A Method to Assist in Verifying Heat Rate Accuracy

Transcription

1 A Method to Assst n Verfyng Heat Rate Accuracy Greg Alder - True North Consultng Frank Todd - True North Consultng Page of

2 . Purpose of Paper Coal fred plants largely depend on a mass and energy balance around the boler versus usng the measured fuel frng rate and heatng value for the calculaton of heat rate. Ths s prmarly because of naccurate coal flow measurements and unknown heatng values, partcularly wth blendng dfferent coal. The mass and energy balance method depends on boler boundary condtons and s largely a functon of the measured feedwater flow. An error n the measurement of feedwater flow, especally from a fouled nozzle, wll contrbute to error n the heat rate calculaton. A fouled nozzle wll show an ndcated flow hgher than actual resultng n an erroneously hgh heat rate. A tool for detectng errors n the mass and energy balance nputs has been developed for nuclear power statons. Ths paper dscusses the applcaton of such a tool for coal fred plants.. Applcablty The methodology descrbed n ths paper s applcable to power plants desrng an alternatve means to estmate feedwater flow. Page of

3 Assumptons. Process Parameter Lnearty wth Respect to Feedwater Flow There are also varous plant parameters n a fossl power plant that are drectly dependent on steam flow through the turbne cycle. These parameters typcally vary lnearly wth feedwater flow for small flow and load changes. The process assumes a lnear relatonshp for each of the nstrument nputs to the calculaton. In cases where ths relatonshp s not lnear, assumng a lnear relaton s acceptable snce ths method s used to detect small changes n feedwater flow. Sgnfcant (greater than approxmately 5%) changes n feed water flow would be dentfed ndependently. Inputs used for ths calculaton must be related to the feedwater flow or have a correlaton wth these parameters. The relatonshp between the plant parameters and flow through the turbne cycle are based on the flud flow characterstcs of the turbne cycle [4, 9, 0, ]. Typcal parameters would nclude, but not be lmted to: Frst stage pressure Steam flow Frst extracton pressure Cold reheat pressure Hot reheat pressure Fnal feedwater temperature Condensate flow Feed pump sucton or dscharge flow Feed pump amps Condensate pump amps It s recommended that -hour average of samples are collected each mnute, for a total of 60 samples n hour but ths may vary dependng on the varablty of the partcular cycle under evaluaton and the ablty of the computer system collectng the data. All data must be collected at full load condtons avodng transents n plant operaton.. Treatment of Systematc Uncertantes Ths process assumes that systematc uncertantes are expressed as a 95% confdence nterval. The systematc uncertantes are those uncertantes that are based on the nstrumentaton characterstcs typcally as descrbed n the vendor documentaton for the nstrument tself and the measurng method. Systematc uncertantes expressed n dfferent ways wll need to be re-evaluated..3 Plant Parameter Uncertanty Adjustments A basc assumpton of ths methodology s that each nstrument s an ndependent ndcator of feedwater flow. The nstruments at the varous locatons n the cycle may have other nfluences n addton to feedwater flow. The further the nstrument s away (downstream n the cycle) from the begnnng of the cycle (man steam flow) the more t can be nfluenced by problems n the cycle. Therefore for the purposes of ths methodology, the nstrument uncertantes are adjusted to reflect the confdence level based on engneerng judgment for each nstrument. These adjustments are appled to account for potental changes n operatng condtons that would Page 3 of

4 cause the relatonshp between the parameter and man steam flow to change. The adjusted uncertanty must always be no less than the nstrument uncertanty to ensure conservatsm, and are stll treated as a 95% confdence nterval..4 Treatment of Random Uncertantes Random uncertantes are assumed to be expressed as the standard devaton of the data under consderaton. The data used for ths analyss are assumed to have a large enough sample sze to estmate t 95 (student s t-value for 95% confdence nterval) at. Ths analyss also assumes that a 95% confdence nterval for uncertanty s acceptable. The recommended method would use the standard devaton of the dataset used for each parameter used n the calculaton. If ths standard devaton s not readly avalable, usng the standard devatons from a known stable tme perod would be acceptable. Ths assumes that the standard devaton does not change sgnfcantly over the perod of tme used to calculate the average value for each parameter. It also assumes that the day to day change n standard devaton s also nsgnfcant wth respect to the method used to estmate flow. If a sgnfcant change to standard devaton occurs, there wll lkely be a correspondng problem wth the flow estmate or the Foulng Indcator as descrbed n Secton 4. Ths would alert the user to nvestgate the reason for the change, and the shft n standard devaton would then be detected..5 Baselne Feedwater Flow Rate It s assumed that the measured feedwater flow s accurate durng the tme perod that the baselne values are beng developed. If ths s the case for the ntal data set then the feedwater flow would be equal to the ndcated value. However, f nozzle foulng has occurred or some other known error n the measured feedwater flow exsts then an estmaton of the feedwater flow s requred to ensure that the baselne values adequately represent the actual feedwater flow condtons. The methodology descrbed n Secton 3.3 s used as an ad n establshng the valdty of ths assumpton..6 Feedwater Flow Estmaton The methodology (Equaton 3-6) descrbed for calculaton of the estmated feedwater flow assumes that all of the errors n the measured feedwater flow are the result of an error n the feedwater flow measurement. Ths assumpton should be valdated before the feedwater flow estmaton s consdered for use. Page 4 of

5 3 Methodology 3. Flow Estmate Calculaton As dscussed n Secton., there are several plant parameters that have strong correlaton wth man steam flow and subsequently feedwater flow. Indvdually, each parameter used provdes an estmate of flow. For example (under normal condtons) f actual man steam flow changes by % then flow through the hgh pressure turbne wll also change by %. Thus, a rato of current frst stage pressure to a benchmark frst stage pressure multpled by a benchmark man steam flow results n an estmate of man steam flow. Unfortunately, the uncertanty of these ndvdual parameters s typcally hgher than desred for ths type of analyss. However, when many parameters are used and correctons appled for certan plant condtons, these parameters can be combned n such a manner as to provde an overall estmate of flow. The resultng estmated computaton of man steam flow can then be used to calculate the feedwater flow and compare to measured feedwater flow to determne f there s a dscrepancy between the two that would ndcate problems wth nozzle foulng or other nstrument problems. 3.. Man Flow Estmate Calculaton These combned parameters can be used as an estmate for the actual man steam flow. Ths estmate can be expressed as: Where N X = W X = X = The estmated man steam flow W = A weghtng factor for each parameter X = The ndvdual parameter N = The number of parameters used to estmate man steam flow (3-) 3.. Weghtng Factors The weghtng factors are calculated by usng the combnaton of the systematc and random uncertanty for each parameter. Often the nstruments are not n the calbraton program or ther operatonal hstory ndcates that the uncertanty s hgher than ndcated by the vendor documentaton. In these cases conservatve estmates are used. Addtonally f there are varous measurements at a smlar pont n the cycle, adjustments must be made to prevent any one pont n the cycle from beng too heavly weghted n the overall estmate of man steam flow. These uncertantes are calculated by the followng: B U = t + S (3-) X Where: U 95 = 95% Confdence nterval for the uncertanty of the parameter t 95 = Student s 95% confdence and n- degrees of freedom (assumed to be for ths calculaton) B = 95% Confdence nterval for systematc uncertanty Page 5 of

6 S = Standard Devaton of the parameter X Usng these uncertantes, the weghtng factor can be defned by: W = U N = U (3-3) Where U = the ndvdual uncertanty calculated for each nstrument usng Equaton 3-. For every parameter except feedwater temperature, the ndvdual parameter values are calculated by multplyng a reference man steam flow value by the rato of the current parameter value to a reference value for that parameter. Ths can be expressed as follows: Flow X predcted = Flow ref (3-4) X ref Where Flow predcted = Man steam flow predcted by parameter X = Indvdual parameter X ref = Reference value of parameter at the reference man steam flow value Flow ref = Reference value of man steam flow For feedwater temperature, the senstvty of flow to feedwater temperature must frst be calculated. Usng a computer model of the turbne cycle n conjuncton wth a lnear regresson model or other sutable method, the rato of change n flow to change n feedwater temperature s calculated. Ths rato s multpled by the dfference of the current temperature to a reference value and then added to the reference flow value. Ths can be expressed as follows: predcted FWTemp ( Tcurr Tref ) S FWTemp Flowref Flow = + (3-5) Where FlowpredctedFWTemp = T curr = T ref = Flow ref = S FWTemp = Man steam flow predcted by feedwater temperature Current value of feedwater temperature Reference value of feedwater temperature at the reference man steam flow value Reference value of man steam flow Senstvty of man steam flow to the feedwater temperature 3... Calculaton The equaton used to estmate the feedwater flow usng the estmated man steam flow and the measured plant values for a fossl plant s as follows: The typcal feedwater flow equaton s as follows. However, ths may be dfferent for each plant. Page 6 of

7 FeedwaterFlow = ManSteamFlow + BlowdownFlow SuperheatSprayFlow (3-6) 3. Identfyng Independent Parameters As dscussed n Secton.3, the ndependent parameters used n ths evaluaton are ntegral to the overall qualty of the result. The followng are used to determne the sutablty of a partcular parameter: Evaluaton of any exstng uncertanty calculatons for the nstrumentaton Verfcaton of nstrument calbratons o Frequency of calbratons o Hstory of calbratons (drft, falures etc.) Revew of hstorcal data o Observaton of unexplaned shfts and determnaton, f possble, the cause and frequency of these shfts. o Observaton of changes after down powers and how long t takes the nstrument to stablze or settle out. Ths s of concern partcularly for low pressure measurements where there are water leg ssues. o Comparsons wth plant computer model and turbne tests as descrbed n Secton 3.3. o Verfcaton that the parameter changes correspond to other plant parameters. 3.3 Determnng Reference Value of Parameters A baselne evaluaton of the plant s performed to ascertan the values of the plant parameters to be used n the estmated feedwater flow calculaton. The ultmate goal s to establsh a set of data that can be used and the 00% load values for the calculaton. Ths evaluaton conssts of the followng steps: 3.3. Plant Systems Evaluaton An evaluaton of the turbne cycle systems and documentaton s performed to dentfy any dscrepances between the turbne vendor thermal kt and the actual plant nstalled condtons. Ths analyss dentfes any obvous problems wth the plant equpment that would go nto the evaluaton. Ths evaluaton, n conjuncton wth other evaluatons, determnes the present condton of the plant rrespectve of the nfluences of feedwater flow Hstorcal Plant Data Evaluaton Plant data are evaluated back to the last sgnfcant plant modfcaton (usually a turbne retroft) to dentfy any plant anomales that should be accounted for n the calculatons. Plant data n the followng systems are ncluded n ths evaluaton: Man Feed Man Steam Condensate Extracton Steam Blowdown Flow Man Turbne Plant Thermal Kt Evaluaton The thermal kt s a desgn document typcally provded by the turbne vendor and t descrbes the desgn thermodynamc parameters of the plant for varous loads. The thermal kt also ncludes varous correctons and other nformaton to determne plant parameters for varatons Page 7 of

8 from desgn condtons. Actual condtons are compared to the plant thermal kt to determne the mpact of desgn dfferences and component degradaton. Common dfferences are the arrangement of feedwater heaters, type of coolng for gland exhaust condensers or vent and dran confguratons. Often plants are operated n a manner dfferent than what s assumed on the thermal kt. For example, the orgnal desgn may have been for partal arc admsson but the plant s operated n full arc due to ven passng concerns. Vendor thermal kts may have actual errors that can be detected by plottng the turbne expanson on a Moller dagram and verfyng a reasonable expanson lne. Ths s accomplshed by readng the enthalpes and pressures off of the heat balance and plottng them on the dagram. In addton to the plant thermal kt, the followng are taken nto consderaton for ths evaluaton: Plant Ppng and Instrumentaton Drawngs Feedwater Heater Desgn Specfcatons Condenser Desgn Specfcatons Boler Desgn Specfcatons Pump Specfcatons Plant Test Data Evaluaton Any turbne performance tests, especally f performed n accordance wth ASME PTC-6 gudelnes, are evaluated to determne dfferences between actual plant data and the values as determned by the test. The calculated estmate of the flow s dependent on the ntal estmate of flow for the ntal reference set. Ideally the collecton of the ntal data set would be drectly followng cleanng and calbraton of the flow nozzles Plant Computer Model Evaluaton A computer model of the turbne cycle s developed usng the vendor thermal kt and other plant models. Ths model s used to provde assurance that the evaluaton would be based on the best desgn nformaton avalable and account for plant boundary condtons. The followng process s used to develop ths model:. Buld a model of the plant based on the vendor desgn condtons. Ths model wll exactly match the plant thermal kt. Based on the revew of other desgn documentaton, change the model for the effects of as-bult plant performance versus the turbne vendor expected performance. 3. Tune the model to the best test data avalable 4. Modfy the model for any plant defcences or operatonal dfferences from the desgn condtons or the test condtons to whch the model was tuned. 5. Once all the correctons are completed the model s used to determne the plant parameters at a partcular load. These can be compared to the plant data to evaluate how well they match desgn condtons. 3.4 Uncertanty of Feedwater Flow Estmate Calculaton The estmate method uses as many plant parameters as possble whch are ndependent and thus can mnmze the uncertanty of the overall result. The overall uncertanty of the estmated feedwater flow can be much lower than the uncertanty of any of the ndvdual measured parameters. Page 8 of

9 The systematc and random uncertantes are also weghted usng the same method that was used for feedwater flow. Usng the weghtng factors calculated for the feedwater flow parameters, the systematc and random uncertantes combne as follows: N B = W B = (3-7) And N S X = W S (3-8) X = Where B and S X are the systematc and random uncertantes, respectvely. The total uncertanty of the estmated flow s expressed as follows: B U = t + S X (3-9) Where: U 95 = 95% Confdence nterval for the uncertanty of the estmated flow t 95 = Student s 95% confdence and n- degrees of freedom (assumed to be for ths calculaton) B = Combned 95% confdence nterval for systematc uncertanty based on Equaton 3-7 S X = Combned random uncertanty based on Equaton Foulng Indcator The Foulng Indcator s calculated by takng the dfference between the predcted and measured flow and dvdng ths by the measured flow (Equaton 3-0). A postve value for Foulng Indcator ndcates that the flow measured s potentally fouled. The resultng value can then be used as a correcton to the plant heat rate f the heat rate s calculated by a frst prncples mass and energy balance approach. FI Flow estmated measured = (3-0) Flow Flow estmated Where: Flow estmated = Estmated Flow value Flow measured = Plant Measured Flow value FI = Nozzle Foulng Indcator Page 9 of

10 4 Results Once the feedwater flow s estmated usng the alternate plant parameters, and the uncertanty of ths estmate s establshed, the estmated values can be compared to the plant measured values.ths dfference can be related to the reference feedwater flow to determne the Foulng Indcator, whch s an ndcaton of the current measured feedwater flow to expected results (Secton 3.5). Page 0 of

11 5 References INPO Topcal Report TR4-34. Revew of Feedwater System Ultrasonc Flowmeter Problems, March 004. EPRI Report TR-8. Feed Water Flow Measurement Applcaton Gude, Stret, S, Langensten, M, and Etschberger, H. ICONE : A NEW METHOD FOR EVALUATION AND CORRECTION OF THERMAL REACTOR POWER AND PRESENT OPERATIONAL APPLICATIONS, Proceedngs of: ICONE3 3th Internatonal Conference on Nuclear Engneerng. Bejng, Chna, May 6-0, Bornsten, B. and Leung, P. Nuclear Plant Turbne Cycles A Senstvty Analyss. ASME Conference, Wnter Annual Meetng, Detrot, Mchgan, November -5, E. Grauf, J.Jansky, M. Langensten. ICONE-8083: Reconclaton of process data n Nuclear Power Plants (NPPs), Proceedngs of: ICONE 8,8th Internatonal Conference on Nuclear Engneerng, Baltmore, MD USA, Aprl -6, Dzuba, L. ICONE : Use of a Best Estmate Power Montorng Tool to Maxmze Power Plant Generaton. Proceedngs of: ICONE4 Internatonal Conference on Nuclear Engneerng, Mam, Florda, USA, July 7-0, INPO Report NX-057 Rver Bend Staton Best Estmate Core Thermal Power, November ASME PTC , Test Uncertanty. 9 Cotton, K.C. Evaluatng and Improvng Steam Turbne Performance. Second Edton, Cotton Fact Inc, Mller, R.W. Flow Measurement Engneerng Handbook. 3rd Edton, McGraw-Hll, 996. Avallone, E.A. and Baumester, T. Marks Standard Handbook for Mechancal Engneers. Nnth Edton; McGraw-Hll Book Company, 987. Page of