# Optimal Solution of Environmental Economic Dispatch Problems Using QPGPSO-\(\omega\)
## 1 Introduction
### Literature Review  
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].