Inrush current
Inrush current, also known as input surge current, is the maximum instantaneous current drawn by an electrical device upon initial energization, often several times greater than the steady-state operating current due to the sudden demand for magnetization or charging.[1] This phenomenon occurs across various equipment, including transformers, electric motors, and power supplies, and typically lasts only a few cycles before decaying to normal levels.[1] Understanding and managing inrush current is essential in electrical engineering to prevent equipment damage, system instability, and protective device malfunctions. In power transformers, inrush current primarily arises from magnetizing the iron core when the device is switched on without load, leading to temporary core saturation influenced by residual flux and the point on the voltage waveform at energization.[2] Peak values can reach 5 to 25 times the transformer's full-load amperage (FLA), with high second-order harmonics that may persist for several cycles and cause sympathetic inrush in nearby transformers.[3][2] These surges can induce mechanical stresses on windings, trigger false differential relay trips, and contribute to power quality issues like voltage dips or overvoltages.[2] For electric motors, inrush current—often termed starting or locked-rotor current—manifests as the high demand to accelerate the rotor from standstill, typically 4 to 8 times the full-load current at full voltage application.[4] Premium efficiency motors may exhibit slightly higher inrush due to design optimizations for reduced losses, potentially leading to nuisance tripping of circuit breakers or fuses during startup.[5] The magnitude is indicated by NEMA code letters on motor nameplates, guiding protective device selection to accommodate this transient without interrupting operation.[4] In switching power supplies, inrush current results from the rapid charging of input capacitors upon power-on, creating a brief surge that can exceed steady-state levels by factors depending on capacitance and input voltage rise time.[6] This can strain upstream power sources, cause voltage sags on the supply line, or activate overcurrent protection if not limited.[1] Mitigation strategies across these applications include NTC thermistors for resistive limiting,[7] soft-start circuits to gradually apply voltage,[6] and point-on-wave switching to avoid peak saturation conditions,[3] thereby enhancing system reliability and longevity.Definition and Fundamentals
Definition
Inrush current, also known as input surge current or switch-on surge, is defined as the maximal instantaneous input current drawn by an electrical device upon its initial energization from a power source. This transient phenomenon occurs specifically at the moment of power application and is distinct from steady-state operating currents, representing a temporary overload that the device imposes on the supply system. Unlike peak current, which refers to the maximum amplitude of current during normal, ongoing operation (such as the crest of an AC waveform), inrush current is a short-lived surge confined to the startup phase and does not recur under steady conditions.[8] The magnitude of inrush current typically ranges from 5 to 100 times the device's steady-state value, depending on the load type, with inductive devices like motors typically 4 to 8 times and transformers up to 25 times the rated current, while capacitive loads in power supplies can reach higher multiples due to rapid charging.[9] Its duration generally spans a few milliseconds to several seconds (e.g., 10-100 ms at 50/60 Hz for many cases), after which the current decays toward nominal levels.[10] In AC systems, a key parameter is the asymmetry of the inrush waveform, arising from the interaction between the switching instant and the supply voltage phase, which introduces a transient DC offset that offsets the current from its symmetric sinusoidal form.[11] This peak value, duration, and asymmetry collectively characterize the inrush event, influencing system design considerations for protection and stability.[11]General Causes
Inrush current primarily stems from the abrupt application of voltage to electrical circuits, prompting a rapid accumulation of energy in storage elements or the initiation of magnetic fields. In capacitive elements, this manifests as the need to charge the capacitor from zero voltage to the supply level, drawing significant current until equilibrium is reached. Similarly, in inductive elements, the sudden voltage induces a quick buildup of magnetic flux through the coil, requiring substantial transient current to overcome the initial absence of opposing electromagnetic forces. These mechanisms result in a surge that can exceed steady-state operating currents by several times, depending on the circuit configuration.[6][12] The high magnitude of inrush current is fundamentally due to the low initial impedance presented by the load at the moment of energization. Uncharged capacitors exhibit effectively zero reactance initially, as there is no voltage across them to impede flow, while unsaturated inductors lack the back electromotive force (EMF) generated by established current, reducing their effective opposition to near the resistive component alone. This minimal impedance Z_{\min} allows the full supply voltage to drive current through a path with limited resistance, amplifying the surge before reactive effects build up and increase the total impedance.[13][14] Differences between AC and DC systems influence the nature and severity of inrush. In DC circuits, the phenomenon is mainly driven by direct charging of capacitors or the transient ramp-up of current in inductors until steady-state back EMF stabilizes the flow, with the surge decaying exponentially based on time constants. In AC systems, the sinusoidal voltage waveform introduces additional variability; the point-on-wave at which switching occurs, combined with any residual flux in inductive elements, can misalign the applied voltage with the existing magnetic state, leading to transient DC offsets that drive the core toward saturation and exacerbate the current peak.[6][10] The approximate magnitude of inrush current follows from Ohm's law applied at the instant of switching:I_{\text{inrush}} \approx \frac{V}{Z_{\min}}
where V is the applied voltage amplitude and Z_{\min} is the circuit's minimum impedance at t = 0. To derive this, consider a general linear circuit under a step voltage input v(t) = V u(t), where u(t) is the unit step function. The steady-state current is I_{ss} = V / Z, with Z = R + j \omega L + 1/(j \omega C) in the frequency domain for AC, or Z = R for DC resistive paths. However, transients arise from initial conditions: capacitors start at v_C(0) = 0, so initial capacitive current i_C(0^+) = C dv/dt effectively sees Z_{\min} \approx R (series resistance); inductors start at i_L(0) = 0, so initial di_L/dt = V / L, with the circuit impedance momentarily dominated by resistance before inductive reactance builds. In both cases, the peak inrush occurs when reactive contributions are negligible, yielding I_{\text{inrush}} \approx V / Z_{\min}, where Z_{\min} typically equals the non-reactive (resistive or source) impedance. For AC, V is the peak voltage, and Z_{\min} may include brief harmonic effects, but the approximation holds for the initial surge. This relation establishes the scale, often 5–10 times I_{ss}, highlighting the need for careful circuit design.[13][6]