Modeling and optimization of a utility system containing multiple extractions steam turbines Xianglong Luo a , Bingjian Zhang b , Ying Chen a, * , Songping Mo a a School of Material and Energy, Guangdong University of Technology, Guangzhou 510006 China b School of Chemistry and Chemical Engineering, Sun-Yat-Sen University, Guangzhou 510275 China article info Article history: Received 21 September 2010 Received in revised form 19 March 2011 Accepted 22 March 2011 Available online 22 April 2011 Keywords: Utility system Multiple extractions Steam turbine Optimization Mathematical modeling abstract Complex turbines with multiple controlled and/or uncontrolled extractions are popularly used in the processing industry and cogeneration plants to provide steam of different levels, electric power, and driving power. To characterize thermodynamic behavior under varying conditions, nonlinear mathe- matical models are developed based on energy balance, thermodynamic principles, and semi-empirical equations. First, the complex turbine is decomposed into several simple turbines from the controlled extraction stages and modeled in series. THM (The turbine hardware model) developing concept is applied to predict the isentropic efficiency of the decomposed simple turbines. Stodola’s formulation is also used to simulate the uncontrolled extraction steam parameters. The thermodynamic properties of steam and water are regressed through linearization or piece-wise linearization. Second, comparison between the simulated results using the proposed model and the data in the working condition diagram provided by the manufacturer is conducted over a wide range of operations. The simulation results yield small deviation from the data in the working condition diagram where the maximum modeling error is 0.87% among the compared seven operation conditions. Last, the optimization model of a utility system containing multiple extraction turbines is established and a detailed case is analyzed. Compared with the conventional operation strategy, a maximum of 5.47% of the total operation cost is saved using the proposed optimization model. Ó 2011 Published by Elsevier Ltd. 1. Introduction Utility systems are an important part of the processing industry and provide utility energy for production systems. As primary component of utility systems, steam turbines are used to drive electric generators or other rotating machinery (compressors, pumps, and fans). The effective operation of a steam turbine is extremely important and directly related to energy utilization in an industrial process. Typically, industrial processes are equipped with steam turbines of various types, such as simple turbines (single inlet and single outlet, e.g., back-pressure turbines and condensing turbines) and complex turbines (e.g., steam turbines with multiple extractions, and steam turbines with multiple injectors). These steam turbines constitute a network where the turbines are inter- connected through steam pipelines. The accurate simulation of these complex turbines and operation optimization of the utility system containing these complex turbines are important ways of improving security and economic efficiency of the processing industry or cogeneration plant. Many simulation and optimization studies have been performed on the modeling and optimization of utility system components. These studies, however, only take into account the macroscopic mass and energy balances of utility systems [1e 11]. Bruno et al. [12] developed a rigorous MINLP (mixed integer nonlinear program- ming) model by fixing the steam pressure levels for the synthesis of utility plants and correlated uniform nonlinear steam turbine effi- ciency. Mavromatis and Kokossis [13] proposed a THM (turbine hardware model) that accounted for the variation of turbine size, operating load, as well as inlet and outlet conditions in a simple way. The THM was established based on pinch and total site anal- ysis combined with the Willan’s line, which describes the rela- tionship between the mass flow rate and the operating load. These studies were later extended by many researchers who improved the model accuracy [14e16]. Chaibakhsh and Ghaffari [17] pre- sented a rigorous steam turbine simulation model and the related parameters were determined by applying GA (genetic algorithms) based on experimental data obtained from field experiments for control purposes. This steam turbine simulation model was later * Corresponding author. Tel./fax: þ86 020 39322581. E-mail address: [email protected](Y. Chen). Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy 0360-5442/$ e see front matter Ó 2011 Published by Elsevier Ltd. doi:10.1016/j.energy.2011.03.056 Energy 36 (2011) 3501e3512
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Energy 36 (2011) 3501e3512
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Energy
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Modeling and optimization of a utility system containing multiple extractionssteam turbines
Xianglong Luo a, Bingjian Zhang b, Ying Chen a,*, Songping Mo a
a School of Material and Energy, Guangdong University of Technology, Guangzhou 510006 Chinab School of Chemistry and Chemical Engineering, Sun-Yat-Sen University, Guangzhou 510275 China
a r t i c l e i n f o
Article history:Received 21 September 2010Received in revised form19 March 2011Accepted 22 March 2011Available online 22 April 2011
0360-5442/$ e see front matter � 2011 Published bydoi:10.1016/j.energy.2011.03.056
a b s t r a c t
Complex turbines with multiple controlled and/or uncontrolled extractions are popularly used in theprocessing industry and cogeneration plants to provide steam of different levels, electric power, anddriving power. To characterize thermodynamic behavior under varying conditions, nonlinear mathe-matical models are developed based on energy balance, thermodynamic principles, and semi-empiricalequations. First, the complex turbine is decomposed into several simple turbines from the controlledextraction stages and modeled in series. THM (The turbine hardware model) developing concept isapplied to predict the isentropic efficiency of the decomposed simple turbines. Stodola’s formulation isalso used to simulate the uncontrolled extraction steam parameters. The thermodynamic properties ofsteam and water are regressed through linearization or piece-wise linearization. Second, comparisonbetween the simulated results using the proposed model and the data in the working condition diagramprovided by the manufacturer is conducted over a wide range of operations. The simulation results yieldsmall deviation from the data in the working condition diagram where the maximum modeling error is0.87% among the compared seven operation conditions. Last, the optimization model of a utility systemcontaining multiple extraction turbines is established and a detailed case is analyzed. Compared with theconventional operation strategy, a maximum of 5.47% of the total operation cost is saved using theproposed optimization model.
� 2011 Published by Elsevier Ltd.
1. Introduction
Utility systems are an important part of the processing industryand provide utility energy for production systems. As primarycomponent of utility systems, steam turbines are used to driveelectric generators or other rotating machinery (compressors,pumps, and fans). The effective operation of a steam turbine isextremely important and directly related to energy utilization in anindustrial process. Typically, industrial processes are equippedwithsteam turbines of various types, such as simple turbines (singleinlet and single outlet, e.g., back-pressure turbines and condensingturbines) and complex turbines (e.g., steam turbines with multipleextractions, and steam turbines with multiple injectors). Thesesteam turbines constitute a network where the turbines are inter-connected through steam pipelines. The accurate simulation ofthese complex turbines and operation optimization of the utilitysystem containing these complex turbines are important ways of
1.
Elsevier Ltd.
improving security and economic efficiency of the processingindustry or cogeneration plant.
Many simulation and optimization studies have been performedon the modeling and optimization of utility system components.These studies, however, only take into account the macroscopicmass and energy balances of utility systems [1e11]. Bruno et al. [12]developed a rigorous MINLP (mixed integer nonlinear program-ming) model by fixing the steam pressure levels for the synthesis ofutility plants and correlated uniform nonlinear steam turbine effi-ciency. Mavromatis and Kokossis [13] proposed a THM (turbinehardware model) that accounted for the variation of turbine size,operating load, as well as inlet and outlet conditions in a simpleway. The THM was established based on pinch and total site anal-ysis combined with the Willan’s line, which describes the rela-tionship between the mass flow rate and the operating load. Thesestudies were later extended by many researchers who improvedthe model accuracy [14e16]. Chaibakhsh and Ghaffari [17] pre-sented a rigorous steam turbine simulation model and the relatedparameters were determined by applying GA (genetic algorithms)based on experimental data obtained from field experiments forcontrol purposes. This steam turbine simulation model was later
applied in the work of Salahshoor et al. [18] for fault detection anddiagnosis of an industrial steam turbine. Tveit and Fogelholm [19]presented a method for finding regression models for steamturbine networks using a simulation model and an evolutionaryalgorithm to finding D-optimal designs. Han and Lee [20] devel-oped a hybrid model of condensing turbine with multiple steaminjectors and proposed an online optimization system for thecondensing turbine network of a chemical plant. Fast and Palme[21] applied artificial neural network models of main component(including steam turbine) models for the condition monitoring anddiagnosis of a combined heat and power plant in Sweden.
Some of the aforementioned models oversimplified steamturbine performance because steam turbine efficiency generallyvaried with inlet and outlet steam parameters significantly, asidefrom design size and operating load. Other research on steamturbine simulations yielded small errors for electric powerprediction and cannot be employed directly in real optimizationprograms because of the complicated calculation of working fluidphysical properties and the large number of iterations. A poorapproximation will occur if the THM is applied to the turbine withmany extractions even though the THM has been verified asaccurate enough for simple steam turbines [14e16]. Medina-Floresand Picón-Núñez [16] proposed algorithms to predict powerproduction for single and multiple extraction steam turbines basedon THM although the turbine performance for various operatingscenarios was only represented using a single weighted averageefficiency. In general, very few studies exist on the accuratemodeling and optimization of multiple controlled and/or uncon-trolled extractions steam turbine in which one or more extractionpressures are maintained at a constant value by changing theflowing areas.
In the remainder of this paper, mathematical models aredeveloped for analysis of performance variations of steam turbinesbased on THM concepts [13], turbine decomposition theory [22],
Fig. 1. General representation of mu
and turbine principles under varying conditions [23,24]. Thesimulation results of the turbine model are compared with theperformance diagram provided by the manufacturer to validate theaccuracy and performance of the developed models under differentoperation conditions. The utility system optimization model isestablished and a detailed case study is elaborated particularly withregard the significant operation cost savings.
In industry utility systems, the number of steam levels andminimum allowed pressure for each steam level are determined byproduction processes. Some steam turbines may be designed withmultiple controlled extractions to provide steam at different levelsfor production processes and uncontrolled extractions for feed-water regenerative heating to improve the total system efficiency.In China, the use of one or two controlled extraction levels withseveral uncontrolled extractions is common and the total numberof extractions can be as many as eight. A general configuration ofa turbine with multiple extractions is illustrated in Fig. 1. This typeof turbine, which includes the flow passage, is composed of manypressure stages and control stages, reheaters, deaerators,condensers, pumps, and so on. The main operating variables of themultiple extraction steam turbines include the enthalpy and massflow rate of each controlled extraction, mass flow rate and pressureof each uncontrolled extraction, and interrelated reheater param-eters. Compared with simple turbines, the multiple extractionssteam turbines are much more complicated wherein multiplecontrolled or uncontrolled extractions are employed. The steampressure consecutively drops across the turbine stages and changeswith load variation. The general representation of steam turbinenetwork composed of multiple extractions turbine is shown inFig. 2(a). In this network, one turbine may have several extractionsto satisfy corresponding ranks of steam demands. In addition, the
ltiple extraction steam turbines.
Fig. 2. General multiple extraction steam turbine network.
X. Luo et al. / Energy 36 (2011) 3501e3512 3503
steam demand may be satisfied by one or more of the controlledsteam turbine extractions. It is unreasonable to consider turbinesimply as turbine with fixed inlet and outlet parameters andmodeled in a conventional way. This brings significant challengesfor the load allocation of all turbines. In this sense, developingmathematical models capable of simulating the proper steamextraction parameter and energy released from steam expansionfor the optimization of complex turbine network as shown inFig. 2(a), is necessary.
3. Turbine model development
The thermodynamic model for multiple extractions presented isbased on the concept proposed by Chou and Shih [14] wherea multiple extraction turbine is modeled using a set of singleturbines in series and the isentropic efficiency model for simpleturbines, based on the improvements made by Medina-Flores andPicón-Núñez [16]. Stodola’s formula [24] is also applied in thisdesign to simulate the uncontrolled extraction steam parameters.
Table 1Regression coefficients for parameters A and B
Regression coefficients for simple turbines
a (MW) 0.1854b (MW/Pa) 0.0433g 1.2057l (MPa�1) 0.0075
3.1. Turbine decomposition
The complex turbine in Fig. 1 is not simply the combination ofsimple turbines because of the uncontrolled extractions. To simu-late a turbine for system optimization, the following assumption orsimplification should be considered: uncontrolled extraction doesnot distinctly affect the performance of whole stages because theflow rate of uncontrolled extraction is very little compared withthat of passing the uncontrolled stage in most cases. Under thisassumption, the complex turbine can be decomposed into Lþ1simple turbines with fixed inlet and outlet pressures, as illustratedin Fig. 2(b), where L is the number of controlled extractions. Andthen the thermodynamic system of a complex turbine is repre-sented by a number of lumped models for decomposed simplesteam turbines in series.
3.2. Simple turbine hardware model
Equations (1)e(2) are common thermodynamic models used tocalculate the inlet and outlet parameters for the decomposedturbines in series. However, the isentropic efficiency hist;z in Equa-tion (1) is not easy to predict. Fortunately, the improved THM [16]provides accurate and general prediction formulation that accountsfor the design load, operating load, as well as inlet and outlet steamparameters. The improved THM is described by Equations (3)e(4)and Table 1 shows the regression coefficients.
houtt;z ¼ hint;z � hist;zDhist;z (1)
hint;zþ1 ¼ houtt;z (2)
hist;z ¼ 65Bt;z
1� A
Dhist;zMdnt;z
! 1� Mdn
t;z
6Mint;z
!(3)
A ¼ aþ bPint;zB ¼ gþ lPint;z
(4)
where Dhist;z is the isentropic enthalpy drop of the decomposedsimple turbine z, which can be regressed as the function of DTsatt;zand Dhint;z with a maximum relative error of 10% [see Equation (5)][13]. However, for a turbine with fixed inlet and outlet pressure,Dhist;z can be regressed separately to reduce the relative error.
Fig. 3. General representation of a surface reheater.
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Equation (6) gives the regression model with a maximum relativeerror of 0.15% for some determined inlet and outlet pressure.
In addition, the decomposed simple turbine with uncontrolledextractions should be decomposed into several stage groups topredict the extraction pressure using Stodola’s formula [24]. Thefour main application conditions for forming a stage group are: 1)constant flowing area; 2) constant flow rate throughout the flowpassage; 3) infinite stages; and 4) homogenous steam flow. Most ofthe pressure stage meets the requirement of conditions 1 and 4. Forcondition 3, it will be accurate if more than 3 stages are selected toform a stage group. For condition 2, the uncontrolled extractionstage can be included in a stage group if the extraction steam isused to heat the condensate water of the turbine itself. Equation (7)is used to derive the uncontrolled extraction pressure model [24]when the steam flow rate does not deviate significantly from thedesign conditions. Equation (8) is used to obtain the uncontrolledextraction enthalpy model in the same way as the controlledextraction enthalpy.
For simplification purposes, it is reasonable to consider that theisentropic efficiency in Equation (8) is equal to hist;z. However,Equation (6) cannot be used to calculate isentropic enthalpy dropbetween the inlet of the decomposed turbine z and the uncon-trolled extraction u because the outlet pressure is unknown. Similarmodels can be regressed as Equation (9) with a maximum relativeerror of 4%.
3.4. Feedwater regenerative heating system simulation model
The feedwater regenerative heating system illustrated in Fig. 1 iscomposed of several surface reheaters. Fig. 3 provides the general
representation of a surface reheater. The mass and energy balanceof reheater u are illustrated in Equations (10)e(19). Equations(10)e(12) are used to derive the mixture mass and energy balancefor inlet steam of reheater u where the waste heat Mwh
t;u mainlycomes from the shaft sealing steam leakage. To simplify thecalculation model, the waste steam enthalpy and flow rate areregarded as constants. Equations (13)e(15) are used to obtain themass and energy balance for reheater u. Equation (16) proves thatthe outlet water temperature of reheater u (i.e., inlet watertemperature of reheater uþ1) is equal to the saturation tempera-ture of the inlet steam pressure subtracting the heat transmissionend difference dTt,u. Equation (17) shows that the drain watertemperature of reheater u is equal to the saturation temperature ofthe inlet steam pressure. The saturation temperature can be rep-resented as a function of pressure through piece-wise linearizationin Fig. 4. Equation (18) derives the general regression model of sub-cool water enthalpy and Equation (19) derives the more accuratepiece-wise regression model in case of known pressure (e.g.,1.2 MPa and 12 MPa).
Muce;mixt;u ¼ Muce
t;u þMwht;u (10)
Muce;mixt;u huce;mix
t;u ¼ Mucet;u hucet;u þMwh
t;u hwht;u (11)
puce;mixt;u ¼ �
1� Dt;u�pucet;u (12)
Mw;int;u ¼ Mw;out
t;u (13)
Mdrwt;u ¼ Mdrw
t;uþ1 þMuce;mixt;u (14)
�Muce;mix
t;u huce;mixt;u þMdrw
t;uþ1hdrwt;uþ1 �Mdrw
t;u hdrwt;u
�ht;u
¼ Mw;int;u
�hw;int;uþ1 �Mw;in
t;u
�(15)
Tw;int;uþ1 ¼ Tsat
�puce;mixt;u
�� dTt;u (16)
Tdrwt;u ¼ Tsat�puce;mixt;u
�(17)
hwðTÞ ¼ 4:4317T � 19:029 35 � T � 325 (18)
hwðTÞ ¼ 4:2449T � 3:1606 p ¼ 1:2; T < 187hwðTÞ ¼ 4:4966T � 23:794 p ¼ 12; T < 324 (19)
Fig. 5. Pressure varying process of controlled extraction.
Fig. 4. Piece-wise linearization of saturation temperature curve on pressure.
X. Luo et al. / Energy 36 (2011) 3501e3512 3505
3.5. Water balance
The feedwater flow rate is generally equal to the turbine inletsteam flow rate if the blowdown water is not considered [seeEquation (20)] and the makeup water flow rate is equal to thecontrolled extraction steam for the production process [see Equa-tion (21)].
Mfdt ¼ Min
t (20)
Mmkt ¼
Xz<CARDðzÞ
Mcet;z (21)
3.6. Electric power generation model
The pressure stage is decomposed again into several stage zonesby extraction point (both controlled and uncontrolled extractions)from outlet to inlet to calculate the electric power generation. Thetotal stage zone S is equal to Z þ U and Equations (22)e(23) derivesthe electric power generation model.
Et ¼Xs
�hint;s � houtt;s
�Min
t;s (22)
Mint;s ¼
Xi˛S;i<s
Mt;i (23)
3.7. Load constraint
To ensure economical and safe operation, the turbine inlet andoutlet steam parameters must be controlled within certain bounds.Equation (24) is used to derive the minimum condensing steamflow rate constraint to sufficiently cool the lower pressure stage.
moutt;z � mconds;min
t z ¼ CARDðzÞ (24)
Generally, the inlet steam flow rate of each decomposed simpleturbine after controlled extraction outlet is controlled througha throttle-governing valve such as rotating diaphragm. The
pressures, before and after the governing valve, change with thesteam flow rate that enters the lower stage. The variation trend isrepresented in Fig. 5 where pcet;z is the pressure of the controlledextraction z and pint;zþ1 is the steam pressure entering the lowerstage; Dprvt;zþ1 is the pressure lost in the throttle-governing valve orfacility;Min
t;zþ1 is the total steam flow rate entering the lower stage;and Min;dn
t;zþ1 is the maximum steam flow entering the lower stagewhen the control valve is fully open, which keeps the extractionsteam pressure in control. Hence, adding a constraint [Equation(25)] is necessary to keep the controlled extraction in control.Equation (26) derives the total inlet steam flow rate balance whileEquation (27) derives the maximum power generation constraint.
mint;z � min;dn
t;z Yt (25)
mint ¼
Xz
mcet;z þ
Xz
Xu
�muce
t;u þmwht;u Yt
�(26)
Et � Emaxt Yt (27)
X. Luo et al. / Energy 36 (2011) 3501e35123506
3.8. Turbine model validation
A CC50-9.5/4.0/1.27 turbine, commonly used in processingutility or cogeneration plants in China, is used as a case study tovalidate the accuracy of the proposed turbine simulationmodel. Thestudied steam turbine has two controlled extractions (with pres-sures of 4 MPa and 1.27 MPa) and five uncontrolled extractions. Thecontrolled extraction and condensing steam flow rate (i.e., theprocess demands are given) are provided while other variables,especially inlet steam flow rate and electric power generation, aresimulated. The deviation error between the simulated results andthe given value is used to validate model accuracy. The corre-sponding constraints [Equations (1)e(23), (26)] incorporate theobjective function [Equation (28)] and are developed using GAMS20.2 and the simulation is conducted employing the CONOPTsolver.
Min SimuObj ¼ mint;1 (28)
In this case study, the heat transfer end difference dTt,u is 3 �C forthe low-pressure reheater and 1 �C for high-pressure reheater. Thepressure loss ratio from the extraction outlet to the reheater is 8%.The product of mechanical efficiency and generating efficiency is0.98. The turbine is decomposed into three simple turbines in seriesbased on the decomposition theory. The turbine configuration andsimulated thermodynamic balance of the design condition areshown in Fig. 6 while the data used in the working conditiondiagram provided by the manufacturer are shown in Fig. 7. Most ofthe simulated parameters fit the data provided by manufacturewell. Some of the simulated uncontrolled extraction enthalpydeviates slightly from the data in the working conditions diagramdue to the simplification of uncontrolled extraction efficiency.However, the inlet steam flow rate and electric power generationare very close to the data in the working conditions diagram. Sevenoff-design conditions are also simulated using the proposed model
Fig. 6. Simulated thermodynamic balances unde
and compared with the balance in the working conditions diagram.The simulation and comparison results are shown in Table 2 andthe maximum deviation of 0.87% for electric power generation isachieved.
4. Optimization model of utility network containing multiplecontrolled extractions steam turbines
4.1. Object function
The objective of optimization is to locate the optimal operatingconditions that minimize the total operation cost to satisfy thesteam and electric power demand of the process. In the proposedstudy, the objective function can be written as Equation (29). Theoperating costs OpCost include boiler fuel cost FuCost [Equation(30)], water cost WatCost (i.e., makeup water cost [Equation (31)]),maintenance and depreciation expense MOCost [Equation (32)],and imported electricity cost EleCost [Equation (33)].
MIN OpCost ¼ FuCostþWatCostþMainDepCostþEleCost (29)
FuCost ¼Xbn
FbnCFOTY (30)
WatCost ¼Xt
CmkMmkt OTY (31)
MOCost ¼ X
bn
MbnMDbn þXtn
EtnMDtn
!OTY (32)
EleCost ¼ CEEpurOTY (33)
r the design conditions of CC50-9.5/4.0/1.27.
Fig. 7. Manufacturer-provided thermodynamic balances under the design conditions of CC50-9.5/4.0/1.27.
X. Luo et al. / Energy 36 (2011) 3501e3512 3507
4.2. Boiler operation model
In this paper, the boiler model presented by Shang [25] isapplied and illustrated as Equation (34).
Fbnqbn ¼�hs � hfw
��ð1þ bbnÞMbn þ abnMmaxbn Ybn
�(34)
4.3. Electricity demand constraints
The total electricity generated by turbines and imported fromlocal electricity grid must be equal to the electricity demand of theprocess [Equation (35)].
Xt
Et þ Epur ¼ Edem (35)
4.4. Steam demand constraints
The total steam generated from the boiler should be greaterthan or equal to the total steam flow entering the turbines [Equa-tion (36)]. For each steam level, the total enthalpy supply (i.e., total
Table 2Simulation and comparison result of typical conditions for CC50-9.5/4.0/1.27.
boiler generated steam enthalpy and turbine extracted steamenthalpy) must be greater than or equal to the net heat demandfrom processing [Equation (37)].Xbn
Mbn ¼Xt
Mint (36)
Xt
Mcet;zh
cet;z � Qdem
z z < CARDðzÞ (37)
5. Case study
5.1. Case description
The utility system of the processing industry illustrated in Fig. 8is mainly composed of four coal-fired boilers (CFB1, CFB2, CFB3, andCFB4) and four multiple extractions turbines (CC50T1, CC50T2,CC25T1, and CC25T2). Turbines CC50T1 and CC50T2 are the sametype as CC50-9.5/4.0/1.27, which has been illustrated in the turbinemodel validation section (Fig. 6 and Fig. 7), while turbines CC25T1and CC25T2 are the same type as CC25-9.5/4.0/1.27 (Fig. 9 illus-trates the turbine configuration and thermodynamic balanceof design condition). The inlet steam pressure (9.5 MPa) and
Fig. 8. Optimal operation scheme (S1) of a utility system in processing industry using the proposed model.
X. Luo et al. / Energy 36 (2011) 3501e35123508
temperature (535 �C) are the same for all four turbines. Eachturbine has two controlled extractions and supply steam at 4.0 and1.27MPa, respectively, for processing. Turbines CC50T1 and CC50T2have five additional uncontrolled extractions for reheaters, whileturbines CC25T1 and CC25T2 have three (one is the high-pressuresteam from the controlled LP extraction). The site data for thestudied utility system are listed in Table 3. The maximum steam
Fig. 9. Simulated thermodynamic balances o
generation load is 400 t/h for boilers CFB1 and CFB2, and 220 t/h forboilers CFB3 and CFB4. The maximum electric power generationloads are 60 MW for turbines CC50T1 and CC50T2, and 30 MW forturbines CC25T1 and CC25T2. The product of mechanical efficiencyand generating efficiency is 0.98 for CC50T1 and CC50T2, and 0.96for CC25T1 and CC25T2. The uncontrolled extraction steamparameters (T/H/M) and the reheater stream parameters (T/H/M)
f design condition of CC25-9.5/4.0/1.27.
Table 3Site data of the studied cogeneration plant.
Site data
Low heat value of coal/kJ∙kg�1 20900Unit price of coal/$∙t�1 120Unit price of makeup water/$∙t�1 0.65Purchased electric power unit cost/$∙MWh�1 105Operation and maintenance of CC50B1, CC50B2/$∙t�1h�1 3.3Operation and maintenance of CC25B1, CC25B2/$∙t�1h�1 4.5Operation and maintenance of CC50T1, CC50T2/$∙MWh�1 10.5Operation and maintenance of CC25T1, CC25T2/$∙MWh�1 13.5Boiler operation model coefficient a of boiler CFB1, CFB2 0.0743Boiler operation model coefficient b of boiler B1, B2 0.0127Boiler operation model coefficient a of boiler CFB3, CFB4 0.0958Boiler operation model coefficient b of boiler CFB3, CFB4 0.0031Demand of MP main steam/MW 227.5Demand of LP main steam/MW 182.3Demand of electric power/MW 100Annual operation time/h 8400
X. Luo et al. / Energy 36 (2011) 3501e3512 3509
under the design conditions are illustrated in Fig. 7 for CC50/4.0/1.27 and Fig. 9 for CC25/4.0/1.27. The thermal efficiency of allreheaters is assumed to be 1. The waste heat parameters areassumed to be constant and equal to the values under the designconditions. The outlet pressures of the condenser pumps are fixedat 1.2 MPa while the outlet pressures of the feedwater pumps arefixed at 12MPa. The maximum controlled HP, MP, and LP extractionsteam flow rates of turbine CC50/4.0/1.27 are 190, 136, and 91 t/h,respectively. The maximum controlled HP, MP, and LP extractionsteam flow rates of turbine CC25-9.5/4.0/1.27 are 100,130, and 60 t/h, respectively. The minimum allowable condensed steam flow ofCC50-9.5/4.0/1.27 and CC25-9.5/4.0/1.27 are 53 and 18 t/h,respectively. The BHM coefficients abn of the four boilers in Fig. 8are 0.0743, 0.0743, 0.0958, and 0.0958, while the coefficients bbnare 0.0127, 0.0127, 0.0031, and 0.0031.
5.2. Turbine decomposition
Based on the proposed algorithm, each turbine in Fig. 8 can bedecomposed into three simple turbines, designated as CC50T1HP,CC50T1MP, CC50T1LP, CC50T2HP, CC50T2MP, CC50T2LP, CC25T1HP,CC25T1MP, CC25T1LP, CC25T2HP, CC25T2MP, and CC25T2LP. Thedesign and maximum steam loads of the decomposed simpleturbines are listed in Table 4. Notably, the steam flow is not uniquethroughout the decomposed simple turbine passport because ofthe uncontrolled steam extractions. However, it is accurate enoughto use inlet flow rate as steam load in THM for every decomposedsimple turbine. Single condensing (no controlled extraction) is notallowable because of the low energy utilization efficiency in thiscase study.
5.3. Results and discussion
The operational planning optimization model for the studiedcogeneration plant is a complex MINLP model [i.e., Equations(1)e(34)]. Two main difficulties exist in relation to model solving:(1) the established MINLP model contains a large number of strongnonlinear equations [i.e., Equations (1), (3), (5), (7)e(9), (11), (15),(22), (34)]. (2) The MINLP model involves a nested feedwater
regenerative heating system simulation model [Equations(10)e(19)] which follows certain rules [e.g., Equations (16)e(17)].
To avoid the infeasibility of the nested feedwater regenerativeheating system simulation, the reheater energy balances of Equa-tion (15) are relaxed as Equation (38). In addition, the domains forsome intermediate variables, such as isentropic efficiency anduncontrolled steam extraction pressure, are set initialized to help inthe optimization model solving. Through these solving strategies,locally optimal results can be easily achieved.�Muce;mix
t;u huce;mixt;u þMdrw
t;uþ1hdrwt;uþ1 �Mdrw
t;u hdrwt;u
�ht;u
� Mw;int;u
�hw;int;uþ1 �Mw;in
t;u
�(38)
The model is developed using GAMS 20.2 and the optimizationis conducted by employing the DICOPT solver. The achieved locallyoptimal solution (S1) is illustrated in Fig. 8. Boilers CFB1, CFB2,CFB3, CC50T1, CC50T2, and CC25T1 are in operation while boilerCFB4 and turbine CC25T2 are shutdown. Keeping all units inoperation is unnecessary due to the relative low steam and elec-trical power demand compared with the utility system loadcapacity for the current case. Boilers CFB1 and CFB2 operate underhigh loads due to their high thermal efficiency and low specificmaintenance cost (maintenance cost for unit steam flow rate).Boiler B3 operates under minimum load and boiler B4 is shutdowndue to their low thermal efficiency and high specific maintenancecost. Turbine CC25T1 operates under low load and CC25T2 isshutdown mainly due to their low isentropic efficiency under thesame load ratio compared with CC50T1 and CC50T2. The relativelyhigher specific maintenance cost is the other reason for keepingCC25T1 and CC25T2 under low load and shutdown conditions,respectively. The total annual operating cost is US$ 162.31M, whichconsists of boiler fuel cost (US$121.15M), maintenance cost(US$36.32 M), and water cost (US$4.85 M).
The operation scheme (S2) based on the conventional operationconcept or engineer’s experience of average load allocation is alsosimulated and the result is illustrated in Fig. 10 for comparison. Asshown in Fig. 10, all boilers and turbines are in operation. The boilerloads, MP extraction loads, LP extraction loads, and condensationloads are 72.6%, 43%, 40.3%, and 75% representing the ratio ofequipment operation load to equipment maximum load, respec-tively. The total annual operating cost is US$171.71 M, whichconsists of boiler fuel cost (US$126.88 M), maintenance cost(US$39.91 M), and water cost (US$4.91 M). Compared with opera-tion scheme S2, scheme S1 yielded US$9.4 M savings in total costs(i.e., 5.47% of conventional operation cost). The savings partlycomes from the increase in total efficiency and partly from thedecrease in maintenance cost. Notably, in S1, the utility systemcould maintain secure operations although one boiler and turbineare in shutdown condition by importing electrical power and/orreducing the steam supply for unimportant users during the systembuffer time (start backup equipment).
As a matter of fact, the plant engineers may care more about theoperation safety than economic cost when the uncertainty ofequipment availability and process demand are not evaluatedthoroughly. Therefore, another operational planning optimizationcase under the assumption of no equipment is allowed to beshutdown for safe operation consideration was also modeled and
Fig. 10. Operation scheme (S2) based on the conventional concept.
X. Luo et al. / Energy 36 (2011) 3501e35123510
solved. The optimal operational planning scheme (S3) is derivedand illustrated in Fig. 11. The total annual operating cost isUS$169.45 M, which consists of boiler fuel cost (US$126.59 M),maintenance cost (US$37.92 M), and water cost (US$4.94 M).Compared with S2, US$2.26 M is saved (i.e., 1.32% of conventionaloperation cost). The reason for the minimal savings is the similarperformance of turbines and boilers. The average load concept isrelatively reasonable for such a utility system. However, the resultswould be different if there are large performance differencesamong the equipment (the utility system is composed of differenttypes of equipment). Nevertheless, the optimization resultsprovided a quantitative and safe operation scheme, especially for
Fig. 11. Optimal scheme (S3) under the assumption
the complicated turbine thermodynamic system in the studiedcase.
The boiler efficiency and turbine isentropic efficiency areillustrated in Fig. 12. Understandably, the boilers with large designcapacity and low maintenance cost are prioritized for operationand can be adjusted based on experience. However, the isentropicefficiency of all decomposed simple turbines does not accord withcertain rules in S1, S2, and S3 and cannot be easily adjusted andthus, only relies on experience. Hence, the simultaneously opti-mization of the whole utility system operation parameters areessential and cannot be substituted by the experience of theengineer.
of no equipment is allowed to be shutdown.
Fig. 12. Turbine isentropic efficiency and boiler thermal efficiency for three schemes.
X. Luo et al. / Energy 36 (2011) 3501e3512 3511
6. Conclusion
Developing nonlinear mathematical models for the optimiza-tion of a utility system containing multiple extraction turbines isalways challenging. In this paper, based on energy balance,thermodynamic state conversion, and semi-empirical relations,the multiple extractions turbine is decomposed into simpleturbines and modeled in series. Thermodynamic properties ofsteam and water are modeled by linearization and piece-wiselinearization. The controlled and uncontrolled extraction param-eters are modeled as well as the detailed feedwater regenerativeheating system. Comparison of the simulated results with thedata in the working condition diagram validates the accuracy ofthe proposed model under some typical variations in the condi-tions. Operation optimization of utility systems containingmultiple extraction turbines is established. An industrial case,with four boilers and four steam turbines with multiple extrac-tions is used to elaborate. Compared with the conventionaloperation strategy, at least 1.32% operation cost is saved withoutconsidering equipment shutdown while 5.47% is saved whenequipment shutdown is allowed. Remarkably, the more turbinescontained in the utility system, the greater the optimizationpotential.
Acknowledgment
This work was supported by the National Natural ScienceFoundation of China (51006025).
ParametersC energy unit price, $$t�1 or $$MW�1;MD Operation and maintenance, $∙t�1h�1 or $∙MWh�1;OTY annual operation time, h.
VariablesCARD the last element of a set;E electric power, MW;F fuel flow rate, t h�1;h steam enthalpy, kJ kg�1;hl saturate water enthalpy, kJ kg�1;hw sub-cooled or saturate water enthalpy, kJ kg�1;M flow rate, t h�1;P pressure, MPa;T temperature, �C;Tsat saturate temperature, �C;h efficiency;D steam pressure drop ratio;Dh steam enthalpy difference, kJ kg�1;DTsat saturation temperatures difference, �C;dT heat transfer transmission end difference, �C;
Binary variableY 1 if equipment is on and 0 if equipment is off.
out outlet;pur purchased;Q heat;rv throttle-governing valve or facility;simu simulation;ss shaft heal heating steam;uce uncontrolled extraction;w water;wh waste heat. ADDIN NE.Bib
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