If it is still under warranty, have it repaired under warranty service. It sounds (smells?) like a defect.
If you're stuck with it, try to locate exactly where the smell is emanating. Some of the wiring and the controller should be inside the door. Removing the outer door wall will expose this. You might see slight smoking or one the wires may feel unusually hot during operation.
If nothing in the door seems out of order, the rest of the wiring is underneath, requiring removal and placing on blocks for further investigation. Even if you find the culprit, there is probably nothing you could do DIY to repair the problem, but you don't know if you don't try. You might find a previous repair using wire with the wrong insulation and simple replacement could solve the problem. If nothing else, identifying exactly where and when in the cycle the problem is can greatly reduce diagnostic charges from the repair person, and garner you certain respect for identifying the problem.
You are probably better off calling an appliance repair person instead of an electrician. Anyone advertising themselves as an electrician will have most of their experience in wiring buildings, not appliances. They would not be clueless, but could struggle with basic things like how to remove the access panel.