The accretion of ice and snow on overhead transmission lines poses a significant and recurring threat to the integrity and reliability of power grids, particularly in regions experiencing cold, wet climates. The process involves supercooled water droplets freezing upon contact with conductors and towers whose surface temperatures are below the freezing point. Subsequent growth and, critically, the shedding of this ice/snow load can induce severe dynamic responses in the lines, including substantial longitudinal bouncing (ice-shedding jumps) and sudden increases in dynamic tension. These phenomena heighten the risk of conductor clashing, insulator flashover, hardware fatigue, and in extreme cases, cascading tower failures. Traditional countermeasures, such as manual de-icing or DC-based ice melting, are often hampered by low efficiency, high operational costs, and significant safety concerns. In this context, the use of unmanned drone technology has emerged as a promising alternative. A novel operational strategy involves a heavy-lift unmanned drone carrying an insulated impact mass to deliberately collide with the iced conductor. The controlled impact imparts a mechanical shock, inducing vibrations intended to fracture and dislodge the ice/snow layer. This method enables potentially efficient, remote, and live-line de-icing operations. However, the dynamic interplay between the impact parameters and the resulting line response—dictating both de-icing efficacy and operational safety—remains insufficiently explored. This paper establishes a finite element simulation model based on an acceleration-driven ice-shedding criterion to numerically investigate the dynamic response process of unmanned drone collision-based de-icing. The study systematically analyzes the effects of multiple factors, including impact location, span length, impact load parameters (magnitude and angle), and ice/snow thickness on critical performance metrics: de-icing rate, dynamic tension amplification, and conductor jump height.
The core challenge in simulating mechanical ice shedding lies in defining a physically accurate failure criterion for the ice/snow-conductor bond. Unlike bulk ice fracture, the detachment of lighter accretions like snow or rime ice from a vibrating conductor is predominantly governed by the failure of the adhesive bond at the interface, rather than the cohesive strength of the accretion itself. Therefore, a criterion based on inertial forces overcoming adhesive strength is adopted. Considering a unit length of ice-covered conductor, the condition for detachment is met when the inertial force induced by conductor acceleration, combined with the gravitational force of the ice, exceeds the adhesive force binding the ice to the conductor.
The force balance for ice-shedding can be expressed as:
$$F_{inertia} \pm G \ge F_{adhesive}$$
where \(F_{inertia}\) is the inertial force of the ice/snow element, \(G\) is its weight, and \(F_{adhesive}\) is the adhesive force at the interface. The sign of the gravitational term depends on the instantaneous direction of conductor motion relative to gravity. The inertial force is \(F_{inertia} = m_{ice} \cdot a\), where \(m_{ice}\) is the mass per unit length and \(a\) is the acceleration of the conductor at that point. The adhesive force is related to the adhesive shear strength \(\tau_{adhesive}\) and the contact area. From this balance, a critical acceleration threshold \(a_{cr}\) for ice detachment can be derived:
$$a \ge \frac{8 D_{cable} \tau_{adhesive}}{\pi \rho_{ice} (D^2 – D_{cable}^2)} \pm g$$
Here, \(\rho_{ice}\) is the density of the ice/snow accretion, \(D\) is the outer diameter of the iced conductor, \(D_{cable}\) is the bare conductor diameter, and \(g\) is gravitational acceleration. For snow, the adhesive shear strength \(\tau_{adhesive}\) can be estimated as a fraction \(k\) of its compressive strength \(P_0\), i.e., \(\tau_{adhesive} = k \times P_0\). Typical parameter ranges for different accretion types are summarized in Table 1.
| Parameter | Snow | Soft Rime | Hard Rime | Glaze Ice |
|---|---|---|---|---|
| Density \(\rho_{ice}\) (kg/m³) | 50 – 600 | 100 – 400 | 400 – 800 | ~900 |
| Adhesive Strength \(\tau_{adhesive}\) (kPa) | 1 – 10 | 10 – 100 | 50 – 500 | 100 – 1000 |
| Cohesive Strength (kPa) | 0.1 – 50 | 5 – 50 | 50 – 500 | 500 – 1500 |
Using the lower-end values for snow density and adhesive strength, the critical acceleration threshold is calculated to be in the range of 63.4 to 87.1 m/s². For this study, a threshold of \(a_{cr} = 70 \text{ m/s}^2\) is adopted for simulating snow/rime shedding. Notably, the critical accelerations for hard rime and glaze ice are orders of magnitude higher (several thousand m/s²), suggesting that the unmanned drone collision method is primarily effective for softer accretions like snow or non-encapsulating rime.
A two-span, single-conductor finite element model is developed in a commercial FEA software environment to simulate the dynamic response. The conductor is modeled using LINK10 elements, capable of simulating cable sag under tension and large displacement behavior. The initial catenary shape of the conductor under its own weight, ice load, and initial tension is determined via static analysis, solving the catenary equation:
$$y = \frac{h}{L_{h=0}} \cdot \frac{2\sigma_0}{q} \sinh\left(\frac{qx}{2\sigma_0}\right) + \cosh\left(\frac{q l}{2\sigma_0}\right) – \sqrt{1+\left(\frac{h}{L_{h=0}}\right)^2} \cdot \frac{2\sigma_0}{q} \sinh\left(\frac{qx}{2\sigma_0}\right) \sinh\left(\frac{q l}{2\sigma_0}\right)$$
where \(h\) is the height difference between supports, \(L_{h=0}\) is the cable length for a level span, \(\sigma_0\) is the horizontal tension, \(q\) is the weight per unit length, and \(l\) is the span length. The ice/snow load is applied as concentrated masses at the nodes, calculated from the accretion thickness \(b\) and density. Damping, a crucial factor for energy dissipation during vibration, is modeled using Rayleigh damping, where the damping matrix \(C\) is a linear combination of the mass matrix \(M\) and stiffness matrix \(K\): \(C = \alpha M + \beta K\).
The de-icing simulation is a two-stage process. First, a transient dynamic analysis is performed where a half-sine wave impact force is applied at a specified node to simulate the unmanned drone-carried mass collision. The equation of motion solved is:
$$M \ddot{u} + C \dot{u} + K u = F(t)$$
where \(\ddot{u}\), \(\dot{u}\), and \(u\) are the nodal acceleration, velocity, and displacement vectors, respectively, and \(F(t)\) is the time-varying impact force vector. Second, during the solution, at each time step, the acceleration of each conductor node is compared to the critical acceleration \(a_{cr}\). If the nodal acceleration exceeds the threshold, the corresponding ice mass at that node is considered shed and is removed from the model in subsequent time steps. This algorithm effectively simulates the progressive shedding of ice along the span. Key response parameters, including the percentage of shed ice mass (de-icing rate), the maximum vertical displacement at the mid-span (jump height), and the peak dynamic tension at the support points, are extracted from the time-history results.
To comprehensively investigate the influence of operational and environmental variables, a systematic parameter study is designed, as outlined in Table 2. The baseline case involves a 400 m span with 10 mm snow thickness, impacted at the quarter-span point with a 1500 N force.
| Case ID | Impact Location | Impact Force (N) | Impact Angle (°) | Span Length (m) | Ice Thickness (mm) |
|---|---|---|---|---|---|
| 1 | 1/10 Span | 1500 | 0 | 200 | 10 |
| 2 | 1/4 Span | 1500 | 0 | 200 | 10 |
| 3 | 1/2 Span (Mid-span) | 1500 | 0 | 200 | 10 |
| 4 | 1/4 Span | 1500 | 30 | 400 | 10 |
| 5 | 1/4 Span | 1500 | 20 | 400 | 10 |
| 6 (Baseline) | 1/4 Span | 1500 | 0 | 400 | 10 |
| 7 | 1/4 Span | 2500 | 0 | 400 | 10 |
| 8 | 1/4 Span | 3500 | 0 | 400 | 10 |
| 9 | 1/4 Span | 1500 | 0 | 400 | 15 |
| 10 | 1/4 Span | 1500 | 0 | 400 | 20 |
| 11 | 1/4 Span | 3500 | 0 | 400 | 20 |
| 12 | 1/4 Span | 2500 | 0 | 400 | 15 |
| 13 | 1/4 Span | 1500 | 0 | 100 | 10 |
Analysis of Impact Location
The location where the unmanned drone executes the collision is a primary operational decision. Comparing Cases 1, 2, and 3 reveals its profound effect. Impacting near the support (1/10 span) results in a lower de-icing rate. The high local stiffness near the tower restricts the amplitude of the generated traveling wave, and its energy dissipates over a shorter distance along the span. Impacting at the mid-span (1/2 span) excites the fundamental symmetric mode most effectively, leading to a high de-icing rate. However, it also produces the largest mid-span jump height, increasing the risk of phase-to-ground or phase-to-phase clearance violations. Strikingly, the quarter-span point (1/4 span) offers an optimal compromise. It achieves a de-icing rate nearly equivalent to the mid-span impact but with a significantly reduced maximum jump height (approximately 0.51 m lower in the simulated cases). This location efficiently excites the line while mitigating the most hazardous dynamic response. Consequently, the quarter-span point is selected as the preferred impact location for subsequent analyses.
Influence of Impact Load Angle and Magnitude
The direction and strength of the impulse delivered by the unmanned drone are critical control parameters. Cases 4, 5, and 6 examine the impact angle. A purely horizontal impact (0°) delivers the maximum force component in the direction most effective for exciting transverse conductor vibrations, yielding the highest de-icing rate. Angled impacts (20°, 30°) introduce a vertical component. While the vertical component initially increases the dynamic tension more sharply (Case 4), the overall de-icing efficiency drops because a portion of the impulse does not contribute to the transverse shaking mode. The 20° angle shows results close to the 0° case, suggesting a small operational deviation may be tolerable. However, for maximum efficacy, a near-horizontal collision is optimal for the unmanned drone operation.
The effect of impact force magnitude is studied via Cases 6, 7, and 8. As expected, increasing the force from 1500 N to 3500 N monotonically improves the de-icing rate. However, this comes at a cost: both the maximum jump height and the dynamic tension surge at the supports increase substantially. The relationship is nonlinear; a doubling of force leads to a more-than-doubling of the jump height and tension increase. This highlights a fundamental trade-off: higher force ensures better ice removal but escalates the mechanical risks to the line and its hardware. An operational unmanned drone system must therefore calibrate the impact energy based on a safety threshold for tension and clearance.
Effects of Ice Thickness and Span Length
The characteristics of the accretion and the line itself are determining factors. Cases 6, 9, and 10, all under a 1500 N impact, demonstrate the effect of ice/snow thickness. Thicker accretion increases the total mass per unit length, raising the inertia that must be overcome for shedding. Consequently, the de-icing rate falls dramatically with increased thickness (e.g., from 21.5% at 10 mm to 7.5% at 20 mm). Interestingly, the increased mass also dampens the vibration amplitude, leading to a lower conductor jump height for thicker ice under the same impact. The tension increase is also slightly lower for thicker ice due to this damping effect. This indicates that for severe ice loads, a single standard impact from an unmanned drone may be insufficient, necessitating either multiple impacts or a higher force, as seen in Cases 11 and 12 where higher forces are required to achieve significant de-icing on thicker ice.
Span length is another crucial design factor (Cases 13, 1, 6). In a short span (100 m), the system is stiffer. An impact generates high accelerations quickly, leading to a very high de-icing rate (81%). However, the energy is confined, causing an extreme surge in dynamic tension, posing a high risk of component failure. In a long span (400 m), the system is more flexible. The impact energy dissipates along the longer conductor, resulting in a much lower de-icing rate (21.5%). The primary risk here shifts from over-tensioning to excessive vertical jumping, as the lower stiffness allows for greater displacements. This dichotomy implies that unmanned drone de-icing protocols must be span-specific: using lower forces on short spans to avoid tension limits and potentially higher forces on long spans to achieve adequate de-icing while monitoring jump height.
| Factor | Effect on De-icing Rate | Effect on Dynamic Risk | Operational Recommendation for Unmanned Drone |
|---|---|---|---|
| Impact Location | Highest at mid-span; high at 1/4 span. | Jump height highest at mid-span; minimized at 1/4 span. | Target the quarter-span (1/4) point for optimal safety/efficacy balance. |
| Impact Angle | Decreases as angle increases from horizontal. | Initial tension spike increases with vertical component. | Execute collision as close to horizontal (0°) as possible. |
| Impact Force | Increases with force magnitude. | Jump height and dynamic tension increase non-linearly with force. | Calibrate force based on span-specific safe tension and clearance limits; avoid over-impact. |
| Ice/Snow Thickness | Decreases significantly with increasing thickness for a given force. | Jump height and tension increase are dampened for thicker ice under same force. | For thick accretions, employ a graded or multiple-impact strategy rather than a single high-force impact. |
| Span Length | Higher in short, stiff spans; lower in long, flexible spans. | High tension risk in short spans; high jump risk in long spans. | Short spans: Use lower impact forces. Long spans: May require higher forces, with strict jump monitoring. |
Conclusion
The simulation-based investigation into the dynamic response of overhead lines subjected to unmanned drone-assisted mechanical de-icing provides critical insights for optimizing this emerging technology. The use of an acceleration-based shedding criterion within a transient finite element framework successfully captures the progression of ice detachment and the concomitant line dynamics. The study concludes that the impact location is paramount; the quarter-span point is identified as the optimal collision site for an unmanned drone, maximizing de-icing efficiency while minimizing the hazardous conductor jump height. The impact should be delivered horizontally to ensure the impulse effectively excites transverse vibrations. While increasing the impact force improves de-icing performance, it does so at the expense of sharply increasing dynamic tension and jump height, establishing a clear trade-off that must be managed via force calibration against predefined safety limits. The efficacy of the unmanned drone method is highly dependent on accretion thickness and span length. Thicker ice requires more energy for removal, suggesting the need for a sequential or graded impact strategy. Operational protocols must be adapted to span characteristics: short spans are tension-critical, requiring gentle impacts, while long spans are jump-critical, potentially allowing for stronger impacts. In summary, the effective and safe deployment of unmanned drone collision de-icing requires a tailored approach that considers the specific line parameters and ice conditions. The findings and recommendations summarized in Table 3 provide a foundational guideline for developing standardized operational procedures for this promising technology, enhancing grid resilience against ice-related hazards.