Methodology for maximising the use of renewables with variable availability

Energy 44 (2012) 29e37

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Methodology for maximising the use of renewables with variable availability Andreja Nemet a, *, Jirí Jaromír Klemes a, Petar Sabev Varbanov a, Zdravko Kravanja b a Centre for Process Integration and Intensification e CPI2, Research Institute of Chemical and Process Engineering, Faculty of Information Technology, University of Pannonia, Egyetem utca 10, 8200 Veszprém, Hungary b Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova ulica 17, SI-2000, Maribor, Slovenia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 October 2011 Received in revised form 22 December 2011 Accepted 23 December 2011 Available online 25 January 2012

A problem when exploiting renewable energy sources, such as wind and solar radiation, is their fluctuating availability. In the presented work, the Heat Integration methodology for batch processes based on Time Slices has been extended to cover the integration of solar thermal energy, thus allowing for dealing with such variations. A procedure for identifying the number and durations of Time Slices for a problem featuring variable renewable energy supply has been formulated, and developed for solar energy utilisation. The main procedural steps involve partitioning of the measured/forecasted heat availability profile using a large number of candidate time boundaries, and then approximating it by a piecewise-constant profile using high-precision. The approximation profile is obtained by subjecting the candidate superset of time-boundaries to MILP optimisation, thus minimising integral inaccuracy compared to the forecasted availability profile. The Time Slice definitions are completed by approximating the heat loads within the Time Slices. The integration of solar thermal energy can be performed for the specified Time Slice, after the optimal number of Time Slices with approximated constant load has been selected. Using heat storage, the heat can be transferred between Time Slices.
2011 Published by Elsevier Ltd.

Keywords: Variations of renewables Renewable availability curve Integration of solar thermal energy Time slices Heat integration

1. Introduction

(ii) A multi-period model involving a series of steady-states, associated with time intervals within the modelling horizon.

An accelerating development of those techniques, methodologies and equipment for exploiting solar energy has taken place, recently. This new development helps to improve the existing technology. An example of this is a water desalination process with integrated solar energy [1]. A lot of attention towards the use of solar energy has focused on photovoltaic panels for producing electricity. There is also a significant potential for utilising solar irradiation as heat. Generally, thermal solar capture frequently offers a higher efficiency compared to photovoltaic panels. The integration of renewables into a process system or another energy use needs a specific approach due to those variations in energy supply availability from renewable sources, as well as fluctuations in the users’ energy demands. Two approaches can be used for integrating renewables and accounting for this variability: (i) A dynamic model optimisation.

formulation,

followed

by

* Corresponding author. Tel.: þ36 88 421 664. E-mail address: [email protected] (A. Nemet). 0360-5442/$ e see front matter
2011 Published by Elsevier Ltd. doi:10.1016/j.energy.2011.12.036

dynamic

The advantage of dynamic models is that they describe the systems’ behaviour very precisely. They are usually employed to solve servo- and regulatory tasks during process control. There are dynamic models that describe those plants using solar thermal energy as a utility [2]. There are several models estimating the solar irradiation [e.g. Refs. 3 and 4], and just a few models estimating the available solar thermal heat and available electricity [5]. Moreover, these models only evaluate a part of the whole capture system, for example, just thermal energy storage [6]. However, dynamic models are unsuitable for design or long-horizon operational optimisation. In the second class of models, assuming steady-states, models are simpler and yet still capable of describing the systems with acceptable accuracy. As some of the variables are discretised, the computational time becomes much shorter. Moreover, the dynamic models might become too complicated for solving larger systems. For such cases, the steady-state models may be the only way to describe the phenomena. The Heat Integration of batch processes is a well described field of research, which uses steady-state. In batch processes, energy demands vary over time. In order to account for these variations,

30

A. Nemet et al. / Energy 44 (2012) 29e37

Batch Process Integration was formulated by Kemp and Deakin [7] who developed two models: (i) Time Average Model, where the heat loads are averaged through the time horizon, and (ii) Time Slice Model, where the Time Slices are obtained by combining the starting and ending time points of the involved process streams. In these Time Slices the Heat Integration can be performed in the same manner as for the continuous processes. A detailed description can be found in Ref. [8]. A batch process scheduling method using mixed integer linear programming (MILP) formulation with heat integration was another step in exploiting batch process heat integration [9]. A similar formulation of the problem was also used to design a Heat Exchanger Network (HEN) [10]. In addition, different, more combinatorial approach, based on the S graph, for batch process scheduling has been developed [11] where also scheduling influence on the HEN synthesis is presented. To enable the integration of heat storage into the system design, combined with pinch analysis, another combinatorial approach, using time decompositions of the processes, has been moreover introduced [12]. Majozi [13] developed a mathematical model for optimising energy usage for multi-purpose batch plant. The evolution of batch heat exchanger network was described by Foo et al. [14]. The methodology of time decomposition was recently extended by Varbanov and Klemes [15] for analysing Total Sites using the integration of renewables. A variety or research works dealing with process integration, including the integration of batch processes, can be found in the thorough review presented by Friedler [16,17]. On the other hand, Ludig et al. [18] modelled a power system model, where they investigated 14 different technologies for producing electricity. They evaluated optimal technology-mix from the viewpoint of cost. An interesting part of this work was how they dealt with the variations of renewable energy sources e.g. wind, hydro, solar. They created equal-length time slices and averaged the load of supply within the time slice. In contrast within the framework present in this work the time horizons of the Time Slices (TSs) and the supply load are a result of a two-stage optimisation. It is a systematic approach compared to the heuristic used previously. The focus of previous work in the field of varying heat supply and demand was either on a variation of the process demand or the energy availability from renewable sources. This current work describes a model and a procedure for integrating solar thermal energy, using processes where both the renewable energy supply and the process energy demands vary. An analogy from batch process integration is used. TSs with loads that are assumed to be constant, are developed for varying the availability of solar thermal energy. The application of TSs, to the problems of integrating renewables into those processes with variable heat demand, can be further extended. The framework for integrate solar thermal energy contains several steps:  Heat recovery within batch processes  Identifying the number of TSs and the values of the TS boundaries for solar irradiation  Estimation of the supply loads  Combination of TSs for process demand and solar thermal energy  Integration of solar thermal energy within each combined TS  Estimation of storage size

2.1. Problem formulation The inaccuracy of the approximation decreases with any increase in the number of TSs. On the other hand, the aim is to minimise the number of time slices, in order to simplify the computations in the following steps of the integration procedure. Acceptability of the resulting time slices and their properties varies from one system to another. It can be expressed at an errorlevel acceptable to the energy systems’ designers. Therefore, the task to be performed can be defined as obtaining the minimum number of TSs with acceptable accuracy. The solar irradiation (G) measurements or the temporal variation of the captured heat flow could be used in order to identify the TS for solar energy availability.

2.2. Approximation of the irradiation profile This procedure is based on optimising the load-levels and selecting items from a discrete superset of candidate time boundaries. These represent the measured Solar Irradiation e G data by constructing a high-precision piecewise-constant profile [19] (Fig. 1). When using a large number of time-intervals, the inaccuracy of this transformation is minimised, and can be neglected. However, this high-accuracy would computationally require very intensive integration because the integration of solar thermal energy has to be performed within each time interval. Therefore, the piecewiseconstant load profile to be obtained has to contain a significantly smaller number of TSs. This can be achieved by a suitable approximation of the irradiation profile. The supply is approximated separately at each time-interval by the minimisation of any inaccuracy represented by those areas occurring between the approximated and real input-supply profiles (Fig. 2). The boundaries of the time-intervals are the candidate boundaries for the final TSs. If there is a difference between two

G /W m-2 600 500

measured data

400

discretization

300 200 100 0 4

6

8

10

12

14

16

18

t/h

Fig. 1. Discretisation of the measured profile/input data for optimising the number of TSs.

The application of this procedure is illustrated within a case study. 2. Determining the number of TSs The trade-off between the inaccuracy and number of TSs should be evaluated, in order to determine the number of TSs.

Fig. 2. Determining the inaccuracy between the input and approximated supply.

A. Nemet et al. / Energy 44 (2012) 29e37

consecutively approximated supply levels, the time-boundary is also a TS boundary. However, when two time-intervals are joined into one TS, the approximated supply-levels should be equal at both time intervals and the time-interval period boundary candidate is deselected as a TS boundary (Fig. 3).

2.3. MILP model formulation A two-stage MILP model has been developed for minimising the number of TSs at acceptable inaccuracy. At the first stage, the number of TSs is minimised, depending on the tolerance of inaccuracy specified by the models’ user. At the second stage, the inaccuracy is minimised at a fixed minimum number of TSs, determined at the first optimisation stage. Initially there is NI number of time-intervals and, hence, NI þ 1 boundaries of time-intervals indexed by the following index and set: Index i for the time-boundaries of the time-intervals, i ˛ I The difference between the real input-supply and approximatedsupply is calculated in each time period separately:

SDi ¼ RSi eASi

ci˛I

(1)

31

ASiþ1  ASi  LV$yi

ci˛I;

isNI þ 1

(5)

To present the selected TS boundaries the binary variable is multiplied with the observed time period boundary:

TSi ¼ yi $tiþ1

ci˛I;

isNI þ 1

(6)

The number of TSs is obtained from Eq. (7). One is add to the sum of selected TS boundaries as the TS boundaries at the beginning and at the end of the observed time horizon were excluded within the model:

X

NTS ¼

yi þ 1

(7)

i ˛ I ; i s NI þ 1

The inaccuracy in each time-interval is determined by multiplying the positive difference between the real and approximated supply with time horizon of the time-interval.

INi ¼ EDi $ðti  ti1 Þ

ci˛I;

isNI þ 1

(8)

The overall inaccuracy is a result of summation of inaccuracies over the time-intervals:

INA ¼

X

INi

(9)

i ˛ I ; i s NI þ 1

Because the difference SDi can have a positive or negative value, it can be represented as the difference between the positive variables PDi and NDi:

and this overall inaccuracy is constrained and should be less than or equal to the 3 fraction of the initial amount of solar irradiation presented as an area (A0) below the measured profile of Fig. 1:

SDi ¼ PDi eNDi

INA  ε$A0

ci˛I

(2)

Note when the SDi has a positive value, the NDi is zero, as a result of minimising the inaccuracy. When SDi has negative value, the PDi is zero. For minimal inaccuracy the difference between the real and approximated supply should be the lowest possible.

EDi ¼ PDi þ NDi

ci˛I

(3)

In Eq. (3) the positive value is obtained for the difference between real and approximated load of supply. Further equations are related to the accepting/rejecting of the time-interval boundary as a TS boundary. The decision is made by the binary variable yi. When there is a positive (Eq. (4)) or negative difference (Eq. (5)) between the two consecutively-approximated supply loads, there is a TS boundary and the value of yi is 1. If there is no difference between these supplies, there is no TS boundary and the value of yi is 0.

ASiþ1  ASi þ LV$yi

ci˛I;

isNI þ 1

(4)

A0 ¼

X

(10) ððtiþ1  ti Þ$RSi Þ

(11)

i ˛ I ; i s NI þ 1

2.4. Optimisation procedure Optimisation is performed over two stages. In the first stage of optimisation, Eqs. (1)e(11) are used with the objective of minimising the number of TSs as follows:

minzI ¼ NTS

(12)

This step requires specifying the acceptable error-level (tolerance) 3 . The result from optimisation is the minimal number of TSs, min NTSI required to meet any constraint about the inaccuracy limit (Eq. (10)). However, after the first stage, the inaccuracy is not optimal. In order to obtain a further reduction of inaccuracy, in the second

NTS 45 40 35 30 25 20 15 10 5 0 0 Fig. 3. Acceptance/rejection of the candidate time period boundary as a TS boundary.

5

10

15

Fig. 4. Selecting an acceptable inaccuracy.

INA/ %

32

A. Nemet et al. / Energy 44 (2012) 29e37

z ¼ w$NTS þ INA

(15)

2.5. Selecting the number of TSs Selecting the number of TSs depends on the accuracy required. Fig. 4 presents the obtained results at different tolerances selected and optimised. As can be seen from Fig. 4, by increasing the tolerance the number of TSs decreases but, however, the inaccuracy becomes too high. On the other hand, if the tolerance is too small, the number of TSs might become too high and, hence, the further steps of integration would be too complex; however, no significant improvement may be achieved. Generally, a tolerance of between 5 and 10% should be acceptable.

Fig. 5. Simplified scheme for the integration of solar thermal energy.

stage of optimisation the same model using Eqs. (1)e(11) is used together with an additional equation (Eq. (13)), which fixes the number of TSs, and the objective as expressed in Eq. (14):

NTS ¼ minNTSI

(13)

minzII ¼ INA

(14)

Optimisation could also be performed over one stage as sometimes it is faster. In this case, the objective function would be a weighted sum of number of Time Slice (NTS) and overall inaccuracy (INA) with a high enough weight w (e.g. 10,000) for NTS, in order that the minimised NTS has priority over the minimum of INA.

3. Estimating the supply loads The supply of the loads is determined separately in each TS. Estimation of the supply-loads depends on the capture system. Different kinds of systems are possible, or even a system coupled with heat pump [20]. A simplified scheme for capture was assumed during this work (Fig. 5). The heat transfer from the collectors in this model can be (i) direct or (ii) indirect. Direct heat transfer is feasible, when solar thermal energy is available and there is a demand in the evaluated TS. If the amount of heat is higher than the demand or the heat transfer is unfeasible in one TS than the heat is transferred to a storage. This heat will be

A

B

C

Fig. 6. Gantt chart for those TSs for supplying A) Solar thermal energy, B) Heat demand and C) Combined for both.

A. Nemet et al. / Energy 44 (2012) 29e37

33

Table 1 Streams for case study [7]. Stream no and type

TS,  C

TT,  C

CP, kW  C1

tstart, /h

tend, h

1. 2. 3. 4.

25 55 140 130

110 115 35 15

10 8 4 3

12 6 0 6

16 24 12 19

Cold Cold Hot Hot

TC ¼

Tin þ Tout 2

(17)

The efficiency also depends on the ambient air temperature. It is the average temperature of the air in each TS separately. 4. Integration of solar thermal energy Fig. 7. Integration of solar thermal energy in one combined TS [22,23].

4.1. Combining the supply and demand available for covering any heat demand in the following TSs. The indirect heat transfer is the described transfer through storage. In order to determine the heat load for direct transfer of solar thermal energy to the process, the irradiation load was multiplied by:  The area of collectors and  The efficiency of the solar collector system. The area usually depends on the investment and the available area of the collectors. Solar collector efficiency varies significantly with changes in the quantities of solar radiation (G), ambient air temperature (TA), and the average internal fluid temperature (TC) [21]:

a1 ðTC eTA Þ þ a2 ðTC eTA Þ2 G

hC ¼ hO e

(16)

when hO is the optical efficiency of the collector and a1 and a2 are the solar collector thermal loss coefficients, which are usually determined experimentally. During the first stage of the evaluation the average fluid temperature can be assumed as arithmetic average of the inlet and outlet temperatures of the collectors [21]:

The first step when combining the supply and demand was determining the TSs for any fluctuating load of solar thermal energy. However, many processes have fluctuating demands. Therefore the solution is to also create TSs as developed for the batch processes [7]. A combination of these two types of TSs can be seen in Fig. 6. The TS boundaries for solar thermal energy and for those processes varying demand are joined together to the combined TS boundaries. 4.2. Integration with the Grand Composite Curve (GCC) Integration of the solar thermal energy should be performed after the combined Time Slices (cTSs) are obtained. The Grand Composite Curve (GCC) [22,23] can be used for the integration of solar thermal energy (Fig. 7). This is not, however, the only option. The use of Total Site analysis [24] and especially a Total Site with renewable sources of energy, including solar thermal energy [25,26], would be an efficient approach when analysing heat recovery and the integration of solar thermal energy. 4.3. Hierarchy for covering heat demand In each Time Slice, there are three different sources of utilities. The following hierarchy [25,26] should be followed in order to cover the heat demand: i) Heat recovery should be maximised. ii) The use of solar thermal energy via direct heat transfer from collectors e immediately, when available. iii) Usage of the energy from the storage-indirect heat transfer of solar thermal energy. iv) As a backup utility with constant availability is required.

Fig. 8. Transferring solar heat from one combined TS to another [7,26].

Thus, integration using direct transfer of solar thermal energy within TS is then performed, after heat recovery. If there is unused heat from the solar source, it is transferred to storage. The solar thermal energy can be unused for different reasons. One is the surplus of solar thermal energy, and the other is a higher demanded temperature than the temperature of heat available from the solar source. The stored heat will be available in other TSs (Fig. 8). This is an indirect way of using the solar thermal heat.

34

A. Nemet et al. / Energy 44 (2012) 29e37

12 - 16 h

6 - 12 h

0- 6 h

T*/ °C

T*/ °C

T*/°C

120

120

120

100

100

80

80

80

60

60

60

40

40

40

20

20

20 0

0

0 0

ΔH/ kW

200

0

16 - 19 h

T*/ °C

100

120

100

100

80

80

60

60

40

40

20

20

0

100

200

kW 300 ΔH/ 400

200

ΔH/ 300 kW

0

250

500

750 ΔH/ kW

19- 24 h

T*/140 °C

120

0

100

heat recovery pocket

0 0

200

kW 400 ΔH/600

Fig. 9. GCCs for each TS separately.

When all the available solar thermal heat from the direct and indirect transfers is integrated, the rest of the demand should be covered by those utilities with constant availability.

5. Case study 5.1. Heat recovery In this case study, the varying demand was presented by the batch process [7]. The streams are presented in Table 1. The Time Slices from the heat demand were the starting and ending times of the streams or changes in the loads for heat demand. The heat recovery was performed. It was done by using Problem Table Algorithm. The Grand Composite Curves (GCCs) for each TS obtained separately are presented in Fig. 9.

G /W m-2

measured data

600 500 400

In the first TS there was an excess of heat, which may be used in the following TS. In the second TS there was a heat recovery pocket (Fig. 9). There was also an excess of heat; however the temperature of the available heat was quite low, below 60  C. There was a significant heat demand in the TS of between 12 h and 16 h. There was also some heat surplus; however, its temperature was too low, 10  C, to be usable in the following TS. In the TS of between 16 h and 19 h, the demand was also significant and there was also an opportunity to store the heat, but the temperature was low. In the last TS, there was just heat demand and no surplus of heat.

5.2. Creating a TS for solar thermal energy The input real-supply profile is presented in Fig. 1 (in Section 2.2). This presents the daily irradiation. The data was taken for a typical summer day in Central Europe. The time-period of the

ΔH / kW

discretization

600

result of optimisation

500 400

300

300

200

200

100

100 0

0

4

6

8

10

12

14

16

Fig. 10. TS boundaries for irradiation.

18

t/h

5

7

9

11

13

15

17

Fig. 11. TSs and approximated loads for solar thermal energy.

t/ h

A. Nemet et al. / Energy 44 (2012) 29e37

5.4. Integration of solar thermal energy

demand TS solar TSs

cTSs

0

2

4

6

35

8

10

12

14

16

18

20

22

/h t24

Fig. 12. Combining the TS together from the Solar TSs and heat demand TSs.

irradiation was from 5:22 to 19:22 as there was no irradiation before or after this period. It was a 14 h time-horizon and the measurements were taken every 15 min. This resulted in 56 measurements [24]. The discretisation of the irradiation can be seen in Fig. 1. The optical efficiency of the tube collectors was h0 ¼ 76%, the coefficients a1 ¼1.53 W m2 and a2 ¼ 0.0003 W m2 [21], the inlet and the outlet temperatures of the solar collector media were 70 and 90  C, respectively, and the area of the solar collectors was 150 m2. The selected acceptable tolerance in this Case Study was 10%. The optimal number of TSs, obtained by the proposed MILP model, was 8. It was an important achievement, as the initial number of time-intervals from the measurements was 56. The minimal inaccuracy at this number of TSs was 9.4%. The TS determined for the irradiation can be seen in Fig. 10. The results, obtained for TS for irradiation, suggested 8 TSs. However, when determining the efficiency of the capture system in the first and last TSs capture of the heat was impossible, as the irradiation was too low. For this reason the number of TSs with a constant load of supply was, in this case 6. Fig. 11 presents the final approximated load profile for the supply of solar thermal energy, and the TS boundaries.

5.3. Combining the TSs After obtaining TSs the (i) heat demand variations and (ii) solar thermal energy supply were joined. In order to combine them, the time-boundaries from both TSs were listed and any duplicates (if existing) were eliminated. As can be seen in Fig. 12, in this case study there were 5 TSs (with 6 time boundaries) from the heat demand and 6 (with 7 time boundaries) from the solar thermal energy supply. Combining them results in 12 cTSs (with 13 time boundaries). This case study clearly showed how important it is to reduce the number of TSs for solar thermal energy supply.

In all the cTSs the heat recovery is done first, as described in the hierarchy for covering heat demand (Section 4.3). The hot utility requirement after heat recovery, DHUR, and the excess of heat, DHE, are shown in Table 2. The next step is to integrate the available solar thermal energy, DHSTE, in the observed TS in order to determine the load of the direct heat transfer of the solar thermal energy, DHDTE. The load of heat demand at the feasible temperature of the heat transfer is also obtained. From these two calculated loads, the amount of exchanged heat and the load of heat transferred to or from the storage of solar thermal energy can also be specified. Another source of heat can also be excess heat, which can also be stored if the temperature allows it. For simplicity, an isothermal storage is assumed. As the time horizon when using the storage is short, it is not far from a real situation. As backup, at least one hot, DHHU, and one cold, DHCU, utility are required, with constant availability. As can be seen from Table 2, not all of the heat demand can be covered from solar thermal energy, because the temperature of the capture is often lower than some of the heat demands. This is also a reason for using a utility with constant availability. The amount of hot utility needed after the recovery is 7435 kWh. This amount is calculated by multiplying the load by the time horizon of the TS. By direct heat transfer from solar thermal energy 2000 kWh can be covered and 1140 kWh can be covered from indirect heat transfer using storage. This means that the demand 3140 kWh can be covered with the solar thermal energy, which is 42.2% of the overall heat demand. The rest of the demand, 4295 kWh, should be still covered from the utility with constant availability. However, the dependency on fossil fuels should be decreased as much as possible, since this energy source has an impact on the environment. 5.5. Determination of storage size In order to estimate the storage size, the amount of the heat stored or used should be determined in each cTS separately e.g. the heat stored at the cTS1 is DH ¼ 220 kW∙6 h ¼ 1320 kWh (Table 2, storage column and Fig. 13). These calculated amounts of heat are presented in the boxes of Fig. 13. The cumulative amount of stored heat is represented by the numbers outside the boxes (Fig. 13). Fig. 13A presents the initial cumulative heat stored. As can be seen, in the last cTS12 the amount of stored heat amount is more than zero. This indicates that smaller storage would be also sufficient. The smallest storage, at which the heat recovery remains the same, would be when the cumulative amount stored at the last cTS is equal to zero (Fig. 13B).

Table 2 Determining the load of solar thermal energy supply and the utility with constant load. cTS

After recovery

Solar thermal energy

Storage from

Duration, h

DHUR, kW

DHE, kW

DHSTE, kW

DHDHT, kW

DHE, kW

0:00e6:00 6:00e6:22 6:22e7:37 7:37e8:52 8:52e10:07 10:07e12:00 12:00e14:22 14:22e16:00 16:00e16:07 16:07e17:22 17:22e19:00 19:00e24:00

e e e e e e 1045 1045 285 285 285 480

420 285 285 285 285 285 60 60 150 150 150 e

e e 57.1 273 461 607 607 402 402.1 157.4 e e

e e e e e e 510 402 100 100 e e

220 e e e e e e e e e e e

Constant available utility

DHSTE, kW e 57.1 273 461 607 97 108 302.1 57.4 100 160

DHHU, kW

DHCU, kW

e e e e e e 535 535 185 185 185 320

200 285 285 285 285 285 60 60 150 150 150 e

36

A. Nemet et al. / Energy 44 (2012) 29e37

Fig. 13. Cascading the amount of heat in storage through different Time Slices at A) maximal storage and B) reduced storage.

The storage for this case study should be large enough to store 1032.4 kWh heat. The result was determined by the maximal amount of heat within the cascade. 6. Conclusions and future work In the presented paper a framework for the integration of solar thermal energy with processes featuring varying demand has been developed. By applying this framework, the amount of solar thermal energy can be determined, which can be potentially used within the process. As part of the algorithm, the current work offers a systematic procedure capable of identifying Time Slices with assumed constant solar thermal energy supply. It is an important step, because to date the Time Slices have mostly been detected heuristically, usually with equal length. However, the solar irradiation varies unevenly and the inaccuracy in such a model was high. The current model enables the user to set the accuracy wanted at the stage of analysis. Higher accuracy will result in larger number of TSs. The presented case study, using utility demand as a base case, illustrated that the demand for a utility with constant availability (usually a fossil fuel) can be reduced by up to 27% by utilising solar thermal energy directly, without any storage. A further decrease of up to 15% (on the same basis) can be achieved by introducing thermal energy storage. The combined reduction of hot utility resulting from these two steps is about 42%. It is a significant

decrease, which should be encouraging taking solar thermal energy in consideration, during the designing of a utility system. The formulated algorithm offers a simple and fast approach with the accuracy left available as a degree of freedom for the user. Another important step for achieving better solutions is the simultaneous evaluation of heat supply and demand. In the future, automation of the developed framework will be pursued. As a further methodology development, shifting process operations in time (rescheduling) should be considered, in order to achieve as a high usage of direct transfer from solar thermal energy, as possible. Acknowledgements The financial support is gratefully acknowledged from the EC FP7 project “Intensified Heat Transfer Technologies for Enhanced Heat Recovery e INTHEAT”, Grant Agreement No. 262205 and Társadalmi Megújulás Operatív Program (TÁMOP-4.2.2/B-10/12010-0025). Nomenclature

DHCU DHDTE DHE DHHU

cold utility requirement, with constant availability, kW direct heat transfer the solar thermal energy to process, kW excess of heat after heat recovery, kW hot utility requirement, with constant availability, kW

A. Nemet et al. / Energy 44 (2012) 29e37

DHSTE DHUR A0 a1, a2 ASi CP cTS EDi

G GCC HEN I i INA INi LV MILP NDi NI NTS PDi RSi SDi t TA TC tend ti Tin Tout TS TS TSi tstart TT yi z zI zII 3

h0 hC

available solar thermal energy, kW utility requirement after heat recovery, kW initial overall amount of irradiation, kWh m2 solar collector thermal loss coefficients, W m2 approximated supply over time-interval i, W m2 heat capacity flowrate, kW  C1 combined time slice the positive and negative difference between the real and approximated supplies together over time-interval i, W m2 solar irradiation, W m2 Grand Composite Curve Heat Exchanger Network set of time boundaries time boundaries of time intervals overall inaccuracy, kWh inaccuracy within time-interval i, kWh large value, maximum difference between real and approximated difference mixed integer linear programming positive difference between the real and approximated supply over time-interval i, W m2 number of time-intervals number of Time Slices positive difference between the real and approximated supply over time-interval i, W m2 real supply irradiation over time-interval i, W m2 supply difference over time-interval i, W m2 time, h ambient air temperature,  C average internal fluid temperature,  C ending time of the heat demand, h time period boundary of time-interval i, h inlet temperature for collectors,  C outlet temperature for collectors,  C Time Slice supply temperature of streams,  C Time Slice boundary, h starting time of the heat demand, h target temperature of streams,  C binary variable, selection of whether the time period boundary is a TS boundary objective function first stage objective function second stage objective function tolerance, % optical efficiency of the collector, % efficiency of the collector, %

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