Energy Fuels 2010, 24, 4961–4970 Published on Web 08/26/2010
: DOI:10.1021/ef100164z
Stochastic Simulation of Pulverized Coal (PC) Processes Juan M. Salazar,† Urmila M. Diwekar,*,† and Stephen E. Zitney‡ † Center for Uncertain Systems Tools for Optimization and Management, Vishwamitra Research Institute (VRI), Clarendon Hills, Illinois 60514, and ‡Collaboratory for Process and Dynamic Systems Research, National Energy Technology Laboratory (NETL), United States Department of Energy (DOE), Morgantown, West Virginia 26507
Received February 9, 2010. Revised Manuscript Received August 11, 2010
An increasing population and electricity demand in the U.S. require capacity expansion of power systems. The National Energy Technology Laboratory (NETL), U.S. Department of Energy (DOE), has invested considerable efforts on research and development to improve the design and simulation of these power plants. Incorporation of novel process synthesis techniques and realistic simulation methodologies yield optimal flowsheet configurations and accurate estimation of their performance parameters. To provide a better estimation of such performance indicators, simulation models should predict the process behavior based on not only deterministic values of well-known input parameters but also uncertain variables associated with simulation assumptions. In this work, the stochastic simulation of a load-following pulverized coal (PC) power plant takes into account the variation of three input variables, namely, atmospheric air temperature, atmospheric air humidity, and generation load. These uncertain variables are characterized with probability density functions (pdfs) obtained from available atmospheric and electrical energy generation data. The stochastic simulation is carried out by obtaining a sample of values from the pdfs that generates a set of scenarios under which the model is run. An efficient sampling technique [Hammersley sequence sampling (HSS)] guarantees a set of scenarios uniformly distributed throughout the uncertain variable range. Then, each model run generates results on performance parameters as cycle efficiency, carbon emissions, sulfur emissions, and water consumption that are statistically analyzed after all runs are completed. Among these parameters, water consumption is of importance because an increasing demand has been observed mostly in arid regions of the country and, therefore, constrains the operability of the processes. This water consumption is significantly affected by atmospheric uncertainties. The original deterministic process model simulation was designed in Aspen Plus, and a CAPE-OPEN compliant stochastic simulation capability is employed to run the uncertainty analysis. Initially, the influences of atmospheric conditions and load change on the performance parameters are analyzed separately to understand their individual influences on the process, and then their simultaneous variation is analyzed to generate more realistic estimations of the process performance.
Besides plant efficiency and environmental emissions, water consumption has been included as one of the most important performance parameters to evaluate potentially new PC plants and capacity expansion of existing plants.4 This performance parameter is strongly influenced by temperature and humidity of the air surrounding the wet cooling tower (the largest water consumer in the process).5,6 Therefore, air temperature and humidity are input variables whose variability needs to be considered for the estimation of the water consumption. The variability of air conditions should be characterized on the basis of either available data or appropriate predictions. This work presents the characterization of these two uncertainties based on available weather information for a group of urban centers in the midwestern U.S. A second input parameter whose variability needs to be accounted for is the generation load. This parameter is important for the load-following plants that need to be part of a grid that includes disperse power sources, such as wind or
1. Introduction Uncertainty analysis has been employed in technical and economic assessments of emerging technologies for electricity generation1,2 and other chemical processes.3 In these new technologies, the phenomenological representations or models of the process involve several parameters whose values are still part of experimental research (involving high degrees of uncertainty) or simply unknown; these parameters are considered as the uncertain variables for the stochastic simulation. Typically, uncertainty is characterized through probability density functions (pdfs), which have been calculated on the basis of the available data or appropriate assumptions. The technology behind a pulverized coal (PC) thermoelectric plant is well-known. Hence, in this analysis, only external conditions, such as weather conditions or demand (generation load), may vary during the normal process operation and are influential for the estimation of the process performance. *To whom correspondence should be addressed. E-mail: urmila@ vri-custom.org. (1) Zhu, Y.; Frey, H. C. J. Air Waste Manage. Assoc. 2006, 12, 1649– 1661. (2) Diwekar, U.; Rubin, E. S. Comput. Chem. Eng. 1991, 2, 105–114. (3) Mizutani, F. T.; Costa, A. L. H.; Pessoa, F. L. P. Braz. J. Chem. Eng. 2000, 3, 307–313. r 2010 American Chemical Society
(4) Feeley, T. J., III; Skone, T. J.; Stiegel, G. J., Jr.; McNemar, A.; Nemeth, M.; Schimmoller, B.; Murphy, J. T.; Manfredo, L. Energy 2008, 1, 1–11. (5) Hensley, J. C. Cooling Tower Fundamentals; SPX Cooling Technologies, Inc.: Overland Park, KS, 2006; p 116. (6) Hamilton, T. H. Power Eng. 1977, 3, 52.
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Figure 1. Schematic representation of a PC process affected by uncertain parameters as variable generation and variable cooling air conditions. This figure was adapted with permission from ref 9.
solar generators.7 Grid requirements are associated with seasonal weather conditions, and therefore, coal-fueled plants need to obey those variations. This work examines available data on generation in the U.S. and uses it for the characterization of the plant load as an uncertain input parameter. Once the uncertain input parameters are characterized, an efficient sampling technique8 is employed to select a set of scenarios under which the PC model is solved to evaluate the performance parameters. Therefore, the stochastic simulation approach requires a process model that can be evaluated under all sampled scenarios, and this work has adapted previously reported9 rigorous Aspen Plus simulator models to estimate the performance parameters under different air conditions and for different load variations. The results from this stochastic analysis provide realistic information on the potential ranges and expected values for efficiency, emissions, and water consumption of a load-following PC power plant that can be built in the midwestern U.S.
electricity of maximum capacity. The process is divided into two main sections: a boiler section and a steam-generation section. The boiler is modeled as a series of two reactors (stoichiometric reactors), and a flue gas desulfurization (FGD) unit is attached to the boiler effluent. The steam section comprises the typical high-, intermediate-, and low-pressure turbine train and is a steamreheating scheme, with feedwater heating from turbine-extracted steam. The main modifications made to the flowsheet were the addition of a cooling tower to the cooling water section (originally, only the condenser was included) and the possibilities to consider different generation loads and different cooling air conditions. 2.1. Process Performance Parameters. Three process parameters were studied in this work, and they were determined through a calculator block within the PC model called WTCONS. The process global efficiency was defined as the power generation divided by the heat power of the fed coal, as shown in eq 1, where coefficient 0.95 considers a penalty of 5% on net generation (which is calculated by the original model accounting for generation losses only) associated with pumps and compressors and 11 666 is the highest heat value of Illinois No. 6 coal. BTU 1 0:95 net generation ðhpÞ 2544:43 h hp η ¼ ð1Þ BTU lb 11666 coal flow rate lb h
2. Model of the PC Process The PC plant model employed in this work is described in detail as case 11 by the report on cost and performance of fossil energy plants9 and represented in Figure 1. Particularly, this is a supercritical steady-state PC model that does not include carbon sequestration technology and is intended to generate 548 MW of
The CO2 and SO2 emissions were calculated as the flow rate of each of these compounds in the clean gas stream (named CLEANGAS in the model) divided by the net power generation, as in eq 2. clean gas material flow rate ðlb=hÞ CO2 or SO2 emission ¼ net generation ðMWÞ ð2Þ
(7) Banjo, D.; Hayashi, S.; Tamura, H.; Okauchi, T. Electr. Eng. Jpn. 2008, 3, 42–49. (8) Kalagnanam, J. R.; Diwekar, U. M. Technometrics 1997, 3, 308– 319. (9) Woods, M. C.; Capicotto, P. J.; Haslbeck, J. L.; Kuehn, N. J.; Matuszewski, M.; Pinkerton, L. L.; Rutkowski, M. D.; Schoff, R. L.; Vaysman, V. Performance Baseline for Fossil Energy Plants. Volume 1: Bituminous Coal and Natural Gas to Electricity Final Report; Department of Energy/National Energy Technology Laboratory (DOE/NETL), Aug 2007; DOE/NETL-2007/1281, Revision 1.
The water consumption estimation is based on a simple scheme reported in the literature to determine the evaporative rates in cooling towers.6 To account for the cooling system in the 4962
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time-dependent factors, such as day of the week. The most commonly available data for this variable are basically the overall demand in the U.S., which is frequently presented as a load curve, a graph of power load versus time, or as a load duration curve, a graph of power load versus the time (duration) that it takes place. These data can be used in different ways to represent the uncertainty of the power system. For instance, one model10 proposes the employment of a monthly load duration curve divided in two sections: one for weekday demand and one for weekend demand, with each section having three load levels. In a 12 month year, the whole structure is repeated 3 times for three different scenarios with their corresponding probability to occur. The structure has been built to model power demand uncertainty for a whole generation grid, and qualitative estimates have been assigned to the probabilities of the scenarios and to the load duration curves. Other variations from weeks to weekend consumption are reported by the literature.11 This paper suggests that weekend consumption is 28.63% of the consumption of the weekday and the reduction only affects the intermediate- and low-pressure turbines of the steam cycle. Daily load curves of the entire U.S. and U.K. grids are studied in refs 12 and 13. These references show how the variability of the U.S. demand in 1 day is covered mainly by small/medium coal plants because the base load is generated by nuclear and large new coal plants, which are not flexible in the capacity of generation.12 On the other hand, the variability of the daily load curve for the U.K. is shown as being affected by the climate change because of the seasons.13 There is scarce literature available about individual plant load variation, only for a 300 MW plant, daily variations on steam flows are studied in ref 14. Finally, one more reference suggests that the power demand can be adjusted to a normal distribution with a standard deviation equal to 1/3 of the mean.7 This normal distribution is the prediction of power load including dispersed sources (such as wind or solar energy sources). These dispersed power sources decrease the demand mean (because normally the generators operate at lower loads than those that they were designed) and increase the standard deviation because of the increase of uncertainty. An important and complete source of information for PC power generation rates is the Energy Information Administration (EIA) website (www.eia.doe.gov). It reports data for individual plants in the U.S. from the EIA surveys 906/920. The reported data contain information on the monthly net generation of each plant in megawatt hours (about 8000 plants in the whole country) until the year 2007. From these data, an estimate of the average monthly load can be calculated by dividing the net generation and the total number of hours per each month. This information along with the monthly peak of each of the electric grid regions (survey 411) was used in this work to characterize the variability of the load for a PC plant rather than any of the other representations described above. 2.2.2. Variation of Atmospheric Conditions. Cooling tower evaporation losses are one of the most significant sources of water consumption in a PC process.15 Therefore, they are an important factor on the general performance of the plant and are strongly affected by fluctuating environmental parameters,
PC plant model, three unit operation blocks are added to the flowsheet, including two flash separators and one heat exchanger. An adiabatic flash separator is used to calculate the wet-bulb temperature from the dry-bulb temperature and relative humidity data. A design specification is employed to calculate the amount of water required to saturate a stream of ambient air. The final temperature of the first flash is the wetbulb temperature. The second flash separator is the simulation of the cooling tower itself and is considered as an operating unit with no liquid outlet, similar to the wet-bulb temperature unit. This unit is coupled with the cooler (which represents the cold side of the condenser), so that the heat removed by the tower is equal to that removed by the condenser. All of these process units are linked through design specifications and calculator blocks to determine the cold water temperature, circulating water flow rate, and air flow rate for a constant volume forced drift cooling tower. The calculation procedure is described as follows: (1) Assume cold water temperature (start loop of design specification CWTEM). (2) Calculate the amount of water flowing through the cold side of the condenser with the added heat exchanger and design specification CFLOW1 until it matches the heat load at the condenser (hot side). (3) Assume air flow through the cooling tower, and calculate all of its individual molar rates with calculator AIRCT (start loop of design specification CAGF). (4) Calculate the water flow rate entering the cooling tower with the air based on the dry-bulb temperature and relative humidity with design specification CTAIR4. (5) Assume the flow rate of water entering the flash unit that simulates the tower (TOWER), and calculate the heat requirement and temperature of the flash unit (start loop of design specification CTEVA1). (6) Calculate the amount of water evaporated in the tower as the difference between the water in the air outlet and inlet streams. (7) Is the heat requirement of the cooling tower equal to the heat load of the condenser? If not, go to step 5 (close loop of design specification CTEVA1). (8) On the basis of the temperature of the air leaving the tower, is the volumetric flow rate constant? If not, go to step 3 (close loop of design specification CAGF). (9) On the basis of empirical data reported in the literature6 and fitted to a quadratic function, check whether the cold water temperature is consistent with the liquid flow rate, gas flow rate, and wet-bulb temperature. If not, go to step 1 (close loop of design specification CWTEM). Once the evaporation losses (E) are calculated, the other components of water consumption are added to the general estimation by calculator block WTCONS. These components are (a) drift losses (D), which are losses because of the air flow carrying out some cooling water by mechanical action and are estimated as 0.02% of the circulating water, (b) blowdown (B), which is the water that is removed in liquid form from circulation to avoid mineral buildup (because of the evaporation of water, some minerals, such as calcium or magnesium, increase their concentration) and to reduce cooling tower fouling and corrosion [B is estimated with eq 3, where C is the number of concentration cycles (number of times that water circulates through the tower), which is assumed to be equal to 4, the evaporation losses (E), and the drift losses (D)], and (c) flue gas desulfurization (FGD) water consumption, which is the summation of water required to prepare the limestone slurry at the required ratio and the makeup water to the reactor. The total water consumption (W) was estimated according to eq 4, with all terms in lb/h. B ¼
E - ðC - 1ÞD C-1
W ¼ E þ D þ B þ FGD
(10) Perez Canto, S. Eur. J. Oper. Res. 2008, 759. (11) Papalexandri, K. P.; Pistikopoulos, E. N.; Kalitventzeff, B.; Dumont, M. N.; Urmann, K.; Gorschluter, J. Comput. Chem. Eng. 1996, S763–S768. (12) Denholm, P.; Holloway, T. Environ. Sci. Technol. 2005, 23, 9016– 9022. (13) Gross, R.; Heptonstall, P.; Leach, M.; Anderson, D.; Green, T.; Skea, J. Proc. Inst. Civ. Eng.: Energy 2007, 31–41. (14) Victorin, K.; Jantunen, M. J.; Itkonen, A.; Ahlborg, U. G.; Staahlberg, M.; Honkasalo, S. Environ. Sci. Technol. 1986, 4, 400–404. (15) Stiegel, G. J., Jr.; Longanbach, J. R.; Rutkowski, M. D.; Klett, M. G.; Kuehn, N. J.; Schoff, R. L.; Vaysman, V.; White, J. S. Power Plant Water Usage and Loss Study; Department of Energy/National Energy Technology Laboratory (DOE/NETL), 2007.
ð3Þ ð4Þ
2.2. Uncertainties Affecting Performance Parameters. 2.2.1. Variation of Load. Power generation in a PC plant varies according to power demand, which is strongly affected by climatic and 4963
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such as air temperature and humidity. Detailed information about air humidity for different locations within the U.S. can be obtained from the real-time weather tool of EnergyPlus energy simulation software, which is available at the Energy Efficiency and Renewable Energy (EERE) website of the U.S. Department of Energy (DOE) (http://www1.eere.energy.gov). The PC models were originally established for a plant located in the midwestern U.S. Therefore, weather data for the years 2006 and 2007 from eight U.S. midwestern urban centers (Chicago, Detroit, Indianapolis, Minneapolis, St. Louis, Des Moines, Kansas City, and Cincinnati) were requested from the software and processed to characterize the variation of the environmental parameters. The estimation of the evaporated water in the cooling tower was originally performed9 according to a simplified empirical model reported in the literature,5 which was recommended for use only in the absence of information about air conditions and tower operation. Therefore, the empirical model does not significantly reflect the variations in weather conditions, and a more elaborate model6 for the estimation of the cooling tower evaporative losses is added to the PC model in this work.
3. Stochastic Simulation Conventional process models are largely based on a deterministic computational framework used for simulation of a flowsheet. An important limitation of these models is their inability to analyze uncertainties rigorously. The stochastic simulation tool used in this work can be employed to successfully evaluate different risk and uncertainty scenarios arising in process design and operation. Uncertainty analysis comprises four main steps: (1) characterization and quantification of uncertainty in terms of probability distributions, (2) generating a sample of possible scenarios from these distributions, (3) propagation through the modeling framework by running the model at each of the scenarios in the sample, and (4) analysis of results.2 This section describes the computational tool employed for the uncertainty analysis of a PC process under weather and load variations and also briefly describes the sampling technique employed to generate the set of scenarios. 3.1. APECS CAPE-OPEN Compliant Capability. Developed by the National Energy Technology Laboratory (NETL) of the DOE, the Advanced Process Engineering Co-Simulator (APECS) is a virtual plant simulator that combines process simulation, equipment simulations, immersive and interactive plant walk-through virtual engineering, and advanced analysis capabilities.16,17 The APECS system uses commercial process simulation software (e.g., Aspen Plus) and equipment modeling software (e.g., FLUENT for computational fluid dynamics) integrated with the process-industry CAPE-OPEN (CO) software standard. Plug-and-play interoperability of analysis tools in APECS is also facilitated by the use of the CO standard. This work uses a CO-compliant stochastic modeling framework for APECS, which enables analyzing the variation of process performance parameters when input parameters to the model, such as atmospheric air conditions and generation requirements, change. (16) Zitney, S. E.; Syamlal, M. Integrated process simulation and CFD for improved process engineering. In Proceedings of the European Symposium on Computer-Aided Process Engineering-12, ESCAPE-12; Grievink, J., Van Schijndel, J., Eds.; The Hague, The Netherlands, 2002; pp 397-402. (17) Zitney, S. E.; Osawe, M. O.; Collins, L.; Ferguson, E.; Sloan, D. G.; Fiveland, W. A.; Madsen, J. M. Proceedings of the 31st International Technical Conference on Coal Utilization and Fuel Systems; Clearwater, FL, 2006.
Figure 2. Characterization of load variation from fall (top) to summer (bottom).
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Figure 3. pdfs of four seasons (fall to summer from top to bottom) for dry-bulb temperature and relative humidity on eight U.S. midwestern cities.
the month m. Once these values are calculated, the plants using bituminous and sub-bituminous coal as fuel were selected. Among these plants, those having a peak load for the month of August between 500 and 600 MW were used to characterize the variation of the average monthly generation. The regions employed for the characterization were FRCC, MRO, NPCC, SERC, and SPP. Average monthly generation for several of these plants during the years 2004-2007 comprised the data that were employed to characterize the uncertainty, which were also segregated by seasons and fitted to normal distributions (this is the type of distribution that best fits the data). The results of the characterization are shown in Figure 2 4.1.2. Atmospheric Conditions. The massive amount of data obtained from the weather stations through the EERE software was organized into four seasons, starting at September 2005 and finishing at August 2007. The original data contained dry-bulb temperature and dew point as humidity information. The dry-bulb temperature data were binned, and a frequency distribution was calculated. For each bin, there is a set of dew point values that correspond to each of the dry-bulb temperature measurements. An average of those dew point values and the central value of the bin were used to calculate a value of relative humidity. The calculated value of the relative humidity is assumed to happen as frequently as the central value of the dry-bulb temperature, and therefore, a frequency distribution for relative humidity can be generated. Histograms of the frequency distributions were fitted to the appropriate pdfs to represent the air condition variability of an average midwestern urban center during each of the four seasons of a year, as shown in Figure 3. 4.2. Stochastic Simulation. The results of the stochastic simulation are presented as pdfs and cumulative distribution functions of each of the performance parameters. Each figure shows the results of a single stochastic simulation, where one or two uncertain variables are considered for
3.2. Sampling. The stochastic modeling capability offers six sampling techniques.18 These are (1) Monte Carlo sampling (MCS), (2) Latin hypercube sampling (LHS), (3) Hammersley sequence sampling (HSS), (4) Latin hypercube Hammersley sampling (LHHS), (5) leaped HSS, and (6) leaped LHHS. This works employs the HSS technique, an efficient sampling technique based on Hammersley points,8 which uses an optimal design scheme for evenly placing the n points on a k-dimensional hypercube. This scheme ensures that the sample set is more representative of the population, showing uniform properties in multi-dimensions, unlike Monte Carlo, Latin hypercube, and its variant, the median Latin hypercube, sampling techniques. 4. Results 4.1. Characterization of the Uncertainties. 4.1.1. Power Demand. To analyze the data available and characterize the load variation for the PC process, two main assumptions were made: (1) During the monthly peak loads, the plants work very close to their maximum capacity. (2) The fraction of the average load that is generated by each plant is the same fraction that the plant contributes at the peak load. With these assumptions, the peak load for each plant can be calculated with eq 5 and used to filter those plants whose maximum generation is similar to the plant represented by the model Gim PTm ð5Þ pim ¼ GTm where pim and Gim are the peak load and the net generation of the plant i during the month m, respectively. GTm is the net generation of the region during the month (summation of the net generation of all plants belonging to the region T during the month m), and PTm is the peak load of the region T during (18) Knuth, D. E. The Art of Computer Programming; Addison-Wesley Publishing Co.: Reading, MA, 1973; Vol. 1: Fundamental Algorithms.
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specific water consumption
similar to design condition and season average
decreases compared to design conditions and is different from season average
increases compared to design conditions and is different from season average
increases for CO2 and is similar for SO2 compared to design conditions; for both, it is similar to season average increases compared to design condition and is similar to season average increases compared to design conditions and is different from season average increases compared to design conditions and similar to season average
decreases compared to design conditions and is different from season average
decreases compared to design conditions and is similar to season average increases compared to design conditions and is different from season average decreases compared to design conditions and is different from season average
load (Figure 4)
decreases compared to design conditions and is similar to season average
air conditions (Figure 6) load and air conditions (Figure 5) performance parameter
water consumption and efficiency emissions
load (Figure 8)
uncertainty uncertainty
air conditions (Figure 7)
season: summer season: winter
either summer or winter. Table 1 presents some conclusions about the expected values of the distributions compared to results obtained from deterministic simulations at design conditions and average season conditions. Figure 4 shows the results of the stochastic simulation for winter under variation of plant load. It can be observed that water consumption is strongly affected by the load variation, and therefore, the average estimation of 2.6 106 lb/h at design conditions (maximum capacity of 548 MW and fall conditions) is almost twice the average value for the winter season when load is varied; this strong difference may be reflected in an extremely oversized design for the cooling tower. This is evidently attributed to the fact that there is less water circulating through the cooling tower because of a lower load to the condenser, and therefore, less evaporation losses may be predicted. The distribution also shows a large variability, which may render the sizing of the cooling tower difficult. Efficiency and emissions are notably worse than those calculated for the original design conditions, and the distributions are skewed toward the estimation at the average conditions of the season; these conditions and large tails representing up to 50% of the cumulative probability in about 2/3 of the domain are observed (emissions). This lack of symmetry in the presence of a fairly symmetric distribution of the uncertain variable (Figure 2) demonstrates the complexity of the models and the importance of their accuracy to determine the appropriate design values to achieve environmental targets. This nonlinearity can be attributed in part to the necessity of bypassing some of the low-pressure feedwater heating stations at low generation values; therefore, feedwater needs to be heated by highpressure stages with larger bleeding rates, reducing the capacity of generation and requiring the increment of fuel, which increases the emission levels. High levels of emissions at low generation rates can be part of the reason to have many values within this long tails. Interestingly, the process water consumption relative to the generation (specific consumption) remains close to the original design estimation, but variability is asymmetric and considerable, demonstrating the importance of stochastic analysis when comparisons are needed even for normalized parameters. A similar behavior can be observed in Figure 5 when air conditions are included as uncertain parameters along with the load variation, which suggests that the influence of load variability is larger than that of atmospheric conditions. From Figures 4 and 5, we can conclude that there is a 100% probability that the efficiency of the cycle is overestimated and the emission from the cycle is underestimated for a load-following plant if maximum capacity is considered for the evaluation. Figure 6 shows the results of the stochastic simulation when only weather variation conditions are considered in a winter season; it confirms that low values of the dry-bulb temperature reduce the water consumption because the cooling tower may make use of sensible heat of the air instead of latent heat from the water reducing the evaporation rate. Low cycle efficiency and high levels of emissions may be attributed to the increase in the fuel flow rate to maintain the boiler efficiency (which is fixed by the model) when cold air is used for the combustion; reaction conditions within the FGD reactors can also be influenced by the employment of very cold air. Specific water consumption shows a similar behavior to absolute water consumption behavior because load is kept constant at the design level for the stochastic simulation. An opposite behavior is observed in Figure 7,
load and air conditions (Figure 9)
Salazar et al. Table 1. Comparison of Expected Values for Performance Parameters Resulting from the Stochastic Simulations with Deterministic Results Obtained at Design Conditions (Fall Maximum Capacity) and Average Season Conditions
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Figure 4. Stochastic simulation results of a PC model for winter under variation of plant load. The red bar represents the original average design conditions (548 MW and fall conditions), and the blue bar represents performance under average conditions of season (313 MW and winter conditions).
Figure 5. Stochastic simulation results of a PC model for winter under variation of electricity generation and air temperature and humidity. The red bar represents the original design conditions (548 MW and fall conditions), and the blue bar represents performance under average conditions of season (313 MW and winter conditions).
where only weather variations are considered in a summer season, because high humidity reduces the cooling capacity of the tower. The consumption of fuel is reduced, and the efficiency of the FGD is increased when warm air is employed for these processes. From Figure 6, it can be concluded that, when
low air temperatures (as those typical of a midwestern winter) are present, there is a 100% probability of overestimating the cycle efficiency and underestimating the cycle emissions when the average fall conditions are used. These estimations are more conservative when the weather variation occurs during a 4967
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Figure 6. Stochastic simulation results of a PC model for winter under variation of air temperature and humidity. The red bar represents the original design conditions (548 MW and fall conditions), and the blue bar represents performance under average conditions of season (313 MW and winter conditions).
Figure 7. Stochastic simulation results of a PC model for summer under variation of air temperature and humidity. The red bar represents the original average design conditions (548 MW and fall conditions), and the blue bar represents performance under average conditions of season (333 MW and summer conditions).
summer season (Figure 7), with 100% probability of being underestimated for the efficiency and overestimated for emissions. In the case of water consumption, the estimation under average conditions is fairly good (overestimated) for the winter but too low (underestimated) for the summer.
Figure 8 shows results of a stochastic simulation that are similar to those presented in Figure 4 for the summer season for absolute water consumption, cycle efficiency, and emissions. These values present a slight improvement because of the fact that pdf of the load variation during summer has a 4968
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Figure 8. Stochastic simulation results of a PC model for summer under variation of electricity generation. The red bar represents the original average design conditions (548 MW and fall conditions), and the blue bar represents performance under average conditions of season (333 MW and summer conditions).
Figure 9. Stochastic simulation results of a PC model for summer under variation of power load and air temperature and humidity. The red bar represents the original average design conditions (548 MW and fall conditions), and the blue bar represents performance under average conditions of season (333 MW and summer conditions).
larger mean and lower standard deviation, making low values of the load less probable to occur than in the winter, and then no large values of fuel are required per kilowatt hour (during summer, the plant is expected to work closer to the maximum capacity). This behavior affects the SO2
emissions more drastically, which are improved and whose mean value becomes closer to the deterministic estimation. However, in the case of specific water consumption, the increment is really dramatic because the reduction of water consumption as a result of the reduction of load is not 4969
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compensated by the decreased efficiency of the cooling tower when hot and humid air flows through it. From the results, it can be concluded that there is a 100% probability of underestimating the specific water consumption in a summer season when average weather conditions and maximum capacity are used in a deterministic simulation. Finally, weather variability increases variability of specific water consumption in summer (comparison between Figures 8 and 9); this situation is not observed in winter (comparison between Figures 4 and 5).
emissions are negatively impacted when the load is reduced because of operational changes in the feedwater heating system (bypass of some stages) and the increase of the fuel consumption per megawatt hour generated. Water consumption is improved when generation is reduced because less heat needs to be rejected by the cooling tower; however, the large variability may result in an extremely oversized design for this equipment and ultimately increase the water consumption. Air conditions affect the performance of the cooling tower, increasing the water consumption during the hot seasons and decreasing it during the winter months; efficiency and emissions are also affected when hot or cold air is employed for the boiler furnace and the FGD reactor. In general, avoiding load-following operation in PC power plants reduces the deterioration and variation of process performances in terms of efficiency and emissions. However, loadfollowing operation is required for grids that involve disperse power sources, such as solar or wind energy generation; in these cases, stochastic simulation analysis certainly provides important information about the variable behavior of the performance parameters.
5. Conclusion Load-following PC plants experience variations on the performance parameters when external input variables, namely, load variation and weather conditions, change. The changes in these external variables can be characterized from available data depending upon the weather seasons because they are strongly related to changes on the climate conditions. The load variation is the most influential input parameter for the efficiency, emissions, and water consumption estimation. Efficiency and specific
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