Raabe J. Hydro power - the design, use, and function of hydromechanical, hydraulic, and electrical еquipment

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Fig. 11.2.11. Simplified. scheme for the speed

of a double regulated KT with hydro

mechanic governor, and control loops for the

gates and the runner vanes in series, assigned to

each other by the cam

Devices for the

temporary speed droop (dash pot) omitted.

speedometer;

control valve;

pressurized oil;

gate servomotor;

cam;

oil head; 7 gate

operating ring;

runner servomotor; 9 spider;

alternator rotor, 11 turbine runner.

Fig.

11.2.8

shows signal flux and function diagram of

double regulated

of the French

firm

Ncyrpic. Here the synchronized actuation of runner and gate servomotor from

speedometer and

acceleron~eter is preferred. Here also metering devices and relays are

electronic as far as reasonably possible.

this connection wide use is made of solenoid valves, see Fig.

11.2.9.

Such

valve

~ransforms the electric current, supplied by one of the electronic governor's output

amplifiers, into a proportional and accurate stroke of a hydraulic distributing valve. The

latter controls,

e.g., a servomotor.

The servo-valves all have cylindrical distributing valves provided with one pair of regulating edges

the usual differential type servomotor is controlled. Depending on the oil flow to be controlled.

the Swiss firm

Vevey

uses servo valves having two or three stages of amplification.

The electro hydraulic first stage (see Fig. 11.2.9) is to transform an electric current into the motion

ofa small double acting servomotor 108.

The latter is controlled by two symmetrical oil distributors,

working without friction. These comprise two diaphragms 117 a, 11 7 b, two nozzles

3 a,

paddle 104, suspended by two leaf springs 103 a, 103

Due to this suspension the paddle can move

vertically without friction. Its travel is only a few tenth of a millimeter, corresponding to the

dearance between the paddle and the nozzles.

an arbitrary position, the paddle is subjected to three vertical forces, namely: that of the spring

105, that due to prestressing of the leaf springs, 103a, 103b and that resulting from the passage of

electric current through the coil 102. The value and the direction of this force is a function of the

intensity and the polarity of the current. The steady state position of this electromagnetic force is

nil.

the case of an upward displacement of the paddle 104, induced by a current in the solenoid 102,

'he

flow of oil from the nozzle

13 a decreases while the flow through the other nozzle 11 3 b increases.

Hence the volume of the oil in the upper chamber of scrvornotor 105 increases and that in the lower

chamber dccreascs. The piston therefore moves downwards. The result is that the upward force on

fie

paddle 104 applied by the spring 105 is reduced. The motion stops when the variation

th~s

brce balances that due to the coil. The paddle then returns to its initial position, midway bct\wen

Fig. 11.2.12. Electro hydraulic runner blade adjustment by a cam according to KaMeWa

AB.

sWeden, with the control loops of gates and runner vanes in series. The input quantity to this servo

is primarily the wicket gate position. The combinator cam 29 which determines

thc relation-

ship

between blade angle and wicket gate opening is in this case connected to the pilot servomotor

*fthe actuator 31. In case large variations in head are encountered, the single cam is changed

dimensional saddle with lateral adjustment to ensure that correct setting can be achieved for

head. A third possibility is to introduce a digital processor instead of the cam or saddle.

The combinator 29 operates a transmitter K

which converts the corrected mechanical guidancs

into an electric signal. The position of the regulating sleeve 9 of the combinator is also via lever 20

tIansformed in the same way by transmitter K2. Both these electrical command signals are

@mpared and amplified in the electric error detector 30, and its output signal is fed to the transducer

1. Pilot valve 1 actuates the regulating sleeve 9 in a direction that tends to eliminate the difference

voltage between transmitters K2 and K6. The regulating sleeve 9 is a valve for the runner

%rvomotor 13. Regulating piston 11 is rigidly connected to the servomotor piston 13. If sleeve 9 and

piston 11 do not assume identical positions, port A and

will be opened either

to discharge and

to pressure or vice versa depending on the sign of the error signal. Thus oil will be passed through

@ncentricducts 14 and 15 in the shaft of the runner servomotor 13 in such a way that the valve ports

will be closed again (feedback). Thus the servomotor piston 13 copies exactly the movements of

sleeve 9.

Maximum closing and opening speeds are set by means of the throttle valves

and 3 respectively.

Reset to a larger blade angle to start, to obtain a greater torque from the turbine, is made entirely

electrical means in the error detector30. Parallel to the electro-hydraulic control there is a manual

control (a general necessity for all important regulating devices in the case of emergency).

the 3-way

valve 27 is turned from Auto to Manual, the hand control valve 28 takes over the control of sleeve

Desired runner blade angle can then be set by hand screw 21. As opposed to systems, in which

the last servo stage is located in the runner hub 18, the system described offers the advantage that

the true position of the blades can be checked. On a common

sczle 24 the position of both the

regulatiilg sleeve 9 and the runner servomotor 13, (i.e. the blade angle), are displayed. Legend

electro hydraulic transduccr,

runner blade position transmitter, K 3 limit switch fully closed,

limit switch fully opened, K 5 dirt indicating switch,

6 gate position transmitter.

pilot valve

piston; 2 throttle valve, closing time; 3 throttle valve, opening time;

Iilter for transducer; 5 dirt

indicator;

shut-off valve; 7 shut-off valve;

filter for transducer and pilot valve; 9 combined

regulating

sleeve/difJerential piston; 10 pressure oil pipe;

regulating piston;

pressure chamber;

13 runner servomotor piston; 14 oil duct to underside of item 13;

15 oil duct to upper side

item

13; 16 oil duct for static pressure to the runner hub; 17 turbine shaft; 18 Kaplan runner hub:

runner servomotor piston rod; 20 bell crank lever; 21 hand screw; 22 balance lever; 23 roller;

scale; 25 pointer for runner blade angle; 26 pointer for regulating sleeve/differential piston

position; 27 three-valve; 28 hand control valve; 29 combinator cam; 30 electronic error detector;

actuator. (Drawing courtesy KaMeWa, AB, Kristineham, Sweden.)

the nozzles 113a and 113 b. The final travel of the piston 108 is proportional to the exciting current

the coil.

The permanence of the magnetic field passing in the coil, the travel of which is very small, and the

negligible hysteresis of the spring characteristic of 105 ensure an accurate correlation between

the

movement of the distributing valve 130 alld the current in the coil 102.

Conclusion: The advantage of an electric governor consists in its high accuracy and in

lhe fact that the number of controlling and controlled parameters accompanying and

supporting the speed control and surveillance of the set is nearly unlimited. Examples

may be temperatures of bearing and alternator, blockage of by-pass outlet,

flow

lubricant, response of breaking elements in the gate drive, water-hammer-induced pres-

sure surge, energy exchange of a neighbouring grid, et~.

[11.39; 11.44; 11.46

11.481.

Moreovcl-

;ln

clcctric governor f~icilitates the col~trol of poucr st:ltions

remote

arm

from a far distant panel.

Fig. 11.2.10:r shows

;in

example of electronic data processing for

gate-regulated

from the

t;ilian

firm

Ilydroart. Fig.

11.2.10

shows special features in the control of

with single servomotors for the gates of the French firm Neyrpic.

Fig.

11.2.1

shows a simplified schemc of a double regulated

with the control

looB

for gates and runner bladcs in series, in which a11 damping dcviccs such as dash pots

haye

been omitted.

Fie.

11.2.12 shows the control scheme of

double regulated

imp&-

mcnted by the

we dish

firm KnMeWa

AD.

Fig.

11.2.13

shows a control scheme of a double regulated

with the control loops

nozzle valve and jet deflector in parallcl implemented

the French firm Neyr~ic.

11.2.3.

Simple

treatment

the

dynamic

hehaviour

governors

11.2.3.1.

Nomenclaturc and assumptions

Symbols: d-deviation from steady state (due to speed

and position of servomotor

piston Am) or zero position (due to valve

s),

positive in the sense of speed rise

As)

or opening

(dm):

11,-mean speed, nl,u-stroke of servomotor piston, s,,-stroke of valve

piston equal to width of ports; related values: speed

Anji~,,,; scrvomotor

111

AI~/ITI,~,

valve s

ds/s,,,j d,.-transient proportionill band (temporary speed droop),

being

0,3 .

4(7)

for

stabilization

of disturbanccs. 'I;-regulating timc (closing

opening),

the servomotor piston needs to cover its stroke

s,,

at full opened valve port (s

and

constant piston speed

In.

<-start up time of set, needed to accelerate the unloaded set

its rated torquc from rest to rated speed

at constant acceleration. TT;-reset (isostatic)'

time, the

lilrl

fold time that an abruptly full-deviated dash pot piston for the elastic

feedback needs to cover its half stroke. &-rate (acceleration) time, the accelerometer

requires to cover the speed rangc

n,,,

valve full-opened and at constant accel-

eration, (see

Fig.

11.2.3).

11.

Assumptions:

No overlap and leakage of valve in its zero position.

Servomotor

piston covers its stroke

s,,

in regulating time

at partial opening of vilIve

proportional band. 3) For

proportional governor with stiff feedback, the valve deviation

depends linearly on deviation of speed

and its integral

tit;

here at steady state

-u(s

(temporary speed droop). For a proportional integral governor with

acceleration

fecdback,

depends linearly on

and its derivative

.t.

No automatic

co~ltrol, torque

11s

speed graph of turbine and generator are parallel to each other.

The

excess of

the turbine's torque over that of generator is proportional to the servomotor

deviation

nl.

water hammer. In the following

dot above

quantity indicates its rate.

11.2.3.2.

Proportional governor, servomotor with stiff feedback (speed governor)

Respecting

and

give the valve deviation

1) and

yield the speed

of piston, regulating time

T,,

6,T,rn.

and

yield

the

set's equation of motion, start

time

T,,

Inserting

(1 1.2-3)

(1 1.2- 1),

then

(1 1.2-2)

with respect to

(11.2-3)

(11.2- 1)

yields the

differential equation

the closed control loop

dPT,T,,f

bTT,,x

(1 1.2L4)

Its

natural oscillation

x,eat

has the natural frequency

i(6:

4~,6,/~J''~]/(2 T,b,).

(1 1.2-5)

559

After

this

thc

feedback-linked

tcrm

6,./(2

-T,S,)

di111ip~ oscill;~tions will1 rising

rary

JI-OO~J

A,.

;IS

set, e.g.,

Icver ratio

linkage.

ern*

11.2.3.3.

Proportio~lal integral governor with ncccleration

fcetlback

(accc!crtllion governor,

govcrnor)

With the rate

tirnc

T,,

respecting

3),

the valve deviation reads

T,x

(1 1.2-6)

Expressi~lg

(11.2-2)

and then

ti1

(11.2-3) ~ives the

differential

equation

oftb

closed control loop, start up time

T,,

.-L

T,T,d,i+

T,i+x=O. (11.2-7)

Here the natural oscillation has a damping term

T,/2

TSp that increases with the rate

(acceleration) time

T,.

11.2.3.4.

Proportional integral governor, servomotor

with

elastic retarding

feedback

(PI

governor)

Let

be the related deviation of the spring-loaded and dash-pot-linked hinge of the valve

actuating lever.

The11

the

spring load becomes

is balanccd by the hydraulic load

the

dash

pot, which. in the case

laminar flow, is proportional to the speed difference

betwecn the

servomotor

(in)

and the dash pot

(0.

Accordingly with

?;.

as the reset (isostztic, isodrome) time,

Now

in the relation (1 1.2-

has to be replaced

Hence

Frorn

this

i)/6,. This in (11.2-8) gives

q(m

s/6,

x/6,). Putting this and

from

1.2-2) in

1.2-9) the differential equation of the governor, input

output

reads

6,TT,iii

(6,K

b,T)m

1.2-

10)

In practice the regulating time

is much smaller than

7;.

Moreover 6, is about 1110th

b,.

Therefore the terms with S,

7;:

are omitted in the last equation. Hence the simplified,

practice-oriented differential

equatlon of the governor

Inserting

her2

from (1 1.2-3) the differential equation of the closed control loop, start

time

T,,

reset time

reads

Here the

~atural frequency has

damping term

1i'(2STT,),

that

inverse to the

transient proportional band

6,.

11.2.4.

Other

time

parameters,

tuning

Start up time of penstock: Because of its inertia, the

now

assumed inelastic water

column in an assumed stiff penstock'of

lellgth

needs

period

T,,

to be speeded

under the head

to its velocity

c,,

due to the rated load. Accounting also for the speed

linked head drop by the pipe loss, assumed to

(c2/2, .then

T,,

follows from the energy

by (artanh

tanh-

T,,

{2/[gH(1

n]}

'I2

artanh {c,[(l

0/(2gH)]1'2}.

(1 1.2- 13)

the usual case ~,/(2gK)'~~

1, this becomes

T,,

cr Ll(g

HI.

11.

Opening time of distributor,

To:

Obviously this has to last longer than the start up time

the penstock. Hence

7;,

To.

111.

Reflection time, closing time: Any shut down of a turbine on a penstock causes water

hammer, propagating with velocity

along the penstock, length L. At the latter's upper

the wave is negatively reflected and returns to the machine after the reflection time

has elapsed

~ccording to Cap. 8.3, decreasing the pipe velocity within the period

by Ac, i.e. by

closing the distributor, generates a pressure rise at the lower pipe end

The closing rate of the distributor is usually decelerated in a stepwise manner towards the

closed position. This has to be done as described in Cap.

8.3

with respect to reflected

water hammer waves, the rotary inertia of the set, and the characteristics of the hydro

turbomachine in the regime concerned, as a function of distributor opening and speed.

fairly dimensioned timing of the closure is signified by the fact, that the maximum

pressure increase, set before and mentioned in Cap. 8.3 is never surpassed but used as

often as possible.

Usually the relative pressure rise due to water hammer is prescribed by

H/H

0,l to

;

for H

1000 m to 10 m. To keep the pipe loss under rated load below

of the head,

the rated pipe speed is chosen in the range

0,l (2gH)'I2. Making the velocity change

in (1

1.2-

16) equal to this

c,,

then

example

I-i

500

1000 m/s with the result AH/H

2,02 demonstrates that at

least in the relevant high head range, a closure within the reflection time would yield

unacceptably high water hammer pressure surges. Hence in high head plants, the time

may be considered as the lowest limit for the closing time

T,.

is known that any closure extending beyond

benefits from the then occurring

attenuation of pressure surge by the negative water hammer waves reflected at the upper

end

of the pipe. Strictly speaking this hdds only for the period

after the time elapsed

T,.

The whole may be understood as

hint that any estimate of the closing time does not

negate the inclusion of

water hammer calculation.

Generally any waterhammer destabilizes the loop of the governor in so far as it creates

pressure

rise

upstream of

closing valve and hence counteracts the intended reduction of flow. Problems of

Eovernor stability together wit11 water hammer are dealt with in the following Cap.

11.3.

Hence any closing time

that is predicted, from the set's moment of inertia

its full load torque

M,,,

and a desirable limit of overspeed

do,

e.g. at short circuit, by application of the equation of

motion

/1(1>0,'(~

1.2.qo

rcquires

;III

cnipiric;~l cnrrcctio~i frlctnr

Thc

similarity requircs

MI,,

(1)'

D'.

dto

(0.

hssu

and

ht:

const;lnt, thc ;~horc yiclds

D5ar.

This rcflects~thc known fact. that

[he

regu,w

"?%

moment of incrtia incrcascs with thc spccd

IV. Slar-t up time of set: Imagine the set with

moment of illcrtia

is to be Speeded

at its rated torque

M,,,

to the rated speed

Hence the start up time of the set

ole

that in any formula with

the effect of added water mass should be accounted

but usually is not. The start

time

of the set should exceed the start up time

the

penstock after

1.2-

J),

according to

To develop the rated torque at start

the opening time of distributor

has to fall short of the start

time of the set according

T,.

The above can be reconciled with

T,,

under

T,,

11.2.5.

Special regulating devices

Kaplnn

turbines: Here usually the control loop

the distributor is connected

parallel to the control loop of the runner (Figs. 11.2.7 and

8).

design with both the

control loogs in series (Fig. 11.2.12), but also different regulating times of the loops

favours a cam-off operation (Cap. 10.5). Both the loops, are connected by a cam (see

Fig. 11.2.12). Sometimes to reduce swell waves in navigable rivers a swell-reducing

cam

is used in case of sudden load rejection (Cap. 3.1).

To avoid

tile

consequences of reversed water hammer after water column separation,

KTs

are usually equipped with an aeration valve on the head cover, operated by the gate

ring

in the case of quick shut down (see also Cap. 8.2).

11.

Francis

turbines: Here sometimes with sets on long penstocks a by-pass outlet is uscd

to reduce water hammer, see Cap. 8.3. Aside the bep also ventilation is used.

111.

Pelron

turbines: Here a sudden load drop is encountered by

deflection of the jet by

means of a jet presser or cutter. The closed control loops of the jet deflector and needle

valve may

be connected

parallel, preferably, (Fig. 11.2.13) or in series (to date rarely

built). Both the loops are connected by a cam. This provides for

ready position of jet

deflector under steady state

per at ion

close to the outer edge

the jet. See Cap. 8.3 [1.50],

[11.2]. Quickly actuating the jet deflector allows dismissal of the cam (Cap. 5.3).

11.3.

Stabi!ity of control with respect to water hammer,

autoregulation of grid,

and

turbine characteristic

11.3.1.

Introduction

the

problem

Let us consider

set, that supplies a grid by itself. This set is controlled either by

govcrncr. It is equipped with a single regulated reaction turbine, i.e., a

or a

of the propeller type. The following characteristics of the turbine are known as

functions of

the

gate opening (for which. the servolnotor position

is taken) and the

rotary speed

,I:

a) Internal efficiency

q(m,

n). b) Unit flow

(I,,

(m,

n).

and n allow easy

inclusion of head oscillations.

The turbine is supplied from a long penstock with elastic response (water hammer), which

may

be single-staged or double-staged, the upper end of which

fed from

large vessel

tank or reservoir) at constant pressure. The turbine is attached to a generator that

an electric grid with a known auto regulating load characteristic due to machine

tools, pumps and blowers, or resistors,

[10.57].

Here the problem arises with respect to dynamic stability of the closed control loop

(consisting of the governor and the controlled system turbine, penstock, grid) how to set

the

reset time

?;:

of a

governor or the rate time

of a PD governor, and the start up

time

of the set, when the characteristics of turbine and grid, the proportional band

6,,

the temporary speed droop

are known or set, a certain damping coefficient is desired.

and

the natural period of the system's oscillation should not coincide with the reflection

t&e

the pipe.

11.3.2. Assurnptions

The natural frequency of

closed control loop, excited by disturbances from the grid, the

pipe system or a change of gate position or speed, is considered at a time elapsed that is

multiple of the pipe reflection time (11.2-13). The amplitudes of all the deviations

considered are infinitesimally small compared with their reference values. All distur-

bances are nondimensional, the time constants real times.

11.3.3. Dynamically equivalent types of governors

First a proportional integral governor with acceleration feed back (PD governor) is

considered, whose measuring element is of the tacho-accelerometric type. According to

Cap.

11.2.3.1 the figures used for the deviation of speed, An, servomotor piston, Anl, and

valve piston, As, respectively, are

which

is the stroke of servomotor piston,

s,,,

that of the valve,

n,,

the rated speed.

According to (1 1.2-6) the valve deviation

is induced by a speed deviation

and its

acceleration

Expressing the valve deviation s by the speed

of the servomotor piston,

according to (1

.2-2), the differential equation of the governor, proportional band (per-

manent speed droop)

a,,

reads

which

the regulating (closing) time, and

the rate (acceleration) time, according

Cap. 11.2.3.1.

Next the simplified

differential

equation for a proportional integral

(PI)

governor (servo-

motor with elastic retarding feedback), according to (1 1.2- 11) is considered. Rearranged

b,T~;-ln

?;:x

(11.3-5)

which Tis the reset (isostatic) time and

the transient proportional band (temporary

speed droop) (see Fig.

11.2.3). Obviously both the governors have a similar dynamic

khaviour when the product of proportional band and regulating time

vanishes

against the reset time

?;:.

According to a proposal of

Fabritz

[11.2], the equivalence of

both the governors exists when the corresponding

coefficients in both relations are set

equal, according to

and

JPT,=6,T.

(11.3-6)

Note that thc rcguI:~tin~ time

here is duc to

tl~e.PD

governor.

11.3.4.

Ishe

controlled

systcrn

(turbine,

grid,

pcrlstock)

1.3.4.1.

Gencral

remarks

the electric grid

With rcfercr~cc to Cap. 11.2.1.3, the grid-induced generator torque

(rated value

M~),

vs speed

(in rps) reads as follows

in which

for a load due to machine tools,

1 for a load due to resistors (under

the assumption of constant voltage at the generator terminals)

and

2 for a load due

to blowers and impeller pumps 111.23; 11.571.

11.3.4.2.

Linkage

turbinc characteristic

and

grid

With

(si,

as the unit discharge and

rl(m,

as the shaft efficiency, both depending

on gate position

rtr

and speed n the torque of the turbi~~e, head

diameter

reads

During unsteady operation, the equation of motion requires

which

indicates deviation from steady state, and

the moment of inertia of the set.

Dividing

!his relation by the rated torque

PN/(27ii~lv), rated output,

iz,

rated

speed, using

the identity (l/iz,) dnldt

(lln,) d(A~t)/dt

and accounting for the start

time of the set according to

the

relntio~~

1.3

-9)

reads

Introducing the load degree

MT/MN, accounting for (1 1.3-7) and taking the incre-

ment

as infinitesimally small then

Em~loying the nondimensional infinitesimally small head deviation h

HIII,

rated

head, after (1 1.3-7) with dm

Am,

An, dH

and introducing the figures,

KQ~

Oziv!Qi

1) (aQi ~lan)~,

KQrn

(n1wlQI 1) (aQl llam)n,

(11.3-13)

Kqn

(~,v/)I) (all!Wrn,

Kqm

(n1,"Ill) (dllIam)n,

(1 1.3- 14)

the term

~CI,/ICI,

(1 1.3- 11) becomes

J~~TI~~~,

A[(K,rn

KQJ

(K,,

KQn

3h/2].

(11.3-15)

The11 using the self control parameter,

K,,

KQn,

(1 1.3-

16)

and accounting for

1.3- 13, (1 1.3- 15),

and

relation (1 1.3-7), the equation

motion

the set, with respect to turbine characteristic and grid load, takes the form