g Estimating Gas Turbine Performance The following is a method for estimating gas turbine performance using performance curves and site data (i.e., elevation, ambient temperature, inlet and exhaust pressure drops, and the type of fuel). Both full load and part load performance calculations are described and illustrated. Typical examples are provided for package power plants. Performance curves are based on the ISO standard (59°F, 60% relative humidity and 14.7 psia). Theses curves do not include the water or steam injection for NOx control due to the many different NOx levels offered. However, the effect of a known water or steam flow can be calculated separately per the dilutent effects curves. This procedure should be used only for the approximation of performance at site conditions and not for performance guarantees. Performance guarantees for this proposal are shown in the “Performance Specifications” section. The
performance curves included are to illustrate the calculation procedure and do not reflect current ratings. Performance curves applicable to the equipment offered in this proposal are listed under “Turbine and Generator Performance Curves” in the “Engineering Data” Section. Nomenclature D
=
differential; i.e. DP is pressure drop
fa
=
inlet DP factor for output
fb
=
exhaust DP factor for output
fc
=
compressor inlet temperature factor for output
fd
=
compressor inlet temperature factor for exhaust flow
fe
=
compressor inlet temperature factor for heat rate
ff
=
inlet DP factor for heat rate
fg
=
exhaust DP factor for heat rate
fh
=
humidity factor for output
fi
=
humidity factor for heat rate
HC
=
heat consumption (fuel consumption in Btu/h)
HR
=
heat rate (Btu/kWh)
KW
=
power output (kW)
P
=
barometric pressure (psia)
Pc
=
effective pressure (psia) at the inlet flange of a package power plant
Tx
=
exhaust gas temperature (°F)
Reference GTS–111D Estimating Gas Turbine Performance
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Wx
=
exhaust flow (lb/h)
EFF
=
thermal efficiency (%)
(LHV) =
based on fuel lower heating value
Subscripts s, i, o s
denotes at site conditions
i
denotes at ISO conditions
o
denotes at site altitude, actual inlet and exhaust DP’s, and compressor inlet conditions of 59°F @ 60% RH.
I. Full Load Performance A. Method 1.
Output (KWs) = (KWi) x (Ps/14.7) x fa x fb x fc x fh
2.
Heat Rate (HRs) = (HRi) x fe x ff x fg x fi Note: Altitude has no effect on heat rate
3.
Heat Consumption (HCs) = (KWs) x (HRs)
4.
Exhaust Temperature (Tx) Read from appropriate curve. Add temperature increase for additional inlet and/or exhaust pressure drops.
5
Exhaust Flow (Wxs) = (Wxi) x (Pc/14.7) x fd Where Pc = Ps – (0.0361 x additional DP (inches of H2O) at inlet)
B. Notes 1.
Round off calculations as follows: Output – To nearest 10 kW or maximum of 4 significant figures Heat Rate – To nearest 10 Btu/kWh Heat Consumption – To nearest 0.1 x 106 Btu/h or maximum of 4 significant figures Exhaust Temperature – To nearest degree F Exhaust Flow – To four significant figures (lb/h)
2.
The ratio Ps/14.7 can be read directly from the altitude correction curve 416HA662
C. Sample Full Load Calculation Package Power Plant – MS7001(EA) Simple Cycle Model PG7111(EA) with an air–cooled generator.
Reference GTS–111D Estimating Gas Turbine Performance
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Site Conditions:
1.
2.
Altitude
= 600 ft
Barometric Pressure Ps
= 14.39 psia (from Curve 416HA662)
Compressor Inlet Temperature
= 90°F
Inlet DP
= 2.5’ H2O (included in rating)
Exhaust DP
= 10” H2O (5.5” H2O is included in rating)
Fuel
= Distillate Oi1
Mode
= Base Load
Design Conditions (ISO) from Curve 499HA733 Output KWi
= 82100 kW
Heat Rate HRi
= 10560 Btu/kWh (LHV)
Exhaust Flow Wxi
= 2358 x 103 lb/h
Calculation of factors.
The ratings for the package power plant include a standard inlet and exhaust pressure drop as stated with the ratings. Therefore the pressure drops used to calculate fa, fb, ff, fg, Pc, and exhaust temperature increase are the pressure drops in excess of the standard pressure drops. The resulting performance decrease effect of additional pressure drop is subtracted from unity to obtain the output multiplication factor. The heat rate percentage effect is added to unity to obtain the heat rate multiplier for additional pressure drops. Output :
f a + 1.0 1 + 0.9953 f b + 1.0 * 0.42 x 4.5 100 4 (curve 499HA733 with additional 4.5” H2 O) f c + 0.890 (from Curve 499HA734) f h + 0.9982 (from Curve 498HA697)
Heat Rate :
f e + 1.025 (from Curve 499HA734) f f + 1.0 1 + 1.0047 f g + 1.0 ) 0.42 x 4.5 100 4 (curve 499HA733 with additional 4.5” H2 O) f i + 1.0048 (from Curve 498HA697)
ǒ
ǒ
Ǔ
Ǔ
Reference GTS–111D Estimating Gas Turbine Performance
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Exhaust Flow :
3.
P c + 14.39 psia * 0 + 14.39 psia f d + 0.930 (from Curve 499HA734)
Calculation of Full Load Conditions at Site: Output KW s + 82100 x 14.39 x 1.0 x 0.9953 x 0.890 x 0.9982 14.7 + 71063 or 71060kW Heat Rate HR s + 10560 x 1.025 x 1.0 x 1.0047 x 1.0048 + 10927 or 10930 BtuńkWh (LHV) Heat Consumption HC s + 71060 x 10930 + 776.7 x 10 6 Btuńh (LHV)
Exhaust temperature is calculated by adding the temperature increase due to pressure drops to the value read from Curve 499HA734: T x + 1006 ) 1.9 (0 ) 4.5) F 4 T x + 1008.1 or 1008 F Exhaust Flow + 2358 x 10 3 x 14.39 x .930 14.7 + 2146.7 x 10 3 or 2147 x 10 3 Ibńh
II. Part Load Performance Part load output, heat rate and heat consumption are calculated in a similar manner as base load using the part load heat consumption curve. Before using the output % off the heat consumption curve, all part load performance must be referenced to 59°F site performance kWo. A. Method 1.
At site barometric pressure with site inlet and exhaust pressure drops and at 59°F compressor inlet temperature, calculate the following base load performance parameters: Output, kWo Heat rate, HRo Heat consumption, HCo This data then becomes the corrected values on which to base the part load calculations.
2.
Reference GTS–111D Estimating Gas Turbine Performance
Calculate percentage of load:
page 4
% load = required load/kWo 3.
From the applicable performance curve, at the percent of load calculated from (2) above and at the compressor inlet temperature, read the percent of design heat consumption. HCs = HCo x % design heat consumption.
4.
Heat rate at required load: HRs = HCs ÷ kWs
5.
Exhaust flow and temperature are calculated in an analogous manner as base load using corrected design outputs as shown above, and the Effects of Modulated Inlet Guide Vanes Curve at the appropriate ambient. The extreme right hand point of each ambient curve on the Modulated Inlet Guide Vane Curve represents the full open IGV position, the knee point in each curve represents the closed IGV position, Note that this curve is for combined cycle machines only. Simple cycle machines, which are not normally concerned with part load Exhaust conditions, operated on a different schedule and can not be calculated using this curve.
B. Sample Part Load Calculation The following sample part load calculations are for the MS7001(EA) simple cycle package power plant used previously. Site conditions: Altitude Barometric pressure Compressor inlet temperature Relative Humidity Inlet DP Exhaust DP Fuel Load required 1.
= 600 ft = 14.39 psia = 90°F = 60%RH = 2.5” H2O (included in rating) = 10” H2O (5.5” H2O is included in rating) = Distillate Oil = 75 percent base load
Calculation of site performance at full load and 59°F at 60%RH: KWo = KWi x (14.39/14.7) x fa x fb KWo = 821000 x 0.9789 x 1.0 x 0.9953 = 79990 kW HRo = HRi x ff x fg HRo = 10560 x 1.0 x 1.0047 = 10610 Btu/kWh (LHV) HCo = KWo x HRo Reference GTS–111D Estimating Gas Turbine Performance
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HCo = 79990 x 10610 = 848.7 x 106 Btu/h (LHV) 2.
Calculation of site performance for 90°F @ 60%RH: Site output (base load) = KWo x fc x fh = 79990 x 0.891 x 0.9983 = 71150 kW At 75% base load, required load = 71150 x 0.75 = 53360 kW % load = 53360/79990 = 66.7%
3.
From Curve 499HA733 at 66.7% design load and 90°F, % design heat consumption = 71% Part load, site heat consumption, HCs = HCo x % design heat rate HCs = 848.7 x .71 = 602.6 x 106 Btu/h (LHV)
4.
Site heat rate HRs = HCs ÷ kWs HRs = 602.6 x 106 ÷ 53360 = 11290 x Btu/kWh (LHV)
5.
Entering the Modulated Inlet Guide Vane Effects Curve (516HA129) at the 66.7% output calculated in Step 2 and, for the 90°F ambient curve; Exh Temp. = 990°F Wexh % design = 75.5% Wexh = Wi x % design Wexh = 2358 x .755 = 1780 x 103 lb/h
Performance With Water or Steam Injection The amount of steam or water injection required to meet a given NOx emission level is not available from a curve because of the many variables impacting this value. In fact, the exact flow is typically not finalized until the field Emissions Compliance Testing. However, given a specific flow value, the resulting effect on output and Heat Rate can be determined using the Injection Effects Curves. For example, taking the “dry” Output and Heat Rate Performance calculated from Example I and, assuming GE has reported (for the specific conditons given) an estimated steam flow to meet 65 ppmvd @ 15% O2 NOx of 42590 lb/h (11.83 pps); The resulting output and Heat Rate would be:
Reference GTS–111D Estimating Gas Turbine Performance
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KW = 71060 x (1 + 0.059) (from curve 499HA899A) = 75250 KW HR = 10930 x (1 – .0275) (from curve 499HA900A) = 10630 Btu/Kw–h (LHV)
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SI and Metric Units Conversion The following is a list of conversion factors most commonly used for gas turbine performance calculations.
Conversion Factors To Convert atm atm bars bars Btu/h Btu/h Btu/hph Btu/lb °F °C °C ft3/min ft3/min gal/mln in. of mercury in. of water (at 4°C) in. of water (at 4°C) J kg kg/cm2 kg/m3 kW lb/in2 l/min l/min scf W
Reference GTS–111D Estimating Gas Turbine Performance
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To kg/cm2 lb/in2 atm lb/in2 kcal/h kJ/h kJ/kWh kJ/kg °R °F °K l/s m3/min l/s kg/cm2
Multiply By 1.0333 14.7 0.9869 14.5 0.2520 1.0548 1.4148 2.326 °F + 459.7 (°C x 9/5) + 32 °C + 273.2 0.4720 0.02832 0.06308 0.03453
kg/cm2
0.00254
lb/in2 Btu lb lb/in2 lb/ft3 hp Pa ft3/s gal/s Nm3 Btu/h
0.03613 9.478 x 10–4 2.205 14.22 0.06243 1.341 6894.8 5.886 x 10–4 0.004403 0.0268 3.4129
GENERAL ELECTRIC MODEL PG7111(EA) GAS TURBINE ESTIMATED PERFORMANCE – CONFIGURATION: NATURAL GAS & DISTILLATE Compressor Inlet Conditions 59 F (15.0 C), 60% Rel. Humidity Atmospheric Pressure 14.7 psia (1.013 bar) FUEL DESIGN OUTPUT DESIGN HEAT RATE (LHV) DESIGN HEAT CONS (LHV) X10–6 DESIGN EXHAUST FLOW X10–3 MODE: BASE LOAD
kW Btu (kJ)/kWh Btu (kJ)/h lb/h (kg)/h
NATURAL GAS 83500 10480 (11060) 875.1 (923.5) 2351 (1066)
DISTILLATE 82100 10560 (11140) 867.0 (914.6) 2358 (1070) PPB 061088
NOTES: 1. Altitude correction on curve 416HA662 REV A 2. Ambient temperature correction on curve 499HA734 REV A 3. Effect of modulated IGV’s on exhaust flow and temp. on curve 516HA129 4. Air cooled generator 7A6 5. Humidity correction on curve 498HA697 REV B – all performance calculated with specific humidity of .0064 or less so as not to exceed 100% relative humidity. 6. Plant performance is measured at the generator terminals and includes allowances for excitation power, shaft driven auxiliaries, and 2.5 in. H2O (6.2 mbar) inlet and 5.5 in. H2O (13.7 mbar) exhaust pressure drops. 7. Additional pressure drop effects: %Effect on Output Heat Rate 4 in. H2O (10.0 mbar) inlet –1.42 0.45 4 in. H2O (10.0 mbar) exhaust –0.42 0.42
Effect on Exhaust Temp. 1.9 F (1.1 C) 1.9 F (1.1 C)
HEAT CONSUMPTION – PERCENT DESIGN
130 0F
120 59 F
110 100 120 F 90 80 70 60 50 40 30 20 10 0
10
DATE: 10/17/89 DA JAQUEWAY
20
30 40 50 60 70 80 90 100 110 120 130 GENERATOR OUTPUT – PERCENT DESIGN
499HA733 REV A
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GENERAL ELECTRIC MODEL PG7111(EA) GAS TURBINE
EXHAUST TEMPERATURE (DEG. F)
Effect of Compressor Inlet Temperature on Output, Heat Rate, Heat Consumption, Exhaust Flow And Exhaust Temperature at 100% Speed FUEL: NATURAL GAS & DISTILLATE OIL DESIGN VALUES ON CURVE 499HA733 REV A DESIGN MODE: BASE LOAD 1040 1030 1020 1010 1000 990 980 970 960 950 940 130 125 120 PERCENT DESIGN
115 110 HEAT RATE
105 100 95 90
EXHAUST FLOW
85
HEAT CONS.
80 OUTPUT
75 70 0
10
20
30
40
50
60
70
80
90
100
110
120
COMPRESSOR INLET TEMPERATURE (DEG. F) DATE 10/17/89 DA JAQUEWAY
Reference GTS–111D Estimating Gas Turbine Performance
499HA734 REV A
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GENERAL ELECTRIC MODEL PG7111(EA) GAS TURBINE Effect of Modulated Inlet Guide Vanes on Exhaust Flow and Temperature As a Function of Output and Compressor Inlet Temperature.
EXHAUST FLOW – PERCENT DESIGN
EXHAUST TEMPERATURE (DEG. F)
FUEL: NATURAL GAS & DISTILLATE OIL DESIGN VALUES ON CURVE 499HA733 REV A DESIGN MODE: BASE LOAD 1100 1050 1000 950 900
0F
850 800 750
30 F 59 F 90 F
700 650
120 F
600 550 500 115 110 105 100 95 90 0F
85 30 F
80 59 F
75 90 F
70 120 F
65 0
10
20
30 40 50 60 70 80 90 100 110 120 130 GENERATOR OUTPUT – PERCENT
DATE 10/17/89 DA JAQUEWAY
516HA129
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GENERAL ELECTRIC GAS TURBINE ALTITUDE CORRECTION FACTOR ALTITUDE VS ATMOSPHERIC PRESSURE AND ALTITUDE VS CORRECTION FACTOR FOR GAS TURBINE OUTPUT AND FUEL CONSUMPTION NOTES: 1. Heat Rate and Thermal Efficiency are not affected by altitude. 2. Correction Factor = P(atm)/14.7 15.5
1
15
0.95 CORRECTION FACTOR
14.5
0.9
14
0.85
13.5
0.8
13
0.75
12.5
0.7
ATMOSPHERIC PRESSURE
12
0.65
11.5
0.6
11
0.55
10.5
0.5 0
1
2
3
4
5
6
7
8
9
ALTITUDE – THOUSAND FEET 416HA662 REV A
4/24/90 F.J. BROOKS
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GENERAL ELECTRIC MS6001, MS7001 AND MS9001 GAS TURBINES CORRECTIONS TO OUTPUT AND HEAT RATE FOR NON–ISO SPECIFIC HUMIDITY CONDITIONS For operation at base load on exhaust temperature control curve 1.01 1.009 ISO SPECIFIC HUMIDITY 0.0064 lb. water vapor/lb. dry air
1.008 1.007 1.006
HEAT RATE
1.005
CORRECTION FACTOR
1.004 1.003 1.002 1.001 1 0.999 POWER OUTPUT
0.998 0.997 0.996 0.995 0.994 0.000
0.005 0.010 0.015 0.020 0.025 0.030 SPECIFIC HUMIDITY (lb. water vapor/lb. dry air)
10/10/89 DA JAQUEWAY
0.03 5
498HA697 REV B
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GE MODEL PG7001(EA) GAS TURBINE EFFECT OF STEAM INJECTION ON OUTPUT BASE LOAD – NATURAL GAS / DISTILLATE
12 11 100F
PERCENT INCREASE IN OUTPUT
10 9 59F
8 45F
7 0F
6 5 4 3 2 CURVE 499HA899A KH CONWAY 4/14/89
1 0 0
2
4
6
8
10
12
14
STEAM INJECTION – LB/S
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16
18
20
GE MODEL PG7001(EA) GAS TURBINE EFFECT OF STEAM INJECTION ON HEAT RATE BASE LOAD – NATURAL GAS / DISTILLATE
6.0 5.5 5.0 100F
PERCENT DECREASE IN HEAT RATE
4.5 4.0 59F
3.5
45F
3.0
0F
2.5 2.0 1.5 1.0 CURVE 499HA900A KH CONWAY 4/14/89
0.5 0. 0
2
4
6
8
10
12
14
16
18
20
STEAM INJECTION – LB/S
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