Explicit analytical solutions of part-load performances of constant rotating speed single shaft gas turbine and its cogeneration are derived based on analytical typical component performances. Their typical part-load operation regularities are summarized as well. For the gas turbine installation, it is found out that the relative gas turbine efficiency variation can almost be summarized as a single curve that is consistent with the practical data. The part-load performances of gas turbine cogeneration are investigated for the industrial process heat supply with saturated steam. It is found out that the variations of the steam flow rate and work/heat ratio are almost not influenced by the gas turbine design values, and it is worth emphasizing that the approach temperature difference in a heat recovery steam generator is likely to be negative in low load condition with high steam parameter and low ambient temperature.