I am working on a cooling system using 4 Peltier modules. I would like to somehow determine the power I need to reduce the temperature of the object attached to the Peltier module by x degrees Celsius. I would like to compare this data with the amount of energy I need to cool the system. The data that I currently have are: Qmax, delta Tmax, Imax, Vmax, and module resistance. Are there any formulas that I can use to find out the power needed to run the Peltier module to reduce the temperature by x degrees?
No, because you're missing one of the most important parameters, and that's the thermal resistance of the object you're cooling.
If the object is superbly well insulated, say in a vacuum with metalised Mylar heat shields, then it will leak practically no heat, and you can use the Peltier module graphs of power versus temperature at zero heat flow.
If the object is less well insulated, and in order of goodness you might have polyurethane insulation, polystyrene insulation, wood or paper, in the open air, or bolted to a heatsink, then your Peltiers will need to remove a significant amount of heat from the object, and you'll have to use those power/temperature graphs at a higher heat flow.