Modeling and optimization of a utility system containing multiple extractions steam turbines

Energy 36 (2011) 3501e3512

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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 b

School of Material and Energy, Guangdong University of Technology, Guangzhou 510006 China School of Chemistry and Chemical Engineering, Sun-Yat-Sen University, Guangzhou 510275 China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 September 2010 Received in revised form 19 March 2011 Accepted 22 March 2011 Available online 22 April 2011

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 mathematical 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.
2011 Published by Elsevier Ltd.

Keywords: Utility system Multiple extractions Steam turbine Optimization Mathematical modeling

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 interconnected 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

* Corresponding author. Tel./fax: þ86 020 39322581. E-mail address: [email protected] (Y. Chen). 0360-5442/$ e see front matter
2011 Published by Elsevier Ltd. doi:10.1016/j.energy.2011.03.056

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 [1e11]. Bruno et al. [12] developed a rigorous MINLP (mixed integer nonlinear programming) model by fixing the steam pressure levels for the synthesis of utility plants and correlated uniform nonlinear steam turbine efficiency. 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 analysis combined with the Willan’s line, which describes the relationship 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] presented 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

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applied in the work of Salahshoor et al. [18] for fault detection and diagnosis of an industrial steam turbine. Tveit and Fogelholm [19] presented a method for finding regression models for steam turbine networks using a simulation model and an evolutionary algorithm to finding D-optimal designs. Han and Lee [20] developed a hybrid model of condensing turbine with multiple steam injectors and proposed an online optimization system for the condensing 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 and diagnosis of a combined heat and power plant in Sweden. Some of the aforementioned models oversimplified steam turbine performance because steam turbine efficiency generally varied with inlet and outlet steam parameters significantly, aside from design size and operating load. Other research on steam turbine simulations yielded small errors for electric power prediction and cannot be employed directly in real optimization programs because of the complicated calculation of working fluid physical properties and the large number of iterations. A poor approximation will occur if the THM is applied to the turbine with many extractions even though the THM has been verified as accurate enough for simple steam turbines [14e16]. Medina-Flores and Picón-Núñez [16] proposed algorithms to predict power production for single and multiple extraction steam turbines based on THM although the turbine performance for various operating scenarios was only represented using a single weighted average efficiency. In general, very few studies exist on the accurate modeling and optimization of multiple controlled and/or uncontrolled extractions steam turbine in which one or more extraction pressures are maintained at a constant value by changing the flowing areas. In the remainder of this paper, mathematical models are developed for analysis of performance variations of steam turbines based on THM concepts [13], turbine decomposition theory [22],

and turbine principles under varying conditions [23,24]. The simulation results of the turbine model are compared with the performance diagram provided by the manufacturer to validate the accuracy and performance of the developed models under different operation conditions. The utility system optimization model is established and a detailed case study is elaborated particularly with regard the significant operation cost savings. 2. Multiple extractions steam turbine network description In industry utility systems, the number of steam levels and minimum allowed pressure for each steam level are determined by production processes. Some steam turbines may be designed with multiple controlled extractions to provide steam at different levels for production processes and uncontrolled extractions for feedwater regenerative heating to improve the total system efficiency. In China, the use of one or two controlled extraction levels with several uncontrolled extractions is common and the total number of extractions can be as many as eight. A general configuration of a turbine with multiple extractions is illustrated in Fig. 1. This type of turbine, which includes the flow passage, is composed of many pressure stages and control stages, reheaters, deaerators, condensers, pumps, and so on. The main operating variables of the multiple extraction steam turbines include the enthalpy and mass flow rate of each controlled extraction, mass flow rate and pressure of each uncontrolled extraction, and interrelated reheater parameters. Compared with simple turbines, the multiple extractions steam turbines are much more complicated wherein multiple controlled or uncontrolled extractions are employed. The steam pressure consecutively drops across the turbine stages and changes with load variation. The general representation of steam turbine network composed of multiple extractions turbine is shown in Fig. 2(a). In this network, one turbine may have several extractions to satisfy corresponding ranks of steam demands. In addition, the

Fig. 1. General representation of multiple extraction steam turbines.

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Fig. 2. General multiple extraction steam turbine network.

steam demand may be satisfied by one or more of the controlled steam turbine extractions. It is unreasonable to consider turbine simply as turbine with fixed inlet and outlet parameters and modeled in a conventional way. This brings significant challenges for the load allocation of all turbines. In this sense, developing mathematical models capable of simulating the proper steam extraction parameter and energy released from steam expansion for the optimization of complex turbine network as shown in Fig. 2(a), is necessary.

3. Turbine model development The thermodynamic model for multiple extractions presented is based on the concept proposed by Chou and Shih [14] where a multiple extraction turbine is modeled using a set of single turbines in series and the isentropic efficiency model for simple turbines, based on the improvements made by Medina-Flores and Picón-Núñez [16]. Stodola’s formula [24] is also applied in this design to simulate the uncontrolled extraction steam parameters.

3.1. Turbine decomposition The complex turbine in Fig. 1 is not simply the combination of simple turbines because of the uncontrolled extractions. To simulate a turbine for system optimization, the following assumption or simplification should be considered: uncontrolled extraction does not distinctly affect the performance of whole stages because the flow rate of uncontrolled extraction is very little compared with that of passing the uncontrolled stage in most cases. Under this assumption, the complex turbine can be decomposed into Lþ1 simple turbines with fixed inlet and outlet pressures, as illustrated in Fig. 2(b), where L is the number of controlled extractions. And then the thermodynamic system of a complex turbine is represented by a number of lumped models for decomposed simple steam turbines in series.

3.2. Simple turbine hardware model Equations (1)e(2) are common thermodynamic models used to calculate the inlet and outlet parameters for the decomposed turbines in series. However, the isentropic efficiency his t;z in Equation (1) is not easy to predict. Fortunately, the improved THM [16] provides accurate and general prediction formulation that accounts for the design load, operating load, as well as inlet and outlet steam parameters. The improved THM is described by Equations (3)e(4) and Table 1 shows the regression coefficients. in is is hout t;z ¼ ht;z  ht;z Dht;z

(1)

out hin t;zþ1 ¼ ht;z

(2)

hist;z ¼

6 A 1 dn 5Bt;z Dhist;z Mt;z

! 1

dn Mt;z

! (3)

in 6Mt;z

in A ¼ a þ bPt;z in B ¼ g þ lPt;z

(4)

where Dhis t;z is the isentropic enthalpy drop of the decomposed sat simple turbine z, which can be regressed as the function of DTt;z in and Dht;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.

Table 1 Regression coefficients for parameters A and B Regression coefficients for simple turbines

a (MW) b (MW/Pa) g l (MPa1)

0.1854 0.0433 1.2057 0.0075

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Equation (6) gives the regression model with a maximum relative error of 0.15% for some determined inlet and outlet pressure.

Dhist;z ¼

DTsatt;z

  in 1854  1931 hin t;z  hlt;z

(5)

out Dhist;z ¼ 0:1780hin pin R2 ¼ 1 t;z  342:29 t;z ¼ 9:5; pt;z ¼ 4; is in in out Dht;z ¼ 0:2323ht;z  449:74 pt;z ¼ 4; pt;z ¼ 1:27; R2 ¼ 1 is in in out Dht;z ¼ 0:4852ht;z  587:64 pt;z ¼ 1:27; pt;z ¼ 0:0059;

R2 ¼ 0:9995

ð6Þ

3.3. Uncontrolled steam pressure model In addition, the decomposed simple turbine with uncontrolled extractions should be decomposed into several stage groups to predict the extraction pressure using Stodola’s formula [24]. The four main application conditions for forming a stage group are: 1) constant flowing area; 2) constant flow rate throughout the flow passage; 3) infinite stages; and 4) homogenous steam flow. Most of the pressure stage meets the requirement of conditions 1 and 4. For condition 3, it will be accurate if more than 3 stages are selected to form a stage group. For condition 2, the uncontrolled extraction stage can be included in a stage group if the extraction steam is used 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 the design conditions. Equation (8) is used to obtain the uncontrolled extraction enthalpy model in the same way as the controlled extraction enthalpy. uce Pt;u

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u uce2   u Mt;u 2 uce;dn2 out;dn2 out t ¼ Pt;z þ uce;dn2 Pt;u  Pt;z Mt;u

in is is huce t;u ¼ ht;z  ht;u Dht;u

u˛zðuÞ

(7)

(8)

For simplification purposes, it is reasonable to consider that the isentropic efficiency in Equation (8) is equal to his t;z . However, Equation (6) cannot be used to calculate isentropic enthalpy drop between the inlet of the decomposed turbine z and the uncontrolled extraction u because the outlet pressure is unknown. Similar models can be regressed as Equation (9) with a maximum relative error of 4%.

Dhist;u

¼ 1000

Dhist;u

0:137hin t;z þ 682:18

uce;mix uce wh Mt;u ¼ Mt;u þ Mt;u

(10)

uce;mix uce;mix uce uce wh wh Mt;u ht;u ¼ Mt;u ht;u þ Mt;u ht;u

(11)

  ¼ 1  Dt;u puce puce;mix t;u t;u

(12)

w;in w;out ¼ Mt;u Mt;u

(13)

uce;mix drw drw Mt;u ¼ Mt;uþ1 þ Mt;u

(14)

  uce;mix uce;mix drw drw drw ht;u þ Mt;uþ1 hdrw Mt;u t;uþ1  Mt;u ht;u ht;u   w;in w;in hw;in ¼ Mt;u t;uþ1  Mt;u

(15)

  w;in  dTt;u ¼ Tsat puce;mix Tt;uþ1 t;u

(16)

  drw ¼ Tsat puce;mix Tt;u t;u

(17)

hwðTÞ ¼ 4:4317T  19:029 hwðTÞ ¼ 4:2449T  3:1606 hwðTÞ ¼ 4:4966T  23:794

pin t;z

35  T  325 p ¼ 1:2; T < 187 p ¼ 12; T < 324

 9; 3400  hin t;z  3500; error  0:7%     uce Tsat pin t;z  Tsat pt;u ¼ 1000 pin t;z 0:1496hin t;z þ 683:51 ¼ 9:5;

Dhist;u

    uce Tsat pin t;z  Tsat pt;u

representation of a surface reheater. The mass and energy balance of reheater u are illustrated in Equations (10)e(19). Equations (10)e(12) are used to derive the mixture mass and energy balance wh mainly for inlet steam of reheater u where the waste heat Mt;u comes from the shaft sealing steam leakage. To simplify the calculation model, the waste steam enthalpy and flow rate are regarded as constants. Equations (13)e(15) are used to obtain the mass and energy balance for reheater u. Equation (16) proves that the outlet water temperature of reheater u (i.e., inlet water temperature of reheater uþ1) is equal to the saturation temperature of the inlet steam pressure subtracting the heat transmission end difference dTt,u. Equation (17) shows that the drain water temperature of reheater u is equal to the saturation temperature of the inlet steam pressure. The saturation temperature can be represented as a function of pressure through piece-wise linearization in Fig. 4. Equation (18) derives the general regression model of subcool water enthalpy and Equation (19) derives the more accurate piece-wise regression model in case of known pressure (e.g., 1.2 MPa and 12 MPa).

puce t;u

in ¼ 4; puce t;u  3:5; 3100  ht;z  3400; error  1%     uce Tsat pin t;z  Tsat pt;u ¼ 1000 pin t;z 0:1391hin t;z þ 603:49 in ¼ 1:27; puce t;u  1; 2900  ht;z  3100; error  4%

(9)

3.4. Feedwater regenerative heating system simulation model The feedwater regenerative heating system illustrated in Fig. 1 is composed of several surface reheaters. Fig. 3 provides the general

Fig. 3. General representation of a surface reheater.

(18) (19)

X. Luo et al. / Energy 36 (2011) 3501e3512

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Fig. 4. Piece-wise linearization of saturation temperature curve on pressure.

3.5. Water balance The feedwater flow rate is generally equal to the turbine inlet steam flow rate if the blowdown water is not considered [see Equation (20)] and the makeup water flow rate is equal to the controlled extraction steam for the production process [see Equation (21)]. fd

Mt ¼ Mtin

(20)

X

Mtmk ¼

ce Mt;z

(21)

z
pressures, before and after the governing valve, change with the steam flow rate that enters the lower stage. The variation trend is represented in Fig. 5 where pce t;z is the pressure of the controlled extraction z and pin t;zþ1 is the steam pressure entering the lower stage; Dprv t;zþ1 is the pressure lost in the throttle-governing valve or in is the total steam flow rate entering the lower stage; facility; Mt;zþ1 in;dn is the maximum steam flow entering the lower stage and Mt;zþ1 when the control valve is fully open, which keeps the extraction steam 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 while Equation (27) derives the maximum power generation constraint. in;dn min t;z  mt;z Yt

3.6. Electric power generation model The pressure stage is decomposed again into several stage zones by extraction point (both controlled and uncontrolled extractions) from outlet to inlet to calculate the electric power generation. The total stage zone S is equal to Z þ U and Equations (22)e(23) derives the electric power generation model.

Et ¼

X

 out in hin t;s  ht;s Mt;s

min t ¼

X

mce t;z þ

z

(25) X X z

wh muce t;u þ mt;u Yt



Et  Etmax Yt

(22)

s in Mt;s ¼

X

Mt;i

(23)

i˛S;i
3.7. Load constraint To ensure economical and safe operation, the turbine inlet and outlet steam parameters must be controlled within certain bounds. Equation (24) is used to derive the minimum condensing steam flow rate constraint to sufficiently cool the lower pressure stage. conds;min mout t;z  mt

z ¼ CARDðzÞ

(24)

Generally, the inlet steam flow rate of each decomposed simple turbine after controlled extraction outlet is controlled through a throttle-governing valve such as rotating diaphragm. The

(26)

u

Fig. 5. Pressure varying process of controlled extraction.

(27)

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3.8. Turbine model validation A CC50-9.5/4.0/1.27 turbine, commonly used in processing utility or cogeneration plants in China, is used as a case study to validate the accuracy of the proposed turbine simulation model. The studied steam turbine has two controlled extractions (with pressures of 4 MPa and 1.27 MPa) and five uncontrolled extractions. The controlled extraction and condensing steam flow rate (i.e., the process demands are given) are provided while other variables, especially inlet steam flow rate and electric power generation, are simulated. The deviation error between the simulated results and the given value is used to validate model accuracy. The corresponding constraints [Equations (1)e(23), (26)] incorporate the objective function [Equation (28)] and are developed using GAMS 20.2 and the simulation is conducted employing the CONOPT solver.

Min SimuObj ¼ min t;1

(28)

In this case study, the heat transfer end difference dTt,u is 3  C for the low-pressure reheater and 1  C for high-pressure reheater. The pressure loss ratio from the extraction outlet to the reheater is 8%. The product of mechanical efficiency and generating efficiency is 0.98. The turbine is decomposed into three simple turbines in series based on the decomposition theory. The turbine configuration and simulated thermodynamic balance of the design condition are shown in Fig. 6 while the data used in the working condition diagram provided by the manufacturer are shown in Fig. 7. Most of the simulated parameters fit the data provided by manufacture well. Some of the simulated uncontrolled extraction enthalpy deviates slightly from the data in the working conditions diagram due to the simplification of uncontrolled extraction efficiency. However, the inlet steam flow rate and electric power generation are very close to the data in the working conditions diagram. Seven off-design conditions are also simulated using the proposed model

and compared with the balance in the working conditions diagram. The simulation and comparison results are shown in Table 2 and the maximum deviation of 0.87% for electric power generation is achieved. 4. Optimization model of utility network containing multiple controlled extractions steam turbines 4.1. Object function The objective of optimization is to locate the optimal operating conditions that minimize the total operation cost to satisfy the steam and electric power demand of the process. In the proposed study, the objective function can be written as Equation (29). The operating 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 FuCost þ WatCost þ MainDepCost þ EleCost FuCost ¼

X

Fbn C F OTY

(29) (30)

bn

WatCost ¼

X

C mk Mtmk OTY

(31)

t

MOCost ¼

X

Mbn MDbn þ

bn

X

! Etn MDtn OTY

(32)

tn

EleCost ¼ C E Epur OTY

Fig. 6. Simulated thermodynamic balances under the design conditions of CC50-9.5/4.0/1.27.

(33)

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Fig. 7. Manufacturer-provided thermodynamic balances under the design conditions of CC50-9.5/4.0/1.27.

4.2. Boiler operation model In this paper, the boiler model presented by Shang [25] is applied and illustrated as Equation (34).

Fbn qbn

   max ¼ hs  hfw ð1 þ bbn ÞMbn þ abn Mbn Ybn

(34)

boiler generated steam enthalpy and turbine extracted steam enthalpy) must be greater than or equal to the net heat demand from processing [Equation (37)].

X

Mbn ¼

Mtin

(36)

t

bn

X

X

ce ce Mt;z ht;z  Qzdem z < CARDðzÞ

(37)

t

4.3. Electricity demand constraints

5. Case study The total electricity generated by turbines and imported from local electricity grid must be equal to the electricity demand of the process [Equation (35)].

X

Et þ Epur ¼ Edem

(35)

t

4.4. Steam demand constraints The total steam generated from the boiler should be greater than or equal to the total steam flow entering the turbines [Equation (36)]. For each steam level, the total enthalpy supply (i.e., total

5.1. Case description The utility system of the processing industry illustrated in Fig. 8 is mainly composed of four coal-fired boilers (CFB1, CFB2, CFB3, and CFB4) and four multiple extractions turbines (CC50T1, CC50T2, CC25T1, and CC25T2). Turbines CC50T1 and CC50T2 are the same type as CC50-9.5/4.0/1.27, which has been illustrated in the turbine model validation section (Fig. 6 and Fig. 7), while turbines CC25T1 and CC25T2 are the same type as CC25-9.5/4.0/1.27 (Fig. 9 illustrates the turbine configuration and thermodynamic balance of design condition). The inlet steam pressure (9.5 MPa) and

Table 2 Simulation and comparison result of typical conditions for CC50-9.5/4.0/1.27. Condition

ce t/h Mt;1

ce t/h Mt;2

out t/h Mt;3

Mtin;gn t/h

Mtin;simu t/h

Etgn MW

Etsimu MW

Relative difference (%)

1 2 3 4 5 6 7

110 123 190 120 120 40 80

52 83 70 136 100 68 80

90.28 53.9 76.6 71 72 78 63

342 350 460 455 400 250 300

342.08 350.37 460.72 454.00 400.27 249.94 300.20

50.26 41 57.2 60.2 53 40 40

50.70 41.18 57.5 60.01 53.04 39.86 39.92

0.87 0.43 0.58 0.24 0.07 0.34 0.19

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Fig. 8. Optimal operation scheme (S1) of a utility system in processing industry using the proposed model.

temperature (535  C) are the same for all four turbines. Each turbine has two controlled extractions and supply steam at 4.0 and 1.27 MPa, respectively, for processing. Turbines CC50T1 and CC50T2 have five additional uncontrolled extractions for reheaters, while turbines CC25T1 and CC25T2 have three (one is the high-pressure steam from the controlled LP extraction). The site data for the studied utility system are listed in Table 3. The maximum steam

generation load is 400 t/h for boilers CFB1 and CFB2, and 220 t/h for boilers CFB3 and CFB4. The maximum electric power generation loads are 60 MW for turbines CC50T1 and CC50T2, and 30 MW for turbines CC25T1 and CC25T2. The product of mechanical efficiency and generating efficiency is 0.98 for CC50T1 and CC50T2, and 0.96 for CC25T1 and CC25T2. The uncontrolled extraction steam parameters (T/H/M) and the reheater stream parameters (T/H/M)

Fig. 9. Simulated thermodynamic balances of design condition of CC25-9.5/4.0/1.27.

X. Luo et al. / Energy 36 (2011) 3501e3512 Table 3 Site data of the studied cogeneration plant. Site data Low heat value of coal/kJ∙kg1 Unit price of coal/$∙t1 Unit price of makeup water/$∙t1 Purchased electric power unit cost/$∙MWh1 Operation and maintenance of CC50B1, CC50B2/$∙t1h1 Operation and maintenance of CC25B1, CC25B2/$∙t1h1 Operation and maintenance of CC50T1, CC50T2/$∙MWh1 Operation and maintenance of CC25T1, CC25T2/$∙MWh1 Boiler operation model coefficient a of boiler CFB1, CFB2 Boiler operation model coefficient b of boiler B1, B2 Boiler operation model coefficient a of boiler CFB3, CFB4 Boiler operation model coefficient b of boiler CFB3, CFB4 Demand of MP main steam/MW Demand of LP main steam/MW Demand of electric power/MW Annual operation time/h

20900 120 0.65 105 3.3 4.5 10.5 13.5 0.0743 0.0127 0.0958 0.0031 227.5 182.3 100 8400

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 all reheaters is assumed to be 1. The waste heat parameters are assumed to be constant and equal to the values under the design conditions. The outlet pressures of the condenser pumps are fixed at 1.2 MPa while the outlet pressures of the feedwater pumps are fixed at 12 MPa. The maximum controlled HP, MP, and LP extraction steam flow rates of turbine CC50/4.0/1.27 are 190, 136, and 91 t/h, respectively. The maximum controlled HP, MP, and LP extraction steam 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 of CC50-9.5/4.0/1.27 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. 8 are 0.0743, 0.0743, 0.0958, and 0.0958, while the coefficients bbn are 0.0127, 0.0127, 0.0031, and 0.0031. 5.2. Turbine decomposition Based on the proposed algorithm, each turbine in Fig. 8 can be decomposed into three simple turbines, designated as CC50T1HP, CC50T1MP, CC50T1LP, CC50T2HP, CC50T2MP, CC50T2LP, CC25T1HP, CC25T1MP, CC25T1LP, CC25T2HP, CC25T2MP, and CC25T2LP. The design and maximum steam loads of the decomposed simple turbines are listed in Table 4. Notably, the steam flow is not unique throughout the decomposed simple turbine passport because of the uncontrolled steam extractions. However, it is accurate enough to use inlet flow rate as steam load in THM for every decomposed simple turbine. Single condensing (no controlled extraction) is not allowable because of the low energy utilization efficiency in this case study. 5.3. Results and discussion The operational planning optimization model for the studied cogeneration 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 strong nonlinear equations [i.e., Equations (1), (3), (5), (7)e(9), (11), (15), (22), (34)]. (2) The MINLP model involves a nested feedwater

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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 regenerative heating system simulation, the reheater energy balances of Equation (15) are relaxed as Equation (38). In addition, the domains for some intermediate variables, such as isentropic efficiency and uncontrolled steam extraction pressure, are set initialized to help in the optimization model solving. Through these solving strategies, locally optimal results can be easily achieved.



 uce;mix uce;mix drw drw drw Mt;u ht;u þ Mt;uþ1 hdrw t;uþ1  Mt;u ht;u ht;u   w;in w;in hw;in  Mt;u  M t;u t;uþ1

(38)

The model is developed using GAMS 20.2 and the optimization is conducted by employing the DICOPT solver. The achieved locally optimal solution (S1) is illustrated in Fig. 8. Boilers CFB1, CFB2, CFB3, CC50T1, CC50T2, and CC25T1 are in operation while boiler CFB4 and turbine CC25T2 are shutdown. Keeping all units in operation is unnecessary due to the relative low steam and electrical power demand compared with the utility system load capacity for the current case. Boilers CFB1 and CFB2 operate under high loads due to their high thermal efficiency and low specific maintenance cost (maintenance cost for unit steam flow rate). Boiler B3 operates under minimum load and boiler B4 is shutdown due to their low thermal efficiency and high specific maintenance cost. Turbine CC25T1 operates under low load and CC25T2 is shutdown mainly due to their low isentropic efficiency under the same load ratio compared with CC50T1 and CC50T2. The relatively higher specific maintenance cost is the other reason for keeping CC25T1 and CC25T2 under low load and shutdown conditions, respectively. The total annual operating cost is US$ 162.31 M, which consists 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 operation concept or engineer’s experience of average load allocation is also simulated and the result is illustrated in Fig. 10 for comparison. As shown in Fig. 10, all boilers and turbines are in operation. The boiler loads, MP extraction loads, LP extraction loads, and condensation loads are 72.6%, 43%, 40.3%, and 75% representing the ratio of equipment operation load to equipment maximum load, respectively. The total annual operating cost is US$171.71 M, which consists of boiler fuel cost (US$126.88 M), maintenance cost (US$39.91 M), and water cost (US$4.91 M). Compared with operation scheme S2, scheme S1 yielded US$9.4 M savings in total costs (i.e., 5.47% of conventional operation cost). The savings partly comes from the increase in total efficiency and partly from the decrease in maintenance cost. Notably, in S1, the utility system could maintain secure operations although one boiler and turbine are in shutdown condition by importing electrical power and/or reducing the steam supply for unimportant users during the system buffer time (start backup equipment). As a matter of fact, the plant engineers may care more about the operation safety than economic cost when the uncertainty of equipment availability and process demand are not evaluated thoroughly. Therefore, another operational planning optimization case under the assumption of no equipment is allowed to be shutdown for safe operation consideration was also modeled and

Table 4 Maximum inlet steam flow rate of decomposed simple turbines/t h1 Flow rate

CC50T1HPCC50T2HP

CC50T1MPCC50T2MP

CC50T1LPCC50T2LP

CC25T1HPCC25T2HP

CC25T1MPCC25T2MP

CC25T1LPCC25T2LP

Design flow rate Maximum flow rate

342 465

328 328

104 104

260 260

180 180

60 60

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Fig. 10. Operation scheme (S2) based on the conventional concept.

solved. The optimal operational planning scheme (S3) is derived and illustrated in Fig. 11. The total annual operating cost is US$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 conventional operation cost). The reason for the minimal savings is the similar performance of turbines and boilers. The average load concept is relatively reasonable for such a utility system. However, the results would be different if there are large performance differences among the equipment (the utility system is composed of different types of equipment). Nevertheless, the optimization results provided a quantitative and safe operation scheme, especially for

the complicated turbine thermodynamic system in the studied case. The boiler efficiency and turbine isentropic efficiency are illustrated in Fig. 12. Understandably, the boilers with large design capacity and low maintenance cost are prioritized for operation and can be adjusted based on experience. However, the isentropic efficiency of all decomposed simple turbines does not accord with certain rules in S1, S2, and S3 and cannot be easily adjusted and thus, only relies on experience. Hence, the simultaneously optimization of the whole utility system operation parameters are essential and cannot be substituted by the experience of the engineer.

Fig. 11. Optimal scheme (S3) under the assumption of no equipment is allowed to be shutdown.

X. Luo et al. / Energy 36 (2011) 3501e3512

Fig. 12. Turbine isentropic efficiency and boiler thermal efficiency for three schemes.

6. Conclusion Developing nonlinear mathematical models for the optimization of a utility system containing multiple extraction turbines is always challenging. In this paper, based on energy balance, thermodynamic state conversion, and semi-empirical relations, the multiple extractions turbine is decomposed into simple turbines and modeled in series. Thermodynamic properties of steam and water are modeled by linearization and piece-wise linearization. The controlled and uncontrolled extraction parameters are modeled as well as the detailed feedwater regenerative heating system. Comparison of the simulated results with the data in the working condition diagram validates the accuracy of the proposed model under some typical variations in the conditions. Operation optimization of utility systems containing multiple extraction turbines is established. An industrial case, with four boilers and four steam turbines with multiple extractions is used to elaborate. Compared with the conventional operation strategy, at least 1.32% operation cost is saved without considering equipment shutdown while 5.47% is saved when equipment shutdown is allowed. Remarkably, the more turbines contained in the utility system, the greater the optimization potential.

Parameters C energy unit price, $$t1 or $$MW1; MD Operation and maintenance, $∙t1h1 or $∙MWh1; OTY annual operation time, h. Variables CARD E F h hl hw M P T Tsat

h D Dh DTsat dT

the last element of a set; electric power, MW; fuel flow rate, t h1; steam enthalpy, kJ kg1; saturate water enthalpy, kJ kg1; sub-cooled or saturate water enthalpy, kJ kg1; flow rate, t h1; pressure, MPa; temperature,  C; saturate temperature,  C; efficiency; steam pressure drop ratio; steam enthalpy difference, kJ kg1; saturation temperatures difference,  C; heat transfer transmission end difference,  C;

Binary variable Y 1 if equipment is on and 0 if equipment is off.

Acknowledgment This work was supported by the National Natural Science Foundation of China (51006025).

Nomenclature

Sets BN S T Z Z(u)

{bn j boilers}; {sj stages}; {t j steam turbines}; {z jdecomposed simple turbines}; {uj uncontrolled extraction belong to decomposed simple turbine z}.

Superscripts ce controlled extraction; conds condense; cw cooling water; dem demand; dn design condition; drw drain water; f fuel; fd feedwater; gn given; is isentropic; in inlet; max maximum; mix steam mixture; min minimum; mk makeup water;

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3512

out pur Q rv simu ss uce w wh

X. Luo et al. / Energy 36 (2011) 3501e3512

outlet; purchased; heat; throttle-governing valve or facility; simulation; shaft heal heating steam; uncontrolled extraction; water; waste heat. ADDIN NE.Bib

References [1] Hui CW, Natori Y. An industrial application using mixed-integer programming technique: a multi-period utility system model. Computers & Chemical Engineering 1996;20(Supplement 2):S1577e82. [2] Iyer RR, Grossmann IE. Optimal multiperiod operational planning for utility systems. Computers and Chemical Engineering 1997;21(8):787e800. [3] Iyer RR, Grossmann IE. Synthesis and operational planning of utility systems for multiperiod operation. Computers & Chemical Engineering 1998;22(7e8): 979e93. [4] Yi HS, Han C, Yeo YK. Optimal multiperiod planning of utility systems considering discrete/continuous variance in internal energy demand based on decomposition method. Journal Of Chemical Engineering Of Japan 2000;33(3):456e67. [5] Yi HS, Kim JH, Han CH, Jung JH, Lee MY, Lee JT. Periodical replanning with hierarchical repairing for the optimal operation of a utility plant. Control Engineering Practice 2003;11(8):881e94. [6] Montero G, Pulido R, Pineda C, Rivero R. Ecotaxes and their impact in the cost of steam and electric energy generated by a steam turbine system. Energy 2006;31(15):3391e400. [7] Pak PS, Lee YD, Ahn KY. Characteristics and economic evaluation of a power plant applying oxy-fuel combustion to increase power output and decrease CO2 emission. Energy 2010;35(8):3230e8. [8] Corrado A, Fiorini P, Sciubba E. Environmental assessment and extended exergy analysis of a “zero CO2 emission”, high-efficiency steam power plant. Energy 2006;31(15):3186e98. [9] Kwak HY, Kim DJ, Jeon JS. Exergetic and thermoeconomic analyses of power plants. Energy 2003;28(4):343e60. [10] Dias MOS, Modesto M, Ensinas AV, Nebra S, Maciel Filho R, Rossell CEV. Improving bioethanol production from sugarcane: evaluation of distillation, thermal integration and cogeneration systems. Energy; 2010. doi:10.1016/ j.energy.2010.09.024.

[11] Sanjay. Investigation of effect of variation of cycle parameters on thermodynamic performance of gas-steam combined cycle. Energy 2011;36(1): 157e67. [12] Bruno JC, Fernandez F, Castells F, Grossmann IE. A rigorous MINLP model for the optimal synthesis and operation of utility plants. Chemical Engineering Research & Design 1998;76(A3):246e58. [13] Mavromatis SP, Kokossis AC. Conceptual optimisation of utility networks for operational variations - I. Targets and level optimisation. Chemical Engineering Science 1998;53(8):1585e608. [14] Varbanov PS, Doyle S, Smith R. Modelling and optimization of utility systems. Chemical Engineering Research and Design 2004;82(5):561e78. [15] Aguilar O, Perry SJ, Kim JK, Smith R. Design and optimization of flexible utility systems subject to variable conditions - Part 1: modelling framework. Chemical Engineering Research & Design 2007;85(A8):1136e48. [16] Medina-Flores JM, Picón-Núñez M. Modelling the power production of single and multiple extraction steam turbines. Chemical Engineering Science 2010; 65(9):2811e20. [17] Chaibakhsh A, Ghaffari A. Steam turbine model. Simulation Modelling Practice and Theory 2008;16(9):1145e62. [18] Salahshoor K, Kordestani M, Khoshro MS. Fault detection and diagnosis of an industrial steam turbine using fusion of SVM (support vector machine) and ANFIS (adaptive neuro-fuzzy inference system) classifiers. Energy 2010; 35(12):5472e82. [19] Tveit TM, Fogelholm CJ. Multi-period steam turbine network optimisation. Part 1: simulation based regression models and an evolutionary algorithm for finding D-optimal designs. Applied Thermal Engineering 2006;26(10): 993e1000. [20] Han IS, Lee YH, Han CH. Modeling and optimization of the condensing steam turbine network of a chemical plant. Industrial & Engineering Chemistry Research 2006;45(2):670e80. [21] Fast M, Palme T. Application of artificial neural networks to the condition monitoring and diagnosis of a combined heat and power plant. Energy 2010; 35(2):1114e20. [22] Chou CC, Shih YS. A thermodynamic approach to the design and synthesis of plant utility systems. Industrial & Engineering Chemistry Research 1987; 26(6):1100e8. [23] Fonseca J, Schneider PS. Simulation of a thermal power plant with district heating: comparative results of 5 different codes. Energy 2006;31(12): 1955e68. [24] Dixon SL. Fluid-mechanics, thermodynamics of turbomachinery. 4th ed. Oxford: Pergamon Press LTD; 1998. [25] Shang ZG, Kokossis A. A transhipment model for the optimisation of steam levels of total site utility system for multiperiod operation. Computers & Chemical Engineering 2004;28(9):1673e88.