## 1 Introduction  
As renewable energy sources such as wind and solar become increasingly integrated into the power system, the intermittency of the electricity supply is increasing significantly. At the same time, the shift from passive consumers to more flexible ones such as Electrical Vehicles (EVs) is adding uncertainty to electricity demand. This combination of variable supply and unpredictable demand creates challenges for power grid stability [1]. Energy flexibility is an effective solution to balance renewable energy fluctuations and ensure a stable power system. Below, energy flexibility is discussed from three perspectives: power supply, electricity demand, and energy storage. On the demand side, flexibility has been explored across different sectors, including residential [2], commercial [3], agricultural [4], and industrial [5]. Each sector has unique electricity demand patterns and flexibility potential, requiring expert knowledge for effective management. Among these, the industrial sector has energy-intensive processes that can provide significant flexibility to the power grid. Industrial plants are categorized into light, medium, and heavy industries. Light and medium industries are usually connected to distribution and sub-transmission networks, while heavy industries are often connected directly to the transmission network. This means that industrial energy management systems can help to support both distribution and transmission grids. Certain industrial processes can be adjusted based on grid requirements. For example, recent studies have shown that crushers and milling machines used in cement manufacturing can change their power consumption with short advance notice [6]. Similarly, in metal smelting, electric furnaces can increase or decrease their power usage with mid-term notice, helping to help stabilize the grid [7]. Many industries also have on-site power generation (self-distributed generation), which can support the grid during power shortages. A recent study has shown that oil refineries can use their Distributed Generation (DG) units to help balance power fluctuations in the grid [8]. In recent years, the water-energy nexus has gained attention as the water industry seeks more efficient energy usage [9]. Research has suggested [10] that restructuring the agricultural sector could improve its ability to integrate more renewable energy sources. Another [11] showed that operation of irrigation pumps can be optimized to provide grid flexibility during peak demand hours, especially when crop water demand coincides with high electricity consumption periods. Recent studies have shown that heat pumps are being used more in livestock industries, e.g., poultry farms, pig farms, and ranches [12]. These heat pumps run on electricity instead of fossil fuels, and can produce 3-5 times more heat than they use in electricity. They can also help to balance electricity demand by adjusting indoor air temperatures. Because the thermal time constant is slower than electricity, heat pumps can be turned off or down when there is not enough renewable power available on the supply side [13]. In addition to heat pumps, cooling plants are energy-intensive industrial plants in the water-energy nexus environment that can provide significant flexibility for both the heat and electricity grids [14]. In cold storage facilities such as those for meat and fish, cooling systems remove heat from the stored goods by consuming electricity. The waste heat that is removed can then be directly fed into the district heating network or used by booster heat pumps to improve the efficiency of district heating [15]. Current research on energy flexibility shows that many potential sources of flexibility in different demand sectors remain underexplored. In order to unlock this flexibility without compromising comfort or safety, expert knowledge is essential. In addition to identifying flexibility potentials, the state of the art also explores various methods for optimizing energy flexibility.