Mitsubishi Heavy Industries Technical Review Vol. 58 No. 1 (March 2021)
1Virtual Measurement Technology for Supporting
Flexible Operation of Steam Turbine

HIROSHI ITO*1SHOICHIRO HOSOMI*2NORIKAZU TEZUKA*3

TOMOHIRO ISHIDA*4

We have been working on the development of virtual measurement technology for predicting
the thermal deformation of steam turbine utilizing model order reduction (MOR) technology thatenables high-speed and high-precision numerical prediction with mathematical reduction of finite
element analysis (FEA) models. This report describes the application of this virtual measurement
technology to actual equipment and the realization of real-time prediction of a steam turbine radial
clearance with an accuracy comparable to that of FEA. This technology is useful for enhancing
clearance management resulting in improvement of performance and safety and is expected tocontribute to improving the flexibility of thermal power generation.

|1. Introduction
Thermal power generation is now expected to play a role in adjusting the balance between
supply and demand of electric power by compensating for fluctuations of variable renewable energy
output in addition to supplying electric power. Therefore, rotating machines for power generation(steam turbines and gas turbines) are required to improve in terms of flexibility, such as improvementof the output change rate and shortening of start-up time. However, a change in the output (a change
in the operating gas flow rate) affects the thermal deformation of the rotor and the stationary parts
such as the outer casing, inner casing, blade ring, etc., as shown in Figure 1, so it causes a problem
in that the risk of contact between the rotor and stationary parts increases. For this reason, theenhancement of clearance management becomes more important by monitoring the clearance
between the rotor and stationary parts in performance and safety improvement. However, physicalsensors are limited in terms of their placement and number of units, and as such cannot monitor all
high-risk areas. Therefore, we have been working on the development of virtual measurement
technology that estimates the radial gap (radial clearance) between the rotor and stationary parts of asteam turbine using a numerical prediction model based on the state quantity (pressure andtemperature of the operating gas), which can be measured easily. The purpose of this development
is to realize virtual measurement that can predict radial clearance in real time with an accuracy
comparable to that of FEA by using a reduced order model, which is obtained by lowering thedimension of the thermal/structural FEA model with MOR, as this numerical prediction model.

*1

Research Manager, Strength Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

*2

Chief Staff Manager, IT Strategy & Planning Department, Digital Innovation Division, Mitsubishi Power. Ltd.

*3

Chief Staff Manager, Steam Turbine Engineering Department, Steam Turbine Technology & Production Integration Division,*4

Strength Research Department, Research & Innovation Center, Mitsubishi Heavy Industries, Ltd.

Mitsubishi Power. Ltd.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 1 (March 2021)
2Figure 1 Outline structure of steam turbine

Thermal factors of fluctuation of radial clearance is illustrated.

|2. Building thermal/structural FEA reduced order model
In the integrity evaluation at the design and development stage, the radial clearance isevaluated by the following procedures (Figure 2(a)): (1) FEA calculation conditions (wall heattransfer coefficient, steam temperature and pressure, rotor centrifugal force, etc.) are set based on
operating conditions (steam temperature and pressure at the inlet and outlet, etc.); (2) The unsteady
temperature distribution of the steam turbine metal parts is calculated using thermal FEA and theresult is used as the thermal load for the structural FEA model to obtain the deformation of the entire
steam turbine; (3) The radial clearance at the evaluation time is calculated by adding/subtracting theradial displacement of the rotor and the stationary parts and the separately calculated displacementof the blade, bearing and outer casing support to/from the initial radial clearance value. Theseevaluation procedures using FEA can obtain accurate results due to precise modeling, but take morethan one day per calculation of one case, so they cannot be applied to virtual measurement that
requires real-time performance. Therefore, we enabled real-time evaluation to realize virtual
measurement by substituting FEA with the reduced order model built using MOR (Figure 2(b)).

Figure 2

Evaluation method of radial clearance

Radial clearance evaluation procedures using FEA in design and development andmodifications therefrom for virtual measurement are illustrated.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 1 (March 2021)
3(1)-(6)For structural FEA, the following descriptions explain the MOR procedureusing proper
orthogonal decomposition (POD) and Galerkin projection. Galerkin projection is a mathematicalmethod that limits the M-dimensional state space that defines the domain of the governing equation(force balance equation with the displacement as an unknown variable) to the N-dimensional
subspace and transforms the problem into N-dimensional one. The solution on this state space isrepresented by an M-dimensional real number vector and the subspace selected is one that contains
a set of actually possible solutions. The specific method for determining the subspace is described
below. As shown in Figure 3, FEA is performed under various calculation conditions in advance toobtain the solution set (snapshots). Then, the Nth-order truncated singular value decomposition isapplied to the snapshot matrix in which these solutions are arranged in columns to obtain the M × Nmatrix U in which the resulting left singular vectors are arranged in columns. This matrix U is also aprojection matrix to the N-dimensional subspace, whereby the desired subspace can be obtained.
Here, N is usually much smaller than M.

Figure 3

Definition of subspace by POD and Galerkin projection

Method to obtain the subspace used for dimension reduction using pre-FEA results and singular value
decomposition is illustrated.

Once the projection matrix U is obtained, the governing equation can be converted into a
reduced order model (simultaneous linear equations the number of unknown variables of which isN) by Galerkin projection shown in Figure 4. Empirically, a value N of about 100 is sufficient. In
this case, by using the reduced order model, the solution can be obtained about 10,000 times fasterthan the original governing equation. Furthermore, by using the projection matrix, the originalvariables can be restored from the reduced order model solution.
In the above, the procedure of MOR is explained assuming linearity, but the actual thermal
deformation phenomenon includes non-linear phenomena such as temperature dependence ofphysical properties and radiation (heat transfer problem). In this development, several reduction
methods for these non-linearities are also applied to improve the accuracy of the reduced order model.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 1 (March 2021)
4Figure 4 Derivation of reduced order model using POD andGalerkin projection
Method to degenerate force balance equation into low-dimensionalmodel using projection matrix U|3. Mechanism of virtual measurement system
Similar to physical measurement, virtual measurement can be used for monitoring andoperation control by displaying the measurement results on the monitoring screen in the power plant,
or for remote monitoring using TOMONITM (trademark of digital solution produced by Mitsubishi
Power, Ltd.). In this development, in order to verify the former usage, the virtual measurement
system shown in Figure 5 was constructed in the special measurement room of the combined cycle
power plant validation facility (T-Point 2).

Figure 5 Overview of virtual measurement system
Outline configuration of virtual measurement system installed in special
measurement room at T-Point 2 is illustrated

3.1

System configuration and real-time calculation method

This system consists of, corresponding to the FEA evaluation procedures (1), (2) and (3)described in the previous chapter, the following three main modules: (a) Calculation condition
creation module that reads operating conditions from the measurement file and creates FEA
calculation conditions; (b) Temperature/displacement calculation module that calculates thetemperature and displacement of the steam turbine using the thermal/structural reduced order model;(c) Post processing module that processes the calculation results in the same way as the procedure(3) to obtain the radial clearance. This system executes modules (a) and (b) in sequence to update thetemperature and displacement state quantities to the latest values when the measurement file isupdated and then outputs the clearance results obtained by executing module (c) to the monitor. This

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 1 (March 2021)
5

is one cycle of virtual measurement processing. The update interval of the measurement file is 1
second and if one processing cycle takes 1 second or more, the measurement file during that period
is skipped. Therefore, the output interval of the virtual measurement value is a multiple of 1 second.

3.2

Method for training reduced order model

It is considered desirable to use the FEA results (snapshots) that reflect actual operation as
training data of the reduced order model. Therefore, based on the operational data in each start modeof cold, warm and hot specified by the inlet metal temperature at start-up, we created the calculation
conditions in module (b) and performed FEA. Using these results, we constructed a thermal and astructural reduced order model which have 80 unknown variables each.

|4. Virtual measurement results
At T-Point 2, we verified the real-time property of virtual measurement and its prediction
accuracy with respect to that of FEA.

4.1

Real-time property verification results

Figure 6 shows the results of aggregating the number of virtual measurements for eachprocessing time of one virtual measurement cycle. As for one cycle of processing time, 1 second and2 seconds accounted for 97% of the total (94% in terms of operating time), so it is indicated that
virtual measurement results can be obtained with a delay of about 2 seconds with respect to themeasured value. Since the change in radial clearance for 2 seconds is small and therefore the time
resolution is sufficient, it was confirmed that real-time virtual measurement can be realized.

Figure 6 Measurement results of virtual
measurement speed

Aggregation results of the numbers of virtual measurement
for each processing time of one virtual measurement cycle
are illustrated. One second and two seconds account for 97%
of the total (94% in terms of operating time).

4.2

Results of verifying prediction accuracy of virtual measurement with respect tothat of FEAIn the high-pressure steam turbine of T-Point 2, virtual measurement of the radial clearance
during a cold start in the approximate position shown in Figure 7(a) was performed with the reducedorder model. The same analysis was also performed with FEA and the difference between the tworesults was calculated. Figure 7(b) shows this difference nondimensionalized by an initial clearance
value. From these results, it was confirmed that the difference between the virtual measurement andthe FEA is less than 10% and that the reduced order model closely approximated the FEA. Note thatthe difference tends to be larger after turbine startup, but this difference can be reduced by building
the ROM with larger degrees of freedom using more snapshots.
From the above, it has been clarified that virtual measurement can predict the radial clearance
in real time with an accuracy comparable to that of FEA.

Mitsubishi Heavy Industries Technical Review Vol. 58 No. 1 (March 2021)
6

Figure 7 Virtual measurement results of radial clearance
The figure on the right shows the difference of the virtual measurement and FEA results of theradial clearances between the rotor and the internal parts for which the approximate positions areshown in the figure on the left. The difference is nondimensionalized by an initial clearance value.
This figure indicates the difference with FEA is less than 10%.

|5. Conclusion
In order to support the safe implementation of the flexible operation of steam turbines, wedeveloped a technology for virtual measurement of the radial clearance using the thermal/structural
reduced order model using MOR based on POD-Galerkin projection. By performing virtual
measurement in the high-pressure steam turbine of T-Point 2, we clarified that the virtual
measurement could predict the radial clearance in real time with an accuracy comparable to that ofFEA. This technology contributes to the improvement of flexibility such as the improvement ofoutput change rate and shortening of start-up time, and can be applied to the thermal deformation
problem of rotating machines such as steam turbines and gas turbines.
In considering future development, it is important for the virtual measurement to improve theprediction accuracy with respect to the actual value in order to use it for operation control. Therefore,
we will work on improving thermal deformation modeling and reducing prediction errors. Flexible
operation tends to increase rotor stress, resulting in a shorter rotor life, so stricter rotor life
management is required to inspect and replace the rotor efficiently. Therefore, we will also work on
the development of technologies for virtual measurement of rotor stress and fatigue.

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