**5.2.1 Process models**

222 Efficiency, Performance and Robustness of Gas Turbines

equations set of each MSS are mathematically independent of the set of equations of any

The ODE are solved numerically with Euler method or trapezoidal rule with one or two corrections. The integration step depends on the dynamic characteristic of the MSS. The determination of the proper integration method and integration step for a MSS is made running the model under a multistep multirate method to find out its "critical transient" (where the method reports more potential numerical instabilities). A numerical analysis involving calculation of Jacobian matrixes, eigenvectors and eigenvalues and its relation

For the simulator, an execution second (cycle) was divided into ten frames of 0.1 s. In this way, any model could be executed with an integration step of 0.1 s, 0.2 s, 0.5 s or 1 s. The sequence matrix indicates the execution precedence of the models defined by the developer. The sequence matrix indicates, besides the execution sequence, the integration method and integration step of each model, and the initial execution frame of each model for each cycle. The definition of the sequence matrix was based on an algorithm that considers the number of inlet and outlet variables (causality variables) between the models to minimise the probability of mathematical instabilities. The sequence matrix data are actually in the

To exemplify the concept of sequence matrix, let say a simulator had four MSS: M1, M2, M3 and M4 and three integration methods. The sequence matrix as defined in Table 2, means that model M2 is the first in being executed in the first frame integrated with the method 1 and has a integration step of 0.1s, followed by model M1 with method 3 and integration step 0.2s; in the second frame model M4 with method 2 and integration step 0.2s is executed followed by model M2; in the third frame model M3 with method 1 and integration step 0.5s

With the tenth frame executed, one simulation second has been finished. The executive program synchronises all the tasks in order to match the simulator time with real time. Typically, each control model is executed just after its controlled process model (and so the

> **M4** 2 2 2 2 2 **M2** 1 1 1 1 1 1 1 1 1 1 **M1** 3 3 3 3 3

The models of the simulator were implemented by the use of generic models, some times getting an improved version, and developing new models. In any case, a general procedure

**M3** 1 1

**Frames (10 frames is a second or cycle) 1 2 3 4 5 6 7 8 9 10** 

is executed, followed by models M2 and M1; and so on.

other MSS.

with the state variables is used.

simulator data base.

sequence matrix is constructed).

**Model**

Table 2. Sequence matrix exemplified

**5.2 General modelling methodology** 

The developing of the MSS of the process is described below, but regarding the general developing methodology, next points are observed:


## **5.2.2 Control models**

In the same way that the real plant, the control models acquire and process the actions realised by the operator on the control screens. The control models generate possible changes (perturbations) on the process models, for example, the demand of the valves to regulate some process variables like levels of tanks, pressures, temperatures, etc.

The DCS has most of the controls but some of them are local (out of the distributed control system). The graphics package VisSim was used for the development of the control models. Printed diagrams from the plant were the sources of the information in the format defined by the Scientific Apparatus Makers Association (SAMA).

The development of control models was carried out in five stages:

• Two hundred SAMA diagrams were reviewed and analysed to include all the control logic for the pre-start and start permissive; speed control; temperature monitoring; load control; and temperature control. As a result of this stage 21 control models were developed.

Models for Training on a Gas Turbine Power Plant 225

For the modelling, fundamental conservation principles were used considering a lumped parameters approach and widely available and accepted empirical relations. The lumped parameters approach simplifies the modelling of the behaviour of spatially distributed real systems into a topology consisting of few discrete entities that represent the behaviour of the distributed system (under certain assumptions). From a Mathematical point of view, the simplification reduces the state space of the system to a finite number, and the partial differential equations of the continuous (infinite-dimensional) time and space model of the physical system into ordinary differential equations with a finite number of parameters.

**No. Process Model No. Control Model No. Process Model No. Control Model** 

turbine 11 Electrical

Factor control 3

Generator Cooling with Hydrogen

12 Generator


control 21 Graphic trends

Instruments 19 Counter and

7 Lubrication Oil 11 Lube oil control 20 System alarms 8 Seals Oil

Figure 8 shows the flow information of MSS. For each MSS, the independent variables (inlets) are associated with the actions of the operators like open or close a valve, trip a

Performance Calculations (Heat Rate and Efficiencies)


13 Generator control

<sup>14</sup>VARS/Power

<sup>15</sup>Prestart and starting logic

<sup>16</sup>Auto-unload control

18 Simulation/Test

timer logic

17 Trip logic

Network 12 Electrical system


control <sup>10</sup>

<sup>2</sup>Supervisory

<sup>3</sup>Rotor cooling control

<sup>4</sup>Inlet Guide Valves control

<sup>5</sup>Temperature control

<sup>7</sup>Combustor control

> Flashback temperature monitoring

<sup>9</sup>System DLN control

<sup>10</sup>Air instrument control

8

Glycol Cooling - Temperature

Table 3. List of process and control models

6 Combustor 13

**5.3.2 Models development** 

1 Fuel Gas 1 Pilot & stage

2 Gas Turbine and Compressors

4 Combustor

5 Compressed Air

<sup>9</sup>Water-Ethylene

<sup>6</sup>Air for

Turbine Metals, Temperatures, and Vibrations

