Anisotropic irradiance models for tilt angle optimization of solar panels

The optimal tilt angles of solar panels have been calculated with using the anisotropic irradiance models and meteorological data for several regions of Ukraine. These models account various conditions for irradiance during the day throughout the year. The formulas for optimization proce-dure and equations for optimal tilt angle have been obtained.

The design of photovoltaic (PV) plants should provide the maximum use of solar radiation for electricity generation. The quantity of produced energy per radiation collecting sur-face unit depends on several factors: the radiation profiles in time, the effectiveness of PV modules, the angles of solar panel inclination and orientation, the operating temperature and the temperature characteristics of PV cells, the characteristics of inverters and other plant components. The most easily changed parameters, which haven’t constructional restrictions, are the inclination and the azimuth orientation of solar panels.

We propose the method to optimize the tilt angles, which uses long-term meteorological data on the inten-sity of direct and diffuse radiation on a horizontal surface, and direct radiation on normal surface. These data may be con-verted into radiation at an incline by known models of solar radiation (for example, [1]). The developed method [2] is based on analytical formulas for optimum angles obtained for a num-ber of well-known models of diffuse radiation (Lee-Jordan, Hay, Hay-Davies, Reindl, Klucher). In the work the optimal angles for several regions of Ukraine for various periods of work photovoltaic plant, including summer, winter and all year, were calculated.

To calculate the optimal tilt angles of solar panels we selected a number of cities : Kiev, Odessa, Zaporozhye, Kher-son and Uzhgorod. The significant distance between this cities and various solar radiation conditions result to substantial dif-ferences of the optimum tilt angles. Table 1 shows as example the results for of south-facing panels in Kiev. The table includes the data obtained by our analytical method for the iso-tropic and various anisotropic radiation models. The parameters of nonlinear equations for were calculated on the basis of the experimental irradiance data for Ukraine [3] which include the averaged for multi-year period the hourly direct, diffuse and reflected irradiance components. Evidently the bigger angles are typical for the winter months and the lower ones - for periods with summer months. The maximal differences between the data obtained by various models are 9 degrees for winter months, 2 degrees for summer months and 5 degrees for all year period.

Table 1. Optimal tilt angles of solar panels for Kiev (Ukraine) calculated for various radiation models

opt tilt table ukr


1. Duffie J.A., Beckman W.A., Solar Engineering of Thermal Processes, 4th Edition// New York: John Wiley & Sons, 2013, 936 p.
2. Гаевский А.Ю., Ушкаленко О.В. Определение оптимальных углов наклона фотоэлектрических панелей// Відновлювана енергетика. – 2016, №1 (44), с. 21-27.
3. Справочник по климату СССР. Украинская ССР. Часть I. Солнечная радиация, радиационный баланс и солнечное сияние // Ленин-град: Гидромет. изд. - 1966. – 126 с.

Source: A. Gaevskii