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Yang et al. Intell Robot 2024;4(4):406-21 I http://dx.doi.org/10.20517/ir.2024.24 Page 412

−1

−1

∥ ∥ = − ˆ = · − −1 · (15)

An adversary can exploit the attack matrix , which satisfies condition ∥ ∥ ≤ . This can allow the
attack to bypass basic detection mechanisms such as BDD. A TSA attack enables an attacker to inject falsified
phase measurement data, causing the system to incorrectly assume that its state estimation is accurate. This er-
roneousstateestimationmayleadtofailuresinpowerdispatchandcontroldecisions, furthertriggeringachain
reaction that affects the efficiency and safety of power generation and transmission. Experimental studies [29]
have shown that TSA can evade BDD detection by subtly adjusting the PMU timing, thus masking timing
discrepancies within acceptable limits of detection mechanisms such as the test. These adjustments, while
2
seemingly minor, allow timing errors to accumulate undetected over time, exacerbating system vulnerabili-
ties. The growing dependency on synchronized measurement data in modern power grids magnifies the risks
posed by such attacks. Therefore, effectively detecting TSA attacks is crucial to ensuring the secure operation
of the power system.

3. TSA DETECTION MODEL
VNNs are a type of neural network model specifically designed to process vector data. They comprise vector
neurons (capsules) that use vector outputs instead of traditional scalar-based feature detectors [30,31] . Each
vector neuron retains instantiation parameters and uses a dynamic routing mechanism to transmit data to the
next layer, while preserving the direction, posture, and spatial information of the target features. Compared to
traditionalneuralnetworks, VNNsarebetteratcapturingtemporalinformationandgeometricrelationshipsin
inputdata. InµPMUmeasurements, thephysicalinformationofmagnitudeandphaseanglearecloselyrelated,
and the use of VNNs can preserve these relationships, allowing for more accurate detection of phase angle
shifts caused by TSA. To address the TSA problem in the park-level energy internet environment, this paper
introduces a multi-layer CNN for multi-scale temporal feature extraction and optimizes the dynamic routing
mechanism of VNNs to better capture the geometric relationships and feature variations in temporal data.
Additionally, a multi-layer perceptron (MLP) is integrated to reconstruct the classification results, enhancing
the model’s robustness and detection accuracy in complex attack scenarios. The structure of the VNN-DM
model is shown in Figure 2. The model consists of a convolutional Layer, a primary capsule layer (PrimeCap),
a convolutional capsule layer (ConvCap), a fully connected capsule layer (FCCap), and a decoder. During
the feature extraction phase, a multi-layer convolutional structure with different kernel sizes is used to extract
multi-scale temporal features. The dynamic routing mechanism enhances the feature classification capabilities
of the capsule network, ensuringthe modeleffectivelyadaptsto feature variationsin data under different attack
modes. Finally, the MLP reconstructs the feature classification results, improving the model’s robustness and
detection accuracy in complex attack scenarios within localized networks.

3.1. Dynamic routing between vector neurons
Dynamic routing establishes a non-linear mapping through an iterative process, enabling more adaptive and
hierarchical information flow between network layers. In this process, the data from each lower-level capsule
(sub-capsule) is passed to the appropriate higher-level capsule (parent capsule) in the next layer. Dynamic
routing adaptively modulates the connection strength between sub-capsules and parent capsules, leveraging
the output of the sub-capsules, thereby increasing or decreasing these connections. Let the data in the sub-
capsule be denoted as . The relationship between sub-capsule and parent capsule can be expressed as:

(16)
ˆ | = + |