State Estimation in Electric Power Systems Leveraging Graph Neural Networks (2201.04056v2)

Abstract: The goal of the state estimation (SE) algorithm is to estimate complex bus voltages as state variables based on the available set of measurements in the power system. Because phasor measurement units (PMUs) are increasingly being used in transmission power systems, there is a need for a fast SE solver that can take advantage of high sampling rates of PMUs. This paper proposes training a graph neural network (GNN) to learn the estimates given the PMU voltage and current measurements as inputs, with the intent of obtaining fast and accurate predictions during the evaluation phase. GNN is trained using synthetic datasets, created by randomly sampling sets of measurements in the power system and labelling them with a solution obtained using a linear SE with PMUs solver. The presented results display the accuracy of GNN predictions in various test scenarios and tackle the sensitivity of the predictions to the missing input data.

• The paper proposes a novel GNN-based method for accurate state estimation in power systems by leveraging graph structures and PMU measurements.
• It employs an attention-driven GNN architecture that adapts to varying grid topologies and remains robust under missing data scenarios.
• The study demonstrates high sample efficiency and real-time inference capabilities, underscoring its practical application potential.

The paper "State Estimation in Electric Power Systems Leveraging Graph Neural Networks" proposes a novel approach for power system state estimation (SE) using Graph Neural Networks (GNNs). The primary purpose of SE in electric power systems is to estimate complex bus voltages, considered as state variables, using available measurements such as those from Phasor Measurement Units (PMUs). These PMUs are increasingly used in transmission power systems due to their high sampling rates, necessitating fast SE solvers.

Key Contributions:

1. Integration of GNNs: The paper introduces the use of GNNs for SE, leveraging their ability to handle graph-structured data. Unlike traditional deep learning methods, GNNs can adapt to varying power system topologies, which reduces training complexity and memory demands.
2. Data Handling: The GNN is trained using synthetic datasets derived from randomly sampled power system measurements. These are labeled with solutions obtained through linear state estimation algorithms incorporating PMUs. The training process accounts for various scenarios, including missing input data, which can occur due to communication issues or PMU failures.
3. Graph Architecture: The GNN operates on graphs with factor-graph-like structures. Factor nodes represent measurement types (e.g., bus voltage and branch current), while variable nodes capture state variables (real and imaginary parts of voltages). This structure allows easy inclusion/exclusion of different measurement types.
4. Attention Mechanism: The GNN layers utilize attention mechanisms for message passing and aggregation, which improves the learning of dependencies between nodes.
5. Robustness Testing: Through extensive testing under scenarios of missing data, the paper demonstrates the robustness of the GNN model. Results show that adding connections between variable nodes enhances prediction accuracy when the system becomes underdetermined due to missing measurements.
6. Sample Efficiency: The paper analyzes the model's performance against different training set sizes, confirming that the GNNs are sample efficient, achieving high prediction accuracy with relatively small datasets.

Implementation Details:

• GNN Layers: Uses separate GNN layers for factor and variable nodes, each comprising trainable functions for message generation, aggregation, and updating node embeddings.
• Augmented Graphs: Extends the factor graph by adding variable-to-variable connections, enabling resilience in lack of measurement scenarios.
• Loss Function: Employs a mean squared error loss function to train the GNN by comparing predicted and actual bus voltages.

Computational Considerations:

• Training: Requires high computational resources, particularly for larger datasets and deeper GNN layers. However, once trained, the model can rapidly infer state estimates from real-time data.
• Distributed Inference: The inference phase can be distributed, as each bus's state variable estimation only requires information from its surrounding $K$-hop neighborhood.

Conclusion and Prospects:

The paper concludes that GNNs offer a promising direction for efficient and robust state estimation in electric power systems, with potential applications in real-time monitoring and control. The use of attention-based GNN architectures with flexible data structures suits the complexity and variability of power system networks, providing a foundation for further research and implementation in the field.