# Cost Analysis and Optimization of Modern Power System Operations
## 3 Implementation and Case Studies  
To implement the unit commitment algorithm, the essential input parameters include generator characteristics, hourly electrical demand, and electricity supply prices [30]. Since the study focuses on a day-ahead scheduling scenario, 24 h data for both demand and electricity prices are required. The algorithm processes these inputs to determine the optimal on/off status of each generator and calculates the total system operating cost. In this study, the system comprises 10 thermal generating units. The key characteristics of each generator--such as minimum and maximum generation capacity, ramp-up and ramp-down limits, start-up and shutdown costs, and generation cost coefficients--are considered for the optimization. These parameters are summarized in the following Table 1.  
In the given table information about different cost coefficients, Start-up/Shut-down cost, Up-time/Down-time, Ramp Up/Down rates, Shut-down/Start-Up rate, and minimum and maximum capacity of different generating units are given. Also, in the above table additional information about duration of time for which a unit has been ON/OFF at the beginning of the operating horizon is given under parameters U\({}_{o}\)/S\({}_{o}\). As the study is conducted for the next 24 h scheduling of available generating units, information about load demand for 24 h is also required for simulation, hence data for load demand (\(L_{t}\)) are given as Figure 2.  
Figure 2 presents the dynamic load profile over the 24 h operating horizon, reflecting the varying electricity demand throughout the day [31]. The load fluctuates significantly, with a minimum observed demand of 834 MW and a peak of 1455 MW. This variation highlights the importance of optimal unit commitment to ensure cost-effective and reliable power system operation. Figure 3 illustrates that electricity prices fluctuate throughout the 24 h operational period rather than remaining constant [32]. The lowest electricity prices are observed during the early hours (from t1 to t6), while the highest prices occur during the intervals t7 to t10 and t17 to t23, reflecting periods of peak demand or constrained supply. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**Unit** & \begin{tabular}{c} **a** \\ **(S/MW2)** \\ **(S/MW)** \\ \end{tabular}  & \begin{tabular}{c} **b** \\ **c** **(S/MW)** \\ \end{tabular}  & \begin{tabular}{c} **c (S)** \\ **(S)** \\ \end{tabular}  & \begin{tabular}{c} **CostSD** \\ **(S)** \\ \end{tabular}  & \begin{tabular}{c} **costst** \\ **(MW/h)** \\ \end{tabular}  & \begin{tabular}{c} **RU** \\ **(MW/h)** \\ \end{tabular}  & \begin{tabular}{c} **RD** \\ **(h)** \\ \end{tabular}  & \begin{tabular}{c} **UT** \\ **(h)** \\ \end{tabular}  & \begin{tabular}{c} **SD** \\ **(MW/h)** \\ \end{tabular}  & \begin{tabular}{c} **SU** \\ **(MW/h)** \\ \end{tabular}  & \begin{tabular}{c} **Pmin** \\ **(MW/h)** \\ \end{tabular}  & \begin{tabular}{c} **Pmax** \\ **(h)** \\ \end{tabular}  & \begin{tabular}{c} **U0** \\ **(h)** \\ \end{tabular}  & \ \begin{tabular}{c} **Uni** \\ **(h)** \\ \end{tabular}  & \begin{tabular}{c} **S0** \\ **(h)** \\ \end{tabular}  \\ \hline g1 & 0.0149 & 12.1 & 82.0 & 42.6 & 42.6 & 40 & 40 & 3 & 2 & 90 & 110 & 80 & 200 & 1 & 0 & 1 \\ \hline g2 & 0.0289 & 12.6 & 50.6 & 50.6 & 50.6 & 64 & 64 & 4 & 3 & 130 & 140 & 120 & 320 & 2 & 0 & 2 \\ \hline g3 & 0.0135 & 13.2 & 100.0 & 57.1 & 57.1 & 30 This study is structured into four distinct case studies, each addressing a different system scenario or operational constraint:  
1. Case 1--Base Scenario (Traditional System):  
The unit commitment problem is solved for a conventional power system comprising 10 thermal generating units. The technical and economic characteristics of these units are detailed in Table 1.
2. Case 2--Reserve Constraint:  
In this scenario, a reserve constraint is introduced in addition to the standard unit commitment constraints. This enhancement is aimed at improving the system's reliability by ensuring adequate spinning reserves are maintained. 3.