# Applications of Probabilistic Forecasting in Smart Grids: A Review
## 5 Uncertainty Modeling  
Uncertainty modeling itself needs comprehensive study. In general, uncertainty modeling aims to capture the dynamics of the uncertain input data and generate scenarios based on their probability distributions [75]. The results are then used as the input of stochastic programming. Figure 5 overviews some uncertainty modelling techniques utilized for stochastic programming. In addition, Table 5 states some selected works using these techniques. Monte Carlo simulation (MCS) is one of the most popular methods for scenario generation purposes. The PDFs of the random variables, forecasting errors of the data, and market variability, in general, are employed by the Monte Carlo simulation method in order to learn the uncertain data and generate their associated scenarios, accordingly [82]. Figure 6 illustrates the steps of achieving output from uncertain inputs, using the Monte Carlo simulation method. Figure 5: Uncertainty modelling techniques utilized in a smart grid environment. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multirow{2}{*}{**Uncertain Parameters**} & \multicolumn{2}{c}{**Uncertainty**} \\  & & **Generation** & **General Objective of the Work** \\ \hline
[76] & Wind generation, generators’ reliability & Sequential MCS & Minimizing the total energy generation costs \\ \hline
[77] & Wind generation, PV generation, & & Minimizing the total energy costs \\ battery storage charging/discharging output, & Sequential MCS & + \\ biomass combined with heat generation, and & & minimizing economic risks \\ thermal energy storage output & & & \\ \hline
[78] & Renewable generation, electricity demand, & Pseudo-sequential & Minimizing energy generation environmental impacts \\ household hot water, and space heating and & & MCS & + \\ cooling parameters & & & Minimizing energy costs \\ \hline
[79] & Renewable generations, electricity demand, and & Pseudo-sequential & Maximizing financial profits \\ water inflow & & MCS & + \\ \hline
[80] & risks & Non sequential & Optimizing net present value and analyzing geothermal energy life-cycle for power and transportation sectors \\ \hline
[81] & Renewable generations & GAN & Generate samples for renewable generations based on historical data \\ \hline \hline \end{tabular}
\end{table} 
Table 5: An overview of selected papers using scenario generation techniques in a smart grid environment. The advantages of the Monte Carlo simulation method can be described as follows [83]:  
* The method is able to sample from random processes and supports all of the distribution functions. * A transfer function is not required. * It does not need a mathematical formulation since it can model a problem in the form of a black box system and can obtain output considering samples of inputs. * The method is relatively easy to implement. * It is able to model both non-differentiable and non-convex problems. Recently, Monte Carlo simulation algorithms have evolved and improved. For example, sequential MCS is able to model uncertainties of inputs in chronological order. With the help of the sequential method, uncertainties of time-series inputs (such as variable generation of renewable energy resources and electricity demand) are implemented in a better way [75]. Pseudo-sequential is another extension of the MCS method which has the ability to converge faster compared to the sequential version. The pseudo-sequential method can sample states through its non-sequential capability and uses chronological simulation for the failed states [75]. Finally, the non-sequential MCS method is another family member of the Monte Carlo method which cannot model uncertainties chronologically and requires high computational costs [75]. Recently, a model-free and data-driven method, called the \"Generative Adversarial Network (GAN)\", has attracted more attention for scenario generation purposes. The model employs artificial neural networks (ANNs) and aims to synthesize some understanding  
Figure 6: A flowchart of generating scenarios by MCS algorithm.