The q-γ-τ matrix equation of thermal system is an important branch for the quantitative analysis method of the thermal system in power plants. The said matrix equation looks upon the superheater of a boiler as a special heater

having comparatively well solved the problem of conventional q-γ-τ matrix equation

in which insufficient consideration had paid to a special auxiliary steamwater system

i.e.

the desuperheating spray water of a boler can affect the internal flow rate variation in the said boiler

being effective extension and supplement of the conventional matrix equation. Finally

verification of the said method has been carried out through practical examples.