies had different weather conditions and different numbers of generating units.

These case studies are available in different research publications. Simulations were conducted on MATLAB R2015a with the system specifications as core i5, 4 GB Ram with a 2.30 GHz processor. The results of the proposed algorithm for the listed test cases were compared with original research papers; the obtained results present the superiority of the proposed optimization algorithm over other algorithms.

The following pages present the case studies and results. Each case study is explained in terms of different parameters, such as Number of thermal, solar, and wind units, and factors, such as weather conditions, including solar irradiance level, ambient temperature, and wind speed, which impact solar and wind generation. Details of fuel-cost parameters, emission parameters, and daily load demand are provided in the original research papers of the case studies. All the case studies’ problems were solved for 24 h on an hourly basis. The results of the case studies include details of thermal unit generations, renewable unit generations on an hourly basis, and graphical representations of the effect of renewable units on fuel cost and emissions. A comparison of CISSA with original algorithms on a 24-h basis in terms of fuel cost, emissions, and total generation cost is presented in tabular as well as graphical forms.

4.1. Case Study 1

This case study contained three thermal units, one wind unit, and one solar unit. In this case study, thermal generating units had convex fuel-cost characteristics. Cost coefficients of thermal units were provided in Ref. [39].

Table 1. List of abbreviations.

CEED Combined Economic Emission Dispatch

SSA Salp Swarm Algorithm

CISSA Chaotic Improved Salp Swarm Algorithm

RES Renewable Energy Sources

LCOE Levelised Cost of Electricity

IERNA: International Renewable Energy Agency

PSO: Particle Swarm Algorithm

ACO: Ant Colony Optimization

ABC-SA: Artificial Bee Colony-Simulated Annealing

MPC: Model Predictive Technique

NSGA: Non-Dominating Sorting Genetic Algorithm

LP: Linear Programming

SPEA: Strength Pareto Evolutionary Algorithm

NPGA: Nichel Pareto Algorithm

FCPSO: Fuzzy Clustering-based Particle Swarm Algorithm

DE: Differential Evolution

AMPSO: Adaptive Modified Particle Swarm Algorithm

ANN: Artificial Neural Network

CDF: Cumulative Distributive Function

PV: Photovoltaic

provides the details of algorithm parameters and the relevant details that were used to solve the dynamic CEED problem.

4.2. Results for Case Study 1

This section presents the results for case study 1 and a comparison of the results between the proposed algorithm (CISSA) and existent research.

Table 2. Algorithm parameters, constraints, and renewable data—case study 1.

Cost Parameters	Solar Cost	Installation Cost 5000 USD/KW
		O and M Cost 1.6 cents/KW
	Wind Cost	Installation Cost 1400 $/KW
		O and M Cost 1.6 cents/KW
	Thermal Cost Coefficients	As Presented in Original Paper
Algorithm Parameters	Constraints	Power Generation Limits
		Power Balance
		Ramp Rate, Dynamic CEED
	Chaotic Map	Logistic
	Chaotic Adjustment Factor	4
	Number of Search Agents	30
	Maximum Iterations	200

presents the details of the load demand for a specific day and hourly generation of three thermal units, one wind unit, and one solar unit, which were generated by CISSA.

Table 3. Hourly load demand and power generation—case study 1.

Hour	$P_{Load} \mathbf{MW}$	$P_{Unit 1} \mathbf{MW}$	$P_{Unit 2} \mathbf{MW}$	$P_{Unit 3} \mathbf{MW}$	$P_{Thermal} \mathbf{MW}$	$P_{Solar} \mathbf{MW}$	$P_{Wind} \mathbf{MW}$
1	140	48.3	40	50	138.3	0	1.7
2	150	51.5	40	50	141.5	0	8.5
3	155	55.73	40	50	145.73	0	9.27
4	160	53.34	40	50	143.34	0	16.66
5	165	64.33583	43.44417	50	157.78	0	7.22
6	170	66.59233	48.46767	50	165.06	0.03	4.91
7	175	63.65604	40.41396	50	154.07	6.27	14.66
8	180	47.26	40	50	137.26	16.18	26.56
9	210	66.38065	48.76473	50.22463	165.37	24.05	20.58
10	230	68.36673	52.04519	52.36808	172.78	39.37	17.85
11	240	74.75121	67.57266	77.46612	219.79	7.41	12.8
12	250	75.86422	70.24693	81.58884	227.7	3.65	18.65
13	240	71.14166	59.01065	63.55769	193.71	31.94	14.35
14	220	69.71556	55.51729	57.60715	182.84	26.81	10.35
15	200	69.58925	55.11917	56.85158	181.56	10.08	8.36
16	180	65.56645	45.42355	50	160.99	5.03	13.71
17	170	64.44637	42.54363	50	156.99	9.57	3.44
18	185	69.48132	54.88047	56.45822	180.82	2.31	1.87
19	200	71.89036	60.6936	66.66604	199.25	0	0.75
20	240	77.52649	74.19455	88.10896	239.83	0	0.17
21	225	75.49918	69.24357	80.10725	224.85	0	0.15
22	190	70.71525	57.77498	61.19978	189.69	0	0.31
23	160	65.07196	43.85804	50	158.93	0	1.07
24	145	54.42	40	50	144.42	0	0.58

presents the data of fuel, emission, and total costs, and emissions of the day generated by CISSA.

Figure 5 presents the effects of RES integration on emissions and fuel costs for case study 1. In the subsequent section, the comparison of different algorithms is presented.

4.3. Comparison of CISSA with ACO

Table 4. Table of costs and emissions for 24 h—case study 1.

Hour	Fuel Cost USD/h	Emission Cost USD/h	Total Cost $/h	Emission Kg/h	Hour	Fuel Cost USD/h	Emission Cost USD/h	Total Cost USD/h	Emission Kg/h
1	6117.58	1035.46	7153.04	85.098	13	7409.49	1072.48	8481.97	97.39
2	6192.45	1010.73	7203.18	84.116	14	7156.16	1029.78	8185.94	90.76
3	6292.17	986.35	7278.52	83.147	15	7126.55	1025.18	8151.73	90.02
4	6235.72	998.96	7234.69	83.648	16	6650.14	971.63	7621.78	82.79
5	6575.46	968.72	7544.18	82.568	17	6557.72	967.76	7525.48	82.48
6	6744.6	977.99	7722.59	83.292	18	7109.39	1022.61	8132.01	89.62
7	6490.63	966.33	7456.97	82.360	19	7539.46	1097.11	8636.58	101.24
8	6093.36	1044.65	7138.02	85.464	20	8510.15	1335.58	9845.74	136.84
9	6751.36	979.09	7730.45	83.481	21	8148.23	1235.47	9383.70	121.90
10	6923.56	996.98	7920.54	85.727	22	7315.70	1055.70	8371.41	94.70
11	8026.89	1204.88	9231.77	117.38	23	6602.59	969.28	7571.87	82.61
12	8216.76	1253.43	9470.19	124.56	24	6261.19	992.89	7254.09	83.40

shows the comparison of the various algorithms to present the effectiveness of the proposed results. Similarly, Figure 6 exhibits the comparison of the two algorithms, while

Table 5. Fuel-cost comparison between CISSA and ACO.

Hour	Fuel-Cost ACO USD/h	Fuel-Cost CISSA USD/h	Hour	Fuel-Cost ACO USD/h	Fuel-Cost CISSA USD/h
1	6106.738	6117.589	13	7384.913	7409.49
2	6176.372	6192.454	14	7150.237	7156.161
3	6289.369	6292.17	15	7126.594	7126.553
4	6243.904	6235.724	16	6639.469	6650.145
5	6570.866	6575.46	17	6543.385	6557.722
6	6729.421	6744.6	18	6846.125	7109.391
7	6507.826	6490.638	19	7529.489	7539.464
8	6086.593	6093.364	20	8518.081	8510.157
9	6727.945	6751.361	21	8149.618	8148.23
10	6913.168	6923.561	22	7314.205	7315.709
11	8032.688	8026.892	23	6588.538	6602.596
12	8221.33	8216.764	24	6267.608	6261.197

presents the differences in the fuel costs.

4.4. Emissions Comparison

The emission rate is a very important factor for the situation at present. In

Table 6. Difference in total daily fuel costs—case study 1.

Daily Fuel-Cost ACO (USD)	Daily Fuel-Cost CISSA (USD)	Difference in Costs
166,664.5	167,047.4	−0.22975%

and Figure 7, the emission comparison is presented to show the efficacy of the proposed model. Almost all hours present lower emissions as compared to the other method.

The overall result related to the emissions is presented in

Table 7. Emission comparison between CISSA and ACO.

Hour	Emission ACO Kg/h	Emission CISSA Kg/h	Hour	Emission ACO Kg/h	Emission CISSA Kg/h
1	93.801	85.09885	13	122.901	97.39708
2	88.0315	84.11613	14	123.799	90.76616
3	92.8705	83.1471	15	122.163	90.02062
4	91.348	83.64843	16	111.688	82.79879
5	99.977	82.56816	17	108.015	82.48869
6	91.907	83.29237	18	95.0325	89.62587
7	83.3145	82.36095	19	132.243	101.2411
8	85.986	85.46453	20	158.8645	136.8401
9	110.045	83.48196	21	144.9085	121.9077
10	109.0235	85.72739	22	104.4275	94.7053
11	148.516	117.3866	23	104.4585	82.61167
12	144.655	124.5634	24	103.7935	83.40703

.

4.5. Total Cost Comparison

The total cost comparison is presented in

Table 8. Reduction in total daily emissions—case study 1.

Daily Emission ACO (USD)	Daily Emission CISSA (USD)	Reduction in Emission
2671.769	2234.666	16.36%

that seems more improved, when compared to the ACO.

For further clarification, the results presented in Table 8 are also shown in Figure 8, whereas

Table 9. Total cost comparison between CISSA and ACO.

Hour	Total Cost ACO USD/h	Total Cost CISSA USD/h	Hour	Total Cost ACO USD/h	Total Cost CISSA USD/h
1	7255.975	7153.048	13	8579.882	8481.979
2	7274.662	7203.188	14	8420.284	8185.941
3	7432.354	7278.523	15	8366.222	8151.738
4	7344.673	7234.69	16	7833.572	7621.781
5	7808.296	7544.184	17	7762.587	7525.489
6	7775.861	7722.598	18	7940.027	8132.01
7	7482.405	7456.976	19	8768.133	8636.582
8	7143.74	7138.023	20	9963.94	9845.741
9	7941.317	7730.453	21	9479.989	9383.708
10	8105.525	7920.543	22	8439.506	8371.415
11	9411.08	9231.774	23	7762.454	7571.879
12	9545.323	9470.199	24	7497.614	7254.09

shows the total daily cost comparison.

In

Table 10. Total daily cost comparison—case study 1.

Total Daily Cost PSO (USD)	Total Daily Cost CISSA (USD)	Cost Saving
195,335.4	192,246.6	1.58%

the daily cost comparison is presented.

4.6. Test Case 2

In 2016, Naveed A. Khan et al. [41] applied the particle swarm optimization algorithm to solve the combined economic emission dispatch for a power system containing 6 thermal and 13 solar units. This problem was solved by CISSA in the current study.

4.7. Description of Case Study 2

The details of the rated power and per unit cost of solar units as provided in the original paper are presented below:

The solar unit details, weather conditions of the day in terms of ambient temperature and solar radiation are given for 24 h in

Table 11. Solar unit details.

Solar Unit No.	Rated Power	Per Unit Cost
1	20	0.22
2	25	0.23
3	25	0.23
4	30	0.24
5	30	0.24
6	35	0.25
7	35	0.26
8	40	0.27
9	40	0.27
10	40	0.275
11	40	0.28
12	40	0.28
13	40	0.28

and

Table 12. Hourly solar irradiance level, ambient temperature, and wind speed.

Hour	Solar Irradiance $\mathbf{Level} \mathbf{W}/{\mathbf{m}}^2$	Ambient Temperature °C	Wind Speed (m/s)	Hour	Solar Irradiance Level $\mathbf{W}/{\mathbf{m}}^2$	Ambient Temperature °C	Wind Speed (m/s)
1	0	30	10.4	13	1013.5	37	13.1
2	0	29	9.7	14	848.2	37	13.4
3	0	28	10	15	726.7	37	13.4
4	0	28	11.1	16	654	38	12.7
5	5.4	28	11.4	17	392.9	38	12.5
6	101	28	12.2	18	215.1	37	11.9
7	253.7	29	14.7	19	385.0	35	10.9
8	541.2	31	16	20	0	34	10.8
9	530.4	33	15.7	21	0	34	10.2
10	793.9	34	15	22	0	33	9.9
11	1078	35	15.9	23	0	32	10.5
12	1125.6	36	14.7	24	0	31	10.5

.

In this study, a wind power plant was integrated into the existent system.

Other relevant data are presented in

Table 13. Algorithm parameters, constraints, and renewable data—case study 2.

Algorithm Parameters	Constraints	Units Generation Limits
		Power Balance
		Ramp Rate, Dynamic CEED
		Prohibited Operating Zones
	Chaotic Map	Logistic
	Chaotic Adjustment Factor	4
	Number of Search Agents	30
	Maximum Iterations	200
Thermal Units	Number of Units	6
	Thermal Cost Coefficients	As Presented in Original Paper
Solar Units	Number of Units	13
	Reference Temperature	25 °C
	Temperature Coefficient	0.0025
	Solar Cost Coefficient	As Presented in Original Paper
Wind Units	Number of Units	33
	Rated Power of Each Unit	1.6 MW
	Wind Speed Rating of Each Unit	Rated: 12.5 m/s
		Cut-in: 3 m/s
		Cut-out: 25 m/s
	Wind Power Cost Coefficient	100

as follows:

4.8. Results for Case Study 2

This section presents the results for case study 2 and a comparison of the results between the proposed algorithm (CISSA) and existent research.

Table 14. Solar unit switching status for the analysis.

Hour	Solar Unit Status
* 10 am	1	0	1	1	1	1	1	1	1	0	0	1	0
11 am	0	1	1	1	1	1	1	0	1	0	0	0	0
12 pm	1	1	1	1	1	1	1	0	0	1	0	0	0
13 pm	1	1	1	1	0	1	0	0	1	0	0	0	0
14 pm	1	1	1	1	1	1	0	1	0	0	1	0	0
15 pm	1	1	0	1	1	1	1	1	1	0	0	0	0

* For the remaining hours, either the solar irradiance level is zero or the solar share is so less so it does not cause an appreciable reduction in fuel costs and emissions; instead, the small reduction is overcome by the increased generation cost due to expensive solar energy.

explains the solar unit switching status determined by a binary version using CISSA.

Table 15. Hourly load demand and power generation values—case study 2.

Hour	${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{a}\mathit{d}} \mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 1} \mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 2}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 3}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 4}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 5}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 6}\mathbf{MW}$	${\mathit{P}}_{\mathit{T}\mathit{h}\mathit{e}\mathit{r}}\mathbf{MW}$	${\mathit{P}}_{\mathit{S}\mathit{o}\mathit{l}\mathit{a}\mathit{r}}\mathbf{MW}$	${\mathit{P}}_{\mathit{W}\mathit{i}\mathit{n}\mathit{d}}\mathbf{MW}$
1	955	304.3	117.5	203.5	90.2	131.8	66.0	913.4	0.0	41.6
2	942	303.4	115.8	202.4	90.0	129.6	63.1	904.3	0.0	37.7
3	953	304.6	117.6	203.6	90.1	132.1	65.8	913.7	0.0	39.3
4	930	302.3	113.9	201.2	80.0	127.2	60.0	884.5	0.0	45.5
5	935	302.7	114.6	201.6	80.0	127.8	61.0	887.8	0.0	47.2
6	963	303.1	117.2	202.8	90.0	131.9	66.2	911.3	0.0	51.7
7	989	305.5	121.1	205.2	94.4	136.9	72.5	935.6	0.0	53.4
8	1023	306.4	127.6	207.9	102.3	140.0	85.4	969.6	0.0	53.4
9	1126	300.8	140.0	210.0	129.1	172.7	120.0	1072.6	0.0	53.4
10	1150	208.9	115.5	182.1	109.2	132.7	119.3	867.7	228.9	53.4
11	1201	210.0	127.5	186.4	120.9	151.6	119.9	916.4	231.2	53.4
12	1235	210.0	134.7	190.7	144.5	129.2	109.8	918.9	262.7	53.4
13	1190	262.2	135.6	170.0	147.6	129.2	120.0	964.6	172.0	53.4
14	1251	269.9	131.1	194.1	120.0	163.9	117.1	996.0	201.6	53.4
15	1263	277.5	137.7	199.8	123.1	171.7	120.0	1029.9	179.7	53.4
16	1250	316.4	170.2	240.0	150.0	200.0	120.0	1196.6	0.0	53.4
17	1221	317.7	169.9	210.0	150.0	200.0	120.0	1167.6	0.0	53.4
18	1202	310.2	164.6	210.0	149.4	197.7	120.0	1152.0	0.0	50.0
19	1159	307.4	160.0	210.0	132.2	185.1	120.0	1114.6	0.0	44.4
20	1092	303.6	139.4	210.0	120.0	165.0	110.1	1048.2	0.0	43.8
21	1023	306.9	128.3	208.4	102.9	150.0	86.0	982.5	0.0	40.5
22	984	308.0	122.6	206.8	95.5	138.5	73.9	945.2	0.0	38.8
23	975	306.3	120.6	205.5	93.5	136.0	71.0	932.8	0.0	42.2
24	960	304.8	118.2	203.8	90.8	132.9	67.2	917.8	0.0	42.2

presents the details of the load demand for a specific day and hourly generation of 6 thermal units, the wind power share of one wind power plant (33 units), and 13 solar units generated by CISSA.

Table 16. Table of costs and emissions for 24 h—case study 2.

Hour	Fuel Cost USD/h	Emission Cost USD/h	Solar Cost USD/h	Wind Cost USD/h	Total Cost USD/h	Emission Kg/h
1	10,769.41	2571.28	0.00	4159.57	17,500.27	955.46
2	10,657.04	2481.15	0.00	3766.10	16,904.29	946.25
3	10,772.03	2563.83	0.00	3934.73	17,270.59	956.46
4	10,410.02	2378.82	0.00	4553.05	17,341.88	929.83
5	10,450.79	2412.59	0.00	4721.68	17,585.06	933.34
6	10,745.16	2597.12	0.00	5171.36	18,513.64	950.05
7	11,048.15	2799.62	0.00	5339.99	19,187.77	974.87
8	11,480.75	3309.59	0.00	5339.99	20,130.34	1003.91
9	12,842.15	5352.70	0.00	5339.99	23,534.84	1084.02
10	10,455.56	3756.24	58,358.00	5339.99	77,909.79	706.03
11	11,066.63	4656.27	57,334.78	5339.99	78,397.67	760.57
12	11,096.41	4951.08	64,748.31	5339.99	86,135.80	786.22
13	11,594.84	5232.45	41,929.00	5339.99	64,096.28	878.29
14	11,927.93	5935.31	50,229.13	5339.99	73,432.36	930.33
15	12,344.18	6348.06	45,113.54	5339.99	69,145.77	985.46
16	14,421.66	8388.20	0.00	5339.99	28,149.86	1315.87
17	14,071.11	7740.05	0.00	5339.99	27,151.15	1243.35
18	13,877.00	7403.10	0.00	5002.73	26,282.83	1208.23
19	13,379.10	6296.92	0.00	4440.63	24,116.65	1152.52
20	12,508.59	4691.81	0.00	4384.42	21,584.81	1067.27
21	11,644.99	3351.94	0.00	4047.15	19,044.08	1016.75
22	11,165.15	2816.71	0.00	3878.52	17,860.38	989.97
23	11,011.32	2729.26	0.00	4215.78	17,956.36	975.64
24	10,824.59	2608.82	0.00	4215.78	17,649.20	959.93

and Figure 9 present the cost and emission values for 24 h in case study 2.

4.9. Comparison of CISSA and PSO

In this subsection, a fuel-cost comparison is presented to show the efficacy of the proposed method. Almost all the results improved, except for hours 11, 12, and 13, while the

Table 17. Fuel-cost comparison between CISSA and PSO.

Hour	Fuel-Cost PSO USD/h	Fuel-Cost CISSA USD/h	Hour	Fuel-Cost PSO USD/h	Fuel-Cost CISSA USD/h
1	11,237	10,769.41	13	10,616	11,594.84
2	11,028	10,657.04	14	11,992	11,927.93
3	11,355	10,772.03	15	12,654	12,344.18
4	10,990	10,410.02	16	14,918	14,421.66
5	10,935	10,450.79	17	14,485	14,071.11
6	11,497	10,745.16	18	14,367	13,877.00
7	11,711	11,048.15	19	13,762	13,379.10
8	12,021	11,480.75	20	12,386	12,508.59
9	13,348	12,842.15	21	12,126	11,644.99
10	11,002	10,455.56	22	11,646	11,165.15
11	10,633	11,066.63	23	11,564	11,011.32
12	10,758	11,096.41	24	11,285	10,824.59

shows the fuel cost comparison between CISSA and PSO.

Figure 10 presents the fuel comparison of the two methods, while

Table 18. Reduction in daily fuel cost—case study 2.

Total Daily Fuel-Cost PSO (USD)	Total Daily Fuel-Cost CISSA (USD)	Cost Saving
288,316	280,564.54	2.7%

shows the main reduction in the overall results.

4.10. Emission Comparison

As previously discussed, emissions are also very important factor; therefore, it was also compared to the PSO, as presented in

Table 19. Emissions comparison between CISSA and PSO.

Hour	Emission PSO Kg/h	Emission CISSA Kg/h	Hour	Emission PSO Kg/h	Emission CISSA Kg/h
1	965	955.46	13	1059	878.29
2	992	946.25	14	1271	930.33
3	849	956.46	15	1411	985.46
4	839	929.83	16	1800	1315.87
5	1023	933.34	17	1594	1243.35
6	1018	950.05	18	1384	1208.23
7	1035	974.87	19	1298	1152.52
8	1112	1003.91	20	1312	1067.27
9	1412	1084.02	21	1232	1016.75
10	989	706.03	22	1050	989.97
11	841	760.57	23	963	975.64
12	944	786.22	24	953	959.93

.

Figure 11 presents the emission comparison of the daily case study, while

Table 20. Reduction in daily emissions—case study 2.

Total Daily Emission PSO (USD)	Total Daily Emission CISSA (USD)	Reduction
27,346	23,710.61	13.3%

shows the main difference of the emissions.

4.11. Total Cost Comparison

The main and total cost comparisons are presented in

Table 21. Total cost comparison between CISSA and PSO.

Hour	Total Cost PSO USD/h	Total Cost CISSA USD/h	Hour	Total Cost PSO USD/h	Total Cost CISSA USD/h
1	19,257	17,500.27	13	97,410	64,096.28
2	18,959	16,904.29	14	82,950	73,432.36
3	19,439	17,270.59	15	71,850	69,145.77
4	18,502	17,341.88	16	27,395	28,149.86
5	18,746	17,585.06	17	26,496	27,151.15
6	19,903	18,513.64	18	26,089	26,282.83
7	20,383	19,187.77	19	24,808	24,116.65
8	20,746	20,130.34	20	22,572	21,584.81
9	23,907	23,534.84	21	21,597	19,044.08
10	80,960	77,909.79	22	20,281	17,860.38
11	98,090	78,397.67	23	22,017	17,956.36
12	107,060	86,135.80	24	21,956	17,649.20

, while Figure 12 presents the same results in a graphical way.

Table 22. Reduction in daily total cost—case study 2.

Daily Total Cost PSO (USD)	Daily Total Cost CISSA (USD)	Cost Saving
931,373	816,881.68	12.3%

presents the main results related to the daily cost in case study 2, while the

Table 23. Hourly clearness index, ambient temperature, and wind speed—case study 3.

Hour	Clearness Index	Ambient Temperature °C	Wind Speed (m/s)	Hour	Clearness Index	Ambient Temperature °C	Wind Speed (m/s)
1	0	15	11.75	13	0.736	19	11.6
2	0	15	9.65	14	0.693	20	15.8
3	0	14	9.25	15	0.748	21	18.5
4	0	13.5	12.9	16	0.496	21	19.3
5	0	14.1	10.5	17	0.120	21	13.5
6	0	14.15	14.52	18	0	21	17.7
7	0	15	12.75	19	0	20	9.1
8	0.162	16	10.9	20	0	19	16.7
9	0.395	17	16.2	21	0	18	11.5
10	0.628	17	9.4	22	0	17.2	9.3
11	0.724	17.7	13.65	23	0	17	11.3
12	0.747	18.2	10.6	24	0	16	11.3

shows the results of the case study 3.

Test Case 3

In Ref. [42], the author employed hybrid back-tracking search algorithm to solve the combined economic emission dispatch of a hybrid grid consisting of seven thermal units, and two solar and wind units; it was solved by CISSA in this study.

Description of Case Study 3

This case study did not provide direct information for the solar irradiance level for the calculation of solar power values. Therefore, in this work, the solar irradiance level on tilted surface was calculated using the information of the clearness index, angle of inclination, and inclination ratio provided in the original study.

Prohibited operating zones, up-ramp limits, down-ramp limits, loss coefficient matrix, fuel cost coefficients, and emission coefficients are provided in the original paper. The

Table 24. Algorithm parameters, constraints, and renewable data—case study 3.

Algorithm Parameters	Constraints	Units Generation Limits
		Power Balance
		Transmission Losses
		Ramp Rate, Dynamic CEED
		Prohibited Operating Zones
	Penalty Factor for Emission Cost	Max–Max Penalty with Interpolation
	Chaotic Map	Logistic
	Chaotic Adjustment Factor	4
	Number of Search Agents	30
	Maximum Iterations	200
Thermal Units	Number of Units	7
	Thermal Cost Coefficients	As Presented in Original Paper
Solar Units	No. of Units	2
	Reference Temperature	25 °C
	Temperature Coefficient	0.0025
	Solar Cost Coefficient	As Presented in Original Paper
Wind Units	Number of Units	3
	Rated Power of Each Unit	30 MW
	Wind Speed Rating of Each Unit	Rated: 15 m/s
		Cut-in: 5 m/s
		Cut-out: 45 m/s
	Wind Power Cost Coefficient	100

shows the results of the case study 3 and related data for optimization.

Results for Case Study 3

This section contains the results for case study 3 and a comparison of the results between the proposed algorithm (CISSA) and existent research.

Table 24 explains the solar unit switching status determined by the binary version on CISSA. Table 15 contains the details of the load demand for a specific day and hourly generation of seven thermal units, wind power share of three wind units, and two solar units generated by CISSA.

Table 25. Solar unit switching status along with the operational hours.

Hours	Solar Unit Switching Status		Hours	Solar Unit Switching Status
1	1	1	13	1	1
2	0	1	14	1	1
3	1	1	15	1	1
4	1	1	16	1	1
5	0	0	17	1	1
6	1	1	18	0	0
7	1	1	19	1	1
8	1	1	20	0	1
9	1	1	21	0	1
10	1	1	22	0	0
11	1	1	23	1	1
12	1	1	24	1	0

represent solar unit switching status for case study 3, while

Table 26. Hourly load demand and power generation—case study 3.

Hour	${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{a}\mathit{d}} \mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 1} \mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 2}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 3}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 4}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 5}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 6}\mathbf{MW}$	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 7}\mathbf{MW}$	${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{s}\mathit{s}} \mathbf{MW}$	${\mathit{P}}_{\mathit{T}\mathit{h}\mathit{e}\mathit{r}}\mathbf{MW}$	${\mathit{P}}_{\mathit{S}\mathit{o}\mathit{l}\mathit{a}\mathit{r}}\mathbf{MW}$	${\mathit{P}}_{\mathit{W}\mathit{i}\mathit{n}\mathit{d}}\mathbf{MW}$
1	636	190.3	10.0	20.0	10.0	218.4	10.0	131.8	15.2	590.5	0.0	60.8
2	710	255.0	10.0	20.0	10.0	228.8	10.0	147.4	13.1	681.2	0.0	41.9
3	858	289.1	10.0	20.0	10.0	295.5	10.0	200.0	14.8	834.6	0.0	38.3
4	1006	370.3	11.4	33.8	15.0	340.0	10.0	180.0	25.6	960.5	0.0	71.1
5	1080	341.8	10.0	70.0	10.0	352.4	10.7	257.3	21.8	1052.3	0.0	49.5
6	1228	370.9	37.3	53.5	20.1	396.4	20.5	276.7	33.1	1175.4	0.0	85.7
7	1302	379.5	39.1	60.0	29.2	407.9	37.0	308.9	29.3	1261.5	0.0	69.8
8	1376	411.4	45.9	60.0	50.9	442.9	55.6	272.6	22.9	1339.3	6.5	53.1
9	1524	404.4	48.6	103.8	70.5	439.4	65.0	324.0	40.9	1455.8	19.0	90.0
10	1622	460.1	65.0	130.7	93.8	463.1	90.0	263.8	31.8	1566.5	47.7	39.6
11	1706	471.1	70.0	87.6	100.0	467.0	100.0	321.7	52.5	1617.4	63.2	77.9
12	1750	488.9	72.4	137.3	100.0	482.1	100.0	297.8	46.1	1678.5	67.2	50.4
13	1672	452.5	70.0	120.0	100.0	462.7	100.0	287.0	44.8	1592.3	65.1	59.4
14	1524	421.9	56.7	105.4	64.9	454.7	75.8	242.7	45.6	1421.9	57.6	90.0
15	1376	370.3	38.3	60.0	30.2	397.9	50.8	323.2	51.6	1270.6	66.9	90.0
16	1154	378.7	18.4	35.1	10.6	365.7	25.8	239.8	39.6	1074.0	29.6	90.0
17	1080	366.1	17.4	29.3	15.2	352.0	10.0	238.0	29.2	1028.0	4.6	76.5
18	1228	359.2	35.6	76.9	18.7	385.8	18.3	279.5	36.0	1174.0	0.0	90.0
19	1376	428.4	38.3	71.3	33.2	431.6	43.3	314.8	21.8	1360.9	0.0	36.9
20	1572	479.0	52.0	121.3	83.2	433.1	70.0	287.8	44.4	1526.4	0.0	90.0
21	1524	419.8	50.5	119.9	65.0	451.4	71.7	317.8	30.7	1496.2	0.0	58.5
22	1228	396.5	10.0	70.0	35.4	413.0	46.7	236.3	18.7	1208.0	0.0	38.7
23	932	276.5	10.0	44.7	10.0	300.0	10.0	243.7	19.6	894.9	0.0	56.7
24	784	274.0	10.0	20.0	10.0	261.7	10.0	161.2	19.5	746.8	0.0	56.7

presents hourly load demand and power generation for case study 3. Figure 13 presents the effect of the RES on the fuel costs, while

Table 27. Table of costs and emissions—case study 3.

Hour	Fuel Cost USD/h	Emission Cost USD/h	Solar Cost USD/h	Wind Cost USD/h	Total Cost USD/h	Emission Kg/h
1	1684.97	462.97	0.00	6075.00	8222.94	1090.56
2	1922.13	638.42	0.00	4185.00	6745.54	1503.72
3	2368.51	1001.32	0.00	3825.00	7194.83	2358.10
4	2835.08	1365.99	0.00	7110.00	11,311.07	3216.37
5	3285.22	1533.16	0.00	4950.00	9768.38	3609.70
6	3940.92	2077.49	0.00	8568.00	14,586.41	4391.42
7	4467.95	2482.02	0.00	6975.00	13,924.97	4884.54
8	5056.10	2895.67	709.69	5310.00	13,971.47	5330.79
9	5941.03	3594.48	2091.94	9000.00	20,627.45	5860.75
10	6947.56	13,586.94	5251.58	3960.00	29,746.09	6502.85
11	7095.38	25,120.92	6957.10	7785.00	46,958.41	7042.57
12	7576.18	32,535.14	7394.75	5040.00	52,546.06	7427.98
13	7163.07	19,498.21	7165.50	5940.00	39,766.78	6622.46
14	5899.94	3432.41	6340.97	9000.00	24,673.31	5596.49
15	4616.87	2637.70	7363.43	9000.00	23,618.00	4855.88
16	3345.12	1690.44	3253.90	9000.00	17,289.46	3859.25
17	3088.54	1531.29	510.38	7650.00	12,780.21	3605.29
18	4015.05	2017.01	0.00	9000.00	15,032.05	4263.56
19	4915.78	3083.80	0.00	3690.00	11,689.58	5677.13
20	6412.34	7875.37	0.00	9000.00	23,287.71	6379.36
21	6180.19	3777.10	0.00	5850.00	15,807.29	6158.51
22	4212.09	2157.85	0.00	3870.00	10,239.94	4561.28
23	2688.76	1104.05	0.00	5670.00	9462.81	2599.83
24	2104.45	788.20	0.00	5670.00	8562.66	1856.37

presents the comparison of the two factors cost and emission. Similarly the

Table 28. Fuel-cost comparison between CISSA and back-tracking algorithm.

Hour	Fuel-Cost Back-Tracking USD/h	Fuel-Cost CISSA USD/h	Hour	Fuel-Cost Back-Tracking USD/h	Fuel-Cost CISSA USD/h
1	1739.589	1684.97	13	6941.36	7163.07
2	1988.247	1922.13	14	5857.941	5899.94
3	2542.618	2368.51	15	4926.561	4616.87
4	3074.557	2835.08	16	3695.878	3345.12
5	3581.365	3285.22	17	3501.643	3088.54
6	4276.38	3940.92	18	4257.873	4015.05
7	4786.714	4467.95	19	5561.865	4915.78
8	5286.673	5056.10	20	6372.498	6412.34
9	5947.907	5941.03	21	6213.253	6180.19
10	6873.24	6947.56	22	4567.662	4212.09
11	7080.213	7095.38	23	2898.383	2688.76
12	7433.955	7576.18	24	2203.567	2104.45

is the fuel cost comparison of both algorithms.

4.12. Comparison of CISSA and Back-Tracking Algorithm

In this subsection, the comparison of back-tracking and CISSA is presented considering the fuel costs and emissions.

i.

Fuel-Cost Comparison

The fuel comparison is shown in Table 28, presenting the two algorithms result.

The results are mostly improved as compared to the back-tracking algorithm, while Figure 14 shows its graphical presentation. In

Table 29. Daily total fuel-cost comparison—case study 3.

Daily Fuel-Cost Back-Tracking (USD)	Daily Fuel-Cost CISSA (USD)	Cost Saving
109,870.4	107,763.22	1.917%

, the daily fuel-cost comparison of the result is presented for case study 3.

ii.

Emissions Comparison

The emissions are also estimated to evaluate the efficacy of the proposed method.

Table 30. Emissions comparison between CISSA and back-tracking.

Hour	Emission Back-Tracking Kg/h	Emission CISSA Kg/h	Hour	Emission Back-Tracking Kg/h	Emission CISSA Kg/h
1	1137.189	1090.56	13	7738.463	6622.46
2	1565.641	1503.72	14	6270.039	5596.49
3	2350.726	2358.10	15	5091.716	4855.88
4	3068.481	3216.37	16	3685.301	3859.25
5	3568.852	3609.70	17	3378.299	3605.29
6	4324.76	4391.42	18	4306.013	4263.56
7	4907.586	4884.54	19	5418.068	5677.13
8	5512.498	5330.79	20	6956.596	6379.36
9	6385.46	5860.75	21	6723.456	6158.51
10	7300.494	6502.85	22	4482.419	4561.28
11	7955.846	7042.57	23	2601.095	2599.83
12	8620.86	7427.98	24	1873.056	1856.37

shows the comparison of both algorithms considering the emissions results. The obtained results in

Table 31. Total daily emissions comparison—case study 3.

Daily Emission Back-Tracking (USD)	Daily Emission CISSA (USD)	Reduction in Emission
114,085.7	108,164.18	5.190433%

are significant and graphically expressed in Figure 15.

Test Case 4

In Ref. [43], A. Sundaram et al. solved the static combined economic emission dispatch for a power system containing 10 thermal units with non-convex characteristics. In this work, three wind units were integrated in the model and the effect of renewable energy on fuel, emission, and total generation costs was analyzed by using CISSA.

Description of Case Study 4

Originally, the paper solved the CEED problem only using thermal units. In this study, wind units were included in the CEED problem and solved with CISSA. The data for the wind units were same as in case study 3. Fuel-cost coefficients, emission coefficients, and prohibited operating zones were provided in the original research paper.

i.

Results for Case Study 4

This section contains the results for case study 4 and a comparison of the results between the proposed algorithm (CISSA) and existent research. Similarly,

Table 32. Algorithm parameters, constraints, and renewable units data.

Algorithm Parameters	Constraints	Inequality
		Transmission Losses
		Equality
		Prohibited Operating Zone
		Non-Convex Characteristics
	Penalty Factor	Max–Max Penalty with Interpolation
	Chaotic Map	Logistic
	Chaotic Adjustment Factor	4
	Number of Search Agents	30
	Maximum Iterations	200
Wind Units	Number of Units	3
	Rated Power of Each Unit	30 MW
	Wind Speed Rating of Each Unit	Rated: 15 m/s
		Cut-in: 5 m/s
		Cut-out: 45 m/s
	Wind Power Cost Coefficient	100

presents the algorithm parameters, constraints, and renewable units data.

The various results are given in the tables, such as

Table 33. Load demand, power generation, and losses of test case 4.

${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{a}\mathit{d}}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 1}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 2}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 3}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 4}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 5}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 6}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 7}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 8}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 9}$ MW	${\mathit{P}}_{\mathit{U}\mathit{n}\mathit{i}\mathit{t} 10}$ MW	${\mathit{P}}_{\mathit{L}\mathit{o}\mathit{s}\mathit{s}}$ MW	${\mathit{P}}_{\mathit{T}\mathit{h}\mathit{e}\mathit{r}}$ MW	${\mathit{P}}_{\mathit{W}\mathit{i}\mathit{n}\mathit{d}}$ MW
2000	55	80	120	130	145	141	236	254	395	447	65	2004	60

,

Table 34. Table of costs and emissions.

Fuel Cost USD/h	Emission Cost USD/h	Wind Cost USD/h	Total Cost USD/h	Emission Kg/h
109,209.55	142,174.14	6075.00	257,458.68	4087.13

,

Table 35. Fuel-cost comparison between CISSA and ABC-SA.

Fuel-Cost ABC-SA (USD)	Fuel-Cost CISSA (USD)	Fuel-Cost Saving by Wind Integration
113,510	109,210	3.78%

and

Table 36. Emissions comparison between CISSA and ABC-SA.

Emission ABC-SA (USD)	Emission CISSA (USD)	Emission Reduction by Wind Integration
4169	4087	1.96%

. Similarly, Table 35 presents a comparison of CISSA and ABC-SA based on fuel costs, while Table 36 presents the emissions comparison that is satisfactory. The total cost comparison is presented in

Table 37. Total cost comparison between CISSA and ABC-SA.

Total Cost ABC-SA (USD)	Total Cost CISSA (USD)	Cost Saving by Wind Integration
330,210	257,459	22.03%

, having a saving of 22%. From all the results, it can be deduced that the proposed method (CISSA) is much better as compared to the PSO, ABC-SA, and back-tracking algorithm.

Comparison of CISSA and hybrid artificial bee colony-simulated annealing.

5. Conclusions

A novel, chaotic, salp swarm algorithm was presented in this study to solve the combined economic emission dispatch problem in the presence of renewable energy resources. The combined economic emission dispatch problem is a complex multi-objective problem, which requires a powerful optimizer to solve it. In this multi-objective study, the CEED problem was converted into a single-objective problem by the use of the price penalty factor and weights. Thus, the single-objective optimization problem created is an overall generation cost minimization problem. The use of RERs was encouraged by penalties on account of unused renewable shares. In addition, it was observed that it is necessary for the optimization algorithm to only decide on justified and reasonable amounts of renewable shares to be added to the generation mix by the integration of renewable energy resources, although fuel costs and emissions were reduced on the account of an increased overall cost generation. Additionally, it is evident from the research that the combination or hybridization of the chaotic map ensures the enhancement in the performance of the salp swarm algorithm in solving multi-objective optimization problems. Four different test cases from different published research papers were solved by formulating them in a CISSA environment in MATLAB software, and the obtained results prove the superiority of CISSA over other optimization algorithms. Additional constraints are included in the original problem. The quality of results is improved in terms of attaining near-global optima.