MUMBAI, Nov 18 (Reuters) - India's coal-fired power output has increased much faster than any other country in the Asia Pacific since Russia's invasion of Ukraine, underscoring the challenges the world's third-largest greenhouse gas emitter faces in weaning its economy off of carbon.Coal fuels nearly three-quarters of the power output of India, which presented its decarbonisation strategy at the United Nation's COP27 climate summit this week - the last of the world's five largest economies to do so.Use of coal globally, including in power generation, has grown since Russia's invasion of Ukraine in late February sent prices of other fossil fuels surging, derailing efforts to transition to cleaner fuels.India's coal-fired power output increased more than 10 percent year-on-year from March to October to 757.82 terawatt hours, an analysis of government data shows, as electricity demand increased off the back of a heatwave and pickup in economic activity.An analysis of data from independent think tank Ember shows India's surge in coal-fired output for the March-to-August period was 14 times faster than the average in Asia Pacific."