**5.1 Execution of the models in the simulator**

For an operators training simulation, the objective is to reproduce the behaviour of, at least, the reported variables in the plant control station in such a way the operator cannot distinguish between the real plant and the simulator performance considering both, the value of the parameters and their dynamics. The models were designed to work for all plant conditions, from 0% to 100% of load including all the possible transients that may be present during an operational session in the real plant. In order to accomplish with these objective, the "ANSI/ISA-S77.20-1993 Fossil-Fuel Power Plant Simulators Functional Requirements" norm was followed and adopted as design specification.

The gas turbine power plant was divided into a set of systems to be simulated, trying these to coincide with the real plant systems. A modelled system is a mathematical representation of the behaviour of the variables of the real system. The model of a simulated system (MSS) in the simulator responds to the operator's actions in the same way that the real system does, in tendency and time.

Each MSS is divided in algebraic and ordinary differential equations (AE and ODE, respectively). The AE may have to be solved simultaneously if necessary but they are independent of their ODE. For this work, different solution methods were adapted for linear and non-linear equations: Newton-Raphson, Gaussian elimination and bisection partition search. They are used depending on the characteristics of each particular model. The final

Models for Training on a Gas Turbine Power Plant 223

developed by the IIE is followed to obtain the final models as described in this section

Typically, the models are divided in process and control. However, there exist some

• Data information of the process is obtained and classified: system description, system operation guidelines, thermal balances, operational curves of the equipment,

• The information is analysed and a functional description of the MSS is made

• Simplifications on the system are stated obtaining a simplified diagram (with the simulated equipment and their nomenclature). In the diagram the modelled equipment and measurements points are included and it is possible to identify, for example, the

The developing of the MSS of the process is described below, but regarding the general

• The flow and pressure network configuration is obtained and the parameters of pumps, valves and fittings are obtained in a excel data sheet being this is a part of the final documentation. If it is modified, the updating of the simulator is automatically

• Energy balances are programmed using the required generic models. Again, parameterisation with excel is performed. The calculations of energy balances consider

• Other equipments are parameterised (boilers, condensers, etc.) using predefined excel sheets considering the simulator generic models or developing adequate 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

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

• 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

regulate some process variables like levels of tanks, pressures, temperatures, etc.

valves controlled automatically from those operated by the operator or locally.

(Roldán-Villasana *et al*., 2009).

operational plant data, etc.

(conceptual model).

**5.2.1 Process models** 

**5.2.2 Control models** 

developed.

common tasks to be done by any of the models:

developing methodology, next points are observed:

possible sets of equations to be solved simultaneously.

by the Scientific Apparatus Makers Association (SAMA).

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

• Main assumptions are stated and justified.

performed by reading the changes.

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

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 with the state variables is used.

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 simulator data base.

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

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 sequence matrix is constructed).


Table 2. Sequence matrix exemplified

### **5.2 General modelling methodology**

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 developed by the IIE is followed to obtain the final models as described in this section (Roldán-Villasana *et al*., 2009).

Typically, the models are divided in process and control. However, there exist some common tasks to be done by any of the models:

