Regime-level accounting

How Energy Is Counted Inside the VENDOR.Max Operating Regime

Inside a working regime there is no single quantity that may be called the power of an installation. There are several physically different processes, each measured by its own variable, on its own boundary, in its own temporal class.

Scope of this page

VENDOR.Max is a nonlinear electrodynamic installation that operates in a controlled discharge-resonance regime. Excitation of the coupled resonant regime is classified, in the functional taxonomy of the project, as discharge-resonance excitation of the Armstrong type; that attribution describes the excitation stage only and is not a classification of the installation as a whole. This page does not describe that architecture. It establishes the rules by which, inside an already established regime, quantities become energy and power.

This page answers one question: which measurable quantity corresponds to which physical process inside an already established operating regime, and which quantities may not be joined to one another.

It does not answer where the energy comes from, how resonant circulation works, by what mechanism a field transfers energy to the carriers of another ensemble, how local conversions compose into a self-consistent operating point, what the balance of the complete device boundary shows, or by what instruments active power is physically measured. Each of those questions has its own page.

There are no numerical values here — measured, calculated or illustrative. The subject is rules, not results.

Short answer

Three validity checks before any arithmetic

Correct energy accounting begins not with a formula but with three validity checks. Regime arithmetic starts after the third one. Before it, any product is a number without physical content.

First

Which variable is natural to this physical channel — and therefore which operation is defined on it at all.

Second

Whether the chosen boundary forms an electrical port — and therefore whether the product of the chosen voltage and current is lawful.

Third

Whether all quantities of the calculation share one temporal class — and therefore whether the resulting numbers are comparable at all.

Routing map

Five classes of quantity

The most frequent error in reading systems of this kind is the attempt to describe five different physical processes with one formula. The separation below makes that attempt impossible.

Event

A finite single conversion over a short time.

Natural variable — event energy

Physics developed here

Circulation

Repeated exchange of energy between forms inside a loop.

Natural variable — charge turnover, apparent power

Resonant circulation

Field transfer

Work of a coupled field on the carriers of another ensemble.

Natural variable — Poynting flux

Energetic price of transfer

Storage

Change of the energy held by a control volume.

Natural variable — rate of change of stored energy

Verification protocol, for the complete device boundary

Output

Directed transfer through a formed customer port.

Natural variable — synchronous port voltage and current

Active power metrology

Large circulation is not large transfer. Large transfer is not large output. A fast event is not a large energy.

The five classes form no hierarchy and do not convert into one another automatically

First check: not every boundary is an electrical port

A boundary is not an object of nature but a model defined by the investigator. From the fact that a surface has been drawn it does not follow that power is defined on it.

Every physical channel has a natural variable, and substituting a variable belonging to another physical channel invalidates the result regardless of instrument quality.

Electrical port: Synchronous \(u(t)\) and \(i(t)\).
Charge packet: \(\int i\,dt\).
Resonant turnover: \(\int \lvert i \rvert\,dt\).
Field transfer: Poynting flux.
Storage element: Change of stored energy.
Thermal boundary: Heat flux.

The universal operation of an electrical port:

\[ E_{\Gamma,\Delta t} \;=\; \int_{\Delta t} u_\Gamma\,dQ_\Gamma \;=\; \int_{\Delta t} u_\Gamma\, i_\Gamma\,dt \]

(1)

From this follows a strict distinction between two notations that look alike and are not physically equivalent.

\(p(t) = u(t)\,i(t)\) is correct always, but only on a strictly defined electrical port and only when both functions are measured synchronously.
\(P = UI\), where \(U\) and \(I\) are separately obtained effective, mean or peak numbers, is not a universal accounting operation and does not apply to an arbitrary internal boundary.

If the surface passes through a distributed region of electromagnetic field and forms no port with unambiguously defined port voltage and current, the natural accounting quantity becomes the Poynting flux:

\[ P_{\mathrm{EM}} \;=\; \oint_S (\mathbf{E}\times\mathbf{H})\cdot\mathbf{n}\,dA \]

(2)

From the inapplicability of \(P = UI\) on some internal boundary it does not follow that there is no power inside the system. The physics does not change — the correct accounting quantity of the chosen boundary does.

Three current processes are not one quantity. In some nodes directed charge transfer is essential, in others oscillation without net transfer, in others still the change of the field. All three are called current and require different operations: the first is integrated with sign, the second by modulus, the third is not a conduction current at all and is accounted through the field flux.

The question of which current you are measuring precedes the question of which current you obtained.

Unity of accounting does not mean sameness of measurement. All channels reduce not to identical instrument readings but to energy over one common observation window.

How a field transfers energy to the carriers of a receiving ensemble

Second check: the one-boundary rule

The first check establishes which operation is defined. The second establishes whether a particular product is lawful.

The most dangerous chain of reasoning about architectures of this kind looks convincing at every step: measure the charge of a pulse; multiply by frequency and obtain a mean current; take a voltage from another point of the system; multiply; call the product output power. Each individual number here may be measured flawlessly — and the product will be the power of nothing.

Six questions before any calculation of power:

Where is the boundary physically drawn?
Which conductors, fields and couplings cross it?
Where is voltage measured?
Where is current measured?
Do they belong to one and the same energy flow?
Do all quantities of the calculation share one temporal class?

A negative or undetermined answer to any of the six means the calculation is not performed — not that it is performed with a caveat.

You may not take the current of one functional level, the voltage of another and the temporal class of a third, and call the product the power of a fourth.

A separate consequence concerns alternating processes. From the same synchronous functions on a boundary, quantities of different meaning are derived: RMS values characterise the corresponding RMS class of the process; their product on a correctly defined port is apparent power and, without accounting for phase and non-sinusoidal relations, is not active power; the signed integral of current over a period may be close to zero; the integral of the modulus shows charge turnover. Only the synchronous integral \(\int u\,i\,dt\) shows the energy that passed through this port over the observation window.

Zero algebraic charge transfer does not mean zero energy transfer: an alternating circuit transfers energy precisely by oscillating.

Why internal turnover is not power

Third check: the temporal-class passport

Two correctly obtained numbers still may not be compared — until it is established that they belong to one temporal class and one window.

Every quantity carries a mandatory passport:

\[ \left\{\, \Gamma,\; \mathcal{Q},\; X,\; [X],\; \text{status},\; \text{type: peak / RMS / mean / event},\; \Delta t,\; \text{duty},\; \text{direction},\; \text{load},\; \text{storage},\; \text{method},\; \mathcal{U} \,\right\} \]

(3)

\(\Gamma\): The boundary of measurement.
\(\mathcal{Q}\): The charge ensemble to which the process belongs.
\(X\), \([X]\): The quantity and its unit.
Status: Measured, calculated, nominal, limiting or illustrative.
Type and \(\Delta t\): The temporal class together with the averaging window.
Duty: The fill factor of a pulsed regime.
Direction, load, storage: The conditions under which the quantity was obtained.
Method and \(\mathcal{U}\): The instrument or means of obtaining it, and the uncertainty of the measured quantity.

Without a complete passport, a quantitative comparison of two quantities is void as engineering evidence. Products of quantities belonging to different temporal classes are not power.

The practical consequence for reading any specification: a pair of voltage and current without a stated boundary, ensemble, temporal class and window does not describe an operating point. It describes two numbers.

How active power is physically measured

Event class

Energy of an event

An event is a finite single conversion occurring over a time short compared with the observation window of the regime. Its energy is defined on the chosen electrical port by integrating the synchronous functions over the duration of the event itself.

\[ E_{\mathrm{event}} \;=\; \int_{\mathrm{event}} u(t)\, i(t)\,dt \]

(4)

Time compression creates no energy: Shortening the release of one and the same previously accumulated portion of energy does not by itself increase the energy of the event: it changes its concentration in time and may raise instantaneous power substantially. Event energy is in all cases given by the integral over its actual duration, and if the shapes of \(u(t)\) and \(i(t)\) themselves change, the value of the integral changes with them.
An event energy belongs to one boundary: A value obtained on one port does not carry over to another port even inside a single node: between them stand their own conversions, losses and, as a rule, a different charge ensemble.
Event accounting is not specific to VENDOR.Max: It applies to any physical channel in which energy is carried by discrete, correctly defined events. What is specific begins not in this arithmetic but in the composition of physical conversions.
An event energy does not say what paid for it: It arrives either from outside the control volume under consideration or from its storage. Only a balance of the control volume over a window long enough to distinguish a steady regime from slow depletion of storage can tell the two cases apart.

The scientific territory of pulsed accumulation, switching and time compression

Regime arithmetic

Average power of an event stream

If energy transfer in some channel does consist of repeating events of one class, the average power of that channel follows from the event energy and the repetition frequency. The formula is physically correct. Its domain of validity is narrow, and outside it the formula ceases to describe anything.

\[ P_{\text{event-stream}} \;=\; \bar{E}_{\mathrm{event}}\, f_{\mathrm{event}} \]

(5)

Conditions of applicability — all of them at once

The events belong to one defined class and one physical mechanism.
The event energy is referred to one explicitly named boundary.
The frequency is the frequency of those events, not any other characteristic frequency of the system.
Event statistics are stationary over the chosen window — or the averaging accounts for the non-stationarity.
Omissions, bursting and the fill factor are accounted for explicitly.
The result refers to this event channel and to no other.
All quantities of the calculation carry matching temporal-class passports.

What the formula does not do

It does not determine the power of another port.
It does not describe resonant circulation, which is not an event stream.
It does not give the magnitude of the customer output.
It does not establish the source of the energy: the relation between event energy and repetition frequency holds equally when the events are fed by an external flow and when they draw on internal storage.

Frequency sets the rate at which events repeat. It is not an explanation of the magnitude of useful output.

Multiplying a small event energy by a high frequency does not close the gap between event and output

How local conversions compose into a self-consistent operating point

Permitted operations

What may be added, and under what condition

Inside an established regime four operations are admissible, and each carries its condition.

Integration: Over one boundary, over synchronous functions, across an explicitly stated window.
Averaging: Over an explicitly defined window, sufficient to represent the repeating process and, when a steady regime is being tested, to distinguish a stable state from slow change of internal storage.
Multiplication: Only of quantities that have passed the one-boundary rule and carry matching passports.
Summation: Only of energies collected over one physical window, on non-overlapping boundaries, accounting for the change of every storage element.

The rule broken last and most often. The correctness of each local quantity does not by itself make the arithmetic between different working planes correct. Local results may be joined only where a physical transition between the planes has been explicitly established and compatibility of boundaries, directions, time windows and regime states is preserved.

Successive summation along a chain of frames is lawful only under a complete non-overlapping partition and with all couplings between frames accounted for. A discrepancy in the result proves a violation of the conditions of joining, not the presence of an unexplained quantity.

The condition of a steady regime is stated through storage: the averaged rate of change of the stored energy of a control volume is close to zero over a long interval. Without that check, any average power may turn out to be the characteristic of slow depletion rather than of a sustained process.

For any internal control volume the balance is written over its own ports: the sum of incoming flows less the sum of outgoing flows equals the rate of change of that volume’s stored energy. The engineering form with an explicit loss term applies only to internal electrical frames. Mixing forms of notation on one boundary is not permitted.

The notation for the input flow of the complete device boundary does not apply to internal boundaries. Internal frames have their own named port flows, and borrowing the external notation creates a false impression that an internal node is externally fed. The balance of the complete device boundary, its measured residual and the inventory of channels belong elsewhere.

What is verified on the complete device boundary

Limit of the page

Where counting ends and a result begins

Between two statements lies the whole difference between an engineering description and a proof.

The first. In a local frame a measurable increase in the organisation of the local process appears — in voltage, in transfer rate, in pulse density, in turnover or in apparent power. This is described by a conversion and follows from it.

The second. An increase in sustained active power. This is a separate experimental result and does not follow from the fact of a conversion.

This page establishes the language and the conditions of correctness of both statements, but does not establish the experimental truth of the second. It defines which quantity corresponds to what and which operations over quantities are lawful. It does not turn correct counting into a confirmed result — that is done by independent measurement under an agreed protocol.

The two places where a local increase arises, and the boundary beyond which there are no further gains, are set out in where is the plus.

Questions

Questions this page is asked

Why can voltage and current not simply be multiplied?

Because the product of separately obtained numbers is power only when both quantities are measured synchronously on one electrical port and belong to one temporal class. Outside those conditions, the product cannot be identified with a defined energy flow.

Is event accounting a feature of VENDOR.Max?

No. It applies to any physical channel in which energy is carried by discrete, correctly defined events. What is specific begins not in this arithmetic but in the composition of physical conversions.

Is the formula “event energy times frequency” correct?

Yes, when all seven conditions of applicability are met. It gives the average power of one event channel and does not give the power of other ports, of circulation, or of the customer output.

May correctly measured quantities of different working planes be added together?

Only where a physical transition between the planes has been explicitly established and boundaries, directions, windows and regime states coincide. The correctness of each term taken separately does not replace that condition.

What does the temporal-class passport do?

It fixes the boundary, the ensemble, the type of quantity, the window, the fill factor, the direction, the state of storage, the method and the uncertainty. Without it, two correctly measured quantities remain incomparable.

Is correct counting enough to confirm performance?

No. Correct counting determines which statements are meaningful. Their truth is established by independent measurement under an agreed protocol.

Reading route

Where this page sits

Understand it, see the path, see the local gains, learn the accounting rules, meet the open question, resolve the circulation misreading, learn how to measure it, read the verification protocol.

Counting rules determine which statements are meaningful. Which of the meaningful statements are true is established by measurement.

Regime-level energy accounting