<p>Combined Economic Emission Dispatch (CEED) is a critical issue in the operation of power systems. This paper proposes a mathematical distributed Goose algorithm (GO) based on an oscillatory dynamic penalty function to solve the CEED problem. By introducing mathematical distributions to replace the random search in the traditional GO algorithm, the global search capability is significantly enhanced. In addition to improving the algorithm, the constraints in the CEED problem are effectively addressed. Six different dynamic penalty functions are designed, including V-shaped, C-shaped, U-shaped, O-shaped, B-shaped, and γ-shaped, along with an oscillatory strategy based on dynamic penalty functions.In the experimental section, the improved GO algorithm is first validated by using the 12 test functions from CEC-BC-2022. The best-performing method is selected and compared with other intelligent optimization algorithms to further validate the effectiveness of the improvement strategy. Subsequently, the improved algorithm is applied to solve the Economic Load Dispatch (ELD) problem for 40-unit and 110-unit systems, demonstrating superior convergence and the ability to handle large-scale, complex problems. The algorithm is then tested on a 6-unit CEED system, where the effectiveness of the mathematical distribution, dynamic penalty functions, and oscillatory strategy is thoroughly validated under practical constraints such as Valve Point Effect (VPE) and Ramp Rate Limits (RRL). Finally, a large-scale 20-unit CEED system is employed to further assess the performance and robustness of the proposed method. The experimental results confirm that the mathematical distribution-based GO algorithm, incorporating dynamic and oscillatory penalty functions, not only achieves efficient and high-quality solutions but also maintains robustness and stability across CEED problems of varying scales, highlighting its effectiveness and applicability for practical power system operations.</p>