* Power output stands at 504.8 bln kWh in July
* Boosted by near 30 pct yearly jump in hydropower
* But slowing economy hits demand from steelmakers, autos (Adds detail)
SHANGHAI, Aug 13 Chinese power generation grew 3.3 percent in July from a year earlier, but the rate of increase eased from the month before as a slowing economy hit production in power-intensive sectors such as steel, autos and machinery.
Power output in the world's top consumer was 504.8 billion kilowatt hours (kWh) in July, boosted by a near 30 percent yearly jump in hydropower generation as thermal production fell, data from the National Bureau of Statistics showed.
Year-on-year growth in power generation eased from a 5.7-percent rate posted in June. Compared to a month ago, however, output rose 10.2 percent, helped by increased air-conditioner usage during the searing summer heat.
Other data released on Wednesday showed China's industrial output rose 9 percent in July from a year earlier, as expected, while fixed-asset investment, an important driver of economic activity, missed forecasts to grow 17 percent in the first seven months from the same period last year, the bureau said.
China's annual economic growth edged up to 7.5 percent in the second quarter of 2014 after hitting an 18-month low of 7.4 percent in the first quarter. Some economists believe further stimulus may be needed to sustain the recovery and offset the drag from the cooling property market.
The rise in July output brings total power generation in the first seven months of the year to 3.12 trillion kWh, data showed, up 5.5 percent from a year ago.
China's thermal coal sector has been hit by a triple whammy of a slackening economy, stubborn oversupply and Beijing's aggressive anti-pollution campaign, which has seen gas and renewables take a growing market share in overall power generation.
Benchmark coal prices on the Bohai-Bay Index for coal with an energy value of 5,500 kcal/kg have fallen over 20 percent this year to stand at 482 yuan ($78.24) a tonne this week, the lowest in more than six years.
Local media has reported that the steady fall in coal prices may prompt the National Development and Reform Commission to cut on-grid power tariffs - a move that could threaten profits of China's top five power groups and cut their profits by 1 billion yuan ($162.3 million) each in the second half of the year.
Under a new coal-power price linkage system implemented since 2013, power tariffs would be adjusted if coal prices rise or fall more than 5 percent during a six-month period.
The China Electric Council in July cut its forecast for 2014 power consumption growth to between 5.5-6.5 percent, down from its February estimate of 7 percent and a rise of 7.5 percent in 2013. (Reporting by Fayen Wong; Editing by Muralikumar Anantharaman and Joseph Radford)