# Developing Neural Network Schemes for Solving AC Power Flow Equations with Low Run-Time Complexity: Pursuing High-Voltage and Equality-Ensuring Solutions

Project: Research

## Researcher(s)

- Minghua CHEN (Principal Investigator / Project Coordinator)School of Data Science
- Steven LOW (Co-Investigator)

## Description

Project Background The modern power grid, with its growing integration of renewables and demand-side innovation, is a complex, dynamic system requiring continuous balance of power generation and demand. Central to this balance are AC power flow equations, which govern the electrical power flow in normal steady-state operation, and solving them is crucial for power system operations and plannings [1]. However, their high dimensionality and non-linearity make traditional iterative methods computationally expensive, challenging real-time power system operations like contingency analysis and state estimation, and impacting grid efficiency and reliability. Recent efforts have employed neural networks (NN) for various AC power flow solutions [2–11]. Using NN’s universal approximation capability [12–14], the idea is to learn the input-to-solution mapping and instantly generate quality solutions for new inputs. While these results have demonstrated promising speedup performance over iterative solvers, they also highlight unique challenges in developing NN schemes for solving power flow equations. • High-voltage solution defficiency. Nonlinear AC power flow equations often yield multiple mathematically-valid solutions for identical inputs, more than 2N where N is the number of buses [15]. However, only one matches the grid’s steady-state equilibrium observed in practice – commonly referred to as the ’high-voltage’ solution because of voltage magnitudes close to nominal values. Meanwhile, existing NN methods often fail to comprehend the complex multi-valued mapping and cannot consistently generate the physically meaningful high-voltage solution, significantly limiting their practical utility. • Power flow equality violation. Ensuring strict compliance with power flow equations is a significant challenge for NN solutions due to inherent prediction errors. Solutions that fail to satisfy these equations, especially at internal buses with zero injection, are not physically viable. Their utilization in grid operations, such as in state estimation, could result in grid instability or substantial operating costs.Project Aim and Description We will address the two issues and devise NN schemes to solve AC power flow equations. Our plan is three-pronged. First, we will provably establish the uniqueness and smoothness of the mapping from input to high-voltage solution. Then by leveraging an efficient NN architecture, we will proficiently learn this high-dimensional yet single-valued mapping, with performance guarantees. Second, we will harness the structure of AC power flow equations to refine our NN design, ensuring that the final solution respects power flow equality at the critical internal buses. This phase will also incorporate our recent embedded-training approach [16] to devise NN schemes capable of solving AC power flow equations under flexible grid topologies, including scenarios with line or generator switching events. Finally, teaming up with an AI industry leader and a grid R&D center of a Fortune 500 utility company, we plan to evaluate our schemes using real-world data and testbed trials, paving ways towards technology transfer.Preliminary Result and Significance of Project We have proved the uniqueness of the mapping from input to high-voltage AC power flow solution under mild conditions [17] and identified an efficient NN architecture [18]. We will build upon the initial success to establish robust theoretical foundations and efficient NNs for quickly and accurately solving AC power flow equations, facilitating the sustainable development of modern power systems. Our developed methodologies will also enhance the toolbox for designing NNs to solve general nonlinear equations.## Detail(s)

Project number | 9043659 |
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Grant type | GRF |

Status | Not started |

Effective start/end date | 1/01/25 → … |