Electrochemical Impedance Spectroscopy (EIS) applies a small sinusoidal current perturbation (typically 10-100 mA RMS at frequencies from 0.001 Hz to 10 kHz) to the battery and measures the complex impedance Z(ω) = V(ω) / I(ω) = Z_real + jZ_imag at each frequency. The Nyquist plot (Z_imag vs. Z_real) reveals three characteristic regions: the high-frequency inductive loop (1-10 kHz) from the battery's internal inductance and cable connections, the mid-frequency charge transfer semicircle (0.1-10 Hz) representing the electrode-electrolyte interface impedance, and the low-frequency Warburg diffusion tail (0.001-0.1 Hz) representing ion diffusion in the electrolyte. For a healthy VRLA battery at 80% state of charge (SoC), the charge transfer resistance R_ct (the diameter of the mid-frequency semicircle) is typically 1-3 mΩ for a 100 Ah cell at 25°C. As the battery ages, R_ct increases due to sulfation of the negative plates (PbSO₄ crystal growth, typical for VRLA) or lithium plating (for Li-ion, especially at low temperatures). The increase in R_ct follows an exponential trend: R_ct(t) = R_ct(0) × exp(t / τ_aging), where τ_aging is the aging time constant (2-5 years for VRLA at 25°C, 5-10 years for LFP at 25°C). A 100% increase in R_ct (doubling) corresponds to approximately 20-30% capacity loss, which the IEEE 1188 standard defines as the end-of-life threshold for VRLA batteries (80% of rated capacity). Our runtime model incorporates the measured R_ct value as a state-of-health input, adjusting the Peukert-compensated runtime by the capacity factor C_actual = C_rated × f_SOH(R_ct), where f_SOH(R_ct) = 1 - 0.3 × (R_ct / R_ct(0) - 1) for R_ct / R_ct(0) < 2.0 (the linear region of the capacity-SOH relationship).

The temperature correction of EIS measurements is critical because both R_ct and the electrolyte conductivity vary significantly with temperature. The Arrhenius temperature dependence of R_ct is: R_ct(T) = R_ct(T_ref) × exp[E_a / k × (1/T - 1/T_ref)], where E_a is the activation energy for the charge transfer reaction (typically 25-40 kJ/mol for VRLA, 30-50 kJ/mol for Li-ion). For a VRLA battery measured at 10°C (283 K) with T_ref = 25°C (298 K) and E_a = 30 kJ/mol, the correction factor is: R_ct_corrected = R_ct_measured × exp[30,000 / 8.314 × (1/298 - 1/283)] = R_ct_measured × exp[3,608 × (0.00336 - 0.00353)] = R_ct_measured × exp[-0.614] = 0.541 × R_ct_measured. The measured R_ct at 10°C is 1.85× higher than the reference value, meaning the battery appears 85% more degraded at 10°C than at 25°C purely due to the temperature effect on charge transfer kinetics. If this temperature correction is not applied, the UPS monitoring system would falsely indicate that the battery has lost 30-40% of its capacity during a winter cold snap—triggering unnecessary battery replacement. Our runtime model automatically applies the EIS temperature correction by reading the battery temperature sensor (typically a 10 kΩ NTC thermistor mounted on the battery terminal) and applying the Arrhenius correction with the battery chemistry-specific activation energy from the manufacturer's datasheet.

The online EIS measurement during UPS operation introduces interference from the UPS inverter's switching noise, which creates harmonics at the inverter's fundamental frequency (typically 50/60 Hz) and its switching frequency (typically 3-20 kHz for IGBT-based UPS inverters). The EIS measurement must inject the sinusoidal perturbation at frequencies that are not harmonics of the inverter frequency to avoid measurement contamination. The standard approach uses a broadband pseudo-random binary sequence (PRBS) perturbation that distributes the measurement energy across a wide frequency range (0.01-1,000 Hz), combined with a synchronous demodulation algorithm that suppresses the inverter harmonics by 60-80 dB of rejection. The PRBS perturbation amplitude must be limited to 0.1-0.5% of the battery's C-rate to avoid disturbing the battery's equilibrium state: for a 100 Ah battery, the PRBS current peak amplitude is 100 A × 0.5% = 500 mA, which at 2 V per cell adds 1 W of perturbation power—negligible compared to the UPS's nominal power draw. The measurement time for a full EIS sweep (0.01-1,000 Hz) using PRBS is approximately 10-30 seconds, compared to 5-15 minutes for a single-frequency sweep at 0.01 Hz (the lowest frequency, requiring 100 seconds for one full period). The PRBS method enables online EIS without interrupting the UPS's power delivery, making it the preferred technique for continuous SOH monitoring in data center UPS systems.

The EIS-capacity correlation model calibration requires a one-time reference measurement on a new battery and periodic validation against a reference discharge test (the IEEE 450 full-capacity discharge test, required annually for VRLA). The reference EIS measurement establishes the baseline R_ct(0) and the Warburg coefficient σ_w(0) = dZ_imag / dω⁻¹/² at low frequencies (the slope of the linear region in the Nyquist plot below 0.1 Hz). The capacity fade model is: C_actual / C_rated = 1 - k_1 × (R_ct / R_ct(0) - 1) - k_2 × (σ_w / σ_w(0) - 1), where k_1 = 0.3 (typical for VRLA) and k_2 = 0.1 (typical for VRLA). The Warburg coefficient σ_w increases as the active material porosity decreases (sulfation or lithium plating blocks the pores), while R_ct increases as the charge transfer surface area decreases. A battery that shows an isolated increase in σ_w (with stable R_ct) is experiencing active material degradation without electrolyte dry-out or sulfation—a condition that can be reversed by an equalization charge (controlled overcharge at 2.35-2.40 V/cell for 24-72 hours). Our runtime model detects this σ_w-dominant degradation pattern and recommends an equalization charge when the capacity estimation drops below 85% but the R_ct is within 120% of baseline. Conversely, an R_ct-dominant degradation (R_ct > 150% of baseline, σ_w within 120% of baseline) indicates sulfation that has progressed beyond recovery (VRLA) or lithium plating (LFP), requiring battery replacement. This diagnostic differentiation prevents unnecessary battery replacement by distinguishing between recoverable and non-recoverable capacity loss mechanisms.