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Ali Rajaei

Publications and source records attributed to Ali Rajaei.

9 recordsLinked to original sources
arXiv2026

Security-Constrained Substation Reconfiguration Considering Busbar and Coupler Contingencies

Substation reconfiguration via busbar splitting can mitigate transmission grid congestion and reduce operational costs. However, existing approaches neglect the security of substation topology, particularly for substations without busbar splitting (i.e., closed couplers), which can lead to severe consequences. Additionally, the computational complexity of optimizing substation topology remains a challenge. This paper introduces a MILP formulation for security-constrained substation reconfiguration (SC-SR), considering N-1 line, coupler and busbar contingencies to ensure secure substation topology. To efficiently solve this problem, we propose a heuristic approach with multiple master problems (HMMP). A central master problem optimizes dispatch, while independent substation master problems determine individual substation topologies in parallel. Linear AC power flow equations ensure PF accuracy, while feasibility and optimality sub-problems evaluate contingency cases. The proposed HMMP significantly reduces computational complexity and enables scalability to large-scale power systems. Case studies on the IEEE 14-bus, 118-bus, and PEGASE 1354-bus system show the effectiveness of the approach in mitigating the impact of coupler and busbar tripping, balancing system security and cost, and computational efficiency.

eess.SY↗
arXiv2025

Transferable Graph Learning for Transmission Congestion Management via Busbar Splitting

Network topology optimization (NTO) via busbar splitting can mitigate transmission grid congestion and reduce redispatch costs. However, solving this mixed-integer nonlinear problem for large-scale systems in near-real-time is currently intractable with existing solvers. Machine learning (ML) approaches have emerged as a promising alternative, but they have limited generalization to unseen topologies, varying operating conditions, and different systems, which limits their practical applicability. This paper formulates NTO for congestion management considering linearized AC power flow, and proposes a graph neural network (GNN)-accelerated approach. We develop a heterogeneous edge-aware message passing GNN to predict effective nodes for busbar splitting actions as candidate NTO solutions. The proposed GNN captures local flow patterns, improves generalization to unseen topology changes, and enhances transferability across systems. Case studies show up to 4 orders-of-magnitude speed-up, delivering AC-feasible solutions within one minute and a 2.3% optimality gap on the GOC 2000-bus system. These results demonstrate a significant step toward near-real-time NTO for large-scale systems with topology and cross-system generalization.

cs.AI↗
arXiv2025

Addressing Model Inaccuracies in Transmission Network Reconfiguration via Diverse Alternatives

The ongoing energy transition places significant pressure on the transmission network due to increasing shares of renewables and electrification. To mitigate grid congestion, transmission system operators need decision support tools to suggest remedial actions, such as transmission network reconfigurations or redispatch. However, these tools are prone to model inaccuracies and may not provide relevant suggestions with regard to important unmodeled constraints or operator preferences. We propose a human-in-the-loop modeling-to-generate alternatives (HITL-MGA) approach to address these shortcomings by generating diverse topology reconfiguration alternatives. Case studies on the IEEE 57-bus and IEEE 118-bus systems show the method can leverage expert feedback and improve the quality of the suggested topology reconfigurations.

eess.SY↗
arXiv2025

Multi-Objective Reinforcement Learning for Power Grid Topology Control

Transmission grid congestion increases as the electrification of various sectors requires transmitting more power. Topology control, through substation reconfiguration, can reduce congestion but its potential remains under-exploited in operations. A challenge is modeling the topology control problem to align well with the objectives and constraints of operators. Addressing this challenge, this paper investigates the application of multi-objective reinforcement learning (MORL) to integrate multiple conflicting objectives for power grid topology control. We develop a MORL approach using deep optimistic linear support (DOL) and multi-objective proximal policy optimization (MOPPO) to generate a set of Pareto-optimal policies that balance objectives such as minimizing line loading, topological deviation, and switching frequency. Initial case studies show that the MORL approach can provide valuable insights into objective trade-offs and improve Pareto front approximation compared to a random search baseline. The generated multi-objective RL policies are 30% more successful in preventing grid failure under contingencies and 20% more effective when training budget is reduced - compared to the common single objective RL policy.

cs.LG↗
arXiv2023

End-to-End Learning with Multiple Modalities for System-Optimised Renewables Nowcasting

With the increasing penetration of renewable power sources such as wind and solar, accurate short-term, nowcasting renewable power prediction is becoming increasingly important. This paper investigates the multi-modal (MM) learning and end-to-end (E2E) learning for nowcasting renewable power as an intermediate to energy management systems. MM combines features from all-sky imagery and meteorological sensor data as two modalities to predict renewable power generation that otherwise could not be combined effectively. The combined, predicted values are then input to a differentiable optimal power flow (OPF) formulation simulating the energy management. For the first time, MM is combined with E2E training of the model that minimises the expected total system cost. The case study tests the proposed methodology on the real sky and meteorological data from the Netherlands. In our study, the proposed MM-E2E model reduced system cost by 30% compared to uni-modal baselines.

eess.SY↗
arXiv2022

Ostrowski quotients for finite extensions of number fields

For $L/K$ a finite Galois extension of number fields, the relative Pólya group $\Po(L/K)$ coincides with the group of strongly ambiguous ideal classes in $L/K$. In this paper, using a well known exact sequence related to $\Po(L/K)$, in the works of Brumer-Rosen and Zantema, we find short proofs for some classical results in the literatur. Then we define the ``Ostrowski quotient'' $\Ost(L/K)$ as the cokernel of the capitulation map into $\Po(L/K)$, and generalize some known results for $\Po(L/\mathbb{Q})$ to $\Ost(L/K)$.

math.NT↗
arXiv2020

Quantum Discrepancy: A Non-Commutative Version of Combinatorial Discrepancy

In this paper, we introduce a notion of quantum discrepancy, a non-commutative version of combinatorial discrepancy which is defined for projection systems, i.e. finite sets of orthogonal projections, as non-commutative counterparts of set systems. We show that besides its natural algebraic formulation, quantum discrepancy, when restricted to set systems, has a probabilistic interpretation in terms of determinantal processes. Determinantal processes are a family of point processes with a rich algebraic structure. A common feature of this family is the local repulsive behavior of points. Alishahi and Zamani (2015) exploit this repelling property to construct low-discrepancy point configurations on the sphere. We give an upper bound for quantum discrepancy in terms of $N$, the dimension of the space, and $M$, the size of the projection system, which is tight in a wide range of parameters $N$ and $M$. Then we investigate the relation of these two kinds of discrepancies, i.e. combinatorial and quantum, when restricted to set systems, and bound them in terms of each other.

math.PR↗
arXiv2019

Relative Polya Group and Polya Dihedral Extensions of Q

We define the relative Polya group for a finite extension of number fields and prove triviality of the relative Polya group for the Hilbert class field. Then we generalize our previous results on Polya S3-extensions of Q to some dihedral extensions of Q.

math.NT↗