If you have a 100W electrical load and you drive 100W plus efficiency losses, say 110W, into the generator, things will be in a state of equilibrium, with 100W being converted from mechanical input power into electricity, and the other 10W of mechanical input power being eaten up by losses.
Now suddenly put 1kW of mechanical power into the machine; at that instant, before the rotational speed can change, the 100W electrical load will continue to present the same mechanical load to the prime mover. Things will not be in equilibrium, and the machine's rotational speed will accelerate. Depending on circumstances, this may or may not increase the electrical load. Certainly the generated voltage will go up, and any simple resistive load will therefor absorb more power, but maybe you have some regulation such that the load continues to draw exactly 100W.
So assume the load continues to draw exactly 100W. Where does the extra 900W of mechanical power go then? The machine's speed must increase until the losses equal the mechanical driving power; so it ends up turning extremely fast, the increased power going into increases in friction in the bearings, windage loss due to the rotating parts, eddy currents in the magnetics (and doubtless a couple of other things I forget at the moment), none of which are desirable.
You would find that, without exceeding the machine's electrical rating, you would quickly exceed its mechanical ratings, i.e., probably long before you got to 1000W, the rotation speed would be several times the suggested speed, and catastrophic failure would likely result. Note you can do this with no electrical load on the generator at all.
If they wrote the firmware right, a reading in kilowatts (kW) is the output of the solar array at that moment. The total "work", taken over time, will be in kilowatt-hours (kWh). The time period is arbitrary; it may be taken over the course of a day, or a month, or it may be a lifetime total.
If you want to work it out yourself, by recording the output each second, you still have to assume that the output over each second was constant. But that will normally be close enough. One second's worth of power, by the way, gives you watt-seconds, a unit not normally interesting unless you are looking at something like an impulse from a capacitor. 3600 consecutive 1-second readings will give you the output that was generated during that hour, and it will be in kWh. Remember, it's a cumulative total, just like filling a swimming pool.
Best Answer
Number 3 with a bit of 2. Conservation of Energy forces the energy input to the grid to equal the energy out in losses / load usage or storage within the system at all times with no exceptions.
When there are small mismatches in the input/output energy, this mismatch is accommodated through the rotational inertia of the electric grid. (this inertia is present in all of the grid connected generators AND motors/loads that are spinning. In the case of North America or Europe, these grids have a very large effective inertia). If there is excess generation, the grid frequency increases. If there is excess load, the grid frequency drops.
Most generators use a control technique that controls the energy input to the prime mover based on the grid frequency. Low grid frequency --> increase energy input; high grid frequency --> lower energy input. This is called Frequency Droop control.
Different generator prime movers have different time responses. Thermal nuclear or coal plants may have a time response on the order of 1/2 - 1 day. Natural gas or water turbines can slew power much, much faster.
Slow responding plants provide "base load", while faster responding plants are "peakers" and follow the variations in the load while the system's inertia makes up the difference.
Small, isolated grids can be more tricky to integrate larger portions of wind or solar; however, it is quite possible. For example, there are many villages in Alaska which get their electricity from a combination of diesel generator sets and wind turbines. Some of these villages get 50+% of their electricity from the wind through a combination of careful system control and "dump loads". These dump loads use the excess electrical energy to heat the water for the village's district heating system.