Equivalent Inductance and Reactive Power Loss Characteristics of Transformer under Late-Time High-Altitude Electromagnetic Pulse
Wang Guyue1, Wang Zezhong1, Liu Chunming2
1. Beijing Key Laboratory of High Voltage and EMC North China Electric Power University Beijing 102206 China; 2. School of Electrical and Electronic Engineering North China Electric Power University Beijing 102206 China
Abstract：The late-time high-altitude electromagnetic pulses (HEMP E3) induce potential differences between grounding points in the power grid, subsequently generating geomagnetic induced current (GIC). E3 GIC causes direct current (DC) bias in power grid transformers, leading to increased harmonics, reactive power loss, vibration, and temperature rise, adversely impacting operational performance. Notably, the widespread increase in reactive power losses of all transformers in the affected area can cause grid-wide voltage fluctuations or even collapse. Therefore, accurate calculation of E3 GIC and its associated transformer reactive power loss is crucial for assessing system risks under E3 and developing effective countermeasures. Existing studies primarily calculate GIC based on the DC parameters of power grids and use the K-parameter method to estimate transformer reactive power loss, assuming a linear relationship with GIC. However, these methods neglect the inductive effects of transformers on GIC or the saturation of reactive power loss under high GIC. Therefore, the paper investigates the hindrance of transformer inductance on GIC and the characteristics of reactive power losses under DC bias induced by E3 GIC. Based on the transient circuit of a single-phase transformer under DC bias, the equivalent inductance of the transformer (including magnetizing and leakage inductance) is derived. It is a nonlinear component influenced by the level of DC bias. Subsequently, a dynamic E3 GIC calculation model for a single power grid transformer circuit is established, considering the transformer inductance effect. The equivalent inductance and reactive power loss characteristics of a single-phase ultra-high-voltage (UHV) transformer are calculated under DC bias through field-circuit coupled finite element simulations. A simplified analytical method for rapid calculation is proposed with a two-segment simplified magnetization curve. It is shown that the equivalent inductance decreases rapidly as the DC current increases. Under low DC, the reactive power loss exhibits an approximately linear relationship with DC current levels. However, the growth slows under high DC, and the saturation characteristics become more pronounced as the DC current increases. These are applied to calculate dynamic GIC and transformer reactive power loss under step voltage as the induced electric field. The results indicate that GIC and reactive power loss are delayed by tens of seconds under a low-induced electric field, and the saturation of reactive power loss becomes more pronounced under a high-induced electric field, suggesting greater overestimation by the K-parameter method. The simplified analytical method yields minor errors, especially under a high-induced electric field. The E3 GIC and the associated transformer reactive power loss are calculated using the dynamic GIC calculation model with a 50 km transmission line as a reference. The results suggest that: (1) The transformer equivalent inductance hinders the rapid growth of GIC, both directly and indirectly delaying dynamic E3 GIC and reactive power loss relative to E3-induced electric field, with more flattened peaks. The waveforms exhibit zero-crossing plateaus. Ignoring the inductive effect can cause misjudgment of equipment damage and event severity. (2) The reactive power loss exhibits saturation characteristics at the E3 peak, which implies substantial errors in the K-parameter engineering algorithm, over predicting by several hundred Mvar. It affects the catastrophic risk prediction in power system response and the scientific accuracy of optimization scheduling decisions. The proposed simplified analytical method can rapidly predict E3 GIC and reactive power loss in the transformer circuit under HEMP E3 while maintaining reasonable accuracy.
王古玥, 王泽忠, 刘春明. 高空电磁脉冲晚期成分作用下变压器的等效电感及无功损耗特性[J]. 电工技术学报, 2025, 40(18): 5728-5741.
Wang Guyue, Wang Zezhong, Liu Chunming. Equivalent Inductance and Reactive Power Loss Characteristics of Transformer under Late-Time High-Altitude Electromagnetic Pulse. Transactions of China Electrotechnical Society, 2025, 40(18): 5728-5741.
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