A novel bi-level optimization scheduling framework for electricity-carbon-water Nexus in power systems

The sustainable development of water-efficient and low-carbon power systems has become an increasingly urgent priority. Existing research primarily utilizes provincial-level power trade data to model the nexus between virtual water and carbon emissions. However, these studies often lack an integrated approach to power flow analysis, limiting their effectiveness in guiding power scheduling decisions. Furthermore, optimization efforts in power systems have focused primarily on carbon reduction, overlooking the need for a holistic optimization that addresses both water conservation and carbon reduction within the electricity-water-carbon nexus. To address these challenges, this paper proposes a bi-level scheduling model for power systems that synchronously optimizes water conservation, carbon reduction, and economic efficiency. The model integrates the coordination of generation, load, and energy storage. In the upper-level optimization, the model determines the optimal generation strategy for water and carbon savings. By accounting for carbon emission flow and virtual water flow, the power grid operator calculates electricity-water-carbon coupling prices at load nodes, based on water and carbon intensities. In the lower-level optimization, load aggregators (LAs) and energy storage operators respond to price signals by formulating optimal load-shifting and energy storage charging/discharging scheduling. To reduce computational complexity, the lower-level problem is transformed into Karush-Kuhn-Tucker (KKT) optimality conditions using the Lagrange multiplier method, enabling the bi-level optimization to be converted into a single-level problem. This is then solved using the Branch-and-Bound method to determine the optimal power flow for the system. Case studies using the improved IEEE 33-node model demonstrate that the proposed optimization model reasonably allocates the water consumption and carbon emission responsibilities to each node, relieving water stress in water-scarce areas, reducing the system's total water consumption and total carbon emissions, reducing wind and photovoltaic curtailment compared to the existing methods. Particularly, the model reduces the system's total water consumption by 29.64% and carbon emissions by 10.68% compared to Scenario 1. It supports the sustainable development of power systems by leveraging flexibility resources on both the load and storage.