59003 - On Virtual Clearance Monitoring of Steam Turbine by Using Model Order Reduction 

With the increasing need for flexible operation (shorter start-up time and higher rate of power change, etc.), clearance monitoring between the rotor and the stationary components (blade/dummy ring, inner ground/outer ground) in steam turbines is becoming more important. This is because as the rate of load change increases, the minimum radial and axial clearances during operation tend to be smaller due to thermal deformation of the steam turbine, and the risk of contact between the rotor and the stationary components becomes higher. This has accelerated the development and practical application of clearance sensors. However, it is difficult to monitor all possible points of contact with only physical sensors due to limited installation locations and the short lifetime in high temperature environments.
From the above background, a virtual monitoring (VM) technique to monitor radial clearances at multiple points of interest has been developed. In this technique, the reduced order models (ROMs) is used to enable real-time prediction. Here, the thermal and structural equations obtained by finite element discretization of the detailed thermo-elastic model of the entire steam turbine are reduced to the ROMs by POD-Galerkin projection based model order reduction (MOR), together with a matrix interpolation method to deal with the temperature dependency of the material properties and a hyper reduction method called DEIM to reduce the radiation term in the thermal equation. The radial clearance VM system with these ROMs consists of the following modules; (1)A boundary condition generator that generates the thermal and pressure boundary conditions from the instantaneous measurement data. (2)Temperature and displacement calculator using the ROMs. (3)A post-processing to evaluate the radial clearances from the temperature and displacement results.
This paper presents application results of the VM system to a stream turbine which constitutes a state-of-the-art GTCC manufactured by Mitsubishi Power, Ltd. Firstly, the detailed system configuration is explained. Then a verification result that the VM system is possible to predict radial clearances at multiple points with a pitch of about 2 sec with finite element analysis(FEA)-like accuracy is presented. 
Secondly, an evaluation result of the error in the radial clearances relative to the eddy-current clearance sensors is described. Here, after training the ROMs with FEA results for three different start-up modes determined based on the inlet metal temperature, the VM was performed under a start-up condition called warm1. And, the obtained start-to-stop radial clearances were compared with the measured values at seven points to evaluate the errors normalized by the average initial values of these sensors. As a result, the maximum RSME and MaxAE are 7.2 and 16.9 %, respectively, at the five points other than the blade ring, which shows relatively good agreement between the VM and the measurements. On the other hand, at the top and bottom of the blade ring, which is considered to move up and down due to unmodeled phenomena such as contact, the RSMEs  are 25.1 and 24.5 %, and the MaxAEs are 32.5 and 29.6 %, which were higher compared to the other five points.
The proposed method is considered as one of the most suitable methods for virtual clearance monitoring that   contribute to improve the flexibility of steam turbine operation.