STATISTICS OF SOLAR IRRADIANCE TIME SERIES FOR KYIV. I. FREQUENCY AND CORRELATION ANALYSES FOR PHOTOVOLTAIC SYSTEM APPLICATIONS

• Date: 2026
• Main Authors: Gaevskii , O., Gaevska , H.
• Format: Article
• Language: Ukrainian
• Published: Institute of Renewable Energy National Academy of Sciences of Ukraine 2026
• Subjects: solar radiation; clearness index; stochastic residuals; time series; Kyiv; stationarity; frequency distribution; KDE approximation; bimodality; ACF/PACF; ARMA models; photovoltaic systems; energy reliability.
• Online Access: https://ve.org.ua/index.php/journal/article/view/625
• Journal Title: Vidnovluvana energetika

Modern photovoltaic (PV) systems demand precise design and power generation forecasting, making the investigation of regional statistical properties of solar radiation increasingly critical. This paper presents a statistical analysis of daily solar irradiation series for Kyiv over the past 10 years, expressed via the clearness index Kt and decomposed into seasonal and stochastic components. It is demonstrated that the frequency distribution of Kt exhibits a bimodal structure with pronounced peaks corresponding to "overcast" and "clear-sky" states. The "saddle" zone between these peaks indicates that intermediate states of variable cloudiness are less frequent and inherently less stable. This bimodality must be accounted for in PV system design, as calculations based solely on long-term monthly averages lead to significant systematic errors, potentially overestimating energy yield during prolonged overcast periods. The primary focus is placed on the stochastic residuals X of the Kt series, which are essential for generation forecasting and sizing battery energy storage systems (BESS). The stationarity of the residual time series, which retains a bimodal distribution, was confirmed via the Augmented Dickey-Fuller (ADF) test. Analysis of the autocorrelation (ACF) and partial autocorrelation (PACF) functions revealed short-term dependencies effectively captured by ARMA (p,q) models. Parameter estimation across this model family identified the ARMA (1,1) model as the most adequate in terms of both accuracy and parsimony, as confirmed by the Akaike Information Criterion (AIC). The results of these frequency and correlation analyses are essential for testing autonomous and backup PV systems through the generation of diverse weather scenarios, including worst-case conditions.