Conventional motoryachts are powered by diesel- or gas-engines. Additionally they use to have a generator on board to supply all household appliances.
Depending on the size of the yacht, in sum 2 or 3 diesel-engines are working for propulsion and household.
Also sailing-yachts need a diesel-engine. Depending on the operational area and the wind- and weather-conditions, additionally to the sails a diesel-engine is needed for the propulsion of the boat. When anchored in a quiet bay, the diesel-engine ensures the energy-supply of the consumers.
Most yachts are using gas for cooking, the open flame heats up the interior of the yacht and cause an imminent threat. On many yachts the consumables like water and energy are managed in a way that enforces the skipper to visit a marina every two or three days to charge the batteries and to buy water for shower and drinking. Larger Yachts operate water-makers, air-conditioning and generators. They do not need to got to a marina but they have to run the generator.
The use of a combustion-engine is inevitably combined with noise, exhausts vibrations and oily films in the water. Is it that, what you are looking for in an otherwise quiet bay?
A conventionally powered boat has a range of 300 to 500 nautical miles under diesel-engine. With a sail the range can be extended — but only when the wind is coming from the right direction and in matching force.