Exercise set

DC-Link Capacitor, Precharge, and DC-DC Converter Exercises

Worked DC-link and DC-DC exercises for hold-up energy, rectifier voltage, ripple, saturation, precharge, discharge, snubbers and release gates.

Branch: Electrical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises practise DC-link and DC-DC converter sizing as an energy, ripple, component-stress and safety-release problem. They cover hold-up capacitance, rectifier voltage, voltage derating, buck and boost ripple, flyback stress, inductor saturation, output-capacitor ripple, DC-link ESR heating, precharge, discharge, stored energy, snubbers, clamp energy, current limits, input inrush and release gates.

The focus is narrower than general power electronics. A DC-link and DC-DC page should answer whether stored energy, ripple current, component ratings, precharge, discharge and current limits are controlled before an inverter, drive or grid interface is released.

How to Use These Exercises

For each calculation, define:

DC-link voltage range, load power and permitted voltage sag;
capacitor bank value, voltage rating, ripple rating, ESR and discharge path;
converter topology, duty cycle, switching frequency and current-limit basis;
safety boundary for stored energy, precharge energy and accessible terminals;
test evidence needed to prove the installed hardware matches the calculation.

The common mistake is selecting capacitors from nominal voltage or capacitance only. DC-link release also depends on ripple current, surge voltage, precharge stress, discharge time, ESR heating, lifetime and service safety.

Release Evidence Notes

DC-link energy evidence should be measured at the terminals that technicians can access. A controller-reported voltage is not enough for lockout or discharge release.

Precharge evidence should include peak current, resistor pulse energy, repetition rate and contactor sequence. A safe average value can hide a destructive first pulse.

Ripple evidence should use RMS ripple current and ESR heating. Peak-to-peak voltage ripple alone does not prove capacitor lifetime or thermal margin.

Current-limit evidence should include tolerances. Inductor saturation, switch current limit, sensing offset, firmware limit and thermal derating should be checked together.

Engineering Boundary Notes

These exercises are simplified design screens. Real converter design requires device datasheets, insulation coordination, creepage and clearance, thermal modelling, EMC review, fault testing, safety standards, manufacturing variation, firmware behaviour, measurement uncertainty and qualified review.

A DC-link pass does not release an inverter system by itself. Gate-drive timing, filters, motor load, protection, cooling, EMI and lifetime must still be validated at the system level.

Scenario Map

Scenario	Exercises	Primary calculation	Engineering decision
Energy and voltage	1-4, 12-13	hold-up, rectifier voltage, derating, discharge time and stored energy	Decide whether the DC link has adequate energy and safety control.
DC-DC component stress	5-10, 15-16	duty cycle, ripple, peak current, capacitor RMS current, clamp and current limit	Decide whether components are inside rating.
Release controls	11, 14, 17-18	precharge pulse, snubber energy, input inrush and release scoring	Decide whether the converter can be energized and serviced.

Exercise 1: DC-Link Hold-Up Capacitance

A converter must support:

P=18\ \text{kW}

for:

t=35\ \text{ms}

while DC-link voltage falls from:

V_1=760\ \text{V}

to:

V_2=640\ \text{V}

Estimate required capacitance using:

E=\dfrac{1}{2}C(V_1^2-V_2^2)

Solution

Energy required:

E=Pt=18{,}000(0.035)=630\ \text{J}

Capacitance:

C=\dfrac{2E}{V_1^2-V_2^2}

C=\dfrac{2(630)}{760^2-640^2}=0.00750\ \text{F}

Therefore:

C=7.5\ \text{mF}

Engineering Comment

Hold-up sizing should include load profile, minimum bus voltage, capacitor tolerance, ageing, temperature and protection response during the sag.

Plausibility Check

Hundreds of joules at hundreds of volts usually require millifarads, not microfarads.

Exercise 2: Rectifier DC-Link Voltage

A three-phase diode rectifier is supplied from:

V_{LL}=480\ \text{V RMS}

Estimate ideal no-load DC-link voltage using:

V_{DC}\approx \sqrt{2}V_{LL}

Then apply a $10\%$ high-line tolerance.

Solution

Nominal DC link:

V_{DC}=1.414(480)=679\ \text{V}

High-line DC link:

V_{high}=1.10(679)=747\ \text{V}

Engineering Comment

Capacitor voltage rating should cover line tolerance, regeneration, switching transients and measurement uncertainty, not only nominal rectified voltage.

Plausibility Check

A $480$ V AC system commonly produces a DC bus near $680$ V, so the result is reasonable.

Exercise 3: Capacitor Voltage Derating

A DC-link capacitor bank is rated:

V_r=900\ \text{V}

The worst expected bus voltage is:

V_{max}=747\ \text{V}

The project requires:

20\%

voltage derating. Check the margin.

Solution

Maximum permitted operating voltage:

V_{perm}=0.80(900)=720\ \text{V}

Margin:

M=720-747=-27\ \text{V}

The capacitor bank fails the $20\%$ derating rule.

Engineering Comment

A capacitor can be below absolute rating and still fail a derating policy. Derating is a reliability and lifetime control.

Plausibility Check

$747$ V is below $900$ V but above the $720$ V derated limit, so the mixed pass/fail interpretation is expected.

Exercise 4: Buck Converter Inductor Ripple

A buck converter has:

V_{in}=48\ \text{V},\qquad V_o=12\ \text{V}

Switching frequency is:

f_s=200\ \text{kHz}

Inductance is:

L=22\ \mu\text{H}

Estimate inductor ripple current using:

\Delta I_L=\dfrac{(V_{in}-V_o)D}{Lf_s},\qquad D=\dfrac{V_o}{V_{in}}

Solution

Duty cycle:

D=\dfrac{12}{48}=0.25

Ripple current:

\Delta I_L=\dfrac{(48-12)(0.25)}{22\times10^{-6}(200\times10^3)}=2.05\ \text{A}

Engineering Comment

Ripple current affects inductor saturation, output capacitor ripple and current-limit margin. It should be checked at voltage and frequency tolerances.

Plausibility Check

The inductor sees $36$ V for a quarter of the cycle, so a ripple of a few amperes is credible.

Exercise 5: Buck Inductor Peak and Saturation Margin

The buck converter in Exercise 4 supplies:

I_o=9.0\ \text{A}

The inductor saturation current at hot temperature is:

I_{sat}=11.0\ \text{A}

Use the ripple current from Exercise 4:

\Delta I_L=2.05\ \text{A}

Calculate peak inductor current and margin.

Solution

Peak current:

I_{pk}=I_o+\dfrac{\Delta I_L}{2}=9.0+1.025=10.025\ \text{A}

Margin:

M=11.0-10.025=0.975\ \text{A}

Percentage margin:

\dfrac{0.975}{11.0}=8.9\%

Engineering Comment

This is a thin saturation margin. Current-limit tolerance, transient load, temperature and ageing could remove it.

Plausibility Check

Ripple adds about one ampere above average current, so a peak near $10$ A is expected.

Exercise 6: Boost Converter Duty Cycle and Input Current

A boost converter raises:

V_{in}=120\ \text{V}

to:

V_o=360\ \text{V}

Output power is:

P_o=6.0\ \text{kW}

and efficiency is $94\%$ . Estimate ideal duty cycle and input current.

Solution

Duty cycle:

D=1-\dfrac{V_{in}}{V_o}=1-\dfrac{120}{360}=0.667

Input power:

P_{in}=\dfrac{6000}{0.94}=6383\ \text{W}

Input current:

I_{in}=\dfrac{6383}{120}=53.2\ \text{A}

Engineering Comment

Boost input current can be much larger than output current. Inductor, switch, diode and input capacitor ratings should be based on input-side stress.

Plausibility Check

Tripling voltage at high power requires tens of amperes at the low-voltage input.

Exercise 7: Flyback Switch Voltage Stress

A flyback converter has input voltage:

V_{in}=36\ \text{V}

Reflected output voltage on the primary is:

V_R=92\ \text{V}

Leakage spike is estimated at:

V_{sp}=38\ \text{V}

The MOSFET rating is:

V_{DS}=200\ \text{V}

Calculate stress and margin.

Solution

Switch voltage stress:

V_s=36+92+38=166\ \text{V}

Margin:

M=200-166=34\ \text{V}

Percentage margin:

\dfrac{34}{200}=17.0\%

Engineering Comment

Flyback voltage stress depends on leakage inductance, clamp design, load, input tolerance and layout. Oscilloscope validation is essential.

Plausibility Check

The switch sees input plus reflected and spike voltages, so a stress well above input voltage is expected.

Exercise 8: Output Capacitor Ripple Current

A converter output capacitor carries triangular ripple current with peak-to-peak amplitude:

\Delta I=2.4\ \text{A}

For a triangular ripple with zero average, use:

I_{rms}=\dfrac{\Delta I}{2\sqrt{3}}

Capacitor ripple rating is:

1.0\ \text{A RMS}

Check the margin.

Solution

RMS ripple current:

I_{rms}=\dfrac{2.4}{2\sqrt{3}}=0.693\ \text{A}

Margin:

M=1.0-0.693=0.307\ \text{A}

The capacitor passes the ripple-current screen.

Engineering Comment

Ripple rating depends on frequency and temperature. A rating at one frequency band may not apply directly to another converter.

Plausibility Check

The RMS value of a triangular ripple should be much lower than peak-to-peak amplitude.

Exercise 9: DC-Link Capacitor ESR Heating

A DC-link capacitor bank has RMS ripple current:

I_{rms}=18\ \text{A}

Equivalent ESR is:

R_{ESR}=11\ \text{m}\Omega

The thermal limit for capacitor self-heating is:

4.5\ \text{W}

Calculate ESR loss.

Solution

ESR loss:

P=I_{rms}^2R_{ESR}=18^2(0.011)=3.56\ \text{W}

Margin:

M=4.5-3.56=0.94\ \text{W}

The bank passes the simplified ESR heating screen.

Engineering Comment

ESR rises with temperature and ageing. The release record should include capacitor temperature or enclosure airflow evidence.

Plausibility Check

Hundreds of ampere-squared times milliohms gives a few watts, so the result is credible.

Exercise 10: DC-Link Precharge Peak Current

A DC link is precharged through:

R_p=47\ \Omega

from a:

V_{DC}=760\ \text{V}

source. Calculate initial precharge current.

Solution

Initial current:

I_0=\dfrac{760}{47}=16.17\ \text{A}

Engineering Comment

Initial current is the highest point of an RC precharge. The resistor pulse rating and contactor sequencing should be checked at this value.

Plausibility Check

$47$ ohms at hundreds of volts should allow current in the tens of amperes.

Exercise 11: Precharge Resistor Pulse Energy

The DC-link capacitance is:

C=5.6\ \text{mF}

and final bus voltage is:

V=760\ \text{V}

Estimate capacitor energy at the end of precharge. In a simple resistor precharge from an ideal voltage source, approximately the same energy is dissipated in the resistor.

Solution

Capacitor energy:

E_C=\dfrac{1}{2}CV^2

E_C=\dfrac{1}{2}(0.0056)(760^2)=1617\ \text{J}

Approximate resistor pulse energy:

E_R\approx 1617\ \text{J}

Engineering Comment

Average resistor power may look small while pulse energy is severe. The precharge resistor must be rated for the event energy and repetition schedule.

Plausibility Check

Millifarads at hundreds of volts store kilojoules, so the result is plausible.

Exercise 12: DC-Link Discharge Time

A DC-link capacitor:

C=4.7\ \text{mF}

is discharged through:

R=18\ \text{k}\Omega

from $760$ V to a safe threshold of $50$ V. Use:

t=RC\ln\left(\dfrac{V_0}{V_f}\right)

Solution

Time constant:

RC=18{,}000(0.0047)=84.6\ \text{s}

Discharge time:

t=84.6\ln\left(\dfrac{760}{50}\right)=84.6(2.721)=230\ \text{s}

Therefore:

t=3.84\ \text{min}

Engineering Comment

Discharge time should be verified at the accessible terminals and documented on the warning label. Failed discharge resistors are a real service hazard.

Plausibility Check

The time is a few time constants, which is expected for a large voltage reduction.

Exercise 13: Stored-Energy Release Threshold

A service rule treats stored energy above:

50\ \text{J}

as a controlled energy hazard. A DC link has:

C=2.2\ \text{mF},\qquad V=420\ \text{V}

Calculate stored energy and decision.

Solution

Stored energy:

E=\dfrac{1}{2}(0.0022)(420^2)=194\ \text{J}

Since:

194>50

the DC link is a controlled energy hazard.

Engineering Comment

Stored energy is a safety fact. It controls lockout, bleed-down verification, warning labels and service tools.

Plausibility Check

Hundreds of volts and millifarads should exceed a $50$ J threshold.

Exercise 14: Snubber Energy per Switching Event

A snubber capacitor has:

C_s=4.7\ \text{nF}

and charges to:

V_s=900\ \text{V}

each event. Calculate energy per event.

Solution

Energy:

E_s=\dfrac{1}{2}C_sV_s^2

E_s=\dfrac{1}{2}(4.7\times10^{-9})(900^2)=0.00190\ \text{J}

Therefore:

E_s=1.90\ \text{mJ}

Engineering Comment

Small energy per pulse can become meaningful loss at high switching frequency. Snubber resistor power and temperature still need review.

Plausibility Check

Nanofarads at high voltage store millijoules, so the scale is plausible.

Exercise 15: Clamp Power from Leakage Energy

A flyback clamp dissipates leakage energy:

E_l=0.28\ \text{mJ}

per switching cycle at:

f_s=85\ \text{kHz}

Calculate clamp power.

Solution

Clamp power:

P=E_l f_s=0.28\times10^{-3}(85\times10^3)=23.8\ \text{W}

Engineering Comment

Leakage-clamp loss can dominate a small converter thermal design. Reducing leakage inductance or using energy recovery may be necessary.

Plausibility Check

Sub-millijoule energy repeated tens of thousands of times per second can produce tens of watts.

Exercise 16: Current-Limit Tolerance Gate

A DC-DC converter must deliver:

I_{load}=12.0\ \text{A}

Peak ripple allowance adds:

1.4\ \text{A}

The nominal current limit is:

I_{lim}=15.0\ \text{A}

with tolerance:

-12\%

Check the worst-case current-limit margin.

Solution

Required peak current:

I_{req}=12.0+1.4=13.4\ \text{A}

Worst-case current limit:

I_{lim,min}=15.0(1-0.12)=13.2\ \text{A}

Margin:

M=13.2-13.4=-0.2\ \text{A}

The converter fails the worst-case current-limit gate.

Engineering Comment

Nominal current limit looks adequate, but tolerance removes the margin. Release should use worst-case sensing, temperature and component tolerance.

Plausibility Check

The required peak and worst-case limit are close, so a small negative margin is plausible.

Exercise 17: Input Capacitor Inrush Charge

An input capacitor bank is:

C=1.8\ \text{mF}

and charges to:

V=380\ \text{V}

Calculate charge drawn from the source during energization.

Solution

Charge:

Q=CV=0.0018(380)=0.684\ \text{C}

Engineering Comment

Input charge and inrush current affect upstream fuses, contactors, EMI filters and soft-start circuits. Charge alone does not define peak current, but it is part of the energization evidence.

Plausibility Check

Millifarads times hundreds of volts gives a fraction of a coulomb to a few coulombs.

Exercise 18: DC-Link Release Gate

A DC-link and DC-DC converter release review has five gates:

Gate	Weight	Result
hold-up and voltage derating	$0.20$	$0.92$
ripple and ESR heating	$0.20$	$0.95$
precharge and discharge safety	$0.25$	$0.88$
current limit and saturation	$0.20$	$0.93$
test evidence and labels	$0.15$	$0.96$

The weighted release threshold is:

S\ge 0.92

and precharge/discharge may not be below $0.90$ . Calculate the decision.

Solution

Weighted score:

\begin{aligned} S&=0.20(0.92)+0.20(0.95)+0.25(0.88)+0.20(0.93)+0.15(0.96)\\ &=0.184+0.190+0.220+0.186+0.144\\ &=0.924 \end{aligned}

The score is:

92.4\%

The score passes, but precharge and discharge safety fails its floor:

0.88<0.90

Release is held.

Engineering Comment

DC-link safety gates should not be hidden inside a weighted score. Stored energy, precharge stress and discharge verification control energization and service risk.

Plausibility Check

The total score barely passes while a critical safety floor fails, so a hold decision is consistent with the rule.

Validation Package Checklist

DC-link voltage range includes line tolerance, regeneration, switching transients and measurement uncertainty.
Capacitor value, tolerance, ageing, ESR, ripple current and thermal evidence are documented.
Precharge checks include peak current, pulse energy, contactor sequence and repetition rate.
Discharge checks are measured at accessible terminals and tied to warning labels.
DC-DC inductor, switch, diode, clamp and current-limit ratings use worst-case current and temperature.
Release evidence includes measured waveforms, component part numbers, labels, service procedure and test configuration.

Common Release Mistakes

Selecting capacitors from capacitance and voltage while ignoring ripple current and ESR heating.
Treating nominal current limit as guaranteed current limit.
Checking precharge peak current but not resistor pulse energy.
Assuming a DC link is safe because control power is off.
Measuring discharge at the controller while accessible terminals remain energized.
Reusing flyback or snubber calculations after layout or transformer leakage changes.
Releasing the converter before labels and service wait times match measured discharge evidence.

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