In recent years, developing Artificial Intelligence (AI) models for complex system has become a popular research area. There have been several successful AI models for predicting the Selective Non-Catalytic Reduction (SNCR) system in power plants and large boilers. However, all these models are in essence black box models and lack of explainability, which are not able to give new knowledge. In this study, a novel explainable AI (XAI) model that combines the polynomial kernel method with Sparse Identification of Nonlinear Dynamics (SINDy) model is proposed to find the governing equation of SNCR system based on 5-year operation data from a power plant. This proposed model identifies the system's governing equation in a simple polynomial format with polynomial order of 1 and only 1 independent variable among original 68 input variables. In addition, the explainable AI model achieves a considerable accuracy with less than 21 % deviation from base-line models of partial least squares model and artificial neural network model.