POWER Quantifying Correction Curve Uncertainty Through Empirical Methods

Proceedings of the ASME 2014 Power Conference POWER2014 July 28-31, 2014, Baltimore, Maryland, USA POWER2014-32187 Quantifying Correction Curve Uncertainty Through Empirical Methods ABSTRACT Christopher R. Bañares General Electric Power & Water Schenectady, NY, USA Evan E. Daigle General Electric Power & Water Ann Arbor, MI, USA The accuracy of a thermal performance test is typically estimated by performing an uncertainty analysis calculation in accordance with ASME PTC 19.1 or equivalent. The resultant test uncertainty estimate is often used as a key factor in the commercial contract, in that many contracts allow a test tolerance and define the test tolerance to be equal to the test uncertainty. As such, the calculated test uncertainty needs to accurately reflect all of the technical factors that contribute to the uncertainty. The test uncertainty is a measure of the test quality, and, in many circumstances, the test setup must be designed such that the uncertainty remains lower than test code limits and/or commercial tolerances. Traditional uncertainty calculations have included an estimate of the measurement uncertainties and the propagation of those uncertainties to the test result. In addition to addressing measurement uncertainties, ASME PTC 19.1 makes reference to other potential errors of method, such as the assumptions or constants contained in the calculation routines and using an empirically derived correlation. Experience suggests that these errors of method can in some circumstances dominate the overall test uncertainty. Previous studies (POWER2011 55123 and POWER2012 54609) introduced and quantified a number of operational factors and correction curve factors of this type. To facilitate testing over a range of boundary conditions, the industry norm is for the equipment Thomas P. Schmitt General Electric Power & Water Fairview, NC, USA Thomas P. Winterberger General Electric Power & Water Schenectady, NY, USA supplier to provide correction curves, typically created using thermodynamic models of the power plant to predict the response of the system to changes in boundary conditions. As noted in various PTC codes (PTC 22, PTC 46, and PTC 6) it is advisable to run the test at conditions as close to the rated conditions as possible to minimize the influence of the correction curves. Experience suggests that large deviations from rated conditions, and the associated influence of the correction curves, can result in decreased accuracy in the final corrected result. A discussion of these types of situations via case studies is discussed, as well as a means by which to reduce the uncertainty contributions from correction curves considerably. INTRODUCTION The following industry code sections are referenced for this discussion. ASME PTC22: Section 3 3.1: Every effort should be made to run the test as close to Specified Reference Conditions as possible, in order to minimize the effect of corrections. Section 5 5: Studies of different gas turbine cycles using the performance curves and equations instead of the simulation model have demonstrated that interactivity between correction factors usually results in differences of less than 0.3%. 1 Copyright 2014 by ASME

ASME PTC46: Section 3.4.2.4: It is desirable to operate the plant during the test as closely as possible to the base reference performance conditions, and within the allowable design range of the plant and its equipment so as to limit the magnitude of corrections to net electrical output and heat rate. Table 3.2 was developed based on achieving the overall test uncertainties described in Table 1.1. Excessive corrections to plant performance parameters can adversely affect overall test uncertainty. Section 5.4: Heat balance studies of different cycles using the performance equations in the above format have demonstrated that interactivity between correction factors usually results in differences of less than 0.2% compared to calculation of the complete heat balance post test with test data. ASME PTC19.1: Section 5 3.5: Uncertainties due to methods are defined as those additional uncertainty sources that originate from the techniques or methods inherent in the measurement process. These uncertainty sources, beyond those contained in calibration, installation sources, data acquisition, and data reduction, may significantly affect the uncertainty of the final results. ASME PTC6.2: Section 3 5.3.2: Every effort should be made to run the tests under specified operating conditions or as close to specified operating conditions as possible to minimize the magnitude of corrections. Table 3 1.3.5 provides limits on the allowable deviations in operating conditions from the reference condition. These limits are based on the analytical uncertainty of the correction methodology and shall not be exceeded. ISO2314: Section 7.1: Every effort should be made to run the test under the specified conditions or as close as possible to the specified conditions, in order to minimize the effect of corrections. These code references recognize the potential for errors in the corrected result due to correction methodology and guide the user to make efforts to test in conditions that are as close to the specified reference conditions as possible. Further, the codes state that there is an acceptable error due to correction methodology of approximately 0.2 0.3%. However the codes do not provide specific guidance on how to estimate the incremental uncertainty levels associated with the correction methodology, and/or how to account for them either in the overall test uncertainty or in the corrected results. This is important, as experience shows that there is potential for errors in corrections to exceed 0.3%. This can happen in cases where insufficient data exist to validate the thermodynamic models used to develop the correction curves at extreme off rated conditions, or as a result of the normal unit to unit variation and its associated impact on estimating the response of the equipment to changes in the boundary conditions. In the event that a volume of data exists that indicates a statistically significant deviation between expected behavior and the as tested behavior of one or more of the corrections, then either the correction curves should be empirically adjusted or the test uncertainty should include a line item that accounts for this uncertainty. For the case where empirical validation is either not possible or impractical, then when developing the pretest uncertainty analysis, it may be technically valid for the manufacturer to include a line item in the analysis that represents an estimate for correction curve uncertainty based on past experience and based on the extent to which the test condition may deviate from the rated condition. The following case studies can demonstrate the magnitude of some of these uncertainties associated with correction methods. NOMENCLATURE GT Gas Turbine OEM Original Equipment Manufacturer GE General Electric Power & Water 2 Copyright 2014 by ASME

CASE STUDY 1 GAS TURBINE UNIT TO UNIT VARIATION For this example, field test data for a number of new and clean gas turbines (n = 57) of the same hardware configuration were used to calculate several key performance metrics for the major components of the units such as compressor efficiency and nozzle flow characteristics. Multiplicative factors were then derived to adjust the unit nominal thermodynamic model to match the observed component performance for each unit, factoring out the effects of boundary conditions like ambient temperature, inlet pressure loss, and fuel composition. This results in sets of factors whose distribution approximates the unit to unit variation in component performance for the fleet relative to the model, independent of test boundary conditions. A statistical analysis of the variation in these factors resulted in a model of typical fleet component variations. This model of fleet variation was combined with a basic model of variation of ambient conditions for a given location to create a fleet of models (n=500) with identical controls settings, each with unique component thermodynamic models, ambient test conditions, and predicted performance mimicking that of the fleet. A multiplicative correction factor was calculated for each of the model runs by taking the ratio of the predicted performance at the ambient test conditions and the predicted performance at the reference conditions using the nominal (unmodified) model, in much the same way that conventional correction curves are generated and applied. Model predictions at the exact test and reference conditions were used to generate corrections in this case, however, so as to eliminate error sources inherent in the usage of correction curves, such as point wise interpolation, curve fitting error, and higher order interdependencies between different correction parameters. Note that measurement uncertainty in ambient conditions and measured performance was ignored for this analysis, since the ambient conditions and resultant as tested performance were generated using computer models. was repeated for reference conditions of 32, 59, and 100 degrees Fahrenheit, so as to represent a variety of guarantee conditions and maximize the range of variation between the reference and as tested conditions. Note that typical engineering control limits such as generator output limits, exhaust temperature limits, and compressor pressure ratio limits were disabled for this study, so as to eliminate errors due to units running off the control schedule that was intended for performance testing. Each model in the fleet was then run a second time, at the reference ambient conditions, so as to determine what the true performance of that unit would have been at the reference conditions. The result at the reference condition was then compared against the same model s performance at the test condition with the correction factor applied. The difference between these two results therefore represents the difference between the true performance of the unit at the reference condition, and the performance calculated by correcting offdesign test data back to the reference condition without accounting for the unit specific component thermal performance behavior. By using the correction process described previously, the majority of error sources due to the use of correction curves (i.e. the interdependence of the correction variables which is neglected using conventional correction curves) were eliminated, with the only remaining effect being the difference between typical unit tounit variations in component performance and the model predictions used to generate the correction factor. Figure 1 illustrates the variation between the theoretical unit performance at reference conditions and that calculated using the model based correction factor. For each case, the correction factor was then applied to the observed model performance, so as to calculate corrected performance at the reference condition in a manner consistent with that used in PTC compliant performance testing. This process 3 Copyright 2014 by ASME

additional uncertainty when usage conditions exceed the nominal range of environmental conditions. Similarly, in the case of a power plant thermal performance test, the uncertainty (or accuracy) accounting needs to take into consideration the incremental additional uncertainty attributable to testing at off reference conditions, inclusive of correction curve interdependencies and unit to unit component variations. Figure 1: Correction Error Due to Performance Variation The highlighted section in the center of the graph represents the typical code limit uncertainty band for a PTC 22 test, for reference (i.e. approximately +/ 0.5%). For cases where the difference between the as tested ambient temperature and the reference ambient temperature are small, the correction approaches unity and as one would expect, the error it introduces becomes negligible. However, as the test condition begins to vary significantly from the reference condition, the influence of unit to unit variations becomes more pronounced. For variations greater than 30 degrees Fahrenheit from the reference condition, the influence of this effect eclipses that of the combined measurement uncertainty, significantly reducing the accuracy of the test result. In other words, the error amounts illustrated in Figure 1 represent solely the incremental error (i.e. uncertainty) contribution from natural unit to unit thermodynamic variations in the equipment components, and does not include any uncertainty associated with the interdependence of correction curves, and does not include the traditional uncertainties associated with measurement errors. The extent to which the uncertainty intervals need to expand in proportion to the extent to which the test conditions deviate from the reference conditions is analogous to the manner in which most instrument suppliers define their instrument uncertainty. For instrument uncertainty, most instrument manufacturers define the nominal uncertainty (or accuracy) to be applicable within a specified range of environmental conditions (such as temperature or humidity) and then give a formula by which the user can estimate the incremental To statistically quantify this effect, the same correction process was used to correct the fleet of 500 units to a reference condition of 59 degrees Fahrenheit from varying ambient temperatures in 10 degree increments, from 29 to 89 degrees Fahrenheit. The resulting variation in corrected performance from each as tested ambient temperature was analyzed, and a symmetrical 95% tolerance interval was calculated as an estimate of the anticipated uncertainty contribution from the ambient temperature correction. Figure 2 illustrates the estimated effect of variation in as tested ambient temperature on correction uncertainty. Figure 2: Estimated Correction Uncertainty as a Function of Variation in Ambient Temperature By combining this uncertainty estimate with that we obtain from propagation of measurement uncertainty, a combined test uncertainty may be calculated. Figure 3 illustrates the post test uncertainty for a typical PTC 22 test, 0.4%, and the combined uncertainty when the correction uncertainty estimate is incorporated. 4 Copyright 2014 by ASME

grow in magnitude in proportion to the extent of offrated conditions found. Figure 3: Incremental Test Uncertainty Due to Correction Error The shaded area indicates the incremental increase in test uncertainty as a result of the correction curve error. As prior industry experience suggests, the incremental uncertainty is very small within a certain range of test conditions, but increases dramatically as the test condition deviates more significantly from the reference condition. Readers should note that this analysis does not address uncertainty inherent in measuring the component performance factors as described at the beginning of this case study. As a result, this analysis represents an approximation of the magnitude of these effects. It is the authors assertion that the conclusion of this case study highlights the existence of this error source, its basic characteristics, a statistically based thermodynamic method of estimating the numeric value of the incremental uncertainty, and perhaps most importantly, the need to factor these considerations into the design and conduct of the performance test. CASE STUDY #2 GAS TURBINE: RATED CONDITIONS EXTREME OFF In addition to the random deviations in performance correction curve behaviors that expand in magnitude as the extent to which the as tested conditions deviate from the rated conditions, there can be times when an additional systematic error is introduced into the corrected test results when the actual turbine response to one or more correction variables deviates considerably from the expected response. And similar to the random errors discussed previously, these systematic errors can One recent GE experience relates to the grid frequency correction, and it was encountered when the as tested condition was significantly offfrequency. Base load performance behavior at offfrequency conditions is not a particularly common scenario for grid connected power generation turbines, and most manufacturers might not have the opportunity to fully characterize the offfrequency response of a GT, especially when it occurs concurrently with extreme high ambient conditions. As such, there is a potential for higher than anticipated correction curve errors resulting from off frequency test conditions. In these situations, when the data warrants, the OEM is obligated, technically, to offer empirically adjusted correction curves that minimize the avoidable introduction of correction error. Recent GE test experience in Pakistan on several heavy duty gas turbines resulted in a data set that was used to empirically adjust the frequency correction curves. The official tests were run at high ambient and low frequency conditions, and the corrected results were noted to be higher than expected. A database of archived GT performance behavior was then downloaded from the plant historian such that a statistically significant amount of data could be studied across the frequency range. These historian data were then processed twice, once through the full set of test corrections including the frequency correction curve (the blue data) and a second time not including the frequency correction (the red data), see Figure 4. As shown in Figure 4, the corrected performance at significant underfrequency test conditions tended to be over stated (the blue data is after using the expected offfrequency correction). The frequency correction was then empirically adjusted with consensus of all parties involved, and the statistical data set was used as validation of the empirical adjustments. This case study exemplified the occasional need of empirically adjusting the test correction curves, when warranted by the data, to avoid an unnecessary avoidable incremental systematic error from corrections curves. 5 Copyright 2014 by ASME

1.6% 1.4% 1.2% 1.0% Corrected Output Error 0.8% 0.6% 0.4% 0.2% 0.0% 0.2% Figure 4: Example of Correction Error from Off Frequency Test Conditions 0.4% 4% 3% 2% 1% 0% 1% 2% Correction Variable Difference to Reference Figure 5: Example of Correction Error Isolated to a Specific Range of the Correction Variable CASE STUDY #3 GAS TURBINE: ERRORS IN AN ISOLATED RANGE CORRECTION Another scenario that can occur is the introduction of a systematic error in the corrected result only in a particular range of a correction variable. In these cases, the turbine s operating behavior for a given boundary condition may be characterized fairly well by the thermodynamic model in one range of conditions and deviate in other parts of the range. Since the thermodynamic models are used to create the correction curves, errors would be confined only to a particular range of the correction curves. This scenario was experienced during testing of a newer model heavy duty gas turbine. It was observed during preliminary testing of the turbine that the corrected output appeared to be overstated when test runs were made at conditions below the reference value of one of the boundary parameters. This prompted further analysis using the historical archived data system of a unit of similar configuration to gather a statistically significant data set with a larger range of the correction variable of interest. Correction curves were applied to the data to obtain corrected output performance and plotted against the range of the variable of interest. The results can be seen in Figure 5. These data showed that the actual turbine performance was significantly better than expected in the low range of this correction variable. If no error in correction curves existed, the error over the range of the variable would be centered on zero. This can be seen in the range of correction variable above the reference value (approximately 0 2%). However, in the correction variable range below the reference, the performance of the turbine appeared to deviate from expected, resulting in significant positive errors in the corrected result when using the theoretical pre test correction curves. Similar to the previous case studies, this error increased in proportion to deviation from the reference condition. The codes recommendations to test as close to reference conditions as possible is applicable in this scenario and can certainly minimize the errors associated with the curves. However, in the event that the performance test cannot be carried out at close to reference conditions, the options are either to adjust the correction curve of interest to reflect the empirical data or to recognize and account for the additional uncertainty in the corrected result due to the correction curve error. CASE STUDY #4 STEAM TURBINE: EXTREME OFF RATED CONDITIONS Both ASME PTC 6 and PTC 6.2 stress the importance of testing as close to specified conditions as possible to minimize the magnitude of corrections. Table 3 1 of PTC 6 and Table 3 1.3.5 of PTC 6.3 list the allowable deviations between test and rated conditions. PTC 6.2 further states that these allowable deviations are based on analytical 6 Copyright 2014 by ASME

uncertainty of the correction methodology and should not be exceeded. One of the variables with a large sensitivity to output and with a greater potential for deviation is steam turbine exhaust pressure or condenser pressure. While PTC 6 and 6.2 have different requirements on exhaust pressure, the allowable deviations are on the order of 0.1 to 0.5 inches of mercury absolute. Figure 6 shows an exhaust pressure correction curve for a large steam unit. The solid line is the response to changes in exhaust pressure as predicted by the steam turbine manufacturer s heat balance modeling program. The dashed line is based on plant data measured over an operating period with controlled conditions. While the two curves show very good agreement in close proximity to the rated exhaust pressure, the curves differ significantly at the outer boundaries of the plot. This plot illustrates the need to minimize deviations in operating conditions as outlined in PTC 6 and 6.2. While these differences could be due to a number of reasons including plant operation and turbine design, the best course of action is to avoid these regions when testing. Figure 6: Steam Output Sensitivity to Exhaust Pressure Historically, uncertainty estimates have not been increased to account for greater deviations from rated conditions on steam turbines. For these situations, consideration should be given to either modifying plant operation to raise or lower exhaust pressure, or waiting until seasonal conditions are more favorable. A decision to delay testing needs to be balanced against the risk of changes associated with increased operating hours. CONCLUSION As noted in each major industry test code, efforts should be made by all parties to conduct the performance test at conditions as close as possible to the reference conditions. In practice, owing to natural effects and commercial requirements it is not always possible, nor is it always practical, to conduct the test at conditions that would yield the lowest achievable uncertainty. It is the responsibility of the testing organization to estimate the test uncertainty as accurately as possible, taking into account all known contributing factors. As discussed herein, the test uncertainty should take into account not only the contributions from measurement errors and their propagation to the corrected results, but also any additional uncertainty contributions that may result from the correction curves or calculation methodology. As shown in this paper, these additional incremental uncertainty contributions from correction curves or calculation methodology can be significant and quantifiable. Statistical means can be employed to estimate the uncertainty stemming from the combination of unitto unit variations and deviations from the reference conditions. As shown herein, these can easily contribute an additional 0.2 to 0.3% incremental test uncertainty. As noted previously, additional analyses are warranted to refine these estimates to consider measurement uncertainty effects on the unit to unit variations, to ensure contributions are not overstated when applied to the overall test uncertainty. Furthermore, additional test uncertainty can result from limitations in correction curves when considering interaction with control system limits. These errors can be reduced by use of model based performance corrections (ASME POWER2014 32184), though industry acceptance and proliferation of this methodology has been historically limited. When a statistically significant data set exists (which is now more common with modern plant historians and industrial internet capabilities) the equipment supplier can empirically adjust correction curves (or the thermodynamic model) to mitigate the impact of off reference test conditions, which could otherwise contribute >1% incremental test uncertainty. While a traditional test uncertainty estimate for a PTC 22 code test that only considers measurement 7 Copyright 2014 by ASME

uncertainty might yield an uncertainty estimate on the order of +/ 0.5%, the actual error of the test result might be well above +/ 1.0% due to errors in the corrections. Proactively recognizing and considering these error sources can improve test accuracy, thereby reducing the risk of understating or overstating the true equipment performance. As such, it is to the benefit of all test parties to take these incremental uncertainties into consideration when defining the test procedure (including correction methodology) and in selecting test conditions as close as possible to the reference conditions. REFERENCES 1. ASME PTC 22 2005 Gas Turbines 2. ASME PTC 46 1996 Performance Test Code on Overall Plant Performance 3. ASME PTC 19.1 2005 Test Uncertainty 4. ASME PTC 6.2 2011 Steam Turbines in Combined Cycles 5. ISO 2314 2009 Gas Turbines Acceptance Tests 8 Copyright 2014 by ASME