Calculate the change in the extraction flow to the lowest pressure feedwater heater, due to the change in condenser pressure, fiom the actual test value. There are two methods depending on if the lowest pressure feedwater heater drain flow is pumped forward, or drains to the condenser.
i)If the drain goes to the condenser, the condensate flow is unchanged therefore:
ii)If the drain is pumped forward, the calculation is slightly more complicated:
Let A ~ S T M= ~ E X T R- h ~ m
Let A ~ O N D=' ~ H T R O U T- ~ C O N D '
Calculate the new exhaust steam flow mEmY= m- + ~ E X T R- mEmy
Calculate the new condenser duty Q' (using the above calculations and the tabulated miscellaneous heat rejected value Qmsc)
Calculate the temperature rise of the condenser circulating water, using the reference condenser circulating water flow (WCW)
Assume an inlet water temperature to the condenser tm'
Calculate the outlet water temperature tom' =tN7+tmE7
Calculate the Log Mean TemperatureDifference
Calculate the Heat Transfer Coefficient U', at the assumed inlet water temperature, and reference cleanliness factor
Calculate the condenser duty from the heat transfer relationship
Q' = U'*A*LMTDY,where A is the surface are of the condenser
Ifthe Q' fiom step "m7'is not equal to the Q' fiom step "g", return to step "i", and repeat steps 7-m" with a different inlet water temperature.
If the condenser duties match, but the inlet temperature is not the temperature that is desired, return to step "ay7,using a different condenser pressure
p)When the duties match, and the inlet water temperature is the desired value, correct the test's net unit heat rate using the heat rate correction curves for condenser pressure
Let C F A=~the~ % change in heat rate for the difference between the actual and design condenser pressure.
Let C F RT~=~ the % change in heat rate for the difference between the calculated condenser pressure at the desired inlet temperature and design condenser pressure.
q)When this has been done for the three or four inlet water temperatures, for a single test run, repeat the procedure for the other test runs.
r)Plot the three or four curves (one for each inlet water temperature) of net unit heat rate versus gross load.
Gallatin Unit 1 Reference Net Unit Heat Rate Curve
For Various Condenser Inlet Water Temperatures
Data from 1957Acceptance Test
1 |
I |
I |
I |
I |
I |
I |
I |
100 |
120 |
140 |
160 |
180 |
200 |
220 |
240 |
Gross Load (MW)
--
~i ~ u3r.8e Example of a Family of Reference Heat Rate Curves
3.7.2Generate Heat Rate Correction Factor Curves
The next step is to generate curves that show how much the unit heat rate is affected by a change in an individual parameter. This is done for every parameter that is to be tracked excluding exit gas temperature, Boiler Outlet 02, combustibles, moisture in fbel, and hydrogen in fbel (the heat rate change due to changes in these parameters is calculated f?om ASME equations, and not correction factor curves). The heat rate correction for all three auxiliary powerlstation service
power parameters is calculated, and therefore no correction factor is needed for these parameters either. Most curves should be plotted as % change in Net Unit Heat Rate versus the parameter value. Note that many turbogenerator manufacturers plot % change in turbine cycle heat rate. If that curve is available, it is acceptable to convert the % change in turbine cycle heat rate to % change in net unit heat rate using a design or performance guarantee test boiler efficiency and station use curves. Also, sometimes the thermal kits will have a family of curves, with each curve for a given gross load. If multiple curves are given, to get the correction factor at any load, interpolate or use a spline fit between the curves.
ParameterValue
Figure 3.9 Example of a Family of Heat Rate Correction Factor Curves w/ the Parameter Value as the X Axis
Some curves are plotted as % change in Net Unit Heat Rate versus gross load. For example a curve of % change in heat rate for 1% attemperation flow versus gross load may be given. Sometimes a single curve will be given (or developed) for parameter. Or, a family of curves may be given, each curve for a specific parameter value (i.e. the graph may have gross load on the x axis and % change in net unit heat rate on the y axis, with one curve for 1% attemperation, another curve for 3% attemperation, etc.)
Figure 3.10 Example of a Family of Heat Rate Correction Factor Curves w/ the Parameter Value as the Z Axis
Some heat rate correction factors will be constants. For example, the heat rate correction factors for turbine section efficienciesare usually a single constant: x % change in net unit heat rate for a 1% point change in section efficiency.
Sections 3.7.2.1 and 3.7.2.2 contain information on where to obtain heat rate correction factors.
3.7.2.1Turbine Vendors Thermal Kit
The supplier of the turbine almost always provides a set of heat rate correction curves for several conditions.
a)Throttle Pressure
b)Throttle Temperature
c)Steam Temperature at Inlet to Intercept Valve
d)Condenser Pressure
e)Final Feedwater Temperature (sometimes)
f ) Reheat Attemperation (sometimes)
g)Superheat Attemperation (sometimes)
3.7.2.2Thermodynamic Model of the Plant
A very usefbl tool to develop heat rate correction curves are the computer based thermodynamic modeling programs that are available. Once a plant has been properly modeled, changes in the cycle can be simulated, and the effects on heat rate (and other parameters) can be seen. There are now both boiler and turbine cycle modeling programs available, however the turbine cycle models, while complicated, are much easier and quicker to use than the boiler models, therefore these are used much more often.
a)Makeup
b)Auxiliary Steam Usage
c)Final Feedwater Temperature/ Feedwater Heaters Out of Service
d)Reheat Attemperation
e)Superheat Attemperation
3.7.3Develop "Expected" Parameters Curves
When the reference heat rate curves and parameter curves are fist developed, the expected parameter curves will be identical to the reference parameter curves (see section 3.7.1.4). Over time, there will be modifications and additions to the unit that permanently change the performance of the unit. When any permanent change(s) to the plant are made, the change must be studied, and the applicable curves should be modified as appropriate. Examples of modificationsthat are sometimes made, and the parameters that are affected include:
Adding additional auxiliary equipment (precipitators, larger ID fans, etc.) This increases station service.
Operating procedures are changed (i.e., changing from full pressure to hybrid variable pressure operation). This would change the expected throttle pressure, and possibly the expected steam temperature and attemperation flow curves.
A significant change in fuel characteristics (burning 40% moisture fuel instead of 10%). Some "expected" parameter curves may need to be changed, including exit gas temperature.
There are various sources for the data that is required to update the curves.
A performance/optimization test after the modification. This method is recommended when there have been any changes in the boiler area for two reasons. First, because the effects of fuel switches, furnace or convection pass modifications, etc. are very difficult to accurately calculate. Second, boiler modifications usually affect several parameters (exit gas temperature, combustibles in ash, Boiler Outlet 02, steam temperatures, and attemperationflow rates).
Manufacturers design data. This method may be acceptable for changes that affect station service for example. If additional fields are added to a precipitator, the manufacturer should be required to provide information on the change in auxiliary power that is to be expected.
Engineering calculations/assumptions.
3.7.4 Calculation of Reference Net Heat Rate
The Reference Net Heat Rate is calculated at the period's average gross load, and condenser inlet water temperature, by calculating a heat rate at each of the three or 4 reference heat rate curves, and then interpolating between theses values based on the water temperature.
1)Calculate average gross load for time interval (GLoadkt).
2)Calculate average cooling water temperature for time interval (CCWTIA,~).
3)Calculate the heat rate from each of the three or four reference heat rate curves (each curve being at a different condenser water inlet temperature), at the average gross load.
4)Perform a spline fit (see Appendix F) of the heat rates from step "C",using the actual average cooling water temperature, to determine the reference net heat rate NUHlhd.
n e f = -Ref, |
Sl, C c w I ~ eSl,c =Ref, |
S2, CCWIRef,S2, m |
~ S3, |
e |
~ |
CCWIRCCs3, C c w I ~ c t ) |
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3.7.5 Actual Net Heat Rate
1)Determine total actual fuel burned in kilograms for the time interval (FSAct)
2)Determine the Higher Heating Value (HT~VA~~)of the fuel (if multiple samples are collected during the period, weight average by amount of coal burned for the period from the coal analysis).
3)Calculate the actual net unit heat rate by multiplying the total quantity of fie1 burned by the hel's higher heating value, and then dividing by the net generation.
3.7.6General Comments on Calculating Heat Rate Deviations for All Parameters
For calculating heat rate deviations for parameters in the turbine cycle, the standard procedure is relatively straight-forward. For each parameter, the heat rate deviation that is calculated is the amount the net unit heat rate would increase by if its value only changed from its expected value to its actual value. In other words, when calculating the heat rate deviation for Throttle temperature, all other parameters are assumed to be at their expected level, and the net unit heat rate is at its expected level. The only turbine cycle exception to this rule is condenser pressure. Its expected level is adjusted up if there are other problems in the cycle. This way, if there are problems in the cycle resulting in additional heat load on the condenser, the expected condenser pressure is the condenser pressure that should be obtainable with the additional heat load.
The boiler cycle losses are calculated in a similar manner, but with an important difference. In addition to the question of when calculating the heat rate deviation for one parameter, should the other parameters be held at their expected value or actual value; there is another pair of questions. Because some parameters have a significant influence on other parameters, should those influences be considered? For example, if the exit gas temperature (no leakage, corrected to reference inlet air temperature) increases, not only does the dry gas loss increase, but both the moisture in fuel loss and the hydrogen loss also increases (because the water vapor leaving the stack will be at a higher enthalpy).
There is not any clear "right" or "wrong" way of looking at these issues. In this procedure, boiler losses are calculated assuming other parameters are at their expected levels (which is consistent with the turbine cycle losses), but if there are additional losses in other areas, they are taken into account. Continuing with the previous example, the heat rate deviation this procedure would calculate for an increase in exit gas temperature would include the increase in dry gas loss (from the expected to actual exit gas temperature), the increase in moisture in &el loss (based on the actual versus expected he1 moisture at the actual exit gas temperature) and the increase in
hydrogen loss (based on the actual versus expected fuel hydrogen and the actual fuel hydrogen at the actual exit gas temperature). The heat rate deviation due to moisture in fuel loss would be calculated at the expected exit gas temperature, and would account for the change (if any) in k e l moisture only.
This procedure will at times slightly under account for some losses. For example, if both the exit gas temperature and the boiler outlet 0 2 are above expected, the heat rate deviation for exit gas temperature is calculated using the expected (lower than actual) boiler outlet 02, and the boiler outlet 0 2 heat rate deviation is calculated using the expected (lower than actual) exit gas temperature. If the total heat rate deviation was calculated in one step using the actual exit gas temperature and the actual boiler outlet 02, that heat rate deviation would be larger than the sum of the two deviations calculated individually .
3.7.7 Air Preheating Steam Coils
The heat rate deviation for air preheating coils is usually based on the flow rate to the coils, or if the flow is relatively constant when they are in service, the number of hours of operation. If multiple sources of steam can be used, then a heat rate deviation must be calculated for each.
1)Establish SCAPH~dvaluefrom reference curve (based on acceptance test or design data, this could be a function of main steadfeedwater flow and or ambient air temperature).
2)Establish SCAPHE, value from expected level curve (based on current plant equipment design.
3)From the curve of heat rate correction factor due to air coil usage versus gross load or flow, determine the HRCFsCAPHat the period's average gross load.
4)Determine the heat rate deviation due to the difference between the expected makeup and the reference makeup.
5 ) |
ARer calculatingthe expected net unit heat rate NUHRE, (see Section 3.7.22), determine |
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the heat rate deviation due to the difference between the actual makeup and the expected |
makeup
3.7.8 Boiler Differential Pressure
The heat rate deviation for the boiler differential pressure is based on the percentage pressure drop between the economizer inlet to the superheater outlet.
1)Establish BDPRefvalue from reference curve (based on acceptancetest or design data).
2 ) |
Establish BDPvalue from expected level curve (based on current plant equipment |
|
design. |
3)From the curve of the heat rate correction factor due to 1% boiler differential pressure versus gross load (or feedwater flow), determine the HRCFBDPat the periods average gross load.
4)Determine the heat rate deviation due to the difference between the expected and the reference boiler differential pressure.
5 ) |
After calculating the expected net unit heat rate N U H R E ~(see~ Section 3.7.22), determine |
|
the heat rate deviation due to the difference between the actual and the expected boiler |
differential pressure.
3.7.9Condenser Pressure
This is a two step procedure. First, the reference condenser pressure is calculated, using the actual unit load, heat rejected to the condenser based on a reference turbine cycle heat rate curve, the reference condenser parameters (tube materials, thickness, etc.), and the reference condenser pressure. Since the reference condenser pressure is calculated using the reference condenser pressure, this is an iterative process. An initial guess is made for the reference condenser pressure. This pressure is then used to determine the heat rejection in the condenser, by adjusting the reference turbine cycle heat rate. Then the condenser characteristics are used to calculate the condenser pressure. If there is a difference between the two pressure, the initial guess is changed, and the calculations are repeated.
A second iterative procedure is used to calculate the expected condenser pressure. The expected condenser pressure is calculated using the actual heat rejected to the condenser (adjusted to the expected condenser pressure and for startup &el), and the expected condenser parameters.
Steps "1" through "4"are calculating some miscellaneous values that will be needed in the later, iterative steps:
1)Calculate heat added by the boiler feed water pumps (PumpQRdW). Obtain from design or acceptancetest curves.
2)If the unit has any auxiliary equipment condensers, calculate their total duty or rate of heat transferred out of the turbine cycle, ( A u x D u ~ Y R fi~-~omEcurves~~) developed across the flow or load range using thermal modeling software.
3)Calculate Generator Loss (GLossR~~E~,,) fi-om manufacturer's curves.
4)Calculate HE1 Inlet Water Temperature Correction Factor (HEITCFRef,kp), based on the actual circulating water inlet temperature (CCWTIAcS
Steps "5" through "24" is an iterative procedure for calculating the reference condenser pressure, based on the "reference" turbine cycle heat rate curve and "reference" condenser characteristics (tube material, tube wall thickness, etc.)
5)Establish reference value for Condenser Circulating water flow rate ( C C w e f )fi-om the condenser characteristics (some constant value), or fiom a curve (i.e., C C W L f vs. lake elevation).
CCWFR~~= constant or f(water elevation)
6)Calculate the reference value for Water Velocity through the tubes ( T u b e W ~ ) ,given the flow rate ( C C m f ) , the number of tubes (TubeNo~~f),and the internal diameter of the tubes (TubelDRef).
Look up the reference value for the Heat Exchange Institute "Material and Gauge Correction Factor" (TubeMGCRef) as a fhnction of the material of the condenser tubes (TubeMatRef)and the tube wall thickness (TubeBWGRd).
Establish reference value for HEI's "Uncorrected Heat Transfer Coefficient" (TubeUhf) based on tube external diameter (TubeOD~~f)and water velocity through the tubes (TubeW~ef).
Establish reference value for Condenser Surface Area (CSArea~~f).
Calculate Reference Gross Turbine Cycle Heat Rate (corrected to design condenser pressure) G T C e e CCO~DCPas a hnction of the period's average gross load (GLoadht)
Use design condenser pressure (CPD~,)as the first guess for calculating CPRef.
From turbolgenerator manufacturer's heat rate correction curve(s) for condenser pressure (percent change in heat rate vs. condenser pressure) determine the HRCF-,
If the manufacturer provides multiple curves based on different steam flows or loads, then the HRCFcp, ref-^= will have to be determined by interpolating or spline fitting between curves.
Calculate the gross turbine cycle heat rate, corrected to the reference condenser pressure, GTCHRR~CC,.
Calculate the rate of heat rejection in the condenser, Condenser Duty (Duty) by taking the total heat input to the turbine cycle, including the heat added by the pumps, and then subtracting the energy converted to electricity, the losses in the generator, and heat rejected in auxiliary condensers (if any).