KHOBAR, Saudi Arabia, May 17 (Reuters) - State-controlled Saudi Electricity Co (SEC) has started up part of its new 2,640 megawatt (MW) Jeddah South power plant and linked it to the grid, the company said on Tuesday.

The project will help meet growing electricity demand from the western region particularly for infrastructure projects in the holy cities of Mecca and Medina where large numbers of Muslim pilgrims spend the fasting month of Ramadan which starts in June this year.

"After three-and-a-half years of continuous work; Saudi Electricity Co has successfully operated and linked the first steam unit to the electricity grid with a capacity of 660 MW," SEC said in an emailed statement.

When the 11.9 billion riyal ($3.12 billion) project was announced in 2012, SEC said it was using super critical boilers for the first time in the kingdom, allowing the plant to reach up to 40 percent efficiency in fuel consumption.

South Korea's Hyundai Heavy Industries (HHI) built the plant while Japan's Mitsubishi Heavy Industries (MHI) 7011.T supplied the equipment. In the statement SEC did not say when the plant would hit full capacity.

The world's largest oil exporter Saudi Arabia burns a significant amount of its crude oil for power generation particularly during peak summer demand.

However, SEC expects the more efficient plant to burn much less fuel oil per unit of electricity produced.

Deputy Oil Minister Prince Abdulaziz Bin Salman said in February Saudi energy consumption was expected to grow by 4-5 percent annually in the next few years, reaching double its current level by 2030 if no efficiency measures are taken.

Last year, the prince said the country expects to save a fifth of its energy use by 2030 through an efficiency drive designed to prevent domestic consumption from eating up oil for export.

(Reporting by Reem Shamseddine, editing by Sylvia Westall and David Evans) ((Reem.Shamseddine@thomsonreuters.com; +966503335202; Reuters Messaging: reem.shamseddine.thomsonreuters.com@reuters.net))