# Cost Analysis and Optimization of Modern Power System Operations
## 1 Introduction  
A basic strategy for meeting electricity demand is to keep all available generators online at all times; however, this strategy is highly uneconomical. A more efficient method involves committing only the required generating units during specific time periods, a process known as unit commitment [1]. The integration of renewable energy sources, Plug-in Electric Vehicles (PEVs), and energy storage systems has significantly enhanced the flexibility and resilience of power systems, but it has also increased the complexity of the unit commitment problem [2]. In addition, there has been a notable shift in operational strategy--from adjusting generation to follow demand, to actively managing demand in response to available supply. The adoption of responsive or flexible demand plays a significant role in reducing operating costs and enhancing system performance [3, 4]. Efficient resource scheduling is critical not only for ensuring reliable electricity generation but also for improving system flexibility, resilience, and economic efficiency. These objectives are achieved by solving the unit commitment problem to minimize total operating cost while subject to key operational constraints such as ramp rate limits and reserve requirements [5, 6, 7]. Moreover, the global shift toward smart grid technologies--driven by increased penetration of renewables and energy storage--has introduced new paradigms in energy generation and consumption [8]. Due to the finite nature of non-renewable energy resources and their lasting environmental impacts, there is a growing global shift toward the integration of renewable energy sources and energy storage systems. With proper management and favorable weather conditions, renewable resources can significantly enhance the versatility and robustness of the power system. Furthermore, the cost of renewable energy has declined substantially in recent years, making it increasingly competitive with conventional resources [9; 10]. As a result, the hybridization of renewable and traditional generation systems has been widely explored in the recent literature [11; 12; 13]. One of the most promising approaches for enhancing power system flexibility and efficiency is the implementation of demand-side flexibility measures, which target management of electricity consumption at the load side. Demand-side management (DSM) systems and efforts to reduce usage during peak periods can effectively lower the overall system load and lead to significant operational cost savings. This strategy accelerates the response time of power supply systems, enhancing flexibility while reducing both operational and capital expenditures [14; 15; 16]. Responsive loads--including residential and industrial consumers as well as PEVs--play a key role in supporting grid stability and contribute to improving the system's flexibility and resilience [17; 18]. In [19], PEVs are specifically highlighted as tools for enhancing grid flexibility. Flexibility in power systems has been defined in multiple ways. In [20; 21], it is described as the network's capability to provide non-served energy, while [18] defines it as the system's ability to respond rapidly to substantial and sudden changes in load. A framework for evaluating power system flexibility using load response and renewable resources is presented in [22]. Furthermore, the approach in [23] assesses system flexibility by incorporating fast-ramping generation units, responsive loads, and energy storage systems. Numerous algorithms have been explored in [24; 25] to address the complexities inherent in the unit commitment (UC) problem. Traditional approaches include methods such as priority listing, dynamic programming, Lagrangian relaxation, branch and bound, Mixed Integer Programming (MIP), and stochastic programming. In addition to these, a variety of intelligent optimization techniques have been applied, including artificial neural networks, binary-coded genetic algorithms, fuzzy logic, and particle swarm optimization.