Optimal PMU Placement Method for Active Distribution Networks Considering Wideband Oscillation Modal Energy Weighting

[Objective] To address the sub-synchronous wideband oscillation problem caused by the high penetration of grid-forming distributed energy resources in active distribution networks， traditional phasor measurement unit （PMU） placement methods based on pure topology suffer from severe dynamic monitoring blind spots. Therefore， an optimal PMU placement method considering wideband oscillation modal energy weighting is proposed. [Methods] This paper establishes a high-order nonlinear differential-algebraic equation model of an active distribution network containing multiple virtual synchronous generators （VSGs） to accurately screen high-risk wideband target modes by extracting the system state-space matrix. Subsequently， a modal energy-weighted Fisher information matrix （FIM） is formulated based on modal eigenvectors and the inverse of the damping ratio， enabling the quantitative evaluation of the spatial localization characteristics of nodal wideband dynamic observability. Building upon this， an improved greedy placement algorithm integrating dynamic FIM scores and static topological gains is proposed， incorporating a spatial large-adjacency penalty mechanism to strictly ensure the global dispersion of measurement nodes. [Results] Tests on a modified IEEE 33-node extreme weak-ring network demonstrate that， under the strict investment constraint of K=14， the proposed method achieves a significant advantage in capturing total wideband dynamic energy compared to traditional integer linear programming （ILP） and unweighted FIM algorithms. The comprehensive observability for the worst-case mode consistently exceeds the safety margin. Both time-domain reconstructed waveforms and empirical mode decomposition-Hilbert-Huang transform （EMD-HHT） frequency-domain integrations verify that the method effectively eliminates the transient monitoring blind spots inherent in traditional configurations. Furthermore， across 50 Monte Carlo parameter perturbation tests， the system maintains exceptional robustness with zero failures. [Conclusions] The proposed method breaks through the physical limitations of pure topological placement， overcomes the low-frequency bias trap of conventional full-state algorithms， and accurately identifies the antinodes of wideband resonant energy. It achieves superior robustness in full-band dynamic perception while ensuring a full-rank static topology， providing rigorous theoretical support for the planning of wide-area dynamic monitoring systems in next-generation distribution networks.