This paper introduces a novel framework for cyber-physical analysis of power distribution systems using a real-time digital twin. The proposed architecture utilizes a digital twin as a real-time reference model that replicates the complex behavior of a power distribution system in order to perform real-time cyber-physical analysis such as detection of potential malicious data manipulations, verification of control actions before being applied to the physical system, and monitoring of the status of the power grid in locations where physical measurements are not available. The implementation in a hardware-in-the-Ioop (HIL) testbed is introduced for power distribution systems that integrate a variety of devices such as protection relays, distributed energy resources, and energy storage. Finally, results in a modified IEEE 13 node test feeder illustrate that the proposed structure is capable of detecting and mitigating cyber attacks, and also validate control commands before being executed.