## 2 Proposed IGDT-Based OCL Strategy
### IGDT-Based OCL Problem
#### 2.1.4 Uncertainty Model in Opportunistic Decision-Making Strategy  
The opportunity function, \(\hat{\beta}\Big{(}x_{i^{t}}^{t},F_{w}\Big{)}\), assesses the feasibility of the lower costs. Therefore, a small value of \(\hat{\beta}\Big{(}x_{i^{t}}^{t},F_{w}\Big{)}\) is desirable. According to Equation (12), the opportunity variable is the lowest value of \(\alpha\) for minimization of energy cost as low as \(F_{w}\). Therefore, it is expected that \(\hat{\beta}\Big{(}x_{i^{t}}^{t},F_{w}\Big{)}\) increases with the reduction of \(F_{w}\) for the energy cost minimization approach First, the robustness OCL problem was solved using the GAMS optimization software in conjunction with the different values of the critical energy costs. The risk-aversion optimization problem was performed on the test system, taking Equations (1)-(5), (10), and (11) into consideration. The system operator then determined the value of the known parameter \(F_{k}\) for 12 iterations (\(k=12\)). As mentioned in Section 2.1.3, the main objective of the robustness mode at each scenario \(k\) was to maximize the percentage of the cooling load increase by increasing \(\alpha\) in such a way that the maximum value of the daily energy cost is smaller than or equal to the predefined critical cost \(F_{k}\). Meanwhile, the cooling capacity of the chillers was satisfactory at each solution. In addition, the total refrigeration production of the chiller units was more than or equal to the overestimated cooling demand, or \begin{table}
\begin{tabular}{c c c c c c} \hline
**Chiller** & \(a_{i}\) & \(b_{i}\) & \(c_{i}\) & \(d_{i}\) & \(Q_{i}^{max}\) **(RT)** \\ \hline
1 & 57.2 & 329.73 & 0.05 & 7.85 & 550 \\
2 & 50.09 & 419.28 & \(-123.8\) & 76.36 & 550 \\
3 & \(-76.29\) & 1226.94 & \(-709.37\) & 296.93 & 1000 \\
4 & \(-72.56\) & 1100.42 & \(-145.77\) & \(-137.1\) & 1000 \\
5 & \(-186.18\) & 1817.08 & \(-1755.59\) & 847.43 & 1000 \\ \hline \end{tabular}
\end{table} 
Table 1: Power consumption coefficients and cooling capacity of chillers. Figure 3: Hourly variations of energy rates. Figure 2: Forecasted value of cooling demand over a sample 24-h time interval. \((1+\alpha)\times CL_{t}^{0}\). Figure 4 shows the optimum value of the cooling demand increase at each iteration of the robustness economic dispatch problem. The vertical axis represents the predefined critical energy cost, \(F_{k}\), at each iteration \(k\). The horizontal axis refers to the maximum value of the cooling load increase, which is obtained by solving the robust short-term scheduling problem. As expected from Equations (3)-(5), (10), and (11), when the building cooling load increased, the value of the refrigeration production of the chillers increased, as did the electrical power consumption of the chillers. Figure 4 shows the optimum value of the cooling load increase at each scenario of the robust economic dispatch problem. It is clear that the daily electricity cost increased, a result which is to be expected as per Equation (1). In the opportunistic optimal cooling energy procurement strategy, the target energy cost, \(F_{w}\), is lower than that obtained from solving the base case study (Equations (1)-(5)) without considering the uncertainty of the cooling load. In other words, the system operator wants the daily electricity purchasing cost to be smaller than the energy cost of the multi-chiller system under \(\alpha=\beta=0\) or the base optimization problem. The system owner wants to reduce the daily energy cost of the five-chiller plant so that it is as low as the target energy cost, \(F_{w}\). Hence, the minimum value of the cooling load decrease, which reduces the energy cost to predefined values \(F_{w}\), must be found by solving the optimization problem (Equations (1)-(5), (13) and (14)). As shown in Figure 5, eight scenarios were considered for the risk-taker decision-making approach (\(w=8\)). As expected from Equations (5) and (13) and displayed in Figure 5, when the cooling demand decreased, the value of the cooling production of the chillers also decreased.