Identification of Metal Temperature Distribution in Steam Turbine During Start-Up Operation Using Particle Filter and Model Order Reduction

In steam turbines (STs), evaluation technology of thermal deformations during transient operations is increasingly important, because of a demand for improvement of operability such as shortening startup time. However, it is still difficult to predict temperatures of metal parts with sufficient accuracy due to complexity of heat transfer phenomena. The present study puts its focus on developing a method to identify metal temperatures of STs during start-up operations using particle filter (PF), a kind of sequential Bayesian filter utilizing ensemble approximation, and model order reduction (MOR) technique. In this method, a self-organizing state-space model is used to calculate time evaluations of metal temperatures, and heat transfer coefficient (HTC) parameters and steam bulk temperature parameters. And an optimal estimate of these is obtained through iterations of a short-time prediction and a correction of variables using measured temperatures. In this state-space model, state variables including HTC and bulk temperature parameters are treated as random variables, and the time evolution of each variable is modeled as follows; (1) Metal temperature is modeled using a reduced order model (ROM) in order to reduce computational time of PF. The ROM is constructed from a finite element model for unsteady heat transfer analysis using MOR technique. (2) HTC is modeled as a random walk model where its changes during one time step is randomly determined using Gaussian noise. Here, the magnitude of this noise is adjusted automatically. (3) Bulk temperature is modeled using prediction formulas with Gaussian noise added. As a validation problem, a cold start-up operation of a ST unit of a gas turbine combined cycle (GTCC) is considered. The proposed method is applied to the problem, and boundary conditions (BCs) are identified using measured temperatures at 68 measurement points. Then, the heat transfer analysis based on finite element analysis (FEA) is performed using the identified BCs. As a result of this FEA, it is confirmed that the calculated metal temperature tends to agree better with measurements compared with that of initial FEA, and that the errors of the calculated temperature at measurement points reduce by 41% on average compared with initial FEA. From this result, it is concluded that this proposed method is effective for metal temperature identification during start-up operations.