**6. Conclusions**

A steam turbine operates with prescribed parameters of the superheated steam at the turbine inlet. To ensure a safe and trouble-free operation of the turbine, the time changes of the inlet steam parameters must not be abrupt and do not differ from permissible values. Too rapid steam temperature changes can cause high stress in the pipeline and the turbine construction elements. To ensure trouble-free operation, the variation of steam temperature at the turbine inlet is necessary.

The paper developed the procedure for solving IHP to determine the time change of pipeline inlet temperature directly behind the boiler based on the prescribed measured steam temperatures before the steam turbine inlet.

The procedure proposed in this paper can be used to control the operation of the boiler so that, at its outlet, the steam temperature is equal to the steam temperature determined from the inverse solution. In this way, changes in the steam temperature upstream of the turbine will correspond to the requirements of the turbine user or changes due to conditions for safe turbine operation.

In summary, it can be stated that the developed mathematical model can be used to simulate transient temperature changes in pressure pipelines used in power plants. It allows us to determine the temperature distribution and stresses occurring in the pipeline wall and to calculate the allowable medium temperature change rate in time so that the allowable stress values are not exceeded.

The permissible temperature time changes at the pipeline outlet can also be determined from the condition of not exceeding thermal stresses, e.g., in components of the quickclosing valve before the turbine or the turbine rotor. The procedure for determining the allowable steam temperature variations downstream of the boiler will be identical to that presented in the paper.

The developed computational algorithm is efficient, allowing quick results of transient processes that occur in the pipeline during its operation.

Future studies will determine the allowable time variation of steam temperature at the turbine inlet due to not exceeding the allowable thermal stresses in the turbine quickclosing valve and the rotor and turbine body. These will be the basis for determining the corresponding changes in boiler outlet steam temperature and, subsequently, for the complete automation of the steam power plant start-up.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Nomenclature**


