# Analysis and Impact Evaluation of Missing Data Imputation in Day-ahead PV Generation Forecasting
## 1 Introduction  
With photovoltaic (PV) systems becoming a mature and environmentally-friendly technology over the past few years, several countries have begun to invest aggressively in PV energy resources. For example, China has increased its PV budget by 30.7% of that of 2017. In addition to developed countries such as China, developing ones such as the Marshall Islands, Rwanda, and the Solomon Islands are also increasingly investing in renewable energy [1], thereby leading to increased PV generation over the past decade [2]. Figure 1[1] depicts the increasing trend of PV power generation, which implies that PV systems are expected to spread globally. However, PV generation depends on weather conditions such as temperature, relative humidity, precipitation, and solar radiation. In other words, the PV output fluctuates frequently because of weather factors. With more PV systems integrating with grids, such fluctuating PV generation can severely impact the stability, reliability, quality, and system operation of power systems while also reducing economic benefits. Therefore, the accurate forecasting of PV generation becomes very important for grid operations involving distributed energy resources. As mentioned in [3], several studies have focused on the prediction of solar power generation and solar radiation in this context. Among the 15,700 solar irradiation and power prediction articles appearing in a Google Scholar search, 6340 were published in 2016. However, there are still problems in accurately forecasting solar power generation because of inaccurate predictions arising due to missing data, where \"missing data\" refers to completely absent data objects/series or imperfect data, i.e., partial data [4]. In this context, it has been reported [5] that when the missing data ratio in the total data is less than 1%, the impact is negligible. Further, missing rates between 1% and 5% correspond to manageable or flexible sample data. On the other hand, missing data rates >5% of the total data require suitable solutions [5]. Further, missing data rates of >15% significantly adversely affect the prediction model [6; 7]. Thus far, PV power generation prediction studies have reported poor performances on rainy days relative to sunny days [8; 9; 10]. This implies that the existence of many missing precipitation data values significantly deteriorates the prediction accuracy. Hence, methods to address the missing data need to be urgently studied. Several studies on missing data imputation have been conducted in multiple contexts. In [5; 6; 7; 11; 12], missing data imputation algorithms based on statistical methods and machine learning approaches such as the \(k\)-nearest neighbors (KNN) method have been proposed. Other studies [13; 14; 15; 16] have proposed missing data imputation methods for solar irradiation. In [13], the authors proposed three missing data imputations that can replace missing data for solar radiation: inverse-distance weighting (IDW), multiple linear regression (MLR), and multivariate imputation by chain equations (MICE). Among these, MICE affords outputs closest to the original solar radiation values when the missing values are replaced. In [14], the authors estimated the temperature and relative humidity for solar irradiance prediction using the Fourier series and support vector machines (SVMs), while in [15], the authors examined several missing weather data imputation methods ranging from simple ones such as mean imputation to complicated ones such as the multilayer perceptron and Markov chain Monte Carlo approaches. In [16], the authors devised two missing imputation methods using atmospheric temperature and relative humidity: the decision matrix and the regression correlation of weather data. The first method affords a minimum correlation coefficient value of 0.95, RMSE of 87.6 W/m\({}^{2}\), NRMSE of 8.29%, and an index of agreement of 0.97 for irradiation.