# Applications of Probabilistic Forecasting in Smart Grids: A Review
## 6 Decision Making under Uncertainties
### Stochastic Programming
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** & **Uncertain Parameters** & **Methods to Capture Uncertainties** & **Objective** \\ \hline \multirow{4}{*}{[86]} & \multirow{4}{*}{\begin{tabular}{c} Prices (day-ahead market and balancing market), renewable generations, loads, driving requirement and the availability of electric vehicles (EV) \\ \end{tabular} } & Two-stage stochastic programming & Proposing a system for microgrid support by maximizing the expected profit of a microgrid aggregator \\ \hline \multirow{4}{*}{[87]} & EVs arrival, and departure time, as well as EVs\({}^{\prime}\) daily traveled miles and types, solar irradiation and wind speed, loads & Two-stage stochastic programming & Maximizing the retailer’s profit (first stage: fuel cell scheduling second stage: distributed generation scheduling) \\ \hline \multirow{4}{*}{[88]} & \multirow{4}{*}{Electricity demand, wind speed} & Two-stage stochastic programming & Minimizing day-ahead dispatch costs of the wind-thermal-hydropower-pumped storage system along with the system’s expected balancing costs \\ \hline \multirow{2}{*}{[89]} & \multirow{2}{*}{Renewable generations and loads} & Two-stage stochastic programming & Minimizing the costs of reserving flexibility services in day-ahead forecasting and their real-time activation \\ \hline \multirow{2}{*}{[90]} & \multirow{2}{*}{Wind generation, demand and market prices} & Two-stage stochastic programming & Maximizing microgrid’s profits participating in day-ahead and real-time markets taking into account the microgrid’s reconfiguration \\ \hline \multirow{4}{*}{[91]} & \multirow{4}{*}{Wind generation, demand and market prices} & \multirow{4}{*}{\
\begin{tabular}{c} Simple \\ scenario-based \\ stochastic \\ programming \\ \end{tabular} } & Obtaining coordinated network expansion planning by minimizing the operation cost of generation \\ \cline{3-4}  & & & Minimizing the annual investment cost of expanding the transmission networks \\ \cline{3-4}  & & Simple & Minimizing the renewable resources’ annual investment costs \\ \cline{3-4}  & & & Minimizing the annual investment and operation costs of energy storage systems \\ \cline{3-4}  & & & Maximizing the flexibility index of the system \\ \hline \multirow{4}{*}{[92]} & \multirow{4}{*}{Renewable generations} & Simple & \multirow{4}{*}{
\begin{tabular}{c} Proving ancillary services from flexible distributed \\ energy resources in a day-ahead operational planning by minimizing network’s costs \\ \end{tabular} } \\  & & & Minimizing the aggregated demand through their \\ \cline{3-4}  & Electricity demand, renewable generations, market prices & Two-stage stochastic programming & Supplying the aggregated demand through their \\ \cline{3-4}  & & & participation in the day-ahead market and maximizing \\ \cline{3-4}  & & & their total expected profits \\ \hline \multirow{4}{*}{[94]} & \multirow{4}{*}{Electricity demand and PV generation} & Multi-stage stochastic programming & Operating an energy community with PV-storage system by minimizing the electricity purchased from the grid \\ \cline{3-4}  & & & Economic dispatch for a hybrid distribution system based on active-reactive power coordination by minimizing the cost of gas-fired operation, power purchasing from the upstream grid, penalty costs related to substations’ power fluctuations, network losses, and the costs of virtual \\ \cline{3-4}  & & & curtailment and load shedding \\ \hline \multirow{4}{*}{[96]} & \multirow{4}{*}{Renewable generations, electric vehicles, loads, and market prices} & Simple & Optimal energy management of microgrids by minimizing operational costs of distributed energy resources, the costs of purchasing power from the upstream network, the costs incurred from the energy not served, and those related to EV batteries’ degradation costs \\ \cline{3-4}  & & & EV batteries’ degradation costs \\ \hline \hline \end{tabular}
\end{table} 
Table 6: An overview of recent papers using stochastic programming for decision making in a smart grid environment.