The invention relates to engine power quantization function selection. A vehicle having and engine and traction battery and a method of operating an engine are disclosed. A controller operates the engine according to quantized engine power levels. The quantization level depends upon a total power demand. For low values of total power demand, the selected quantization level may be at least equal to the total power demand. For high values of total power demand, the selected quantization level may be less than or equal to the total power demand. In between low and high values, the selected quantization level may be the quantization level nearest the total power demand. The traction battery may receive or provide power depending on the selected quantization level.