| Summary: | With the increase in PV system installations, the available free land and rooftops for these systems may become scarcer, and therefore sloped fields facing the north may be utilized for that purpose. In deployments of PV collectors in multiple rows, either on horizontal or sloped planes, the second and subsequent rows are subject to two effects: shading and masking. Both effects reduce the electric energy generated by the PV systems. Multiple rows of collectors are deployed on horizontal planes and on sloped planes facing south, and literature on the topic has been published. No literature deals analytically with deployments of PV fields on north-facing slopes in the northern hemisphere, to the best of our knowledge. The present study develops explicit analytical expressions for the shadow height and length cast on a collector row by a row in front in multiple-row PV systems installed on slopes facing north. In addition, analytical expressions are developed for row spacing and sky view factors, altogether leading consequently to the determination of shading and masking losses. Having the developed expressions, a comparison was made between PV deployments on north-facing sloped planes to PV deployments on horizontal and south-facing slopes regarding shading and masking losses. The main finding is that the percentage of masking losses (diffuse radiation) may exceed the percentage of shading losses (beam radiation) in PV fields. At the local site <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mn>32</mn></mrow><mo>∘</mo></msup><mo> </mo><mi mathvariant="normal">N</mi></mrow></semantics></math></inline-formula>, collector inclination angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>=</mo><msup><mrow><mn>25</mn></mrow><mo>∘</mo></msup></mrow></semantics></math></inline-formula> and sloped-plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>=</mo><msup><mrow><mn>10</mn></mrow><mo>∘</mo></msup></mrow></semantics></math></inline-formula>, for example, the percentage of masking losses for a horizontal plane is 6.90%; for a sloped plane facing south, the losses are 5.39%, and for a sloped plane facing north, the losses are 6.86%. In comparison to the masking losses, the percentage of shading losses for the horizontal plane is 0.83%; for the sloped plane facing south, the losses are 0.42%, and for the sloped plane facing north, the losses are 1.37%.
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