# Applications of Probabilistic Forecasting in Smart Grids: A Review
## 3 Renewable Generation and Load Probabilistic Forecasting
### Wind Probabilistic Forecasting  
There are studies trying to relate a known PDF to wind generation. They mainly adopted Gaussian and beta distributions to probabilistically forecast wind power using parametric methods [40]. Some research also tried other types of distribution functions. For example, ref. [41] proposed a modified version to generalize logit-normal distribution for wind power. Reference [42] considered the same distribution for wind generation. The authors of [43] took wind power as a double-bound variable and obtained the appropriate distribution based on this assumption. In another study, ref. [44] solved an economic dispatch problem using a versatile probability distribution for wind generation. However, it was also discussed that relating specific distributions to the distribution of wind power cannot be applied since in some cases, the predictive error of wind power distribution is changing over the prediction horizons [45]. A huge number of papers have been proposed that utilized non-parametric probabilistic forecasting models for wind generation. For instance, considering QRF-based methods, ref. [46] proposed a novel direct quantile regression (DQR) method to probabilistically predict wind power, generating quantiles without using statistical inference. The prediction was based on multi-step 10-min forecasts that combined the extreme learning machine (ELM) and QRF models to make the non-parametric probabilistic forecast and use it in a linear programming problem. Their proposed novel approach was finally compared to four different forecasting techniques, including the bootstrap-based ELM (BELM)-normal distribution, the BELM-beta distribution, the persistence model, and the radial basis function-neural network (RBF-NN) model. The final results demonstrate that the model proposed by [46] performs better in terms of the sharpness criteria. In this regard, the proposed DQR model performed 25% better compared to the persistence model and its performance was 20% better than the RBF-NN probabilistic forecasting model. In addition to the sharpness criteria, DQR model presented a more acceptable computational time equaling 63.89 s, according to the result section of [46]. As another example, ref. [47] presented a joint quantile regression (JQR) model that reproduces kernel Hilbert spaces for wind power probabilistic forecast utilizing the primal-dual coordinate descent technique. The work then employed the multi-objective salp swarm algorithm (MSSA) to optimize the final results. It then tested the forecasting model and compared it with other models on a one-step-ahead and a multi-step-ahead basis. Figure 4: Probabilistic forecasting models for PV generation. Another method for obtaining the non-parametric distribution of wind power is the use of KDE. However, the model is highly impacted by using different kernel functions. In other words, the appropriate kernel function should be selected based on the type of the random variable so to avoid the boundary effects on the PDF of wind generation [52]. To resolve this issue, ref. [17] proposed applying a tri-level adaptation function integrated with a fuzzy inference system. As examples of ensemble forecasting models, authors of [48] suggested a multi-distribution ensemble (MDE) forecasting model that is integrated with competitive and cooperative strategies. In this way, the work tried three different distributions as the ensemble members. Based on the comparison results presented by the paper, the MDE integrated with the cooperative model performed better in an hour-ahead forecast. However, the MDE integrated with the competitive model had a better performance in longer horizons including two-to-six-hours- and 24 h-ahead. Three different neural network-based probabilistic forecasting models were also presented by [49]. The work combined the ensemble deep learning method with empirical wavelet transform decomposition (EWT), which outperformed the other models considered in the paper. ref.