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Agrivoltaic systems represent a key technology for reaching sustainable development goals, by reducing the competition of land used for food versus land used for electricity. Moreover, agrivoltaic systems are at the centre of the nexus between electricity production, crop production, and irrigation water savings. In this study, an optimisation model for vertically mounted agrivoltaic systems with bifacial photovoltaic modules is developed. The model combines three main sub-models: solar radiation and shadings, photovoltaics, and crop yield. Validation of the sub-models is performed showing good agreement with measured data and commercial software. The optimisation model is set as multi objective to explore the trade-offs between competing agrivoltaic key performance indicators. Oats and potatoes are used as reference crops in this study. The results show that the row distance between bifacial photovoltaic module structures significantly affects the photosynthetically active radiation distribution. The resulting crop yield of oats and potato is reduced by about 50% as row distance decreases from 20 m to 5 m. The implementation of an agrivoltaic system for the investigated crops at the chosen location shows a land equivalent ratio above 1.2, which justifies the use of the technology for reaching national sustainability goals.