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The pressure control in the pressurized water reactor (PWR) primary loop is key to secure the safe operation. The pressurizer (PZR) unit is responsible for attaining this task. Thus, the PZR unit's modeling is an important issue for the tracking control purpose and performance analysis concerning the turbine load. This paper develops a mathematical model to accurately predict the PZR unit pressure in the normal and load power changes. The model is a nonequilibrium three region model developed based on the thermodynamics of mass and energy for the water and steam in the PZR. The variations of the pressure and the temperature due to thermodynamic variables (enthalpy, density) and the mechanical work effect are considered in the developed model. The model also addresses other thermodynamic processes such as bulk flashing, spray condensation, interface condensation, wall condensation, and rainout flow. The inlet and outlet flow rates of the primary circuit (PC) and the average temperature and the hot leg temperature are included in the developed model. Based on data generated from the VVER-1200 simulator, parameter estimation, verification, and validation of the developed model through load power changes are achieved. Besides, a comparison with other models given in literature has been performed. This comparison indicated that the developed model is more sensitive against the minimum variation of PZR dynamics. Finally, a closed-loop PZR pressure control system, including a conventional Proportional Integral Derivative (PID) controller, was designed to test the control purpose's developed model. The simulation results over typical load change transients have been demonstrated the feasibility, effectiveness, and accuracy of the developed nonlinear model of PZR for dynamic modeling and control purposes.