Two of the state's electric utilities, N.H. Electric Cooperative and Liberty Utilities, have announced sharp rate cuts while a third, Unitil, has filed paperwork with the N.H. Public Utilities Commission requesting a 37-percent reduction for power costs starting June 1. Eversource, formerly Public Service of New Hampshire, is expected to file a mid-year rate adjustment in May that would take effect July 1. A company spokeswoman wouldn't say what direction rates were headed.  “What we have seen in the wholesale markets would indicate the rate could go down,” Tom Frantz, director of the electric division for the N.H. Public Utilities Commission, said of Eversource.  New England has limited natural gas pipeline capacity.