Modeling of Turbine

Dynamic response is influenced by two factors 1.Entertained steam between the inlet steam valve and first stage of turbine (high pressure). 2.The storage action in the reheater which causes the LP stage lag behind that of HP stage Therefore turbine transfer function is characterized by two time constants. For simplicity of analysis it will be assumed that the turbine can be modeled to have single time constant.

Time constant range is 0.2 to 2.5sec

Modeling of generator Two aspects are there in modeling of generator: 1.It should correlate the electrical power output consumed by load. (classical model or simplified network model). 2.It should correlate mechanical aspect with electrical output. (Swing equation).

Classical model of generator The machine is modeled by an equivalent voltage source behind an impedance. Several assumptions are taken in this model.

Assumptions Voltage regulators are not present and manual excitation is used. This implies that in steady-state the magnitude of the voltage is determined by field current which is a constant. 2.Damper circuits are neglected 3.Transient stability is judged by the first swing, which is normally reached in one or two sec. 4.Flux decay in field circuit is neglected(short period).

5. The mechanical power input to the generator is constant. 6 5.The mechanical power input to the generator is constant. 6.Salinency has little effect and can be neglected in transient stability analysis. 7.losses are neglected.

Classical Generator Model Generator is connected to an Infinite bus through two lossless transmission lines. E’ and xd’ are constants. δ is governed by the swing equation.

Simplifying the system Combine xd’ & XL1 & XL2 jXT = jxd’ + jXL1 || jXL2 The simplified system.

Steady state model In this model the generator reactance is equal to synchronous reactance(Xd or Xs). Transient state model In this model the generator reactance is equal to direct axis transient reactance(Xd’). This is also called constant flux model.

The swing equation 2H d2 δ = Pacc =Pm-Pe ωo dt2 P = Tω α = d2 δ/dt2, acceleration is the second derivative of angular displacement w.r.t. time ω = dδ /dt, speed is the first derivative. H= constant

Accelerating Power, Pacc Pacc = Pmech - Pelec Steady State => No acceleration Pacc = 0 => Pmech = Pelec

Turbine speed governing system

FLY BALL SPEED GOVERNER LINKAGE MECHNAISM FLY BALL SPEED GOVERNER

FLY BALL SPEED GOVERNER This is the heart of the system. Which senses the change in speed. As speed increases fly balls moves out wards. Point B moves downwards. The reverse happens when the speed decreases.

LINKAGE MECHANISM ABC is a rigid link pivoted at B. CDE is a rigid link pivoted at D. It provides a movement to the control valve in proportion to change in speed. It also provides a feedback from the steam valve movement.

SPEED CHANGER It Provides steady state power output setting for the turbine. Its downward movement opens the upper pilot valve so that more steam is admitted to the turbine under steady conditions. The reverse happens for upward movement of speed changer.

HYDRAULIC AMPLIFIER It comprises pilot valve Main piston Low power level pilot valve movement is converted into high power level piston valve movement. This is required to open or close the steam valve against high pressure steam.

Speed Governing System Model Let the operating conditions be characterized by

FLY BALL SPEED GOVERNER LINKAGE MECHNAISM FLY BALL SPEED GOVERNER

FLY BALL SPEED GOVERNER LINKAGE MECHNAISM FLY BALL SPEED GOVERNER

Linear incremental model Let the point A is moved downwards by a small amount It is a command which causes the turbine output to change

FLY BALL SPEED GOVERNER LINKAGE MECHNAISM FLY BALL SPEED GOVERNER

Let us model these events mathematically Movement at A moves C which in turn moves E First we see events contributing to C Then we see events contributing for E We correlate both and obtain a transfer function model .

FLY BALL SPEED GOVERNER LINKAGE MECHNAISM FLY BALL SPEED GOVERNER

Two factors contribute to the movement of C

FLY BALL SPEED GOVERNER LINKAGE MECHNAISM FLY BALL SPEED GOVERNER

It is the amount by which pilot valve opens. The movement of D It is the amount by which pilot valve opens. It is contributed by C and E ?

The movement of E can be correlated with oil flow entering from pilot piston whose movement is w.r.t. to D. Assumptions: 1.Inertial reaction forces are negligible. 2.The rate of oil admitted to the cylinder is proportional to port opening of

The volume of oil admitted to cylinder is proportional to the time integral of

Apply Laplace transform Eliminate C and D from above

EXCITATION SYSTEMS

Functions of Excitation Systems The functions of an excitation system are: To provide direct current to the synchronous generator field winding, and - To perform control and protective functions essential to the satisfactory operation of the power system.

CHARACTERISTICS OF EXCITATION SYSTEM The basic requirement of a closed loop excitation system is to hold the terminal voltage of a generator at a set value independent of the change has to contribute the following functions: a) Maintenance of stable operation of a machine under steady state, transient and dynamic conditions. b) Satisfactory operation with other machines connected in parallel. c) Effective utilization of machine capabilities without exceeding machine operating limits.

Power system considerations: The performance requirements of the excitation system are determined by a) Generator considerations: Supply and adjust field current as the generator output varies within its continuous capability. Respond to transient disturbances with field forcing. Consistent with the generator short term capabilities: rotor insulation failure due to high field voltage rotor heating due to high field current stator heating due to high VAR loading heating due to excess flux (volts/Hz) Power system considerations: Contribute to effective control of system voltage and improvement of system stability.

Elements of an Excitation System

Exciter: provides dc power to the generator field winding. Regulator: processes and amplifies input control signals to a level and form appropriate for control of the exciter. Terminal voltage transducer and load compensator: senses generator terminal voltage, rectifies and filters it to dc quantity and compares with a reference; load compensator may be provided if desired to hold voltage at a remote point. Power system stabilizer: provides additional input signal to the regulator to damp power system oscillations. Limiters and protective circuits: ensure that the capability limits of exciter and generator are not exceeded.

Types of Excitation Systems Excitation Systems are classified into three broad categories based on the excitation power source: DC excitation systems: Which utilizes a DC generator with commutator. AC excitation systems: Which use alternators and either stationary or rotating rectifiers to produce the direct current needed. Static excitation systems: In which the power is supplied through transformers and rectifiers.

Standard IEEE Models IEEE has standardized 12 model structures for representing the wide variety of excitation systems currently in use (IEEE Standard 421.5-1992): These models are proposed for use in transient and small-signal stability studies.

Automatic voltage regulator (e.g. IEEE AVR Type 1) Heb je geen europese ? ==> zal eens zoeken, deze stond in Kundur, en was ook gedefinieerd in de Eurostag modellen (en die gebruikten voornamelijk Belgische en franse voorbeelden als ik me dat goed herinnerde...) (dirk)