# 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** &
\begin{tabular}{c} **Methods to Capture** \\ **Uncertainties** \\ \end{tabular} & **Objective** \\ \hline
[111] & Wind speed, demand, and solar irradiance & \
\begin{tabular}{c} Conditional value at risk \\ (CVaR) combined with \\ robust optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing the costs of an energy hub participating in \\ energy and reserve markets \\ + \\ Minimizing the emissions of pollution \\ \end{tabular} \\ \hline
[105] & Wind and photovoltaic generations & \
\begin{tabular}{c} Two-stage adjustable \\ robust optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing the costs of multi-energy system that supplies \\ both electricity and heat loads \\ \end{tabular} \\ \hline
[102] & Load and energy price & \
\begin{tabular}{c} Hybrid stochastic/robust \\ optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing planning, operation and resilience costs of the \\ distribution networks considering earthquake and \\ flood situations \\ \end{tabular} \\ \hline
[112] & Energy price and PV generations & \
\begin{tabular}{c} Hybrid stochastic/robust \\ optimization \\ \end{tabular} &
\begin{tabular}{c} Maximizing the profits of a household customer \\ \end{tabular} \\ \hline
[113] & Wind and PV generations, loads, and \begin{tabular}{c} market-clearing prices \\ \end{tabular} & \
\begin{tabular}{c} P-robust (a combination \\ of robust and stochastic \\ programming) \\ \end{tabular} &
\begin{tabular}{c} Minimizing the operating costs of diesel engine, micro \\ turbine, procurement costs, costs of pollutant treatment, \\ and costs of reimbursing incentive-based demand \\ response programs \\ \end{tabular} \\ \hline
[114] & \begin{tabular}{c} Availability of microgrid equipment, active \\ and reactive loads, parameters of EVs, energy \\ price, wind and PV generations \\ \end{tabular} & \
\begin{tabular}{c} Hybrid stochastic/robust \\ \end{tabular} &
\begin{tabular}{c} Minimizing the microgrid’s costs including the cost of \\ buying energy, the operation cost of non-renewable energy \\ sources, the reliability costs in terms of non-supplied loads \\ \end{tabular} \\ \hline
[115] & Renewable distributed generations & \
\begin{tabular}{c} Robust model combined \\ with prediction control \\ \end{tabular} &
\begin{tabular}{c} Maximizing the amount of load restoration that is \\ controlled by the output of the power units and \\ remote-controlled switches \\ \end{tabular} \\ \hline
[116] & Electricity demand and facility & \
\begin{tabular}{c} Robust optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing the installation costs of power plants, \\ high-voltage/low-voltage substations, and feeders, feeders’ \\ power transmission costs \\ + \\ Minimizing the storage power cost, power losses’ costs in \\ feeders, feeder failures’ costs \\ \end{tabular} \\ \hline
[98] & PV and wind generations, & Robust optimization &
\begin{tabular}{c} Minimizing the annual costs of the regional \\ distribution networks \\ \end{tabular} \\ \hline
[103] & \begin{tabular}{c} Wind generation, outages, La Niña and El \\ Niño events (a long-term warming happening \\ for the central and eastern Pacific and \\ vice versa) \\ \end{tabular} & \
\begin{tabular}{c} Robust optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing investments’ and operations’ costs of \\ the system \\ \end{tabular} \\ \hline
[99] & Unbalanced power percentage & \
\begin{tabular}{c} Robust optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing the annual investment costs of transmission \\ network lines as well as the costs related to battery \\ superconducting magnetic hybrid energy storage system \\ under maximum the load-shedding conditions \\ + \\ Reducing the insufficient supply if N-k faults happen \\ \end{tabular} \\ \hline
[117] & Random N-K contingency, wind and \begin{tabular}{c} PV generation \\ \end{tabular} & \
\begin{tabular}{c} Robust optimization \\ \end{tabular} &
\begin{tabular}{c} Minimizing the investment costs of building candidate \\ lines, the generation costs of conventional generators, the \\ costs related to scheduling downward and upward \\ spinning-reserves, costs of renewable generation \\ curtailment and load-shedding \\ \end{tabular} \\ \hline
[106] & \begin{tabular}{c} Market participants’ offers and bids as well as \\ real-time market prices \\ \end{tabular} & \
\begin{tabular}{c} Robust optimization \\ \end{tabular} &
\begin{tabular}{c} Maximizing profits of a virtual bidder (optimal \\ bidding strategy) \\ \end{tabular} \\ \hline
[107] & Wind generation and electricity prices & \
\begin{tabular}{c} Robust MPC-based \\ optimization \\ \end{tabular} &
\begin{tabular}{c} Maximizing the profits and minimize the operating costs of \\ a wind-storage system (optimal bidding strategy) \\ \end{tabular} \\ \hline
[118] & Renewable generations and electric vehicle & \
\begin{tabular}{c} Robust optimization \\ \end{tabular} &
\begin{tabular}{c} Optimal location and sizing of renewable distributed \\ generation and the charging stations based on \\ maximization the station’s total payoff \\ \end{tabular} \\ \hline
[119] & Loads and renewable generations & Robust optimization &
\begin{tabular}{c} Designing generation resources for a microgrid to meet its \\ demand by minimizing the total generation costs of \\ the resources \\ \end{tabular} \\ \hline
[100] & Loads, wind and PV generations & Robust optimization &
\begin{tabular}{c} Positioning and sizing of the energy storage system by \\ minimizing the operation costs of the flexible energy \\ resources as well as those of the network \\ \end{tabular} \\ \hline
[101] & PV generation & Robust optimization &
\begin{tabular}{c} Planning of distributed battery energy storage from a DSO \\ viewpoints by minimizing the batteries’ degradation and \\ operation costs \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}