Load curve data in power systems refers to users' electrical energy consumption data periodically collected with meters. It has become one of the most important assets for modern power systems. Many operational decisions are made based on the information discovered in the data. Load curve data, however, usually suffers from corruptions caused by various factors, such as data transmission errors or malfunctioning meters. To solve the problem, tremendous research efforts have been made on load curve data cleansing. Most existing approaches apply outlier detection methods from the supply side (i.e., electricity service providers), which may only have aggregated load data. In this paper, we propose to seek aid from the demand side (i.e., electricity service users). With the help of readily available knowledge on consumers' appliances, we present an appliance-driven approach to load curve data cleansing. This approach utilizes data generation rules and a Sequential Local Optimization Algorithm (SLOA) to solve the Corrupted Data Identification Problem (CDIP). We evaluate the performance of SLOA with real-world trace data and synthetic data. The results indicate that, comparing to existing load data cleansing methods, such as Bspline smoothing, our approach has an overall better performance and can effectively identify consecutive corrupted data. Experimental results also show that our method is robust in various tests.