Relationship between grid frequency and load in power system

Higher output power of generator (hundreds of MWs) has bigger impact on the system frequencies than low power generators, because of its massive spin momentum (torque). The active (R) load acts directly on generator speed because it creates strong magnetic field in stator that is perpendicular rotor's spinning magnetic field thus forcing an opposite momentum(torque) which slows down the turbine, this is fixed with a speed governor which controls turbine speed by manipulating its spin momentum (burn more gas, add more heat, increase hydroflow etc.).

The stable hertz system is kind a: sum of generating torques (where some means of matter or stuff creates/converts energy that spins turbines) = sum of opposing load torques, where as I said more torque having generator is more stable there, The stronger the system you have (massive MW generators), then less you could feel the hertz influence and stability problems from small generation failure or increased load.

While capacitive(C) and reactive(L) loads does not do anything to speed, it just shifts stator current phase+-90 deg (using voltage phase as a reference) forcing stator magnetic field to vary (in capacitive load stator voltage increases, in reactive load stator voltage decreases ), this is fixed with automatic voltage regulator which increase or decrease rotor excitation current to output stable volts and as a result vars are produced or consumed in the generator. That's why you have a lot of capacitor banks in the industry to spin those electric motors, because they drain a lot of inductive current dropping voltage very low during startups.

Some loads can not continue to operate during low frequency. For examples, the performance of pumps can be affected by under frequency conditions.

Usually at frequencies between 53-55 Hz, continued operation due to the reduction in the output of the pumps will become critical. The turbine limitations is more important than the generator and it is not possible to operate a turbine below 57 Hz (severe damage can occur). For over frequency protection is limited by turbine system and do not depends on loads or the electrical power system. There are under-frequency/over-frequency relaying set points, load shedding schemes, control and protection that should be coordinated with loads, turbine limits and stability for under frequency operation.

For larger systems, there will be a relationship between the rate of change of the load and the rate of change of the frequency. For smaller systems, speed has an inverse relationship to load. There are two modes for operation of a standalone generator, Isochronous and droop. Isochronous is where the speed is kept constant for the load. Typically when generators operate in parallel. For a standalone generator, droop is used where a slight drop in frequency is permitted for a higher load. The details of these can be found either for the generator supplier, or try Woodward literature.

So it is general the relation is the capability of loads to keep operating under low frequency conditions. The relation and limit is usually set and can be found with simulations.