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PRIME MOVERS AND GOVERNING PRIME MOVERS AND GOVERNING SYSTEMSSYSTEMS

Copyright © P. KundurThis material should not be used without the author's consent

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Prime Movers and Governing SystemsPrime Movers and Governing Systems

1. Hydraulic Turbines and Governing Systems

hydraulic turbine transfer function

special characteristics of hydraulic turbines

nonlinear hydraulic turbine model

governors for hydraulic turbines

tuning of speed governors

2. Steam Turbines and Governing Systems

steam turbine configurations

steam turbine models

steam turbine controls

3. Gas Turbines and Governing Systems

simple-cycle configuration

combined-cycle configuration

Outline

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Hydraulic Turbines and Governing Hydraulic Turbines and Governing SystemsSystems

The performance of a hydraulic turbine is influenced by the characteristics of the water column feeding the turbine:

water inertia

water compressibility

pipe wall elasticity in the penstock

The effect of water inertia is to cause changes in turbine flow to lag behind changes in turbine gate opening

The effect of elasticity is to cause traveling waves of pressure and flow in the pipe - a phenomenon referred to as water hammer

typically, the speed of propagation of such waves is about 1200 meters/sec

traveling wave model required only if penstock is very long

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The representation of the hydraulic turbine and water column in stability studies usually assumes that (a) the penstock is inelastic, (b) the water is incompressible, and (c) hydraulic resistance is negligible

The turbine and penstock characteristics are determined by three basic equations relating to:

velocity of water in the penstock

turbine mechanical power

acceleration of water column

1. Hydraulic Turbine Transfer Function1. Hydraulic Turbine Transfer Function

Figure 9.2: Schematic of a hydroelectric plant

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The velocity of the water in the penstock is given by

whereU = water velocityG = gate positionH = hydraulic head at gateKu = a constant of proportionality

The turbine mechanical power is proportional to the product of pressure and flow; hence,

The acceleration of water column due to a change in head at the turbine, characterized by Newton's second law of motion, may be expressed as

whereL = length of conduitA = pipe areaρ = mass densityag = acceleration due to gravityρLA = mass of water in the conduitρag∆H = incremental change in pressure at

turbine gate

HGKU u=

HUKP pm =

( ) ( ) HaAdt

UdLA g ∆ρ−=∆ρ

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For small displacements (prefix ∆) about an initial operating point (subscript "0") we can shows that

where

Tw is referred to as the water starting time. It represents the time required for a head H0 to accelerate the water in the penstock from standstill to the velocity U0. It should be noted that Tw varies with load. Typically, Tw at full load lies between 0.5 s and 4.0 s.

Equation 9.11 represents the "classical" transfer function of the turbine-penstock system. It shows how the turbine power output changes in response to a change in gate opening for an ideal lossless turbine.

ST21

1

ST1

G

P

w

wm

+

−=∆∆

0g

0w Ha

LUT =

(9.11)

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Special Characteristics of Hydraulic Turbines

The transfer function given by Equation 9.11 represents a "non-minimum phase" system

Systems with poles or zeros in the right half of s-plane are referred to as non-minimum phase systems; they do not have the minimum amount of phase shift for a given magnitude plot. Such systems cannot be uniquely identified by a knowledge of magnitude versus frequency plot alone.

The special characteristic of the transfer function may be illustrated by considering the response to a step change in gate position. The time response is given by:

Figure 9.3 shows a plot of the response of an ideal turbine model with Tw = 4.0 s

( ) Ge31tPtT

2

mw ∆

−=∆

−

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Figure 9.3: Change in turbine mechanical power following a unit step increase in gate position

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Immediately following a unit increase in gate position, the mechanical power actually decreases by 2.0 per unit. It then increases exponentially with a time constant of Tw/2 to a steady state value of 1.0 per unit above the initial steady state value

The initial power surge is opposite to that of the direction of change in gate position. This is because, when the gate is suddenly opened, the flow does not change immediately due to water inertia; however, the pressure across the turbine is reduced causing the power to reduce.

With a response determined by Tw, the water accelerates until the flow reaches the new steady value which establishes the new steady power output

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Governors for Hydraulic TurbinesGovernors for Hydraulic Turbines

The speed/load control function involves feeding back speed error to control the gate position. In order to ensure satisfactory and stable parallel operation of multiple units, the speed governor is provided with a droop characteristic. Typically, the steady state droop is set at about 5%,

such that a speed deviation of 5% causes 100% change in gate position or power output; this corresponds to a gain of 20.

For a hydro turbine, however, such a governor with a simple steady state droop characteristic would be unsatisfactory

Requirement for a Transient Droop

Hydro turbines have a peculiar response due to water inertia: a change in gate position produces an initial turbine power change which is opposite to that sought.

For stable control performance, a large transient (temporary) droop with a long resetting time is therefore required. This is accomplished by the provision of a rate feedback or transient gain reduction compensation as shown in Figure 9.8

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The rate feedback retards or limits the gate movement until the water flow and power output have time to catch up

The result is a governor which exhibits a high droop (low gain) for fast speed deviations, and the normal low droop (high gain) in the steady state

Figure 9.8: Governor with transient droop compensation

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Mechanical Hydraulic GovernorMechanical Hydraulic Governor

On older units, the governing function is realized using mechanical and hydraulic components

Speed sensing, permanent droop feedback, and computing functions are achieved through mechanical components; functions involving higher power are achieved through hydraulic components

A dashpot is used to provide transient droop compensation. A bypass arrangement is usually provided to disable the dashpot if so desired.

Water is not a very compressible fluid; if the gate is closed too rapidly the resulting pressure could burst the penstock

Consequently, the gate movement is rate limited

Often, the rate of gate movement is limited even further in the buffer region near full closure to provide cushioning

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Figure 9.9: Schematic of a mechanical-hydraulic governor for a hydro turbine

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Parameters Sample dataTp = Pilot valve and servomotor time

constant0.05 s

Ks = Servo gain 5.0

TG = Main servo time 0.2 s

Rp = Permanent droop 0.04

RT = Temporary droop 0.4

TR = Reset time 5.0 s

ConstraintsMaximum gate position limit = 1.0Minimum gate position limit = 0Rmax open = Maximum gate opening rate 0.16 p.u./s

Rmax close = Maximum gate closing rate 0.16 p.u./s

Rmax buff = Maximum gate closing rate in buffered region

0.04 p.u./s

gbuff = Buffered region in p.u. of servomotor stroke

0.08 p.u.

Figure 9.10: Model of governors for hydraulic turbines

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Electro-Hydraulic GovernorElectro-Hydraulic Governor

Modern speed governors for hydraulic turbines use electric-hydraulic systems. Functionally, their operation is very similar to those of mechanical-hydraulic governors

Speed sensing, permanent droop, temporary droop, and other measuring and computing functions are performed electrically

Electric components provide greater flexibility and improved performance with regard to dead-bands and time lags

Dynamic characteristics of electric governors are usually adjusted to be essentially similar to those of mechanical-hydraulic governors

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Tuning of Speed Governing SystemsTuning of Speed Governing Systems

There are two important considerations in the selection of governor settings:

Stable operation during system islanding conditions or isolated operation; and

Acceptable speed of response for loading and unloading under normal synchronous operation

For stable operation under islanding conditions, the optimum choice of the temporary droop RT and reset time TR are as follows:

For loading and unloading during normal interconnected system operation, the above settings result in too slow a response. For satisfactory loading rates, the reset time TR should be less than 1.0 s, preferably close to 0.5 s.

The dashpot bypass arrangement can be used to meet the above conflicting requirements

( )[ ]M

wwT T

T15.00.1T3.2R −−=

( )[ ] wwR T5.00.1T0.5T −−=

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2. Steam Turbines and Governing 2. Steam Turbines and Governing SystemsSystems

A steam turbine converts stored energy of high pressure and high temperature steam into rotating energy

the heat source may be a nuclear reactor or a fossil fired boiler

Steam turbines with a variety of configurations have been built depending on unit size and steam conditions

normally consist of two or more turbine sections or cylinders coupled in series

A turbine with multiple sections may be

tandem-compound: sections are all on one shaft with a single generator, or

cross-compound: sections are on two shafts, each with a generator; operated as a single unit

Fossil-fuelled units can be of tandem-compound or cross-compound design

may be of reheat or non-reheat type

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Figure 9.16: Common configurations of tandem-compound steam turbine of fossil-fueled units

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Figure 9.17: Examples of cross-compound steam turbine configurations

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Nuclear units usually have tandem-compound turbines

moisture separator reheater (MSR) reduces moisture content, thereby reducing moisture losses and erosion rates

Large steam turbines for fossil-fuelled or nuclear units are equipped with four sets of valves

main inlet stop valves (MSV)

main inlet control (governor) valves (CV)

reheater stop valves (RSV)

reheater intercept valves (IV)

The stop valves (MSV and RSV) are primarily emergency trip valves.

The CVs modulate steam flow during normal operation.

The CVs as well as the IVs limit overspeed.

Figure 9.18: An example of nuclear unit turbine configuration

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Steam Turbine ModelSteam Turbine Model

For illustration, let us consider a fossil-fuelled single reheat tandem-compound turbine, a type in common use

Figure 9.21(a) identifies the turbine elements that need to be considered

Figure 9.21(b) shows the block diagram representation

The CVs modulate the steam flow for load/frequency control

the response of steam flow to CV opening exhibits a time constant TCH due to charging time of the steam chest and inlet piping

TCH is of the order of 0.2 to 0.3 s

The IVs are used only for rapid control of turbine power in the event of an overspeed

control about 70% of total power

the steam flow in the IP and LP sections can change only with the build-up of pressure in the reheater volume

the reheater time constant TRH is in the range 5 to 10 s

the steam flow in LP sections experiences a time constant TCO associated with the crossover piping; this is of the order of 0.5 s

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Parameters

TCH = time constant of main inlet volumes and steam chest

TRH = time constant of reheater

TCO = time constant of crossover piping and LP inlet volumes

Pm = total turbine power in per unit of maximum turbine power

Pmc = total turbine mechanical power in per unit of common MVA base

PMAX = maximum turbine power in MW

FHP,FIP,FLP = fraction of total turbine power generated by HP, IP, LP sections, respectively

MVAbase = common MVA base

Figure 9.21: Single reheat tandem-compound steam turbine model

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Simplified Transfer Function of a Steam Simplified Transfer Function of a Steam TurbineTurbine

A simplified transfer function of the turbine relating perturbed values of the turbine power and CV position may be written as follows:

It is assumed that TCO is negligible in comparison with TRH, and that the CV characteristic is linear

( ) ( )

( ) ( )RHCH

RHHP

RHCH

HP

CH

HP

CV

m

sT1sT1

TsF1

sT1sT1

F1

sT1

F

ΔV

ΔP

+++=

++−+

+=

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Turbine ResponseTurbine Response

The response of a tandem-compound turbine to a ramp down of the CV opening is shown in Figure 9.22.

has no peculiarity such as that exhibited by a hydraulic turbine due to water inertia

governing requirements more straightforward

Figure 9.22: Steam turbine response to a 1-second ramp change in CV opening

TRH=7.0 s, FHP=0.3; TCH and TCO negligible

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Steam Turbine ControlsSteam Turbine Controls

Functions:

The governing systems have three basic functions:

normal speed/load control

overspeed control

overspeed trip

In addition, the turbine controls include a number of other functions such as start-up/shut-down controls and auxiliary pressure control

The speed/load control is a fundamental requirement

achieved through control of CVs

the speed control function provides the governor with a 4 to 5% speed drop

the load control function achieved by adjusting speed/load reference

The overspeed control and protection is peculiar to steam turbines

of critical importance for safe operation

speed should be limited to well below the design maximum speed of 120%

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The overspeed control is the first line of defense

involves fast control of CVs and IVs

limits overspeed following load rejection to 0.5 to 1.0% below overspeed trip level

returns the turbine to a steady-state condition with turbine ready for reloading

The overspeed or emergency trip is a backup protection

designed to be independent of the overspeed control

fast closes the main and reheat stop valves, and trips the boiler

The characteristics of steam valves are highly nonlinear

compensation is often used to linearize steam flow response to the control signal

compensation may be achieved by a forward loop series compensation, a minor loop feedback, or a major loop feedback.

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Governing Systems

Systems used for the above control functions have evolved over the years:

older units used mechanical-hydraulic control

electro-hydraulic control was introduced in the 1960s

most governors supplied today are electro-hydraulic or digital electro-hydraulic

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The functional block diagram of a mechanical-hydraulic control (MHC) system is shown in Figure 9.25

the speed governor is a mechanical transducer which transformers speed into position output

the speed relay is a spring loaded servomotor which amplifies the speed governor signal

the hydraulic servomotor provides additional amplification to the energy level necessary to move the steam valves

Figure 9.31 shows the block diagram of an MHC speed governing system, including the overspeed control (auxiliary governor) applicable to a specific make

Figure 9.25: Functional block diagram of MHC turbine governing system

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Figure 9.31: MHC turbine governing system with auxiliary governor

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The electro-hydraulic control (EHC) systems use electronic circuits in place of mechanical components associated with the MHC in the low-power portions

offer more flexibility and adaptability

Fig. 9.33 shows an example of EHC governing system. It has two special features for limiting overspeed: IV trigger and power load unbalance (PLU) relay.

the IV trigger is armed when the load (measured by reheat pressure) is greater than 0.1 p.u. It is designed to fast close IVs when the speed exceeds set value.

the PLU relay is designed to fast close CVs and IVs under load rejection conditions. It trips when the difference between turbine power and generator load exceeds a preset value (0.4 p.u.) and the load decreases faster than a preset rate.

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Fig. 9.33 EHC governing system with PLU relay and IV trigger

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3. Gas Turbines3. Gas Turbines

The heat source is a hydrocarbon-based fuel

in either gaseous or liquid state

fuel is burned directly in the working fluid

like any internal combustion engine, requires external source for startup

The power produced by the gas turbine is used to drive an alternator to produce electrical power at frequencies compatible with local grids

Exhaust heat is often used to generate steam, which can be used for a process, as in the case of cogeneration

simple-cycle configuration

Alternatively, steam produced using exhaust heat can be used in a steam turbine to generate additional electrical power

combined-cycle configuration

Many variations in configurations and controls

no standard models

CIGRE TF: 38.02.25 report published in April 2003 addresses modeling issues