The rapid growth in greenhouse gases (GHGs), the lack of electricity production, and an ever-increasing demand for electrical energy requires an optimal reduction in coal-fired thermal generating units (CFTGU) with the aim of minimizing fuel costs and emissions. Previous approaches have been unable to deal with such problems due to the non-convexity of realistic scenarios and confined optimum convergence. Instead, meta-heuristic techniques have gained more attention in order to deal with such constrained static/dynamic economic emission load dispatch (ELD/DEELD) problems, due to their flexibility and derivative-free structures. Hence, in this work, the elephant herd optimization (EHO) technique is proposed in order to solve constrained non-convex static and dynamic ELD problems in the power system. The proposed EHO algorithm is a nature-inspired technique that utilizes a new separation method and elitism strategy in order to retain the diversity of the population and to ensure that the fittest individuals are retained in the next generation. The current approach can be implemented to minimize both the fuel and emission cost functions of the CFTGUs subject to power balance constraints, active power generation limits, and ramp rate limits in the system. Three test systems involving 6, 10, and 40 units were utilized to demonstrate the effectiveness and practical feasibility of the proposed algorithm. Numerical results indicate that the proposed EHO algorithm exhibits better performance in most of the test cases as compared to recent existing algorithms when applied to the static and dynamic ELD issue, demonstrating its superiority and practicability.