Data security of machine learning applied in low-carbon smart grid: A formal model for the physics-constrained robustness

Abstract

Towards the low-carbon goal, a smart grid features remote connection, data sharing, and cyber–physical integration to increase the flexibility of energy supplies, to reduce electricity wastage, and to enhance safety under intermittent renewables. In this context, machine learning (ML) is increasingly employed in smart grids to solve tasks that require deep data analytics. However, it is well recognized that ML models are vulnerable to adversarial examples that might be contained in open shared data, which creates opportunities for potential attackers to launch cyberattacks. In particular, system operating states acting as critical inputs to ML-based smart grid applications (MLsgAPPs) can be manipulated by malicious actors to mislead the system operator into making wrong decisions that in turn may cause major blackouts and other damaging cascading events. It is thus imperative to advance vulnerability assessment for MLsgAPPs.In this paper, we propose a physics-constrained robustness evaluation framework for MLsgAPPs, which is a first attempt of using tree ensemble (TE) models. Unlike adversarial attacks against prior studied image-classification tasks, adversarial examples against TE-based smart grid applications (TEsgAPPs) must not only cheat human intuition but also follow laws of physics and bypass error-checking mechanisms for power systems. Thus, formulation of the traditional robustness evaluation problem must be reconsidered to account for domain-specific misclassification, physical limit, power balance, and error-bypass constraints, in order to obtain tight lower bounds of the magnitudes of tolerated adversarial perturbations. We adopt a formal modeling approach to construct a discrete tree structure and to specify the model evasion conditions. We propose an efficient robustness evaluation method by transforming variables considering ℓ1 and ℓ∞ norms, followed by a generalization that expands the variable space to admit other types of norms. Using TE-based power system security assessment as an example, comprehensive simulations are conducted for evaluating the physics-constrained robustness under different TE models and model parameters.