An introduction to the Modeling of Thermal Power Plants M. S. R. Murty

Introduction Mathematical models help in analyzing the dynamic performance of engineering systems. The extent of details incorporated in the model depends on the purpose of analysis or study. The design studies are done using very detailed mathematical models. The mathematical models used for control studies are less- detailed and often low-order models (LOM) or approximate models are used. The models used in the operator training simulator (OTS) are based on the type of malfunctions are disturbances that are simulated. Similarly the hardware-in-the-loop testing simulators used for testing the control loops as part of factory acceptance tests (FAT) include the details that are necessary to interconnect the hardware control cabinets and the simulation system. The mathematical models of thermal power plant comprising- boiler, turbine, generator their controls and auxiliaries have been described in the literature extensively. Low order or reduced order models are used for the boiler, turbine and generator for control system tuning and analysis. In this paper, low order models of boiler and turbine are briefly described. The simulation aspects of these models are described in another paper along with simulation results. Thermal power plant: Basic scheme A simple scheme of thermal power plant is shown in Fig. 1. Boiler generates superheated steam at design pressure and temperature and supplies to the steam turbine. Fuel and air provide the inlet energy to convert water to the steam in the boiler drum. The super heaters super heat the saturated steam received from the drum. The steam causes the rotation of the steam turbine and the generator coupled to it. With the result electric power is produced and fed to the grid as shown. Several other such machines supply power to the grid. Steam after expansion in the turbine goes to the condenser and is fed back to the boiler through heaters etc., in regenerative cycle.

Steam

Fig. 1 Thermal Power Plant: Simple scheme

BOILER

PRESSURE, Water TEMPERATURE

GCV

TURBINE

SPEED

GRID G

Fuel Air GENERATOR

MW, MVAR,

C

1

Control Aspects

portant parameters to be controlled are:

rminal voltage e to be maintained at set value like

hen ever power output is to be changed, the steam admission to turbine is changed

he boiler is shown in more detail in Fig. 2 to explain some of the control aspects. The

Fig. 2 Boiler schematic diagram

athematical Model of Boiler

he mathematical model of boiler for the purpose of studying the steam pressure control is described here. Steam pressure in any vessel depends on the balance of rate of flow of steam at the inlet and outlet as shown below.

Im Steam pressure, steam temperature Turbine speed/ frequency Power output, generator teThere are several other parameters in the boiler that ardrum level, furnace pressure, reheater temperature, oxygen content in flue gas etc., Wusing governor control valve (GCV), shown in the Fig. 1. Tcirculation system consists of drum , down comers and risers (or water walls). The steamgeneration is changed by manipulating fuel and air shown to maintain the steam pressure. To maintain the steam temperature at the desired value, spray water in the desuperheater. The feed water control valve (FCV) is manipulated to maintain the drum water level.

FW

PSH SSH DESH FCV

SCV

Fue

Superheat

Spray

steam to turbine

l

M T

2

Steam Vessel

Steam inflow Steam

outflow

Steam pressure

Fig. 3 Steam Vessel The mass (rate) balance equation is written as:

nflow - Outflow) = Rate of change of stored mass

Wi – Wo = [d/ dt ] (ρ Vs)

here Wi, Wo = mass flow rate of steam in and out respectively in vessel

Vs = volume of the steam vessel

v) assumed uniform in the vessel.

aplace transforming and referring the variables to their nominal values (with subscript

the boiler model drum, super heater and the connected piping are represented by the and . Tv

presents the time constant of super heater.

ted

(I W ρ = density of steam Density (ρ) is a function of steam pressure (p L‘u’) the above equation can be written in transfer function form: (Wiu – Wou) = [( 1/ Tsv. s) pv ]where Tsv have the units of seconds. Inabove type of transfer function. Tu represents the time constant of the drumre The steam flow through super heater is related to the pressure drop across it as indicaby the parameter Csh. The block diagram showing the boiler model is shown in the figure below.

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Fig. 4 Boiler Storage behaviour Model Firing system and Thermal Inertia The steam generation in the boiler is subjected to a time constant which depends upon the firing system time lag and the ‘thermal inertia’. Thermal inertia may be defined as the time constant associated with the virtual steam production (Wv) in the boiler when the firing intensity (F) is changed by the firing system. The firing system time constant and the thermal inertia time can be represented by the transfer functions as shown in Fig. 5. The firing system has a transport lag term ( e –Td s ) which represents the dead time associated with coal mills.

Σ

Σ

Σ

1 (Tu) s

1 (Tv).s

Csh

Boiler storage

Pipe line storage

Pressure drop

ps

pd

+

-

Steam generation

Wv Drum pressure

+-

Wsh

-+

Turbine steam pressure

Wt

Turbine flow

4

Fig. 5 Firing System and Thermal Inertia Model The firing command is given by the pressure controller or combustion controller which is of proportional – integral- derivative (PID) type. Combining the above blocks the complete mathematical model of the boiler for the simulation of pressure control loop is given in Fig. 6.

Fig. 6 Boiler Mathematical Model

e –Td s

(1 + Tm. s)

F W v1 CF ---------- firing command

(1 + TV. s)

Firing System

Thermal Inertia

pd

ps

5

In Fig. 6, Blspm is the set point for steam generation (or power output) and pr is the pressure set point. All the variables are in non-dimensional form. Steam demanded by the turbine is shown as xmd. The unit delay term (e –Td s ) has been replaced by cascaded first order block [ 1/ (1 + Tm s)3] for convenience in simulation. The pressure controller is shown as PI controller with Akpp as the proportional gain and Tnpp as the reset time. Turbine and Governing System Model As shown in Fig. 7, steam from boiler enters the turbine through control valve. When ever the control valve opening changes, steam flow changes and this acts as the disturbance for the pressure control lop described in the boiler model. The governing system controls the turbine control valve to maintain speed (at no load and in emergencies), power output when connected to grid and steam pressure also when situation demands. The protection system shown in the figure operates on stop valve ahead of governor control valve.

CV

SV

SP

Permissives

STEAM

SPEED

POWER

PRESSURE

○ GRIDG

PT

ProtectionSystem

GOV.SYSTEM

SP : SET POINT

CV : CONTROL VALVE

SV : STOP VALVE

BASIC GOVERNING AND PROTECTION SCHEME

ST

Fig. 7

6

The turbine shown in the above comprises of HP turbine, IP turbine and LP turbine. After HP turbine steam goes to the reheater and enters after reheating IP turbine through another set of control valves (IPCV) as shown in Fig. 8.

Steam HPCV

Fig. 8 Steam Turbine Scheme The mathematical model of the turbine and governing system is shown in the form of transfer function block diagram in Fig. 9. Various parameters used are defined in the nomenclature. The large steam turbine has three stages referred to as High pressure ( HP) turbine, Intermediate pressure (IP) turbine and Low pressure ( LP) turbine. The steam after expansion HP turbine gets reheated and then admitted in IP turbine through IP control valves. In the mathematical model the control loops of HP and IP turbines are included.. The steam volumes of HP, IP and LP turbine cylinders and the boiler reheater steam volume determine values of time constants THP, TIP, TLP, and TRHT shown in the figure. Reheater volume is quite large and the value of TRHT can be as large as 20 seconds. The controller blocks are shown in detail in Fig. 10. The calculation of TA is shown below for a sample case.

Reheate

IPCVCondenser

LPT

HPT IPT G

R H

7

Fig 9 Mathematical Model of Turbine and Governing system

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29Feed forward provision

KSVS

Speed Controller: Proportional Derivative

Load Controller : Proportional Integral

Load

Load Ref

SpeedRef SPEED

CONTROLLER

LOADCONTROLLER

SELECTIONLOGIC

EH

To Hyd.Amplifier

speed

Ks(1+VsTs.S)(1 + Ts . S)droop

KPL + 1TILS

KS

Fig. 10 Speed and Load Controller Conclusions The low-order mathematical model of boiler and detailed model of steam turbine governing system are presented in this paper. These models are used in the power industry for controller tuning, simulator testing etc., Depending on the specific application details can be incorporated. Bibliography 1. THE FLEXIBILITY OF THE SUPERCRITICAL BOILER AS A PARTNER IN POWER SYSTEM DESIGN AND OPERATION Part 1I: Application and Field Test Results F. Laubli F. H. Fenton, Jr. 2. ‘Simulation of Power Plant Response under Free Governor Mode of Operation’, Icfai Journal of Science & Technology, Vol. 1, No.3, Mar. 2006. 3. Design of a Fuzzy Logic Controller for a Heat Recovery Steam Generator (Co-author: A.Gangadhaara Rao),International Conference on "Emerging Trends in Electrical Engineering" during January 12-14,2007 in Science City, Kolkata.

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4. RETROFITTING STEAM TURBINES WITH MODERN CONTROL PLATFORMS by Ronald Hitzel, PowerGEN 2003 – LasVegas, Nevada Dec. 9-11 5 Working group on prime mover and energy supply, 'Dynamic models for fossil fuelled steam units in Power Systems studies', IEEE, PWRS-6, No 2, May 6. F. P. de Mello 'Boiler models for system dynamic performance studies', IEEE 90 SM 305-3 PWRS 7. Y. Zhang, G. P. Chen, 0. P. Mallik. 'A multi input power system stabiliser based on Artificial Neural Networks', IEEE, 1993 8. A Drum Boiler Model for Long Term Power System Dynamic Simulation M. E. Flynn and M. J. 0’ Malley, IEEE Transactions on Power Systems, Vol. 14, No. 1, February 1999 Apendix Rotor Inertia Transfer function At steady state : Turbine Torque (Pm) = Load Torque( (Pel)

During transient : Speed = ∫((Pm – Pel) / Ta ) dt Ta = Acceleration time or inertia constant (function of moment of inertia) Typical values of Ta are 7 - 12 sec . Example for 250 MW turbine: TA = (1.097 × 10-2) (J) (n/1000)2 (1/P) = 8.3 sec. (Sec.) J = Moment of Inertia of rotor system,Kg-m2 = 20978.86 n = Rotor speed = 3000 rpm P = rated power = 250 MW

Nomenclature With reference to Fig. 9 FG 1 Function used to realize opening and closing time of control valve FG 2 Function relating lift versus steam flow of control valve KHP, KIP KLP Proportional factors representing shares of power developed by HP,

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IP and LP turbines respectively, per unit KPL Proportional gain of load controller, p.uKS Proportional gain of speed controller, p.u KVI Proportional gain used to simulate IP control valve action, p.u nref Speed reference setting, p.u. n Turbine speed or frequency, p.u Pel Electrical load, p.u PHP Steam pressure before HP control valve, p.u Pref Reference power setting, p.u PRHT Reheater steam pressure, p.u TFPH, TFPI TLC Time constants of hydraulic relays, seconds THP , TIP , TLP Time constants of HP, IP and LP turbines respectively, seconds TIL Time constants in load controller block, sec. TRHT Time constant of reheater,sec TS Time constants in speed controller block, sec. TVH ,TVI Time constants of HP and IP control valves respectively, sec

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