This paper proposes an underground power cable dqn model that can be used for both electric machines analysis and control at or around the fundamental rated power frequencies (50Hz or 60Hz). The model can be used as an observer to estimate the cable output states. This makes the far end measurements available through estimations for long cable applications such as electrical submersible pumps and wind generations. The model can be used also in simulation analysis with accelerated simulation time. Advantages include fast computation, decoupled network, and ability to work under unbalanced supply or network conditions without requiring an interface stage, such as the Eigen vectors calculation, between the cable and electric machine models. Detailed model derivations and analyses, including balanced, unbalanced, and transient conditions, are provided. Verifying using MATLAB SIMULINK, the model has a higher accuracy in balanced and unbalanced conditions when compared to the per-phase shifted frequency analysis (SFA) model in simulations, along with one of the shortest computation times among all simulated models. For the experiment, the researchers design a test consisting of a 20 ft cable operating at 6 kHz used to emulate an equivalent 2,000 ft cable with the proposed cable model as an observer., the results prove to be accurate, with the maximum error between the measured cable output and the model output estimation at 0.12%. Therefore, the model is verified by the experiments in the same given conditions as the simulations, and it can be considered as a reference in the future.