In this paper, we develop a physically motivated compact model of the charge-voltage (Q-V) characteristics in various III-nitride high-electron mobility transistors (HEMTs) operating under highly non-equilibrium transport conditions, i.e. high drain-source current. By solving the coupled Schrödinger-Poisson equation and incorporating the two-dimensional electrostatics in the channel, we obtain the charge at the top-of-the-barrier for various applied terminal voltages. The Q-V model accounts for cutting off of the negative momenta states from the drain terminal under high drain-source bias and when the transmission in the channel is quasi-ballistic. We specifically focus on AlGaN and AlInN as barrier materials and InGaN and GaN as the channel material in the heterostructure. The Q-V model is verified and calibrated against numerical results using the commercial TCAD simulator Sentaurus from Synopsys for a 20-nm channel length III-nitride HEMT. With 10 fitting parameters, most of which have a physical origin and can easily be obtained from numerical or experimental calibration, the compact Q-V model allows us to study the limits and opportunities of III-nitride technology. We also identify optimal material and geometrical parameters of the device that maximize the carrier concentration in the HEMT channel in order to achieve superior RF performance. Additionally, the compact charge model can be easily integrated in a hierarchical circuit simulator, such as Keysight ADS and CADENCE, to facilitate circuit design and optimization of various technology parameters.