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Time-domain simulations are a critical tool for power system operators. Depending on the instability mechanism under consideration and the system characteristics, such as the time constants of controllers, either phasor or Electro-Magnetic Transient (EMT) models should be employed. On the one hand, EMT models provide a detailed-modeling of the system dynamics, thus increase the reliability of stability analysis; on the other end, using these models increase the computational times of simulations, slowing down the security assessment process. To decrease computational time, system operators could resort to phasor-mode simulations for a (hopefully large) subset of disturbances. This paper investigates the appropriateness of phasor-approximation models on simulating events related to power supply and balance stability in zero-inertia systems. First, the stability boundaries, which each model is able to identify, are analyzed; then sufficient conditions for control parameters are derived, which allow using phasor-approximation models to monitor power sharing among grid-forming converter-based resources. Time-domain simulations are performed in PowerFactory DigSilent to verify the results.