Do you have an example for a dynamic simulation including a synchronous generator in parallel with a battery?
In the attached example project the battery is connected to the grid using a PWM converter. The grid contains a synchronous machine which supplies a load. After the initialization the synchronous machine is feeding the load completely. The set value of the battery PWM generation is changed by a frequency PI-control, so that the battery is absorbing the excess of power or generating power in case of under- or over-frequency. The synchronous machine contains only a voltage controller. The turbine power is considered constant. A variation in the active power of the load is compensated by varying battery active power. The battery system returns the frequency always back to the nominal frequency (as long as the converter is not overloaded).
The model of the battery itself is a voltage source, thus not reflecting any capacity constraints for long-term simulations. An extension of the model would be possible by substituting the simple voltage source by a more complex DSL model. You could find also a battery model within PowerFactory templates.