Energy Consumption Model for Indoor Cannabis Cultivation Facility

Nafeesa Mehboob | Hany E. Z. Farag | Abdullah Sawas

Institute of Electrical and Electronics Engineers

Hence, the steady-state mass balance equation in each time interval t is represented for each room r and stage s , as follows:\begin{align}&\hspace {-1.2pc}\Delta \omega _{t,r,s} \=&\left ({\dot {M}^{trans}_{t,r,s} + \dot {M}^{vent}_{t,r,s} \cdot \omega ^{O}_{t} + \dot {M}^{inf}_{t,r,s} \cdot \omega ^{H}_{t} - \dot {M}^{D}_{t,r,s} \cdot \omega _{t,r,s}}\right) \cdot dt \\tag{12}\end{align} View Source\begin{align}&\hspace {-1.2pc}\Delta \omega _{t,r,s} \=&\left ({\dot {M}^{trans}_{t,r,s} + \dot {M}^{vent}_{t,r,s} \cdot \omega ^{O}_{t} + \dot {M}^{inf}_{t,r,s} \cdot \omega ^{H}_{t} - \dot {M}^{D}_{t,r,s} \cdot \omega _{t,r,s}}\right) \cdot dt \\tag{12}\end{align} where \Delta \omega {t,r,s} is the change in humidity ratio ({kg{water}}/{kg_{air}} ) in grow room r and stage s in time interval t , \dot {M}^{trans}{t,r,s} is the mass flow rate (kg{water}/hr ) of water due to evapotranspiration, \dot {M}^{vent}{t,r,s} is the mass flow rate of air due to ventilation, \omega ^{O}{t} is the humidity ratio of the outside air, \dot {M}^{inf}{t,r,s} is the mass flow rate of air due to infiltration, \omega ^{H}{t} is the humidity ratio of the hallway air, \dot {M}^{D}{t,r,s} is the mass flow rate of air due to dehumidification. Therefore, the power consumption by dehumidification units P^{D}{t,r,s} in each room and stage is computed in proportion to the computed dehumidifier air flow rate as follows:\begin{equation} P^{D}_{t,r,s} = \frac {\dot {V}^{D}_{t,r,s}}{\dot {V}^{D,rated}_{r,s}} \cdot P^{D,rated}_{r,s} \cdot \alpha ^{D}_{t,r,s}\tag{22}\end{equation} View Source\begin{equation} P^{D}_{t,r,s} = \frac {\dot {V}^{D}_{t,r,s}}{\dot {V}^{D,rated}_{r,s}} \cdot P^{D,rated}_{r,s} \cdot \alpha ^{D}_{t,r,s}\tag{22}\end{equation} where P^{D,rated}{r,s} is the aggregate rated power of the dehumidifier(s) in room r and stage s . This energy balance equation considers thermal energy contributions through HVAC, sensible heat (thermal energy added due to supplemental lighting), latent heat (thermal energy added due to plant evapotranspiration) as well as thermal energy lost/removed through conduction and convection, ventilation, and door opening events. Hence, the steady-state energy balance equation in each time interval t is represented for each room r and stage s , as follows:\begin{align*}&\hspace {-1.6pc}\Delta Q^{stored}{t,r,s} \=&\left ({\,Q^{hvac}{t,r,s} + Q^{L}{t,r,s} + Q^{trans}{t,r,s} - Q^{C}{t,r,s} - Q^{vent}{t,r,s} - Q^{inf}{t,r,s}\,}\right) \\tag{26}\end{align} View Source\begin{align}&\hspace {-1.6pc}\Delta Q^{stored}{t,r,s} \=&\left ({\,Q^{hvac}{t,r,s} + Q^{L}{t,r,s} + Q^{trans}{t,r,s} - Q^{C}{t,r,s} - Q^{vent}{t,r,s} - Q^{inf}{t,r,s}\,}\right) \\tag{26}\end{align*} where \Delta Q^{stored}{t,r,s} is the change in stored thermal energy (W \cdot hr ) in grow room r and stage s in time interval t , Q^{hvac}{t,r,s} is the thermal energy contribution of the HVAC system (positive when operating in heating mode and negative when in cooling mode), Q^{L}{t,r,s} is the thermal energy contribution due to lighting, Q^{trans}{t,r,s} is the thermal energy contribution due to evapotranspiration, while Q^{C}{t,r,s} is the thermal energy lost due to conduction and convection, Q^{vent}{t,r,s} is the thermal energy lost due to ventilation requirements, and Q^{inf}{t,r,s} is the thermal energy lost due to air infiltration resulting from door opening events. Hence, to compute the HVAC thermal energy added/removed in heating/cooling mode (Q^{hvac,heat}{t,r,s}/Q^{\vphantom {D^{l}}hvac,cool}{t,r,s} ) respectively for time interval t in room r and stage s , the change in stored thermal energy without HVAC contribution \Delta Q^{\prime stored}{t,r,s} is computed:\begin{align*} \Delta Q^{\prime stored}{t,r,s} = \left ({\,Q^{L}{t,r,s} + Q^{trans}{t,r,s} - Q^{C}{t,r,s} - Q^{vent}{t,r,s} - Q^{inf}{t,r,s}\,}\right) \\tag{37}\end{align*} View Source\begin{align*} \Delta Q^{\prime stored}{t,r,s} = \left ({\,Q^{L}{t,r,s} + Q^{trans}{t,r,s} - Q^{C}{t,r,s} - Q^{vent}{t,r,s} - Q^{inf}{t,r,s}\,}\right) \\tag{37}\end{align*} The resulting temperature without HVAC contribution at time interval t+1\,\,K^{\prime }{t+1,r,s} in room r and stage s is then computed:\begin{equation} K^{\prime }_{t+1,r,s} = \frac {3.6 \cdot \Delta Q^{\prime stored}_{t,r,s}}{C^{air}_{p} \cdot \rho _{t,r,s} \cdot V_{r,s}} + K_{t,r,s}\tag{38}\end{equation} View Source\begin{equation} K^{\prime }_{t+1,r,s} = \frac {3.6 \cdot \Delta Q^{\prime stored}_{t,r,s}}{C^{air}_{p} \cdot \rho _{t,r,s} \cdot V_{r,s}} + K_{t,r,s}\tag{38}\end{equation} If the HVAC(s) in room r and stage s is in heating mode during time interval t and the resulting temperature is lower than the lower temperature limit (\underline {K}{r,s} - K^{\prime }{t+1,r,s} >0 ), then the thermal energy added by hvac Q^{hvac,heat}{t,r,s} can be computed using:\begin{equation*} \underline {K}{r,s} - K^{\prime }{t+1,r,s} = \frac {3.6 \cdot Q^{hvac,heat}{t,r,s}}{C^{air}{p} \cdot \rho _{t,r,s} \cdot V{r,s}}\tag{39}\end{equation} View Source\begin{equation} \underline {K}{r,s} - K^{\prime }{t+1,r,s} = \frac {3.6 \cdot Q^{hvac,heat}{t,r,s}}{C^{air}{p} \cdot \rho {t,r,s} \cdot V{r,s}}\tag{39}\end{equation*} If the computed HVAC(s) thermal energy Q^{hvac,heat}{t,r,s} exceeds the total rated heating capacity of the HVAC system Q^{hvac,heat,rated}{r,s} in room r and stage s , then the added HVAC thermal energy is set to Q^{hvac,heat,rated}_{r,s} .