Automated Fault Detection and Diagnosis (AFDD) algorithms play a crucial role in mitigating energy wastage and inefficient operation of the HVAC systems. By continuously monitoring data from Building Automation Systems (BAS) sensors, these algorithms can identify the abnormal behavior of the chiller system. However, to design a successful algorithm selecting proper sensors and features that can reflect normal and abnormal behavior of the system is essential. Identifying the key parameters and high-impact variables for AFDD can occur through expert-driven selection, based on empirical studies or via automated methods such as filters, wrappers, and embedded techniques for feature selection. In doing so, this study proposes combining a wrapper method with Principal Component Analysis (PCA). Through an exhaustive search, the ideal number of features crucial for AFDD is identified. Notably, the selection of variables through the wrapper method relies on the classifier and the algorithm. Unlike the prior research that predominantly utilized supervised classifiers such as Support Vector Machines or Random Forests, an unsupervised algorithm, PCA, is adopted to select the optimum number of features and sensors for AFDD. The study implements a Step Forward feature selection technique within PCA to progressively identify the most effective feature subsets tailored for steady-state fault detection. Using steady-state behavior of the system, the proposed PCA-Wrapper method identifies eleven features that yield MAR and FAR values below 5%.