If the kilowatt meter is digital, it will not show "real" frequently. It shows an average reading. To see properly, what is going on with the frequency, use an analog meter for quickly measurements and an O-scope, like Kloppk susgested. The O-scope is of course the best method.
There are several different types of frequency irregularities. One is called a "hunt", or surge. Rarely seen in the small generators. It comes about normally due to a non functional electrical governor actuator system. It's normally a short surge, the gov system corrects, Clowers the engine speed) then the governor sciences low speed and over corrects. And on and on and on and on. If left un attended, it can hunt 100 times a minute, or more. Or it can be a very slow hunt. In any case, bad for the end user. Then come the slow decrease, ( very seldom but can happen, an increase) of frequently. This is 99.99999999% a fuel problem. The slow increasing problem, is also a fuel problem. But as I said, rare. One last problem. An over speed/max frequently problem. I have only seen it a few times. Always an injector pump problem. Mechanical problem every time.
if you know someone with an O-scope, try that first, before jumping to conclusions. Your Electricions meter may not be right. But first check it with the O-scope. If the O-scope shows dirty frequency, then we can think about what might be the problem. We might think about calling Dieseladdict in, he is an EE. Electrical Engineer, I believe.