Quantifying the transient inertial and damping support of voltage-dependent loads: an analytical framework

Declining system inertia necessitates quantifying intrinsic frequency support mechanisms. While load voltage dependency influences dynamics, its specific impacts on transient inertial and damping support remain under-quantified. This paper establishes an analytical framework to quantify voltage-dependent load contributions to the initial Rate of Change of Frequency (RoCoF) and frequency nadir. By employing a Center of Inertia (CoI) framework to mathematically isolate load voltage dependence from network oscillations, closed-form expressions are derived for two physical mechanisms. First, the instantaneous power reduction from the subtransient voltage dip functions as an equivalent inertia, proportional to the system's base mechanical inertia and scaling linearly with grid impedance and load sensitivity. Second, load voltage sensitivity provides an effective damping torque that increases the damping ratio, suppressing the frequency nadir. Furthermore, the study reveals a critical trade-off with Automatic Voltage Regulators (AVR), where aggressive voltage recovery compromises this natural damping support. Time-domain simulations validate that voltage-dependent loads provide a self-regulating defense mechanism, particularly effective in weak grids.