Proactive Optimization and Control of Heat-Exchanger Super Networks

9th International Symposium on Advanced Control of Chemical Processes 9th International Symposium on Advanced June 7-10, 2015. Whistler, British Columbia,Control Canadaof Chemical Processes 9th International Symposium on Advanced Control of Chemical Processes Available online at www.sciencedirect.com June 7-10, 2015. Whistler, British Columbia, Canada 9th International Symposium on Advanced Control of Chemical Processes June 7-10, 2015. Whistler, British Columbia, Canada June 7-10, 2015. Whistler, British Columbia, Canada

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Proactive Optimization and Control of Heat-Exchanger Super Networks Proactive Optimization and Control of Heat-Exchanger Super Networks Proactive and Control of Heat-Exchanger Super Networks Proactive Optimization Optimization and Control of Heat-Exchanger Super Networks Xiaonan Wang, Ahmet Palazoglu and Nael H. El-Farra* Xiaonan Wang, Ahmet Palazoglu and Nael H. El-Farra*  Xiaonan and Xiaonan Wang, Wang, Ahmet Ahmet Palazoglu Palazoglu and Nael Nael H. H. El-Farra* El-Farra*    *Department of Chemical Engineering & Materials Science, *Department of Chemical Engineering & Materials Science, *Department of Chemical Engineering & Materials Science, *Department of Chemical Engineering & Materials Science, University of California, Davis, CA 95616 USA (e-mail: [email protected]) University of California, Davis, CA 95616 USA (e-mail: [email protected]) University University of of California, California, Davis, Davis, CA CA 95616 95616 USA USA (e-mail: (e-mail: [email protected]) [email protected]) Abstract: This paper presents an integrated approach for the optimization and control of heat-exchanger Abstract: This paper an integrated approach optimization and control of heat-exchanger networks (HENs) thatpresents are managed proactively, where for boththe renewable energy generation and time-varying Abstract: This paper presents an approach for the optimization and control of heat-exchanger Abstract: This paper presents an integrated integrated approach for the optimization and control ofand heat-exchanger networks (HENs) that are managed proactively, where both renewable energy generation time-varying electricity pricing are considered in calculating the utility cost and revenues. A real-time optimization networks (HENs) that are managed proactively, where both renewable energy generation and time-varying networks (HENs) that are managed proactively, where both renewable energy generation andand time-varying electricity pricing are considered in calculating the utility cost and revenues. A real-time optimization strategy is carried out to deal with the resulting variability in energy resource availability costs. The electricity pricing are considered in the utility cost and revenues. A real-time optimization electricity pricing are to considered inthecalculating calculating thewhere utility transitions cost and resource revenues. A real-time optimization strategy is carried out deal with resulting variability in energy availability and costs. The heat-exchanger super structures are first defined between the included HEN substrategy carried out deal with the resulting variability in availability and costs. The strategy is isare carried out to to deal withare thefirst resulting variability in energy energy resource resource availability and costs. subThe heat-exchanger super structures defined where transitions between the included HEN structures assumed to be instantaneous. The optimal configurations are sent to the local controllers as heat-exchanger super structures are first defined where transitions between the included HEN subheat-exchanger super structures are first defined where transitions between the included HEN substructures are assumed to be instantaneous. The optimal configurations are sent to the local controllers as structural set points to be implemented. The explicit nonlinear models of heat exchangers built in Aspen structures are assumed to be instantaneous. The optimal configurations are sent to the local controllers as structures are assumed to be instantaneous. The optimal configurations are sent to the local controllers as structural set points to be implemented. The explicit nonlinear models of heat exchangers built in Aspen Plus® are set adopted totodescribe the dynamic behaviors of the HENs. Theof dynamic models arebuilt incorporated structural points be implemented. The explicit nonlinear models heat exchangers in Aspen structural set points to be implemented. The explicit nonlinear models of heat exchangers built in Aspen Plus® are adopted to describe the dynamic behaviors of the HENs. The dynamic models are incorporated not only for simulating the local control scheme but also the supervisory level to account for the structural Plus® are to describe the dynamic behaviors of The models are incorporated Plus® areforadopted adopted tooperational describe thecontrol dynamic behaviors of the the HENs. HENs. The dynamic dynamic models for are the incorporated not only simulating the local scheme but also supervisory level to account structural transitions that incur and possibly capital costs. not only for simulating the local control scheme but also the supervisory level to account for the not only forthat simulating the local control scheme but also the supervisory level to account for the structural structural transitions incur operational and possibly capital costs. transitions that incur and capital costs. Keywords: Heat-exchanger networks, Optimization, Dynamics, Renewable energy, © 2015, IFAC (International Federation of Automatic by Elsevier Ltd.Economics All rights reserved. transitions that incur operational operational and possibly possibly capitalControl) costs. Hosting Keywords: Heat-exchanger networks, Optimization, Dynamics, Keywords: Heat-exchanger Heat-exchanger networks, networks, Optimization, Optimization, Dynamics, Renewable Renewable energy, energy, Economics Economics  Dynamics, Renewable energy, Economics Keywords:

 1. INTRODUCTION   1. INTRODUCTION 1. INTRODUCTION Large-scale chemical petrochemical processes are highly 1. or INTRODUCTION Large-scale chemical or petrochemical processes are highly energy intensive and usually require energy recovery systems Large-scale chemical or petrochemical processes are highly Large-scale chemical or petrochemical processes are highly energy intensive and usually require energy recovery systems to guarantee highand efficiency and lowenergy cost. A heat-exchanger energy intensive usually require recovery systems energy intensive and usually require energy recovery systems to guarantee high efficiency and low cost. A heat-exchanger network (HEN) aims at utilizing internal flow streams to to guarantee high efficiency and cost. A heat-exchanger to guarantee highaims efficiency andsolow low cost. Aflow heat-exchanger network (HEN) at utilizing internal streams to satisfy outlet temperature targets that operating costs can be network (HEN) aims at utilizing internal flow streams to network (HEN) aims(1978)). at targets utilizing internal flow streams to satisfy outlet temperature so that operating costs can be minimized (Linnhoff Attributed to the significance of satisfy outlet temperature targets so that operating costs can be satisfy outlet temperature targets so that operating costs can be minimized (Linnhoff to the significance of determining energy (1978)). cost in Attributed chemical processes, the HEN minimized (Linnhoff (1978)). Attributed to significance of minimizedproblem (Linnhoff (1978)). Attributed to the the significance of determining energy cost in chemical processes, the HEN synthesis has been widely studied with the objective determining energy cost in chemical processes, the HEN determining energy cost in chemical processes, the HEN synthesis problem has been widely studied with the objective to minimize overall (e.g., Dipama al. (2008); synthesis problem hasinvestment been widely studied withetthe synthesis problem been Gundepsen widely studied theal.objective objective to minimize overall investment (e.g., Dipama et (2008); Gorji-Bandpy et al.has (2011); et al.with (1988); Yee and to minimize overall investment (e.g., Dipama et al. (2008); to minimize overall investment (e.g., Dipama et al. (2008); Gorji-Bandpy et al. (2011); Gundepsen et al. (1988); Yee and Grossmann (1990); Zamora and Grossmann (1998); Ciric and Gorji-Bandpy et al. (2011); Gundepsen et al. (1988); Yee and Gorji-Bandpy et al.Another (2011); Gundepsen et studies al.(1998); (1988); Yeewith and Grossmann (1990); Zamora and Grossmann Ciric Floudas (1991)). category of deals Grossmann (1990); Zamora and Grossmann (1998); Ciric and Grossmann (1990); Zamora and Grossmann (1998); Ciric and Floudas (1991)). Another category of studies deals with optimal operation of HENs following the synthesis step (e.g., Floudas (1991)). Another category of studies with Floudas operation (1991)). Another category of studies deals deals with optimal of HENs following the synthesis step (e.g., Aguilera and Marchetti (1998); Glemmestad (1999); optimal operation of HENs following the synthesis step (e.g., optimal operation of HENs following the synthesis step (e.g., Aguilera and Marchetti (1998); Glemmestad (1999); Lersbamrungsuk et al. (2008)). Aguilera (1998); Aguilera and and Marchetti Marchetti (1998); Glemmestad Glemmestad (1999); (1999); Lersbamrungsuk et al. (2008)). Lersbamrungsuk et al. (2008)). A traditional HEN is expected to be operated under the Lersbamrungsuk et al. (2008)). A traditional HEN is expected to be operated under the condition of maximum heat integration and minimum utility A traditional HEN is expected to be operated under the A traditional HEN is high expected toutilities be and operated under the condition of maximum heat integration minimum utility consumption due to the cost of (González (2006)). condition of maximum heat integration and minimum utility condition of maximum heat integration and minimum utility consumption due to the high cost of utilities (González (2006)). With the emerging trend incost energy management systems to consumption due high of utilities (González (2006)). consumption due to to the the high cost ofsuch utilities (González (2006)). With the emerging trend in energy management systems to integrate renewable generation, as wind and solar With the emerging trend in energy management systems to With the emerging trend in energy management systems to integrate renewable generation, such as wind and solar resources, renewable and to supply heat and power not only to residential integrate generation, such as wind and solar integrate renewable generation, such as wind and solar resources, and to supply heat and power not only to residential users but also totoprocess industries, the electricity can be “zeroresources, and supply heat not only to resources, andas toprocess supply heat and and power power notrenewable only can to residential residential users also to industries, the electricity be “zerocost” but as well “zero emission”, making energy a users but also to process industries, the electricity can be “zerousers but also to process industries, the electricity can be “zero-a cost” as well as “zero emission”, making renewable energy promising power alternative (Wang et al. (2014)). Furthermore, cost” as well as “zero emission”, making renewable energy a cost” as well as “zero emission”, making renewable energy promising power alternative (Wang et al. (2014)). the time-varying electricity prices with respect toFurthermore, supply anda promising power alternative (Wang et al. (2014)). Furthermore, promising (Wang et al.respect (2014)). Furthermore, the time-varying electricity prices to supply and load bringspower more alternative opportunities for with electricity users to manage the time-varying electricity prices with respect to supply and the time-varying electricity prices with respect to supply and load brings more opportunities for electricity users to manage their interaction with the power grid and optimize economic load brings more opportunities for electricity users to manage load brings more opportunities for electricity users to manage their interaction with the power grid and optimize economic performance. their their interaction interaction with with the the power power grid grid and and optimize optimize economic economic performance. performance. Despite the wide implementation of renewable resources, the performance. Despite wide implementation renewable resources, the discrete the generation and inherentof uncertainty in renewable Despite the wide of renewable resources, the Despite the wide implementation implementation ofuncertainty renewable resources, the discrete generation and inherent in renewable resources continue to pose significant challenges. The timediscrete generation and inherent uncertainty in renewable discrete generation and inherent uncertainty in renewable resources continue to pose significant challenges. The timevarying electricity pricing also requireschallenges. more comprehensive resources continue to significant The timeresources continue to pose pose significant challenges. The timevarying electricity pricing also requires more comprehensive scheduling to lower the energy cost. Receding horizon varying electricity pricing also requires more comprehensive varying electricity pricing also requires more comprehensive scheduling to lower the energy cost. Receding horizon scheduling scheduling to to lower lower the the energy energy cost. cost. Receding Receding horizon horizon

optimization is thus a meaningful strategy that can incorporate optimization is thus aa meaningful strategy that can future conditions, such as the energy generation andincorporate loads, and optimization is thus meaningful strategy that can incorporate optimization is thus a meaningful strategy that can incorporate future conditions, such as the energy generation and loads, and coordinate the real-time operation with as much information future conditions, such as the energy generation and loads, and future conditions, such as the energy generation and loads, and coordinate the real-time operation with as much information as possible.the Onreal-time the otheroperation hand, although the overall steadycoordinate with as much information coordinate the real-time operation with asthe much information as possible. On the other hand, although overall steadystate operating cost can be reduced by adjusting the operational as possible. On the other hand, although the steadyas possible. thecan other hand, although the overall overall steadystate operating cost be reduced by adjusting the operational states of the On plant, frequent changes may cause safety issues state operating cost can be reduced by adjusting the operational state operating cost can be reduced by adjusting the operational states of the plant, frequent changes may cause safety issues and harm the equipment, and ultimately economic states of frequent changes may cause safety issues states harm of the the plant, plant, frequent changes may cause safety issues and the equipment, and ultimately economic performance. To avoid infeasible solutions, it is necessary to and harm the equipment, and ultimately economic and harm the equipment, and ultimately economic performance. To avoid infeasible solutions, it is necessary to take the dynamic models that describe the state transitions into performance. To avoid infeasible solutions, it is necessary to performance. To avoid infeasible solutions, it is necessary to take the dynamic models that describe the state transitions into consideration andmodels look forthat reasonable control strategies as well. take the dynamic describe the state transitions into take the dynamic models that describecontrol the state transitions into consideration and look for reasonable strategies as well. consideration and look for control as In this paper, methodology of proactive consideration andan lookinnovative for reasonable reasonable control strategies strategies as well. well. In this paper, innovative methodology of proactive reconfiguration ofan HENs is introduced. The methodology is In this paper, an innovative methodology of proactive In thisat realizing paper, ofan innovative methodology ofoperational proactive reconfiguration HENs is introduced. The methodology is aimed – at any given time the optimal reconfiguration of HENs is introduced. The methodology is reconfiguration of HENs is introduced. The methodology is aimed at realizing – at any given time the optimal operational state ofatthe HEN within angiven existing super network.operational Based on aimed realizing – at any time the optimal aimed at realizing – at any given time the optimal operational state of the HEN within an existing super network. Based on extensive research on HEN synthesis, a reconfiguration stepon is state HEN within an existing network. Based state of of the theresearch an synthesis, existing super super network. Based on extensive on aadesign, reconfiguration step is proposed toHEN unitewithin theHEN simultaneous operation and extensive research on HEN synthesis, reconfiguration step is extensive research on HEN synthesis, adesign, reconfiguration step is proposed to unite the simultaneous operation and control activities. Assuming, for simplicity, that the synthesis proposed to unite the simultaneous design, operation and proposed to unite the out, simultaneous design, operation and control activities. Assuming, for simplicity, that the synthesis step is already carried which means that all necessary control activities. Assuming, for simplicity, that the synthesis control activities. Assuming, forthe simplicity, that all the necessary synthesis step is already carried out, which means that exchangers, utility units, and connecting structure are all necessary step is already carried out, which means that step is already carried out, which means that all necessary exchangers, utility units, and the connecting structure completely defined, this work demonstrates a re-configuration exchangers, utility units, and the connecting structure are are exchangers, utility units, and the connecting structure subare completely defined, work aa re-configuration step to realize the this transitions between the possible completely defined, this work demonstrates demonstrates re-configuration completely defined, this workgeneration, demonstrates a re-configuration step the transitions between the substructures based on load and cost. step to to realize realize thereal-time transitions betweenpower the possible possible substep to realize the transitions between the possible substructures based on real-time generation, power load and cost. Both the steady-state optimization and dynamic control are structures based on real-time generation, power load and cost. structures based on the real-time power load andlevels. cost. Both optimization and control are considered to close loop atgeneration, the supervisory and local Both the the steady-state steady-state optimization and dynamic dynamic control are Both will the steady-state optimization and dynamic control are considered to close the loop at the supervisory and local levels. We first discuss the HEN reconfiguration problem considered to close the loop at the supervisory and local levels. considered to close the loop at the supervisory andthe local levels. We first discuss reconfiguration problem statement Section 2. Then proactive We will will and first formulation discuss the theinHEN HEN reconfiguration problem We will first discuss the HEN reconfiguration problem statement formulation Section Then the supervisory 3 to statement and andoptimizer formulationis in in described Section 2. 2. in ThenSection the proactive proactive statement andoptimizer formulation in described Section 2. in ThenSection the operating proactive supervisory is simultaneously decide the HEN sub-structure and supervisory optimizer is described in Section 33 to to supervisory optimizer is issues described in the Section 3 the to simultaneously decide the and operating states. In Section 4, several regarding control of simultaneously decide the HEN HEN sub-structure sub-structure and operating simultaneously the HEN sub-structure andwith operating states. Section 4, regarding the of target HEN aredecide discussed. Conclusions, states. In In Section 4, several several issues issues regardingalong the control control future of the the states. In Section 4, several issues regarding the control of the target HEN are discussed. Conclusions, along with future research directions, are presented in Sectionalong 5. target HEN are discussed. Conclusions, with future target HEN are discussed. Conclusions, along with future research are presented 5. research directions, directions, are presented in in Section Section 5. 2. HEATare EXCHANGER NETWORK research directions, presented in Section 5. 2. HEAT EXCHANGER NETWORK 2. HEAT EXCHANGER NETWORK 2. HEAT EXCHANGER NETWORK 2.1 Problem Statement 2.1 Problem Statement 2.1 Problem Statement 2.1 Problem Statement

2405-8963 © 2015, IFAC (International Federation of Automatic Control) Copyright 2015 IFAC 593Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2015 responsibility IFAC 593Control. Copyright © 2015 IFAC 593 10.1016/j.ifacol.2015.09.032 Copyright © 2015 IFAC 593

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Here, we focus on the optimal design, operation and control within a hierarchical framework as shown in Fig.1. Under market fluctuations, such as varying electricity pricing and supply of renewable resources, a steady-state optimization over a short time horizon is performed to generate the operating set-points for the heat flows and temperature targets, which are subsequently sent to the local controllers for tracking. The local controllers (PID or MPC) are adopted to realize optimal operation and effectively handle process disturbances.

2.2 Problem Formulation A key issue when designing a HEN structure is the pinch point, which acts as a thermodynamic bottleneck that limits the maximum energy integration and poses feasibility constraints (Floudas (1995)). Hence, a procedure of decomposition by the pinch temperature is always required to guarantee the feasibility of temperature and energy balance. However, instead of specifying the minimum approach temperature and the corresponding pinch point(s) a priori, these parameters can be optimized simultaneously with the matches and network (e.g., Yee and Grossmann (1990), Ciric and Floudas (1991)). In this work, a similar multi-stage optimization scheme is adopted and described as follows. Given the simplification of the super structure by considering a number of stages, NS, all possible matches are allowed within each stage. Also, the isothermal mixing assumption can assign the same temperature as a single variable to each stream after splitting at the end of every stage. Two other types of variables are defined which are continuous variables for the heat flow, and binary variables representing the existence of a process or utility match at each stage.

Fig. 1. Overview of the proactive optimization and control problem.

The synthesis problem for HENs is based on the idea of matching a set of hot process streams, H, to be cooled, and a set of cold streams, C, to be heated. Each stream has a specific heat capacity Cp and flow rate m, along with their inlet and target outlet temperature. Also, the hot and cold utilities, HU and CU, are available to guarantee the temperature requirements to be satisfied in spite of how much heat is recovered in network heat exchangers.

The objective, while searching within the super structure, is to find the sub-network that minimizes the cost for specific heat exchange requirements, i.e. satisfying temperature targets of cold and/or hot outlet streams. Three cost terms are considered which are the utilities cost, co-generation revenues from renewables and amortized depreciation cost for heatexchangers:

The objective of a traditional synthesis problem is to decide the HEN with the least total annualized cost which includes not only the energy cost, but also the capital cost for heatexchangers corresponding to the equipment area required (Floudas (1995)). In our case, the starting point is an existing super structure that includes several potential HEN substructures (networks) so that the fixed cost can be neglected while emphasizing only the energy and operating costs. Fig. 2 shows an example of a super structure consisting of two hot process streams and two cold process streams with no bypassing or stream splitting.

NH

j 1

NH

NC

k 1

i 1

j 1

(1)

where  ,  and  are the weighting factors to weigh the significance of each cost term. NH and NC are the number of hot and cold streams. Ci and Hj are the load of cold and hot utilities located over the hot and cold streams of i and j respectively. CCU and CHU represent the price of the cold and hot utilities, respectively. We note here that CCU and CHU are not fixed but dependent on the utility sources. The prices may vary significantly according to whether the utilities are powered by the electricity from renewable generation or electricity purchased from the grid with varying pricing.

CU1

H2 CU2

E4

i 1

NE

  ( CHE Qk   CHEhCi   CHEc H j )

E2

E3

NC

min J   ( CCU Ci   CHU H j )   (Cele _ sell Psell )

H1 E1

593

As an example, Fig. 3 shows at a fixed time instant when the renewable generation is Prenewable associated with a power to utility ratio  re , if the total demand is less than the current

C1 E1

HU1

E3

available renewable generation (see Pdemand_1 in Fig. 3), the unit cost of utility will be equal to Cre and the total cost is also reduced by the profits of selling extra electricity from renewable resources generation back to the grid. When the total demand is larger than the renewable generation (see Pdemand_2 in Fig. 3), the unit cost of utility will be a combination of two parts described as a step function:

C1 E2

E4

HU2

Fig. 2. A typical super structure for a heat-exchanger network comprised of two hot and two cold streams (no bypassing or stream splitting).

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CHU

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NC  Cre , when  H j  Prenewablere   j 1  NH C / ele , when  H j  Prenewablere ele buy _  i 1 

- Targets of outlet temperatures:

(2)

Ti out  Ti target , i  N H T jout  T jtarget , j  NC

Cele_buy is the price of electricity purchased from the grid as a raw source for utilities, while ele is the efficiency of electricity

(7)

- Feasibility of temperatures:

converted to required utilities. Cele_sell and Psell are the price and amount of electricity sold back to the grid, which is treated as a revenue term from the renewable energy co-generation. CHE, CHEh, and CHEc are the unit operating costs of heat exchanged depending on the type of exchanger. NE is the number of total exchangers actively in use excluding the utility powered heaters or coolers.

Ti out  Ti , Ns  …  Ti ,1  Ti ,0 , i  N H T jout  T j , Ns  …  T j ,1  T j ,0 , j  NC

(8)

(Also guaranteed by the assumption of isothermal mixing.) c)

Capacity

- Availability from all utility resources: The utilities are assumed unlimited since the power can be purchased from the grid. However, the price varies when the sources are different, as previously shown in Fig. 3. - Maximum and Minimum heat exchanger capacity limits (yi,j,l are 0-1 binary variables):

0  Qi , j ,l  yi , j ,l Qi , j ,l ,max , i  N H , j  NC , l  N S d)

(9)

Logical constraints

Fig. 3. Demonstration of the relation between utility cost and power.

- Matches that take place denoted by yi,j,l binary variables.

The following set of constraints are considered:

The topology or structure of the HEN can then be decided according to active matches and heat duties with respect to each stage.

a)

Heat/ Energy balance

- Overall for each stream:

3. SUPERVISORY OPTIMIZATION

NC

NC

NC

j 1

j 1

j 1

NH

NH

NH

i 1

i 1

i 1

(mC p )i (Ti  Ti )   Qi , j ,1   Qi , j ,2 …  Qi , j , Ns  Ci , i  N H (3) in

out

(mC p ) j (T jout  T jin )   Qi , j ,1   Qi , j ,2 …  Qi , j , Ns  H j , j  NC

A MILP model is developed to formulate the potential matches between the hot and cold process streams and generate optimal set-points from the supervisory level optimization. The data used to illustrate this model is listed in Table 1. Table 1. Process stream data

- For each stream at each stage:

Stream

for l  1, 2,…, N S

H1 H2 C1 C2

NC

(mC p )i (Ti ,inl  Ti ,out l )   Qi , j ,l , i  N H

(4)

j 1 NH

in (mC p ) j (T jout ,l  T j ,l )   Qi , j ,1 , j  N C i 1

(mC p ) j (T

b)

out j

(5)

 T )  H j , j  NC Ns j

Temperature

Tout (K)

443 423 293 278

333 313 353 348

Enthalpy (kW) 77 110 -102 -91

In order to decide the optimal ΔTmin simultaneously with the network configuration, two stages are considered in this formulation that equals the minimum number of hot streams or cold streams in this case (Ciric and Floudas (1991)).

- Assignment of inlet temperatures:

Ti ,0  Ti in , i  N H

Tin (K)

Before demonstrating the proposed methodology, a pinch point and first-law analysis for the specific HEN is conducted as shown in Fig. 4 to assist understanding of the problem. The minimum approach temperature between hot and cold streams ΔTmin is set as 20K. As a result, the pinch temperatures are at 313K for hot streams and 292K for cold streams, and the minimum utility targets are 4.1 kW hot utilities in total with 0 kW cold utilities required.

- Utility matches: (mC p )i (Ti Ns  Ti out )  Ci , i  N H

mCp (kW/K) 0.7 1.0 1.7 1.3

(6)

T j ,0  T , j  NC in j

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443

423

423

403

373 368

353

333

313

313

293

H 5  40 kW

278

H 5  19.5 kW

H1  14 kW H 2  50 kW

H1

H2

0. 7 kW/K

1.0 kW/K

0 0 0 0 2.94

0 0 0 2.94 0

91.5 0 0 2.94 0

H 3  0 kW

348

298

91.5 0 0 2.94 0

Q_H2_C2_2 Q_H1_W Q_H2_W Q_C1_S Q_C2_S

Temperature (K)

595

H 4  45.5 kW

C1 C2 ΔTmin =20K 1.7 kW/K 1.3 kW/K

Fig. 4. Pinch point and first-law analysis for the given streams.

A receding horizon optimization can repeatedly optimize the control inputs and plan actions over a finite time-span into the future to deal with uncertainties. Here, we adopt a one-hour horizon length so that the weather information and electricity pricing are updated on an hourly basis. The electricity generated from renewables bears the priority of utility placement due to the low cost of wind and solar energy. Using the actual weather data and time-varying pricing information to purchase electricity from the grid (see Fig. 5), the reliability of applying a hybrid cogeneration system can be improved through hourly forecasting and update of available solar and wind energy, as well as the cost of purchasing electricity. 500 450

Cost to buy electricity from the grid ($/kWh)

Solar Wind

C1

(293 K) 78.8 kW

20.4kW

H1

E1

0.231

(443 K)

0.224

400 Electricity Generation (kW)

Fig. 6. Optimal heat-exchanger networks under real-time conditions over a day.

(333 K) 20.4 kW

0.200

E2

350

C2

(278 K)

H2

300

(313 K)

91.5 kW (423 K) E3

250

(348 K)

200

(351 K)

150 2.94 kW

100

S3 (353 K)

50 0 0

4

8

12 Time (hour)

16

20

24

(a) Configuration 1 (Off-peak hours) C1

Fig. 5. Renewable generation and electricity price from the grid over a typical summer day in the Sacramento Valley.

(293 K) 78.8 kW

By minimizing the total cost with the set of constraints stated in Section 2, the results of heat duties and temperature setpoints according to the optimal solution can be achieved and are shown in Table 2 and Fig. 6, respectively.

23.4kW

H1

E1 (443 K)

(333 K) 23.4 kW E2

C2

(278 K)

H2

Table 2. Results of MILP optimization

(313 K)

91.5 kW (423 K)

Heat duty (kW) Q_H1_C1_1 Q_H1_C1_2 Q_H1_C2_1 Q_H1_C2_2 Q_H2_C1_1 Q_H2_C1_2 Q_H2_C2_1

0:00 – 11:00 0 78.8 0 0 0 20.5 0

11:00 – 14:00 78.8 0 0 0 23.4 0 88.5

14:00 – 17:00 78.8 0 0 0 20.5 0 91.5

E3

17:00 – 24:00 0 78.8 0 0 0 20.5 0

(345 K) (353 K)

2.94 kW S2

(348 K)

(b) Configuration 2 (Peak-hours) Fig. 7. Two different HEN sub-structures at different times of a day. 596

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The optimal results for time periods 0:00 – 11:00 and 17:00 – 24:00 yield exactly the same HEN structure, which corresponds to configuration 1 in Fig. 7. The peak-hour (11:00 – 14:00) operation with high renewable energy output leads to a different strategy as demonstrated by configuration 2 in Fig. 7. Notice that although the numerical solution returns a different optimal set for the time period 14:00 – 17:00, the realized configuration of HEN substructure is actually the same as the one during 0:00 – 11:00 or 17:00 –24:00, considering the multi-stage formulation of Q and T as variables at the same time. As a result, there are only two operational states within a day, and the structural transitions occur at 11:00 and 14:00 hours.

transition process for further quantitative analysis. The flow diagram in Fig. 9 demonstrates the super HEN structure which uses valves and splitters to provide possibilities of bypasses and splitting and encompasses potential sub-structures. In the absence of any control structures, the system will exhibit open-loop behaviour. For the first structural change, the outlet temperature of cold stream 1 increases from 351K to 353K, and cold stream 2 decreases from 348K to 345K. The required actions are setting the position of valve V3 from 50% to 62% opening, then V4 50% to 46% at the same time. As can be seen from the open-loop temperature profiles in Fig. 10 (black and blue lines), the system is able to meet the targets regardless of the performance. After the peak-hour periods, the temperatures can be reset to initial states. However, if some variations appear with respect to flow rates or temperature, the system can no longer keep operating at the optimal state. As also shown in Fig. 10, at time 19:00, the inlet temperature of hot stream 2 has a sudden increase by 10K caused by process variations, the open-loop system cannot meet the targets set by the optimal operation trajectory.

With this switching scheme, the minimal cost of the system is shown is Fig. 8. During the mid-day when the renewable generation is high, the plant can even make a profit from selling electricity back to the grid.

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Fig. 8. Optimal real-time economic performance over a day.

4. DYNAMIC CONTROL Although online optimization can provide the theoretical setpoints to be implemented, it may lead to too frequent transitions during the dynamic operation, or the operation may even become infeasible. Dynamic models are necessary for further control and optimization if the transitions are not assumed instantaneous but incur some cost and expend energy. Heat-exchangers are complex devices for which the prediction of their operation from first principles is virtually impossible. As a result, process simulation tools such as Aspen Plus® can be utilized to demonstrate their potential especially when simulating dynamic behavior.

Fig. 9. The super HEN structure corresponding to the optimal results.

The control variables in a HEN system are of three kinds: (a) process stream bypasses around heat-exchangers, (b) utility stream flow rates in service units and (c) splits of process streams. The addition of the new splitters or bypasses can provide the HEN more flexibility so that some functionally uncontrollable problems can be solved. However, the bypasses or splits will change the configuration of the network, leading to transitions which may be time- and energy-consuming. Although in this two-hot-two-cold stream case study, the optimal configuration at each time step can be realized within reasonable time due to its simplicity, and justifies neglecting the transition-state cost, it is still necessary to study the

Fig. 10. Dynamic behaviours of the system switching between different states with open-loop and closed-loop structures.

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To better deal with process disturbances, local controllers are necessary. Two key components in charge of the temperature transitions are the temperature controllers TC_1 and TC_2 for cold streams 1 and 2, respectively. In order to drive the outlet temperature of cold streams to the targets, the manipulated variables can be either the hot or cold stream inlet flow rates. By changing the valve positions (direct acting, air-to-open for cold stream inlet and reverse, air-to-close for hot stream), the outlet temperature of the cold streams will vary to meet the setpoints. For the temperature control, properly-tuned Proportional-Integral (PI) controllers were designed to orchestrate the required sub-structure re-configuration. As indicated in Fig. 10 for the closed-loop temperature profiles (green and red lines), the settling time can be shortened compared with the open-loop system at the two switching times. And more importantly, when there are any disturbances, the set-points can always be tracked. Thus, the fast and effective substructure changes can be realized, and stable operation of the HEN can also be guaranteed when there are no configuration changes.

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Dipama, J., Teyssedou, A., & Sorin, M. (2008). Synthesis of heat exchanger networks using genetic algorithms. Applied Thermal Engineering, 28(14), 1763-1773. Floudas, C. A. (1995). Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press, New York. Glemmestad, B., Skogestad, S., & Gundersen, T. (1999). Optimal operation of heat exchanger networks. Computers & chemical engineering, 23(4), 509-522. González A H, Odloak D, Marchetti J L. (2006). Predictive control applied to heat-exchanger networks. Chemical Engineering and Processing: Process Intensification, 45(8): 661-671. Gorji-Bandpy, M., Yahyazadeh-Jelodar, H., & Khalili, M. (2011). Optimization of heat exchanger network. Applied Thermal Engineering, 31(5), 779-784. Gundepsen, T., and Naess, L. (1988). The synthesis of cost optimal heat exchanger networks: an industrial review of the state of the art. Computers & Chemical Engineering, 12(6), 503-530.

5. CONCLUSIONS AND FUTURE WORK This paper introduced a proactive methodology to re-configure in real-time the optimal operation and control strategies of a HEN within a given super structure. In the proposed hierarchical approach, a steady-state optimization decides the real-time operation rules under varying renewable energy generation and electricity pricing, while local controllers orchestrate the required structural changes to realize the optimal strategy. Significant economic benefits with respect to plant energy cost can be achieved through the new operational scheme.

Lersbamrungsuk, V., Srinophakun, T., Narasimhan, S., & Skogestad, S. (2008). Control structure design for optimal operation of heat exchanger networks. AIChE Journal, 54(1), 150-162. Linnhoff, B., & Flower, J. R. (1978). Synthesis of heat exchanger networks: I. Systematic generation of energy optimal networks. AIChE Journal, 24(4), 633-642. López-Maldonado, L. A., Ponce-Ortega, J. M., & SegoviaHernández, J. G. (2011). Multiobjective synthesis of heat exchanger networks minimizing the total annual cost and the environmental impact. Applied Thermal Engineering, 31(6), 1099-1113.

Based on this preliminary study, a number of future research directions remain to be explored. A more complex case study demonstrating how to handle additional streams in a complex HEN is under study to fully demonstrate the re-configuration process. Furthermore, the steady-state objective function can incorporate other important factors such as the explicit equipment cost at the design stage and the transition cost in the dynamic operation to yield a more comprehensive formulation. In addition, in lieu of simple PI controllers, model predictive control can add value to link the supervisory optimization and local tracking considering its strength in handle the necessary forecasting and model updates. Finally, energy storage can be considered as an integral part of the reconfiguration strategy to manage the transition cost in a more realistic manner.

Wang, X., Teichgraeber, H., Palazoglu, A., & El-Farra, N. H. (2014). An economic receding horizon optimization approach for energy management in the chlor-alkali process with hybrid renewable energy generation. Journal of Process Control, 24(8), 1318-1327. Yee, T. F., & Grossmann, I. E. (1990). Simultaneous optimization models for heat integration—II. Heat exchanger network synthesis. Computers & Chemical Engineering, 14(10), 1165-1184. Zamora, J. M., & Grossmann, I. E. (1998). A global MINLP optimization algorithm for the synthesis of heat exchanger networks with no stream splits. Computers & Chemical Engineering, 22(3), 367-384.

REFERENCES Aguilera, N., & Marchetti, J. L. (1998). Optimizing and controlling the operation of heat‐exchanger networks. AIChE Journal, 44(5), 1090-1104. Ciric, A. R., & Floudas, C. A. (1991). Heat exchanger network synthesis without decomposition. Computers & Chemical Engineering, 15(6), 385-396.

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