Non-Intrusive Load Monitoring (NILM) approaches refer to the analysis of the aggregated electrical signals of Home Electrical Appliances (HEAs) in order to identify each of them. It has emerged as a promising solution to help residential consumers to reduce their electricity bills through a breakdown of energy consumption. NILM methods are either event-based or non event-based. This categorization depends on whether or not they rely on the detection of HEAs' significant state transitions (e.g. On/Off or state change) in power consumption signals. This paper focuses on event-based approaches and particularly in multivariate change detection algorithms. It aims at highlighting the benefits provided by a multivariate approach for change detection using the appropriate electrical features. To do so, we first propose to improve by extending four existing change detection algorithms in the multidimensional case. The studied detection algorithms are first detailed and compared to each other and to their existing scalar versions through numerical simulations. Then, a new feature selection algorithm for change detection is proposed and assessed when combined with the most efficient detector among the four investigated ones. Finally, the feature selection method for detection purposes is applied to two different NILM case studies. The first one uses power features derived from the BLUED current and voltage measurements and the second one is based on real-world current and voltage measurements acquired using our own acquisition system. The results show a significant improvement in terms of performance and accuracy of the multivariate approach over the classical scalar one when using the features selected by the proposed algorithm.