Minimal heating and cooling in a modern rose greenhouse*

4th IFAC Conference on Modelling and Control in Agriculture, Horticulture and Post Harvest Industry August 27-30, 2013. Espoo, Finland

Minimal heating and cooling in a modern rose greenhouse  P.J.M. van Beveren ∗ J. Bontsema ∗∗ G. van Straten ∗∗∗ E.J. van Henten ∗,∗∗ ∗

Farm Technology Group, Wageningen University, P.O. Box 317, NL-6700AH Wageningen, The Netherlands, e-mail: [email protected] ∗∗ Wageningen UR Greenhouse Horticulture, P.O. Box 644, NL-6700AP Wageningen, The Netherlands ∗∗∗ Biomass Refinery and Process Dynamics Group, Wageningen University, P.O. Box 17, NL-6700AA Wageningen, The Netherlands Abstract: Need for reduction of energy use in greenhouse production has increased. First objective was to develop and validate a dynamic air temperature model. Second objective was to minimize total energy input to the greenhouse, for pre-set temperature boundaries. Optimal control techniques were used to minimize total energy input (cooling and heating). Results confirm that air temperature is on the upper boundary when cooling is applied and on the lower boundary when heating is applied. This work is a first step toward optimal deployment of a large array of possible options for the grower to optimally satisfy heat or cooling. Keywords: Temperature control, dynamic modelling, greenhouse, optimal control 1. INTRODUCTION Pressure on growers to reduce energy consumption in greenhouse crop production has increased over the last years. On one hand Dutch growers need to increase energy efficiency as international competition increases. On the other hand growers are forced to save energy as legislation for reducing consumption of fossil fuel and exhaust of greenhouse gas emissions becomes more strict (Montero et al., 2011). To save energy, various strategies are used by growers. One strategy is to use more diverse equipment. An example of this is the semi-closed greenhouse as proposed by Van’t Ooster et al. (2007), in which various high-level technology systems were compared via simulations. Closed and semi-closed greenhouse concepts include storage of heat in aquifers (long term) and short term buffers, heat pumps and heat exchangers. However, control of these systems is a problem due to e.g. the different types of energy, complexity of energy facilities, different time scales (Van Henten and Bontsema, 2009), and changing weather conditions. No solution for optimal energy utilization has been defined so far (Vadiee and Martin, 2012). This study is part of the project ’Optimal management of energy resources in greenhouse crop production’, which aims to solve complex control of equipment by developing a decision support tool to help growers utilize energy resources more effective. This study is seen as a first step toward optimal deployment of a large array of possible options for the grower to optimally satisfy heat or cooling demand within pre-set climate conditions in the greenhouse. In  This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs.

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order to satisfy demands, we must first calculate the required total energy input to achieve the pre-set greenhouse climate. The first objective of this study was to develop and validate a dynamic temperature balance of greenhouse air, using the following equipment: a shadow screen, artificial lighting, natural ventilation, pipe rail heating, and heat exchangers (heating or cooling). The second objective was to minimize the total energy input to this greenhouse, for a given lower and upper temperature boundary. Lower and upper temperature constraints were also imposed by (Van Henten et al., 1997). Most authors use an economic criterion to minimize both heating and ventilation costs, for example Gutman et al. (1993), or to maximize profit, for example Ioslovich et al. (2009) and Van Straten et al. (2002). Minimizing the total energy use without an economic criterion has, as far as we know, only be used by Chalabi et al. (1996), but they used a steady-state temeprature model. Temperature boundaries are usually made according to a predefined pattern specified by the grower. Growers use weather predictions, status of the crop, specific knowledge of the crop, production prognosis, and experience to define the desired temperature pattern and the desired distance between those boundaries. Using a lower and upper boundary would be more energyefficient than current practice, as energy-efficient climate control allows fluctuating temperatures and humidities within boundaries that are optimal for the crop (Dieleman and Hemming, 2009). We used optimal control techniques and a physics-based dynamic temperature model to minimize total energy input to the greenhouse. In this study, the first results of optimization with one state (temperature) and one control (total energy input) were shown. The

10.3182/20130828-2-SF-3019.00026

IFAC AGRICONTROL 2013 August 27-30, 2013. Espoo, Finland

outcome of the optimization is an optimal temperature trajectory for which energy input is minimal. 2. MATERIALS AND METHODS

Φvent

2.1 Greenhouse model The greenhouse of interest was a 4 ha commercial greenhouse producing cut roses, located in Bleiswijk, the Netherlands. This greenhouse was equipped with a shadow screen, artificial lighting, natural ventilation, pipe rail heating, and heat exchangers. A light blocking screen was used to prevent light emission during night. It was assumed that this screen had no effect on air temperature. The general notation of the dynamic model in state space form is represented by x˙ = f (x, u, v, p, t)

with

x(t0 ) = x0

(1)

Φcover

Φsun

Φlamps

Tair Φheat_ex

Φpipe

Φtrans

where t is the time, x the state, u the control input, v the external inputs and p the parameters. A physics based temperature model, based on greenhouse climate models as described by Van Henten (1994), De Zwart (1996), Van Ooteghem (2007) and Vanthoor et al. (2011) was made, where the non-linear function f describes greenhouse air temperature Tair over time, 1 dTair = (Φsun − Φcover dt ccap − Φtrans + Φlamps + Φenergy ) For simulation: Φenergy = −Φvent ± Φhe + Φpipe

(2)

(3)

where Φsun is incoming radiation, Φcover is heat loss through the cover, Φtrans heat extraction due to crop transpiration, Φlamps is heat due to artificial lighting, and Φenergy is the energy input term. Φenergy is an important container concept in this study. A negative energy flux Φenergy extracts heat from greenhouse air (cooling) and a positive energy flux adds heat to greenhouse air (heating). For simulation and model validation Φenergy was replaced by Equation 3, where Φvent is heat exchange with outdoor air due to natural ventilation, Φhe is active cooling or heating by the heat exchangers, and Φpipe is heating by the pipe rail heating system. Fluxes are schematically shown in Figure 1. All these fluxes Φ are expressed in W m−2 floor area. Greenhouse air was assumed to be perfectly mixed.

Fig. 1. Schematic overview of fluxes affecting greenhouse air temperature Tair . Fluxes Φpipe , Φvent and Φhe (dashed lines) were only used for simulation and model validation. For minimizing energy input these terms were aggregated to the control input Φenergy .  tf min J(u(t)) = Φ2energy dt (5) t0

The goal function J was quadratic in order to penalize larger perturbations more than smaller perturbations. Moreover, heating and cooling are both minimized with the same term. Another option could be to replace the quadratic term in Equation 5 by the absolute value of Φenergy . Greenhouse air temperature should stay between a lower and an upper temperature boundary. Boundaries were represented by the time dependent state inequality constraint xmin (t) ≤ x(t) ≤ xmax (t)

(6)

min

Total energy input Φenergy (heating or cooling) was used as the control input u. External inputs v(t) were described by

where x was the lower temperature boundary and xmax was the upper temperature boundary. Control input Φenergy was constrained by the control inequality constraint

v(t), t0 ≤ t ≤ tf

umin (t) ≤ u(t) ≤ umax (t)

(4)

where v(t) were measured climate data from the greenhouse process control computer. A more extensive description of used data is presented in section 2.3. The optimal control trajectory u∗ (t), t0 ≤ t ≤ tf that minimizes total energy input over time can be found by minimizing the cost function J over time:

283

min

(7) max

where u was the maximal cooling capacity and u was the maximal heating capacity. We assumed constant capacities of 200 W m−2 for both cooling and heating. 2.2 Energy fluxes Fluxes affecting greenhouse air temperature Tair are presented in more detail in the next sections.

IFAC AGRICONTROL 2013 August 27-30, 2013. Espoo, Finland

Radiation Energy added to the greenhouse air by incoming radiation was computed using Equation 8, where the constant greenhouse cover transmission τcov (−) is multiplied by measured outside radiation Irad W m−2 . Φsun = τcov Irad



Φlamp = η PE

 W m−2

(8)

The greenhouse transmission coefficient τcov changes when the shading screen is closed. Therefore, this coefficient is adapted to screen closure as described later. Heat loss through the cover Convective heat loss through the cover Φcover is described by Φcover = ccov

Ao (Tair − Tout ) Af



W m−2





W m−2



(10)

where χcrop is the effective water vapour concentration at crop level, χair is the  effective  water vapour concentration of greenhouse air g m−3 , L is the amount of energy  −1 needed to evaporate water from a leaf J g , and ge is the   transpiration conductance m s−1 . Transpiration conductance depends on LAI (Leaf Area Index), the ratio of latent to sensible heat content of saturated air, boundary layer resistance,  and stomatal resistance. Stomatal resistance rs s m−1 was calculated via rs = 82 + 570 e

Rn −γ LAI



1 + 0.023 (Tair − 24.5)

2

 (11)

  where Rn is net radiation at crop level W m−2 . The crop specific parameter γ was reported to be 0.008 for roses, whereas for tomato γ was reported to be 0.4 (Bontsema et al., 2010). Shading screen A shading screen is applied in the greenhouse. This screen effects the incoming radiation to the greenhouse, therefore, τcov was adapted according to the screen closure Clscr , 



W m−2





(13)

where η is the part of electric energy consumption of the lamps that is transformed into heat, released to greenhouse air (−), fon is the fraction of lamps that is switched on (%) and PE is therated electric power of artificial lighting installed W m−2 . Natural ventilation For simulation, realized window opening for lee and wind side were used (Figure A.3). Ventilation flux was calculated with the model of De Jong (1990). Heat loss was then calculated as follows Φvent = φvent ρair Cp air (Tair − Tout )

Crop transpiration Energy release from greenhouse air due to crop transpiration Φtrans is described in the following section. These calculations are based on transpiration calculation as described by Stanghellini and De Jong (1995).



fon 100

(9)

where ccov the heat  is −2  transfer coefficient of the cover −1 K material W m , A0 is the greenhouse  2  cladding area m , Af is the greenhouse floor area m2 and Tout is outdoor temperature (◦C).

Φtrans = ge L (χcrop − χair )

Artificial Lighting Lamps in the greenhouse add heat to greenhouse air. This was calculated via



W m−2



(14)

where  indoor  φvent is total ventilation flux from  to outdoor −3 air m3 s−1 , ρair density of air kg m and Cp air  specific heat capacity of air J kg−1 K−1 . Heat exchanger Heat extracted (or added) from greenhouse air by heat exchangers is calculated via

Φhe = αhe

0.5 (The in − The out ) − Tair Af



W m−2



(15)

where αhe is a calibrated parameter that describes heat transfer between heat exchanger and greenhouse air   W m−2 K−1 , The in and The out are in and out flowing water temperature of the heat exchanger (◦C). Pipe rail heating Heat added by pipe rail heating was calculated based on average pipe temperature obtained via averaging measured in and outgoing pipe temperature (Figure A.4). The amount of heat added was described by Φpipe = αpipe (Tpipe avg − Tair )



W m−2



(16)

is heat transfer coefficient from pipe to air where−2αpipe W m K−1 , and Tpipe avg average pipe temperature (◦C). 2.3 Used data Real climate data (5 minute time interval, both indoor R and outdoor) was collected from the HortiMaX process control computer of the grower. Crop transpiration calculations were compared with measurement data from a R ) in the greenhouse. weighing gutter (HortiMaX Prodrain Measured indoor temperature was used to validate greenhouse air temperature.

(12)

Climate conditions To simulate indoor temperature, measured outdoor temperature Tout was used. Measured indoor and outdoor temperature are shown in Figure 2.

where τscr is the transmission coefficient of the shading screen (-) and Clscr the screen closure (%). Clscr = 100% means that the screen is completely closed.

Measured indoor humidity data were used instead of a model for calculating crop transpiration. Measured indoor and outdoor humidity (Figure A.2), and outdoor radiation

τtot = τcov

(1 − τscr ) Clscr 1− 100

(−)

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IFAC AGRICONTROL 2013 August 27-30, 2013. Espoo, Finland

levels in the greenhouse (3 and 4 July, 2012). The Relative Root Mean Square Error (RRMSE) for this period was 30%. Average deviation was 14(30) g m−2 h−1 . Calculated values follow the measured values very well during day time, but show a less accurate prediction during night time.

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Fig. 2. Measured indoor (solid line) and outdoor (dashed line) temperature (◦C). (Figure A.1) for the period of interest are shown in Appendix A. Equipment Recorded data of equipment were used for closure of the shading screen, switching artificial lighting, window opening (wind and lee side), pipe temperature, and in and outgoing temperature of the heat exchangers. Opening of the shadow screen (solid line) and use of artificial lighting (dashed line) is shown in Figure 3. Screen closure of 0% means that the screen is fully open. Lamps were switched on in four different levels: 100 % on, 66 23 % on, 33 13 % on. 100

Status (%)

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Temperature (◦ C)

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100

0

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Fig. 4. Measured (solid line) and simulated (dashed line)   crop transpiration g m−2 h−1 for 28 June, 2012 through 4 July, 2012. Greenhouse air temperature Measured temperature was compared with simulated temperature Tair to validate the model. Initial simulated temperature was equal to the first measured temperature. Important parameters were: heat transfer coefficient from pipe to air αpipe , heat transfer factor from heat exchanger to air αhe , capacity of greenhouse air and construction ccap , greenhouse cover transmission τcov , and light transmission of the screen τscr . These parameters were chosen based on literature and greenhouse data.

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Table 1. Parameter values

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Fig. 3. Closure of the shadow screen (solid line) and use of artificial lighting (%). 2.4 Optimal control solver The optimal control problem was solved with PROPT Matlab Optimal Control Software, which is a platform for solving applied optimal control and parameter estimation problems (Rutquist and Edvall, 2010). A daily optimization procedure was performed. Data processing, model building, validation, and optimal control formulation with PROPT were done in Matlab (version 7, The MathWorks Inc., Natick, USA)). 3. RESULTS The greenhouse temperature model was validated to obtain reliable control trajectories. For simulation, realised control inputs u and measured external inputs v were used. Results of crop transpiration and greenhouse air temperature validation are presented in section 3.1. Results of minimizing total energy input are presented in section 3.2. 3.1 Validation of the model Crop transpiration Figure  4 showsmeasured and calculated crop transpiration g m−2 h−1 for 28 June trough 4 July, 2012. Crop transpiration is larger at higher light 285

Symbol αpipe αhe ccap τcov τscr

Parameter value 4 192 33000 0.7 0.3

Units W m−2 K−1 W m−2 K−1 J m−2 K−1 − −

Simulated and measured greenhouse air temperature are shown in Figure 5 for April 20, 2012 through April 24, 2012. RRMSE for this period was 8%. Main differences occurred during night time. Validation for the period May 20, 2012 through May 24, 2012 resulted in a RRMSE of 8% as well. We believe that the difference between measured and simulated temperature is mainly caused by the fact that the system is narrowed down to the minimum subsystem (e.g. no long and short wave radiative heat transfer was taken into account) and the fact that the presented model is not a stand-alone temperature model (e.g. no humidity balance is present yet, but measured data were used). Figure 6 shows two lines: the solid line being the fluxes that are not part of the control input Φenergy (being incoming radiation, heat loss through cover, crop transpiration, and heat from artificial lighting), and the dashed line being fluxes that are part of the control input (being natural ventilation, pipe rail heating, and heat or cold from heat exchangers). For the 5 days shown in the figure, 35% of total in and outgoing energy was part of the input Φenergy . Heating was mainly applied during night time and cooling was mainly applied during day time when there was a surplus of heat due to incoming radiation. Total heat added by pipe rail heating and heat exchangers was

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Temperature (◦ C)

IFAC AGRICONTROL 2013 August 27-30, 2013. Espoo, Finland

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Fig. 5. Measured (solid line) and simulated (dashed line) greenhouse air temperature after calibration (◦C) for April 20, 2012 through April 24, 2012.

Fig. 7. Optimal greenhouse air temperature Tair for minimum energy input(solid line) with lower and upper temperature boundaries (◦C) for April 20, 2012 through April 24, 2012.

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200

100

150

Energy (W m−2 )

Energy (W m−2 )

200

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100 50 0 −50 −100 −150

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Fig. 6. Sum of energy fluxes not part of Φenergy (solid line), of energy fluxes part of Φenergy (dashed line) and sum W m−2 for April 20, 2012 through April 24, 2012. 39 MJ for the 5 day period. Cooling was 31 MJ in total realized by natural ventilation. The net-energy added to the greenhouse was 7 MJ. 3.2 Minimal energy input Total energy input to the greenhouse Φenergy was minimized with the model as described in section 2.1. Both heating and cooling where minimized as it was one input. Only control input Φenergy could be adjusted by the optimal control procedure to minimize total energy input. The grower decides himself whether to shift boundaries and could compare himself the energy use of different scenarios. Lower and upper temperature boundaries for minimization were based on measured greenhouse air temperature ±0.5◦C, because this was assumed to be the desired greenhouse air temperature by the grower from the point of view of providing a good environment for the roses. Alternative boundaries, e.g. using a heating and ventilation line from the climate computer were seen as a less desired air temperature pattern and, therefore, not used. Measured air temperature was filtered with a moving average filter with a span of 75 points. The result of the minimization is shown in Figure 7. The corresponding energy input that realizes this result is shown in Figure 8. Energy input Φenergy over the 5 day period was 7 MJ (12 MJ of heating and 5 MJ of cooling). The net energy input is comparable with the simulated energy input, whereas total heating and cooling was much higher for the simulation. In practice there are different reasons to heat and ventilate at the same time. Reasons for heating in practice (minimum pipe temperature) could be to prevent condensation and diseases from the greenhouse or achieve a desired air flow of greenhouse air. Maintaining a minimum pipe temperature costs energy, and also leads to more 286

Fig. 8. Energy input Φ  energy that minimizes the goal function J W m−2 for April 20, 2012 through April 24, 2012. cooling to obtain the desired climate. When boundaries were relaxed (±1◦C of smoothed measurement), net energy input was 6 MJ (10 MJ of heating and 4 MJ of cooling). Optimized greenhouse air temperature is on the lower boundary when total energy input Φenergy is positive and heating is needed, and on the upper boundary when total energy input Φenergy is negative and cooling is needed (Figure 6). A positive energy flux means that greenhouse air temperature increases, whereas a negative energy flux means that greenhouse air temperature decreases. As temperature is on the lower boundary, energy flux Φenergy is positive and heating has to be applied. As temperature is on the upper boundary, energy flux Φenergy is negative and cooling has to be applied to keep temperature below or on the upper boundary. 4. CONCLUSION Air temperature of a modern rose greenhouse was described with a physics-based temperature model and resulted in a Relative Root Mean Square Error smaller than 10%. Optimal control techniques were used to calculate optimal temperature trajectories between pre-set boundaries that minimize the total energy input to the greenhouse. Results confirm that air temperature is on the upper boundary when cooling is applied and on the lower boundary when heating is applied. Effects of shifting boundaries can be quantified in terms of total energy input and might help growers to set temperature boundaries and to provide insight in the effect of changing boundaries on energy use. Relaxing temperature boundaries leads to lower values of the net energy input. More research is needed to investigate underlying reasons of decisions in current practice regarding heating and cooling. The model will be extended with a humidity and carbon dioxide

IFAC AGRICONTROL 2013 August 27-30, 2013. Espoo, Finland

Bontsema, J., Stanghellini, C., Driever, S., and Kempkes, F. (2010). Test of the dll for the calculation of the crop transpiration and crop temperature. (Unpublished). Chalabi, Z., Bailey, B., and Wilkinson, D. (1996). A realtime optimal control algorithm for greenhouse heating. Computers and Electronics in Agriculture, 15(1), 1–13. De Jong, T. (1990). Natural ventilation of large multi-span greenhouses. Ph.D. thesis, Wageningen University. De Zwart, H. (1996). Analyzing energy-saving options in greenhouse cultivation using a simulation model. Ph.D. thesis, Wageningen University. Dieleman, J. and Hemming, S. (2009). Energy saving: from engineering to crop management. In International Symposium on High Technology for Greenhouse Systems: GreenSys2009 893, 65–73. Gutman, P., Lindberg, P., Ioslovich, I., and Seginer, I. (1993). A non-linear optimal greenhouse control problem solved by linear programming. Journal of agricultural engineering research, 55(4), 335–351. Ioslovich, I., Gutman, P.O., and Linker, R. (2009). Hamilton–jacobi–bellman formalism for optimal climate control of greenhouse crop. Automatica, 45(5), 1227– 1231. Montero, J., Ant´on, A., Torrellas, M., Ruijs, M., and Vermeulen, P. (2011). Environmental and economic profile of present greenhouse production systems in Europe. Wageningen UR [etc.]. Rutquist, P. and Edvall, M. (2010). PROPT - Matlab Optimal Control Software. Tomlab Optimization Inc., 1260 SE Bishop Blvd Ste E, Pullman, WA, USA. Stanghellini, C. and De Jong, T. (1995). A model of humidity and its applications in a greenhouse. Agricultural and forest meteorology, 76(2), 129–148. Vadiee, A. and Martin, V. (2012). Energy management in horticultural applications through the closed greenhouse concept, state of the art. Renewable and Sustainable Energy Reviews, 16(7), 5087–5100. Van Henten, E. (1994). Greenhouse climate management : an optimal control approach. Ph.D. thesis, Wageningen University. Van Henten, E. and Bontsema, J. (2009). Time-scale decomposition of an optimal control problem in greenhouse climate management. Control Engineering Practice, 17(1), 88–96. Van Henten, E., Bontsema, J., and Van Straten, G. (1997). Improving the efficiency of greenhouse climate control: an optimal control approach. Netherlands Journal of Agricultural Science, 45(1), 109–125. 287

Appendix A. OUTDOOR CONDITIONS 1000

Radiation (W m−2 )

REFERENCES

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Fig. A.1. Measured outdoor Radiation W m

−2



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Humidity (%)

We would gratefully thank HortiMaX B.V., Boonekamp Roses B.V., and Lek Habo Groep B.V. for the useful discussions and sharing data.

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Fig. A.2. Measured indoor (solid line) and outdoor (dashed line) humidity (%) 100

Window opening (%)

ACKNOWLEDGEMENTS

Van Ooteghem, R. (2007). Optimal control design for a solar greenhouse. Ph.D. thesis, Wageningen University. Van Straten, G., Van Willigenburg, L., and Tap, R. (2002). The significance of crop co-states for receding horizon optimal control of greenhouse climate. Control Engineering Practice, 10(6), 625–632. Van’t Ooster, A., Van Henten, E., Janssen, E., Bot, G., and Dekker, E. (2007). Development of concepts for a zero-fossil-energy greenhouse. In International Symposium on High Technology for Greenhouse System Management: Greensys2007 801, 725–732. Vanthoor, B., Stanghellini, C., Van Henten, E., and De Visser, P. (2011). A methodology for model-based greenhouse design: Part 1, a greenhouse climate model for a broad range of designs and climates. Biosystems Engineering, 110(4), 363–377.

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Fig. A.3. Window opening (%) for wind side (solid line) and lee side (dashed line). 50

Temperature (◦ C)

balance, such that boundaries can be set for humidity and carbon dioxide concentration as well. The model will then be further extended with models of heating and cooling equipment to be able to optimize deployment of a large array of possible options for the grower to optimally satisfy heat or cooling demand within pre-set climate conditions in the greenhouse.

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Fig. A.4. Pipe temperature (solid line), and ingoing (dashed line) and outgoing (dashdotted line) temperature of the heat exchangers (◦C).