Modeling and understanding dendrite growth on lithium metal anodes during charging is vital for improving battery safety. The phase field method has become an increasingly popular tool to achieve this due to its flexibility in handling complex morphologies and coupled physical processes. However, quantitative phase field models under realistic electrochemical conditions are rare. In this work, we derive a thermodynamically consistent phase field model in the grand potential framework. The design of this model emphasizes quantitative modeling of electrodeposition with experimental loading conditions and realistic length and time scales. First, electrostatic potentials in both the electrode and the electrolyte are considered to account for the interfacial potential difference. Second, the electrochemical driving force can be large even with an applied voltage of a few hundred millivolts; therefore, the grid size usually must be as small as a few nanometers to maintain a stable phase field profile. This hinders the modeling of system sizes of practical interest. To solve this problem, a mapping approach is introduced to maintain stability with moderate grid sizes and realistic applied voltages. Third, we thoroughly compare the phase field model with results from a sharp interface model for various cases that permit analytical solutions. Numerical studies demonstrate that the proposed model can quantitatively reproduce the sharp interface results. Moreover, lithium has highly anisotropic interfacial energy, which leads to corners on the equilibrium electrode-electrolyte interface shape. A convexification method is used to remove the ill-posedness due to this strong anisotropy. Finally, a parallel solver is developed to handle large systems. The overall framework is demonstrated by studying lithium dendrite morphologies under various conditions. In future work, the model can be used as a computational tool for the high-throughput screening process in battery design.