Some surge protectors work by "redirecting" surges to the equipment ground, which is pretty much the definition of a ground fault. In this case, it's definitely possible that surge suppressors could be tripping GFCI receptacles/breakers (given a large enough surge).
As for the AFCIs... When electrical contacts separate, they often create an arc between the contacts. This arc spans the gap until the contacts are too far apart, and the arc can no longer be sustained. It's possible (in theory) that the GFCI tripping could create a large enough arc, for long enough to cause the AFCI to trip. It's not likely that a properly functioning GFCI would do this, but if the GFCI was old and worn it could be opening the contacts slow enough that a detectable arc is being produced.
Determining if the GFCI tripping is causing the AFCI to trip, is a simple test. Simply press the test button on the GFCI. If the AFCI trips, you'll have figured out half the problem. If the ACFI does not trip, you could repeat the test using a receptacle tester with a GFCI test function.
If it's determined that the GFCI is causing the AFCI breaker to trip, replacing the GFCI receptacle may resolve that part of the issue.
Figuring out if the surge suppressor is tripping the GFCI, is a more difficult proposition. It will likely require you to monitor the supply voltage over some time, to identify and document possible surges.
Combination-type AFCI (Arc Fault Circuit Interrupter) receptacles (and breakers, too) are generally be designed to trip when any of the following conditions are met:
- Series-arc (arcs between hot and neutral/ground)
- Parallel arc (arcs where a single wire (hot or neutral) has a defect, or bad connection)
- Ground Faults (generally > 40 mA of unbalanced current)
The techniques for diagnosing tripping of receptacles are the same as for diagnosing tripping of AFCI breakers. It is pretty much taking the circuit apart until you find the problem, though there are some special meters that can make the process faster.
Arcs
The AFCI contains a microprocessor that uses proprietary heuristics to determine if an arc has occurred, for example, some number of short high current spikes within some amount of time. Unfortunately, this can also prevent the use of some "desired" loads (I'd posit that spark gap devices like Tesla coils would trip the AFCI, though I don't have any evidence of such). Older AFCIs are more sensitive to various "good" loads and may trip more easily, but the new models are reasonably resistant to false-tripping because of false-positive arcs. Certain motors and lighting (especially dimmers) can also cause tripping, though this often indicates a true problem with the motor/dimmer that should itself be corrected.
Loose connections is the circuit can cause arcs, and thus cause nuisance tripping, too.
Ground Faults
AFCIs are designed to detect ground faults, similar to GFCI receptacles. They trip when the current in the hot wire is not equal to that of the neutral. While GFCIs are set to trip when the difference of these currents is around 4 mA, AFCIs are set to trip at around 40 mA. Ground faults occur when the neutral and ground wires are connected together downstream of the interrupter.
Troubleshooting
One way to detect ground faults is with an ohmmeter. If a ground fault is occurring, it often can be seen as a low-resistance path between neutral and ground (except for some special loads like motors). You can use an ohmmeter at the circuit breaker panel to measure the resistance between neutral and ground. Be careful about working around electricity, it is dangerous. First turn off the power to your circuit via the branch circuit breaker, or the main breaker. Verify that the power is off on that circuit, preferably by using a non-contact voltage detector on the "hot" and "neutral" wires for the circuit. Next, disconnect the neutral from the neutral terminal block. Measure the resistance between the neutral wire, and ground. It should be >10 Mohm, but if the two are shorted together in your circuit well enough to trip a ground fault device, it will be less than around 30 kohm (120 V/4mA).
After separating the circuit into parts, if the trip is gone, then you know that the parts of the circuit still receiving power are "good", and can be left connected. If the circuit still trips, then the disconnected part is likely "good", and you should leave it disconnected during further troubleshooting.
Another way to detect the ground faults is to put a large load on the circuit. I would use a space heater, but an 100W incandescent light bulb could work too. These are purely resistive loads that won't be detected as arcs. If it trip soon after turning it on, then you have a ground fault, or less likely, a bad connection causing an arc in your circuit. The ground faults could happen only when the circuit is loaded, for example when the wires heat up, and the thermal expansion causes the wires to contact each other. The fault is more likely to be detected by the AFCI when your load is closer to the actual location of the fault, so plugging your load into the AFCI receptacle itself may not cause it to trip, since the fault is too far away....
The ground fault current will be roughly proportional to the load of the circuit, so to cause the fault, you might have to have a large load on the circuit in order to cause the trip.
To correct this, you will need to go to each device (receptacle/lamp, etc), and disconnect the "upstream" from the "downstream" wiring until you find the problem. If the ground fault disappears, then you know that the fault happens in the part of the circuit that was disconnected. Divide an conquer until you have found the location of the ground fault, and fix it. Note that the problem could be inside the wall, perhaps where a nail was sunk through your electrical cable.
If the problem is an arc, the problem should be approached in the same way. Check all of your connections to make sure that they are tight, and divide the circuit until you locate the section of cable that is your problem.
I tend to think that your lights are not causing the issue because you have tried a number of different lights, and they are all causing tripping issues, but causing the tripping by using a 100W light bulb or space heater would confirm that it isn't a problem caused by fluorescent lighting. Normally the problem would be caused by a failing ballast in your fluorescent light, so that should be replaced.... The only way to further diagnose this is to see if the trip ever happens if the fluorescent are turned off. Worst case, your lights could have a little problem and your fan could have a little problem, each of which individually won't trip the breaker, but does when both are on together.
As for a "better way", Siemens has an "Intelli-arc" meter that will report the magnitude of arcing, total current, and unbalanced (ground fault) current. This tool could make your process go faster by helping you differentiate betweenn arcing and ground-fault conditions, and reporting conditions that are below the trip threshold of your receptacle. One option for beakers is to examine their indicators lights. They will report if the trip was caused by an arc, but these indicators are not on the receptacles.
Best Answer
The dimmers are spewing radio-frequency hash into the power line, which confuses the AFCI into a false trip. It makes sense that it's more reproducible on an intermediate dimmer setting, because that's when the dimmer chops the line voltage aggressively, not when it's fully on or fully off.
Bypass capacitors could help with this: 1 to 10 nF capacitors, X1/Y2 rated ceramic or film, minimum 250VAC working voltage rating. This diagrams shows three caps: between hot and neutral, hot and ground, and between neutral and ground.
The basic idea is that 60 Hz AC will not pass through these capacitors because the frequency is too low, but radio frequencies pass through easily. So the capacitors provide a short circuit shunt path for high frequencies, reducing how much of it spews back upstream from the dimmer.
This looks simple, and it is, but it has to be done properly. Capacitors have long, uninsulated terminals, creating opportunities for short circuits if you're not careful.
Instead of these ad-hoc capacitors, you can install an EMI filter upstream from the light dimmer. EMI filters have a more sophisticated circuit which includes inductors.
One more thing: the Lutron dimmer company sells a filtering component that they call a lamp debuzzing coil.