Which engine do you have? If it's a Kohler it may have a stator that produces Ac voltage and you would also have a rectifier/regulator to convert the AC to DC volts. You can use a volt meter set on AC volts and with the engine at 1/2 throttle or better you can measure the ac output voltage off the stator should be about 30 volts.
If that looks ok switch your meter to Dc volts and measure that. Be careful working around that engine. You can measure the DC volts across the battery terminals, should see around 14 volts. If you only have 12 volts your rectifier is probably defective.. Hal