Differential privacy (DP) has been widely used to protect the privacy of confidential cyber physical energy systems (CPES) data. However, applying DP without analyzing the utility, privacy, and security requirements can affect the data utility as well as help the attacker to conduct integrity attacks (e.g., False Data Injection(FDI)) leveraging the differentially private data. Existing anomaly-detection-based defense strategies against data integrity attacks in DP-based smart grids fail to minimize the attack impact while maximizing data privacy and utility. To address this challenge, it is nontrivial to apply a defensive approach during the design process. In this paper, we formulate and develop the defense strategy as a part of the design process to investigate data privacy, security, and utility in a DP-based smart grid network. We have proposed a provable relationship among the DP-parameters that enables the defender to design a fault-tolerant system against FDI attacks. To experimentally evaluate and prove the effectiveness of our proposed design approach, we have simulated the FDI attack in a DP-based grid. The evaluation indicates that the attack impact can be minimized if the designer calibrates the privacy level according to the proposed correlation of the DP-parameters to design the grid network. Moreover, we analyze the feasibility of the DP mechanism and QoS of the smart grid network in an adversarial setting. Our analysis suggests that the DP mechanism is feasible over existing privacy-preserving mechanisms in the smart grid domain. Also, the QoS of the differentially private grid applications is found satisfactory in adversarial presence.