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J. agric. Engng Res. (2001) 78 (4), 407}413
doi:10.1006/jaer.2000.0647, available online at http://www.idealibrary.com on
SE*Structures and Environment
A Strategy for Greenhouse Climate Control, Part I: Model Development
M. Trigui; S. Barrington; L. Gauthier
Department of Agricultural and Biosystems Engineering, Faculty of Agricultural and Environmental Studies, Macdonald Campus of McGillUniversity, 21 111 Lakeshore Road, Sainte Anne-de-Bellevue, Que&bec Canada H9X 3V9; e-mail of corresonding author:
[email protected]&partement des Sols et de Ge&nie Agroalimentaire, Faculte& des sciences de l'agriculture et de l'alimentation, Universite& Laval, Cite& Universitaire,
Que&bec Canada G1K 7P4
(Received 11 September 1998; accepted in revised form 6 September 2000; published online 23 January 2001)
This paper presents an algorithm developed to predict the dynamic ambient greenhouse air conditions which
optimize net pro"ts for the production of a greenhouse tomato crop. Pro"ts are equated to the crop yield value
less the energy costs for heating and dehumidi"cation and the CO
injection cost. The climatic conditions
considered are CO
level, temperature, relative humidity and incident radiation. These are varied dynamically
for every time interval spanning the harvesting period.
The algorithm has two sub-programs. For sets of selected internal climatic parameters, the "rst calculates
crop yield, and the second calculates energy costs (heating and dehumidi"cation) with reference to predicted
exterior climatic conditions (solar radiation, temperature, wind velocity and relative humidity). These twoalgorithms are then used to predict the particular set of climatic parameters, adjusted for each time interval over
the harvesting period, that will maximize the crop yield value less the energy costs.
2001 Silsoe Research Institute
1. Introduction
In North America, greenhouse production has
increased steadily despite high-energy costs (Statistics
Canada, 1995). By increasing the air tightness of modern
greenhouse structures for reduced energy use, problemsof high relative humidity have occurred. However, this
air tightness has also provided an opportunity to develop
and use computer programs to optimize the climate
inside greenhouses. The objective of this project was,
therefore, the development of a program capable of con-
tinuously adjusting the set-point of ambient greenhouse
air conditions (AGAC) for relative humidity, temper-
ature, CO
and incident radiation, to maximize the crop
yield value less energy cost, being termed net pro"t in this
text.
Several projects have developed programs to optimizeAGAC, but these programs have been limited to one or
two parameters. Daytime temperature is a major factor
a!ecting crop yield and energy consumption. Seginer
et al. (1991) formulated a model to optimize this para-
meter using Pontryagin's control strategy (Pontryagin
et al., 1962). For a crop of lettuce, the model predicted
that the set-point for daytime temperature should be
slowly decreased throughout the growing period as of the
"rst day. Nevertheless, some day-to-day #uctuations
need superimposition, in response to exterior temper-
atures and incoming radiation. While this strategy wasfound to be consistent with the physiological need of the
crop, the daily economic gain was minimal at $0)05 m\.
Further economic gains were anticipated with the hourly
adjustment of the temperature set-point.
Stanghellini and van Meurs (1992) proposed a climate
control algorithm based on the use of a set-point for crop
transpiration rate rather than for temperature and/or
relative humidity. The model was able to predict plant
transpiration rate with a maximum error of 10%. Never-
theless, the desired transpiration rate could only be
achieved as well as the AGAC could be controlled insidethe greenhouse. Relative humidity and incident radiation
were the two main factors in#uencing the transpiration
set-point.
Jolliet (1994) developed the HORTITRANS model, pre-
dicting greenhouse relative humidity, crop transpiration
0021-8634/01/040407#07 $35.00/0 407 2001 Silsoe Research Institute
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Notation
A ground surface area of the greenhouse,m
b coe$cient, K\
CE
CO
injection rate, g [CO
] m\ s\
CGT
CO#ux by ventilation and in"ltration,
g [CO
] m\ s\
CM
exterior CO
concentration, g [CO
]
kg\ [air]
CR
greenhouse interior CO
level at time t,
g [CO
] m\
CN?
air-speci"c thermal heat capacity,
J kg\ [dry air] K\
cR, c
, c
, empirical constants, dimensionless
c
, c
, c
,
c
, c
, c
E?BB
mass of water vapour added or
removed by humidi"cation or de-
humidi"cation, kg [water] m\ s\
EA
water vapour condensation rate on
walls, kg [water] m\ s\
EGT
water vapour removed by in"ltration
and ventilation, kg [water] m\ s\
ER
transpiration rate of the plants, kg
[water] m\ s\eA
interior air water vapour pressure at the
wall, Pa
eG
interior air water vapour pressure, Pa
eM
exterior air water vapour pressure, Pa
eQ
air saturation water vapour pressure,
Pa
eR
external parameters (CO
, temperature,
relative humidity, incoming radiation,
energy cost, product value) at time t,
g [CO
] m\, K, %, Wm\, $ J\,
$kg\
, respectivelyf(x
R, p
R, e
R) the estimated harvest value calculated
from the AGAC inside at time t,
$m\ s\
G(CR
,R) net rate of photosynthesis, g [CO
]
m\ s\
g(xR, p
R,
uR, e
R)
the cost of maintaining the AGAC at
time t, $m\ s\
GEJ
global rate of photosynthesis, g [CO
]
m\ s\
gQ
leaf conductance to CO
, kg [air]
m\
s\
h average height of the greenhouse, m
H?
Hamiltonian function, $m\ s\
HA
heat #ux through the glazing,
W m\
HD
heating system heat #ux, Wm\
HQ heat transferred between the soil andthe air, Wm\
HGT
the greenhouse heat lost by ventilation
and air in"ltration, W m\
HT
the energy cost per unit #oor area to
ventilate the greenhouse, W m\
hA
heat transfer coe$cient between the air
and the walls, W m\ K\
hGT
sensible heat transfer coe$cient due to
the air renewal, W m\K\
hP
greenhouse relative humidity, %
hR
heat transfer coe$cient between the
plants and the air, W m\ K\I*
foliar surface index, m [leaves]m\
[#oor area]
J objective function, $m\
K!
cost of CO
injection, $ g\ [CO
]
KD
heating energy cost, $ J\
KE
estimated harvest value, $kg\ [har-
vested]
KT
ventilation energy cost, $ J\
p!
cost of CO
injection, $ g\ [CO
] m\
p2
heating energy cost, $m\K\
pR variations in plant state at time t, kg[fruit mass] m\
pU
dehumidi"cation energy cost, $kg [dry
air]kg\ [water] m\
Q ventilation and in"ltration rates, m s\
R photosynthetically active radiation,
W m\
RB
respiration rate, g [CO
] m\ s\
RL
net incident radiation, W m\
RP
reference respiration rate per unit crop
mass, g [CO
] g\ [crop CO
] s\
t time interval, st
beginning of the harvesting period, s
tD
end of the harvesting period, s
M
exterior air temperature, K
P
reference temperature, K
Q
soil temperature, K
R
greenhouse air temperature, K
;A
global heat transfer coe$cient between
the inside air and the glazing,
W m\ K\
;Q
global heat transfer coe$cient between
the inside air and the soil, W m\
K\
uBR
latent heat #ux, W m\
uR
greenhouse climate control parameters
(heating, dehumidi"cation, lighting and
CO
injection) at time t, W m\, g
[CO
] m\
M. TRIGUI E A .408
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