## 1 Introduction  
Energy and food sustainable production is a major concern of actual society [1; 2]. Several researchers have shown that photovoltaic energy production in a greenhouse could cover the energy demand of farms and get additional incomes for producers for energy selling to a general electricity network [3; 4; 5; 6; 7; 8; 9; 10]. Therefore, the decrease in the use of fossil fuels can reduce the production of polluting gases in intensive agriculture [11; 12; 13; 14]. In addition, photovoltaic energy production for agriculture use can be especially interesting in remote areas where connection to a general electricity network is not available or at a high-cost [15; 16; 17; 18]. Plants growing, crop yields and the quality of fruits can be improved by controlling greenhouse climatic conditions using self-produced photovoltaic energy [19]. The main drawback of installing roof top greenhouse photovoltaic panels is the shading that these structures produces inside the greenhouse, reducing photosynthetic active radiation (PAR) radiation for crop production. In low latitude countries, such as Spain, Italy, Greece and other Mediterranean countries, solar radiation can satisfy PAR requirements of crops in greenhouses. In fact, in these countries summer period solar radiation results in being excessive, having negative effects in greenhouse crops, due to a high radiation and temperature reaching inside the greenhouse and being needed to be reduced by farmers through techniques like whitening of roof-tops or shading-screens [20; 21; 22]. However, in winter periods, this radiation is not excessive, becoming in many cases a limiting factor of greenhouse crops. The installation of roof top greenhouse photovoltaic panels in the Southern Eastern area of Spain can be an interesting proposal for farmers, due to the high number of annual solar hours in the area [23; 24; 25]. The main drawback is that conventional photovoltaic panels are completely or partially opaque in order to maximize solar energy production. Thus, there is a reduction of the radiation that is available for the crops [2; 18]. The reduction of radiation inside the greenhouse due to the photovoltaic panel installation needs to be deeply studied, because it can affect crop growth and yields, mainly in periods when solar radiation is lower [1; 25; 26]. During high radiation periods, shading is one of the main ways to reduce solar radiation inside the greenhouses, using materials that reflect and absorb part of the spectrum of the solar radiation [15]. Therefore, the use of photovoltaic panels during these periods can provide beneficial shadings on the crop and generate new economic incomes to the farm, or reduce costs due to electricity production. However, during low solar radiation periods, an excessive shading surface can reduce radiation inside the greenhouse too much and cause negative effects on crops [27; 28; 29; 30]. Photovoltaic modules installed on the top of the greenhouse permanently during all the cropping season (and during several years) can produce excessive shading during low solar radiation periods. Although the shading effects in greenhouses has been widely studied [31]. It is very interesting to know which is the maximum level of shading produced by opaque roof-top greenhouse photovoltaic panels without affecting crop production. In South-European greenhouses, structures are usually oriented East-West, being this structure orientation used for most of researchers in studies about photovoltaic energy production [18; 24; 25; 32; 33]. [PERSON] et al. [34] studied electric energy generated by roof-top greenhouse photovoltaic panels in a North-South oriented greenhouse located in Japan. However, this study did not evaluate the effects of shading in the crop. Therefore, it can be very interesting to study effects on crop production of roof-top greenhouse photovoltaic panels in a North-South oriented greenhouse. Recently, several studies on crop effects of shading caused by roof-top photovoltaic panels have arisen [24; 25; 35; 36].