control structure selection for the elevated-pressure air...

Control Structure Selection for the Elevated-Pressure Air SeparationUnit in an IGCC Power Plant: Self-Optimizing Control Structure forEconomical OperationKosan Roh and Jay H. Lee*

Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701,Republic of Korea

*S Supporting Information

ABSTRACT: The air separation unit (ASU) is one of the core elements of integrated gasification combined cycle (IGCC)power plants. The ASU separates air into pure oxygen and nitrogen, to be sent to the gasifier and the gas turbine, respectively.This system consumes about 10% of the gross power output generated in IGCC, so its economical operation is important forlowering the overall power generation cost. The use of an elevated-pressure air separation unit (EP ASU), in which the operatingpressure is higher than in a conventional ASU, is known to lead to significant energy savings. In this research, controlled variableselection for an EP ASU was studied, considering both the controllability and economics, that is, with the objective ofmaintaining economically near-optimal operations in the presence of anticipated load changes. The main tool used for this wasthe so-called “minimum singular value rule” within the overall framework of self-optimizing control (SOC). For the purpose ofselecting and testing self-optimizing control structures, equation-based modeling of EP ASU was carried out and implemented onthe commercial software platform gPROMS. Then, the minimum singular value rule was applied using steady-state gain matrices(obtained from the simulator) to select a small number of candidate sets for controlled variables, to which rigorous analysesbased on nonlinear simulation and optimization could be applied to pick the top choice. Before the minimum singular value rulewas applied, however, certain process insights and heuristics were used to reduce the number of candidate sets down to amanageable level. The economic losses as a result of adopting a fixed control structure were assessed by comparing the hourlyoperating costs achieved under SOC with the equivalent values obtained by performing full nonlinear optimizations for the givenscenarios. In addition, for the suggested control structure, proportional plus integral (PI) control loops were designed, and theirdynamic performance was tested in order to make sure that it is attractive in terms of not only economics but also controllability.The finally selected control structure is compared with those presented in previous works.

1. INTRODUCTIONThe integrated gasification combined cycle (IGCC) is one ofthe promising alternatives for utilizing fossil fuel for electricitygeneration in a more eco-friendly way. IGCC power plants areknown to give higher energy efficiency than the conventionalpulverized-coal-fired (PC) power plants (estimated to be about40% vs 37%, respectively). In addition, the gasification stepproduces a high-pressure, high-concentration CO2 stream thatmay be more amenable to CO2 capture (as in “precombustion”capture). An IGCC system is composed of a gasification unit,an air separation unit (ASU), a syngas purification unit, and acombined cycle involving a gas turbine and a steam turbine, asdescribed in Figure 1.Despite its promise, commercial adoption of IGCC has been

slow, and keys to its more widespread use are thought to lie inlowering the cost and ensuring better stability of the operation.Currently, the cost of electricity produced by IGCC is notcompetitive compared with conventional PC power plants.More capital and operating costs are required for IGCC,although the fuel cost is less than in a PC power plant. TheNational Energy Technology Laboratory (NETL) of the U.S.Department of Energy reports that more than 80% of the totalelectricity use within IGCC is consumed by the ASU system(Table 1). This amount represents more than 10% of the grosspower output in a typically sized IGCC plant (Figure 2). For

this reason, the ASU is the part that has received muchattention for optimization and control studies.The ASU produces highly pure oxygen (usually at 95%

purity) to be fed to the gasification unit. Under cryogenicconditions, ambient air is separated into pure oxygen and

Special Issue: John Congalidis Memorial

Received: September 4, 2013Revised: February 25, 2014Accepted: April 4, 2014Published: April 4, 2014

Figure 1. Overall schematic diagram of an IGCC power plant system.

Article

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© 2014 American Chemical Society 7479 dx.doi.org/10.1021/ie402909j | Ind. Eng. Chem. Res. 2014, 53, 7479−7488

pubs.acs.org/IECR

nitrogen products through heat-integrated distillations. TheASU includes several gas compressors that compress ambientair, oxygen, and nitrogen to high pressures of 20−60 bar. Thiscompressing energy is mainly responsible for the high operatingcost of the ASU. The elevated-pressure ASU (EP ASU) hasbeen proposed as an alternative to the conventional ASUsystem. The operating pressure of an EP ASU [10−15 bar for ahigh-pressure column (HPC), 3−5 bar for a low-pressurecolumn (LPC)] is higher than that of the conventional system(5−6 bar for an HPC, 1.5−2 bar for an LPC). The higher aircompressor power and the difficulty of the separation due tothe raised operating pressure are more than offset by thesavings in the compressing energy at the O2 compressor,especially when the ASU is integrated with the gas turbine toreceive a high-pressure air feed. However, the EP ASU presentssome additional control challenges due to the high degree ofintegration and consequently the stronger interaction andhigher complexity.2

In this work, we studied the problem of plant-wide controlstructure selection for an EP ASU of the IGCC, focusing on theoperating cost. For a unit of such high economic importance, itis sensible to consider the economics explicitly (in addition tothe controllability) in selecting the control structure. Most ofthe prior research works on ASU control focused on modelingof the cryogenic rectification columns and control of theindividual columns or plant-wide control of the entire ASUsystem. These works applied proportional plus integral (PI)controllers and model predictive controllers to the ASUsystems, with attention given strictly to the regulation undervarious load and feed condition changes.3−10 However, they didnot consider the economics explicitly in selecting the controlstructure and designing the controllers. A standard way toincorporate economics into control is to add a real-time steady-state optimizer layer (typically a linear program) that recalculatesthe set points of the dynamic controllers according to changingoperational conditions on a periodic basis. However, the

effective use of real-time optimization (RTO) in an industrialsetting is known to be difficult because of complications such aspotential inconsistencies between the optimizer layer and theregulatory layer and the increased complexity of theoperators.11 In this work, we investigated a simpler and moremanageable option, self-optimizing control (SOC), in whichcontrolled variables (CVs) are selected in such a way that theirregulation at fixed set points ensures near-optimal operation inspite of disturbances and load changes.12 SOC has been appliedto various chemical processes,13−16 but it has not beenconsidered for the ASU system to date.For the purpose of this study, an equation-based dynamic

model of an EP ASU system was built on the commercialsimulation platform gPROMS. SOC was to be applied to thismodel to screen through all of the potential sets of CVs andobtain a small number of candidates that would be desirable forthe purpose of maintaining near-optimal operations in thepresence of certain oxygen load decrease scenarios. Theminimum singular value rule, one of the simplest tools toapply for SOC, was used for this purpose.17 Before theminimum singular value rule could be applied, however, thenumber of candidate sets had to be reduced to a manageablelevel (thousands), and for this, process insights and heuristicswere used to preselect or eliminate certain variables. Forexample, operational feasibility considerations were used toscreen out some of the candidate CV sets. It should be notedthat the SOC rule considers the economic loss only and doesnot consider such issues as controllability or operationalfeasibility. After the application of the minimum singular valuerule reduced the candidates down to a small number, the finalselection was made by calculating the economic loss figuresthrough rigorous simulations. We also examined the degree ofpotential economic loss caused by adopting the simpler controlstructure identified by the SOC method over the full-scale real-time economic optimization coupled with model-based con-trollers. In addition, controllability of the selected controlstructure was verified by designing PI controllers and runningclosed-loop simulations under oxygen load decrease scenarios.Finally, our suggested control structure was compared withthose proposed by the previous research works in this area.The main intention of article is to show the potential benefits

and complications in applying SOC to a complex process suchas an EP ASU and to demonstrate that the best choice ofcontrol structure may change when the economics areconsidered in addition to the controllability. Hence, attentionis to be given to the overall methodology and thought processrather than the appropriateness of specific assumptions or thefinal control structure that results.

2. PROCESS DESCRIPTION AND PROBLEMDEFINITION2.1. Process Description. Basically, the ASU is the process

for producing oxygen, nitrogen, and optionally argon. Thissystem is used in IGCC power plants to supply pure oxygen tothe gasifier. Ambient air is compressed to a high pressure andseparated by a two-stage distillation process operated at a verylow temperature using the difference in the boiling points. Forthis research, the details of the overall process and the designspecification of the EP ASU are the same as in previousworks.1,10,18

The core part of the ASU is a cryogenic rectification column,which consists of two thermally integrated columns and isoperated at near 100 K. Even though the cryogenic rectification

Table 1. Internal Electricity Use in an IGCC Power Plant1

IGCC unit electricity use percentage (%)

air separation unit 81.17pump 7.57gasifier 4.28transformer loss 2.31combined cycle 1.00cleaning 0.96miscellaneous 2.71total 100.00

Figure 2. Typical use of gross power output by an IGCC power plant.1

Industrial & Engineering Chemistry Research Article

dx.doi.org/10.1021/ie402909j | Ind. Eng. Chem. Res. 2014, 53, 7479−74887480

column was invented back in 1910 by the Linde Company, it isstill considered to be the most efficient technology for pro-ducing large amounts of oxygen. In a typical IGCC powerplant, more than 1000 tons of pure oxygen per day is necessaryfor gasifying coal. For this reason, the cryogenic rectificationcolumn is a suitable choice.19 The flow sheet of the ASU systemis given in Figure 3.Air is a good source of oxygen because it is free and easy

to supply. In most situations, the air feed stream (Air-1) istaken from the atmosphere. It is compressed to a high pressure(∼15 bar) using the main air compressor (MAC, COM-1),which accounts for a majority of the electrical energy con-sumption in an ASU system. In an EP ASU, we have an optionto bring highly compressed air (Air-2) from the gas turbine(GT). This option is called the “air extraction” option, and byusing it we can reduce the air compression energy. In this study,20% of the air feed was assumed to be extracted from the GT.1

Air-2 has very high temperature (700 K). It can be cooledthrough a heat exchange with gas stream S33 (the nitrogenproduct stream). Streams S1 and S2 are mixed together andcooled to the atmospheric temperature (308 K) at cooler C-1.In this study, we assumed that the air feedstock is clean, dry,and CO2-free.S4 is divided into two substreams (S5 and S8) at the air

splitter (S-1). Liquid air must be put into the HPC to meet the

energy balance. For that, one substream is compressed to ahigher pressure (29 bar) at the boost air compressor (BAC,COM-2) and condensed at the adiabatic expansion valve (VX-1).S7 and S8 flow into the primary heat exchanger (PHX, HX-1).

Three cold product streams (S17, S21, and S23) also gointo HX-1 and are heated to the ambient temperature. As aresult, S7 and S8 are cooled to around 130 K. At the middle ofHX-1, a small side stream (S12) is split off and sent to theexpander turbine (T-1), which provides the supplementaryelectricity. S20 is depressurized and sent to the middle ofthe upper column (the LPC). By passing through VX-1, S10(liquid phase) and S11 (vapor phase) flow into the lowercolumn (the HPC).The two columns are operated at different pressures. The

HPC (10 bar) is placed below the LPC (3 bar). Both columnsin an EP ASU have higher operating pressures than those inconventional ASU systems. In this study, tray-type columnswere chosen. The two columns are integrated physically by theintegrated condenser/reboiler (F-1). The pressure differenceresults in a temperature difference between the top of the HPCand the bottom of the LPC. Therefore, there is heat transferfrom the HPC to the LPC. The integrated condenser/reboilerperforms as a condenser for the HPC and a reboiler for theLPC, respectively. As a result, no extra utility for reflux coolingand boil-up is required for the distillation.In the HPC, the cold air streams are separated into highly

pure liquid nitrogen at the top (S15) and a liquid oxygenmixture at the bottom (S13). S15 is split into two streams, S16and S17, at the nitrogen splitter (S-2), and S17 is sent to HX-1.S13 and S16 are cooled at the subheat exchanger (SHEX, HX-2)with the vapor nitrogen stream (S22). S18 and S19 come out ofHX-2 and flow into the LPC. Additionally, S20 comes from T-1and is put into the LPC. In the LPC, vapor oxygen (95% purity)is obtained at the bottom (S21) and vapor nitrogen (96.5% purity)is obtained at the top (S22). Three product streams [the high-pressure nitrogen (S17), the low-pressure oxygen (S21), andthe low-pressure nitrogen (S22)] are sent to HX-1 and heatedto the ambient temperature.

Figure 3. Overall process flowsheet of the EP ASU in an IGCC power plant with the unit naming rule given in Table 2.

Table 2. Unit Naming Rule for the EP ASU

symbol unit

C coolerCOM gas compressorHX heat exchangerF condenser/reboilerT turbineVX adiabatic expansion valveV flow control valveHPC high-pressure columnLPC low-pressure column



S24 is compressed above 65 bar and sent to the gasificationunit. S27 is precompressed at COM-3 and then mixed withS28. After being mixed, S30 is compressed to 26 bar at COM-4and cooled in the primary and secondary nitrogen coolers (C-3and C-4). It is then sent to the syngas combustor of the GT.The nitrogen product is used to decrease the peak flamingtemperature during the gas combustion process. If the amountof nitrogen product is not sufficient, superheated steam isinjected into the gas combustor as a makeup material.1 Theoxygen and nitrogen product compressors are also parts thatconsume much energy in the EP ASU system.To model the cryogenic rectification column, a modified

equation-based model given by Roffel et al.3 was applied in ourstudy. It is an equilibrium-based tray tower model. The Peng−Robinson equation of state (EOS) was selected as the physicalproperty model for the simulation of the EP ASU systembecause it is known to be accurate for gas streams beingprocessed under cryogenic conditions.20 The overall simulationwas performed on the commercial simulation packagegPROMS.2.2. Problem Definition. The aim of this study was to

obtain the control structure that enables the EP ASU to operatenear an economic optimum in the presence of a given set ofoperational scenarios. The targeted control strategy is classicaldecentralized control using single-loop PI controllers, which isstill a common industrial practice, especially in power plants. Inthe following description, first all of the potential manipulatedvariables (MVs) and controlled variables in the EP ASU processare listed. Next, the cost function, constraints, and operationalscenarios are defined. Then, to obtain reference values, theminimum achievable operating costs for the various scenariosare obtained by solving the nonlinear optimization problemsdirectly. In order to reduce the huge number of possible CVsets down to a level manageable for SOC, certain variables arepreselected or eliminated using various physical considerationsand heuristics.2.2.1. Degree of Freedom Analysis. We initially identified

22 available MVs in the EP ASU process for the SOC analysis.In addition, we identified 42 candidate CVs. The MV and CVcandidate lists are available in Tables S1 and S2, respectively, inthe Supporting Information.It should be noted that mass fractions of minor components

such as argon were excluded from the list. It was assumed thatcontrolling the purities of nitrogen and oxygen that make upmost of the product stream is reasonable. Also, even betweennitrogen and oxygen, regulating the component present in alarger fraction is sensible. That is the reason why nitrogen massfractions for S13, S15, S22 and oxygen mass fraction for S21were chosen as candidate CVs.Among the 22 available MVs, three (MV7, MV5, and MV6)

were assumed to be assigned to control the liquid level controlin the LPC (CV41), condenser/reboiler (CV42), and HPC(CV40), respectively. The MVs that determine outlet liquidflow rates are located near columns and the condenser/reboiler,so they are appropriate choices to control the liquid levels.The feed rate of air from the gas turbine (MV2), which is

one of the external feed streams, is considered to be fixedbecause it is associated with the GT compressor part;manipulating it would bring in some additional complex issuesthat are beyond the scope of this study. The flow control valveposition of V-2 (MV4), which determines the flow rates of S11and S12, was also excluded from the list of MVs because therange available for manipulation of the split ratio at HX-1

(which has a nominal value of 0.956) was judged to be toonarrow for effective control. Instead, we assumed that it isadjusted to maintain the flow rate of the air feed stream S12(CV3) at a constant value. The LPC bottom rate (MV9)should control the oxygen production rate to satisfy the oxygenload from the gasification unit, so it was also excluded from thisanalysis.The remaining 16 (=22 − 6) MVs were considered in the

next analysis step along with the 38 (=42 − 4) candidate CVs.2.2.2. Definition of the Cost Function and Constraints. For

a meaningful problem definition of CV selection for economicoperations, the cost function J that is to be minimized must bechosen. In this study, J is the hourly operating cost spent by thewhole EP ASU system, as defined formally by eq 1:

∑ ∑= + + Δ

−

J p W p Q p F

p W

ii

jj Nelec load, CW duty, steam

elec turbine

2

(1)

where pelec is the price of electricity ($/kWh), Wload,i is thepower load of compressor i (kW), pCW is the cooling duty cost($/kWh), Qduty,j is the cooling duty of cooler j (kW), psteam isthe steam cost for nitrogen makeup at 460 psia ($/ton), ΔFN2

isthe difference betwee the actual and nominal nitrogen productrates (kg/s), and Wturbine is the power load of the turbine (kW).The values of the cost parameters (pelec, pCW, and psteam) arelisted in Table S3 in the Supporting Information. The followingconstraints were enforced:1

(1) oxygen product specification:(A) purity: zO2

≥ 0.95 mol/mol

(B) temperature: TO2≤ 390 K

(C) pressure: PO2≥ 65 bar

(2) nitrogen product specification:(A) temperature: TN2

≤ 450 K

(B) pressure: PN2≥ 26 bar

(3) flow direction constraints:(A) PT‑1 ≥ PLPC(B) PHX‑1,hot ≥ PHPC

(4) main air compressor outlet pressure constraint: PCOM‑1 ≥16.2 bar

(5) air cooler outlet temperature constraint: TC‑1 ≤ 308 K(6) low-pressure nitrogen compressor outlet pressure con-

straint: PCOM‑3 ≥ PHX‑1,cold(7) primary nitrogen cooler outlet temperature constraint:

TC‑3 ≤ 365.8 K(8) adiabatic expansion valve outlet pressure constraint (to

prevent the reverse flow direction): PVX‑1 − PHPC ≥4 bar

(9) non-negativity constraints (for flow rates, pressures, tem-peratures, mass fractions, etc.)

The hourly operating cost was calculated as the sum of thetotal compressing cost, the total cooling cost, the nitrogenmakeup cost, and the supplementary power generation cost.The electricity price pelec was set as the generation cost for theIGCC power plant because the electricity used in the EP ASUtypically comes directly from the IGCC plant. Also, pelec wasassumed to have a fixed value for simplicity. The coolant usedwas assumed to be water. The nitrogen makeup cost wascalculated to take on both positive and negative values. Whenthe nitrogen production rate becomes greater than the nominal



level as a result of certain disturbances, less makeup steam isused, and vice versa. The expander turbine generates a smallamount of electricity during the depressurization of the airstream split at the PHX (HX-1), which has a negative effect onthe operating cost.2.2.3. Chosen Operational Scenarios. It was assumed that

under the nominal conditions, the EP ASU production ofoxygen is run at its full capacity (968 tons/day) and the IGCCpower plant needs to cover a base load of power demand.When the electricity demand for the IGCC power plant isdecreased, less coal is gasified into syngas. Hence, the oxygenproduction rate in the EP ASU should be reduced in acorresponding manner. In this study, 5%, 10%, and 15%decreases in the oxygen production rate were considered as theoperational scenarios. Of course, the temperature and pressureof the ambient air feed change continuously with time. In thisstudy, it was assumed that the temperature of the air feed iscontrolled at its set point in the air cooler (C-1) and similarlythat its pressure is controlled at its set point in the MAC(COM-1). Also, it was assumed that the air flow coming fromthe GT is well controlled at the GT site, so disturbances relatedto this were not considered.2.2.4. Active Constraints and the Optimal Operating

Conditions. It can be argued immediately that in order tominimize the hourly operating cost J, several CVs should becontrolled at their limits set by the constraints given in eq 1.Such constraints are called “active constraints”. For example,TO2

needs to be controlled at its upper bound (given by

constraint 1-B) because the cooling duty of the oxygen cooler(C-5) should be minimized to minimize the operating cost.Constraint 1-A was also assumed to be an active constraintunder the optimal operating conditions. To produce oxygen ofhigher purity in the LPC, a lower pressure is favored. However,a lower operating pressure of the LPC means increased powerloads at the O2 compressor (COM-5) and low-pressure N2

compressor (COM-3) because of the decreased inlet pressuresto the compressors. Therefore, the oxygen purity, which is sameas the LPC’s bottom product purity (CV38), needs to becontrolled at its lower limit of 95%. All of the assumed activeconstraints are listed in Table 3.

At the same time, some of the other CV candidates should beexcluded from consideration when these variables are chosen tobe controlled at the limits of their constraints. For instance, ifthe LPC bottom product purity (CV38) is controlled, then inpractice it is difficult to control the LPC top product purity at

the same time because the top and bottom product puritiesstrongly interact with each other. The CV candidates excludedon the basis of such considerations are listed in Table 3.Following the guidelines for input−output pairing suggested byAraujo et al.,21 the MV pairings for the 10 CVs can be chosen aslisted in Table 3.After such an a priori assignment, the number of remaining

CV candidates is 23 (=38 − 15). In addition, the number ofdegrees of freedom also gets reduced to 6 (=16 − 10); theseremaining degrees of freedom are listed in Table 4. From the

remaining 23 CV candidates, six of them should be chosen forone-to-one pairing, so the number of possible candidate sets isreduced to 100 947 (23C6) before application of the SOCmethod. This work makes the next analysis step easier becauseof the reduced number of candidates.To get reference cost values, the optimal steady-state values

of these variables and the corresponding cost values were foundfor each load change scenario case by using the nonlinearoptimization solver provided by gPROMS. The calculatedreference values can be found in Table 7.

3. METHODOLOGYSelf-optimizing control is a methodology for selecting controlledvariables that are to be kept at constant set points during theoperation in order that near-optimal operation with an accept-able loss (with respect to some well-defined cost function) ismaintained in the presence of selected disturbances and set-pointchanges.12

As the first step, the optimization problem needs to bedefined as the cost function minu Ju(u, d) subject to theconstraints g(u, d) ≤ 0, where u contains the available MVs(degrees of freedom for the optimization) and d thedisturbance variables. SOC searches for the control structure(choice of CVs and MVs) that minimizes the loss L, which isdefined as the cost achieved when the selected CVs are kept attheir set points, Ju(u, d), minus the optimal cost, Jopt(d), asshown in eq 2:17

= − ≈ = || ||L u d J u d J d e J e z( , ) ( , ) ( )12

12u y yy yopt

T2

2(2)

where Jyy = (G−1)TJuuG−1, ey = y − yopt, z = Juu

1/2(u − uopt) =Juu

1/2G−1ey. In these expressions, G is a static gain matrix, Juu isthe Hessian matrix of the cost function J with respect to thevariables u, y is the vector of CVs, and ey is a combined errorvariable vector accounting for both the set-point error (whenuncontrolled) and the implementation error. G−1ey thusrepresents the change in u needed to control ey to zero.There are two methods to distinguish the loss: the

“minimum singular value rule” and the “exact local method”.In this study, the minimum singular value rule was used toselect the CVs because it is easier and simpler to apply than the

Table 3. Assumed Active Constraints and Related CVs andMVs

constraint boundCVindex

predesignated MVindex

excluded CVindex(es)

1-A lower 38 8 371-B upper 20 201-C lower 32 142-A upper 25 192-B lower 34 134 lower 26 10 4, 55 upper 6 166 lower 33 12 21, 237 upper 24 188 lower 28 22

Table 4. Remaining Degrees of Freedom (MVs)Participating in the Optimization

MV index MV specification unit

1 ambient air feed rate Air-13 valve position of V-1 V-111 boost air compressor load COM-215 expander turbine load T-117 BAC cooler duty C-221 reflux ratio in condenser/reboiler F-1



exact local method, but the latter can certainly be used forbetter accuracy within the overall procedure.17 We assume thatthe individual MVs are scaled in such a way that every elementof the MV variable vector u has the same effect on the costfunction (i.e., Juu = αU, where U is a unitary matrix and α is ascalar constant). In addition, the CVs are also scaled in such away that the error variables are unity and their 2-norms are lessthan 1.17 As a result of the scaling of the MV vector u and theCV vector y, the worst-case loss can be expressed as

σ

σ α

ασ

= || ||

= ′

= ′

=′

|| ′ || ≤|| ′ || ≤

−

−

L z

J G

G

G

max max12

12

[ ( )]

12

[ ( )]

21

( )

uu

n

ee

11

22

11/2 1 2

11/2 1 2

2

yy2

2

(3)

where σ1 is the largest singular value, σn is the minimumsingular value of an n × n matrix, ey′ is the scaled combinederror variable vector, and G′ is a scaled static gain matrixcalculated using a diagonal scaling matrix Dy for the CVs andanother diagonal scaling matrix Du for MVs as follows:

′ = −G D GDy u1

(4)

The way to calculate two diagonal scaling matrices ismentioned in the appendix of the paper by Halvorsen et al.17

Hence, to find the minimum-loss case, it is sensible to maximizeσn(G′).Generally, one has a large number of candidate CV sets from

which to choose. The static gain matrix G′ was obtainedthrough the simulation on gPROMS, and the singular valueswere calculated by using the SVD function in MathWorks’MATLAB software.

4. RESULTS

4.1. Reduction of the Candidate Controlled VariableSets. 4.1.1. Additional Prior Screening of the ControlledVariable Sets. There were 100 947 possible CV sets left at thispoint. Before the calculation of the minimum singular value ofthe static gain matrix of each possible set, the number ofcandidates was further reduced by eliminating a large numberof sets that are infeasible because of certain physical oroperational characteristics. Table 5 shows groups of CVsrequiring special considerations leading to such eliminations.

The category “mandatory” means that one of CVs out of thegroup must be chosen. On the other hand, the “optional”category presents the option of choosing either just onevariable or none as a CV. For example, in the mandatorycategory, there are two possible choices (column operatingpressures) for group 2. For safety reasons, at least oneoperating pressure should be controlled. However, bothoperating pressures cannot be controlled simultaneouslybecause the thermal interaction between the two columns isvery strong. Thus, only one CV should be chosen out of thisgroup. As an example in the optional category, only one of thetwo temperature variables measured at the top and bottom ofthe HPC can be selected because they are also highlyinteracting. However, it is not required that either of them bechosen.For groups 3, 4 and 7, the “two-point control” issue arises.

Only a few industrial distillation columns use a controlstructure that controls both the top and bottom puritiesbecause the dynamic performance is typically poor as a result ofthe strong interaction between these two variables.12,22 Also,the purities and temperatures in a distillation column arestrongly correlated; hence, choosing only one temperaturevariable among the top and bottom points is recommended.For groups 1, 5, 6, 8, 9, 10, and 11, only one CV can be

selected out of each group because there is only one MVavailable to control the variables in the group. Therefore, theyare designated as the “lack of MV” cases.The above exercise reduced the number of candidate sets

from 100 947 to 1470, to which the SOC calculation wasactually applied. The minimum singular values of the scaledstatic gain matrices G′ for these cases were calculated toidentify a few top candidates, for which a rigorous simulation-based analysis was then performed.

4.1.2. Ranking According to the Minimum Singular ValueRule. The minimum singular value of the scaled static gainmatrix G′ for each controlled variable set was calculated usingthe SVD function in MATLAB. The size of the scaled gainmatrix G′ is 6 × 6. The best 10 sets of CVs in terms of theminimum singular value criterion are listed in Table 6. The twoCVs common to the 10 best sets are the sub air feed rate to theHPC (CV1) and the HPC pressure (CV29). The choices of theother four CVs vary among the sets. The 10 best sets wereconsidered as the final candidates in the next step.

4.2. Loss Evaluation. For the 10 selected CV sets, the lossvalues (as defined in eq 2) were calculated with respect to eachof the three oxygen load changes by running the steady-statesimulations in a corresponding manner (i.e., by fixing thechosen CVs at their set-point values). The evaluated hourly

Table 5. List of CVs Excluded from Consideration Because of Impracticality

group number CV index category unit limitation

1 1, 2 mandatory V-1 lack of MVs2 29, 31 mandatory HPC and LPC thermal interaction3 12, 13 optional HPC one-point control4 35, 36 optional HPC one-point control5 35, 39 optional HPC lack of MVs6 14, 15 optional HPC and SHEX lack of MVs7 18, 19 optional LPC one-point control8 16, 19 optional LPC and SHEX lack of MVs9 17, 30, 31 optional LPC and T-1 lack of MVs10 7, 27 optional COM-2 lack of MVs11 10, 22 optional HX-1 lack of MVs



operating costs for the three oxygen load changes for each setare shown in Table 7.In the simulations, some of the CV sets gave infeasible

results. “Infeasible” here means that there was no solution ofMVs or degrees of freedom satisfying the given set points of theCVs and the constraints. For example, the control structurewith the best predicted loss value did not give a feasiblesolution. As all of the selected CVs were controlled at their setpoints, the bottom liquid holdup level of the LPC could not becontrolled with such a control structure because the split ratioof the N2 splitter was bounded at 1. As for the third-best setpredicted by the SOC analysis, the difference between theoperating pressure of the LPC and the expander turbine (T-1)outlet pressure was forced to be zero. In order to keep the LPCtop temperature (CV19) at its set point, the expander turbineoutlet temperature had to be increased by lowering theexpander turbine load (MV15) (as the expander turbine loaddecreases, the outlet temperature increases). This causedreverse flow between the two units. The reason why theseinfeasible sets were favored by the singular value criterion isthat the SOC method is not able to consider the operationalconstraints in the formulation. It simply estimates the expectedloss with respect to the optimal case assuming that the chosenCVs can be controlled at their respective set points. The morecomplex the studied process, the greater is the number ofinfeasible sets that pass through. If the prior screeningperformed in our analysis (section 4.1.1) had been skipped,

more infeasible cases would have shown up in this step; theidentification of such infeasible cases would have been muchmore time-consuming.After the six infeasible sets (1, 3, 4, 5, 7, and 10) were

excluded, the four remaining sets were 2, 6, 8, and 9. It wasverified that for these CV choices it was possible to satisfy all ofthe constraints in the presence of the oxygen load changescenarios.The calculated annual losses for the remaining four CV sets

are presented in Table 8. From Table 8, the second-best set

shows the smallest loss with respect to the oxygen load changes,in agreement with the ranking by the SOC analysis. However,the loss differences between the second- and sixth-best sets(hereafter termed CV group #1) are small, and choosingbetween them would be a matter of ease of control. In addition,the eighth- and ninth-best sets (termed CV group #2) dosimilarly. Though CV groups #1 and #2 are all ranked withinthe top 10 CV sets given by the SOC analysis, the annual lossdifferences between the two groups are not negligible.Depending on the CV selection, the estimated overall power

generation cost in an IGCC power plant can vary significantly.For example, when the large change (15% load decrease)occurs, the difference between CV groups #1 and #2 is around$2,370,000/yr. For the given power capacity (629 MW),power generation cost ($0.0779/kWh), and availability (80%),it is estimated that the cost difference between the twogroups amounts to ∼0.94% of the total annual operating costof the IGCC power plant. In other words, just a small dif-ference in the CV choices makes a huge difference in terms ofeconomics.To compare the SOC and RTO approaches, the expected

additional cost savings for implementing an RTO system to anEP ASU should be considered. The ease of operation affordedby the simple control structure obtained by SOC may very wellbe considered to outweigh the extra savings that is realized by

Table 6. List of the 10 Best CV Sets According to theMinimum Singular Value Criterion

rank1st CVindex

2nd CVindex

3rd CVindex

4th CVindex

5th CVindex

6th CVindex 100·σ6

a

1 1 8 11 15 19 29 10.6272 1 8 11 15 29 30 10.4463 1 8 15 27 29 30 10.3004 1 8 15 19 27 29 10.2895 1 10 11 15 19 29 10.2006 1 10 11 15 29 30 10.0707 1 8 19 27 29 30 9.7508 1 10 15 27 29 30 9.3899 1 8 14 27 29 30 9.35110 1 10 15 19 27 29 9.350

aσ6 is the sixth singular value, which is the minimum singular valueobtained by the SVD function in MATLAB.

Table 7. Results of the Hourly Operating Cost Evaluation forthe Selected CV Sets at Oxygen Load Changes of 5%, 10%,and 15%

hourly operating cost ($/h)

CV set list 5% 10% 15%

1 infeasible for all cases2 3,859.15 3,723.89 3,590.903 infeasible for all cases4 infeasible for all cases5 infeasible for all cases6 3,860.23 3,725.41 3,592.447 infeasible for all cases8 3,970.16 3,946.29 3,923.819 3,972.56 3,950.51 3,929.1710 infeasible for all cases

optimal case 3,699.93 3,572.71 3,451.80

Table 8. Results of the Loss Evaluation for the Surviving CVSets at the Three Oxygen Load Changes

annual loss ($/yr)

CV group CV set 5% 10% 15%

#1 second-best 1,115,862 1,059,473 974,835sixth-best 1,123,424 1,070,146 985,663

#2 eighth-best 1,893,811 2,618,068 3,307,836ninth-best 1,910,597 2,647,651 3,345,464

Table 9. Chosen MV and CV Pairings for the Selected CVs

pairingindex

CVindex CV description

pairedMVindex

paired MVdescription

1 1 sub air feed rate to HPC 3 position of valveV-1

2 8 BAC cooler outlettemperature

17 BAC cooler duty

3 11 adiabatic expansion valveoutlet temperature

11 BAC load

4 15 SHEX hot stream outlettemperature

21 reflux ratio incondenser/reboiler

5 29 HPC pressure 1 ambient air feedrate

6 30 expander turbine outletpressure

15 expander turbineload



using a more complicated RTO system that requires a rigorousnonlinear plant (dynamic) model and a two-layer (optimizationlayer/regulatory control layer) control structure.4.3. CV Selection Including Controllability Analysis.

For the oxygen load change, the controllability of the selectedCV set was validated by the dynamic simulation usinggPROMS. In the previous section, three liquid holdup levels,one flow rate, and 10 CVs that are associated with the activeconstraints were already paired with certain MVs. Six input−output pairings for the selected CVs (given by the second-bestCV set in the previous section) are listed in Table 9. Thepairing was done through RGA analysis.

To keep all 20 CVs at their set points, 20 PI controllers weredesigned, and their tuning parameters were decided throughthe internal model control (IMC) tuning rule. Then the con-trollers were implemented in the gPROMS simulator. Theoverall control structure implemented on the simulated EPASU is described in Figure 4. The PI controller naming rulesare as follows:

• PI_X_Level: PI control loop for liquid holdup level• PI_X_Flow: PI control loop for flow rate• PI_Act_X: PI control loop for CV bounded to active

constraints• PI_X: PI control loop for SOC CV

Figure 4. EP ASU control structure with PI loops designed for the chosen CV set.

Figure 5. Dynamic responses of the various manipulated variables for the three tested scenarios: (a) ramp change in the oxygen load; (b) BAC load;(c) HPC reflux ratio; (d) air feed flow rate; (e) expander turbine load; (f) LPC top flow rate.



To test the closed-loop performance, ramp changes in theoxygen production rate at the speed of 1.5%/min were appliedto the simulated process with controllers installed. Threedifferent size ramps of 5%, 10%, and 15% decreases were tested.At 1000 s, the system was subjected to a decreasing ramp, andat 35 000 s, an increasing ramp (1.5%/min) was applied toreturn the oxygen load to the nominal value. The dynamicchanges of various MVs, including the oxygen production rate,are presented in Figure 5.Figures 6 describes the dynamic responses of those CVs with

noticeable changes as well as conditions of the nitrogen productin the face of the oxygen load changes of 5%, 10%, and 15%. Allof the CVs, including the oxygen product and HPC pressure,were controlled at their set points without significantdeviations. At the same time, the offset in the LPC pressure,which was not directly controlled, was less than 0.3 bar, whichis considered acceptable from the safety aspect. Also, the purityand production rate of the nitrogen product decreased as theoxygen production rate decreased.4.4. Comparison of the CV Selection with Those of

Previous Studies. In this section, the control structure of theASU system developed in the previous part is compared withthose appearing in previous studies of ASU control.3,4,7,8,10 Theauthors and publication year, target process, control strategy,and selected CVs for these works are summarized in Table 10.

The results of CV selection for an ASU system in this studyshow some differences with the control structures chosen in theprevious published works, which did not consider theeconomics. For instance, even though only the oxygen purityhad to be controlled in this work and control of the thenitrogen purity was optional, the purities of both oxygen andnitrogen products together were controlled. Also, someprevious works3,10 suggested control of the LPC pressurepaired with the LPC top flow rate, while others did notconsider the control of the operating pressure at all. On theother hand, the HPC pressure was chosen as a CV in this work.In addition, our selected control structure contained morecontrol loops, additionally including temperature, pressure, andflow rate controls, which contribute to the economicaloperation of the whole EP ASU plant.

5. CONCLUSIONIn this paper, a control study for the economical operation ofthe elevated-pressure air separation unit (EP ASU) in an IGCCpower plant has been presented. To obtain a classical controlstructure that minimizes the effect of disturbances on theoperating cost, the method of self-optimizing control was applied.The minimum singular value rule, when used in conjunction withadditional analyses based on physical insights and heuristics, wasshown to be effective in reducing the number of candidate

Table 10. Summary of Previous ASU Control Studies

author (year) target process control strategya product purity controlb column pressure control etc.

Roffel et al. (2000)3 cryogenic column MPC O2, HP and LP N2 LPC pressureTrierweiler and Engell (2000)4 cryogenic column PID control O2, HP and LP N2 uncontrolledHuang et al. (2009)7 cryogenic column nonlinear MPC O2, LP N2 uncontrolled two temperature controlsGuo et al. (2009)8 cryogenic column MPC O2, HP and LP N2 uncontrolledMahapatra and Bequette (2012)10 whole EP ASU plant PI control O2, HP and LP N2 LPC pressure one temperature controlthis work whole EP ASU plant PI control O2, HP and LP N2 HPC pressure extra 14 CVsaMPC denotes model predictive control; PID control denotes proportional−integral−derivative control. bHP and LP denote high pressure and lowpressure, respectively.

Figure 6. Dynamic responses of the various controlled variables for the three tested scenarios: (a) oxygen purity; (b) nitrogen purity; (c) nitrogenproduction rate; (d) HPC first-stage pressure; (e) LPC first-stage pressure; (f) adiabatic expansion valve outlet temperature.



controlled variable sets from a very large number (more thanbillions) down to just a few, to which a rigorous nonlinearsimulation/optimization-based analysis could be applied.Through loss evaluation and controllability considerations,the best CV set was identified. It was verified through theoptimization study that SOC indeed pointed to appropriatechoices of CV sets for which economic losses were the smallestfor the chosen load changes. Also, it was shown that potentialcost savings from the appropriate selection of the CVs are notnegligible. To verify the dynamic controllability under thechosen control structure, 20 PI controllers were designed andinstalled on the simulator and the closed-loop performanceswere checked. Finally, the selected control structure wascompared with those suggested by previous studies. Thisanalysis will be extended to an entire IGCC plant model in thefuture.

■ ASSOCIATED CONTENT

*S Supporting InformationList of available MVs, list of candidate CVs, and values of thecost parameters. This material is available free of charge via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected]. Phone: +82-42-350-3966. Fax:+82-42-350-3910.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This research was supported by the Basic Science ResearchProgram through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science andTechnology (2011-0006839) and by the Advanced BiomassR&D Center (ABC) of the Global Frontier Project funded bythe Ministry of Education, Science and Technology (ABC-2011-0031354).

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(8) Guo, T.; Lu, J.; Xiang, W.; Ding, W.; Zhang, T. DynamicModeling and Multivariable Model Predictive Control of the AirSeparation Columns in an IGCC Power Plant. Presented at the WorldCongress on Engineering and Computer Science 2009, San Francisco,October 2009.(9) Chen, Z.; Henson, M. A.; Member, S.; Belanger, P.; Megan, L.Nonlinear Model Predictive Control of High Purity DistillationColumns for Cryogenic Air Separation. IEEE Trans. Control Syst.Technol. 2010, 18, 811−821.(10) Mahapatra, P.; Bequette, B. W. Design and Control of anElevated-Pressure Air Separations Unit for IGCC Power Plants in aProcess Simulator Environment. Ind. Eng. Chem. Res. 2013, 52, 3178−3191.(11) Engell, S. Feedback Control for Optimal Process Operation. J.Process Control 2007, 17, 203−219.(12) Skogestad, S. Plantwide Control: The Search for the Self-Optimizing Control Structure. J. Process Control 2000, 10, 487−507.(13) Larsson, T.; Hestetun, K.; Hovland, E.; Skogestad, S. Self-Optimizing Control of a Large-Scale Plant: The Tennessee EastmanProcess. Ind. Eng. Chem. Res. 2001, 40, 4889−4901.(14) Engelien, H. K.; Skogestad, S. Selecting Appropriate ControlVariables for a Heat-Integrated Distillation System with Prefractiona-tor. Comput. Chem. Eng. 2004, 28, 683−691.(15) De Araujo, A. C. B.; Govatsmark, M.; Skogestad, S. Applicationof Plantwide Control to the HDA Process. ISteady-StateOptimization and Self-Optimizing Control. Control Eng. Pract. 2007,15, 1222−1237.(16) Panahi, M.; Skogestad, S. Economically Efficient Operation ofCO2 Capturing Process Part I: Self-Optimizing Procedure forSelecting the Best Controlled Variables. Chem. Eng. Process. 2011,50, 247−253.(17) Halvorsen, I. J.; Skogestad, S.; Morud, J. C.; Alstad, V. OptimalSelection of Controlled Variables. Ind. Eng. Chem. Res. 2003, 42,3273−3284.(18) Rubin, E. S.; Berkenpas, M. B.; Frey, H. C.; Chen, C.; McCoy, S.T.; Zaremsky, C. J. Technical Documentation: Integrated GasificationCombined Cycle Systems (IGCC) with Carbon Capture and Storage(CCS); Carnegie Institute of Technology, Department of Engineeringand Public Policy, Paper 76, 2007; http://repository.cmu.edu/epp/76(accessed April 14, 2014).(19) Smith, A. R.; Klosek, J. A Review of Air Separation Technologiesand Their Integration with Energy Conversion Processes. Fuel Process.Technol. 2001, 70, 115−134.(20) Aspen Plus User Guide; Aspen Technology, Inc.: Cambridge,MA; www.aspentech.com (accessed April 14, 2014).(21) de Araujo, A. C. B.; Hori, E. S.; Skogestad, S. Application ofPlantwide Control to the HDA Process. IIRegulatory Control. Ind.Eng. Chem. Res. 2007, 46, 5159−5174.(22) Skogestad, S.; Morari, M. Control Configuration Selection forDistillation Columns. AIChE J. 1987, 33, 1620−1635.



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