## 1 Introduction  
The use of photovoltaics (PV) for power production needed for the operation of greenhouses addresses the problem of land occupation for their installation, land that could be valuable for food production [1]. One solution is to place them in the greenhouse cover itself. However, this can lead to a decrease in available photosynthetically active radiation (PAR) at the plant level, making it difficult for the plants to grow, as well as altering other parameters describing the thermal and flow field developed inside the greenhouse (e.g., temperature, pressure, velocity, etc. ), which are influenced by the cover materials transmissivity. As a solution to this problem, it is suggested to use semi-transparent PVs in film form which do not burden the greenhouse statics and in addition allow quantities of natural light to enter since they are not completely opaque like ordinary PV panels. However, these also limit the entry of PAR and are expected to alter the internal microclimate by many mechanisms (smaller amounts of available PAR, lower heat exchange through the cover, modification of the thermal and flow field, etc.). The issue of PV integration into the greenhouse cover has been a matter of great concern to the scientific community in recent years investigating: (a) to what extent they are able to meet greenhouse energy needs and/or (b) to what extent they influence plant growth in the greenhouse. The majority of the research works begin with experiments or field measurements trying to develop some analytical models for the expansion of the measurement results. Therefore, one issue that is being investigated is how the geometry of the greenhouse cover affects the performance of PV. In [2], the power production of four amorphous-silicon photovoltaic modules were measured, and an analytical model was developed. The PVs were arranged in an arch formation at the northern end of the Gothic-arch style roof of a north-south oriented greenhouse. The investigations in [3,4] focus on the ability to meet with the cover-integrated PV the power demand for the internal climate control of a greenhouse with Welsh onion crops. They measure the energy production and the solar radiation inside the greenhouse for a 12.9% PV covering and in parallel they develop an analytical model for the prediction of solar energy at specific points inside the greenhouse during the day. In [5], the electricity production, the greenhouse temperature, and the PAR radiation are measured in experimental configuration with PVs causing 20% shading, and an analytical model is developed in order to expand the conclusions. In [6], the power produced by bifacial PVs covering 37% of a greenhouse cover is investigated. The other issue is the effect of PVs on the internal microclimate and productivity of the greenhouse. The integration of semitransparent PV panels placed at a distance of 8 cm from the greenhouse pitched roof, covering 20% of the roof, causes solar radiation reduction of 35%-40% and a temperature reduction of 1-3 \({}^{\circ}\)C according to field measurements for tomato and lettuce crops [1,7]. In [8], the replacement of the 50% of a pitched roof with multi-crystalline PV measuring the temperature and the solar radiation inside the greenhouse is examined. With field measurements the influence of roof integrated PVs on the evapotranspiration rate, and consequently on water management, is also approached [9]. Finally, the effect of the PV incorporation on the roof depends on the percentage of cover but also on the cultivation with tomato and lettuce being less vulnerable than onion [1,3,5,7]. Calculating the available PAR inside a greenhouse throughout a solar day requires extensive and difficult calculations that become even more difficult in the case of an arched greenhouse.