Focused child case · power electronics · verified 28 July 2026

Make the DC-link assumption visible before selecting hardware.

Two inspectable relationships estimate voltage ripple for an ideal triangular capacitor-current waveform and minimum capacitance for a defined constant-power energy pulse.

Engineering question

What capacitance follows from the stated waveform or energy window?

These are first-pass checks for exposing current, frequency, energy, bus-voltage, and allowable-drop assumptions before switching, lifetime, thermal, tolerance, and component studies.

DC-link system map with source, capacitor, converter, load, ideal ripple waveform, voltage window, and sizing equation — Explanatory architecture
Source, capacitor, converter, and load define the boundary; waveform and voltage-window assumptions determine which relationship applies.
Open full-size figure

Energy-pulse relationship

C_min = 2E / (V₁² − V₂²)

A transparent check—not a component selection.

The companion ripple relationship assumes a zero-mean triangular capacitor-current waveform: ΔV_pp = I_pp / (8 f C).

Parameter	Unit	Physical Domain	Constraint & Invariant
V₁ (Initial bus voltage)	V	V₁ > 0	Must exceed minimum voltage: V₁ > V₂
V₂ (Minimum post-pulse voltage)	V	0 < V₂ < V₁	V₂ = V₁ − ΔV; ΔV < V₁ required
E (Pulse energy)	J	E > 0	E = P · Δt for constant power P and duration Δt
C_min (Minimum capacitance)	F	C_min > 0	Invalid windows (ΔV ≥ V₁ or non-finite inputs) rejected

Worked numerical example (agrees with reference figure and CSV):

For a 20 kW pulse of duration 20 ms on an 800 V bus with an allowed voltage drop of 80 V (V₂ = 720 V):

Pulse energy: E = 20,000 W × 0.020 s = 400 J
Voltage window difference: V₁² − V₂² = 800² − 720² = 640,000 − 518,400 = 121,600 V²
Minimum capacitance: C_min = (2 × 400 J) / 121,600 V² = 800 / 121,600 F ≈ 6.58 mF (0.00658 F)

Verified result

Inputs, units, and sensitivities stay on the figure.

Two-panel plot of ideal triangular capacitor-current ripple versus capacitance and energy-pulse capacitance versus allowed bus-voltage drop — Illustrative · retained generated output
Ripple and energy-pulse sensitivity

The figure states 20 App at 10 kHz and a 20 kW, 20 ms pulse at 800 V. It is generated from the pinned Python relationships, not manually invented data.

Model source
Repository `mohammadrezwankhan/battery-power-models` · commit `7d9f61f` · `src/dc_link.py`

Figure generator
Private portfolio repository; generator has no established public license and is unavailable anonymously.

Verification
Python 3.10+ analytical calculation; MATLAB parity checked; illustrative parameter sweep

Download source CSV Download retained SVG Download retained PNG Inspect source
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Validation and evidence

Three automated checks cover the released DC-link relationships.

Triangular ripple

The unit test verifies the implemented I_pp / (8 f C) relationship.

Energy pulse

A valid constant-power pulse produces positive capacitance from the exact capacitor-energy change.

Invalid voltage window

The implementation rejects an allowed drop that equals or exceeds the initial bus voltage.

Parity boundary

MATLAB equivalents are present. The automated six-test repository count comes from the Python suite across thermal and DC-link families.

Reproduction instructions

Run the model separately from the retained website figure.

1. Run the model (battery-power-models repository)

Clone the pinned model repository to execute the analytical functions and unit tests:

git clone https://github.com/mohammadrezwankhan/battery-power-models.git
cd battery-power-models
git checkout 7d9f61f1ebdca73f9facce5129f79805b1747ed0
python src/dc_link.py
python -m unittest discover -s tests -v

Prerequisites: Python 3.10+ (standard library only). Optional MATLAB parity script matlab/dc_link_ripple.m is provided for environments with a licensed MATLAB runtime.

2. Rebuilding the website figure is unavailable to public readers

The retained SVG, PNG, and CSV are downloadable. Rebuilding this site figure depends on a generator in the private portfolio repository; it has no established public license and is unavailable anonymously.

The public battery-power-models Python source remains runnable independently. Retaining these generated outputs does not mean the private website generator is publicly reproducible.

3. Inspect retained results

Inspect or download the retained dataset directly: Download dc-link-sizing.csv.

Engineering boundary

Replace idealized inputs before making a component decision.

The ripple relationship assumes an ideal zero-mean triangular capacitor current at one stated frequency.
The energy-pulse relationship assumes a constant-power pulse and an exact capacitor-energy window.
ESR, ESL, RMS heating, switching harmonics, controller interaction, voltage dependence, tolerance, temperature, aging, reliability, packaging, fault behavior, and derating are omitted.
Use manufacturer data, mission profiles, stability studies, thermal analysis, lifetime calculations, and hardware validation before selecting a capacitor bank.

Parent and related context

Use the relationships to expose assumptions, not to skip detailed design evidence.Return to parent overview Open pinned repository

Evidence summary

Reviewed 2026-11-12; evidence records retain their own scope and dates.

Portfolio source record: 6 tests · source-reported · 7d9f61f · 7d9f61f1ebdca73f9facce5129f79805b1747ed0
Current release: Unknown from the reviewed evidence.
Current verification: Successful hosted run · 2026-11-10 · target 31cad57f6224a6460e07a68c74df7c219549be61
Repository head at 2026-10-17 inventory: 682d43c769e82c0fe0c8d6ed2a2934c9fad6be35 · inventory snapshot only