# Cost Analysis and Optimization of Modern Power System Operations
## 3 Implementation and Case Studies
### Case 1: Unit Commitment of 10 Thermal Power Plants for Dynamic Load
Therefore, solving the unit commitment problem remains critical for ensuring efficient and smooth operation of the power system. Figure 6: Reserve provision by thermal units for 24 h.  
Since wind energy is a part of the generation portfolio in this case, the estimated 24 h wind energy availability profile is provided as Figure 2:0  
As shown in Figure 7, wind energy availability is intermittent and varies significantly throughout the 24 h period. This intermittency presents challenges for reliable power system operation. To address this, modern power systems incorporate energy storage systems (ESS), which help smooth out fluctuations by storing surplus energy during periods of low demand or low prices and releasing it during high demand or high price periods. For this study, a battery energy storage system (BESS) is employed. The system is characterized by the following parameters:  
* Maximum state of charge (\(SOC_{max}\)): 300 MW
* Initial state of charge (\(SOC_{0}\)): 100 MW at the start of the operating horizon
* Minimum charging/discharging power: 0 MW
* Maximum charging/discharging power: 0.2 \(\times\)\(SOC_{max}\) = 60 MW  
Like all real-world technologies, storage systems are not 100% efficient. For this study:  
* Charging efficiency: 95%
* Discharging efficiency: 90%  
To accurately capture the behavior and cost implications of integrating wind energy and battery storage, the objective function is modified. In addition to minimizing traditional operating costs (fuel, startup, and shutdown), the revised objective function now includes a wind energy curtailment penalty. This ensures that any unused or curtailed wind energy is factored into the economic assessment, encouraging maximum utilization of available renewable resources. The updated objective function is given as follows:  
Figure 2:1  
Also, some additional constraints and modifications are performed, such as,  
Figure 2:2  
Figure 2:3  
After modifying and including the above three equations, the unit commitment algorithm is applied in GAMS for this case, and the following outputs are found at Figure 2:4  
Figure 2:5 Availability of wind energy for 24 h.  
As illustrated in Figure 8, the operation of the Energy Storage System (ESS) plays a critical role in balancing supply and demand throughout the 24 h horizon. For instance, at time t1, the ESS discharges 10 MW to help meet the load demand, compensating for a shortfall in power from both renewable and thermal generation sources. Conversely, at time t6, the ESS charges 60 MW, effectively storing excess energy that is not immediately required to meet demand. This ability to shift energy temporally--absorbing surplus generation during low-demand periods and releasing it during high-demand or supply-deficient periods--contributes to significant operational cost savings. Moreover, the inclusion of ESS enhances the flexibility and resilience of the power system by reducing reliance on expensive peaking units and minimizing renewable energy curtailment. Overall, the strategic use of storage enables a more efficient, economical, and reliable power system, especially in systems with high penetration of intermittent renewable resources. Figure 9 depicts the schedule of four generating units in a day. The MIP-based optimization model presented in this study is generalizable in structure, but its practical applicability and scalability do depend on system characteristics such as grid size, complexity, and regional regulations. The core MIP formulation is suitable for small to medium-sized power systems, such as regional grids, microgrids, or isolated networks. However, for very large-scale power systems (e.g., national grids with thousands of units and buses), the computational burden can grow rapidly due to the increase in binary and continuous variables. In such cases, decomposition methods or heuristic/metaheuristic strategies may be preferred to balance accuracy and tractability.