HomeMy WebLinkAboutTerror Lake Unit 3 Hydroelectric Project Thermodynamic Efficiency Measurements - Feb 2014 - REF Grant 7040013KEA
Terror Lake Power plant
Thermodynamic Efficiency Measurements, Unit 3
Measurement date: 1 - 2 February 2014
Draft report
2014-03-03 Assignment no.: 5132673
Assignment no. 5132673
Document no.o502
Revision:01
Terror Lake Unit 3 report.docx 03.03. 2014|Page 2 of 24
Summary
Norconsult AS was engaged by KEA to perform measurement of turbine efficiency on unit
3 at Terror Lake Power Plant near Kodiak, Alaska in January/February 2014. The
measurements were performed using the thermodynamic method according to the
guidelines given in IEC 60041 [1].
The performance guarantee for efficiency is given as a weighted unit efficiency. For
verification of the unit efficiency, the measured turbine efficiency has been multiplied with
the generator efficiency, which was not measured by Norconsult. The generator efficiency
was previously measured, and the results made available.
The guarantees given on the unit efficiency are fulfilled.
The guaranteed unit output is given at a lower net head than the test head. As the highest
load measured was limited by the generator capacity, it was impossible to perform a
measurement to verify the guaranteed unit output. Nevertheless, as shown in chapter 2.4,
it is probable that the guaranteed unit output is fulfilled. This should however be verified by
testing with the correct net head.
This is the draft of the measurement report. Both Andritz and KEA should approve of any
changes in the report before the final report is issued by Norconsult.
01 2014-03-3 Version 01 — Draft H. Hulaas L. Parr H. Hulaas
Revision Date:Description Prepared Checked Approved
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.
Norconsult AS | P.O.Box 626, NO-1303 Sandvika | Vestfjordgaten 4, NO-1338 Sandvika
Assignment no. 5132673
Document no.o502
Revision:01
Terror Lake Unit 3 report.docx 03.03. 2014|Page 3 of 24
Contents
1 INTRODUCTION...................................................................................................................................................5
1.1 ABOUT THIS REPORT .................................................................................................................................................5
2 RESULTS...............................................................................................................................................................6
2.1 GUARANTEES ..........................................................................................................................................................6
2.2 EFFICIENCIES............................................................................................................................................................7
2.3 UNCERTAINTIES .....................................................................................................................................................11
2.4 TURBINE POWER AT FULL LOAD .................................................................................................................................11
2.5 TEST COMMENTS ...................................................................................................................................................12
3 BACKGROUND...................................................................................................................................................13
3.1 ABOUT THE MEASUREMENTS—OBJECT OF TEST ..................................................................................................13
3.2 THE THERMODYNAMIC METHOD ...............................................................................................................................13
3.3 PERSONNEL...........................................................................................................................................................14
3.4 LOG .....................................................................................................................................................................14
4 MEASUREMENT SETUP......................................................................................................................................15
4.1 FIXED AND MEASURED VALUES ..................................................................................................................................15
4.2 PREPARATION OF THE UNITS FOR THE TESTS .................................................................................................................15
4.3 INSPECTION OF THE UNIT .........................................................................................................................................15
4.4 THE TESTS .............................................................................................................................................................15
4.5 TEST SETUP ...........................................................................................................................................................16
5 CHECKS AND FIXED VALUES...............................................................................................................................20
5.1 CHECKS CARRIED OUT AT SITE....................................................................................................................................20
5.2 FIXED VALUES ........................................................................................................................................................20
5.3 GENERATOR EFFICIENCY...........................................................................................................................................20
5.4 THE PHYSICALPROPERTIES OF WATER..........................................................................................................................21
6 CALCULATIONS..................................................................................................................................................22
6.1 LIST OF SYMOBLS ....................................................................................................................................................22
6.2 TURBINE EFFICIENCY ...............................................................................................................................................23
6.3 UNCERTAINTIES .....................................................................................................................................................23
List of figures
FIGURE 2-1 UNIT GUARANTEE EFFICIENCY VS FLOW AT SPECIFIED HEAD. ........................................................................8
FIGURE 2-2 UNIT EFFICIENCY VS GENERATOR POWER AT SPECIFIED HEAD.......................................................................9
FIGURE 2-3 TURBINE EFFICIENCY VS TURBINE POWER AT SPECIFIED HEAD. ...................................................................10
Assignment no. 5132673
Document no.o502
Revision:01
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List of tables
TABLE 2-1 GUARANTEED AND MEASURED VALUES............................................................................................................6
TABLE 2-2 MEASURED VALUES ...........................................................................................................................................7
TABLE 3-1 LOG...................................................................................................................................................................14
TABLE 4-1 MEASUREMENT EQUIPMENT...........................................................................................................................16
TABLE 4-2 LOCATION OF THERMOMETERS.......................................................................................................................17
Enclosures
1-1 Technical specifications —turbine and generator
2-1 Calculated values
2-2 Measurement uncertainties
2-3 Figure:Estimated guarantee power output at 1136 ft
3-1 Short description of the thermodynamic method
4-1 Fixed and measured values
4-2 Test-and instrument setup
4-3 Measuring vessel at turbine inlet
4-4 Sampling pipes at turbine outlet
4-5 Agilent 34970 thermometer multiplexer
4-6 Pt-100 thermometers calibrations
4-7 Digiquartz pressure gauge
5-1 Thermometer checks on site
5-2 Generator efficiency
5-3 Runner inspection
6-1 Formulas for calculation of efficiency
6-2 Formulas for calculation of uncertainty
Terror Lake Power Plant Unit 3
Draft Report — Thermodynamic efficiency measurements
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1 Introduction
1.1 ABOUT THIS REPORT
This is the draft report from the efficiency measurements of unit 3 at Terror Lake
Hydroelectric Power Plant performed on 1
th and 2
nd February 2014. Both Andritz and KEA
should approve of this report before the final report is issued by Norconsult.
The purpose of the test was to verify the guarantees given on turbine efficiency and power.
The technical specifications of the turbine and generator is given in Enclosure 1-1.
The enclosures are numbered according to the chapter where they first appear.
Terror Lake Power Plant Unit 3
Draft Report — Thermodynamic efficiency measurements
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2 Results
2.1 GUARANTEES
The guarantee unit efficiency vs. flow is given in Figure 2-1 on page 8. In calculating the
unit efficiency, the generator efficiencies are taken from the Generator Test Report, see
Enclosure 5-2/2.
The values are compared with the guarantees in Table 2-1 below.
Table 2-1 Guaranteed and measured values
Guarantee SUM
Flow [cfs]20.0 40.0 60.0 80.0 120.0
Unit Efficiency [%]80.73 85.33 86.96 87.51 87.47
Weighing Factor 0.02 0.08 0.24 0.40 0.26
Weighted Efficiency [%]1.61 6.83 20.87 35.00 22.74 87.06
Measured Values (interpolated)
Flow [cfs]20.0 40.0 60.0 80.0 120.0
Unit Efficiency [%]
79.26 85.01 86.90 87.48 87.56
Weighing Factor
0.02 0.08 0.24 0.40 0.26
Weighted Efficiency [%]
1.59 6.80 20.86 34.99 22.77 87.00
Weighted Efficiency Including the Uncertainty (± 0.78%)87.78
The guaranteed weighted efficiency at 1275 ft net head is 87.06%. The measured
weighted efficiency at 1275 ft net head incl. the uncertainty of ± 0.78% is 87.78%. The
guarantee is therefore fulfilled.
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Draft Report — Thermodynamic efficiency measurements
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2.2 EFFICIENCIES
The turbine, generator and unit efficiency is given in Table 2-2 below. The generator power
and flow are referred to the specified net head of 1275 ft using the laws of affinity. The
generator efficiencies are interpolated based on previously measured values as
documented in Enclosure 5.2. The calculated values are shown in Encl. 2-1.
Table 2-2 Measured values
Test
No.
No.
Of
Needles
Test
Head
[ft]
Generator
Power
at
sp. head
[MW]
Flow
at
sp. Head
[cfs]
Turbine
efficiency
[%]
Generator
efficiency
(ref Encl.
5.2)
[%]
Unit
Efficiency
[%]
301 6 1301.86 7.57 79.87 90.42 96.83 87.55
302 6 1302.61 7.57 79.84 90.37 96.83 87.51
303 6 1302.23 7.59 80.12 90.32 96.84 87.46
304 6 1300.82 12.44 131.82 89.33 97.54 87.13
305 6 1301.35 9.72 102.24 90.30 97.27 87.84
306 4 1300.90 7.45 78.78 90.25 96.80 87.36
307 4 1299.71 5.58 59.33 90.44 96.04 86.86
308 4 1299.45 3.82 41.39 90.00 94.59 85.13
309 2 1299.90 3.63 39.44 90.09 94.35 85.00
310 6 1302.23 7.25 76.66 90.23 96.74 87.29
311 2 1301.19 1.78 20.58 89.01 89.41 79.58
312 2 1300.78 2.92 32.06 90.16 93.16 84.00
313 6 1298.67 11.41 120.44 89.79 97.46 87.51
The unit efficiency vs. unit power at specified head is shown in Figure 2-2 on page 9.
The turbine efficiency vs. turbine power at specified head is shown Figure 2-3 on page 10.
Turbine Type:
Rated Output:
Rated Head:
Rated Speed:
Diameter:
Pelton vertical
11.47 MW (at 1136 ft)
720 rpm
T :2.65 ºC
Performed Date:
Performed by:
Measuring Method:
- acc to:
Test Head:
1th -2nd Feb 2014
Harald Hulaas
Thermodynamic
IEC 60041 (1991)
New Runner
Old Runner
Guarantee
Refurbishment
- after
- before
X
1298.7 ft - 1302.6 ft
Customer:Kodiak Electric Association
Project:
Document:
Thermodynamic Efficiency measurements
Unit Efficiency at 1275 ft Net Head
Project No.5132673 Date2014-02-28
Sign.H. Hulaas
X
Terror Lake Power Plant Unit 3
1275 ft
7980818283848586878889900 10 20 30 40 50 60 70 80 90 100 110 120 130 140Guarantee6 Needles4 Needles2 NeedlesUnit efficiency [%]Flow at rated head [cfs]
1060 mm
Figure 2-1 Unit Guarantee Efficiency vs Flow at Specified Head.
Turbine Type:
Rated Output:
Rated Head:
Rated Speed:
Diameter:
Pelton vertical
11.47 MW (at 1136 ft)
720 rpm
T :2.65 ºC
Performed Date:
Performed by:
Measuring Method:
- acc to:
Test Head:
1th -2nd Feb 2014
Harald Hulaas
Thermodynamic
IEC 60041 (1991)
New Runner
Old Runner
Guarantee
Refurbishment
- after
- before
X
1298.7 ft - 1302.6 ft
Customer:Kodiak Electric Association
Project:
Document:
Thermodynamic Efficiency measurements
Unit Efficiency at 1275 ft Net Head
Project No.5132673 Date2014-02-28
Sign.H. Hulaas
X
Terror Lake Power Plant Unit 3
1275 ft
1060 mm
Figure 2-2 Unit Efficiency vs Generator Power at Specified Head.7980818283848586878889900 1 2 3 4 5 6 7 8 9 10 11 12 13 14 155 Needles4 Needles2 NeedlesUnit efficiency [%]Generator power at rated head [MW]
Turbine Type:
Rated Output:
Rated Head:
Rated Speed:
Diameter:
Pelton vertical
11.47 MW (at 1136 ft)
720 rpm
T :2.65 ºC
Performed Date:
Performed by:
Measuring Method:
- acc to:
Test Head:
1th -2nd Feb 2014
Harald Hulaas
Thermodynamic
IEC 60041 (1991)
New Runner
Old Runner
Guarantee
Refurbishment
- after
- before
X
1298.7 ft - 1302.6 ft
Customer:Kodiak Electric Association
Project:
Document:
Thermodynamic Efficiency measurements
Turbine Efficiency at 1275 ft Net Head
Project No.5132673 Date2014-02-28
Sign.H. Hulaas
X
Terror Lake Power Plant Unit 3
1275 ft
1060 mm
Figure 2-3 Turbine Efficiency vs Turbine Power at Specified HeadTurbine efficiency [%]
Terror Lake Power Plant Unit 3
Draft Report — Thermodynamic efficiency measurements
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2.3 UNCERTAINTY
A standard calculation of measurement uncertainty has been made, and the uncertainty in
the turbine efficiency is estimated to be ± 0.72%. Assuming the uncertainty in the
generator efficiency is ±0.3%, the uncertainty of the unit efficiency is ±0.78%. The flow is
calculated within ±0.95%, and the turbine power is within ±0.62%.
The spreadsheet calculating the uncertainties is given in Enclosure 2-2. See also
Enclosure 6.2 for the calculation formulas.
2.4 GUARANTEED UNIT OUTPUT
The guaranteed unit full load power output measured at the generator terminals with 1136
ft net head on the turbine is 11.47 MW.
As the highest load measured was limited by the generator capacity, it was impossible to
perform a measurement to verify the guaranteed unit output. We have therefore given a
calculation below, which shows that it is likely that this guarantee is fulfilled. See Enclosure
2-3.
The highest power measured at 1275 ft. is at 12.44 MW and 131.82 cfs (point A). The
needle opening is at 65.4% (point B).
Using the affinity laws, the corresponding flow and power at 1136 ft. and constant opening
(point A’) is:
=
.=.
= 124.43
..
= 10.46
Assuming constant efficiency
1 we extrapolate from point A’ to point A’’ (the guarantee
power at 11.47 MW). Reading the values at A’’ from the graph, we get
Q’’ = 137.30 cfs
P’’ = 11.47 MW
1 There exists a Hill Chart for the turbine, but Norconsult does not currently have access to it.
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By extrapolating the curve for flow vs. needle opening from B’ to B’’ we predict the opening
at this point to be 76.8%.
As the needle opening of 76.8% is far from the maximum opening of 100%, it is highly
probable that the guarantee power of 11.47 MW at 1136 ft. is met. This should however be
verified when the net head of 1136 ft. occurs.
2.5 TEST COMMENTS
2.5.1 Test conditions
The test conditions were very good with stable temperatures and pressures for all test
points.
2.5.2 Net head during the test
During the test, the maximum and minimum net head were 1302.6 ft and 1298.7 ft, or
1.86% to 2.17% of specified head. A span of ±2 % in the net head is the limit of the
standard IEC 60041 Ch. 6.1.2.2.c for referring the measured turbine power and flow
without also correcting the measured turbine efficiency using the turbine Hill chart. The
measured efficiencies should therefore be corrected using the procedure above. As the
Hill chart of Terror Lake unit 3 from Andritz has not been made available for the Chief of
Test, this correction is not performed. KEA has to approve this before the final report is
issued.
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3 Background
3.1 ABOUT THE MEASUREMENTS — OBJECT OF TEST
Norconsult AS was engaged by KEA to perform measurement of turbine efficiency on unit
3 at Terror Lake Power Plant near Kodiak, Alaska in January/February 2014. The
measurements were performed using the thermodynamic method according to the
guidelines given in IEC 60041 [1].
Representatives from both Andritz S.A. and KEA were present during the measurements.
3.2 THE THERMODYNAMIC METHOD
The thermodynamic method results from the application of the principle of conservation of
energy (first law of thermodynamics) to a transfer of energy between water and the
runner/impeller through which it is flowing.
The specific mechanical energy at the runner may be determined by measurement of the
performance variables (pressure, temperature, velocity and level) and from the
thermodynamic properties of water.
To establish the efficiency, the need to measure the discharge is eliminated by using the
specific mechanical energy together with the specific hydraulic energy.
A short summary of the thermodynamic method is given in Enclosure 3-1.
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3.3 PERSONNEL
The test was performed by:
Harald Hulaas Norconsult AS, Norway
Present during the measurements:
Linsay Bernrot Andritz Hydro
Daniel J. Hertrich HATCH
3.4 LOG
Table 3-1 shows the time schedule of the installation and tests.
Table 3-1 Log
Date Time Task
2014-01-30 16:00 Arrival Terror Lake power plant
2014-01-31 07:30 - 10:00 Pre-test meeting about the measurements and governor
settings
10:00 - 16:00 Instrument set-up and checking
2014-02-01 07:00 - 09:00 Finalizing test set-up. Bleeding of pressure lines.
09:00 - 10:00 Thermometer zero checks
11:00 - 11:30 Distribution of thermometers
12:00 - 12:20 Efficiency test point no 301
12:20 - 12:40 Test point 302; Exchange of the inlet and main outlet
thermometer to verify zero.
12:50 - 19:00 Test point 303 – 309. Thermometer check
2014-02-02 07:00 - 07:40 Thermometer check
07:45 - 12:00 Test point 310 – 313.
12:00 - 12:30 Thermometer check
13:00 - 18:00 Dismantling of instruments, packing
2014-02-03 09:30 Leaving site
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4 Measurement setup
4.1 FIXED AND MEASURED VALUES
The fixed and measured values are given in Enclosure 4-1.
4.2 PREPARATION OF THE UNITS FOR THE TESTS
The measuring vessel at the inlet and the measuring pipes at the outlet were mounted.
The cooling water upstream the thermometers at the outlet was diverted downstream the
thermometers using a temporarily installed plastic pipe.
The brook intakes were not closed or diverted during the test.
4.3 INSPECTION OF THE UNIT
The runner was inspected. No significant wear was observed. See Enclosure 5-2.
4.4 THE TESTS
For checks done before and after the tests, see Chapter 5.
4.4.1 Observations during the tests
No special incidents were observed during the measurements.
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4.5 TEST SETUP
The test setup and the location of the instruments are shown in Enclosure 4-2. The figure
shows both electric and hydraulic connections. Table 4-1 summarizes the equipment used
for the test. The measuring vessel at inlet is shown in Enclosure 4-3, and the sampling
pipes at the outlet are given in Enclosure 4-4.
Table 4-1 Measurement equipment
Measurement Instrument Spec ID / comm.
Temperature Turbine inlet 1-1 Agilent 34970A Data
acquisition unit.
Enclosure 4-5
s/n 44010890
Temperature difference 1-1 2-1 Pt-100 thermometers Enclosure 4-6
Table 4-2
Pressure Pipe wall inlet pabs1’Paroscientific Digiquartz Enclosure 4-7
s/n 115416
Inlet temperature probe pabs1-1’762-1K pressure
transducer
Atmospheric pressure
Power Generator power Pg MWh-meter Power plant
instrumentation
Stop watch
Turbine
opening
Servo motor stroke s Read at governor Power plant
instrumentation
Flows Inlet temperature probe qrot Kylala rotameter 0-10 l/min
Water level Tail water level ZTWL Measuring band with
beeper signal
YAMAYO
Million
Data
acquisition
Pressures and
temperatures
PC
Other
equipment
Inlet temperature probe Norconsult design Enclosure 4-3
Outlet temperature
frame
Enclosure 4-4
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4.5.1 Temperature
The thermometers were located as shown Table 4-2 below.
Table 4-2 Location of thermometers
Thermo-
meter Channel Measured parameter Location
11 Probe at turbine inlet. Cable length 30 m
21 Centre pipe Turbine outlet, centre pipe. Cable length 30 m
22 Right pipe
Turbine outlet, right pipe. Cable length 30 m
23 Left pipe
Turbine outlet, left pipe. Cable length 30 m
To measure pressure and temperature of the water on the inlet of the turbine, a pitot probe
measuring vessel was used as shown in Enclosure 4-3. The probe had a DN50 flange and
was mounted on the flange for the spiral case aeration.
At the turbine outlet three perforated pipes were set. One thermometer was used in each
pipe, and moved to two different heights for each measurement point. Thus the
temperatures were measured at 6 points for each test point. See Enclosure 4-4.
All temperatures were recorded for a period of at least 3 minutes. The average values from
the period are used in the calculations. The temperature curves/files are not attached in
this report, but are available from our archive.
4.5.2 Pressures
Pipe wall pressures downstream of the main inlet valve:
The pressure downstream of the main inlet valve was measured by the precision pressure
gauge using four connected pressure taps.
Pressure in inlet temperature probe:
The pressure by the thermometer in the inlet temperature probe was measured by the
precision pressure gauge through the pressure taps of the probes.
All pressures were connected to the same precision pressure transducer via a manifold of
valves. The measured pressures are referred to the level of the precision pressure gauge.
The pressures were recorded on the computer for at least three minutes at the same time
as the temperature difference over the turbine was recorded.
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The recorded values of the precision pressure gauge are not given in the report, but are
available from our archive.
Ambient pressure:
The ambient pressure was read from a barometric Tissot T-touch watch during the
measurements. The readings were verified by the precision pressure transducer at the end
of the measurements. The atmospheric pressure was read of each test run.
4.5.3 Water levels
The water level at the outlet was measured using a measuring band with a beeper signal.
The reference of the measurement was the floor above the tail water level. The level at the
outlet was measured once per test run. Several consecutive measurements were made,
and the values averaged to obtain the value used in the calculations.
4.5.4 Needle opening
The needle opening was read at the governor screen. The opening was given in [%].
4.5.5 Generator power
The generator power, active and reactive, was read from the instrumentation of the power
plant.
In addition to manual readings from the display in the control room, the active generator
power was calculated by recording the kWh-meter during a time period measured by a
stop watch.
The displayed active and reactive powers were read once per test run.
The readings of the kWh-meter were performed during a 10 min period of the test run
4.5.6 Other measurements
The flow through the inlet probe were measured using a rotameter. The flow in the turbine
inlet temperature probe was adjusted to 4 l/min.
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4.5.7 General test procedures
The thermodynamic method was performed by the direct method according to guidelines
given in IEC 60041, 3. ed. 1991-11 [1].
The test runs were started as soon as the temperature difference over the turbine had
stabilized, and the pressure variation in the penstock due to the change in unit load had
reduced sufficiently. The measuring sequence was:
1. Piezometer pressure at inlet pipe
2. Measuring vessel pressure, temperature and temperature difference between inlet
and outlet
3. The thermometers were moved to the next height (upper or lower pos).
4. Repeat 1 or 2 for check
The sequence 1 – 3 would be altered to suit the situation in order to save time.
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5 Checks and fixed values
5.1 CHECKS CARRIED OUT AT SITE
5.1.1 Check of thermometers
To record an eventual drift in the thermometers during the test, checks of zero difference
temperature of the thermometers were performed before and after the test. The checks
were made by putting all thermometers together in one of the perforated pipes at the outlet
while the unit was running and water flowing past the pipe. See Enclosure 5-1.
Also for test point 302 the inlet thermometer was swapped with the main thermometer at
the outlet during the same turbine set-point. The difference between the measured
temperature difference in test 301 and 302 was well within 1 mK.
5.2 FIXED VALUES
All fixed values used in the calculations are given in Enclosure 4-1/1.
5.2.1 Levels
The level of the turbine centre, the turbine floor and the reference level of the draft tube
outlet level measurement are taken from drawings and ref /2/. The level of the precision
pressure gauge and the thermometers on the turbine outlet were measured at site.
5.2.2 Inlet and outlet flow area
The diameter on the inlet pressure measurement section and the draft tube outlet flow
area are taken from drawings.
5.3 GENERATOR EFFICIENCY
The generator efficiency used in the calculations is shown Enclosure 5-2. The curve was
handed over from KEA before the measurements started.
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5.4 RUNNER INSPECTION
The runner was inspected by Andritz before the measurements. The inspection report is
given in Enclosure 5-3.
5.5 THE PHYSICAL PROPERTIES OF WATER
p, are calculated according to formulas
specified in Enclosure 5-1, IEC 60041.
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6 Calculations
6.1 LIST OF SYMOBLS
Symbols
A - area m
2
a - isothermal factor m
3/kg
cp - specific heat capacity J/kg °C
d - diameter m
E - specific hydraulic energy J/kg
Em - specific mechanic energy J/kg
e - absolute uncertainty
f - relative uncertainty %
g - specific gravity m/s
2
H - head m
j - loss % el. M
n - unit speed o/min
P - power MW
p - pressure bar
Q - flow m
3/s
s - servo motor stroke mm
T - temperature °C
t - time s
v - velocity m/s
z - level m
z1’ - level of precision pressure gauge m
z2’ - water level at draft tube outlet m
- efficiency %
- temperature C
- density kg/m
3
Indices
0 - measurement section at the inlet of the turbine, upstream of the main inlet valve
1 - measurement section at the inlet of the turbine, upstream of the main inlet valve
11 - thermometer at turbine inlet
2 - measurement section at turbine outlet
21 - thermometer at turbine outlet
3 - measurement location of leakage flow from the upper labyrinth seal
abs - absolute
amb - atmospheric
G - generator
i - precision pressure gauge (instrument)
n - nominal values
ov - headwater
T - turbine
uv - tailwater
wk - Winter-Kennedy
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6.2 TURBINE EFFICIENCY
The formulas and a sample calculation is given in Enclosure 6-1. The input data for the
calculations are given in Enclosure 4-1. The calculated values are given in Enclosure 2-1
in spreadsheet format.
The calculations are performed according to the guidelines given in the standard IEC
60041, 3. ed. 1991-11 [1].
Deviations from zero differential pressure between the thermometers are taken into
account in the determination of the temperature differences, by taking the average of the
deviation measured before and after the test. Furthermore, for the final determination of
the temperature differences, the temperature-dependent deviation from zero differential
pressure is also taken into account.
The velocity in the water flowing past the inlet and outlet thermometers is not taken into
account in the calculations because:
• the inlet probe is designed in such a way that the velocity head is measured
together with the static head p11 in the probe.
• the flow velocity past the outlet thermometer is small, and may be disregarded.
These simplifications have negligible influence on the results.
6.3 UNIT EFFICIENCY
The unit efficiency is calculated from the measured turbine efficiency and the generator
efficiency. The generator efficiency (see Enclosure 5.2) was previously measured - not by
Norconsult. The given generator efficiencies are interpolated using a polynomial for the
generator loss. All bearing losses are included in the generator efficiency.
6.4 UNCERTAINTIES
Standard calculations of uncertainty are used, with calculation of both random and
systematic uncertainties.
The uncertainty analysis is presented in Enclosure 6-2. The input data for the calculations
are given in Enclosure 4-1. The calculated uncertainties are given in spreadsheet format in
Enclosure 2-1.
Terror Lake Power Plant Unit 3
Draft Report — Thermodynamic efficiency measurements
Terror Lake Unit 3 report.docx 2014-03-03 |Page 24 of 24
References
/1/IEC 60041 "Field acceptance tests to determine the hydraulic performance of hydraulic turbines,
storage pumps and pump turbines", 3. ed. 1991-1
/2/Terror Lake Hydroelectric Power Plant, Turbine efficiency measurements, unit no 1 & no. 2, Head
loss tests, 18 – 20 July 2006. Norconsult report 18
th August 2006.
Enclosure 1-1/1
Enclosure 1-1/2
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
Sign.
Page
H. Hulaas
Terror Lake Power Plant Unit 3
Calculated values
2-1/1
VGM /41/NC/8.12
5132673 Terror Lake Turbin 3 01-f eb-2014
Test No 301 302 303 304 305 306
Time 12.10 12.10 12.50 14.50 15.40 16.40
No of needles [mm]6 6 6 6 6 4
Pressure at 1 p1 [kPa]3977.7 3979.9 3978.6 3933.8 3961.0 3975.5
Pressure at 2 p2 [kPa]102.3 102.3 102.3 102.4 102.3 102.3
Pressure at 1-1 p1-1 [kPa]3996.6 3998.0 3996.0 3985.1 3989.7 3990.9
Pressure at 2-1 p2-1 [kPa]106.2 106.2 106.2 104.4 103.3 105.2
Altitude Tail Water Level zTWL [m]29.65 29.7 29.7 29.5 29.4 29.6
Isothermal coeff. Em1-1 a 10
-3 [m 3/kg]1.00366 1.00365 1.00333 1.00307 1.00302 1.00291
Specific heat capacity Em1-2 cp [J/kg K]4195.8 4195.8 4195.8 4195.8 4195.8 4195.7
Density, inlet [kg/m3]1001.89 1001.89 1001.89 1001.89 1001.89 1001.89
Density, E [kg/m3]1000.92 1000.92 1000.92 1000.91 1000.92 1000.92
Density, outlet [kg/m3]999.96 999.96 999.96 999.96 999.96 999.96
Em1-2, Pressure term ap [J/kg]3904.6 3906.0 3902.8 3892.7 3898.2 3896.9
Em1-2, Temperature term cp[J/kg]-406.9 -408.1 -407.9 -440.1 -406.3 -408.2
Em1-2, Potential term g(z11-z22)[J/kg]24.5 24.5 24.5 24.5 24.5 24.5
Mechanical Energy Em [J/kg]3522.2 3522.4 3519.4 3477.1 3516.4 3513.2
Turbine Power PT [MW]8.06 8.06 8.09 13.13 10.30 7.93
Turbine Discharge Q [m 3/s]2.29 2.29 2.29 3.77 2.92 2.25
Velocity, High Pressure Side v1 [m/s]6.89 6.89 6.91 11.36 8.81 6.79
E, Pressure term 1/*p [J/kg]3871.8 3874.1 3872.8 3827.9 3855.2 3869.6
E, Velocity term v2/2 [J/kg]23.7 23.7 23.9 64.6 38.8 23.1
E, Potential term gz
Hydraulic Energy E [J/kg]3895.6 3897.8 3896.6 3892.4 3894.0 3892.7
Turbine Efficiency [%]90.42 90.37 90.32 89.33 90.30 90.25
Head H [m]396.81 397.03 396.92 396.49 396.65 396.51
Head H [ft]1301.9 1302.6 1302.2 1300.8 1301.3 1300.9
Rated Turbine Power Prt [MW]7.82 7.81 7.83 12.75 9.99 7.70
Rated Discharge Qrt [m 3/s]2.3 2.3 2.3 3.7 2.9 2.2
Rated Discharge Qrt [cfs]79.9 79.8 80.1 131.8 102.2 78.8
Uncertainty in Efficiency f()[%]0.72 0.72 0.72 0.72 0.72 0.72
Uncertainty in Flow f(Q)[%]0.94 0.94 0.94 0.95 0.94 0.94
Uncertainty in Power f(PT)[%]0.62 0.62 0.62 0.62 0.62 0.62
Rated Generator Power Pg,rt [MW]7.57 7.57 7.59 12.44 9.72 7.45
Generator effic iency g [%]96.83 96.83 96.84 97.54 97.27 96.80
Unit efficiency tot [%]87.55 87.51 87.46 87.13 87.84 87.36
Deviation from rated head 2.11 % 2.17 % 2.14 % 2.03 % 2.07 % 2.03 %
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
Sign.
Page
H. Hulaas
Terror Lake Power Plant Unit 3
2-1/2Calculated values
V GM /41/NC/8.12
5132673 Terror Lake Turb in 3 0 1-feb-2014
Test No 307 308 309 310 311 312 313
Time 17.30 18.20 19.10 7.45 8.50 9.40 11.30
No of needles [mm]4 4 2 6 2 2 6
Pressure at 1 p1 [kPa]3981.9 3988.0 3989.9 3980.7 3997.9 3994.4 3938.0
Pressure at 2 p2 [kPa]102.3 102.4 102.4 102.3 102.3 102.3 102.3
Pressure at 1-1 p1-1 [kPa]3990.0 3990.8 3990.2 3997.0 3996.6 3992.8 3978.2
Pressure at 2-1 p2-1 [kPa]105.2 105.3 104.8 105.2 104.7 104.3 104.3
Altitude Tail Water Level zTWL [m]29.6 29.6 29.5 29.6 29.5 29.5 29.5
Isothermal coeff. Em1-1 a 10
-3 [m 3/kg]1.00276 1.00264 1.00264 1.00306 1.00308 1.00302 1.00292
Specific heat capacity Em1-2 cp [J/kg K]4195.7 4195.7 4195.7 4195.7 4195.7 4195.7 4195.8
Density, inlet [kg/m3]1001.89 1001.89 1001.89 1001.89 1001.89 1001.89 1001.88
Density, E [kg/m3]1000.93 1000.93 1000.93 1000.92 1000.93 1000.93 1000.91
Density, outlet [kg/m3]999.96 999.96 999.96 999.96 999.96 999.96 999.96
Em1-2, Pressure term ap [J/kg]3895.5 3895.7 3895.6 3903.6 3903.9 3900.3 3885.2
Em1-2, Temperature term cp[J/kg]-402.8 -420.8 -416.1 -412.2 -462.9 -415.4 -420.7
Em1-2, Potential term g(z11-z22)[J/kg]24.5 24.5 24.5 24.5 24.5 24.5 24.5
Mechanical Energy Em [J/kg]3517.2 3499.4 3504.1 3515.9 3465.5 3509.4 3489.1
Turbine Power PT [MW]5.98 4.15 3.96 7.73 2.04 3.22 12.03
Turbine Discharge Q [m 3/s]1.70 1.18 1.13 2.19 0.59 0.92 3.44
Velocity, High Pressure Side v1 [m/s]5.11 3.57 3.40 6.61 1.77 2.76 10.37
E, Pressure term 1/*p [J/kg]3876.1 3882.0 3883.9 3874.8 3892.0 3888.5 3832.2
E, Velocity term v2/2 [J/kg]13.1 6.4 5.8 21.9 1.6 3.8 53.8
E, Potential term gz
Hydraulic Energy E [J/kg]3889.1 3888.4 3889.7 3896.7 3893.5 3892.3 3886.0
Turbine Efficiency [%]90.44 90.00 90.09 90.23 89.01 90.16 89.79
Head H [m]396.15 396.07 396.21 396.92 396.60 396.48 395.84
Head H [ft]1299.7 1299.5 1299.9 1302.2 1301.2 1300.8 1298.7
Rated Turbine Power Prt [MW]5.81 4.03 3.85 7.49 1.98 3.13 11.70
Rated Discharge Qrt [m 3/s]1.7 1.2 1.1 2.2 0.6 0.9 3.4
Rated Discharge Qrt [cfs]59.3 41.4 39.4 76.7 20.6 32.1 120.4
Uncertainty in Efficiency f()[%]0.72 0.72 0.72 0.72 0.72 0.72 0.72
Uncertainty in Flow f(Q)[%]0.95 0.95 0.95 0.94 0.96 0.95 0.94
Uncertainty in Power f(PT)[%]0.62 0.62 0.63 0.62 0.63 0.63 0.62
Rated Generator Power Pg,rt [MW]5.58 3.82 3.63 7.25 1.78 2.92 11.41
Generator efficiency g [%]96.04 94.59 94.35 96.74 89.41 93.16 97.46
Unit efficiency tot [%]86.86 85.13 85.00 87.29 79.58 84.00 87.51
Deviation from rated head 1.94 % 1.92 % 1.95 % 2.14 % 2.05 % 2.02 % 1.86 %
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
Sign.
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H. Hulaas
Terror Lake Power Plant Unit 3
Uncertainty Analysis
2-2
VGM/41/NC/8.12
5132673 Terro r Lake Turbin 3 0 1-feb -2014
Test No 301
Time 12.10
No of needles 6.0
Spec. mechanical energy, Em1-2
Pressure terms
* a·epabs11 [J/kg]±4.0
* a·epabs21 [J/kg]±1.4
* (pabs11 - pabs21)·ea [J/kg]±7.8
* eEp e(Ep)[J/kg]±8.9
Temperature terms
* (T11 - T21)·ecp [J/kg]±2.0
* cp·e(T11-T21)[J/kg]±4.2
* energy distribution inlet, eE10 [J/kg]±7.0
* energy distribution outlet, eE20 [J/kg]±21.1
* eET e(E )[J/kg]±22.8
Elevation terms
* g·ez11 [J/kg]±0.5
* g·ez21 [J/kg]±1.0
* eEz e(Ez)[J/kg]±1.1
Corrective terms
* edEm1-2 e(dEm1-2)[J/kg]±0.0
Rss-sum
* eEm1-2 e(Em1-2)[J/kg]±24.5
*fEm f(Em)[%]±0.69
Spec. hydraulic energy, E
Pressure terms
* 1/·e pabs1 [J/kg]±4.0
* 1/·e p2 [J/kg]±0.1
*1/2·(p abs1 - p abs2)·e [J/kg]±3.9
*e Ep e(Ep)[J/kg]±5.5
Velocity terms
* v1·e v1 [J/kg]±0.4
* v2·e v2 [J/kg]
*e Ev e(Ev )[J/kg]±0.4
Elevation terms
* g·ez1 [J/kg]±0.1
* g·ez2 [J/kg]±0.1
*eEz e(Ez)[J/kg]±0.1
Corrective terms
* edE e(dE)[J/kg]±0.0
Rss-sum
*eE e (E)[J/kg]±5.5
*fE f(Em)[%]±0.14
Turbine Power e(PT)[MW]±0.05
Turbine Discharge e(Q)[m 3/s]±0.02
Turbine Power f(PT)[%]±0.59
Turbine Discharge f(Q)[%]±0.92
Efficiency f(Eta)[%]0.71
Test No 301
Time 12.10
No of needles 6.0
Spec. mechanical energy, Em1-2
Pressure terms
* a·epabs11 [J/kg]±0.4
* a·epabs21 [J/kg]±0.0
* (pabs11 - pabs21)·ea [J/kg]±0.0
* eEp e(Ep)[J/kg]±0.4
Temperature terms
* (T11 - T21)·ecp [J/kg]±0.0
* cp·e(T11-T21)[J/kg]±4.2
* energy distribution inlet, eE10 [J/kg]±0.0
* energy distribution outlet, eE20 [J/kg]±0.0
* eET e(E )[J/kg]±4.2
Elevation terms
* g·ez11 [J/kg]±0.0
* g·ez21 [J/kg]±0.0
* eEz e(Ez)[J/kg]±0.0
Corrective terms
* edEm1-2 e(dEm1-2)[J/kg]±0.0
Rss-sum
* e Em1-2 e(Em1-2)[J/kg]±4.2
* fEm f(Em)[%]±0.11
Spec. hydraulic energy, E
Pressure terms
* 1/·e pabs1 [J/kg]±0.4
* 1/·e p2 [J/kg]±0.0
* 1/2·(p abs1 - p abs2)·e [J/kg]±0.0
* e Ep e(Ep)[J/kg]±0.4
Velocity terms
* v1·e v1 [J/kg]±0.1
* v2·e v2 [J/kg]
* e Ev e(Ev )[J/kg]±0.1
Elevation terms
* g·ez1 [J/kg]±0.0
* g·ez2 [J/kg]±0.0
* eEz e(Ez)[J/kg]±0.0
Corrective terms
* edE e(dE)[J/kg]±0.0
Rss-sum
* e E e(E)[J/kg]±0.4
* fE f(Em)[%]±0.01
Turbine Power e(PT)[MW]±0.02
Turbine Discharge e(Q)[m3/s]±0.01
Turbine Power f(PT)[%]±0.20
Turbine Discharge f(Q)[%]±0.23
Efficiency f(Eta)[%]0.11
Total Uncertainty
Uncertainty in Efficiency f()[%]0.72
Uncertainty in Flow f(Q)[%]0.94
Uncertainty in Power f(PT)[%]0.62
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
Sign.
Page
H. Hulaas
Terror Lake Power Plant Unit 3
Flow vs Needle Openingat 1275 ft Net HeadFlow vs Generator Powerat 1275 ft Net HeadFlow vs Needle Openingat 1136 ft Net HeadFlow vs Generator Powerat 1136 ft Net HeadNeedle opening [%]
Generator Power [MW]Extrapolatedto 11.47 MW
2-3Estimated guarantee power at 1136 ft
ENCLOSURE 3
x:\nor\oppdrag\sandvika\800\vannkraft\8000000\avdeling.hyd\100079 hydrauliske målinger\rapporter\o1000 maler\engelsk\3
description of thermodynamic method.doc 12.06.2012
A BRIEF DESCRIPTION OF THERMODYNAMIC EFFICIENCY MEASUREMENT
The method is based on measuring the total energy (thermal, kinetic and potential) entering and leaving
the turbine. The energy is measured per unit mass of water and therefore it is not necessary to measure the
total flow. Simplified we have, according to the law of conservation of energy ("the first law of
thermodynamics") this relation:
Em Energy "produced" (mechanical energy delivered to the shaft)
+ Ej Energy loss (friction- and hydraulic losses)
= E Total available energy for the turbine (related to the hydraulic net head)
The general expression of turbine efficiency:T = Em/E = (E - Ej)/E
A thermodynamic measurement using the direct method
1 actually determines Ej. Losses
2 in the turbine are
transferred to the water resulting in a temperature increase. The temperature increase is measured as a
temperature difference between the inlet probe(s) and outlet probe(s). Other necessary measurements such
as pressures, elevations, generator output etc. are about the same as for any other efficiency test method.
However, it is not necessary to measure the generator output very accurate as it is only of minor
importance for calculation of efficiency.
To understand the relation between temperature increase and turbine losses it is useful to remind of the
basic laws of physics for transition of from potential energy to heat energy:
- If m kg water is in a reservoir H meters above the tail water, it represents potential energy
equivalent to Epotential = m·g·H. Here g is gravity (9.81 m/s
2).
- If water is heated the relation between temperature increase and heat energy is Eheat = m·cp·
where cp is the water’s specific heat (4200 J/(kg·C)) and temperature increase.
- Imagine that the potential energy of the water in a reservoir Epotential completely is transferred to
heat Eheat by discharging it freely through a valve at the tail water level. The temperature increase
resulting from this can be found by combining the two equations for equal energies
3. In metric
units we get:H = 428·[m].
An example can illustrate this for a thermodynamic measurement. Assume a hydropower unit with net
head H=428 m. The temperature difference between inlet and outlet is measured to be:= 0.1 °C. The
relation above lets us convert this to a head loss: Hloss= 428·0.1 = 42.8 m. Consequently the turbine
efficiency (the ratio: "produced" energy / available energy) becomes:
T= (428 - 42.8)/428 = 0.9, i.e. 90% efficiency
This description is very simplified and explains only the principle of measurement. For details the
appropriate standard is: International Standard IEC 41, 3. ed. 1991-11.
1 Two methods exist; the direct (covered here) and the indirect (partial expansion method). Today the direct method is mostly used. The principal for the
indirect method is that water from the turbine inlet probe is discharged through a throttling valve. The valve is adjusted until the throttling gives a temperature
after the valve equalto the temperature measured at the outlet of the turbine. The turbine efficiency is then the ratio: (turbine nethead - valve pressure drop) /
(turbine net head).
2 Meaning hydraulic losses; boundary friction, singular losses, turbulence etc.
3 All the potential energy is transferred to pressure, then converted to velocity through the valve, which further turns into heat in the turbulence after the
valve.
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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Terror Lake Power Plant Unit 3
Fixed values
4-1/1
Kunde KEA
Plant Terror Lake
Turbine No 3
Project No 5132673
Date februar-14
Signature Hulaas
Rated Output [MW] 11.789
Rated Speed [rpm] 720
Rated Head [mVs] 388.62
Width, Draft tube gate [m]99999
Hight, Draft tube gate [m]99999
Diameter, Inlet [m] 0.6500
Area, Inlet [m] 0.3318
Altitude pressure transducer [m] 33.02
Altitude T1-1 [m] 31.34
Altitude T1-2 [m] 29.25
Altitude floor over outlet [m] 32.15
Altitude bottom of outlet [m] 28.80
Altitude inlet pipe Centre [m] 31.55
Altitude average jet contact [m] 31.55
Constant, kWh-meter 0.001
Latitude of Power Plant 57.70
Altitude of Runner [m] 31.55
Gravity [m/s
2] 9.8172
Uncertainty in:Systematic Random
Pressure Transducer p1-1 [%] ±0.10% ±0.01%
Pressure Transducer p' [%] ±0.10% ±0.01%
Pressure Transducer pamb [%] ±0.10% ±0.01%
Altitude of Ztr [m] ±0.01
Altitude of ztwl [m] ±0.10
Altitude of z1-1 [m] ±0.05
Altitude of z2-1 [m] ±0.10
Altitude of z1 [m] ±0.01
Altitude of z2 [m] ±0.01
Altitude of z3 [m] ±0.05
Temperature T1-1 [°C] ±0.01 ±0.001
[°C] ±0.001 ±0.001
Energy Distribution at 1-1, E10 [%] ±0.20%
Energy Distribution at 2-2, E20 [%] ±0.60%
Density of water [%] ±0.10%
Isothermal factor of water a [%] ±0.20%
Specific heat capacity of water cp [%] ±0.50%
Turbine inlet flow area A1 [%] ±0.10%
Turbine outlet flow area A2 [%]
Generator Power [MW] ±0.50% ±0.20%
Generator Efficiency [MW] ±0.30%
Additional terms [%]
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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Terror Lake Power Plant Unit 3
Measured values
4-1/2
[MW][MVar][s]uv[m]rot[l/min]amb[kPa]abs1'[kPa]abs1-1'[kPa]1-1[°C][°C]gen[MW]gen[%]T2-1[m][]1121[°C]1122[°C]1122[°C]1121[°C]1122[°C]1122[°C][%][%][%][%][%][%]
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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Terror Lake Power Plant Unit 3
3Bleeding
Rotameter
Measuring Vessel tapping
Test set-up
4-2/1
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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Terror Lake Power Plant Unit 3
SeenupstreamABCDXXXDiameter AreaNo of tapsDiameterAreaNo of tapsinsert lenght zNo of vesselsPressureXXXXThermometerUsedNot usedCollected SeparatedUsedNot usedUsed only for calibrationCollectedSeparatedDownstr. MIVPlaced at vent valvSep. locationOther locationUpstr. MIVModel A6 pitots4 pitotsOO270180090Used only for calibrationThermometerAs seen from AModel BModel CModel DMovable todifferentheightsThermometer
31.55 m90270O180028.80 mXOOx4-2/2
29.25 m32.28 m
Client:KEA
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Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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Terror Lake Power Plant Unit 3
4-3Measuring vessel
Measuring vessel DN50
Client:KEA
Project:
Thermodynamic efficiency meaasurements
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4-4Perforated pipes at outlet
AAFlowSection A-APerforated pipesThermometer ThermometerThermometer
Enclosure 4.5/1
Enclosure 4.5/2
Enclosure 4.5/3
Enclosure 4.5/4
Enclosure 4.5/5
Enclosure 4-6/1
Enclosure 4-6/2
Enclosure 4-6/3
Enclosure 4-6/4
Enclosure 4-6/5
Enclosure 4-6/6
Enclosure 4-6/7
Enclosure 4-6/8
Enclosure 4-6/9
Enclosure 4-6/10
Enclosure 4-6/11
Enclosure 4-6/12
Enclosure 4-6/13
Enclosure 4-6/14
Enclosure 4-6/15
Enclosure 4-6/16
Enclosure 4-6/17
Enclosure 4-6/18
Enclosure 4-6/19
Enclosure 4-6/20
Enclosure 4-6/21
Enclosure 4-7/1
Enclosure 4-7/2
Enclosure 4-7/3
Enclosure 4-7/4
Client:KEA
Project:
Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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Terror Lake Power Plant Unit 3
5-1Thermometer controll
Dato 2012-02-01 2012-02-02 2012-02-02
Time 09:17 07:00 12:00
Water temp 1-1 [°C]3.632 3.830 3.720
11-21 [°C]0.0000 0.0001 -0.0001
11-22 [°C]0.0002 0.0003 -0.0001
11-22 [°C]0.0006 -0.0002 -0.0004
Diff temp
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
Date, Time
-
-
-
Zero check of thermometers
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Thermodynamic efficiency meaasurements
Pr. No.5132673 Date2014-02-15
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5-2/1Generator Efficiency
Client:KEA
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Thermodynamic efficiency meaasurements
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Generator Efficiency
5-2/1
Generator efficiency [%]
Page 1 of 2
RUNNER INSPECTION REPORT
Andritz Hydro Inc.
Report number: N/A
Power house: Terror Lake AL Unit : 3 Date: January 31st, 2014
Initiated by: Customer request
Deviation report
Intervention report
X Others: Norconsult (Harald
Hulaas)
Subject:Efficiency Test report
Description:Runner and Nozzle Inspection
Prior to conducting the efficiency test it was required to inspect the runner for any defects that
may impact the results. While the unit was shut down we entered the tailrace and inspected
the runner and nozzles. A couple of spots were noticed on the runner to have what seemed to
be paint or epoxy on it, but these were on the edges and appeared to not be of concern. Nozzle
#4 appeared to have some sort of a small scratch on the nose cone, but when inspected by hand
it was discovered to be negligible. The runner appeared to be in excellent condition.
Pictures shown below:
Enclosure 5-3/1
Page 2 of 2
Enclosed report: Yes X No Following intervention (s) to come: Yes No
Planned date:
People attending: Lindsay Bernrot
Customer:
(Lloyd Shanley)
Hatch :Dan Hertrich, (Joe Earsley)
Norconsult: (Harald Hulaas)
Note: The name of involved persons, but not necessarily present, should be within parenthesis.
Prepared by: Lindsay Bernrot Date: January 31, 2014
Enclosure 5-3/2
THERMODYNAMIC EFFICIENCY MEASUREMENTS
FORMULAS AND SAMPLE CALCULATION
28.02.2014 1
Enclosure 6.1/1
THERMODYNAMIC EFFICIENCY MEASUREMENTS
The formulas for calculating the efficiency are given in the following, together with a sample calculation.
Note that deviations from this sample calc and the values in the spreadsheet are due to
rounding errors.
Measured values, test point 301
Table 1 Measured values, test point 301
pamb [kPa] - Ambient pressure = 102.3
A1 [m2] - Area of the high pressure side = 0.3318
PG [MW] - Generator power = 7.814
g [m/s
2] - Gravity = 9.8172
z 1'[m] - Level of pressure transducer high pressure side = 33.02
z 1-1 [m] - Level of thermometer 1-1, High pressure side = 31.75
z 2-1 [m] - Level of thermometer 2-1, Low pressure side = 29.25
z 1 [m] - Level of turbine centre = 31.55
pabs 11'
[kPa] - Measuring vessel pressure high pressure
side
= 3984.2
p abs 1'
[kPa] - Pipe wall pressure high pressure side = 3963.3
G [Hz] - Generator efficiency = 96.90
1-1 [°C] - Temperature at the high pressure side = 2.513
[°C] - Temperature difference = -0.0970
THERMODYNAMIC EFFICIENCY MEASUREMENTS
FORMULAS AND SAMPLE CALCULATION
28.02.2014 2
Enclosure 6.1/2
The Turbine Efficiency
The efficiency is given by
m
T
E
E
[%]
Em is the mechanical energy of the water, and E is the hydraulic energy of the water. The relationship
between E and net head Hn is
E = H
.g
Calculation of Isothermal Coefficient and Specific Heat Capacity
For calculation of the isothermal coefficient and specific heat capacity the average conditions at point 1-1
(the inlet vessel) and 2-1 (at the outlet frame) have to be used.
The pressure in the measuring vessel is
11 11' 1' 11
33.02 31.75 1000.92 9.81723984.2 3996.6 kPa1000
absp p z z g
The pressure at the outlet thermometer is
21
21 1000
29.65 29.25 999.96 9.8172 102.3 106.2 kPa1000
twl
amb
z z gp p
The mean absolute pressure between inlet and outlet is
11 21
3996.6 106.2 2051.42 2
aver
p pp kPa
The mean temperature between inlet and outlet is
1 1 2 1 1 1
2 2 2.513 ( 0.0975)2.562 C2 2 2
aver
a and pC is taken from tables or formulas
THERMODYNAMIC EFFICIENCY MEASUREMENTS
FORMULAS AND SAMPLE CALCULATION
28.02.2014 3
Enclosure 6.1/3
3-3a= 1.00366 10 m kg and 4195.8 J kg CpC
Calculation of Density
For calculation of density the average conditions at turbine inlet and turbine outlet have to be used.
The average pressure between outlet and inlet is approximately
1' 1' 1 2' 2' 11 2
2 2
3963.3 102.3 2032.82
p g z z p g z zp pp
kPa
The average temperature is
11 21 2.562 C2aver
3
is taken from tables and formulas
1000.92 kg m
Mechanical Energy
The mechanical energy is given by
2 2
1 1 2 1
1 1 2 1 (1 1)(2 1) 1 1 2 1
=2
m p T V Z
p
E E E E E
V Va p p C g z z
Pressure Term
11 21
-3 31.00366 10 3996.6 106.2 10 3904.6 J kg
pE a p p
THERMODYNAMIC EFFICIENCY MEASUREMENTS
FORMULAS AND SAMPLE CALCULATION
28.02.2014 4
Enclosure 6.1/4
Temperature Term
(11)(21)
4195.8 0.0970 407.0 J kg
T p
E C
Velocity Term
The pressure measured in the measuring vessel is the total pressure, including the velocity head, and the
same is the case for the measuring frame at the outlet. Thus the velocities are included in the pressure
term
2 2
1 1 2 1 02V
V VE
Potential Term
11 21
=g z
9.8172 31.75 29.25 24.5 J kg
ZE z
Total Mechanical Energy
3904.6 407.0 0 24.5 3522.2 J kg
m p T V z
E E E E E
Turbine Power and Discharge
To calculate the flow, we need the value of the density at the high-pressure side, given by the pressure
and temperature
1 1'
3963.3
p p
kPa
1-1 = 2.513 °C
3
is taken from tables and formulas
1001.89 kg m
THERMODYNAMIC EFFICIENCY MEASUREMENTS
FORMULAS AND SAMPLE CALCULATION
28.02.2014 5
Enclosure 6.1/5
The turbine power is given by
7.814 8.06 W0.9690
G
T
G
PP
M
The flow is given by
3
68.06 10 = 2.293522.2 1001.89
T
T
m
PQE
m s
Hydraulic Energy
2 2
1 2
1 2 1 22
p V z
V VE p p g z z
E E E
The Pressure Term
1 1' 1' 1
9.8172 33.02 31.55 1000.923963.3 3977.7 kPa1000
absp p g z z
2 102.3ambp p
The total pressure term is
1 2
3977.7 102.3 1000 3871.8 J/kg1000.92
p
p pE
THERMODYNAMIC EFFICIENCY MEASUREMENTS
FORMULAS AND SAMPLE CALCULATION
28.02.2014 6
Enclosure 6.1/6
The Velocity Term
According to IEC 60041:1991, chapter 11.2.5.2.2, v2 is taken as zero.
2
2
2 2
1 2
1
2
2
1
2 2
2.29 1 23.8 J/kg2 0.3318
V
V V QE A
The Potential Term
The high and low pressure reference is the same, i.e. the turbine centre, then
0zE
Total Hydraulic Energy
= 3871.8+23.8= 3895.6 J/kg
p V z
E E E E
3895.6 396.81m9.8172
n
EHg
Calculation of Turbine Efficiency
3522.2 100 90.42 %3895.6
m
T
E
E
Calculation of Unit Efficiency
90.42 96.83% 87.55 %
Tot t Gen
THERMODYNAMIC EFFICIENCY MEASUREMENTS
UNCERTAINTY ANALYSIS
hah 20140228 -1 -
Enclosure 6.2/1
Uncertainty analysis
1 ABOUT THE UNCERTAINTY ANALYSIS
The uncertainty of a measured value is given in absolute or relative terms.
The absolute uncertainty of a measured value X is eX and thus the relative term is
X
X
efX
Each component has a systematic and sometimes a random component. The tables given in this
analysis indicate which components to be taken into account.
The formulas for the systematic and random uncertainties are the same.
The systematic uncertainty is denoted X sysf and the random uncertainty is denoted X ranf
The uncertainty analysis is performed in spreadsheet at a 95% confidence interval, according to the
formulas below.
1.1 Uncertainty in Mechanical Energy Em
The uncertainty in mechanical energy is:
2 2 2 2 2 2
10 20
0.52
(3 2)p v zm
m
E E E E E E EE
E
m m
e e e e e e eefE E
1.1.1 Pressure Term
21/ 2
2 2 2 2 2
11 21 11 21
2
' ' ' 'p abs abs table Temp abs abs
E p p a a
e e e a e e p p
Uncertainty term Systematic Random
epabs11'[kPa] Measuring vessel pressure x x
epabs21'[kPa] Outlet pressure x x
e z1’' [m] Elevation of pressure transducer x
e z11 [m] Elevation of thermometer 1-1 x
e z21 [m] Elevation thermometer 2-1 x
tableae [dm3/kg] Isothermal factor; due to
uncertainty in tabulated values
x
e a Temp [dm3/kg] Isothermal factor; due to
uncertainty in temperature
x x
THERMODYNAMIC EFFICIENCY MEASUREMENTS
UNCERTAINTY ANALYSIS
hah 20140228 -2 -
Enclosure 6.2/2
1.1.2 Temperature term
21 22 2 2 2
T table Temp
E pCp Cp
e e e e c
Uncertainty term Systematic Random
tableCpe [J/kg C]Specific heat capacity; due to
uncertainty in tabulated values
x
TempCpe [J/kg C]Specific heat capacity; due to
uncertainty in temperature
x x
e [°C] Measured temperature difference x x
1.1.3 Velocity term
2
11 21
2 2
11 21vE v v
e v e v e
Both V1-1 and V2-1 is included in the pressure measurements, so that
e E V 0 J / Kg
This is true for both the systematic and random part.
1.1.4 Elevation term
2
11 21
2 2
zE z z
e e g e g
The uncertainty in determining the gravity is neglected.
Uncertainty term Systematic Random
11ze [m] Elevation of thermometer 11 x
21ze [m] Elevation of thermometer 21 x
THERMODYNAMIC EFFICIENCY MEASUREMENTS
UNCERTAINTY ANALYSIS
hah 20140228 -3 -
Enclosure 6.2/3
1.1.5 Uncertainty in energy distribution
The systematic uncertainty due to lack of investigation of the energy distribution of the high-pressure
side is taken as (Ref. IEC 41 -1991 ch. 14.7)
mEEe%2.010
and at the low pressure side (Ref. IEC 41 -1991 ch. 14.7)
mEEe%6.010
The random part of this uncertainty is zero.
1.2 Uncertainty in Hydraulic Energy, E
The uncertainty in hydraulic energy is
0.52 2 2
p V Z
E E EE
E
e e eefE E
Pressure term
21 22 2 2 2
1' 2'
1' 2'p abs abs
E p p abs abs
e e e f p p
Uncertainty term Systematic Random
1'abspe [kPa] Pressure high pressure side x x
2'abspe [kPa] Pressure low pressure side x x
f [%] Density x
1.2.1 Uncertainty in turbine power, flow and velocity term
The uncertainty in the measured turbine output is
2 2 2
G G
P P
f f f
The uncertainty in flow is given by
THERMODYNAMIC EFFICIENCY MEASUREMENTS
UNCERTAINTY ANALYSIS
hah 20140228 -4 -
Enclosure 6.2/4
1Q P Em
e f f
where
e f
The uncertainty in the velocity head term is
21
1
1
vE Q
Qe e A
Uncertainty term Systematic Random
GPf [%] Power measurements x x
G
f [%] Generator efficiency x
Eme [J/kg] Total mechanical energy x x
1.2.2 Potential Term
2 22
1' 2'zE z z
e e g e g
Uncertainty term Systematic Random
1'ze [m] Elevation of pressure
measurement at inlet
x
2'ze [m] Elevation of pressure
measurement (or tail water
level) at outlet
x
1.3 Uncertainty in efficiency
The uncertainty in the turbine efficiency is
2 2
mE E
ef f f