Justice-Flexibility-Oriented Modeling of Multi-Carrier Sustainable Microgrids

As power systems become increasingly user-centric and participatory, fairness is emerging as an important consideration in operational decision-making. However, justice-related aspects are often assessed only after system operation, limiting their role in scheduling strategies. An Operational Energy Justice (OEJ) model is proposed in this paper to incorporate equality in load-shedding distribution as a measurable and optimizable objective in multi-energy microgrid scheduling. A novel justice index based on load-shedding distribution among load points is introduced. The proposed model includes energy justice, economic cost, environmental impact, flexibility, and load shedding. In addition, a flexibility evaluation criterion is developed to assess the capability of the electric-thermal system to adapt to varying operating conditions. Three test systems are employed to validate the proposed approach and assess both effectiveness and scalability. The results demonstrate that incorporating the justice objective leads to an approximately 0.41% increase in operational cost compared with the corresponding fairness-unaware operating point, while simultaneously reducing total load shedding and substantially improving the equality of curtailment distribution. Furthermore, a controlled comparison with an identical total amount of load shedding shows that achieving a fairer distribution of curtailment requires only a 0.45% increase in operational cost. The findings confirm that the integration of justice into microgrid scheduling enables just, flexible, economical, and sustainable operation of the systems.