* Tuesday power use expected to set June record * Several days of triple-digit temperatures likely * ERCOT urges conservation to avoid straining grid June 26 (Reuters) - The Texas power grid expected demand Tuesday to break the June peak record for a second day in a row and urged consumers to continue cutting back on power use to avoid straining the system as much of the state broils under triple-digit temperatures. The Electric Reliability Council of Texas (ERCOT), the grid operator for most of Texas, forecast peak demand Tuesday would reach 66,415 megawatts (MW), easily surpassing the June record set Monday of 65,047 MW. Before Monday, the June record was 63,102 MW set last year. The state's all-time peak use was 68,379 MW set in August last summer during a protracted heat wave and drought. Real-time power prices briefly exceeded $100 per megawatt-hour Monday afternoon. Next-day power prices for Tuesday traded between $165 and $175 per MWh. The extreme heat hit Sunday when the mercury reached 100 degrees Fahrenheit (38 Celsius) in Houston, San Antonio and Dallas, the three biggest cities in the Lone Star State, prompting residents to crank up air conditioners. Triple-digit highs were forecast for several more days this week, with several high enough to set records, AccuWeather.com forecast. ERCOT said in a release it was looking closely at anticipated electric use and available generation. The grid agency said adequate generation resources should be available to serve the load without activating emergency programs that could lead to curtailment of power to certain industrial customers or broader rolling outages. ERCOT said its plan for the week takes into account current power-plant outages and the possibility of losing additional resources. The grid agency has projected power use will peak at 67,492 MW this summer, about 1,300 MW above what would be expected in a normal weather scenario. One megawatt is enough to serve about 200 Texas homes during hot weather when air conditioners run for extended periods. ERCOT has warned that rolling outages could occur this summer given the state's limited amount of surplus generation. An extended heat wave and drought last summer forced ERCOT to declare emergencies on six days and curtail power to interruptible customers on two days in August to avoid widespread rolling outages. The state's shrinking reserve margin has led regulators to implement a number of wholesale market changes to encourage construction of new power plants over the long-term. Energy companies have returned several idled power plants to service to bolster the summer supply after a new coal-fired plant expected to be operational was delayed. The biggest transmission and generation companies in ERCOT include Luminant and Oncor, units of privately held Energy Future Holdings, CenterPoint Energy, American Electric Power, PNM Resources, NRG Energy, Exelon , NextEra Energy and Calpine.