Hello John and thanks for the replies.
1) You have a couple of options here. First off, If the generator RPM's are not properly synchronized for a 60 hertz output, that could be one reason as to the cause of the problem. In other words, if the generator output is less or greater than the required 60 hertz frequency, the generator sine wave output will be out of synch and not producing the required 60 hertz frequency. A test instrument such as an oscilloscope can confirm the output sine wave shape, peak-to-peak and RMS voltages. Any local generator maintenance shop can perform this test and advise you as to the output quality of the wave form, etc.
2) Generators are widely known for not providing clean power. The cheaper the generator, the less quality of power will result from it. Depending upon the quality characteristics of the generator, a power line conditioner may assist in the problem. One of the best methods for power conditioning is the use of a UPS. The better solution for your application is to use a Line Conditioner. Please note that some Line Conditioner manufacturers will void the warranty if used on a generator. It appears that the Eaton model Line Conditioners do not limit a warranty on their products when used on a generator.
I would recommend a line conditioner for your application versus a UPS. A UPS is generally used for battery backup purposes such as computers but they do provide quality power conditioning. However, you do not require battery backup for your application.
Since the furnace is rated at 120 volts and 15 amps, you would need a Line Conditioner that is rated at 120 volts and 20 amps. The 125% NEC rule is to compensate for the "in-rush" current upon startup of the fan/blower motor. Thus the reason why I would recommend a Line Conditioner rated at 20 amps and not 15 amps.
Here is a link to the Eaton website for Line Conditioners
Prior to purchasing a Power/Line Conditioner, I would recommend that you contact and visit your nearby electrical supply store. They may have different models and manufacturers and can best assist you in your application.
3) The National Electrical Code requires that the over protection device rating of the electrical supply to be sized @ 125 % of the furnace amperage rating. Therefore, using 13.8 amps times 1.25 = 17.25 amps which is less than the 20 amp over current protected receptacle on the generator. Therefore, your generator can support the furnace load without a problem.
4) In addition, using a 10/3, 50 foot extension cord at 120 volts and a 20 amp load results in a 2.4 voltage drop or an overall 2% VD. National Electrical Code recommends a maximum of a 3% VD, therefore, using the 10/3 cord is OK.
Hope this helps.........If you have any additional questions, let me know and I'll be glad to answer them for you.
Otherwise, don't forget to rate me before you log Off.
The next time you have an electrical question, you can also request for me at:http://www.justanswer.com/home-improvement/expert-your-electrician