*2.6. Engine Speed Governor*

In this paper, the governor is modeled as a proportional-integral (PI) controller with the actual engine rotational speed as the feedback signal [1,5,8,9,12,13]. In addition, scavenging air and torque limiters are also incorporated in the governor model for protecting the engine integrity during fast transients.

As similar with the turbocharger shaft, the engine crankshaft rotational speed *Ne* can be calculated by integrating the following equation:

$$\frac{dN\_c}{dt} = \frac{60}{2\pi} \cdot \frac{Q\_b - Q\_p}{f\_c + f\_{sh} + f\_p} \tag{15}$$

where *Qp* is the propeller resisting torque; *Je*, *Jsh* and *Jp* are the moment of inertia of the engine, shaft system and propeller, respectively.

As the main focus of this paper is to investigate the engine steady-state performance and transient response by using MVEM, the extra propeller moment of inertia caused by the entrained water is neglected; in addition, the hydrodynamic characteristic of the propeller and ship hull is also neglected. For simplicity, the propeller resisting torque is calculated by using the propeller propulsive characteristic curve that passes through the engine MCR point [13]:

$$Q\_{\rm p} = K\_{\rm p} N\_{\rm e}^2 \,\, K\_{\rm p} = Q\_{\rm b,MCR} / N\_{\rm e,MCR}^2 \tag{16}$$
