# Adaptive Solar Power Forecasting based on Machine Learning Methods
## 5 Simulation Results
### Performance Evaluation of ASPF
\(\Delta_{2}\) does not update when BPNN is not working as shown in Figure 9d for the 6 th and the 7 th day. Figure 9c illustrates the \(\Delta_{1}\) in EMS, and if there is no similar day or the number of similar days is 1, \(\Delta_{1}\) is constant. When the number of similar days is larger than 1, it means several similar days are in the database, and \(\Delta_{1}\) should be lowered in order to find possible similar days as the data increases. In this way, the efficiency of ASPF keeps improving. Please note that, we plot the results for sunny day in Figures 9 and 10, however, our simulation results are not only effective for sunny days, but also for PV power revision in other weather types, such as cloudy, rainy day. It can be seen in Tables 7 and 8, because the data in \(group\) 1 or \(group\) 2 can be any weather types. The results from _group_ 2 are shown in Figure 10. The number of similar days increase, the change in \(\Delta_{1}\) and \(\Delta_{2}\) are even more apparent than _group_ 1. This change depends on the number of operation days. Tables 7 and 8 record the detailed steps in _group_ 1 and _group_ 2. Here, SI is an indicator of the existence of similar days: 1 indicates similar days exist, while 0 means no similar day. TS represents the number of similar days when SI \(\geq\) 1. WD is the MxAE in \(P_{sdm}/P_{rev}\), and \(P_{act}\) is less than \(\Delta_{2}\). In contrast, BD indicates that the MxAE is greater than \(\Delta_{2}\). NS is the opposite of SI, and NS = 1 means no similar day. \(WD^{{}^{\prime}}\) and \(BD^{{}^{\prime}}\) are used to record the states of our revised prediction performance after updating. In Table 7, BD is 1 in the 13 th day, which means the similar day's actual value has a large deviation from the 13 th day's actual solar power. In addition, then, ASPF retrains the network using the 13 th day's data at the end of the 13 th day. When there is similar day close to the 13 th day at the 18 th day, the 13 th day's actual solar power is adopted as day-ahead revised power and the MxAE is less than \(\Delta_{2}\). The same situation also happens in _group_ 2, as shown in Table 8. In _group_ 2, at the 3 rd day, there is no similar day, solar power is revised by BPNN and then stored in database as shown in Table 8. In addition, the 25 th day is similar to the 3 rd day's information, so the 3 rd day's actual solar power is used as the 25 th day's revised power, and the result is acceptable as shown in Figure 10d. This reveals that as the number of data increases, the results of adopting similar day's actual power become more accurate, and the predictive input message can be identified and compensated adaptively. Through the above simulations, it is reasonable to use the similar day's actual value as the solar forecast power if the forecasting data satisfies the certain condition, which limits the deviation of the predicted data be less than \(\Delta_{1}\). Also, because BPNN updates the network when MxAE exceeds \(\Delta_{2}\), this also ensures that BPNN can effectively predict the data in different situations. In the case of 98%, BPNN can get satisfactory results in this system. Furthermore, in order to verify the wide applicability of our proposed ASPF algorithm, we run similar simulation for the PV power predicted by MLR, and compare the result. Firstly, 150 days data from 1 January 2016 to 31 August 2016 are randomly selected as the initial database to get the MLR predictive PV power. Then, we select 120 days from 1 September, to 31 December 2016 as testing data. According to the results of _k-means_, the data of the testing days is classified into three groups, which contain 43, 51, and 26 days, respectively.