## 3 Methodology to Develop and Execute a Redispatch Model in Real-Time Operation
### Mathematical Methodology to Implement the Modeling of a Redispatch
#### 3.2.7. Mathematical Formulation Defining Maximum Dispatch Power for System Security
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Zone Electric** & **Location in Chile** & **Bus** & **Demand Category** & **Factor Demand** \\ \hline \multirow{8}{*}{North} & \multirow{4}{*}{Antofagasta} & \multirow{2}{*}{PARINACOTA\_220} & Residential & 0.95 \\  & & & POZO ALMONTE\_220 & Residential & 0.95 \\  & & COLLAHUASI\_220 & Copper Mining & 2.38 \\ \cline{2-5}  & & ENCUENTRO\_220 & Copper Mining & 3.81 \\  & & CRUCERO\_220 & Copper Mining & 4.76 \\  & & TOCOPILLA\_220 & Residential & 0.95 \\  & & MEJILLONES\_220 & Residential & 1.43 \\  & & CAPRICRONIO\_220 & Copper Mining & 1.43 \\  & & LABERINTO\_220 & Copper Mining & 3.81 \\  & & ANDES\_220 & Copper Mining & 5.71 \\ \hline \multirow{8}{*}{North Center} & \multirow{4}{*}{Atacama} & DIEGO DE ALMAGRO\_220 & Copper Mining & 1.90 \\  & & CARDONES\_220 & Copper Mining & 2.38 \\  & & MAITENCILLO\_220 & Copper Mining & 2.86 \\ \cline{2-5}  & & Coquimbo & PAN DE AZUCAR\_220 & Commercial Tourism & 3.81 \\ \hline \multirow{8}{*}{Center} & \multirow{4}{*}{Valparaiso} & VENTANAS\_110 & Residential & 0.48 \\  & & AGUA SANTA\_110 & Commercial Tourism & 1.43 \\  & & QUILLOTA\_110 & Residential & 0.95 \\  & & SAN PEDRO\_110 & Residential & 1.90 \\  & & LAS VEGAS\_110 & Residential & 1.90 \\ \hline \multirow{8}{*}{South Center} & \multirow{4}{*}{Metropolitan} & EL SALTO\_220 & Residential & 7.62 \\  & & CCRRO NAVIA\_220 & Residential & 7.62 \\  & & CHENA\_220 & Residential & 7.62 \\ \cline{2-5}  & \multirow{2}{*}{O’Higgins} & ALTO JAHUEL\_220 & Farming Industry & 5.71 \\  & & ALTO JAHUEL\_154 & Farming Industry & 2.86 \\ \cline{2-5}  & & COLBUN\_220 & Farming Industry & 0.95 \\  & & ANCOA\_220 & Farming Industry & 0.95 \\  & & ITAHUE\_154 & Residential & 1.90 \\ \cline{2-5}  & & Nuble & CHILLAN\_154 & Residential & 1.43 \\ \hline \multirow{8}{*}{South} & \multirow{2}{*}{Bio-Bio} & CHARRUA\_220 & Residential & 10.48 \\ \cline{2-5}  & & La Araucania & TEMUCO\_220 & Residential & 2.38 \\ \cline{1-1} \cline{2-5}  & \multirow{2}{*}{Los Rios} & VALDIVIA\_220 & Commercial Tourism & 1.90 \\ \cline{1-1}  & & PICHIRROPULLI\_220 & Livestock Industry & 1.43 \\ \cline{1-1}  & & UERTO MONIT\_220 & Fishing Industry & 2.38 \\ \cline{1-1}  & & CHILOE\_220 & Fishing Industry & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Demand participation factor by electrical zones. 2.1 Real-Time Extreme Scenario 1: Partial Deviation of Water-Deficit Wind Generation in Reservoir Power Plants Compete with the Unlimited Resource of Coal-Fired Gas-Fired Thermal Power Plants with Higher Variable Generation Costs  
This actual scenario considers the availability of gas-coal thermal generation with 100% gas volume and abundant coal stock. The variability of this real scenario is presented in wind generation with 40% of its programmed forecast, while hydroelectric generation from reservoirs and run-of-river is affected by a hydro reduction for generation of 30% of its programmed forecast, as shown in Figure 8.  
In this situation the redispatch model for real-time extreme scenario 1 is effective with respect to a dispatch of plants using the economic merit list, because Figure 8 indicates on the primary axis the power increases and decreases in megawatts of the plants used in the redispatch. The gas-fired thermal power plants favorably show an increase in generation ranging from 2200 to 3200 MW. This redispatch allows reducing coal-fired thermal generation by 200 to 300 MW. Diesel-fired thermal generation is reduced by 1900 to 3600 MW. The secondary axis of Figure 8 shows the marginal costs obtained in the redispatch ranging from 70 to 123 USD/MWh.