Environmental sustainability, rapid depletion and constantly fluctuating prices of fossil fuels are currently forcing the incorporation of renewable energy sources (RESs) into power grids [1,2]. The recent research predominantly focused on exploring energy generation using various renewable resources [3,4,5]. However, these RESs present their own limitations, both climatic and technical, as their resource availability is subject to variations caused by climate conditions. In addition, the extraction of bulk power from major renewable energy sources (such as solar and wind) is primarily feasible in locations that are situated far away from major load centers. Thus, there is a requirement for properly designed dispatch mechanisms to transmit the produced power from the source to the load in an efficient and economically effective manner [6,7].

RESs have issues; however, they still manage to produce good results in their power generation performance, such as wind; biofuel and solar systems produced approximately 700, 671, and 659 GWs of installed capacity till 2020 [8,9]. However, the high variability of resource availability requires a well-designed metaheuristic optimization algorithm for the calculation of economic dispatch (ED) [10]. The developed ED algorithm should not only provide the efficient dispatch of power, but also account for the penalties imposed as a result of resource variability.

Pakistan presents a significant potential for RESs and there is a growing trend towards utilizing these emission-free resources for power generation. The authors conducted an extensive survey of the availability of wind resources in the southern regions of Pakistan, as documented in [11,12]. A detailed survey of the regions rich in solar-based power generation in Pakistan and the prospects of its hybridization with wind energy sources was presented in [13,14]. In [15,16,17], the authors deliberated on the potential of extractable bio-fuel-based energy in the country and examined various scenarios for extracting energy from waste materials. The authors in [18,19,20] provided a comprehensive analysis of several renewable energy-based projects that were executed in various appropriate locations to generate environment friendly electricity.

The ED problem (EDP) is a computational mechanism used to determine the optimal distribution of generated electric power in order to meet the load demand, while minimizing the production cost [21]. Obtaining the optimum solution for EDPs is a critical requirement for a sustainable power network, while considering various operational constraints. The developed algorithm should not only consider the operational limitations of RESs, but also the constraints of thermal systems, such as ramp rate limits (RRLs), and prohibited operating zones (POZs) should be taken into account [22,23].

Initially, deterministic techniques were employed to achieve the optimal solution for basic EDPs. These classical techniques were effective in optimizing small- to medium-scale thermal power systems, without taking into account the operational constraints [24,25,26]. However, the shortcomings of these deterministic algorithms became evident when attempting to solve complex dispatch problems that involved operational constraints. Modern power systems comprise a significant number of generating units and necessitate the consideration of several operational constraints, such as RRL, POZ, losses, and multiple fuel cost functions. Accomplishing feasible solutions in such systems mandates the utilization of sophisticated optimization algorithms.

The researchers worked on the development of metaheuristic optimization algorithms for achieving the optimal solution of constraints-based EDPs incorporating thermal and hybrid power systems. The utilization of the genetic algorithm (GA) and its variants for obtaining optimal solutions to various categories of EDPs was surveyed by the authors in [27,28], and they also compared the performance of these algorithms. In [29,30], the authors presented a review and application of the artificial bee colony (ABC) algorithm and its hybridized variant for solving the multi-area economic dispatch (MAED) problem. They also considered factors, such as of POZ, losses, VPL effects, tie-line constraints, and multiple fuel scenario.

A comprehensive analysis of the utilization of the standard PSO and its various variants for obtaining optimal solutions to both constrained and unconstrained EDPs was presented in [24,25,26,31,32,33,34]. Additionally, the authors also compared the performance of these algorithms with other notable metaheuristic techniques. However, the focus was primarily on achieving optimal solutions for EDPs based on thermal power plants (TPPs). The application of the bat algorithm (BA) and its variants for solving different instances of EDPs, while taking into account the integration of wind power systems, was presented in [35,36]. The developed algorithms were evaluated on 25 benchmark standard functions, and the outcomes were compared with other metaheuristic techniques for the selected test cases [37].

Due to the escalating power demand (PD) and the high rate of carbon emissions from TPPs, the integration of RESs into existing power networks is of utmost importance [38,39]. According to the research, load frequency control is challenging because of uncertain power generation and variable load demands [40,41,42]. The designed version of the PSO approach was utilized to attain an optimal solution for various categories of EDPs that involved both TPPs and RESs. In [43], the authors addressed the optimization of EDPs by taking into account the concept of virtual power plants (VPPs) comprising wind farms and hybridized TPPs. However, they did not consider the penalty costs associated with under- and overestimations of the wind power framework. The resolution of EDPs that involve wind and PV frameworks, as well as TPP combinations, was presented in [44], with the consideration of penalty functions only for the wind power system. In [45], the authors presented the mathematical expressions for calculating the costs of power systems that integrate wind and solar PVs with conventional TPPs. EDPs involving a combination of a PV system and a biofuel plant as an alternative to fossil fuels was solved in [46].

The extensive utilization of TPPs leads to a high emission rate of hazardous substances that cause severe environmental pollution and negatively impact the health of the general public [47]. In addition to the integration of RESs, the researchers also emphasized the importance of developing mechanisms for the optimal calculation of emissions with the goal of reducing them [48,49,50,51,52]. The incorporation of economic and environmental considerations is essential to attain eco-friendly power-generation and dispatch mechanisms, which can be achieved through a combined CEED approach.

Global particle swarm optimizer with inertial weights (GPSO-ω) is a variant of PSO algorithm, which is a stochastic optimization technique used to solve complex optimization problems. QPGPSO-ω, which is an extension of GPSO-ω, was utilized in [53] for the solution of ED-IEEE standard (3, 6, 13, 15, 40, and 140) units for Korean grid thermal test systems under various constraints. QPGPSO-ω outperformed several other methods in solving the EDP, showcasing superior results. However, in this study, QPGPSO-ω is applied to address the challenges of EDPs specifically related to the integration of RESs and the consideration of CEED. The main focus of this study is as follows:

Validation of the QPGPSO-ω methodology for solving only RES-based EDs with resource variability.

Validation of the QPGPSO-ω methodology for solving regional load sharing dispatch.

Utilization of QPGPSO-ω to solve the CEED problem for ten-unit TPPs, which is a significant challenge in power systems due to various constraints, such as VPL effects and losses.

The study is structured in the following sections. Section 2 provides the mathematical formulations of the EDPs under consideration. In Section 3, the proposed methodology is described in detail, including a flowchart and pseudocode. The results and their implications are discussed in Section 4, whereas the concluding remarks are mentioned in Section 5.

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https://www.mdpi.com/2076-3417/13/12/6867