Smart grid, through networked smart meters employing the non-intrusive load monitoring (NILM) technique, can considerably discern the usage patterns of residential appliances. However, this technique also incurs privacy leakage. To address this issue, we propose an innovative scheme based on adversarial attack in this paper. The scheme effectively prevents NILM models from violating appliance-level privacy, while also ensuring accurate billing calculation for users. To achieve this objective, we overcome two primary challenges. First, as NILM models fall under the category of time-series regression models, direct application of traditional adversarial attacks designed for classification tasks is not feasible. To tackle this issue, we formulate a novel adversarial attack problem tailored specifically for NILM and providing a theoretical foundation for utilizing the Jacobian of the NILM model to generate imperceptible perturbations. Leveraging the Jacobian, our scheme can produce perturbations, which effectively misleads the signal prediction of NILM models to safeguard users' appliance-level privacy. The second challenge pertains to fundamental utility requirements, where existing adversarial attack schemes struggle to achieve accurate billing calculation for users. To handle this problem, we introduce an additional constraint, mandating that the sum of added perturbations within a billing period must be precisely zero. Experimental validation on real-world power datasets REDD and UK-DALE demonstrates the efficacy of our proposed solutions, which can significantly amplify the discrepancy between the output of the targeted NILM model and the actual power signal of appliances, and enable accurate billing at the same time. Additionally, our solutions exhibit transferability, making the generated perturbation signal from one target model applicable to other diverse NILM models.