Modern power systems increasingly rely on hierarchical architectures where distribution networks and microgrids must operate in tight coordination to balance renewable generation, storage, and load. Three-port converters—devices that interface multiple energy sources and storage systems—present a particular optimization challenge because carbon emissions flow differently across their interconnected ports, making traditional dispatch methods inadequate.
Researchers addressed this gap by developing a carbon-tracking framework that explicitly models how carbon intensity propagates through converter ports. This represents a significant advance over empirical estimation methods, which typically underestimated emissions by up to 11% by treating hybrid nodes as black boxes.
The core innovation lies in converting the inherently nonlinear optimization problem into a mixed-integer second-order cone programming (MISOCP) formulation. By applying McCormick envelope relaxation to bilinear carbon-flow terms and SOCP relaxation to power-flow constraints, the authors created a convex problem solvable by standard solvers while retaining binary variables needed to represent battery charging and discharging decisions. This approach reduces computational complexity and eliminates sensitivity to initial values—a persistent problem in nonconvex optimization.
In case studies, the framework coordinated distribution and microgrid operations to maximize renewable utilization while minimizing both carbon emissions and electricity costs. Results showed photovoltaic penetration increased to 84.11%, solar curtailment dropped to 11.89%, and overall system costs decreased by 6.94% compared to baseline dispatch strategies. Carbon emissions fell 10.22% without sacrificing grid reliability.
The methodology provides a practical pathway for utilities managing complex, distributed architectures with high renewable penetration. As regulatory pressure for carbon reporting intensifies and converter-based resources proliferate, this real-time carbon-aware coordination approach becomes increasingly valuable for both operational efficiency and compliance with climate commitments.
