gas turbine seminar -19 - energiforsk.se€¦ · gas turbine combined cycle -gtcc • gas turbine...
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Gas Turbine Seminar -19Lund University
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 2
December 2017…
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 3
German and European wind power – VGB
Courtesy of VGB, ”ELECTRICITY GENERATION 2018|2019 – Facts and Figures
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 4
German wind power – VGB
Courtesy of VGB, ”ELECTRICITY GENERATION 2017|2018 – Facts and Figures
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 5
Flexibility
Load
Star
t Steady state Active generation control
Spinning reserve off-peak turndown
SS
Shut
dow
n
Load
LF
Cou
rtesy
of S
iem
ens
• Primary frequency response Speed droop Spinning reserve Automatic and fast
• Secondary frequency response Spinning/non-spinning reserve 30 s start, full capacity <15 min Frequency restoration
• Tertiary reserves
Rating
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 6
Flexibility
• Start-up– Air attemperation– Sky venting– Cascaded steam bypass with massive attemperation
• Ramping• Peak
– Firing level– Compressor flow– Inlet cooling– Wet compression
• Turn-down– MECL– EGR/Inlet heating– Variable PT
• Lock-out
LoadSt
art Steady state Active generation control
Spinning reserve off-peak turndown
SS
Shut
dow
nLoad
LF
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 7
GT & GTCC – large gas turbine start-up
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 8
GE LM6000 Hybrid EGT
250 ms
5 min
10 MW (4.3 MWh) Li-Ion BatteryAttributes without fuel burn:• Instant (250 ms) response, always ready• 50 MW of operating reserve• Primary frequency response (FCR-N)• 5…-8 MVAR voltage support• 134 MWs inertia with synchronous condensing• Black start technology• Demand charge savings (?)Attributes with fuel burn:• 50 MW peaking power• 25 MW of high-speed frequency regulation• 10 MW peaking power• Self-managed BESS state of charge
Typical cost figures (Lazard):• Battery 190…442 USD/kWh• Converter etc. 60…151 USD/kWh
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 9
Grid codes
• UK National Grid Code (NGC):– Nominal power down to 49.5 Hz– Stay on-line with pro-rata output down to 47 Hz– Stay on line up to 52 Hz with reduced output (68 percent)– Brown-out requirements e.g. 0V for 0.14 s– Response rates
• Nordic– Stay on-line down to 47.5 Hz (30 minutes)– …
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 10
Speed droop – load and frequency relation
0 50 100
50
51
52
49
48
Freq
uenc
y, H
z
Load, %Normal (4 %) droopDead band & 6 % droop“Zero” droop – island operation
0 100 %
nom
ffDroop d PP
0
regulating
nomgen
P
PP fd f
“Regulating power”
Speed drop is defined as:
Recast to yield the convenient form:
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 11
Multiple alternators – power response
0 100 %
nom
ffDroop d PP
Freq
uenc
y, H
z f0f
ΔP1 ΔP2
P10 P1 P20 P2
Power output, MW
d1 d2
d1 > d2
100nomregulating
nom
PP f P fd f
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 12
Inlet fogging and wet compression
• Inlet fogging – all water evaporates before the blading Hot and dry sites
• High-fogging – water evaporates within the compressor Reduced blade lifing because of erosion
Figu
res
cour
tesy
of:
Jans
ohn
et a
l, “M
oder
n G
as T
urbi
ne S
yste
ms”
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 13
COE
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 14
P&W FT4000
Performance• 140 MW nominal output in twin-engine configuration• Wet compression for improved performance above
ISO conditions• Single or dual engine operation (common alternator)• 50 or 60 Hz performance with no penalty• 41% (+) thermal efficiency without external cooling
Operational• Less than 10 minutes start-up time• 30 MW/min ramp rate• Synchronous condensation with spinning PT, a FT8
has a windage loss of 500…1,000 kW• NO maintenance penalty for start/stop!• Fleet has 17,500 OH’s and 1400 cycles
P&W has substantial experience in synchronous condensation without SSS-clutch!
>900 engines>20 years>40 MOH
360 USD/kW – 24,750,000 USD
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 15
Cost of Electricity – COE
var
Capital Fuel Maintenance
fix
Operation
OMf money unitCOE OMH P
CAPEXP H kWh
var ,1
Emissions Replacement capacity
nc efix
i p iieff eff eff eff eff
S P S EOMCAPEX fCOE OM c mP H P H P H
3 00
/
0.947817 10 3.6293.071MJ kWhMMBtu MJUSD MMBtu
f kf f k USD kWh
1,
1 1
N
N
i ii N
i
Where:
0.124
4 0.43
3700 578360 9.3 10
C SP
P U D kWP
APEX
3var
3
3.0...3.5 10
10...15 0.50...1.50 10installed
per annum
OM USD kWh
OM USD kW USD kWh
CAPEX Capital Expenditure
β Annuity factor
P Power
H Annual operating hours
f Fuel cost [USD/kWh]
i Interest rate
N Number of years
OMfix Fixed OM-spending [USD]
OMvarVariable OM-spending [USD/kWh]
COE = CAPEX + OPEX
10 percent interest rate (i) and 25 years (N) gives β = 0.11
N.B. All OM costs are engine dependent! One may(typically) expect a service cost equivalent to a newengine during 80,000 operating hours.Simple cycle
GTCC
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 16
Lazard’s data
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 17
The expensive (?) way – equivalent hours…
1 1 11 1 1
tripsstarts nnOH
fuel firing starts load rate Trips
creep and oxidation LCF
EOH F F F F F
Where:EOH equivalent operating hoursOH actual operating hoursFfuel factor depending on fuelFfuel factor depending on firing levelnstarts number of “fired” startsFstarts number of hours per startFload rate load rate factor
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 18
LifingM
iner
-Pal
mgr
en
Robinsonf r
N t DN N
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 19
Operational hours
Factored Hours = (K + M I) (G + 1.5 D + Af H + 10 P)
Actual Hours = (G + D + H + P)
G = Annual Base Load Operating hours on Gas FuelD = Annual Base Load Operating hours on Distillate FuelH = Annual Operating Hours on Heavy FuelAf = Heavy Fuel Severity Factor (Residual = 3 to 4, Crude = 2 to 3)P = Annual Peak Load Operating HoursI = Percent Water/Steam Injection Referenced to Inlet Air FlowM&K = Water/Steam Injection Constants (see GE documentation)
hoursHours ActualHours Factored
24000 intervaleMaintenanc
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 20
Number off cycles
• Actual Starts = (NA + NB + NP)• S = Maximum Starts-Based Maintenance Interval (Model Size Dependent)• NA = Annual Number of Part Load Start/Stop Cycles (<60% Load)• NB = Annual Number of Base Load Start/Stop Cycles• NP = Annual Number of Peak Load Start/Stop Cycles (>100% Load)• E = Annual Number of Emergency Starts• F = Annual Number of Fast Load Starts• T = Annual Number of Trips• aTi = Trip Severity Factor = fcn(Load, Trip during accel. = 2, Peak = 10) • η = Number of Trip Categories (i.e. Full Load, Part Load, etc.)
η
1iiTiPBA T1aF2E20N1.6NN0.5 Starts Factored
900Maintenance interval Starts
Factored Starts Actual Starts
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 21
The service market
• Approximately 40,000 non-flying units• The total service market was 23.9 BUSD 2017
– Expected annual growth is 8…9 percent until 2025 (41.6 BUSD)– Large OEM margins
• Loads of variants…
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 22
Gas Turbine Combined Cycle - GTCC
• Gas turbine load is primarily controlled by the compressor IGV/VSV for maintaining high firing
• Higher flue gas temp but same limitations in admission temperature to the steam turbine → spray cooling
• No gain in lifing due to part load since the engine is fired at almost nominal level with constant cf. load
• Factor of two for each 10°C → misery factor
HRSG HT-section
EGT vs. load
Max adm.
1p
dTdQ m c
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 23
Improved GTCC control strategy
• Control the admission temperature rather than firing with only a minute performance drop
• Lower firing level → improved part-load lifing• No hardware modifications – only safe control
modifications (watch out for rumble…)
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 24
Engine fundamentals
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 25
State-of-the-art-GT (Single-shaft)• DLE – Dual Fuel• >1,600 °C• Can-Annular• Axial fuel staging• Fuel flexibility• Fuel saturation
• 3D Aero airfoils• Multistage VSV• “Super Finish”• Field-replaceable blades
• >600 °C• 1,000 kg/s• <25 ppm NOx• >10 ppm CO• No toxic emissions
• Four-stage turbine• Single-crystal Ni-based super-alloys• TBC• 3D Aero vanes and blades• ACC• Advanced film cooling• Micro-channel cooling
• Hydrogen cooled• 99 % Efficiency• 600 MW
• Welded rotor• Bolted rotor• Hirth-coupling• Hydraulic ACC
Future enablers (short term)• 1,700 °C• Ceramic matrix components• Additive manufacturing (AM)• Data analytics• Controls and optimization• No vane #1
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 26
Single- vs. multi-shaft industrial I
• Only power generation (torque issues)
• Part-load (pro’s and con’s) –effective way of controlling engine flow
• Exhaust size limitations (lower speed or high outlet velocity)
• Efficient exhaust• 50/60 Hz direct drive for large
units• Beam rotor with two bearings
• Both power and driver • Part-load (pro’s and con’s)• Lower starter power• “Free” power turbine speed
(lower outlet velocity level)• Typically less efficient exhaust
(lower recovery levels)• Three-shaft aero-derivatives• PT over-speed risk at load
rejection
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 27
Single- vs. multi-shaft industrial II
• Physical speed set by grid and gear ratio (<100 MW)
• Locus of operation at different ambient temp’s with nominal firing could be seen as a “running line”
• Typically reduced surge margin ay high ambient temperatures (COT/T1)
• Grid code requirement of 6% under-speed at +50°C – may be problematic!
• Typical speed range 60…105 %• Compressor speed is decoupled
from load• The running line is, more or less,
a function of firing – not ambient temp – for a certain engine
• No real grid code issues
N/√T
m*
PR
ISO DPN/√T
m*
PR
Power
ISO DP
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 28
Compressor and grid code…
• Grid code requires only speed (47 Hz) and temperature variation• Fouling has to be taken into consideration• The load shall be nominal down to 49.5 Hz and then “pro rata” with
frequency (hence over-firing or extra IGV) down to 47 Hz (UK)
1.081.041.000.960.920.880.840.80
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
Normalized relative flow
Nor
mal
ized
pre
ssur
e ra
tio Surge line
Locus of nominal firing
100 % N/T0.595 %89 %
88 %
5%@50°C 6%@47 Hz
Design point
1%
Based on Wolfgang Kappis, ”Compressors in Gas Turbine Systems, in ”Modern Gas Turbine Systems”
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 29
Min Emission Compliance Load – MECL
NOx
CO
Exha
ust t
empe
ratu
re, °
C
Emis
sion
s, m
ass/
unit
time
EGT
IIIIII
10 30 50 70 90
Maximum EGT
IGV
clos
ed
GT load, percent
MECL
Staging to prevent from:• Lean blow out (LBO)• Combustion dynamics issues
UHC
Nominal firing
Base
d on
Gül
enin
Gos
wam
i”En
ergy
Con
vers
ion”
, 2nd
ed.
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 30
-15 0.7
-10 0.8
-5 0.9
Inlet guide vane – single shaft unit
-30° -20° -10° 10°
des
desm m
des desm m Close Open
Design point
Based on: Farkas F., “The Development of a Multi-Stage Heavy-Duty Transonic Compressor for Industrial Gas Turbines”, ASME 86-GT-91
Turn-down to 45 percent mass flow at design speed has been demonstrated
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 31
Typical preliminary design – single shaft
Shaft speed set by grid (50 or 60 Hz)
Exhaust temperature (COT) 870…950 K
Inlet H/T ratio ≈ 0.55Outlet H/T ratio ≤ 0.92
Firing temperature (COT) 1,600…1,900 K
Stage #1 rim speed = 400…425 m/sTip Mach # ≤ 1.3
Optimize:• Loading• Flow fcn (H/L)• Reaction• Stress
LOAD
0.50mc u
0.65mc u
AN2
Cp=f(AR, α, …)3000 (or 3600) rpm S.F. = 1.2
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 32
Typical preliminary design – single shaft
Shaft speed set by turbine AN2 and exit M#
Inlet H/T ratio ≈ 0.55Outlet H/T ratio ≤ 0.92
Firing temperature (COT) 1,600…1,800 K
Stage #1 rim speed = 400…425 m/sTip Mach # ≤ 1.3
Optimize:• Loading• Flow fcn (H/L)• Reaction• Stress
LOAD 0.50mc u
0.65mc u
AN2
Cp=f(AR, α, …)
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 33
Typical preliminary 2-S design choices• GG Speed set by flow@3000 (850…1000@3000)• Flow• COT (firing)• Pressure ratio
LOAD
Speed?Speed?
• Stage count*• Flow path shape/size• Stress/lifing
Gas generator
Performance
Power Turbine
*Single-stage CT is only possible below PR = 18
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 34
Typical preliminary design – gas generator
Inlet H/T ratio ≈ 0.55Outlet H/T ratio ≤ 0.92
Firing temperature 1,600…1,800 K
Stage #1 rim speed = 400…425 m/sTip Mach # ≤ 1.3
Compressor Power + Losses = Turbine Power
Optimize:• Loading (H/L)• Flow fcn• Reaction• Stress
Optimize:• Loading• Flow fcn (H/L)• Reaction• Stress
Optimum ITD area ratio ≈ 1.3
0.65mc u 0.50mc u
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 35
Ventilation work – spinning PT
• The spinning power turbine will feed work into the ”entrapped” air by increasing the angular momentum
• It is “standard” to assess the work with the equation from the model by Traupel:
• The preceding equation shows why only non-geared PTs can be operated at nominal speed in ventilation
• The trick:
32 2 2
3@500
@250
1
2~ 8 !!!1
V
V
V
P C D l u
PP
I.e. if one assumes 600 kW at 3000 rpm then the windage power at 6000 rpm will be 4,800 kW!
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 36
Synchronous condensation
Twin-shaft with spinning PT
Twin-shaft with SSS-clutchSingle-shaft with SSS-clutch
• Synchronous condensation without firing Spinning PT? SSS-clutch Faster starts and less starter power
• Massive flywheel for increased inertia?
• Inertia in a future grid <4 m/s?• Power absorption
Single shaft compressor issues? Gearbox (forcing)
• Spinning PT – fast start• 600…900 kW windage, i.e. only non-
geared PT’s (~speed3)• P&W FT8, P&W FT4000, GE LMS-100,…
Flyw
heel
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 37
The technology S-curve
Existing technology curve
The breakthrough!
Existing technology advancement
Diminishing returns!
New technology introduction
Time
Figu
re o
f mer
it Time
USC
Effic
’y
Infancy Expansion Maturity
LMS100J-class
Effic
’y
Infancy Expansion Maturity
?
Effic
’y
Infancy Expansion Maturity
Based on Gülen in Goswami ”Energy Conversion”, 2nd ed.
New technology curve!• Hydrogen
Fuel cellGas turbine
• Fission energy?• Low-temp geothermal• Solar• Massive wind + storage
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 38
Vad är egentligen framtiden?
• Vi kommer till 65 procent verkningsgrad?• Mer el i framtiden…• Ångturbiner begränsas till 700°C (?)
– Max EGT 725°C– Keramiska skovlar?
• MHPS har sålt en trycksatt SOFC med 72 % verkningsgrad
– En bränslecell är ingen värmemotor och behöver inte fundera på Carnot…
• Pressure gain combustion?• Ingen ledskena #1• CCS?
– Post-combustion och flexibilitet?– Bättre med OxyFuel?
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 39
New carbon-free fuels
• Hydrogen• Ammonia
– How?– NOx-issue!
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 40
Hydrogen
“…I believe that water will one day be employed as fuel, thathydrogen and oxygen which constitute it, used singly or together,will furnish an inexhaustible source of heat and light, of anintensity of which coal is not capable…”
Jules Verne – The Mysterious Island (L’Île mystérieuse), 1874
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 41
Hydrogen – possibilities for power
Natural gasSMR (Steam
Methane Reforming)
Electrolysis
Wind power
Solar power
Water
CCS
H2 Pipeline H2 Storage
CO2
H2
Conversion to synthetic CH4
Natural gas
Carbon
Conversion to liquid ammonia
N2
Conversion back to H2
Storage
NH3
Grid
H2
inje
ctio
n
Zero-emission power plants*
Intermittent renewable power production:
*64% (+) efficiency for GTCC
• Wobbe index?• Flame speed?• Loads of home appliances!
9:1!!!
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 42
NOx – Water emulsion
60 80 100 120
20
40
60
80
100
NO
x @
15 [p
pmvd
]
Unit load [%]20 40 80 100
0.00.2
WFR [%]600
0.40.60.8
1.0
1.2
NO
x/N
Ox d
ry[-]
Dry Wet
20.2 1.41WFR WFRwetNOx eNOx
Based on: Lechner and Seume, “Stationäre Gasturbinen”, figures 10-14 and 10-16
Lefebvre 9.6:
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 43
State-of-the-art combined cycle – GTCC
Combustor
~ 600°C (+) steam admission
~ 0.02 bar(a)
COT ~ 1,500…1,650°C (+)PR ~ 19…25
~ 40%
100%
1CC GT SC HRSG GT
SCR
~ 20%
Compressor Turbine
~ 625…680°C
~ 1.4…1.5 kg/MWs
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 44
The combined cycle – GTCC
Entropy, s
Tem
pera
ture
, T Gas turbine expansion
Rankine
BraytonSteam turbine expansion
Condenser
COT
EGT
N.B. Schematic!
EvapEco
SHTem
pera
ture
Q m h
Exergy destruction ~ shaded area
TTD
PPT
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 45
Exergy by heat transfer – QChengel and Boles chapter 8
T1 T2
1
QT
2
QT
0
2
1 TQ
T
0
1
1 TQ
T
Heat:
Entropy:
Exergy:
Temperature:
EvapEco
SHTem
pera
ture
Q m h
Exergy destruction ~ shaded area TTD
PPT
01heatT
X QT
01heatT
X dQT
Q Q
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 46
Basic Eco-Reboiler coupling
1
2
3
4
53
5
66 7 8
9
a b
c
d e 1. GT2. HRSG3. ST4. Condenser5. Alternator6. FGC7. Absorber8. Regenerator9. Reboiler
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 47
Economizer-Reboiler Coupling
T
Q
Feed water temperature
Increased heat recovery
1
p
dTm cdQ
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 48
Plant performance – Summary
Single-pressure
conventional reboiler
Single-Pressure
Single-Pressure Reheat
Dual-Pressure Reheat
Triple-Pressure Reheat
Chilled Ammonia
Single-Pressure with
Reheat
Triple-Pressure Reheat
conventional reboiler
% 49.79 50.80 51.50 51.81 51.76 52.27 51.62
MEA MEA MEA MEA MEA NH3 MEA48.00
49.00
50.00
51.00
52.00
53.00
Eco-Reboiler
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 49
Reserver
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 50
Cycle performance – Carnot analogy
T
s
Higher PR
Lower PR
33’
2’
2
4’
4
1
3
1
3
1 1Lcarnot
H
T TT T
3 2 3 22 3
3 2 3 2
1
2 1
4 1 4 14 1
4 1 4 1
1
4 3
4 1
2 3
ln
ln
1TH
h h T TTs s T T
T T PRh h T TTs s T T
T T PR
TT
0.75...0.8GT TH
Carnot factor
2 3T
2 3T
4 1T
4 1T
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 51
Cycle thermodynamics – Sir John Horlock
T1
T3
1
2
3
4
Unavailable heat rejection loss
Expansion irreversibility
Compression irreversibility
3 2 3 22 3
3 2 3 2
4 14 1
4 1
ln
ln
p
p
in
in c
c
h h T TQTs s T TdQ
TT TTT T
2 3 4 1
3 1
1 1in outT TT T
2 3 2 31
3 4 1 4 1
in
out
T TTT T T
2 3 4 1
outinin out
QQT T
1in
out
4 1
2 3
1
3
1 1
1 1
out out
inin
out out
in in
Q TTQTT
Cycle widening (internal irreversibility):
External irreversibility:
Hence:Tref
T
S
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 52
Grid stability
𝜏𝐸
𝑃1 2⁄ · 𝐼 · 𝜔
𝑃 1 2⁄ · 2 · 𝜋 · 𝑓 ·𝐼
𝑃 𝐽
𝐽 𝑠⁄ 𝑠
The inertia constant:
The inertia constant is typically within the range of 5 and 10 seconds:
Nominal power = 500 MW5 s. 2500 MJ10 s. 5000 MJ
500048 ·
10.4 260 𝑘𝑔
Energy required during a start @ 5000 MJ, as 48 MJ/kg natural gas:
This is equivalent of some 280000 cups of tea!
Production means Inertia constant [s]
Nuclear 6.4
Hydro 3.4
Thermal 2.8
Wind- and PV power 0
HVDC import 0
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 53
Grid stability
1 2 109876543
Grid demand (4500 MW)
10 units á 500 MW running at 90 % load – 4500 MW
𝑓 𝑡 𝑓∆𝑃
𝑃 ·𝑓
𝜏 · 𝑡
0.00
10.00
20.00
30.00
40.00
50.00
60.00
0 20 40 60 80 100 120
Freq
uenc
y
Time
Speed/frequency vs. time @tau=10 s.
𝑑𝑓𝑑𝑡 @
∆𝑃2 · 𝜏 · 𝑃 · 𝑓
Lund University / LTH / Energy Sciences / TPE / Magnus Genrup / 2019-09-26 Page 54
Grid stability – impact from inertia…
𝑑𝑓𝑑𝑡 @
∆𝑃2 · 𝜏 · 𝑃 · 𝑓
𝑑𝑓𝑑𝑡
∆𝑃 𝑎100 · 𝑃 · 𝑓 𝑓
𝑃𝑃 · 𝑓 ·
12 · 𝑓 · 𝜏