Reducing greenhouse gas emissions caused by power production can effectively address climate changes [
1]. Therefore, the installation of photovoltaic (PV) power generation systems is significantly increasing with the decreasing installation costs [
2], reaching 39 GW in 2010 and 760 GW in 2020 [
3]. However, as opposed to the existing dispatched power generations, the power generation of PV relies on the weather conditions, thus varying drastically and uncertainly. The high penetration of PV power generation makes it difficult to maintain the balance between demand and supply in electric power systems. This uncertain variability in PV generation can significantly impact the stable and economical operation of power systems [
4,
5]. Therefore, power system operators require forecasting of PV generation output; particularly, short-term forecasting is required to determine the need for demand response, and a quick-start generator is required for the stable operation of the power grid [
4]. To date, different forecasting methods have been proposed for various time scales using solar radiation forecasting or direct PV power forecasting. PV forecasting can be classified into persistent forecasting, physical approach, and statistical approach [
6,
7]. The physical approach forecasts solar irradiance data from a numeric weather predictor atmospheric model. A common approach for regional PV output using numeric weather predictor (NWP) data is to upscale a set of representative regional PV systems. Saint-Drenan et al. [
8] proposed a method to probabilistically forecast the PV output of the entire forecast area from the reference PV power and meteorological data obtained from NWP. Ma et al. [
9] proposed a method to correct the NWP irradiance using the measured irradiance and optimized the prediction model using the particle swarm optimization algorithm. Statistical approaches include forecasting models based on a learning process that uses variables with historical influence. These forecasting models attempt to reduce errors by using the difference between the model’s forecasted and actual data. Therefore, this approach has high-forecasting accuracy for time periods during which the model input patterns are smooth. However, forecast errors increase during periods associated with abrupt changes in weather variables commonly referred to as “drastic change periods”, such as solar radiation, temperature, and humidity [
6]. Statistical methods can be divided into two categories, namely time-series-based and artificial intelligence forecasting models [
6]. Artificial intelligence is a popular technique for forecasting PV output generation. Among them, NN is one of the most used forecasting models. Bacher et al. [
10] reported that autoregression model forecasting can be effective for short-term forecasting based on the results obtained using NWP, observed PV data, and data from both sources. Reikard [
11] estimated the solar radiation intensity using the autoregressive integrated moving average (ARIMA) method and compared it with that obtained from the artificial neural network (ANN) method. Neural networks use different sets of input data to forecast future output patterns and improve the accuracy of the model by carefully selecting different influential parameters. Pedro and Coimbra [
12] implemented an ANN method optimized by a genetic algorithm (GAs/ANN) and compared it with the persistent forecast, ARIMA method, and k-nearest neighbors (kNN) method. They verified that GAs/ANN is superior to the other forecast methods. Zhou et al. [
13] used two long short-term memory models to forecast the temperature and PV output and combined them to enhance the forecast accuracy. Behera et al. [
14] implemented an optimal design methodology for an extreme learning machine-based forecasting model of a PV system and compared its results with those of existing models, such as the backpropagation model. Alamoudi et al. [
15] analyzed the performance of photovoltaic panels using an adaptive neural network-based fuzzy inference system (ANFIS) to determine the self-consumption and sufficiency rates of a PV system, and used response surface methodology (RSM) to determine the optimal operating conditions of the PV panels. They used the ANFIS to analyze the performance of photovoltaic panels to determine the self-consumption and sufficiency rates of PV systems, and a response surface methodology (RSM) to determine the optimal operating conditions of the PV panels. In addition to these approaches, forecasting methods based on image processing techniques have been proposed. Studies have been conducted to estimate solar radiation from satellites and grand-based sensors. Hammer et al. [
16] proposed a method for estimating solar radiation from satellite images and a statistical method for estimating the movement of clouds. Perez et al. [
17] reported that satellite-derived cloud motion-based forecasts are better models for short-term forecasts than NWP-based solar radiation forecasts. Bright et al. [
18] proposed a method for selecting reference PVs to support PV output nowcasts from satellite images. Feng et al. [
19] developed a deep convolutional neural network for global horizontal irradiance one hour ahead of the sky image. Chu et al. [
20] proposed a reforecasting model to improve the forecasting by reforecasting with an ANN and optimizing with a GA from the sky racking technique, ARIMA, and kNN forecasting. Chow et al. [
21] estimated cloud motion from the optical flow method using a sky-imaging system, and the best forecasting may be obtained depending on the smoothness parameter.
The existing method uses the optical flow for forecasting, wherein the motion field between two consecutive images is estimated. This motion field is obtained by minimizing the objective function, comprising the data term and regularization term, by using the variational method [
24,
25]. The parameter
of the regularization term is a model of the smoothness of the motion field obtained using this function. This parameter is important because the obtained motion field is highly affected by the parameter. Previously [
23,
26], the mesh size and interpolation method for blank values when converting to a mesh distribution were determined. In [
23], the proposed method was evaluated based on the forecasting results by only
. In addition, the mesh size determined in the previous studies was small relative to the geographic transitions of actual weather conditions, and the estimations based on this mesh size can drive the objective function to local minimum. Therefore, there were many periods in which the estimated motion vectors did not match the actual motions in rapidly changing weather conditions. In this study, a multiscale approach was used to address this issue. This makes it possible to obtain a motion vector field that is more appropriate to the actual motions by finding the global minimum of the objective function, and to properly evaluate the effect of changing the parameter
. The purpose of this study is to examine the effect of changing this parameter λ and to show the improvement of the prediction results from previous studies. In this study, the prediction of 101 PV power systems is executed with several values of the parameter
, and the prediction error distribution of each PV is evaluated. The PV distribution in Japan (latitude 31.20
6′–39
80′ and longitude 129
60′–141
60′) was normalized every 30 min for one year from 2013 to 2014, converted to geographically distributed mesh data, the motion of the NV distributions was estimated, and then the forecast was evaluated. The PV output volatility is important when evaluating a forecast. Certain periods exist, such as clear days, when it is easy to forecast the PV generation. These times reduce the error difference when evaluating the motion estimations of each parameter, making it difficult to evaluate the parameters. Pedro and Coimbra [
12] reported that developing seasonal models for each period of variability should improve the evaluation of the forecasting method. The objective of this method is to forecast the PV output during periods when the output of multiple PVs changes. As the changes in the PV output over a wide range differ from place to place, capturing the changes in multiple PV outputs is difficult. Therefore, in this study, the period when the output of PVs in a certain area within a 15-km-radius in Japan changed drastically within 30 min was extracted and evaluated. This paper evaluates the proposed method with the multiple PV output changed periods in a certain area where the output changes are correlated to each other. The contributions of this study can be summarized as follows.