1. The Physics of Short Circuits (Lorentz Force)

When a short-circuit fault occurs, thousands of amps flow through parallel busbars. The interaction between the magnetic fields creates a massive Lorentz Force.
In a 3-phase fault, the force oscillates. The peak force ($F_m$) is proportional to the square of the peak current ($i_p^2$) and inversely proportional to the spacing ($a$).
$$ F_m = \frac{\mu_0}{2\pi} \frac{\sqrt{3}}{2} \frac{i_p^2}{a} $$
where $\mu_0 = 4\pi \times 10^{-7}$. Reducing phase spacing to save space drastically increases the force. Doubling the current quadruples the force.

2. Natural Frequency & Resonance

The busbar is a mechanical beam. If the electromagnetic force frequency ($2 \times f_{sys} \approx 100 \text{Hz}$ or $120 \text{Hz}$) aligns with the busbar's Natural Frequency ($f_c$), resonance occurs.

IEC 60865 defines dynamic response factors $V_F$ (for insulators) and $V_\sigma$ (for stress) based on the ratio $\eta = f_c / f_{force}$.

• Stiff System ($f_c$ high): The busbar resists movement. $V \approx 1$.
• Flexible System ($f_c$ low): The busbar swings. Stresses might be lower due to flexibility, but displacement is high.
• Resonance ($f_c \approx 2f$): $V$ factors spike, potentially multiplying the static force by 3-5x.

3. The Plasticity Factor ($q$)

Unlike standard structural design where we stay below Yield Strength ($R_{p0.2}$), IEC 60865 allows busbars to slightly deform plastically during a rare fault event. This optimizes material usage.
For rectangular bars, the shape factor allows the outer fibers to yield while the core remains elastic.
Allowable Stress = $q \times R_{p0.2}$. typically $q=1.5$ for rectangular copper sections. This means we can load the bar to 1.5x its yield strength safely for a momentary fault.

4. Edge vs. Flat & Multi-Bar

Edge-to-Edge: The force acts against the "Height" of the bar (Strong Axis). High stiffness ($J$), high natural frequency. Best for high fault levels.
Flat-Facing: The force acts against the "Thickness" (Weak Axis). Low stiffness. The bars will bow significantly. Only suitable for low fault levels or very short spans.

Multi-Conductor ($n > 1$): Using 2 or 3 bars per phase increases ampacity and cooling. If spaced properly, the total Inertia ($J$) is the sum of individual inertias. This tool approximates this by $n \times J_{single}$ assuming effective spacer coupling.

5. Insulator Selection

The force transferred to the support ($F_d$) is often the limiting factor. It is not just the static peak force; it includes the dynamic amplification ($V_F$) and a reaction factor (typically 1.0 to 1.1 for continuous beams).
$$ F_d = V_F \cdot V_r \cdot \alpha \cdot F_m \cdot l $$
Ensure the insulator's Cantilever Strength Rating > $F_d$. Common ratings are 4kN, 6kN, 10kN. Upgrading insulators is often cheaper than adding more supports.