Uncertainty-Aware Power Flow Analysis in Electrical Systems

Power systems are evolving rapidly with high shares of variable renewable generation, bidirectional flows from distributed energy resources and increasingly dynamic load profiles. Traditional deterministic power flow methods assume fixed inputs and may underestimate the operational limits and risks introduced by fluctuating generation and demand. Uncertainty-aware power flow analysis seeks to characterise the range or probability distributions of voltages, currents and power flows under uncertain injections and consumption. Key approaches include probabilistic load flow, which employs sampling or polynomial expansions to estimate statistical moments of state variables; interval arithmetic methods that propagate bounds without requiring probability density functions; and hybrid or robust formulations that combine scenario-based optimisation with chance constraints. Recent advances have addressed computational tractability by linearising AC network equations, leveraging affine arithmetic to reduce overestimation in interval bounds, and developing fast sensitivity analysis tools to identify critical network nodes. By quantifying the impact of renewable intermittency, load forecast errors and device correlations, uncertainty-aware analyses enable more reliable grid operation, informed planning of capacity expansion and enhanced decision support for real-time control under variable conditions.

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Uncertainty-Aware Power Flow Analysis in Electrical Systems publication trend

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Technical terms

Interval Power Flow: A deterministic method that computes upper and lower bounds of network variables by propagating interval-valued inputs through power flow equations.

Probabilistic Load Flow (PLF): An approach using statistical sampling or series expansions to estimate probability distributions or moments (mean, variance) of system states under random inputs.

Affine Arithmetic: An extension of interval arithmetic that tracks correlations between interval variables to reduce overestimation in bound calculations.

Monte Carlo Simulation: A numerical technique that generates random samples of uncertain inputs to approximate the statistical behaviour of power system states.

Sensitivity Analysis: A procedure to quantify how variations in input uncertainties affect network outputs, often used to prioritise control and investment in grid assets.

References

1. Optimal Allocation and Sizing of Distributed Generation Using Interval Power Flow. Sustainability (2023).
2. Complex affine arithmetic based uncertain sensitivity analysis of voltage fluctuations in active distribution networks. Frontiers in Energy Research (2024).
3. On the problem of calculating steady state modes of electric power systems under conditions of interval data uncertainty. E3S Web of Conferences (2023).
4. Interval Power Flow Analysis of Linearised AC Power Flow Model Based on Improved Affine Arithmetic Method. IET Generation Transmission & Distribution (2025).