Accuracy evaluation of various methods to … · A RELATIVE ACCURACY EVALUATION OF VARIOUS METHODS...

EPRI Heat Rate Improvement Conference 2005 January 25-27, 2005 • Cedar Rapids, Iowa

A RELATIVE ACCURACY EVALUATION OF VARIOUS METHODS TO DETERMINE LONG TERM COAL-BURNED VALUES FOR COAL PILE

INVENTORY RECONCILIATION

Joseph R. Nasal, P.E. GENERAL PHYSICS CO~PO~ATION

David A. Hightower CITY OF COLORADO SPRINGS

ABSTRACT

This paper presents the results of an engineering study conducted on the City of Colorado Springs' Utilities (CCSU) on Martin Drake Unit # 7 (140 MWe. PC fired) to evaluate the relative accuracy of using various methods to determine "coal burned" over a five month period of time. Since coal-burned is used for calculating coal pile inventory estimates as well as a common means of determining thermal performance. CCSU was interested in the relative accuracies and "agreement of results" associated with using various methods to determine coal consumption at the Martin Drake Station.

The scope of the study included examining and comparing plant operational data over five months, using three distinctly different methods to determine unit heal rate and coal consumption, these included:

I. Using a high accuracy and routinely-calibrated belt scale that supplied coal 10 the unit's coal bunker (Input-Output Method)

2. Using an on-line performance monitoring system to calculate and archive real-time turbine cycle heat rate (ASME. PTC 6) and boiler efficiency (ASME. PTC 4 ) on a minute-to-minute basis (Heat Balance Method), and

J. Using a "Modified Design Curve Method" that is based on design turbine cycle heat rate data modified for actual operating conditions and equipment degradation to determine heat input from the boiler, in combination with ASME PTC 4 based boiler efficiency calculations.

The study showed that the Heat Balance Method was the most accurate method of calculating coal consumption. As a backup measure, heat input (fuel consumption) should also be calculated using the Modified Design Curve Method. Use of the belt scale (Input-Output Method) to determine coal consumption was shown to have less accuracy than the other two calculation methods.

INTRODUCTION An engineering study was performed by General Physics to improve the methods of determining coal consumption at CCS' Martin Drake Station. The scope of work included examining three different methods: 1) the Heat Balance Method, which is based upon a design heat balance of the steam cycle using primary feedwater flow and other process measurements to calculate turbine· cycle heal rate; 2) the Modified Design Curve Method which uses the original design turbine cycle heat rate curve, modified for actual operating conditions and equipment degradation to determine heat input from the boiler; and 3) the Input/Output Method which uses the belt scale coal (Tons/day) readings and the daily coal heating value lab analysis to determine heat input calculations.

Based upon the analysis detailed below, the Heat Balance Method shows to be the most accurate method of calculating boiler heat input. As a backup measure, heat input (fuel consumption) should also be calculated using the Modified Design Curve Method. Use of the belt scale to determine boiler heat input is shown to have less accuracy than the other calculation methods.


HEAT BALANCE METHOD The purpose of evaluating the Heat Balance Method was to determine if there is any significant improvement in the heat input (fuel consumption) calculations used in an On-line Performance Monitoring System when the primary feedwater flow is calculated from other related data versus direct readings from the feedwater flow meter. Currently the primary flow is read from a snapshot value of the flow indication in PI, and a 5 minute "dampened" value is then stored in the EtaPRO Performance Monitoring System's (PMS) archive, Using the dampen feature in EtaPRO helps to reduce large fluctuations in the data that are common with indicated flow rates. The result of this dampened flow rate, along with several other process data, is used to calculate the turbine cycle heat input. The turbine cycle heat input is then divided by boiler efficiency (using the loss method) to determine unit heat input, and then used to calculate consumption based on the daily coal lab analysis.

A study of the turbine cycle heat input calculation from raw data to final result uncovered no errors in the calculation methodology used by the PM$. The method was broken down into individual steps, and the exact method used in the PM$ was reproduced in an Excel spreadsheet. The result based upon raw data obtained from the historian (PI), matched the results of the PMS calculation stored in PI. Note that although the methodology used is correct, the result can be corrupted by bad data, transient data, and low load data obtained from PI.

The calculation results were next compared against the results of coal consumption obtained from the belt scale-over a time period from January - May, 2003. The turbine cycle heat input is divided by the calculated boiler efficiency, and the result is used to calculate the amount of coal burned in MMBtu/day. Differences were noted between the belt scale and the heat balance method calculation, although no consistency in the deviations was found due to other operational parameters.

The current PMS calculation results were also plotted against gross generation to determine the amount of scatter present in the data. For a typical load of 140 MW (+/- 0.5 MW), the turbine cycle heat input averaged 1250.1 MMBtu/hr, with twice the standard deviation equal to 20.9 MMBtu/hr (Table I). Essentially this indicates that for a given population of data at 140 MW, the turbine cycle heat input will be calculated with +/- 20.9 MMBtu/hr 95% of the time (Figure I). This equates to a deviation in gross heat rate of +/-166.2 Btu/kWh, and a deviation in turbine cycle heat rate of +/- 149.6 Btu/kWh. The calculated uncertainty of 2.73% shown in Table 2 compares well to the calculated turbine cycle heat input, for which two standard deviations is equivalent to 1.68%.

Average (MMBtu/hr)

Standard Deviation (M MBtu/hr)

Accuracy (%)

+/- Gross Heat Rate I (MMBtu/hr)

+/- Turbine Cycle Heat Rate (MMBtu/hr)

Existing EtaPRO PM S Calculation

1250.1 10.5 1.68% 166.2 149.6

Using 1st Stage Pressure 1248.4 8.0 1.28% 126.7 114.0 Using C RH Pressure 1248.5 13.9 2.23% 221.0 198.9 Using Final FW Temp 1248.2 20.2 3.23% 319.9 287.9

Table I: Turbine Cycle Heat Input Calculation Methods Comparison at 140 MW (+/- 0.5 MW)


Table 2: Turbine Cycle Heat Input Calculated Uncertainty

The next step involved reproducing the above calculation, but substituting a calculated value for the primary flow instead of using the indicated (metered) flow rate. The methods evaluated include first stage pressure, cold reheat pressure, and final feedwater temperature as indicators of primary flow. Another method considered was reading feedwater flow rates at a high frequency (e.g. every four seconds) to improve the data.

For the first stage pressure, the original design curve of pressure vs. throttle flow was considered. However, over time the original curve does not match the current operating data, most likely due to nozzle block degradation. For example, at a first stage pressure of 800, 1000, and 1200 psia, the design curve predicts that throttle flow will be approximately 605, 760, and 910 kpph respectively. However, the data in PI from the installed feedwater flow meter indicate that throttle flow at these pressures was actually 672, 830, 988 kpph (average) respectively (Table 3). Although there is some deviation in throttle flow versus first stage pressure in the data, the design values are on the low end of deviations and therefore it was recommended that the curve not be used in this evaluation.

To obtain the relationship for first stage pressure, a constant value was calculated based on the equation W=C*√(P/v), where W is the first stage steam flow, C is the nozzle constant, P is the first stage pressure, and v is the first stage specific volume. Using a range of unfiltered PI data, the constant value was calculated for each timestamp and an average of the constants was then calculated. Steady-state filtered data was also used in the analysis over a greater range of time; however the resulting average constant value remained the same. The average constant was then use4d in the turbine cycle heat input calculation to determine first stage flow, throttle flow and finally primary feedwater flow. As noted previously in Table 1, the original method of calculating turbine cycle heat input produced a standard deviation of 10.5 MMBtu/hr at 140 MW. When the first stage pressure method was introduced, the standard deviation was reduced to 8.0 MMBtu/hr (Table 1), a slight improvement. This improvement in accuracy is most likely due to the fact that the calculation of flow from first stage pressure and specific volume produces a slightly more stable

Bi tSi UTi θ Ui2 UR (%)

Barometric Pressure 0.1500 0.0000 0.1500 0.0071 0.0000 Boiler Feedwater Flow 1.4142 2.0047 2.4533 1.0564 6.7164 Boiler Feedwater Pressure 0.1500 0.6977 0.7136 0.0010 0.0000 Boiler Feedwater Temp 0.5558 0.1054 0.5657 1.0770 0.3712 Below Seat Packing LO 0.4029 0.0000 0.4029 0.2062 0.0069 Above Seat Packing LO 0.4029 0.0011 0.4029 0.1691 0,0046 Percent Load 0.4500 0.0269 0.4508 0.0003 0.0000 First Stage Efficiency 0.4500 0.0065 0.4500 0.0005 0.0000 First Stage Enthalpy 0.6040 0.2315 0.6469 0.0024 0.0000 N2 Leakage Flow 0.6040 0.0157 0.6042 0.1690 0.0104 N I Inner Leakage Flow 0.4805 0.0043 0.4805 0.1690 0.0066 N1 Outer Leakage Flow 0.4805 0.0002 0.4805 0.1715 0.0068 N I Total Leakage Flow 0.5034 0.0042 0.5034 0.1690 0.0072 Throttle Flow 1.0000 1.3954 1.7167 0.1690 0.0842 FW H 5 Extraction Flow 1.5025 0. 1626 1.5113 0.1690 0.0653 Reheat Steam Flow 1.6332 1.7825 2.4175 0.1690 0.1670 2.7288

First Stagc Pressure (psia) Design Throttle Flow (kpph) Actual Throttle Flow (from metered Feedwater Plow) (kpph)

800 605 672 1000 760 830 1200 910 988

Table 3: Comparison of predicted throttle now to metered feedwater flow, using first stage

pressure design curve


result that dampens the flow value over time.

The next method considered was to use cold reheat pressure as an indication of primary now. As with first stage pressure, the cold reheat now was calculated using the indicated flows and calculated leakage flows, and then a constant value was calculated based on cold reheat pressure and specific volume. The constant was then used in the turbine cycle heat input calculation to determine the heat input and also the coal consumption. A comparison of this method to the original method resulted in a standard deviation of 13.9 MMBtu/hr (Table 1) versus 10.5 MMBtu/hr. A reduction in accuracy is most likely due to the fact that the calculated feedwater now must be calculated from cold reheat flow and several other flows, which increases the uncertainty of the calculation.

The third method evaluated used final feedwater temperature as an indication of primary now. For this method, a relationship between final feedwater temperature and the indicated primary now was established using steady-state filtered and unfiltered data. The resulting relationship was plotted and a curve fit equation was used to calculate feedwater now. As before, the turbine cycle heat input was recalculated using the new primary now. The result compared to the existing calculation was a standard deviation 20.2 MMBtu/hr (Table I), which is considerably less accurate. This increase in the uncertainty is most likely due to the error in curve-fining the final feedwater temperature-to feedwater flow. Although the relationship is linear, there is still significant variations in feedwater flow for a given final feedwater temperature.

The final method evaluated was to increase the frequency of feedwater now readings to improve accuracy. An analysis was done on the feedwater flow readings compared to the gross generator output to determine the accuracy of the data. For a given range of generator output averaging 140.3 MW, the approximate uncertainty of the data was 1.49 MW (twice the standard deviation), or 1.06%. For the same time period, the feedwater flow rate uncertainty was 16 kpph, or 1.67%. This is within the expected measurement uncertainty of the data, which for flow rate is typically 2%. Note that the feedwater data used was the "'dampened'" result from the PMS. This indicates that dampening the data results in a smoother data set with fewer outliers. Therefore, it is not necessary to increase the frequency of flow readings as this would not improve the accuracy of the result. Based upon the above results, it can be concluded that using a different method to calculate the primary flow does improve the calculated result, but only slightly. This also indicated that the current method is appropriate and should produce accurate results for steady-state operation above very low loads. Tons of coal burned is determined from this method by taking the calculated turbine cycle heat input, dividing by the boiler efficiency to obtain the total boiler heat input. This result is then divided by the heating value of the fuel measured in the lab to arrive at the mass of the coal burned in the boiler. A graphical comparison of the four methods discussed above is shown in Figure 2. The daily amount of coal burned predicted by each method is plotted against gross generation for each day. Note that all four methods produce similar results, although the final feedwater temp indication for primary now shows the most scatter of all the methods.

MODIFIED TURBINE CYCLE I-O DESIGN CURVE METHOD The second method considered in this study was to use the turbine cycle heat rate vs. gross generation design curve as a basis for calculating the coal heat input. The curve was adjusted for various operational parameters and also for equipment degradation. The adjusted turbine cycle heat input divided by calculated boiler efficiency (loss method) results in the amount of coal burned.

For this method, the original turbine cycle design I-O curve of Unit 7 was obtained. The calculation existed in the PMS in order to determine the effect on heat rate of various operational data. The corrections to the design curve are also calculated in the PMS, and include corrections for feedwater temperature, reheat steam temperature, condenser pressure, main steam temperature, hotwell temperature, reheat spray flow. superheat spray flow, and main steam throttle pressure.


Also present in EtaPRO are the design and actual efficiencies of the HP and IP steam turbine sections which are used to modify the curve to account for equipment degradation. The effect of the deviation in efficiency of each section on heat rate is determined individually with respect to the other sections. In this manner one can separate out individual section degradation and its effect on heat rate.

An Excel spreadsheet was built to reproduce these calculations and test the corrections against the design curve. All of the above correction factors as well as the efficiency calculations and the design turbine cycle heat rate were input into the spreadsheet and tested against a range of PI data.

For the first test; turbine backpressure, HP efficiency, and IP efficiency corrections were used, as these are usually the largest contributors to heat rate degradation. The other operational corrections were typically small (less than 0.5%). The application of these three produced a fairly smooth curve that matched the design curve (Figure 3) offset above the curve by an expected deviation. However, this curve predicted a heat input that was much less than that calculated using the heat balance method described above, as well as the belt scale method.

The net effect of all corrections was considered next. This includes all of the corrections listed above and also includes the LP turbine efficiency. LP turbine design and actual efficiencies are determined from the Used Energy End Point (enthalpy), which is calculated from a heat balance around the LP turbine by the PMS. LP turbine efficiency appeared to be low compared to design, which would cause the LP efficiency correction factor to be slightly higher than normal.

The total correction was then applied to the design curve. It should be noted that the data was filtered this time for steady-state operation only, in order to eliminate any effects of rapid load changes. This unfortunately reduces the amount of visible data at lower loads. The final result obtained matched the calculated turbine cycle heat rate (heat balance method) closely, although it appeared to be slightly higher (Figure 4). This would indicate that the calculated LP efficiency was lower than expected, causing the correction to be greater than it should. However, once any issues with the LP efficiency are corrected it would appear that the modified curve method is a viable solution in calculating turbine cycle heat input (and heat rate). It also confirms that the heat balance method previously discussed is accurate.

To obtain the amount of coal burned (similar to the heat balance method), the turbine cycle heat input from the modified design curve is divided by boiler efficiency to gel total heat input to the boiler. The mass of coal burned is then the unit's heat input divided by the healing value of the coal determined in the laboratory.

INPUT/OUTPUT METHOD The final method considered in this study is the Input/Output method, which relies on the belt scale readings for coal consumed and the daily lab analysis of the coal. The tons of coal delivered to the unit and the associated heating values are used to calculate the heat input to the unit rather than calculations through a heat balance or correcting design curves.

A series of historical data for coal consumption and heating value was obtained from CSU dating back to January 2003. A coal sample is collected once per day, and it is assumed that the heating value is constant for the entire day. Currently, the PMS uses a coal heating value which must be changed manually by the user. According to PI data pulled over the last year, this value had been changed only once in the PMS, from 10,614 Btu/lb to 10,343 Btu/lb. The lab analysis, however, varies considerably from day to day over the course of January-May 2003 period.

The total coal consumption for Unit 7 in MMBtu per day was plotted against the total generation in MWh per day (Figure 5). For comparison, the other methods under consideration were also plotted. Coal consumption was converted from Tons per day to MMBtu per day with a constant heating value, which is the average of all Unit 7 coal heating values for the time period. A table of results for a specific range of generation is included to compare both average coal consumption and standard deviation over the generation range (Table 4).


Table 4: Coal Consumption of Various Methods Compared to Belt Scale with Average Heating Value

It can be seen that the belt scale readings produce more scatter for a specific amount of gross generation that either the heat balance method or the design curve method. The heal balance method which uses its stage pressure to indicate primary flow appears to be the most stable method to determine coal consumption.

In order to eliminate the variability of the healing value from the lab analysis, the same results were plotted against the belt scale readings using the actual daily heating value instead of an average value (Figure 6). Note that the belt scale readings of coal consumption have a higher standard deviation than before (Table 5) over the range of gross generation. It appears that the variability in the lab analysis from day to day produces more uncertainty in the calculated results of tile belt scale conversion from Tons/day to MMBtu/day.

Table 5: Coal Consumption of Various Methods Compared to Belt Scale with Variable Heating Value

A second set of plots shows the same data as before, however the heat balance and design curve methods are converted from MMBtu/day to Tons/day, using both a constant heating value (Figure 7) and the actual daily heating value (Figure 8). By plotting the actual Tons/day measured by the belt scale without converting to MMBtu, one can eliminate the lab analysis from biasing the belt scale readings. The results of the calculations over a range of gross generation are also tabulated for constant heating value (Table 6) and actual heating value (Table 7).

Table 6: Coal Consumption of Various Methods Compared to Bell Scale with Average Heating Value

Average (MMBtu/Day)

Standard Deviation (MMBtu/Day)

Belt Scale Reading 32953.2 1794.4

Modified Design Curve Method 33913.6 1195.8 Existing Heat Balance Calculation 33310.5 370.5 Using 1st Stage Pressure 33254.7 255.7 Plant Daily Generation (MWh) 3340.9 21.5

Average (MMBtu/Day)

Standard Deviation (MMBtu/Dav)

Belt Scale Reading 33129.4 1856.6 Modified Design Curve Method 33913.6 1195.8 Existing Heat Balance Calculation 33310.5 370.5 Using 1st Stage Pressure 33254.7 255.7 Plant Daily Generation (MWh) 3340.9 21.5

Average (Tons/Day) Standard Deviation (Tons/Day)

Belt Scale Reading 1533.9 83.5 Modified Design Curve Method 1578.6 55.7 Existing Heat Balance Calculation 1550.5 17.2

Using 1st Stage Pressure 1548.0 11.9

Plant Daily Generation (MWh) 3340.9 2 1.5


It can be seen that even the unbiased coal consumption from the belt scale measurement has a higher standard deviation (less accuracy) than either the heat balance or design curve methods. Note that introducing the actual heating value to convert from MMBtu to tons per day results in significantly more scatter in the data in Figure 8 and the standard deviation of the results in Table 7. The use of actual heating value produces worse results with higher uncertainty than using an average or constant heating value.

Table 7: Coal Consumption of Various Methods Compared to Belt Scale with Variable Heating Value

SUMMARY AND CONCLUSIONS Three methods for calculating heat input from the boiler (tons of coal burned) were investigated in order to determine the most accurate methodology. The Heat Balance Method was tried with multiple calculations of primary feedwater flow to determine the most reliable means of measurement. It was apparent that all of the methods produced similar results over a constant gross generation, although using first stage pressure as an indication of primary now seems to produce the least deviation. The primary feedwater flow measurement seems to have been well calibrated and is a consistent source of information based upon the analyzed data. Therefore the heat balance method above 50% generator load is the most reliable method for determining boiler heat input and has the least amount of scatter.

The design curve method was of significant interest to the results. By correcting the turbine cycle heat rate design curve based on current operating conditions and major equipment degradation, one can obtain a heat input which correlates well to the values obtained using the heat balance method. This calculation method is recommended as a check to the heat balance, and should be used at lower loads as the heat balance method does not seem to have enough accuracy below 50% generator load.

Finally the Input/Output method was attempted to see if the time delay in receiving the lab analysis or the coal burned was the cause of the deviations between the different methods. Analyses from January through May of 2003 were used to calculate the coal heat input to the boiler; however, this method did not improve the current calculation and in fact produced slightly worse results than using a constant heating value.

The preceding analyses were calculated on an hourly and daily basis. However, it is of interest to know what the results are based upon a weekly and monthly computation. Therefore a comparison of the belt scale readings versus the current PMS heat balance calculation was tabulated over the January - May 2003 period. The results for the weekly analysis are shown in Figure 9 and the monthly analysis in Figure 10. Days of low or no load operation were not considered, nor were days where the belt scale readings were not available. While there is variation in the data over a weekly and monthly basis, the total amount of coal burned for the entire five month period is nearly identical between the belt scale measurement (190,885 tons) and the heat balance calculation (190,685 tons). The difference of 200 tons is approximately 0.1%, which is well below the uncertainty of either the belt scale measurement or the heat balance calculation.

Average (Tons/Day) Standard Deviation (Tons/Day)

Belt Scale Reading 1533.9 83.5 Modified Design Curve Method 1571.3 78.4 Existing Heat Balance Calculation 1543.2 50,3 Using 1st Stage Pressure 1540.7 5 1.1

Plant Daily Generation (MWh) 3340.9 21.5


In conclusion, it appears that the best method for obtaining heat input to the boiler and subsequently the amount or coal burned on an hourly or daily basis is the Heat Balance method. As a backup, the Design Curve method should be implemented to check the results of the heat balance and also at lower loads. Once the boiler heat input is calculated, the heating value obtained from lab analysis can be used to determine the total mass of coal burned. This methodology will result in the most accurate results over a short period of time. However, over a weekly or monthly period either the heat balance calculation or the belt scale may be used to track coal consumption since a longer period of time is insensitive to the uncertainties of either the belt scale measurement or the heat balance calculation.

Another recommendation is to have more frequent updates of the average coal heating value into the PMS to provide the most current coal analysis for the calculations. The average of the daily values should be used rather than the actual daily value so that the uncertainty of the result is reduced. Although the feedwater flow measurement is well calibrated, continued maintenance of this measurement will clearly benefit the PMS calculations. It is necessary to also check the feedwater flow calculation to ensure the proper flow calculation methodology is used for the type of meter that is employed. Finally it is also recommended that if these changes are implemented, an automatic report should be set up to monitor the new results. The report should be generated on a weekly or monthly basis and report the differences between the methods. The author would like to acknowledge the pro-active role played by the City of Colorado Springs’ Electric Generation Department for funding this study and actively participating in the data gathering and evaluation process. I would also like to acknowledge the efforts of Steve R. Fennel, P.E. for his efforts in assimilating the data used in this study as well as applying the appropriate statistical methods and writing the original report upon which this paper is based.


Figure 1: Boiler Heat Input Heat Balance Method with 95% Confidence Intervals


Figure 2: Comparison of Boiler Heat Input from Belt Scale and Heat Balance Methods


Figure 3: Original Design Curve vs. Modified Design Curve Corrected for HP/IP Efficiency and Condenser Pressure


Figure 4: Original Design Curve vs. Modified Curve (HP/IP/Cond Corrections), Actual TCHR and Modified Curve (all Corrections)


Figure 5: Comparison Coal Burned (MMBtu/day) using Constant Heating Value


Figure 6: Comparison Coal Burned (MMBtu/day) using Lab (Variable) Heating Value


Figure 7: Comparison of Coal Burned Values (Tons/day) using Constant Heating Value


Figure 8: Comparison of Coal Burned (Tons/day) using Lab (Variable) Heating Value


Figure 9: Comparison Coal Burned (Tons/day) based on weekly data

Year 2003

1/2 1/9 1/16 1/23 1/30 2/6 2/13 2/20 2/27 3/6 3/13 3/20 3/27 4/3 4/10 4/17 4/24 5/1 5/8 5/15 5/22

Belt Scale

9459 7500 10831 10184 9231 5859 10653 7797 8571 10238 7561 9359 9511 9951 10837 11138 10754 10693 11261 5487 3582

EtaPRO 9629 7398 10694 10459 9232 5873 10838 7799 9170 10347 7594 9422 9508 10032 10508 10780 10599 10593 10451 5692 3960


Figure 10: Comparison Coal Burned (Tons/day) based on monthly data

Accuracy evaluation of various methods to … · A RELATIVE ACCURACY EVALUATION OF VARIOUS METHODS...

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