Automated planning is the field of Artificial Intelligence (AI) that focuses on identifying sequences of actions allowing to reach a goal state from a given initial state. The need of using such techniques in real-world applications has brought popular languages for expressing automated planning problems to provide direct support for continuous and discrete state variables, along with changes that can be either instantaneous or durative. PDDL+ (Planning Domain Definition Language +) models support the encoding of such representations, but the resulting planning problems are notoriously difficult for AI planners to cope with due to non-linear dependencies arising from the variables and infinite search spaces. This difficulty is exacerbated by the potentially huge fully ground representations used by modern planners in order to effectively explore the search space, which can make some problems impossible to tackle. This paper investigates two grounding techniques for PDDL+ problems, both aimed at reducing the size of the full ground representation by reasoning over the lifted, more abstract problem structure. The first method extends the simple mechanism of invariant analysis to limit the groundings of operators upfront. The second method proposes to tackle the grounding process through a PDDL+ to classical planning abstraction; this allows us to leverage the amount of research done in the classical planning area. Our empirical analysis studies the effect of these novel approaches over both real-world hybrid applications and synthetic PDDL+ problems took from standard benchmarks of the planning community; our results reveal that not only the techniques improve the running time of previous grounding mechanisms but also let the planner extend the reach to problems that were not solvable before.