For intelligent power utilisation of demand side management, the implementation of non-intrusive load identification is an important technology. This study proposed an event-based non-intrusive load identification algorithm for residential loads combined with underdetermined decomposition and characteristic filtering. This method first needs to monitor the circuit in real time. After detecting an electrical switching event, the load decomposition and identification are performed. By combining the operating habits of the electrical equipment, the problem that the single current signal is difficult to solve by multi-dimensional under-determination is optimised as a one-dimensional under-determination problem. The objective function is established based on the sparsity of current in the frequency domain. The two-step iterative shrinkage threshold algorithm is used to get the optimal solution to achieve load decomposition. Then, according to the unique harmonic components of each power load, this study establishes the characteristic filtering to filter the decomposition current, which realises load recognition. The algorithm is verified by actual data measured in a household. It can obtain the individual load current and accurately judge the load status, which proves the accuracy and effectiveness of the algorithm.