Day-To-night heat storage in greenhouses

In cold-climate locations, where natural gas is burned during the day to enrich greenhouses with carbon dioxide, water tanks (buffers) are often used to store the surplus daytime heat for nighttime heating. A practical control strategy for filling (charging) and emptying (discharging) of the buffer, based on a virtual value (costate) of the stored heat (the state), is suggested and illustrated by simulation. Heating and ventilation decisions are obtained by maximizing, at each time step, the virtual increase in value of the greenhouse system (including stored heat). As long as the heat buffer is neither empty nor full, the virtual value (co-state) of the stored heat remains constant. When the buffer is full (towards the end of a day), this value is gradually decreased, until the buffer starts to discharge. When the buffer empties (towards the end of a night), the virtual value is gradually increased, until recharging of the buffer starts again. This heuristic strategy is meant to minimize the time that the buffer is empty or full, because in these states the buffer is inactive (ineffective). Simulations with an annual weather sequence show the following: (1) the winter-Time virtual value of stored heat is about equal to the actual cost of heat, while in summer it is close to zero; (2) the utilization of the buffer, judged by the time on the storage bounds (full or empty), is roughly uniform along the year; (3) the performance of the system improves asymptotically with an increase of the installed capacity of the buffer; (4) expensive energy (heat) results in reduced intensity of cultivation (less heat and less yield).