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The param-eters of proposed functions are inpidually adjusted for the operational range of each subsection by using genetic algo-rithms as an optimization approach. Finally, the responses of the turbine and generator models are compared with theresponses of the real plant in order to validate the accuracy and performance of the models over different operationconditions.In the next section, a brief description of the plant turbine is presented. It consists of a general view of the steam turbineand its subsystems including their inputs and outputs. It follows by the analytical model development and the training pro-cedure of proposed models based on the experimental data. The next section presents the simulation results of this work bycomparing the responses of the proposed model with the actual plant. The last section is the conclusion and suggestions forfuture studies.2. System descriptionA steamturbine of a 440 MWpower plant with once-through Benson type boiler is considered for themodeling approach.The steam turbine comprises high, intermediate and low-pressure sections. In addition, the system includes steam extrac-tions, feedwater heaters, moisture separators, and the related actuators. The turbine configuration and steam conditions atextractions are shown in Fig. 1.The high-pressure superheated steam of the turbine is responsible for energy flow and conversion results power gener-ating in the turbine stages. The superheated steam at 535 C and 18.6 MPa pressure from main steam header is the input tothe high-pressure (HP) turbine. The input steam pressure drops about 0.5 MPa by passing through the turbine chest system.The entered steam expands in the high-pressure turbine and is discharged into the cold reheater line. At the full load con-ditions, the output temperature and pressure of the high-pressure turbine is 351 C and 5.37 MPa, respectively. The coldsteam passes through moisture separator to become dry. The extracted moisture goes to HP heater and the cold steamfor reheating is sent to reheat sections. The reheater consists of two sections and a de-superheating section is consideredbetween them for controlling the outlet steam temperature.The reheated steamat 535 C and with 4.83 MPa pressure is fed to intermediate pressure (IP) turbine. Exhaust steamfromIP-turbine for‘ the last stage expansion is fed into the low-pressure (LP) turbine. The input temperature and pressure of thelow-pressure turbine is 289.7 C and 0.83 MPa, respectively. Extracted steam from first and second extractions of IP is sent toHP heater and de-aerator. Also, extracted steam from last IP and LP extractions are used for feedwater heating in a train oflow-pressure heaters. The very low-pressure steam from the last extraction goes to main condenser to become cool and beused in generation loop again.3. Turbine model development
The behavior of the subsystems can be captured in terms of the mass and energy conservation equations, semi-empiricalrelations and thermodynamic state conservation. The systemdynamic is represented by a number of lumpedmodels for eachsubsections of turbine. There are many dynamic models for inpidual components, which are simple empirical relations between system variables with a limited number of parameters and can be validated for the steam turbine by using real sys-tem responses. In addition, an optimization approach based on genetic algorithm is performed to estimate the unknownparameters ofmodelswithmore complex structure based on experimental data.With the respect tomodel complexity, a suit-able fitness function and optimization parameters are chosen for training process, which are presented in Appendix A. Themodels training process is performed by joining MATLAB Genetic Algorithm Toolbox and MATLAB Simulink. It makes it possiblemodel training be performed on-line or based on recorded data in simulation space (Appendix B).3.1. HP-turbine modelThe high-pressure steam enters the turbine through a stage nozzle designed to increase its velocity. The pressure dropproduced at the inlet nozzle of the turbine limits the mass flow through the turbine. A relationship between mass flowand the pressure drop across the HP turbine was developed by Stodola in 1927 [31]. The relationship was later modifiedto include the effect of inlet temperature as follows:_ min ¼ KffiffiffiffiffiffiTinpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip2in p2outqð1Þwhere K is a constant that can be obtained by the data taken from the turbine responses. Let k be defined as follows:k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip2in p2outTinsð2ÞBy plotting k via inlet mass flow rate based on the experimental data, the slope of linear fitting is captured as K = 520 (Fig. 2).Generally, Eq.