In this paper a nonlinear dynamic model for a solar thermal Organic Rankine Cycle (ORC) power plant is identified and validated using experimental data gathered on a real 4kWelec ORC based solar thermal power plant prototype. The applied identification structure enables the dynamics of the key quantities (variables to be regulated and constrained variables) to be captured. This leads to a control-oriented model that is used to design a constrained optimal control strategy for the ORC power plant that has to track rapidly some reference electrical power while respecting the system constraints in terms of temperatures and pressures for some key thermodynamic variables. Prior to the control design step, an analysis of the admissible desired steady states is performed to derive feedforward terms that enhance the controller performances. The time responses obtained with the proposed control methodology suggest that a significant reduction in the energy buffer size, consisting in a battery bank associated to the ORC power plant, can be performed.