simulation a dynamic modeling

[Aljanabi, 4(1): January, 2015] ISSN: 2277-9655

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IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH

TECHNOLOGY

SIMULATION A DYNAMIC MODELING THEORY OF STEAM TURBINE BASED ON

AGENTIC A LOGARITHM Dr Shaker H.Aljanabi*, Dr Sabah.A.Nassif, Alaa Siham Hamid

* Electrom. Eng. Dept.University of Technology.

Electrom. Eng. Dept.University of Technology.

Electrom. Eng. Dept.University of Nahrain.

ABSTRACT

In the present paper, a thermodynamic analysis of steam turbine type (K–800–23.5–0.034), power plant has been

carried out. The power plant system was simulated and a detailed parametric study undertaken, which involved

environmental parameters, such as the temperature of cooling water entering the condenser and the inlet ambient air

temperature, as well as some other operational parameters, such as excess air percentage and stack exhaust

temperature. It was noted that the excess air percentage should be maintained below 10% and stack exhaust

temperature should keep to a minimum. A detailed analysis of exergy losses was made. It was observed that the

relative exergy losses in the combustor and evaporator are the highest compared with other parts of the plant. Finally,

many recommendations have been suggested for improved plant performance. The present study helped to identify

plant site conditions that cause losses of useful energy to take place and also helped to resolve some problems

encountered in steam turbine type (K–800–23.5–0.034), capacity unit. Developing nonlinear mathematical models

based on system identification approaches during normal operation without any external excitation or disruption is

always a hard effort, assuming that parametric models are available. This study included on using soft computing

methods would be helpful in order to adjust model parameters over full range of input–output operational data. In this

study, based on energy balance, thermodynamic state conversion and semi – empirical relations, Different parametric

models are developed for the steam turbine subsections. In this case, it is possible the model parameters are either

determined by empirical relations or they are adjusted by applying genetic algorithms as optimization method.

Comparison between the responses of the turbine – generator model with the responses of real system validates the

accuracy of the proposed model in steady state and transient conditions. The study presents the usage of the cycle –

tempo and Matlab/Simulink package to implement the model of the power plant unit (VPPM), which is the basis for

the Virtual Power Plant (VPP). This environment facilitates virtual modeling approach at component and system levels

KEYWORDS: Steady state, Transient conditions, Exergy losses, a gentic a logarithm.

INTRODUCTION

The growing demand of power has made the power

plants of scientific interest. The steam turbines have

been widely employed to power generating due to

their efficiencies and costs. With respect to the

capacity, application and desired performance, a

different level of complexity is offered for the

structure of steam turbines. For power plant

applications, steam turbines generally have a complex

feature and consist of multistage steam expansion to

increase the thermal efficiency. It is always more

difficult to predict the effects of proposed control

system on the plant due to complexity of turbine

structure. Therefore, developing nonlinear analytical

models is necessary in order to study the turbine

transient dynamics. These models can be used for

control system design synthesis, performing real-time

simulations and monitoring the desired states [1].

Identification techniques are widely used to develop

mathematical models based on the measured data

obtained from real system performance in power plant

applications where the developed models always

comprise reasonable complexities that describe the

system well in specific operating conditions [2].

System identification during normal operation without

any external excitation or disruption would be an ideal

target, but in many cases, using operating data for

identification faces limitations and external excitation

is required [3]. Assuming that parametric models are

available, in this case, using soft computing methods

would be helpful in order to adjust model parameters

over full range of input–output operational data.

Genetic algorithms (GA) have outstanding advantages

over the conventional optimization methods, which

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allow them to seek globally for the optimal solution. It

causes that a complete system model is not required

and it will be possible to find parameters of the model

with nonlinearities and complicated structures [4]. In

the recent years, genetic algorithms are investigated as

potential solutions to obtain good estimation of the

model parameters and are widely used as an

optimization method for training and adaptation

approaches. Rekha Rajan et. al, [5], Investigated the

effectiveness of different controllers for the speed

control of Tandem compound single reheat steam

turbine. The speed of a Tandem compound single

reheat steam turbine is controlled using the proposed

MPC (model predictive control) controller. Then the

results of the comparison of the proposed controller

with the traditional PID controller and fuzzy PID

controllers were also presented in this work.

According to the simulation results in MATLAB,

showed that the proposed MPC can improve the

robustness and small overshoot and fast response

compared to the conventional PID and fuzzy PID. In

the area of turbine speed control the faster response to

research stability, the better is the result for the plant.

M S Jamel et. al, [6], carried out a simulation of a 200

MW gas – fuelled conventional steam power plant

located in Basra, Iraq. The thermodynamic

performance of the considered power plant is

estimated by a system simulation. A flow – sheet

computer program, “Cycle – Tempo” was used for this

study. The simulation results were verified against

data gathered from the log sheet obtained from the

station during its operation hours and good results

were obtained. Operational factors like the stack

exhaust temperature and excess air percentage were

studied and discussed, as were environmental factors,

such as ambient air temperature and water inlet

temperature. In addition, detailed exergy losses were

illustrated and described the temperature profiles for

the main plant components. Orosun Rapheal and

Adamu Sunusi Sani, [7], modeled physical boiler

system was modeled as a multivariable plant with two

inputs (feed water rate and oil – fired flow rate) and

two outputs (steam temperature and pressure). The

plant parameters ware modeled by identification based

on experimental data collected directly from the plant.

The routines of system identification toolbox with

structure selection for autoregressive moving average

together with recursive least square (ARX) were used

to identify the model. The identified ARX ode was

validated using Akaike's Final Prediction Error (FPE)

criterion. The identified model was further

subjected to test, using the validation input data;

simulated model outputs for both temperature and

pressure agree closely with the actual plant outputs

with error of 8% and 9% respectively. Furthermore,

Proportional Integral Derivative (PID) Controller was

developed to control the identified model. Simulation

studied was carried out; the results obtained indicated

the effectiveness of this technique. The controller was

able to track the temperature and pressure set points

steadily and rapidly. Von cand. Ing. Jordi Bassas, [8],

dealed with the development of a thermo – hydraulic

model of a Nuclear Power Plant steam turbine and its

implementation in the system code ATHLET. The

model was based on Stodola’s cone law and simulated

the pressure drop and the enthalpy drop along the

different turbine stages as well as the steam and water

extractions. The influence of the steam and water

extractions on the turbine behavior as well as the

importance of an accurate model for the steam and

water extractions were carefully explained. Heat and

mass balances of the Nuclear Power Plant Philipsburg

2 (located in Philipsburg in Karlsruhe (Germany) are

presented. Two units, the first a BWR (boiling water

reactor) and the second a PWR (pressurized water

reactor)) were used for reference purposes as well as

for validation purposes of the implemented model.

The comparison between steady state simulations and

the real plant data indicated a satisfactory accuracy of

the model and of the thermodynamic approach used.

Hataitep Wongsuwarn, [9], used thermodynamic

properties of substance in numerical simulation and

controller of industrial process. The Neuro fuzzy

system (NFs) and subtractive clustering were used to

calculate energy properties within the experimental

steam power plant. Neurofuzzy models are

constructed from each subsystem of thermodynamic

properties, such as saturated water or superheat

steams. Comparing experimental results of nonlinear

Neurofuzzy model with several back propagation

neural networks (BNNs), showed that the NFs

modeling was closed to thermodynamic properties

than neural network. Moreover, the proposed NFs

model was used properly for the experimental steam

power plant. Thus, the proposed NFs modeling should

be applied to any plant based on using for

thermodynamic properties. Leyzerovich and

Alexander. S, [10], presented a study to improve the

capacity of generating steam turbine. It was designed

with the power arrived to (1000 MW) through the

mechanical and thermal of re – design to increase the

final stage for the low – cylinder pressure in the range

of 1200 – 1500 mm in diameter. This study included

methods to improve the efficiency of steam turbines

and theoretically increase of the power through the

increase of steam temperature for the superheat as well

as increases the steam temperature of re – heating for

the intermediate – pressure of inside the cylinder. This






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study were used a computer programs to simulate the

expansion in the steam turbine, geometric dimensions,

specifications steam, metals used …..ete. Cornell.

Daniel et. al, [11], Presented the design method of the

steam turbine up to the power of (758 MW) through

the re – implementation of the high and medium

design mechanically and thermally in the cylinder

pressure by reducing the distance between the turbine

stages. This study included improvement of flow

factor, increasing the fixed and moving blades lengths,

and increasing of annular space for the passage of

steam through the stages. The study reported the

development of certain types and specific models of

steam turbines such as (model – D115) – Inc. (General

Electric), which led to the work of very desirable

balance between the costs, generated power through

the turbine and the improvement of efficiency in

turbine on the other hand. Behrooz Vahidi et. al, [12],

published a paper for deriving the parameters of an

IEEE governor – turbine model (particularly turbine

model) based on a practical study case consisting of a

200 MW tandem compound, single reheat steam unit

and its available heat balance data was presented. The

main focus of this work was on presenting a regular

procedure and using only available heat balance data

of the steam unit, to be suitable for training the

principles and details of such an approach for

educational purposes. Unavailable parameters were

approximated with simple thermodynamic

assumptions, resulting in good correspondence to

typical values. The model response to step changes for

special scenarios was simulated and presented as well.

Ali Chaibakhsh and Ali Ghaffari, [13], considered a

steam turbine of a 440 MW power plant with once –

through Benson boiler for the modeling approach.

They characterized the transient dynamic of steam

turbine, by developing a non – linear mathematical

model firstly, based on the energy balance,

thermodynamic principles and semi – empirical

equations. Then, the related parameters of developed

models were either determined by empirical relations

or they were adjusted by applying Genetic Algorithm

(GA). A nonlinear function was developed to evaluate

specific enthalpy and specific entropy at the region

when the flow deviates from perfect gas behavior,

especially in the intermediate and low pressure stages.

Comparison between the response of the turbine –

generate – model with the response of real system

validated accuracy of the improved model in steady

state and transient conditions. The presented turbine–

generator model can be used for control system design

synthesis, performing real–time simulation desired

states in order to have safe operation of a turbine –

generator particularly during abnormal conditions

such as turbine over – speed.

The main objectives of the present work to build up

the theoretical model to simulate steam turbine power

station. Use two analytical and simulation techniques

that implicitly satisfy the traditional designer

parameters and provide enough flexibility and

accuracy to represent any steam turbine power plant.

As well as Using the two packages Mat lap and Cycle

– tempo to predict the optimal state of parameters that

was used by turbine systems using genetic algorithms.

The sources of exergy destruction were determined

and categorized so that feasible recommendations

could be made, moreover comparing the actual

thermal efficiency of the power plant that can be

obtained by applying the second law of

thermodynamics.

THE SIMULATION MODEL The modeling of steam turbine plant is built using

firstly the techniques of Matlab version (V2013a with

m– files Simulink and the second techniques is cycle

– Tempo (Release 5) software Simulink to describe the

thermodynamics , mass and heat balances for all

component, at steady and unsteady (Transient) states.

This program is used to Simulink the steam power

plant with typical station of power 800MW

capacity. The compatibles of steam power station type

(K–800–23.5–0.0034). as well as the power plant of

the Dura in Baghdad type (K–160–13.34–0.0068) is

studied. The simulation model used to solve these two

stations for steady state conditions using software

Matlap and cycle – tempo programs, while unsteady

state (transient case) using Matlap program only for

the cases 60%, 80% and 100%. The Genetic

Algorithm to tuning the PID (Proportional + Integral

+ Derivative ) controller is built using m – file that

drives the simulation of steam turbine model.

The simulation model can be capture in the term of

mass and energy equation, semi – empirical equation

and equation of state. There are many dynamic

models for individual components, which are simple

empirical relations between system variables with a

limited number of parameters. In addition, an

optimization approach based on genetic algorithm is

performed to estimate the unknown parameters of

models with more complex structure based on

practical data. The models training process is

performed by joining MATLAB Genetic Algorithm

Toolbox and MATLAB Simulink and Cycle-tempo

program.The power model consists of models of

steam turbine, a control system, a generator and a

power grid. To formulate components' models,

unsteady conservation equations for a mass, energy






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and momentum have been used. In order to implement

the model in Simulink and to maintain the amount of

simulation time within the time available, some

models were developed in both advanced and

simplified versions. All models' components are

connected through ports enabling and propagating

current steam parameters (temperature,

pressure…….etc.) and / or mass / energy flow rates.

High pressure steam turbine section

To build a model for the high – pressure cylinder

included several steps, fig. (1): A relationship between

mass flow and the pressure drop across the HP turbine

was developed by Stodola formula [14];

G = 𝐾1𝜆 (1)

Where, 𝐾1 is a constant that can be obtained by the

data taken from the turbine responses, and 𝜆 can be

defined as formula;

𝜆 = √𝑃1

2−𝑃162

𝑇1 (2)

by plotting 𝜆 via inlet mass flow rate based on the

experimental data (taken from cycle – tempo prog.),

the slop of linear fitting is captured as K1=714.37 ,

is shown in fig.(2). Indicates the accuracy of the

defined constant and CP = 1.697 .

Then, K2 =CP ηs

HP

1000 (3)

The transfer function of the input and output pressure

is; P16

P1=

𝑆

𝜏s+1 (4)

The input and output pressure relation for high

presser cylinder based on experimental data ( taken

from cycle – tempo prog.), is shown in fig.(3). It

shows a quite linear relation with the slope of S=

0.26101.

Where: time constant 𝜏 is determined by formula;

𝜏 = 𝑃1

𝐺 V

𝜕𝜌

𝜕𝑃 (5)

Noting that the time constant for high pressure

cylinder are normally between 0.1 and 0.4s, here

the time constant chosen to be about 0.4s. By the

dynamic model of high pressure turbine , the

pressure, mass flow rate and temperature of steam

at input and output of each section is required. The

input and output relation for steam pressure and steam

flow rate are defined in previous section. the steam

temperature at turbine output (𝑇16) can be captured

in the terms of entered steam pressure and

temperature. By assuming that the steam expansion

in high pressure turbine is an isentropic process , it

is simple to estimate the steam temperature at

discharge of HP turbine by using ideal gas pressure-

temperature relation by formula;

𝑇16

𝑇1= (

𝑃16

𝑃1)(

𝑛−1

𝑛) (6)

Then, find the out temperature (𝑇16) from last stage

in high pressure turbine.

𝑇16 = 𝑇1(𝑃16

𝑃1)(

𝑛−1

𝑛) (7)

Then we found the enthalpy and entropy , by

using the thermodynamic property equations for steam

(superheated and saturated) . The energy equation

for adiabatic expansion , which relates the power

output to steam energy declining by passing through

the high pressure turbine, determine by formula;

𝑊𝐻𝑃 = 𝜂𝐻𝑃𝐺(ℎ1 − ℎ2) = 𝜂𝐻𝑃𝐶𝑝𝐺 (𝑇1 − 𝑇2) (8)

Then ,

𝑊𝐻𝑃 = 𝜂𝐻𝑃𝐶𝑝𝐺 (𝑇1 − 𝑇1 (𝑃2

𝑃1)(

𝑘−1

𝑘)) =

𝜂𝐻𝑃𝐶𝑝𝐺 (𝑇1 + 273.15) ` (9)

And find the mass flow rate at any stage in high

pressure cylinder by using heat and mass balance

Intermediate and low – pressure turbine section

The intermediate and low-pressure turbines have

more complicated structure in where multiple

extractions are employed in order to increase the

thermal efficiency of turbine. The steam pressure

consecutively drops across the turbine stages. The

condensation effect and steam conditions at extraction

stages have considerable influences on the turbine

performance and generated power. In this case,

developing mathematical models, which are capable to

evaluate the released energy from steam expansion in

turbine stages, is recommended. The steam

thermodynamic properties can be estimated in term

of temperature and pressure as two independent

variables. A variety of functions to give

approximations of steam/water properties is

presented, which are widely used in steam power

plant applications. To build a model for the I –

pressure cylinder included several steps. Find the

thermodynamic properties of steam and water

(enthalpy, liquid phase ℎ𝑓 , enthalpy, vapor phase ℎ𝑔

, enthalpy, tow- phase ℎ𝑓𝑔 , entropy, liquid phase 𝑠𝑓 ,

enthalpy and vapor phase ℎ𝑔 ) . The relation between

the input mass flow rate from reheated to I – P

cylinder and the mass flow rate at all extraction based

on experimental data ( using cycle- tempo program )

.It shows a quite linear relation with the slope at (

extraction.3 and extraction .5) of ( 𝑆3= 0.024727 &

𝑆5=0.03602).

The transfer function of the input and output mass is; ṁ𝑒𝑥

𝐺𝐼𝑃=

𝑆

𝜏𝑠+1 (10)






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Where, 𝐺𝐼𝑃 is the mass flow rate inlet the

intermediate pressure cylinder, The time response of

the transfer function.

By considering steam expansion at turbine stages

be an ideal process, the energy equations for steam

expansion in turbine, which relates the power output

to steam energy declining across turbine stages can

be captured. Therefore, the work done in IP turbine

can be captured as follows;

WiP = GIP(h4 − hex18) + (GIP − ṁex19)(hex18 −hex19) + (GIP − ṁex18 − ṁex19)(hex19 −hex23) + (GIP − ṁex18 − ṁex19 − ṁex23)(hex23 − hex24) (11)

Then, the power for IP turbine determine by

formula;

WIP = ηsIPCWiP (12)

Finally the mass flow rate at any stage in

intermediate pressure cylinder by used heat and mass

balance. To build a model for the L – pressure

cylinder included several steps. The relation

between the input mass flow rate I – P to L – P

cylinder and the mass flow rate at all extraction

based on experimental data ( using cycle – tempo

program) ,which shows a quite linear relation with

the slope at ( extractuin.7 and extractuin.8 ) of ( 𝑆7=

0.06254 & 𝑆8= 0.040443 ). The transfer function of the

input and output mass is; ṁ𝑒𝑥

𝐺𝐿𝑃=

𝑆

𝜏𝑠+1 (13)

Now, the low-pressure turbine consists of two

extraction levels. The work done in LP turbine can be

captured as follows;

WlP = GLP(h25 − hex25) + (GLP − ṁex25)(hex25 −hex26) (14)

Where, 𝐺𝑙𝑃 is the mass flow rate inlet the low

pressure cylinder.

Then, the power for LP turbine determine by formula;

WLP = ηsLPCWlP (15)

Then the overall generated mechanical power ( 𝑃𝑚)

can be captured by summation power in turbine

stages determine by formula;

Pm = WHP + WIP + WLP (16)

TURBINE PERFORMANCE UNDER

TRANSIENT CONDITIONS The model performs initially steady state analysis,

based on input specifications defined by the user like

power output or initial steam and condensing

pressures, and more specific parameters regarding

either power block or boiler and turbine efficiency,

which can be set according to default values or

modified voluntarily. The result is summarized by the

heat and mass balance of both power block and steam

generator at rated operation. New stable results are

calculated according to the heat input and on the

variable load at transient condition. In practical at load

variations, both mass flow rate pressures are expected

to decrease simultaneously. During operation, a

turbine may run an appreciably long time with varying

steam flow rate in start – up and shut – down regimes,

often with substantial deviations of the initial and final

steam parameters from the rated values. The rated

conditions can also be disturbed owing to salt

deposition in the steam path or when a turbine is run

with some blades in turbine stages having been

removed or when the geometry of blade cascades has

been distorted due to cross flexure of blade edges. In

order to estimate property, the variations in the

efficiency and reliability of the operation of a turbine

and its stages under transient conditions, i.e. deviating

strength calculations for these off – design conditions

[15]. Transient performance is calculated in an

iterative resolution of steam generator and steam

turbine models, since they are interrelated through the

thermodynamic properties of live steam calculated

with the Matlab and tempo – cycle program. For

transient condition, the extraction pressure and inlet

pressure to each turbine section is calculated using

Stodola's Cone law as follow [16];

ṁ

ṁ0=

𝑃𝑎

𝑃𝑎,0√

𝑃𝑎,0 𝑣𝑎,0

𝑃𝑎 𝑣𝑎√

1−(𝑃𝑏𝑃𝑎

)𝑛+1

𝑛

1−(𝑃𝑏,0𝑃𝑎,0

)𝑛+1

𝑛

(17)

Where: (P) the pressure and (v) the specific

volume. The sub index (a) stands for the inlet value,

(b) for the outlet value and (0) for the design values,

and 𝑛 for wet steam the calculation of the polytrophic

exponent is (Traupal )[17];

𝑛 =𝑘

1+𝑘𝑃(𝑣𝑠𝑡𝑒𝑎𝑚−𝑣𝑙𝑖𝑞𝑢𝑖𝑑)

ℎ𝑓𝑔 (1−𝜂𝑇)

(18)

Where: 𝜂𝑇 the overall efficiency of the turbine.

REHEATER MODEL The superheated steam from main steam header

is fed toward the high pressure turbine , and from

high pressure turbine is discharged into the cold

reheat header. The steam temperature in cold reheat

line is (304°C). The outlet reheated steam temperature

should be constant 540°𝐶 , at the full load condition;

the outlet reheated steam pressure is 3.42MPa. the

reheated dynamics increase nonlinearity and time

delay of the turbine and should take into account as

a part of turbine model. The parameters of this






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model are determined either from construction data

such as fuel and water steam specification. We have

developed accurate mathematical model for

subsystems of boiler based on the thermodynamics

principles and energy balance. The equation for the

superheated temperature model is as follows; dT4

dt= K2(K1ṁfuel + ṁ2(T2 − T4 + B1) + B2)

………… (19)

Where: 𝐾1 = 𝐻𝑣𝐶𝑃 , 𝐾2 =1

𝜌𝑠𝑉𝑠 , 𝐵1 =

𝑘1

𝐶𝑃 , 𝐵2 =

𝑘0𝜌𝑠𝑉𝑠

The heat flow can be captured by using calorific value,

lower heating value (𝐻𝑣) of the fuel and the

temperature output from the high pressure turbine (T2)

, the temperature output from the reheater (𝑇4) , the

mass flow input to reheater (ṁ2). In this model the

steam quality has significant effects on output

temperature and should be considered in related

equations. The transfer function for fuel flow rate and

steam quality is as follows; 𝛼

ṁ𝑓𝑢𝑒𝑙=

9.45039𝑒−6

20𝑠+1 (20)

GENERATOR MODEL The turbine – generator speed is described by the

equation of motion of the machine rotor , which

relates the system inertia to deference of the

mechanical and electrical torque on the rotor.

Applying the swing equation of asynchronous

machine to small perturbation, we have;

Md2δ

dt2 = Pa = Pm − Pe (MW) (21)

Where: M is called inertia constant, and 𝛿 is

torque angle or swing angle , 𝑃𝑎 is acceleration

power (MW) , 𝑃𝑚 is mechanical power input in

(MW) and 𝑃𝑒 electrical power output in (MW) .

𝑃𝑚𝑎𝑥 =𝐸𝑉

𝑋 (S.S.S limit) (Steady state stability limit)

………... (22)

Then;

𝑃𝑒 = 𝑃𝑚𝑎𝑥 sin 𝛿 =𝐸𝑉

𝑋 sin 𝛿 (23)

The electrical power can be captured in term of

terminal voltage (V), machine excitation voltage (E),

direct axis synchronous reactance (𝑋) .

Where; M =𝐺𝐻

𝜋𝑓 b(24)

Then the equation (19) can write for the system

operating frequency electric𝑓(𝐻) ; GH

πf

d2δ

dt2 = Pa = Pm − Pe MW (25)

Dividing throughout by (G) machine rating (base) in

MVA. H

πf

d2δ

dt2 = Pa = Pm − Pe In pu (𝛿 it is measured by

radian) (26)

H

180f

d2δ

dt2 = Pa = Pm − Pe In pu (𝛿 it is measured by

degree) (27)

COMPUTER PROGRAM To describe the performance of each study, a computer

program has been written to work under Mat lab

software and compared with the cycle – tempo

software. The program enables at each node through

the thermodynamic cycle by using the appropriate

thermodynamic relations. And build the Simulink and

model by use the two programs for the steam turbine

at steady state and transient with change the load and

taken the GA at power, pressure and mass rate. A flow

– sheet computer program, “Cycle – Tempo” is used

for the study. The selected case study is Russia power

station (K–800–23.5–0.034) and Dura type (K–160–

13.34–0.0068) steam power plant located in Baghdad,

Iraq. The superheated steam enters the two – stage

single reheat steam turbine at 22.3MPa, 560,

640Kg s⁄ and 3.51MPa, 530 , for high and

intermediate pressure stages, respectively. Steam

enters the low pressure stage with a pressure of 6.934

bar; the condenser pressure is 0.034MPa. The

simulation process and the most important parameters

are described in this section. The parameters can be

changed to build and simulate different cases and a

flow-sheet computer program, “Cycle – Tempo”

(Cycle – Tempo – Release 5), is used for that purpose.

It is a well – structured package for steady state

thermodynamic modeling and analysis of systems for

the production of electricity, heat and refrigeration.

RESULTS AND DISCUSSION Figure (4) indicated thermal efficiency of the cycle

versus steam pressure at turbine inlet temperature for

Russia power station (K – 800 – 23.5–0.0034).

Thermal efficiency increases with increases steam

pressure at turbine and inlet temperature. As well as

thermal efficiency increases with increases steam

temperature. Figure (5) reveal thermal efficiency

versus steam temperature at turbine inlet temperature

for Russia power station (K – 800 – 23.5–0.0034). The

efficiency of the cycle increases with increase steam

temperature as well as increases with increases steam

pressure. The internal exergy efficiencies of the power

cycles are depicted in figure (6) for the single reheat

systems. The internal exergy efficiencies are primarily

determined by the isentropic efficiencies of the steam

turbine. In general these isentropic efficiencies are

higher as the steam volume flow rate is higher. The

internal efficiencies of the single reheat systems are in

full agreement with this rule. The internal exergy

efficiencies of the power cycles are higher if the steam






[467]

temperature is higher, and are lower if the steam

pressure is higher. Figure (7) depicted the reversible

efficiency versus steam temperature for Russia power

station (K – 800 – 23.5–0.0034). The reversible

efficiency as well as increases with steam pressure.

Figure (8) show the response of the turbine – generator

for Russia power station (K – 800 – 23.5–0.0034). The

load responses in steady state and transient conditions

over an operation range between 50% and 100% of

nominal load. This figure indicated the behavior of the

turbine – generator system. Figure (9) illustrated the

response and pressure model at high pressure turbine

and Russia power station (K – 800 – 23.5–0.0034).

This figure indicated that the time responses of the

proposed transfer function. As well as a good

agreement between real and model. Figures (10), (11)

and (12) reveal the response of pressure – mass model

to H.P.T, I.P.T and L.P.T to Russia power station (K –

800 – 23.5–0.0034). As it is clearly seen, the results

indicated a good agreement between real and pressure

– mass model data. Figures (13), (14) and (15)

indicated convectional water – steam cycle for Russia

power station (K – 800 – 23.5 – 0.0034). The design

calculations were three loads and power 100%, 800

MW, 90%, 720MW and 80%, 640MW respectively.

These calculations were by using cycle – tempo

program. Figures (16), (17) and (18) reveal

convectional water – steam cycle for Dura power

station (K – 160 – 13.34 – 0.0068). The design

calculations were three loads and power 100%,

160MW, 90%, 144MW and 80% and 128MW. These

calculations were by using cycle – temperature

program. When using two program software cycle –

tempo and Mat lab gave the same results in simulation

of power plant. The results indicated that the

extraction pressure increases with increases inlet

pressure of I.P.T. as well as the extraction exergy

increases with increases inlet exergy of H.P.T and

I.P.T. The reversible efficiency increases with

increases steam temperature as well as increases with

steam pressure.

CONCLUSION The conclusions can be drawn from the results of

theoretical study were as follows:

1. In this study were using two model pressure

– mass flow model and pressure model.

2. The pressure drop across the turbine stages

are approximately linear and can be defined

by the first order transfer function

3. The response of pressure model at high

pressure turbine indicated that the time

responses of the proposed transfer function.

4. Inlet pressure increases with increases overall

power the relation between them linear

relation.

5. The inlet exergy increases with increases

power.

6. The extraction mass increases with increases

mass flow rate of I. P.T.

7. The efficiency of the cycle increases with

increases steam temperature and steam

pressure.

8. The internal exergy efficiencies of the power

cycle are higher if the steam temperature is

higher, and are lower if the steam pressure is

higher.

REFERENCES 1. W.C. Tsai, T.P. Tsao, C. Chyn," A

nonlinear model for the analysis of the

turbine-generator vibrations including

the design of a flywheel damper,"

Electrical Power and Energy Systems,

vol. 19, pp. 469–479, 1997.

2. M. Nagpal, A. Moshref, G.K. Morison,

P. Kundur, "Experience with testing and

modeling of gas turbines," IEEE Power

Engineering Society Winter Meeting,

pp. 652–656, 2001.

3. M. Wang, N.F. Thornhill, B. Huang,"

Closed-loop identification with a

quantizer, Journal of Process

Control,",pp. 729–740, 2005.

4. G.J. Gray, D.J. Murray-Smith, Y. Li,

K.C. Sharman, T. Weinbrunner,

"Nonlinear model structure

identification using genetic

programming, Control Engineering

Practice,",pp. 1341–1352, 1998.

5. Rekha Rajan, Muhammed Salih. P, N.

Anilkumar, Speed controller design for

steam turbine, International Journal of

Advanced Research in Electrical,

Electronics and Instrumentation

Engineering Vol. 2, Issue 9, September

2013.

6. M S Jamel, A Abd Rahman,and A H

Shamsuddin," Simulation of existing gas

– fuelled conventional steam power

plant using Cycle Tempo". 2013.

7. Orosun Rapheal.and Adamu Sunusi

Sani," Modeling and Controller Design

of Industrial Oil – Fired Boiler

Plant".2012.

8. Von cand. Ing. Jordi Bassas,"

Development and implementation of a






[468]

Nuclear Power Plant steam turbine

model in the system code ATHLET ",

Master Thesis, 2011.

9. Hataitep Wongsuwarn ," Modeling of

Thermodynamic Properties based on

Neuro fuzzy System for Steam Power

Plant ".2010.

10. Cornell. Daniel, Retzlaff. Klaus, Talley.

Sean, "Dense pack steam turbine", GE

Power Generation, paper No. 4204,

2001.

11. Philip S. Bartells, Christine K Kovach,"

Development of a Dual – Extraction

Industrial Turbine Simulator using

General Purpose Simulation Tools ".

2002.

12. Behrooz Vahidi, Senior Member, IEEE,

Mohammad Reza Bank Tavakoli, and

Wolfgang Gawlik ," Determining

Parameters of Turbine’s Model Using

Heat Balance Data of Steam Power Unit

for Educational Purposes". 2007.

13. Ali Chaibakhsh,Ali Ghaffari,"

Simulation Modeling Practice and

Theory". 2008.

14. David H.Cooke," Modeling of off –

design multistage turbine pressures by

Stodola's ellipse",thesis, 1983.

15. Kirillov,I.I, Ivanov, V.A, Kirillov .A.I, "

Steam turbine and steam turbine plants",

Leningrad , Mashinostroenie, fitst

edition, 1978.

16. David H.Cooke," Modeling of off –

design multistage turbine pressures by

Stodola's ellipse",thesis, 1983.

17. Wolfgang Sanz,"Design of Thermal

Turbomachinery",Ankara, Institute for

Thermal Turbomachinery and Machine

Dynamics, Graz University of

Technology,Austria, April 2008.






[469]

Fig.(1).High pressure turbine model.






[470]

λ

Fig.(2).Mass flow rate versos λ for Russia power station (K – 800 – 23.5 – 0.0034).

Fig.(3).Pressure ratio of the high pressure turbine cylinder input and output for Russia power station (K – 800 – 23.5 –

0.0034).

0.4 0.5 0.6 0.7 0.8 0.9 1100

200

300

400

500

600

700M

ass F

low

R

ate

(kg

/s)

Experimental

linear

K = 741.37

8 10 12 14 16 18 20 22 241

2

3

4

Input Pressure (MPa)

Outp

ut

Pressure (

MP

a)

Experimental

linear

S= 0.26101






[471]

Fig.(4 ) Cycle efficiency versus steam pressure at turbine inlet temperature for Russia station (K – 800 – 23.5–0.0034).

Fig.(5) Cycle efficiency versus steam temperature at turbine inlet temperature, for Russia station (K – 800 – 23.5–0.0034).

Fig.(6) The internal exergy efficiency versus steam temperature (single reheat) for Russia power station (K – 800 – 23.5–

0.0034).

520 540 560 580 600 620 640 6600.45

0.46

0.47

0.48

0.49

0.5

0.51

Steam Temperature at Turbine Inlet ( C )

Th

erm

al E

ffic

ien

cy

- - - - 350 bar

-- - -- 300 bar

-- -- --250 bar

--------180 bar

520 540 560 580 600 620 640 6600.82

0.84

0.86

0.88

0.9

Steam Temperature atTurbine Inlet ( C )

Inte

rnal E

xerg

y E

ffic

iency

-------180 bar

-- -- --250 bar

-- - -- 300 bar

- - - - 350 bar

180 200 220 240 260 280 300 320 340 3600.45

0.46

0.47

0.48

0.49

0.5

0.51

Steam Pressure at Turbine Inlet ( bar )

Therm

al E

ffic

iency [

-]-- -- -- 650 C

-- - -- - 620 C

- - - - - 600 C

-- - -- - 580 C

-- -- -- 560 C

-------- 530 C






[472]

Fig.(7) The reversible efficiency versus steam temperature at turbine inlet for Russia power station (K – 800 – 23.5–0.0034)

Fig.(8 ).Response of the turbine – generator for Russia power station (K – 800 – 23.5–0.0034).

Fig.(9).Response of pressure model at H.P.T for Russia power station (K – 800 – 23.5–0.0034).

500 1000 1500 2000 2500

200

400

600

800

1000

Time (Min)

Ove

rall

Pow

er

(MW

)

Real

Model

500 1,000 1,500 2,000 2,500

0

1

2

3

4

Time (Min)

Pre

ssure

(M

W)

Model

Real)

520 540 560 580 600 620 640 6600.54

0.55

0.56

0.57

0.58

0.59

0.6

Steam Temperature at Turbine Inlet ( C )

Re

vers

ible

Eff

icie

ncy

- - - - -350bar

-- - -- -300bar

-- -- -- 250bar

--------180bar






[473]

Fig.(10).Response of pressure–mass flow model at H.P.T for Russia power station (K – 800 – 23.5–0.0034)

Fig.(11 ).Response of pressure – mass flow model at I.P.T for Russia power station (K – 800 – 23.5 – 0.0034)

Fig.(12 ).Response of pressure – mass flow model at L.P.T for Russia power station (K – 800 – 23.5–0.0034).

20 40 60 80 100

100

200

300

400

500

600

Time (Min)

Ma

ss f

low

ra

te

(Kg/s

)

Real

Model

20 40 60 80 100

0

100

200

300

400

Time (Min)

Mass F

low

Rate

(K

g/s

)

Real

Model

500 1000 1500 2000 2500

200

300

400

500

600

700

Time (Min)

Ma

ss F

low

Ra

te (

Kg/s

)

Real

Model






[474]

Fig.(13).Convectional water – steam cycle at Russia power station, design calculation at 100% load and power 800MW

Pm = 484660.31 kW

LHV fuel = 28938 kJ/kg

b = 95 %

Pm = 249084.47 kW


b = 95 %

Pel = 719995.06 kW

el = 98.5 %

Pel = 10987.08 kW

m = 99.62 %

Pm = 2762.57 kW

m,e = 98.13 %

102102

1.000 12.00

50.47 26995.004

101101

3.000 19.36

81.47 26995.004

100100

213.5 562.99

3417.39 567.388

3737

49.16 244.75

1060.44 31.796

3636

275.1 263.15

1149.26 567.388

3535

276.1 238.78

1036.58 567.388

3434

32.60 196.80

838.75 84.961

3333

12.70 182.70

775.15 96.401

3232

4.408 129.10

542.61 15.197

3131

2.489 93.73

392.78 40.749

3030

0.7537 52.01

217.72 69.340

2929

10.77 49.82

209.40 85.367

2828

0.1216 49.70

208.02 85.367

2727

0.1293 50.95

2468.68 16.026

2626

0.8018 124.20

2726.86 28.591

2525

2.648 237.19

2943.07 25.552

2424

4.690 299.16

3063.80 15.197

2323

0.02800 22.96

2408.78 26.346

2222

8.266 373.05

3210.33 26.346

2121

8.266 373.05

3210.33 19.480

2020

8.794 373.48

3210.33 45.826

1919

13.51 428.03

3319.03 11.440

1818

1717

52.30 352.15

3071.29 31.796

1616

277.1 190.83

824.19 567.388

1515

278.1 176.73

763.38 567.388

1414 8.266 171.78

726.90 567.3881313

9.266 144.66

609.46 451.508

1212

9.766 124.79

524.59 451.5081111

10.27 89.42

375.22 451.508

1010 10.77 47.69

200.53 451.508

99

10.77 47.20

198.46 366.141

88

11.27 23.05

97.67 366.141

77

0.02800 22.96

96.23 366.141

66

0.02800 89.46(X)

2358.00 339.795

55

30.55 540.00

3545.14 482.427

33.61 541.33

3545.14 482.427

44

33.61 296.05

2972.88 482.427

33

33.61 296.05

2972.88 535.592

22

205.3 560.00

3417.39 567.388

11

102101

100

21

20

F

19

18

17

16

F

15

F

14

1312

F

11

F

10

F

9

8

F

7

6

5

43

2

1

p T

h m

p = Pressure [bar]

T = Temperature [°C]

h = Enthalpy [kJ/kg]

m = Massflow [kg/s]

X = Steamquality [%]

P = Pow er [kW]

Pel = Electrical Pow er [kW]

e = Electrical eff iciency [%]

Pel = Electrical losses [kW]

m = Mechanical eff iciency [%]

Pm = Mechanical losses [kW]

m,e = Mechanical*Electrical eff. [%]

LHV fuel = Low er heating value fuel [kJ/kg]

b = Boiler eff iciency [%]

Conventional water/steam cycle at Russia power station, design calculation at 90% load (720 MW)






[475]

Fig.(14).Convectional water – steam cycle at Russia power station, design calculation at 90% load and power 720 MW

Pm = 430497.19 kW


b = 95 %

Pm = 221433.48 kW


b = 95 %

Pel = 639993.44 kW

el = 98.59 %

Pel = 9174.64 kW

m = 99.58 %

Pm = 2762.22 kW

m,e = 98.17 %

102102

1.000 12.00

50.47 24053.648

101101

3.000 19.36

81.47 24053.648

100100

188.1 562.69

3443.18 495.436

3737

43.46 237.15

1024.15 26.183

3636

242.4 255.82

1114.48 495.436

3535

243.4 232.08

1005.24 495.436

3434

28.79 190.67

811.25 70.318

3333

11.26 176.36

747.17 80.426

3232

3.937 125.30

526.38 12.959

3131

2.227 90.68

379.92 34.893

3030

0.6759 49.62

207.73 59.660

2929

9.869 47.71

200.52 73.111

2828

0.1094 47.61

199.25 73.111

2727

0.1164 48.84

2472.17 13.451

2626

0.7190 125.38

2729.99 24.767

2525

2.369 238.56

2946.86 21.935

2424

4.188 300.51

3067.81 12.959

2323

0.02731 22.54

2421.28 20.412

2222

7.369 374.39

3214.69 20.412

2121

7.369 374.39

3214.69 16.557

2020

7.839 374.78

3214.69 36.969

1919

11.98 428.63

3322.47 10.108

1818

1717

46.24 354.26

3091.40 26.183

1616

244.4 185.61

799.82 495.436

1515

245.4 171.30

738.18 495.436

1414 7.369 167.04

706.15 495.4361313

8.369 140.98

593.63 398.453

1212

8.869 121.59

510.97 398.4531111

9.369 86.97

364.90 398.453

1010 9.869 45.92

193.04 398.453

99

9.869 45.52

191.36 325.341

88

10.37 22.63

95.82 325.341

77

0.02731 22.54

94.49 325.341

66

0.02731 90.01(X)

2362.54 304.930

55

26.98 540.00

3548.64 425.118

29.68 541.18

3548.64 425.118

44

29.68 297.99

2990.92 425.118

33

29.68 297.99

2990.92 469.253

22

180.9 560.00

3443.18 495.436

11

102101

100

21

20

F

19

18

17

16

F

15

F

14

1312

F

11

F

10

F

9

8

F

7

6

5

43

2

1

p T

h m

p = Pressure [bar]



m = Massflow [kg/s]


P = Pow er [kW]









Conventional water/steam cycle at Russia power station , design calculation at 80% load ( 640 MW)






[476]

Fig.(15 ).Convectional water – steam cycle at Russia power station, design calculation at 80% load and power 640 MW

Pm = 120705.24 kW


b = 95 %

Pm = 45721.10 kW


b = 95 %

Pel = 160008.39 kW

el = 97.8 %

Pel = 3655.05 kW

m = 98.34 %

Pm = 2762.50 kW

m,e = 96.14 %

102102

1.000 20.00

83.95 42685.328

101101

3.000 21.36

89.83 42685.328

100100

138.7 537.22

3426.46 149.458

3737

178.7 251.00

1091.14 149.458

3535

11.20 161.66

682.99 25.916

3232

1.660 87.95

368.41 5.641

3131

0.1596 55.29

2471.09 2.359

2525

0.6383 90.47

2661.96 6.064

2424

1.766 178.48

2828.27 5.641

2323

1919

11.91 386.40

3232.45 6.610

1818

1717

1616

179.7 184.87

793.18 149.4581515

180.7 154.66

663.10 149.458

180.7 154.66

663.10 149.458

1414 4.990 151.77

639.79 149.4581313

5.990 111.44

467.74 115.691

1212

6.490 82.95

347.79 115.6911111

6.990 51.00

214.01 115.691

1010

40.45 361.99

3123.80 19.306

99

88

7.490 38.56

162.08 115.691

77

0.06800 38.49

161.12 115.691

66

0.06800 91.45(X)

2513.18 101.627

55

36.20 535.00

3528.28 130.153

44

4.990 284.36

3032.44 7.851

33

39.82 359.92

3120.07 130.15322

133.4 535.00

3426.46 149.45811

102101

100

21

20

F

15

F

14

1312

F

11

F

10

F

7

6

5

4

3

2

1

p T

h m

p = Pressure [bar]



m = Massflow [kg/s]


P = Pow er [kW]









Conventional water/steam cycle at Dura power station , design calculation, 100% load ( 160 MW)






[477]

Fig.(16 ).Convectional water – steam cycle at Dura power station, design calculation at 100% load and power 160 MW

Pm = 108774.95 kW


b = 95 %

Pm = 41552.39 kW


b = 95 %

Pel = 143999.03 kW

el = 97.63 %

Pel = 3565.92 kW

m = 98.16 %

Pm = 2762.57 kW

m,e = 95.79 %

102102

1.000 20.00

83.95 39215.098

101101

3.000 21.36

89.83 39215.098

100100

125.7 537.03

3440.19 134.763

3737

161.9 245.57

1065.45 134.763

3535

10.18 157.00

662.71 22.636

3232

1.513 85.49

358.04 5.013

3131

0.1465 53.50

2473.86 2.073

2525

0.5828 90.98

2663.75 5.402

2424

1.610 179.02

2830.27 5.013

2323

1919

10.83 386.79

3235.05 5.909

1818

1717

1616

162.9 180.90

775.04 134.7631515

163.9 150.85

645.76 134.763

163.9 150.85

645.76 134.763

1414 4.543 148.27

624.68 134.7631313

5.543 109.05

457.59 105.192

1212

6.043 81.05

339.77 105.1921111

6.543 49.64

208.32 105.192

1010

36.73 363.43

3135.17 16.727

99

88

7.043 37.60

158.05 105.192

77

0.06459 37.54

157.15 105.192

66

0.06459 91.82(X)

2526.46 92.704

55

32.87 535.00

3531.61 118.036

44

4.543 284.92

3034.81 6.935

33

36.16 361.36

3131.38 118.03622

120.9 535.00

3440.19 134.76311

102101

100

21

20

F

15

F

14

1312

F

11

F

10

F

7

6

5

4

3

2

1

p T

h m

p = Pressure [bar]



m = Massflow [kg/s]


P = Pow er [kW]









Conventional water/steam cycle at Dura power station , design calculation at 90% load (144 MW)






[478]


Pm = 96855.25 kW

Pm = 37390.89 kW

Pel = 127998.83 kW

el = 97.4 %

Pel = 3484.90 kW

m = 97.94 %

Pm = 2762.52 kW

m,e = 95.35 %

102102

1.000 20.00

83.95 35727.004

101101

3.000 21.36

89.83 35727.004

100100

112.7 536.83

3453.64 120.284

3737

145.3 239.67

1037.63 120.284

3535

9.162 152.11

641.50 19.519

3232

1.366 82.82

346.83 4.402

3131

0.1335 51.60

2476.97 1.778

2525

0.5272 91.52

2665.57 4.752

2424

1.453 179.55

2832.27 4.402

2323

1919

9.747 387.18

3237.65 5.210

1818

1717

1616

146.3 176.56

755.29 120.2841515

147.3 146.75

627.23 120.284

147.3 146.75

627.23 120.284

1414 4.096 144.48

608.36 120.2841313

5.096 106.39

446.33 94.714

1212

5.596 78.92

330.80 94.7141111

6.096 48.14

202.00 94.714

1010

33.02 364.87

3146.18 14.308

99

88

6.596 36.65

154.04 94.714

77

0.06135 36.59

153.20 94.714

66

0.06135 92.24(X)

2542.00 83.782

55

29.55 535.00

3534.92 105.976

44

4.096 285.48

3037.16 6.052

33

32.50 362.79

3142.32 105.97622

108.4 535.00

3453.64 120.284

11

102101

100

21

20

F

15

F

14

1312

F

11

F

10

F

7

6

5

4

3

2

1

p T

h m

p = Pressure [bar]



m = Massflow [kg/s]


P = Pow er [kW]







Conventional water/steam cycle at Dura power station, design calculation at 80% load (128 MW)






[479]


Pm = 96855.25 kW

Pm = 37390.89 kW

Pel = 127998.83 kW

el = 97.4 %

Pel = 3484.90 kW

m = 97.94 %

Pm = 2762.52 kW

m,e = 95.35 %

102102

1.000 20.00

83.95 35727.004

101101

3.000 21.36

89.83 35727.004

100100

112.7 536.83

3453.64 120.284

3737

145.3 239.67

1037.63 120.284

3535

9.162 152.11

641.50 19.519

3232

1.366 82.82

346.83 4.402

3131

0.1335 51.60

2476.97 1.778

2525

0.5272 91.52

2665.57 4.752

2424

1.453 179.55

2832.27 4.402

2323

1919

9.747 387.18

3237.65 5.210

1818

1717

1616

146.3 176.56

755.29 120.2841515

147.3 146.75

627.23 120.284

147.3 146.75

627.23 120.284

1414 4.096 144.48

608.36 120.2841313

5.096 106.39

446.33 94.714

1212

5.596 78.92

330.80 94.7141111

6.096 48.14

202.00 94.714

1010

33.02 364.87

3146.18 14.308

99

88

6.596 36.65

154.04 94.714

77

0.06135 36.59

153.20 94.714

66

0.06135 92.24(X)

2542.00 83.782

55

29.55 535.00

3534.92 105.976

44

4.096 285.48

3037.16 6.052

33

32.50 362.79

3142.32 105.97622

108.4 535.00

3453.64 120.284

11

102101

100

21

20

F

15

F

14

1312

F

11

F

10

F

7

6

5

4

3

2

1

p T

h m

p = Pressure [bar]



m = Massflow [kg/s]


P = Pow er [kW]







Conventional water/steam cycle at Dura power station, design calculation at 80% load (128 MW)






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NOMENCLATURE

A, B C,D,E Constant in equation –

T Temperature oC

G Inlet mass flow rate Kg/s

M Extraction mass Kg/s

S Entropy kJ/kg.k

H Enthalpy kJ/kg

ℎ0 Enthalpy of main steam kJ/kg

V specific volume 𝑚3/𝑘𝑔

hrh Enthalpy of reheater kJ/kg

hc′

Enthalpy of condensate (in the ideal Rankine cycle) kJ/kg

hext Enthalpy of extraction kJ/kg

𝐺𝑐 steam flow rate to the condenser Kg/s

ṁ𝑒𝑥 Mass flow rate at extraction Kg/s

WIP Power for IP turbine MW

WiP work done in IP turbine MW

E Machine excitation voltage (V)

WLP Power for LP turbine MW

WlP Work done in LP turbine MW

WHP Power for HP turbine MW

P Pressure MPa

𝑃0 Ambient pressure bar

𝑇0 Temperature of the environment oC

𝑇𝑜𝑔 Fuel gas temperature oC

Tin Inlet temperature K

𝑃𝑐 Final pressure of steam at condenser MPa

QB Heat added to the boiler kJ/kg

Qrh. Heat added to the reheater kJ/kg

𝜌 Specific density Kg/𝑚3

ρs Density of steam Kg/𝑚3

XC Steam quality %

Vs Specific volume of steam m3/ Kg

V Terminal voltage (V)

Nel Nominal electrical power for steam turbine plant MW

Nef Effective power MW

𝑁𝑖 Internal power MW

𝑑𝑧 Diameter m

𝑙2𝑧 Height of moving blades m

Ω Axial surface area m2

ṁfuel Mass of fuel Kg/s

𝑚𝑔 Mass of gas Kg/s

𝑐𝑃𝑔 Specific heat at constant pressure of gas kJ/kg.k

ms Mass of steam Kg/s

𝑚𝑤 Mass of water Kg/s

cPw Specific heat at constant pressure of water kJ/kg.k

Iofwh Irreversibility of open Feed water heater kJ

Ifwhc Irreversibility of closed Feed water heater kJ

Es Exergy of steam kJ

𝑋 direct axis synchronous reactance (X)

M inertia constant Kg.m2/s

𝛿 rotor angle (rad)

𝜏 time constant (s)






[481]

n polytrophic exponent –


simulation a dynamic modeling

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