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(1) has a sufficient accuracy where water steam is the working fluid. A comparison between the model re-sponse and the experimental shown in Fig. 3 indicates the accuracy of the defined constant. It is possible to define the steam specific heat as a function of pressure and/or temperature. Here, for more simplification,water steam is considered ideal gas. In addition, the turbine efficiency can be expressed as a function of the ratio of bladetip velocity to theoretical steam velocity. In this paper, turbine efficiency is considered as a constant value. Then,WHP ¼ gHP Cp _ min Tin Tinpoutpin k 1k ðÞ !¼ gHP Cp _ min ðTin þ 273:15Þ 1 poutpin k 1k ðÞ !ð6ÞThe nonlinear model proposed for HP turbine is a parametric model with unknown parameters, which are associated withefficiency and specific heat. These parameters can be defined by performing a training approach over a collection of input–output operational data. The model parameters adjustment is executed through a set of 650 points of data and for transientand steady state conditions in the range of operation between 154 and 440 MW of load. The error E is given by the meanvalue of squared difference between the target output y* and model output y as follows:E ¼ 1NX Nj¼1ðy j yjÞ2ð7Þwhere N is the number of entries used for training process.The optimized value for specific heat, Cp, in order to reach the best performance at different load conditions, is obtained2.1581 and consequently, the polytrophic expansion factor, k, be equal to 1.2718. The efficiency of a well-designed HP tur-bine is about 85–90%. A fair comparison between the experimental data and the simulation results shows that the obtainedHP turbine efficiency equal to 89.31% is good enough to fit model responses on the real system responses. The proposedmodel for HP turbine is presented in Fig. 6, where K1 ¼ K ¼ 520 and K2 ¼ Cp gHP=1000 ¼ 1:921 10 3.The outlet steamfromthe HP turbine passes through the moisture separator to become dry. There are obvious advantagesin inclusion of steam reheating and moisture separation in terms of improving low pressure exhaust wetness and need forless steam reheating. In this section, a considerable fraction of steam wetness is extracted which supplies the required steamfor feedwater heating purpose at the HP heaters. The outlet flow from moisture separation is captured as follows:sdqdt¼ð1 bÞ _ min q ð8Þwhere b is the fraction of moisture in output flow. In the technical documents, it is declared that the amount of liquid phaseextracted as moisture form steam mixture is approximately 10% of total steam flow entered to HP turbine.3.2. IP and LP turbines modelThe intermediate and low-pressure turbines have more complicated structure in where multiple extractions are em-ployed in order to increase the thermal efficiency of turbine. The steam pressure consecutively drops across the turbinestages.
The condensation effect and steam conditions at extraction stages have considerable influences on the turbine per-formance and generated power. In this case, developing mathematical models, which are capable to evaluate the releasedenergy from steam expansion in turbine stages, is recommended. At turbine extraction stages, where in the sub-cooled re-gions, steam variables deviate from prefect gas behavior and the thermodynamic characteristics are highly dependent onpressures and temperature of each region. Therefore, developing nonlinear functions to evaluate specific enthalpy and spe-cific entropy at these stages of turbines is necessary. The steam thermodynamic properties can be estimated in term of tem-perature and pressure as two independent variables. A variety of functions to give approximations of steam/water propertiesis presented, which are widely used in nuclear power plant applications [32–36]. In 1988, very simple formulations were presented by Garland and Hand to estimate the light water thermodynamic prop-erties for thermal-hydraulic systems analysis. In the proposed functions, saturation values of steamare used as the dominantterms in the approximation expressions. This causes that these functions have considerable accuracy at/or near saturationconditions. However, these functions are extended to be quite accurate even in the sub-cooled and superheated regions[37]. The approximation functions for the thermodynamic properties in sub-cooled conditions are presented as follows:Fðp; TÞ¼ FsðpsðTÞÞ þ RðTÞ ðp psÞ ð9Þwhere ps is the steam pressure at saturation conditions. The proposed equations to estimate steam saturation pressure, ps,asa function of temperature are listed in Appendix C. In addition, the approximation functions for the thermodynamic prop-erties in superheated conditions are presented as follows:Fðp; TÞ¼ FgðpÞþ Rðp; TÞ ðT TsÞ ð10Þwhere Ts is the steam saturation temperature. The equations to evaluate steam saturation temperature, Ts, as a function ofsteampressure are presented in Appendix D. It is noted that, these functions are not able to cover the entire range of pressurechanges and therefore the pressure range is pided into many sub-ranges. The proposed functions are quite suitable for esti-mating the water/steam thermodynamic properties; however, these functions are tuned for a given range from 0.085 MPa to21.3 MPa and they have not adequate accuracy for very low-pressure steam particularly for the extractions conditions. Inthis paper, it is recommended that these functions be tuned inpidually for each input and output and at desired operationalranges. It should be mentioned that pressure changes have significant effects on the steam parameters and therefore, it isfocused on adjusting the first term of functions, which depend on pressure and the functions RðTÞ and RðP; TÞ are consideredthe same as presented by Garland and Hand.The working fluid at different turbine stages can be single or two phases. In this condition, it should be assumed that bothphases of steam mixtures are in thermodynamic equilibrium and liquid and vapor phases are two separated phases. Thesteam conditions at each section are presented in Table 1. The proposed functions for specific enthalpy for liquid phaseand specific entropy in both liquid and vapor phases are defined by three parameters as follows:F ¼ aðpÞbþ cwhere three parameters a, b and c are adjusted for four different steam conditions at 35, 50, 75 and 100% of load. In addition,the proposed function for specific enthalpy in vapor phase is defined by three parameters and one constant as follows:F ¼ aðp dÞ2þ bðp dÞþ cHere, the constant d can be chosenmanually with respect to pressure variation ranges. The error E is given by themean valueof absolute difference between the target output y* and model output y as follows:E ¼ 1NX Nj¼1jy j yjj ð11Þwhere N is the number of entries used for training process.