Technology / Technical guide
Converter Instantaneous Power, Storage & Dissipation
Input and output power need not match at every instant, even in an ideal lossless converter model. Electrical storage can absorb or release energy while the circuit changes. Adding dissipation to that account explains why a transient input–output difference is not automatically a measured conversion loss.
Keep changing storage inside the power balance.
The boundary, sign convention and averaging interval determine whether a difference means storage, dissipation or another transfer path.
01 / Power definition
Voltage and current must belong to the same port.
With the passive sign convention, instantaneous electrical power is p = vi, where current enters the terminal labelled positive voltage.
With the passive sign convention, instantaneous electrical power is p = vi, where current enters the terminal labelled positive voltage. Positive power enters that element’s boundary. Defining delivered output as positive instead changes the signs in a system-level balance.
OpenStax explains electrical power as a rate of energy transfer. Voltage and current must describe matching points and times. Multiplying an average voltage by an average current does not generally reproduce the average of their instantaneous product when both vary.
02 / Complete boundary
Count every included transfer before naming the difference.
For a declared electrical converter model, define total pin as power entering its included input ports and pout as power leaving its included output ports.
For a declared electrical converter model, define total pin as power entering its included input ports and pout as power leaving its included output ports. With nonnegative dissipation ploss, its energy balance is pin − pout = dWstored/dt + ploss.
Additional auxiliary or other transfer paths must either appear among those ports or be explicitly outside the chosen boundary. Ignoring a path changes the account. The balance does not establish which topology, storage components or auxiliary circuits any actual converter contains.
03 / Storage terms
Electric and magnetic energy can change independently.
For ideal constant linear elements, a capacitor stores ½Cv² and an inductor stores ½Li².
For ideal constant linear elements, a capacitor stores ½Cv² and an inductor stores ½Li². A multi-element model includes the applicable sum of those storage terms. Mutual coupling or nonlinearity requires the appropriate energy model instead of blindly adding independent constant-L expressions.
The DC bus guide focuses on one capacitor boundary. The LCL guide adds distinct inductive and capacitive states, showing why unchanged capacitor voltage alone does not prove every stored-energy term is steady.
04 / Transient example
A shortfall at the output can charge storage.
Consider a hypothetical interval with pin = 100 W, pout = 80 W and ploss = 5 W.
Consider a hypothetical interval with pin = 100 W, pout = 80 W and ploss = 5 W. The balance gives dWstored/dt = 15 W. If those assumed values remain constant for 2 s, stored energy increases by 30 J.
The input–output difference is 20 W, but only 5 W is dissipated under these stated assumptions. The rest changes storage. This arithmetic represents no MARSTON waveform or efficiency, and a different storage change can instead make output temporarily exceed input without creating energy.
05 / Periodic average
Repeating the storage state removes one averaged term.
Over an interval T, average storage power is [Wstored(T) − Wstored(0)]/T.
Over an interval T, average storage power is [Wstored(T) − Wstored(0)]/T. If a periodic model returns to exactly the same storage state at the interval ends, that term is zero even while energy moves in and out of individual elements throughout the cycle.
Under that particular boundary, average input minus average output equals average dissipation. An arbitrary transient window may not satisfy the endpoint condition. A cyclic waveform and a visually steady display are different evidence for whether the energy state actually repeats.
06 / Efficiency scope
A ratio needs matched ports and a useful interval.
Efficiency interpretation belongs to defined input/output energy or power quantities under applicable conditions.
Efficiency interpretation belongs to defined input/output energy or power quantities under applicable conditions. A transient ratio can be affected by release of previously stored energy; it should not be used as a universal steady conversion-efficiency claim. Source, converter and delivered-load boundaries remain distinct.
No MARSTON instantaneous waveform, component energy, loss figure or efficiency is assigned. The guide supplies no load-step test, discharge procedure or operating adjustment; it explains conservation and why unmatched instantaneous readings cannot independently identify dissipated power.
Related technical guides: LCL Filter States, Free Oscillation & Boundary Conditions · DC Capacitor Charging, Initial Voltage & Inrush Current · Thermal Resistance, Heat Capacity & Transient RC Models.
For an additional magnetic-storage topic, review inductor air gaps and stored energy.
General background: OpenStax: electrical power as an energy-transfer rate · OpenStax: ideal capacitor stored energy · OpenStax: linear inductive energy and its changing power. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Port power | p = vi in W | Matched voltage/current references and times. |
| System balance | pin − pout = dWstored/dt + ploss | Declared transfer ports and signs. |
| Storage energy | ½Cv² and ½Li² in J | Ideal independent constant linear elements. |
| Window average | ΔWstored/T in W | Endpoints and interval are explicit. |
| Periodic condition | Same stored energy at both endpoints | Zero averaged storage change does not mean no instantaneous exchange. |
Engineering questions.
Is instantaneous input–output difference always loss?
No. Stored energy and other declared transfer paths can contribute.
Can output briefly exceed input without creating energy?
Yes. Previously stored energy can be released within the stated balance.
Does unchanged bus voltage prove all storage is constant?
No. Other capacitive or inductive states can still change.
When is average storage power zero?
When the chosen interval has equal initial and final stored energy.
Is the 30 J example a product measurement?
No. It follows from invented constant powers over an assumed interval.
Does this establish MARSTON converter efficiency?
No actual waveform, loss result, topology or efficiency claim is assigned.
Technical enquiry
Discuss the technical question.
Input and output power need not match at every instant, even in an ideal lossless converter model. Share the model and applicable operating or design information for an engineering discussion.