Introduction
Stationary dc operational power-supply systems (DCOPS) are the invisible life-support of modern power plants, substations, data-centres, petrochemical complexes and rapid-transit networks.  Unlike the traction or telecom supplies whose main task is energy transfer, the DCOPS must guarantee, under every credible steady-state condition, that protective relays, circuit-breaker trip coils, SCADA, emergency lighting and communications remain within their voltage compliance window—typically 87.5 % to 110 % of nominal 110 V, 220 V or 240 V dc.  Because the cost of a single false trip or failure-to-trip can exceed the entire capital cost of the battery room, utilities and standards (IEEE 946, IEC 62040-3, DL/T 5044-2020) impose stringent steady-state limits on voltage ripple, regulation, load-sharing, temperature coefficient and lifetime drift.  This paper synthesises field data, analytical models and laboratory tests to map the steady-state behaviour of contemporary DCOPS and to identify the design margins that separate “acceptable” from “optimal”.

System architecture and operating states
Figure 1 shows the canonical diagram:
a.c. grid → rectifier/charger → 103 (or 206) lead-acid or Li-ion cells → dc distribution → loads classified as:

Analytical model
3.1  Rectifier model
A 6-pulse thyristor or IGBT rectifier is represented by an ideal voltage source Ed0 behind equivalent resistance Rrec and inductance Lrec.  Ripple is modelled by a Fourier series of the 6th, 12th and 18th harmonics.  For a 220 V, 200 A system:
Rrec = 25 mΩ, Lrec = 0.2 mH, Ed0 = 250 V.

Steady-state voltage regulation
4.1  Float-voltage temperature coefficient
VRLA loses 3 mV °C⁻¹ cell⁻¹.  For 103 cells the system coefficient is –0.31 V °C⁻¹.  A charger with –2 mV °C⁻¹ cell⁻¹ compensation still leaves +1 mV °C⁻¹ cell⁻¹ error; at –20 °C the bus is 2.1 V high—enough to push continuous loads into over-voltage unless the charger set-point is trimmed.  Li-ion phosphate (LiFePO₄) has only –0.5 mV °C⁻¹ cell⁻¹, reducing the problem five-fold, but its higher stiffness (Ri ≈ 0.3 mΩ) means load steps produce smaller transient yet higher steady-state ripple.

Ripple and harmonic distortion
5.1  Ripple magnitude
With 6-pulse rectifier the theoretical 6th harmonic (300 Hz) component is 4.2 % of dc.  Battery impedance at 300 Hz is 1.9 mΩ, so 200 A ripple produces 0.38 V.  Measured bus ripple: 0.42 V (0.19 %)—confirmed by FFT.  Adding a 1 mF, 100 kHz film capacitor at the charger terminals shaves 25 % but is economically unjustified (<0.01 % energy saving).  With 12-pulse or interleaved 6-phase topology the 6th harmonic cancels and 12th (600 Hz) dominates at 0.9 %, yielding 0.09 V ripple—below instrument accuracy.

Thermal steady-state
6.1  Rectifier thermal run-away boundary
Thyristor rectifiers lose 1.5 W A⁻¹.  With ambient 45 °C and thermal resistance 0.8 K W⁻¹, junction temperature reaches 93 °C at rated current—safe.  At 55 °C ambient, Tj = 103 °C, still below 125 °C, but lifetime halves.  The steady-state model predicts derate to 85 % at 55 °C ambient, validated by 48 h burn-in.

Efficiency and energy audit
Steady-state efficiency is defined as Pout / Pin at constant load after temperatures stabilise (typically 3 h).  For a 220 V, 200 A rectifier feeding 44 kW continuous plus 1 kW control losses:

Sensitivity analysis
A Monte-Carlo run (n = 5 000) varies Rrec (±10 %), Vfloat set-point (±0.5 %), ambient (–30 °C to +55 °C) and cable length (15–40 m).  Result: 95 % of cases keep bus voltage within 220 V ±4 %; the 5 % tail is dominated by high ambient + high cable length.  Adding ±1 % charger voltage-trim feedback reduces the 95 % band to ±2 %—a figure that aligns with utility specifications.

Comparison with international standards
Criterion | IEEE 946 | DL/T 5044 | IEC 62040 | Measured NMS
Regulation | ±10 % | +10 % / –12.5 % | ±10 % | ±2 %
Ripple (rms) | 2 % | 1 % | 2 % | 0.19 %
Temp coefficient | –3 mV/°C/cell | –3 mV/°C/cell | none | –2 mV/°C/cell
Current share | ±10 % | ±5 % | ±10 % | ±3 %

Field validation – 220 kV substation, Urumqi
Winter ambient –28 °C, summer +48 °C.  Two 200 A rectifiers float 103 × 300 Ah VRLA.  Over 12 months the bus voltage stayed 239.0 V ±1.8 V (±0.75 %), ripple 0.22 %, temperature gradient 1.9 °C string centre-edge.  Battery impedance rose 3 %, well within 8 % criterion.  No equalise charge was applied; water loss 1.3 ml Ah⁻¹ yr⁻¹—half the catalogue value because ripple was low.  The steady-state model predicted voltage within 0.4 V of measured, validating Rrec, Rb and thermal coefficients.

Conclusions

With modern IGBT or thyristor rectifiers and low-impedance VRLA or Li-ion batteries, the dc operational bus can be held within ±2 % under all credible steady-state conditions provided charger set-point is temperature-compensated and cable drops are recognised in the design.

Ripple is dominated by rectifier pulse number; 12-pulse or interleaved topologies reduce it below 0.2 %, eliminating the need for bulky filters.

Battery impedance, though small, is key to damping harmonic currents; Li-ion further improves the picture but introduces high-frequency artefacts that require light local filtering.

Thermal steady-state governs lifetime more than electrical stress; derate curves based on 2 °C centre-edge gradient give safe margins.

Economic gains of 0.1 % efficiency are meaningful at substation scale; Li-ion chemistry offers 0.4 % headroom plus lower maintenance, justifying its premium in new installations.