Nordic Grid - FNR Frequency Containment · 2018-01-31 · Assignment no.: 5157038 Document no.: 01...

Statnett SF

Nordic Grid - FNR Frequency

Containment

Generating Equipment Performance - Review

Report

Assignment no.: 5157038 Document no.: 01 Version: R-EXT

2016-03-31

Assignment no.: 5157038 Document no.: 01 Version: R2 R-EXT

Nordic Grid - FNR Frequency Containment | Generating Equipment Performance - Review

c:\users\anwe\downloads\rep_nordic grid - fnr freq-rext.docx 2016-03-07 | Page 2 of 68

Client: Statnett SF

Client’s Contact Person:

Consultant: Norconsult AS, Nedre Fritzøegate 2, NO-3264 Larvik

Assignment Manager: Terje Ellefsrød

Technical Advisor: Terje Ellefsrød

Other Key Personnel: Einar Kobro, Hans Åke Glawing

R2

R02 2016-03-07 Reviosed after comments from workgroup

Terje Ellefsrød

Version Date Description Prepared by Checked by Approved by

This document has been prepared by Norconsult AS as a part of the assignment identified in the document. Intellectual property

rights to this document belongs to Norconsult AS. This document may only be used for the purpose stated in the contract

between Norconsult AS and the client, and may not be copied or made available by other means or to a greater extent than the

intended purpose requires.




Summary

The report identifies what type of hydro turbines and distributions between different types, number of

units, operating heads and accumulated power associated to the Nordic Grid, limited to units > 10MW.

Essential performance characteristics of the common turbine types are discussed including dead

bands and backlash issues. Many of these parameters are not commonly discussed in the industry

literature and must be considered to be presented as average expected values. Many are however

supported by tests by Norconsult and others.

The conclusion is that power dead band for the machine park overall can be expected to be about

0.5% weighed on MW installed but will have substantial variations from unit type to unit type.

Because Pelton turbines in the system are employed with stability neutral governors (governors with a

structure that retains an almost constant phase and gain margin in isolated operation regardless of

droop setting) and have very moderate deadband and backlash, these turbines will most likely – and

according to test results - dominate in the corrective action related to 60sec swing around 30mHz

amplitude. It appears quite likely that this mentioned pelton turbine control action is oscillating with

units with backlash and time delays and short integral time that renders the response to be too late

and too aggressively. Governor parameters tuning to lower the gain at the subject frequency – to not

exceed the dead band - would reduce the tendency to self- oscillate at this particular frequency but the

phenomena would then probably shift to a lower frequency with higher amplitude. If HPC (parallel

structure block diagram) with moderate transient gain and short integral time is employed to avoid

“penalty” from dead band, Phase shifts will be substantial and most likely result in oscillating

frequency.

Influence from dead band and traditional governor tuning for HPC and Hyx governors is discussed for

different droops and test amplitudes. Test amplitude <0.1Hz will be problematic.

Discussion of BERTA test amplitude and bandwidth correlation to the dead bands is included.

Finally, some suggestions to what may be done to improve – or avoid further deterioration – of the

control performance has been made.




Contents

Introduction 8 1

Database 10 2

Turbines tested in FCR program 15 3

Francis turbines 16 4

Guide vane rotation 16 4.1

Friction in guide vane stem journals 16 4.1.1

Sub-classification of Francis Turbines 24 4.1.2

Francis turbines with conventional regulating ring 24 4.2

Francis turbines without pressure regulating 4.2.1

valves 24

Francis turbines with pressure regulating valve 25 4.2.2

Individual Guide Vane Control 26 4.3

Time delays 26 4.3.1

Improved control accuracy 27 4.3.2

Medium size Francis turbines 125MW>Pn>10MW 27 4.4

Kaplan Turbines 28 5

Kaplan Turbines guide vanes 29 5.1

Runner Blade Control 31 5.2

Pelton Turbines 39 6

Servo Valve Pressure Gain 41 7

Solutions to Dead Band 48 8

Power Feedback 48 8.1.1

Dead band Compensation 48 8.1.2

Discussion 50 9

Mechanical Backlash and lost motion for specific 9.1

groups 50

Overall totalized dead bands 51 9.2

Governor performance and tuning issues 52 9.3

Practical implication of deadband 53 9.4

Bandwidths – participation 56 9.5

Verification of small signal response for Pelton 9.5.1

turbines 63




Amplitude of test frequency 64 9.6

Likelihood of conformance with requirement 9.7

characteristics 64

Improvements 65 9.8

Address reduced basic performance of 9.8.1

equipment over time 65

Improvement – control philosophy 66 9.8.2

Improvements – testing for certification 66 9.8.3

References 67 10




Error! No filename specified in document reference on page 1 Figure 1 Distribution of turbine capacity versus total MW and total unit count ..................................... 10 Figure 2 Mix of unit type in the Nordic System (% of installed MW in units >10MW) ........................... 11 Figure 3 Distribution of Francis turbine capacity versus total Francis MW and total Francis unit count11 Figure 4 He (Design Head) distribution for Francis Turbines in the Nordic Grid ................................... 12 Figure 5 Distribution of Pelton turbine capacity versus total Pelton MW and total Pelton unit count .... 13 Figure 6 Distribution of Francis turbine MW per country ....................................................................... 13 Figure 7 Distribution of Kaplan turbine MW per country ....................................................................... 14 Figure 8 HPC 640 block diagram as applied in Dinorwig .................. Fel! Bokmärket är inte definierat. Figure 9 Control Loop applied in Dinorwig Verification Model–– ...... Fel! Bokmärket är inte definierat. Figure 10 Amplitude and Phase diagram from test of HPC 640 compared to modelling Fel! Bokmärket

är inte definierat. Figure 11 Block diagram for the predominant types of Norwegian governors (T f=0.1Td) Fel! Bokmärket

är inte definierat. Figure 12 From Hymatek homepage ................................................. Fel! Bokmärket är inte definierat. Figure 13 Kaplan Turbine Load rejection HY10 governor. Delay <0.15sec, runner and guide vanes

move simultaneously. ........................................................................ Fel! Bokmärket är inte definierat. Figure 14 Test result from 6GB4 governor controlling Kaplan turbine ................ Fel! Bokmärket är inte

definierat. Figure 15 Approximate distribution of different governors controlling Norwegian generators 2014 ... Fel!

Bokmärket är inte definierat. Figure 16 He 81 m 90MW – New bushings c.o.f 0.05, worn 0.20-0.30 ................................................ 17 Figure 17 He 400m Francis Turbine New Bushings c.o.f 0.11, worn state 0.22 ................................... 17 Figure 18 Guide Vane Force Indication H440m turbine, worn state (red) versus new state (blue). ..... 18 Figure 19 Indication of operating force, individually controlled guide vanes, turbine He 100m, 450MW

after replacement of journal bearing - GV 15 & 20 ............................................................................... 18 Figure 20 Indication of operating force, individually controlled guide vanes, turbine He 100m, 450MW

after 18months operation following journal bearing replacement GV 15 & 20 ...................................... 19 Figure 21 Cross Section He=500 m Francis turbine ............................................................................. 21 Figure 22 Cross Section He=150m Francis Turbine 2010 .................................................................... 21 Figure 23 Cross section of guide vane system with 28 guide vanes He 495m 2008 design ................ 22 Figure 24 Calculated influence on discharge dead band (specific Francis units) from GV stem twisting

c.o.f 0.15 ................................................................................................................................................ 23 Figure 25 Graphic representation of tabular presentation of Guide Vane Twisting .............................. 23 Figure 26 Example of guide vane mechanism with strong linkage rotation near closed position ......... 25 Figure 27 Example of typical high head guide vane control scheme with moderate linkage rotation... 26 Figure 28 Distribution of Kaplan Turbines versus number of Kaplan units and total Kaplan MW ........ 28 Figure 29 Distribution of Kaplan Turbines head versus number of Kaplan units and total Kaplan MW 29 Figure 30 KMW Kaplan 1985 (new measurement) - requires alternating GV servomotor force only at

near full discharge. 6% of force capacity to overcome friction. ............................................................. 30 Figure 31 LMZ Kaplan – GV servomotor force alternates across the full operating range.

Approximately 10% of servomotor capacity is required to overcome friction. ....................................... 30 Figure 32 New Kaplan 18m head GV operating force. Alternating force required for range <65% and

>85%. Friction is about 10% of servomotor force capacity. .................................................................. 31 Figure 33 Measured GV servomotor by William Forsstrøm, “Eksamensarbete 30hp” force 10% of

capacity to overcome friction, alternating force not required for normal operating range > 15 deg ...... 31 Figure 34 Operating force indication (Russian Kaplan 20m head turbine in Norwegian plant) friction

300kN of 1500kN = 20% - oil filled runner hub- backlash is not an issue for 70% and higher opening.

............................................................................................................................................................... 34 Figure 35 Nohab Kaplan 1965,33m head Friction 25% of servomotor capacity – oil filled runner,

approximately 1.5-2% lost motion is apparent from chart at positions above 6 deg.- .......................... 34 Figure 36 From "Eksamensarbete 30hp" – 2015 by William Forsström - Selsfors G1 He 22m

Friction requires 25% of runner servomotor capacity – oil free runner ........................................ 35 Figure 37 Kaplan with new runner (oil free) he 16m, friction requires 15% of the operating force. Lost

motion about 0.5% average................................................................................................................... 35




Figure 38 Kaplan Turbine MELK ø6.0m – 30 years operation conventional hub. Chart suggests 3%

lost motion ............................................................................................................................................. 36 Figure 39 Commissioning test from 1985 (KWM) ................................................................................. 36 Figure 40 Load rejection 1985 KMW Kaplan......................................................................................... 37 Figure 41 Force indication Kaplan Turbine Runner blades (bronze bushing oil filled) ......................... 37 Figure 42 Cross section of Pelton injector used from the early 60’s ..................................................... 39 Figure 43 Servo Valve Pressure Gain ................................................................................................... 42 Figure 44 Servo Valve Characteristic at Dinorwig ................................................................................. 44 Figure 45 Probable average power dead bands for hydro units in Nordic Grid .................................... 51 Figure 46 Accumulated probable dead band for total number of installed Hydro units in Nordic Grid,

distribution per unit installed .................................................................................................................. 52 Figure 47 Correlation between amplitude and steady state response for typical Norwegian Hyx and

Vattenfall HPC tuning Droop 2% This chart is amplitude independent (no dead bands accounted for)

............................................................................................................................................................... 54 Figure 48 Correlation between amplitude and steady state response for typical Norwegian Hyx and


............................................................................................................................................................... 55 Figure 49 Correlation between amplitude and steady state response for typical Norwegian Hyx and


............................................................................................................................................................... 55 Figure 50 Proposed Performance requirement ..................................................................................... 56 Figure 51 Influence on response vs ω from governor (Hyx with standard settings, Droop 2%)

connected to turbines with different position dead bands) compared to response – for frequency

amplitude 0.1Hz ..................................................................................................................................... 57 Figure 52 Influence on response vs ω from governor (Hyx with standard settings, Droop 2%)


amplitude 0.05Hz ................................................................................................................................... 57 Figure 53 Influence on response vs ω from governor (Hyx with standard settings, Droop 2%)


amplitude 0.03Hz ................................................................................................................................... 58 Figure 54 Influence on response vs ω from governor (Vattenfall HPC standard settings, Droop 2%)


amplitude 0.1Hz ..................................................................................................................................... 58 Figure 55 Influence on response vs ω from governor (Vattenfall HPC standard settings, Droop 2%)












amplitude 0.1Hz ..................................................................................................................................... 61 Figure 61 Influence on response vs ω from governor (Vattenfall HPC standard settings, Droop 10%)


amplitude 0.05Hz ................................................................................................................................... 62




Figure 62 Influence on response vs ω from governor (Vattenfall HPC standard settings, Droop 10%)


amplitude 0.03Hz ................................................................................................................................... 62




Introduction 1

Hydropower units provide a dominating portion of Frequency Containment Reserves [FCR] in the

Nordic Grid. A series of frequency sweep tests of 12-14 units carried out by producers and Gothia

Power at various units indicates quite wide spread in response from unit to unit.

To better understand FCR-N (Frequency Containment Reserve,Normal ) capability in the Nordic Grid,

Norconsult has been retained to perform a desktop analysis of characteristic data of hydropower units

in the system.

The first task has been to update unit database Norconsult has been keeping for the Norwegian

hydropower units to cater for changes (upgrades, decommissioned units, and new units) during the

period from last update of the database (2000)

In addition, a database of Swedish units has been created based on Kuhlin’ s plant database (Kuhlin,

2015) of Swedish hydro plants, broken down to unit level by detailed input from Norconsult experts in

Sweden and the survey database from Nordic Grid (Data, 2015).

Finnish units have been added based on survey data (Data, 2015) and available information posted by

the major Finnish owners of hydro plants (Kemijoki, PVO, and Fortum). Overview of types of

governing systems have been offered by Fortum Oyj, ans PVO.

1.1.1.1 Control Features of Hydro Turbines

The review presented here was initiated as a response to temporary conclusions by the FCR Project team presented Sep 22 2015, where dead bands (backlash) of 0.003 to 0.006pu were introduced to non-linear simulation models to match observed oscillation. Power oscillations have assumed to be the root cause of the oscillations. The power oscillations is initially assumed to come from the load variations. This is now studied in a separate “Imbalance study” project. Tests performed indicate that not all units participating in frequency control damp these oscillations properly.

.

To better understand if specific unit characteristic inflicts higher or lower susceptibility to dead bands

and dead times, this data collection and data analysis starts with a broad sorting of plants in Finland,

Norway and Sweden into the typical unit type (Francis, Pelton, Kaplan), capacity [MW] and operating

head (for Francis turbines.

Review of the mechanical design of the significant types of turbines (Pelton, Francis and Kaplan)

illustrates major differencies regarding probable dead bands between governor setpoint change and

obtained MW change.

This review suggests that high head Francis turbines such as what represents 40% of installed

Francis capacity (MW) or 25% of the total hydro capacity will probably be associated with mechanical

/hydraulic dead band 0.30% to 0.80% depending on many factors such as basic design and wear.).

According to this study, Medium and low head Francis turbines will have less mechanical / hydraulic

band, from 0.1% to 0.4% pending the wear and design features.

Kaplan turbines, the second most dominating type of turbines in the system from a MW standpoint

(23% of installed hydro capacity) will according the design features identified in this study be

hampered with a mechanical backlash dead band related to the runner blade control. Runner blade

positioning factors strongly into reaching desired power setpoint at medium and high discharges.




Magnitudes of runner blade positioning dead bands have been evaluated based on common hub

designs and based on this review often reach 1%. For older designs with control valve located in the

hub the dead band will be higher. Guide vane stem twisting is in most cases an insignificant

contributor to dead band on Kaplan units.




Database 2

The Norconsult database of hydropower units connected to the Nordic System contains a total of

45900MW of hydro turbines >10MW for Finland, Norway and Sweden. This amounts to a total of

about 964 turbines. The database contains also small hydro units <10MW<1MW for Norway. Based

on (Kuhlin, 2015) and Norconsult database, Approximately 5000MW is installed in hydro units

<10MW. Such units are rarely equipped with a droop type governor and therefore disregarded in this

review.

Figure 1 Distribution of turbine capacity versus total MW and total unit count

From this chart, it’s evident that 35% of the installed capacity is concentrated in 10% of the units, or

<100 units.




Figure 2 Mix of unit type in the Nordic System (% of installed MW in units >10MW)

Figure 3 Distribution of Francis turbine capacity versus total Francis MW and total Francis unit count




Figure 4 He (Design Head) distribution for Francis Turbines in the Nordic Grid

Figure 5 Distribution of Kaplan turbine capacity versus total Kaplan MW and total Kaplan unit count




Figure 6 Distribution of Pelton turbine capacity versus total Pelton MW and total Pelton unit count

Figure 7 Distribution of Francis turbine MW per country




Figure 8 Distribution of Kaplan turbine MW per country.

Figure 2 and Figure 4 show that high head Francis turbines makes up 0.6 x 0.4= 24% of the hydro

capacity in the Nordic countries and Kaplan turbines 23%, total 47%. This is a significant observation

since the dead bands for these types of units as discussed in Chapter 4 and 5 and summarized

derived throughout the discussions and presented in 9.2 will render such units providing insignificant

control input for the amplitude 0.03Hz at 60s period frequency illustrated in Figure 52 to Figure 63

Pelton turbines are exclusively installed in Norway

Since the distribution of units is spread out among a wide range of unit capacity ranges, many different

technologies are applied. When also taking into account that the three dominating unit types (Francis,

Kaplan and Pelton) are in use, it’s likely to find unique issues related to frequency control, partially

because of how the equipment is constructed and partially because of features of the water conduits

they are associated with.




Turbines tested in FCR program 3

A series of tests with “Hardware in the loop” were carried out by Gothia power (Power, 2014). These

tests involves disconnecting the frequency measurement input to the governor and replacing it with a

synthetic frequency source with variable amplitude and where oscillations at any frequency and

amplitude can be overlaid the common 50Hz signal. Response from the unit is derived by measuring

the power fed to the grid. The measured power will therefore include inertial effect from the

generator’s speed change as response to actual power grid frequency fluctuations at the time of

measurement. It can be expected that this error grows with lower frequency oscillation amplitude. At

frequency ampliutudes mostly applied, 0.10Hz and above, such effect is not significant.

Name Turbine Type

Governor Type Guide vane control Head [m] Power [MW]

S1 Kaplan Regulating ring 20 24

S2 G1 Kaplan “Standard Vattenfall”****

Regulating ring

S3 Kaplan Deriaz

“Standard Vattenfall”****

Individual*** 60 75

S4 G1 Francis “Standard Vattenfall”****

Individual*** 135 170

S5 Francis “Standard Vattenfall”****

Regulating ring 86 150

F1 Kaplan Vertical

Kejo Regulating ring 21 61

F2 Kaplan Vertical

KTR-2102 Regulating ring 33.5 49

F3 Kaplan Vertical

Regulating ring 15 20

N1 Pelton 5 Jet Hymatek1x Individual* 670 80

N2 Pelton 4 Jet Voith 6GB94 Individual* 810 92

N3 Pelton 6 Jet Kværner TC210 Individual* 850 280

N4 Pelton 5 jet Hymatek1x Individual* 1160 280

N5 Francis Hymatek1x Regulating ring 540 92

N6 Francis Andritz 1703 Regulating ring 287 120

*individual injector control, mechanical pilot **individual injector control, electronic***Fieldbus control,

**** Standard Vattenfall is similar to standard Swedish.

Kaplan, Francis and multi jet pelton turbine types have been tested. S3 is a typical since this is the

only Deriaz turbine in the system.




Francis turbines 4

Francis turbines power 60% of the installed Nordic hydropower capacity.

Common head range for Francis turbines is 50 to 600m, the distribution according to unit count and

MW accumulated is presented on Figure 4. The 50 percentile point (average weighed on Unit

capacity) is 230m, based on unit count the average head is 150m.

The 10% (about 45turbines) highest capacity Francis turbines Pe>125MW represents 35% of installed

Francis MW capacity, making it potentially a stereotype community of units to be reviewed.

Guide vane rotation 4.1

Flow control and therefore power control for Francis turbines is by rotating the guide vanes by twisting

the guide vane stems.

For low specific speed high head Francis turbines, the guide vane needs to be rotated around 10 -15

degrees from speed – no load to full rated load. For Francis turbine with high specific speed (low

operating head, around 60m for medium and large size units) the guide vanes must be twisted about

25 degrees from speed no load to rated power. Values can be interpolated.

The operating lever that in turn is connected to the linkage and the operating lever are attached to the

top of the stem. This stem will twist to transfer the torque.

Friction in guide vane stem journals 4.1.1

Without getting into the factors that determines the stem diameter, it is clear that from a regulating

accuracy point of view, the shaft will have to twist to overcome friction that occurs at the opposite end

of where the regulating arm is attached to the link (and regulating ring). Friction will always oppose the

motion and hence the twisting is not affected by changes absolute torque direction, only the difference

in torque.

Examples of friction in the guide vane systems when new and after years of operation are not

commonly available in the literature. Therefore, Norconsult in-house test data for operating pressure in

servomotors during operation or test data made available to Norconsult have been used based on.

Four examples:

Figure 9 Francis Unit He 81m, 90 MW (increase in friction 4x – 6x after 30 years

Figure 10 Francis Unit He 400m, 125MW (increase in friction 2x after 30 year

Figure 11 Francis Unit He 500m 320 MW (increase in friction 3 – 3.5 x after 25 years

Figure 12 Francis Unit He 100m 450MW (increase 1.8 x after 1.5 years)

Each of the figures charts the force that is derived from measured oil pressure at closing side and

opening side of the guide vane servomotors as a function of the position of the guide vane. The log

can be taken manually while moving the guide vanes slowly or automatically with a logging system

recording at frequency about 10Hz or higher opening pressure, closing pressure and servomotor

position. All measurements are made while unit is in service connected to the grid. If there were no




friction, force when guide vanes are moving towards open would be identical to force measured when

guide vanes are closing. Different force at the same position when guides vanes are moved in

alternate directions is due to friction force.

The friction is acting opposite to the direction of motion. Therefore, the difference between the force

when moving towards open and the force when moving closed is 2 x the friction force.

Figure 9 He 81 m 90MW – New bushings c.o.f 0.05, worn 0.20-0.30

Figure 10 He 400m Francis Turbine New Bushings c.o.f 0.11, worn state 0.22




Figure 11 Guide Vane Force Indication H440m turbine, worn state (red) versus new state (blue).

Figure 12 Indication of operating force, individually controlled guide vanes, turbine He 100m, 450MW after replacement of journal bearing - GV 15 & 20




Figure 13 Indication of operating force, individually controlled guide vanes, turbine He 100m, 450MW after 18months operation following journal bearing replacement GV 15 & 20

To calculate the absolute coefficient of friction, the guide vane lever, arm, regulating ring and

servomotor configuration must be taken into account.

Further, the friction associated to the regulating ring and servomotor should be deducted. This friction

is a function of th regulating ring’s weight and bearing arrangement. The weight of the regulating ring

is generally a proportional to the servomotor force capacity. The coefficient of friction (c.o.f) can be

assumed similar to the guide van stems. Hence, the friction that is associated to the regulating ring

corresponds to a certain percentage of the servomotor force capacity. Based on this approximation, it

has been established that regulating ring friction corresponds to 0.75% of servomotor force capacity.

Single servomotors controlling the guide regulating ring and twin servomotors with one servomotor

expanding and one withtracting when the regulating ring moves, result some times in imbalanced

force pairs. This force imbalance must also be taken into account since it’s influence will skew the

apparent guide vane stem friction.

The radial force in the journals of the guide vanes caused by water factors into the calculation of

friction torque, (NTNU, 2006), Figure 14. The factors Ω and α denotes empirical factors pending the

specific speed and angle of the guide vane position respectively to make up the specific radial force.

The empirical data can be derived from evaluation of pressure in the vanless space from model tests,

from prototype tests or from CFD calculations. For calculations in this report pressure in vaneless

space from model tests for one turbine of medium head (150m) extrapolated to higher and material

from lower heads around guide vane position fro b.e.p has been used and extrapolated.




Figure 14 Calculation of friction torque for guide vanes (NTNU, 2006)

For the calculations, the guide vane ring pitch diameter, D0 the height of the guide vanes (B0), the

stem diameter (d) and number of guide vanes have been accounted for according to the specific

turbines design drawings.

Also of importance when calculating the dead band is the length of the guide vane stem and the angle

guides vanes are turned from speed no load to full load. This is also an empirical correlation,

presented on page 17 (NTNU, 2006).

By taking such measurements from observations made on 4 Francis turbines when new and after

operating for 1.5 – 30 years it has been possible to obtain a better idea of the guide vane stem friction

coefficients and to a certain extent the development of the friction with time.

Friction coefficients are expected to range from 0.06 for new greaseless bushings to 0.25 for worn

systems. This is well within published values from manufacturers and dedicated friction measurements

to mechanical systems - old and new - that Norconsult do.

It is possible to break down servomotor force measurements to derive coefficient of friction, albeit with

some level of uncertainty margin. The dominant uncertainty According to the measurement data and

calculation according The lifetime span for friction to increase appears to be q bit shorter than what is

commonly used for overhaul interval but the statistically available data is insufficient for reliable

conclusions. An average coefficient 0.15 for the overall population of Francis turbines with time from

overhaul spanning from 1 to 40years seems like a sensible but slightly optimistic value.




Figure 15 Cross Section He=500 m Francis turbine

Figure 16 Cross Section He=150m Francis Turbine 2010




Figure 17 Cross section of guide vane system with 28 guide vanes He 495m 2008 design

Among the group of turbines (Large Capacity Francis Turbines) making up 35% of the overall

dominant Francis turbine population, 55% of the capacity originates from the Norwegian high head

Francis units with H>300m.

With “average” coefficient of friction assumed to be 0.15, the stem twisting invoked dead band will

most likely be affected by the design head as shown in Figure 18 and Figure 19.




Figure 18 Calculated influence on discharge dead band (specific Francis units) from GV stem twisting c.o.f 0.15

Figure 19 Graphic representation of tabular presentation of Guide Vane Twisting

This review implies that dead band from twisting of the stems is quite pronounced with high head

Francis turbines with all units reviewed with 400m and higher head yielding between 0.2 and 0.3%

dead band from this source while units with 120m and lower head yields <0.10% dead band from this

source.

Figure 4 show that 27% of the Francis turbine capacity in the Nordic grid originates from units with

head over 400m, 12% from units with head above 500m.

A theoretical relative deflection of about double magnitude compared to comparable units from 1980’s

and earlier appears for designs 2008 and later due to lower stiffness in the guide vane stem relative to

the friction torque.

Pnom [MW] Head [m] Installed Yr Dead Band ±[%]

50 46 1988 0.08

90 81 1983 0.07

34 120 1981 0.10

35 150 2010 0.47

35 157 2008 0.10

125 400 1965 0.22

320 460 1989 0.26

57 495 2008 0.47

55 500 1973 0.25

190 680 2015 0.42




Sub-classification of Francis Turbines 4.1.2

The population of Francis turbines above 125MW represents 35% of the Francis turbine capacity and

represents potentially stereotype group, with two distinct classes of units:

Medium head 60-170m large units in Sweden (about 3900MW)

High head high capacity in Norway (units >approximately 300m head) (about 5000MW)

Two of medium head turbines have been tested in Sweden. S5 G1 and S4 G1

N6 (also a tested unit) in Norway is near the classification with head and output that is marginally

lower but with technical design features that matches many of the units inside the classification.

Francis turbines with conventional regulating ring 4.2

A common class of Francis turbines features guide vanes (20-28psc) controlled by 1 or more

servomotors rotating a regulating ring that in turn is connected to guide vane stems by individual

linkages to arms on the guide vane stems.

Beside discharge capacity and head, and type of guide vane control system, there are two other

classifications of Francis turbines; with and without pressure regulating valves.

Francis turbines without pressure regulating valves 4.2.1

The majority of medium and low head Francis turbines have no pressure regulating valve. Within the

class discussed here, Francis turbines > approximately 125MW, 85% or about 8000MW has no

pressure regulating valve (Norconsult, 2015).

For turbines without pressure regulating valve, the guide vane linkage geometry is typically arranged

with a strong opening tendency near closed position. There are various reasons for this.

Abrupt closing off of the flow near zero flow condition may result in waterhammer. By

arranging linkages and arms with strong rotation tendency of the link near closed position, the

rate of changing flow at a given motion of the servomotor can be reduced by as much as

factor 3 compared to flow change around 50-70% opening, , see Figure 20.

The linkage geometry above also increases the available torque that can be transferred near

closed position for a given servomotor capacity, albeit at slightly longer total servomotor stroke

than would otherwise be necessary

In a scenario with loss of oil, theoretically the guide vanes will not slam totally shut but remain

slightly open, avoiding high overspeed if disconnected from the grid while avoiding high

waterhammer as would potentially be the case if guide vanes were self-closing also near

closed position.

Generally, these types of turbines will for moderate wear rates and moderate friction not require

alternating force from the guide vane servomotors in the normal operating range. This will reduce the

impact from backlash.

However, if c.o.f increases to more than 0.15-0.20 impact from backlash may become an issue for

this type of turbine according to common layout principles for the guide vanes.




Figure 20 Example of guide vane mechanism with strong linkage rotation near closed position

Francis turbines with pressure regulating valve 4.2.2

Among the larger capacity high head Francis turbines in Norway in the category discussed here, about

1000MW (12% of the segment’s population) includes or was originally designed with a pressure relief

valve to allow guide vanes to close fast. This reduces transient overspeed and – pressure for large

load throw off. The pressure relief valve will not affect optimal governor tuning for small signal stability.

There is, however, a tendency for the guide vanes for turbines with pressure relief valves to be

balanced closely around neutral water torque for wide operating ranges, see Figure 10 and.Figure 11

The main rational for different balancing of the guide vanes in these scenarios with pressure relief

valve is improved linearity between guide vane angle ( and water discharge) and servomotor positon

since servomotor displaced oil is directly attracting pressure relief valve motion. Strong un-linearity

would tend to reduce the effectiveness of a pressure regulating valve. Minimizing un-linearity is thus

prioritized.

This requires smaller operating forces overall and makes alternating force requirement from the

servomotor more likely even with moderate friction.

Linkage backlash will be triggered if alternating force is required. Medium and large size high head

Francis turbines where pressure regulating valves are most common have lever motion in the range of

300mm in the active load range. With journal diametrical clearance in each end of the linkage “as new”

0.25mm, the lost motion can amount to (0.5/300)=±0.08% as new and ±0.16% in a worn state.




Figure 21 Example of typical high head guide vane control scheme with moderate linkage rotation

Individual Guide Vane Control 4.3

A relevant design feature of the high capacity Francis turbines as it relates to frequency control is

related to applications with individual guide vane control, without regulating ring. About 2000MW

Francis turbines in the system features individual guide vane controls without a regulating ring, all in

Sweden and all >120MW.

S4 (one among the tested turbines) features this type of control.

At S6 G5 (450MW) the OEM hydraulic system with mechanically linked multiple control valve system

is still in place. S6 G5 is also the newest of the individual control systems.

At all other sites, the mechanically linked system has been replaced with individual proportional valves

for each guide vane servomotor.

Time delays 4.3.1

Based on test results in S4 featuring modernized control systems for the guide vane servomotors, the

guide vane controls are associated with delays of about 300- 400 msec from sources in the digital

position controller system that is unique to this type of system.

Delays introduced by cycle time in the Fieldbus system have been reported by Waplans ( (Waplans,

2001) related to S3 conversion) to about 130ms. In addition there is a servo positioner cycle time of 30

ms. Time delays in the speed governor itself is not accounted for here.

Gothia Power modelling of S3 with baseline in recorded guide vane position equalized time constant

of 600msec (not modelled as time delay) appeared to match measurements well. However, this test

was applied with very high frequency oscillation amplitude (0.5Hz) and 20% droop and with more

realistic values time constant and time delays would most likely worsen.




It seems therefore likely based on the tests and published material that individually controlled guide

vane systems with modernized fieldbus control will be associated with abnormal time delays. Only S6

G5 remains in service with the original analogue mechanical hydraulic servo control.. All other

individual guide vane control systems will have high likelihood of serial bus related time delays.

Improved control accuracy 4.3.2

Important arguments for the individual guide vane control when introduced in 1965 included better

frequency control responses (Nohab, 1970). This improvement was in particular argued for the wing

servomotor scheme. Also contributing to smaller dead bands would be the uni-directional guide vane

torque where even worn joints would not result in backlash.

Finally, the regulating ring by itself has journals and supports that become worn. Elimination of the

regulating ring and linkages was also considered an improvement, in particular in the region of

operation where water hydraulic forces are close to neutral.

All wing servomotors have been replaced by conventional individual servomotors today.

Medium size Francis turbines 125MW>Pn>10MW 4.4

Medium size Francis turbines (<125MW approx.) in the Nordic System are always controlled by one or

more servomotors and a regulating ring.

There are units of this size range across the entire range of heads that are common for Francis

turbines.




Kaplan Turbines 5

The second most dominant group of units in the Nordic system based on accumulated MW are the

Kaplan turbines.

Vertical Kaplan turbines are generally applied for heads 10 – 45m and horizontal Kaplan bulb turbines

from 4 – 15m head.

The flow control and thus power control on Kaplan turbines combine moving guide vanes and runner

blades.

Individual control of guide vanes is applied for some large Kaplan bulb turbines. The contribution of

bulb turbines in the FCR-N picture is however insignificant.

35% of the overall Kaplan turbine capacity is installed in units > 50MW. The average head of Kaplan

turbines weighed on MW is 23m.

Figure 22 Distribution of Kaplan Turbines versus number of Kaplan units and total Kaplan MW




Figure 23 Distribution of Kaplan Turbines head versus number of Kaplan units and total Kaplan MW

Two Kaplan turbines in Sweden and one in Norway feature individual guide vane servomotors. This

applies to the largest Kaplan unit in the system, 180MW S7 in Sweden, 150 MW S8 and Norwegian

N7 110MW.

S7 and N7 uses mechanically control guide vane valves while S8 uses digital bus controlled individual

valves.

S8 U1 is in the process of being replaced by a new plant and it can thus be said that Kaplan turbines

with individually controlled guide vanes is not a significant population, representing less than3% of the

installed Kaplan capacity.

Kaplan Turbines guide vanes 5.1

The guide vanes are in a similar fashion as Francis turbines twisted to guide water onto the turbine.

The influence from twisting the stem is, however, much smaller than for Francis turbines because of

lower head, tendency of larger margins between normal operating torque and design torque for off

cam conditions because of Kaplan characteristics and shorter stem relatively seen. Dead band caused

by guide vanes stem twisting will be 0.01% to 0.03% in most cases.

Figure 24-Figure 27 illustrate guide vane force indication for 4 Kaplan turbines ranging in head from

13-20m and output 20-100MW. Of the 4 units, servomotors for 2 units can position the guide vanes

without alternating the force in the common 70%-80% opening range. The two other turbines will be

exposed to backlash in the linkage system. (positions is not exposed to backlash in the guide vane

control system




Figure 24 KMW Kaplan installed and tested 1985 (“As new” measurement) - requires alternating GV servomotor force only at near full discharge. 6% of force capacity to overcome friction.

Figure 25 LMZ Kaplan – GV servomotor force alternates across the full operating range. Approximately 10% of servomotor capacity is required to overcome friction.




Figure 26 New Kaplan 18m head GV operating force. Alternating force required for range <65% and >85%. Friction is about 10% of servomotor force capacity.

Figure 27 Measured GV servomotor force (Forsström, 2015) 10% of capacity to overcome friction, alternating force not required for normal operating range > 15 deg

Runner Blade Control 5.2

There are two main variations of the runner blade controls:

a) The main hydraulic regulating valve controlling flow ported installed external to the turbine,

porting oil through borings or pipes through the shaft centreline to the opening side and

closing side




b) A pilot servo valve controlled first stage in turn controlling the position of a valve internal to the

rotating shaft. This valve is distributing governor oil to either side of the piston. There is no

actual feedback of the blade position for this system, only the set point (position of the control

valve)

(Hansson, 1977) writes

“In order to improve the accessibility of the control valve of the runner servomotor this has been

moved to the combinator on top of the unit or in certain cases been placed outside the rotating

system. This has also brought about a higher precision in the governing and a more reliable

indication of the actual position of the runner blades.”

Gradually, upgrade projects retires the hub mounted control valves of the 60’s and earlier Kaplan turbines. The position dead band incurred from the internal valve is hard to estimate. But around 1.0% is a fair estimate. Very high accuracy of runner blade positioning has not commonly been a design objective, moderate oil consumption in the runner blade control system has been the highest priority. Figure 34 shows positon dead band is about 1º or 3%. runner blade position for a 1985 issue large Kaplan turbine

According to information received from a Finnish producer, their machine park includes 27 Kaplan units up to 50 MW

10 renovated high pressure units

11 low pressure units where runner blades main relay valve is located inside the rotating shaft

6 low pressure units, where main control valve is outside of the rotating shaft.

11units means 40% when based on unit count. From the producer data summary 4 of 17 Kaplan turbines employ internal control valve, corresponding to 26% of the installed capacity. The subject units were Tampella units installed in 1970-71. Survey data from another Finnish producer(19 Kaplan turbines, 970MW) shows that 10 units, 370MW or 40% of the turbine capacity uses control valve in the hub and no direct feedback of blade position. It would be a fair assumption that most Tampella units installed prior to 1970 have not been converted to oil – free runner hubs feature this type of runner blade control. Swedish data in this respect has not been available but it is a fair assumption that the situation is similar to Finland, with 30-40% of the installed Kaplan power with runner blade control without direct feedback. This type of mechanisms are gradually being replaced when Kaplan hubs are replaced. But it is a relatively slow development.




Figure 28 Kaplan hub internal parts, typical layout applicable for most units

Figure 29 to Figure 33 illustrates indication of operating force for 5 Kaplan turbine runner (hubs). 3 of

the hubs require alternating force from the servomotor.

Figure 34 shows the backlash reported in the commissioning report (KWM 1985)

Figure 35 shows load rejection for the same KMW Kaplan turbine (1985) where runner closing time

constant / delay is readily visible.




Figure 29 Operating force indication (Russian Kaplan 20m head turbine in Norwegian plant) friction 300kN of 1500kN = 20% - oil filled runner hub- backlash is not an issue for 70% and higher opening.

Figure 30 Nohab Kaplan 1965,33m head Friction 25% of servomotor capacity – oil filled runner, approximately 1.5-2% lost motion is apparent from chart at positions above 6 deg.-




Figure 31 Selsfors G1 He 22m Friction requires 25% of runner servomotor capacity – oil free runner (Forsström, 2015)

Figure 32 Kaplan with new runner (oil free) he 16m, friction requires 15% of the operating force. Lost motion about 0.5% average (Norconsult Archive)




Figure 33 Kaplan Turbine MELK ø6.0m – 30 years operation conventional hub. Black line represents 0 force. Step in position with limited force pick up around 0 force suggests 3% backlash lost motion (Erich Wurm, 2013)

Figure 34 Commissioning test from 1985 (KMW)




Figure 35 Load rejection 1985 KMW Kaplan

Figure 36 Force indication Kaplan Turbine Runner blades (bronze bushing oil filled)

The friction requires generally 15% to 30% of the capacity of the hydraulic piston.

An often used principle is that the friction well exceeds the waterhydraulic force and demands a pulling

force to close and pushing force to close. Or vice versa. In either case, all gaps in the two journals on




the linkage connecting the crosshead to the blade lever will have to be made up to effectively twist the

blade.

One out of six (16%) of tested units in our archive do, however, show that the design of the blades will

cause no dominant influence from hub linkage wear since torque direction to position blades do not

alter when blades are controlled in the generally most used range 60% and higher.

The travel of the piston is typically around 150mm for the average Kaplan hub. Expected typical as

new linkage clearance is around 0.25mm, in worn state around 0.5mm. The total lost motion from the

linkage alone will thus be from ±0.25 to ±0.5mm or 0.5/150.

The links are further tilted about 30-40 degrees relative to the motion of the piston, affecting the

relative lost motion by a factor 1.4 on the lower link.

Total expected lost motion from the linkage system is therefore from “new” (0.125*1.4+0.125) =

±0.35mm to common “worn” level ±0.25*1.4+0.25=±0.7mm.

For a typical system this will result in lost motion dead band 0.35%-0.7% in the runner blade

positioning for most Kaplan hubs.

Analysis of test results included in this report suggests that the lost motion in the hub is in reality

larger, maybe because hub wear in general is allowed to grow well above “common” assumption of

double clearance or/and that wear of crosshead guides and blade trunnions journals influences the

backlash also.

The effective influence on power dead band from a runner backlash will incur a reduced MW

response, not a total absence of response within the runner dead band since partial response will be

obtained from guide vane motion. But the total discharge and power response requires both guide

vane AND power to respond. Typical correlations around best efficiency point: a is guide vane pos, α

is rummer blade position and Q is flow, all values pu.

dQ/dα=1.0 –1.25

dQ/da=1.9-2.4

5.2.1.1 It means that the response to a linearized flow discharge request change will

respond to about 50% according to the guide vane backlash and the rest according

to runner backlash. At the same time, however, the efficiency will typical drop 0.4%-

0.6% per 1% off cam guide vane position and the power response will only be 25%.

The runner blade motion is responsible for the remaining 75% power. Statistical

significance

Results from 6 tested units are used to qualify general characteristics of the Kaplan population

regarding the units under one (not affected by backlash) or another (affected by backlash) category.

This is a so called Bernoulli distribution (Pishro-Nik, 2014). According to this theory,

p is1/6 and hence Var X=0.134 in other words there is a reasonable likelihood that between (0.16-

0.134= 0.026= 2.6%) and 0.16 + 0.134 = 0.294 (29.4%) of the Kaplan turbines will not be affected by

backlash. For the purpose of this presentation where we are presenting characteristic tendencies and

the general lack of availability of such test data, the uncertainty is large but the tendency is still clear.

Backlash in Kaplan hubs is a potentially significant issue.




Pelton Turbines 6

The Pelton turbines make up about 17% of the Nordic grid hydropower capacity. Pelton turbines in the

Nordic grid are exclusively found in Norway.

The Pelton turbine uses oil hydraulically controlled injector needle valves to control the water free jet

discharge onto the runner.

There are two common control systems, each used on about 50% (Norconsult, 2015) of the installed

Pelton turbine capacity:

1. Primary injector control where each injector has its own electro-hydraulic servo valve, with

deflectors controlled over separate control valve(s)

2. Primary deflector control where the deflector position controls hydromechanical servovalves

that for each needle. For this system there is three series positioning loops; a pilot stage, a

main stage and 2-6 parallel injector stages.

There are no mechanical links associated to transfer of the main control force on modern Pelton

turbines, the oil hydraulic piston is only dm’s from the jet needle.

Figure 37 Cross section of Pelton injector used from the early 60’s

Friction in the system will typically be within 10% of the available oil hydraulic force. The servo gain is

often high (typically >30), resulting in very modest dead band associated to servo valve pressure gain.

A specialty that may hamper control dynamics at varying degree is the low oil temperature of the oil

that is residing in the servomotor, often surrounded by very cold water. The high viscosity oil resulting

will reduce performance of valves and incur increased losses in oil pipes.




Injector needle control valves on category 2 type systems has often lapping that results in injector

needle control time constant of about 1-1.5s for position errors <1%

Injectors for 4 – 6 jet Pelton turbines can typically be taken out of use (closed) for part load operation.

Pending logics applied in the governor, this may or may not inflict noticeable change to the transient

response. Needle selection control algorithms will most likely influence part load small signal PID

response for 50%-70% of the Pelton capacity.

Strong un-linearity ratio of about 2-4 from no load to full load between discharge and injector needle

position on most Pelton turbines is predominant in particular for units with primary needle control.

Linearization is normally incorporated for feed forward control but PID control is predominantly

adapted without linearization.

HY1x governors can set PID linearization by selecting ON/OFF parameter locally at the governor

panel. HY1x governors control 25% of the Pelton turbine even though this function is normally

deactivated capacity.




Servo Valve Pressure Gain 7

The servo valve is generally controlled by the governor via a closed loop positioning system.




Figure 38 Servo Valve Flow Characteristic and Pressure Gain (Rexroth, 2009)

10% ΔP=0.3%U




The servo valves features a pressure gain, it typically is similar to Figure 38 for the high response type

valves.

What this means is that friction in the controlled system will invoke a dead band caused by the servo

loop pressure gain characteristic.

With friction force 10% of the system capacity and servo loop gain is 10 (this is a common value for

standard sized Francis and Kaplan guide vane control valves) according to the authors experience

and also referenced in (R&D, 2015) the dead band invoked will be about 0.03%. Smaller requests for

position shift will not activate motion.

For larger friction, the dead band will grow proportionally. For Kaplan hubs, one can expect friction to

account for 0.1% lost motion or more because of valve pressure gain characteristic. It is common to

use less gain than 10 on the Kaplan runner control loop.

It is also possible that some units employ servo valves with positive lapping to lower oil consumption.

It invokes dead band, such as reported for Dinorwig where positive lapping is 2/60=3% (see Figure

39). With servo loop gain 10 it will cause dead band 0.3% in addition to dead band related to pressure

gain.

Examples are for instance if the servo valve’s capacity is such that it administrates closing from open

within 4 sec - or rate of motion 25%/sec, - the valve’s controller can normally not use gain much

higher than 10, in order for the servo loop to remain stable. If the servo valve’s overlap is 1%, the

postion dead band logically will become 0.1% since position errors are multiplied with the gain.

There is generally a wide range of electro-hydraulic proportional valves in use. Manufactured by 3-4

main international supplier such as Bosch Rexroth, Vickers, Moog, Atos




Figure 39 Servo Valve Characteristic at Dinorwig (German Ardul Munoz-Hernandez, 2012)

The band widths, dead bands and linearity, three important factors for the main control valve

functional features, cannot be predicted with any accuracy out detail review of the exact model

number of the valve as well as the application it is used in. Valve data presented from PVO (Fel!

Hittar inte referenskälla.) and Kemijoki Fel! Hittar inte referenskälla. describe predominantly

4WRLE . . M characteristic, which is a fine metered characteristic according to Figure 38. BOSCH

Valve 811404 is also used in the Finnish system (Kemijoki) and is equivalent to 4WRL. Bosch

811 404 059/061 are high bandwidth valves used by Kemijoki for pilot control of 2 stage systems.

Test results from our files indicate that servo loop time constant less than 0.30 sec can be expected

for high pressure systems with the 4WRLE or equivalent performance valve connected to 10ms cycle

time digital controller (Figure 42)

With an assumption that Hydraulic control valves in “standard Swedish” system also conform

approximately to what is used in Finland and Norway, reported characteristics (R&D, 2015), time

delays in the order of magnitude seen for S2, S3, S5 and S4 imply that the digital processing is

hampered with time delays that are long enough to cause measureable negative influence on the

performance. Figure 40




Figure 40 Table of derived time delays, dead bands, and time constants

S2 S3 S5 S4




Figure 41 Valve spool positioning bandwidth characteristics – for commonly used 4WRL (Rexroth, 2009)




Figure 42 Step test with 150bar hydraulic system, 4WRLE16V– 200M valve, Servo Loop gain 35, Ty approx. 0.25

Figure 43 Step test with 150bar hydraulic system 4WRLE25 V370M, Servo loop gain 10, Ty approx. 0.25s

Older systems that have two stage control valves have considerable positive valve lapping resulting in

valve dead band similar to . This is often compensated for by introducing a dither in the hydraulic

control circuit of the control valve at a frequency higher than the actual bandwidth of the main

hydraulic system.




Solutions to Dead Band 8

Power Feedback 8.1.1

In grids with strict focus on power response, power control is often employed. Power control on a large

grid can be arranged to operate in parallel with a frequency governor with gate feedback. The power

feedback will – with a phase shift in accordance to it’s time constant - compensate for unlinearities and

dead bands inside the unit. Power feedback is typically implemented in parallel with position feedback

and entered through the droop input. It can thus be implemented with short or long time constants.

Power feedback is destabilizing for speed control schemes, the degree of destabilizing depends on

many factors such as the type of turbine, controller time constants and the grid.

Hydraulically induced power oscillations with static guide vanes are well known and that makes power

feedback that is not very much dampened also a potential source of self induced oscillations, since the

inertia of the generator has a very short time constant for power change, different from the H ensuring

long time constant for frequency swing. The power feedback is generally designed to conform to grid

codes and isn’t typically founded on control theory. Moderately filtered power feedback will have to

employ a dead band by itself since the system will regardless oscillate if there is a controller dead

band.

Dead band Compensation 8.1.2

There is widespread experience with digital compensation algorithms to reduce the negative effect of

dead band and backlash in industrial mechanical systems (Ellis, 2012).

Mechanical governors have employed analog stiction compensation for 100years by “dither” – a high

frequency modulated signal to keep the control valve in motion and avoid stiction. The dither is often

used in conjunction with control valves with a small positive overlap. Stiction is related to dead band,

but not identical.

We are aware of about approximately 30 – 35 modern control valves used on hydro turbines that

employ dead band compensation algorithm simply by adding or subtracting a compensation feed

forward signal (=the dead band) to the valve position signal depending on if the control signal is

towards open or towards closed. This increases the mechanical motion in the valve by a factor 103

(very approximatively) but after 12-15 years of experience none of the valves have experienced

premature wear. In addition, many modern valves also employ digital dead band compensation in the

drive electronics.

Dead band in valves is, however, easy to map and compensation is normally quite feasible provided

the controller and valve has plenty of basic bandwidth.

Dead band compensation for guide vane or runner blade control requires a bit more elaborate

alorithms, in particular because dead bands vary over time and vary depending on guide van and

runner blade position. Absence of signal noise is a precondition for any compensation according to

this principle. Which is a problem by itself.

Another issue as that the subjective change to the object under investigation (a large hydro turbine)

will not be of the positive kind. The servomotor will react fast during a short time to compensate fast

for the backlash. That is a prerequisite for improved dead band performance. The absolute motion will




increase compared to before the compensation. In a world with minimized to machinery, this will

probably not be viewed as an improvement unless there are benefits associated. From the viewpoint

of operators of large machines that cost millions of euro in outage time and labor to overhaul changes

that seem to potentially invoke shorter time between overhauls will not be viewed positively.

The units that - over time when many regulating units with dead band have been improved - will

benefit are units with small deadbands, and of course reduced frequency oscillation.




Discussion 9

This report has identified probable dead bands associated to the turbine itself:

Mechanical Backlash and lost motion for specific groups 9.1

High head Francis turbines:

Turbine Component New Average Worn Comment

Servo valve 0.03% 0.03% 0.05%

Guide vane stem 0.2% 0.3% 0.4%

Lost motion in linkages

0.10% 0.25% 0.32% Applicable if alternating force is required

Total 0.4% 0.6% 0.8%

Medium – Low Head Francis Turbines


Servo valve 0.03% 0.03% 0.05%

Guide vane stem 0.08% 0.12% 0.16%

Lost motion in linkages 0.05% 0.1% 0.15% Applicable if alternating force is required, probably less typical than for high head Francis turbines

Total 0.15% 0.25% 0.4%

Kaplan Turbines backlash/insensitivity


Servo valve GV 0.03% 0.03% 0.05%

Servo valve Runner 0.06% 0.06% 0.06%

Guide vane stem 0.01% 0.03% 0.05%

Lost motion in linkages Of guide vanes

0.05% 0.1% 0.15% Applicable if alternating force is required, probably less typical than for high head Francis turbines

Lost Motion Hub 1.0% 2% 3%

Total* 0.9% 1.7% 2. 6%




These figures apply for layout with control valve for hub externally to the unit. Add 1% for units with

control valve internally in the hub.

Pelton Turbines probable backlash/insensitivity

Turbine Component New Average Near rehab Comment

Servo valve deflector 0.01% 0.02% 0.05%

Servo valve injectors 0.02% 0.03% 0.05%

Total 0.03% 0.05% 0.1%

Overall totalized dead bands 9.2

If weighed according to installed per unit capacity according to turbine type, and head with average

values for Kaplan and Pelton suggested above and in addition a head dependant guide vane stem

flexing as represented by Figure 19 for Francis turbine guide vane control, the overall representative

average dead band is 0.54% weighed on MW full load capacity.

Guide vane linkage backlash related dead band will have significance for some turbines among the

Francis and Kaplan units. The degree of widespread exposure from such backlash is not well mapped.

We see signs from test results that high head Francis turbines designed for pressure relief valve are

over proportionally exposed to this backlash. The magnitude of backlash is not included in this figure

since this effect probably will be somewhat limited and hard to predict in general terms. .

Figure 44 Probable average power dead bands for hydro units in Nordic Grid




Figure 45 Accumulated probable dead band for total number of installed Hydro units in Nordic Grid, distribution per unit installed

The 30 statistically based most exposed Kaplan Turbines contributes with a probable 41MW of dead

band while the 30 most exposed Francis turbines contribute with 17MW of probable dead band. Large

Kaplan turbines and high head large Francis turbines contributes. This is data based on calculations,

assumptions, generalization and extrapolation reflected in this report by multiplying the relative dead

bands according to Figure 44 with the respective units full load MW capacity ( the dead band is

generally function of unit capacity, not the load it has at a given time).

Governor performance and tuning issues 9.3

ASEA/ABB HPC series governors are well documented regarding bandwidth and accuracy.

The same applies to Hymatek HYx series governors.

Common for both is that bench tests and practical experience illustrates that the governors perform

well with high dynamic bandwidth. Quality of speed measurement / frequency measurement is good

with resolution better than 0.01Hz. Derivative gain can be used without problems.

The HPC, however, employs filter on frequency measurments and a filter for derivative gain that

appears to make derivative action a bit less efficient in large grids than otherwise would be the case.

Andritz’ 1703 and earlier governors bench tests haven’t been produced for our review.

Governors that use commercial frequency measurement systems often refrain from using derivative

gain.

From the standpoint of choosing governor parameters, the parameters used for various Finnish plants

differ substantially from owner to owner, despite plants having relatively similar characteristics. There




are similar tendencies in the other regions (Norway and Sweden), probably due to varying degree of

focus towards the setting and various performance characteristics of the equipment.

Vattenfall’s governor parameters is tuned for response characteristics according to time constant of

60sec. With average values for Tw and Ta the tuning parameters are significantly different from what

results in optimal stability. According to theoretical assessment, tuning to optimally take responsibility

of much more regulation than the individual unit’s steady state capacity is from a theoretical standpoint

to use proportionally higher transient gain in accordance to percentage of rotating H external to the

plant that is NOT participating in governing, and about same integral time as for isolated optimal

regulation.

Most if not all Swedish plant would in theory obtain better phase margin and wider stability margins by

implemeting derivative action in the governor.

Norwegian governors are also tuned differently from plant to plant. In particular the use of derivative

gain differs a bit which has a substantial influence on what parameters the P and D should have to

meet the optimal tuning objective of stable operation on isolated grid.

However, it is clear that the Norwegian principle of tuning governors need to change away from

isolated stability to meet the grid owner’s objective function of having only a portion of the system’s

plants to offer the system regulation.

Practical implication of deadband 9.4

In the following pages we will present how the gain of HPC- based (including Vattenfall) and Hyx type

governor acts with standard setting with Droop 4% and 10% respectively and no dead band.

Droop 4% corresponds to 1/0.04= 25 steady state steady gain (Stationary FNR). While Droop 10%

means gain 1/10%=10.

For these parameters, Figure 49 and Figure 50 illustrate well the essential difference between the

stability neutral Hyx deafault parameters and Vattenfall default parameters for the two different

settings. For droop 4%, / Ep1, both governors will, if governor Speed no load - 100% stroke and full

power scaling is 1:1 and linearized, match or surpass the requirements marginally for frequency

ω>0.04s-1

but fail to pass the grid criterion for gain for ω<0.04s-1

.

Figure 46 Dp/Df equation for Hyx governor

Figure 47 Dp/Df equation for HPC governor

y ( )1

Droop

1 Ti

11

Droop KpTi

1 Td

1 Tf

1

1 TY

1 Prel Tw

1 PrelTw

2

y1 ( )Kp Ki

Droop Kp Ki

1 Kd

1 T f

1

1 T Y

1 Prel T w

1 PrelT w

2




For droop 10% /Ep0, Hyx type governor passes the requirement by a substantially wider margin, with

about factor of 3.5 at the critical ω<0.1s-1

and stays above the critera all frequencies.

Increasing droop by factor 2.5 from 4% to 10%, decreases influence response of the Hyx governors in

the critical frequency range (in this example 77 sec cycle time or ω<0.08s-1

) from gain 1.01 to 0.84 or

x 1.15, disproportionate to static gain increase by 2.5.

By employing the average deadband for Pelton and Kaplan turbines and a head dependant deadband

for the Francis turbines (according to Figure 19), ignoring the outliers associated to “New” turbines the

MW weighed expected deadband for the Nordic system hydropower is 0.54%

Figure 48 Correlation between amplitude and steady state response for typical Norwegian Hyx and Vattenfall HPC tuning Droop 2% This chart is amplitude independent (no dead bands accounted for)

Bp 2 % ep 2 %

Td 0 Kd 0

Ti 10 Ki 0,83

Kp 3 Kp 1,00

Ty 0,3 Ty 0,3

Tf 0 Tf 0

Tw 1 Tw 1

Norwegian (Hyx default)

ΔHz ΔHz (%) Steady State (ω=0) 0,38 0,08

ΔF (Hz) Variation SS response

0,1 0,200 % 10,0 % 0,35 % 1,08 %

0,05 0,100 % 5,0 % 0,18 % 0,54 %

0,03 0,060 % 3,0 % 0,11 % 0,32 %

Vattenfall


0,1 0,200 % 10,0 % 0,28 % 1,59 %

0,05 0,100 % 5,0 % 0,14 % 0,79 %

0,03 0,060 % 3,0 % 0,09 % 0,48 %

SWE HPC

ω s-1

NOR Hyx

0

5

10

15

20

25

30

35

40

45

50

0,001 0,01 0,1 1

Gai

n

ω

NOR (Hyx)

HPC

Performancerequirement

AMPLITUDE ±100mHz

Bp 2 %

The theoretical

servomotor motion to activate guide vane

stem twisting taking into account PID parameters commonly

used & time constant for servo loop

Td 0

Ti

Kp

Ty

Tw

Tf

10

3

0,3

0

1






Bp 4 % ep 4 %

Td 0 Kd 0

Ti 10 Ki 0,42

Kp 3 Kp 1,00

Ty 0,3 Ty 0,3

Tf 0 Tf 0

Tw 1 Tw 1




0,1 0,200 % 5,0 % 0,35 % 1,01 %

0,05 0,100 % 2,5 % 0,17 % 0,50 %

0,03 0,060 % 1,5 % 0,10 % 0,30 %

Vattenfall


0,1 0,200 % 5,0 % 0,18 % 0,85 %

0,05 0,100 % 2,5 % 0,09 % 0,42 %

0,03 0,060 % 1,5 % 0,05 % 0,25 %

SWE HPC

ω s-1

NOR Hyx

0

5

10

15

20

25

0,001 0,01 0,1 1

Gai

n

ω

NOR (Hyx)

HPC


AMPLITUDE ±100mHz

Bp 4 %

The theoretical




Td 0

Ti

Kp

Ty

Tw

Tf

10

3

0,3

0

1

Bp 10 % ep 10 %

Td 0 Kd 0

Ti 10 Ki 0,17

Kp 3 Kp 1,00

Ty 0,3 Ty 0,3

Tf 0 Tf 0

Tw 1 Tw 1




0,1 0,200 % 2,0 % 0,33 % 0,84 %

0,05 0,100 % 1,0 % 0,17 % 0,42 %

0,03 0,060 % 0,6 % 0,10 % 0,25 %

Vattenfall


0,1 0,200 % 2,0 % 0,12 % 0,40 %

0,05 0,100 % 1,0 % 0,06 % 0,20 %

0,03 0,060 % 0,6 % 0,04 % 0,12 %

SWE HPC

ω s-1

NOR Hyx

0

1

2

3

4

5

6

7

8

9

10

0,001 0,01 0,1 1

Gai

n

ω

NOR (Hyx)

HPC


AMPLITUDE ±100mHz

Bp 10 %

The theoretical




Td 0

Ti

Kp

Ty

Tw

Tf

10

3

0,3

0

1




The Hyx governors and similar “Norwegian” governor models are connected to on one side Pelton

turbines with inherent small deadband and also to large high head Francis turbines with relatively

large dead band. Pelton turbines will therefore regardless of permanent droop respond with typically

gain 4-5 (if linearization is employed) in the typical 77s (ɷ=0.08 s-1

) oscillation range.

Bandwidths – participation 9.5

The ability to regulate according to the grid owner’s requirements will depend on how the requirement

is formulated. With the performance requirement as presented on Figure 49 (ignoring for a moment

how phase shifts influences stability, which is also important), a comparison between the requirement

to Vattenfall and Norwegian (here represented by HYx default parameters and HPC parameters

according to Vattenfall standard) suggest a wide margin between expected performance and

requirement.

Figure 52 to Figure 63 shows how approximately dead bands in the mechanical system will influence

the responses (gain df/dP) theoretically for turbines controlled by either governor, for test frequencies

according to requirment Figure 51 and for droops 2 and 10% respectivelty and for frequency

amplitudes 0.1, 0.05 and 0.03 Hz

Figure 51 Proposed Performance requirement

Proposed Performace requirement

# ω [rad/s]T (=2pi/ω) [s] r [1 + j] R [1] r [1 + j] R [1]

1 0,006 1000 0,0531208499335989 + 0,00801043545138432i0,89 0,0831030985462923 + 0,0125316520264118i0,05

2 0,010 599 0,0531208499335989 + 0,0133622116796606i0,77 0,0832776108086811 + 0,0209479529260724i0,05

3 0,017 359 0,0531208499335989 + 0,0222895124810228i0,58 0,0837233955337374 + 0,0351303428321561i0,05

4 0,029 215 0,0531208499335989 + 0,0371811477435214i0,39 0,0847493699872375 + 0,0593190592884844i0,06

5 0,049 129 0,0531208499335989 + 0,0620218925246829i0,25 0,0868363546998003 + 0,101386838974874i0,08

6 0,081 77 0,0531208499335989 + 0,103458752238588i0,15 0,0910840541474806 + 0,177396306774263i0,13

7 0,135 46 0,0531208499335990 + 0,172579600187236i0,09 0,100752811408207 + 0,327326839316450i0,24

8 0,226 28 0,0531208499335989 + 0,287880123782100i0,06 0,122287110407245 + 0,662715836154696i0,51

9 0,377 17 0,0531208499335989 + 0,480212989130140i0,03 0,157225029844710 + 1,42131576663740i1,16

10 0,628 10 0,0531208499335989 + 0,801043545138433i0,02 0,176121217619460 + 2,65584539239001i2,22

Performance - Ms Robust stability - Mt




Figure 52 Influence on response vs ω from governor (Hyx with standard settings, Droop 2%) connected to turbines with different position dead bands) compared to response – for frequency amplitude 0.1Hz






Figure 55 Influence on response vs ω from governor (Vattenfall HPC standard settings, Droop 2%) connected to turbines with different position dead bands) compared to response – for frequency amplitude 0.1Hz





















The illustrations show clearly that the Hyx high transient gain and low integral gain setting will most

likely result in failure to reach the target response stipulated by the new criterion even for amplitude

0.10Hz and dead band > 0.25%. The much dampened power feedback that is activated occasionally

in Norwegian governors has not been taken into account.




Response from units controlled by a governor with settings used by Vattenfall will more significantly be

affected by dead band at fast oscillations, since the transient gain is lower. This is well illustrated in

Fel! Hittar inte referenskälla.. A dead band will also affect the phase somewhat, this is also

discussed in S5 FCR test report in detail. Like S5 tests illustrated, the block diagram makes it easier to

meet the criteria with very low droop when dead band is present, opposite to the Hyx governor.

Practically all Pelton turbines and an unknown but probably considerable portion of Francis turbines

designed for low to medium head exposed only to limited guide van stem flexing and will have total

lost motion in the range <0.15%.

Pelton turbines power 17% of the Nordic grid’s hydropower installed capacity. 50% of the Francis

turbine capacity (30% of the total installed hydropower capacity) is found in this “good” group of

turbines. But it can be expected that wear issues (not basic design) will exclude 25% of also these

francis turbines.

Dominant portions of the Pelton turbines feeds from large seasonal storages in Norwegian mountains.

Common practise would be for such units to operate mostly at peak hours and in the winter and

spring, less in the summer.

Low head Francis turbines < 100m represents 25% of installed Francis capacity or 15% of the

installed overall Hydro capacity. Rivers with little reservoir storage often feeds such units.

A mix of small and big reservoirs would probably feed medium head Francis turbines 100-200m head.

With the expected dead band in Kaplan hubs according to 9.1, it is evident that many units with only

position feedback will experience substantial problems to respond much at all for low amplitude

oscillations.

However, Kaplan units where runner blade operating torque is balanced such that friction does not

become dominating and require force direction to change for closing and opening, can be expected to

perform reasonably well, pending the control parameters employed in the runner blade control loop.

We expect based on a small number of reviewed units that between 3% and 30% of the units will not

be affected by hub mechanism backlash (see 5.2.1.1. )

Measurements of force required to operate the runner blade and guide vane mechanisms are very

useful and if made correctly and accurately, results will contribute to very valuable information

regarding why some units perform well and some not. And insight to why units perform better in some

load ranges than other.

From a stability standpoint, power feedback can be used with a very long time constant to gradually

correct for errors such as steady state error caused by un-linearity and backlash. Its bandwidth must

however be far lower than the 60s period. Preferably 200-300 sec.

Verification of small signal response for Pelton turbines 9.5.1

Full scale tests in S5, resulted in 0.022Hz (22mHz) for a measurement reported for at N3 and 0.039Hz

(39mHz) sinusoidal frequency fluctuation for Skjomen at 77sec (or actually 100s and 60s)

The response from three units (Unit 3 in N3, Units 1 and 3 in Skjomen) suggests gain of about 6.5-7

with moderate phase shift in the subject ɷ=0.08 s-1

range with this moderate frequency oscillation

amplitudes . All three units are Pelton turbines. All uses Hy-6 governors that according to the common

practise at the time of installation (mid 80’s) most likely has higher transient gain than Hyx current

“default” for grid operation as well as shorter Ti. Most likely these parameters are Kp 2.5 and Ti=5,

Tn= 0.4 in grid operation. That results theoretically in gain about 7 at ɷ=0.10 s-1

or 60s period time.

It should be noted that N3 Unit 2 was subject to specific plant tests, while Unit 3 were logged during

S5. N3 unit 2 was not tested with 20mHz frequency input, only down to 100mHz.




No other tests in the program has resulted in substantial response from 30mHz oscillation in this

frequency range except where frequency has been generated internally and power feedback is

employed.

Total Pelton turbine installation is 7650MW (17% of total hydropower capacity). Typical control output

from Pelton turbines in the subject ɷ=0.08 s-1

0.03Hz band may be as much as about 25-35MW.

Pelton turbines therefore is most likely a dominating contributor to stabilize swings initiated by other

segments of the grid. Most likely, there is a swing effect against units in the system with 180 degree

phase shift because of unstable parameters. This could be swings against other pelton turbines with

so long time constant in the needle control loop that stability margin becomes marginal or it could be

against units that employ power control feedback. Most likely it is a combination. According to this

review, it is unlikely that other types of units successfully respond without a substantial phase shift for

the subject amplitude and critical bandwidth.

The number of Pelton turbines on line at a given time is not well known and probably quite variable

due to large seasonal storage volumes. But the implementation of automatic needle control often

encourages owners to keep these units on line instead of starting and stopping to avoid wear of

spherical valve and SF6 breaker systems and to avoid start up failure caused by the sometimes not

cooperating spherical valve control. But that is just a tendency, not necessarily a common widespread

pattern.

With 0.03Hz the steady state control input is 1.5% for 4% droop. It is evident that already for steady

state, the low bandwidth power feedback (if employed) will have dominating effect.

At ɷ=0.1 s-1

(60 s period) the control response is 0.3% and well below the theoretical average dead

band of approximately 0.54%.

At ɷ=0.4 s-1

(16 s period) the control response is in theory 0.1% - 0.2% and motion will probably

hardly be seen at the guide vane servomotor, and with very high likelihood totally absent on power

response for a dominant portion of the turbines.

Amplitude of test frequency 9.6

Based on the review presented in Figure 49 test amplitudes 0.05Hz and lower will only yield

marginally acceptable test results for a small portion of the units, probably only Pelton turbines and a

few unique Francis turbines.

To meet the required response despite dead bands, the apparent solution – also for test amplitude

0.1Hz - will be to increase transient gain, lower integral time or introduce power feedback with short

filtering time constant. All of these factors will be reducing the stability margins of the system.

Unconventional governor parameters will probably be used to reach conformity but that is probably a

secondary effect that is not very desirable or at least should be kept under some type of guided

control.

Likelihood of conformance with requirement characteristics 9.7

The likelihood for operators/owners of plants to demonstrate successful conformity to the test criteria

depends on the governor performance, turbine dead bands and amplitude of test frequency.

The required response pattern is more adapted to the HPC parameter set/structure than the Hyx. This

can easily be seen by the conformity in general shape of the HPC governor to the requirement than




the Hyx. This is not surprising after having seen the difference in setting philosophy. It is therefore a bit

unclear what paradigm change will be adaptable or allowed for changing parameters to meet the

requirement.

If no paradigm change is going to happen regarding parameter settings and the parameter differences

as they are practised today remain, Norwegian governors will typically only successfully meet the

criteria with reasonable certainty down to 6% droop.

Most Kaplan units and worn Francis units with alternating force requirement to operate the governors

will not meet the criteria. Probably 5000MW.

For Swedish units with Vattenfall structure, parameters and governor performance, moderate droop is

on paper attractive. With low droop the integral time is very short and backlash less significantly

hampers the passing criteria, the response But the governors appears to be affected by time lags, of

unknown reason. If dead band is also added to this such as in S5 and most Kaplan turbines, the

required performance can only be met by more aggressive permanent gain and maybe some

derivative action. We cannot exclude a need to address time lags identified.

For the Norwegian governor parameters, high droop will make passing the criterion easier since the

critical response at the “critical” badwidth <0.1 Hz proportional to the static droop while the response is

nearly constant. This will of course reduce the participation factor MW/Hz.

Improvements 9.8

This review points at actual participation among units in the grid during the 0.03Hz range “permanent”

frequency oscillation at ɷ=0.1 s-1

(60 s period) is probably limited when it comes to active power

response. Controller output should be common but without obtaining actual change in active power.

The actual participation is likely to be predominantly limited to Pelton turbines, units with HPC

structure governor and low droop and units that employ power feedback. There is high likelihood of

180 degree phase shift between the pelton turbines and the other two groups of machines.

Address reduced basic performance of equipment over time 9.8.1

Dead bands and backlash identified to with high level of likelihood to occur and others that potentially

occur in this report are predominantly inherent to selection of design parameters of the turbines by

OEM, friction forces. Magnitude of dead band predominantly incurred by wear is hard to estimate, but

we have illustrated probable values.

It is a bit worrying to see that recent designs may feature substantially larger probable dead bands

compared to designs commonly manufactured and installed pre 2000.

a) Dead bands invoked by unit design features like twisting of high head francis turbine guide

vane stems and backlash could be addressed over time by more stringent specifications in

this regard. It’s not realistic to improve typical traditional figures much but it is realistic to avoid

further detoriation.

b) Contemplate if there is need or desire to invoke control parameter structures that avoids the

somewhat unnecessary but probable counterphase Pelton – high dead band low droop units.

Many - actually most - systems world wide employs frequency dead bands. Employing

“mandatory” dead bands would on one side worsen the frequency a bit but on the other hand

even out the playing field regarding offering regulation.

c) For Kaplan turbine hubs, the coming years will involve numerous modernization projects. It

would be valuable to discuss design properties of the blade balance to reduce tendency of




alternating force backlash with the predominant owners and manufacturers to correct

unsatisfactory trends that may develop in that field.

d) Turbine governors should preferably adapt to requirements in IEC 61362:2012, with the

inherent demands of bandwidths and mandated bench tests under laboratory conditions.

e) Control schemes for individual guide vanes could be discussed to identify what improvements

could be achieved to future generations of controllers.

f) Timing of overhauls may currently happen without considerable attention to deteriorating

control performance. Tests, analysis and focus according to discussions in previous chapters

would potentially improve this situation to benefit the system as a whole.

g) Information exchange between producers/owners of the generating facilities and the

responsible party for safe operation could be enhanced by demanding parameters like

governor mode and/or activated droop to be reported real time from SCADA.

Improvement – control philosophy 9.8.2

Dead bands can in the control theory be compensated for. This compensation can be implemented at

the output stage of the controller such as discussed in8.1.2

Derivative action in the governor has a considerable stabilizing effect to many schemes, in particular

plants with long Tw and normal to short penstock lengths. However, for derivative gain to be

introduced effectively, high quality frequency measurements and high bandwidth governors are

required.

Improvements – testing for certification 9.8.3

BERTA tests have been replaced with internal logics testing for some known scenarios. This will not

fully represent resolution and bandwidth of the frequency measurement. Test results will tend to

indicate better response than the reality.

BERTA tests to uncover the very unit specific - and essential - properties of friction and lost motion will

be very complicated and time demanding. Replacing / complementing BERTA tests with certification

of the governor conceptual design and bench tests, measurement of operating force and backlash

pattern on the individual unit guide vanes and runner hubs in association with certification can be

considered.




References 10

Data, F. P. (2015). Survey in Phase 2. Retrieved from Service.Projectplace:

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Ellis, G. (2012). Control System Design Guide: Using Your Computer to Understand and Diagnose

Feedback Controllers. Butterworth-Heinemann.

Erich Wurm, A. H. (2013). Consequences of Prinary control to the residual life of Kaplan runners.

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Forsström, W. (2015). Utredning av frekvensregleringens påverkan på mekanisk utrustning i en

kaplanturbin. Uppsala: DiVA.

German Ardul Munoz-Hernandez, S. P. (2012). Modelling and Controlling Hydropower. Springer

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Hansson, H. G. (1977). Development of the Kaplan Turbine. Retrieved from Actuation test equipment:

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Kuhlin, L. (2015). Info om Svensk vattenkraft. Retrieved from https://vattenkraft.info/

Nohab. (1970). Guide Vane Control. IAHR Symposium. Stockolm: IAHR.

Norconsult. (2015). Database of Hydro Plants in Norway.

NTNU, N. (2006). 8-Guide Vanes In Francis Turbines . Retrieved from NTNU Homepage:

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%20Guide%20Vanes%20in%20Francisturbines.pdf

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0990637204. Kappa Research, LLC.

Power, G. (2014). FCR Tests Individual Unit Test Results .

R&D, V. (2015). Test Report S2 VRD-R024.

Rexroth, B. (2009). Datasheet RE 29086/01.09 4WRL 10...35. Data Sheet for Proportional Valve

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Waplans. (2001). Digital regulators take the strain at... S3. Hydropower & Dams Spotlight on ...

uprating and refurbishment.

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