I have a hourly series of solar radiation in a location (global, beam and diffuse radiation) and I am calculating the new solar radiations considering a titled solar panel. The site latitude is -45º (south hemisphere) and my results are:

The annual energy obtained in a tilted panel to 45º is: 343.95 kWh The annual energy obtained in a tilted panel to 50º is: 364.6 kWh The annual energy obtained in a tilted panel to 55º is: -109.06 kWh The annual energy obtained in a tilted panel to 60º is: 475.47 kWh The annual energy obtained in a tilted panel to 40º is: 1114.62 kWh The annual energy obtained in a tilted panel to 35º is: 336.62 kWh The annual energy obtained in a tilted panel to 30º is: -59.09 kWh

I used the math expression from Solar Engineering of Thermal Processes book. Can anyone explain me why the negative results? Is a valid result a negative number?

Thanks

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