Accurate identification of load voltage exponent and frequency characteristic parameters under steady-state operating conditions is essential for the stability assessment and control of power systems. However, since internal load disturbances are often correlated with system-side voltage and frequency fluctuations, the conventional ordinary least squares （OLS） method may yield significant bias in such scenarios. To address this issue, this paper introduces the instrumental variable （IV） method and under the assumption that internal disturbances follow short-range correlated colored noise, establishes a statistical estimation framework for load characteristic parameters identification to resolve the endogeneity problem. Firstly, the formation mechanism of endogeneity in closed-loop systems and the resulting estimation bias are analyzed. Secondly, an IV-based identification procedure is established, which consists of steps such as correlation analysis, instrumental variable construction with multi-port information, and parameter estimation using the two-stage least squares method. The unbiasedness and variability characteristics of IV estimation are systematically analyzed, and criteria for selecting the lag order L are proposed. Finally, simulation studies are carried out to investigate the influence of different IV parameter settings on the estimation results, and the proposed method is validated from multiple perspectives, including endogeneity intensity and the proportion of static versus dynamic load components. The results demonstrate that the proposed method can markedly enhance the accuracy of load characteristic parameters identification under steady-state conditions with strong internal disturbances.