A physics engine, and a verification tool enforced on top of it. PhysWall inverts a closed, published, non-linear physical law at a single measurement point — and refuses when the inverse is not unique. Seven laws, one engine, and the same refusal in all of them.
This one is finished enough to ship, and we are not shipping it.
Not a teaser and not a waiting list. It exists, it runs, and the reason it is not here is written below in full.
You give it a feeder: the current at the substation, the current each customer draws, the conductor and the length. It works out what the resistive losses should be, compares that to the energy that went missing, and reports whether the difference is explained.
Unexplained energy on a distribution feeder has a name in the industry. It is called non-technical loss, and in most cases it means theft.
The model treats the feeder as a flat list: every customer on its own branch, each contributing I²R for their own current.
A real feeder is a tree. The segment nearest the substation carries the sum of everything downstream, and I²R is quadratic — so a trunk carrying four customers' current does not lose four times as much. It loses far more.
four customers, 50 / 40 / 30 / 20 A, 0.15 Ω per segment flat model each on its own branch 810 W tree trunk carries the sum 4,590 W ⚠ and 4,590 assumes the largest customer sits nearest the source. Reverse the order and the same four customers on the same tree give 6,690 W — 46% more, from nothing but who is standing where.
The flat model understates the real loss badly, and how badly depends entirely on the shape of the network. On a fan, where every customer really does have their own run, the two agree. On a long radial feeder they differ by a factor.
Straight into the unexplained column. The tool would report energy it cannot account for, on a feeder where nothing is wrong, because it modelled the wrong shape.
And someone would be accused of stealing electricity they did not steal.
That is not an ordinary bug. A wrong number in an antenna calculation wastes an afternoon. A wrong number here goes into a file with a name on it.
It detects that it has been handed a tree. The ratio of voltage drop to I·R along a run is close to 1 on a fan and rises sharply on a radial feeder, and the tool reports that ratio and warns.
It knows. It just cannot yet compute the right answer. That is a better place to be than not knowing, and it is still not good enough to put in front of a utility.
We assumed no utility publishes feeder data. That was wrong. In Britain it is a licence condition: Ofgem's Data Best Practice guidance requires every distribution operator to publish aggregated consumption at low-voltage feeder level, and it has been live since February 2024. All of them agreed a common format.
⚠ And then we got that half wrong too. Consumption at feeder level and at substation level are not two sides — they are the same smart-meter total, rolled up twice. The injection side is a different dataset entirely, published by one operator, covering a subset of transformers.
Whether the two share an identifier scheme is unverified. Without that there is no balance, only two numbers.
And the published data carries no topology at all: no node, no conductor, no impedance. A location is a point, not a connection. Which means it is itself the flat shape — so it cannot fix the 57%, because it has the same assumption baked in.
For a while this looked like a way in: transformer and feeder together are two levels of a tree, not a flat list, and two levels recover part of what a full topology would. Run at the size of a real feeder and that part is a few percent. The recovery goes as roughly one over the number of customers, and a low-voltage feeder serves tens to hundreds of them.
The correction was right and it moved nothing. What follows is what would actually be needed.
From the published methodology: if a meter was not reachable during a half-hour, its reading is not in the aggregate.
So the consumption total is systematically low by an unknown amount. And injection minus consumption looks like loss — when it may be a meter that did not answer.
That is precisely the case where a tool should refuse. Not a reason to abandon this. The strongest reason to finish it properly.
We wrote that current is published at BSP and GSP and nowhere useful. That was not the whole picture. The network runs:
GSP 132 kV voltage and current, published
BSP 33 kV voltage and current, five-minute averages
primary substation 11 kV half-hourly transformer flows
distribution sub 400 V LV Load Monitor — current and
voltage, on a subset of sites
LV feeder 400 V and this is where the loss is
The LV Load Monitor is one level above the feeder, not three. NGED's own description says the datasets carry current and voltage measurements "where available", on a subset of individual LV substations.
⚠ A subset is not the network, and one level above is not on it. But the gap between what is published and what the calculation needs is a great deal smaller than this page said a week ago, and saying so is cheaper than being caught by it.
Not effort, and not method. Four inputs, and the operator has all of them:
current the feeder data carries energy, not amperage, and
loss goes as current squared. Current IS published
in two places: at BSP and GSP, three and four
levels above the feeder, and — on a subset
of sites — in NGED's LV Load Monitor, which
sits one level above. That last one is close
enough to be worth a look, and it is a subset, not
the network
resistance which needs conductor length and cross-section,
and neither is published
a fast enough
sample the data is a half-hour average, and loss follows
the peak. <I²> is always at least <I>², so an
average understates it — possibly by more
than the topology does
order within
a feeder which customer sits behind which. The published
data gives the transformer and the feeder, which
is two levels of a tree, and on a real feeder of
fifty-odd customers that recovers a few percent
of what a full topology would
Every one of those exists. A distribution operator holds all four for every feeder it runs. They are not published, and this is not a problem that can be solved from outside.
A different question, and one the published fields do support: when injection and consumption disagree, is that energy missing, or was it never measured?
The consumption figures carry aggregated_device_count —
how many meters actually reported in that half hour. If that number moves
between intervals, a meter did not answer, and the shortfall is measurement
rather than loss. Somebody is accused of theft on the difference between
those two.
A network link carries the sum of everything routed through it, exactly as a feeder carries the sum of everything behind it. Delay adds along a path; so does the logarithm of survival probability. The structure is identical.
It is also a field with a name and thirty years of work behind it — network tomography, since 1996. And its central result is the same refusal this site is built on: link-level properties cannot be uniquely determined from end-to-end measurements. They named the smallest unit that can be: a minimal identifiable link sequence.
So this is not an opening. It is a field that reached the same conclusion first and went further with it. Anyone arriving now has reading to do before writing a line — and this page says so rather than discovering it later.
take the topology as an INPUT, not an assumption solve the feeder properly, segment by segment and validate against a feeder with real measurements
A day of work, roughly. And it will not be released the day it is finished either — a tool that can accuse someone of a crime earns its release the slow way.
We could have left it off the site and said nothing. Nobody would have asked.
But every other page here argues that a tool should say what it cannot determine. A tool held back for a specific, stated reason is that same argument, applied to ourselves.
A feeder is a tree: one path to every point, so the inverse is unique. A water network is looped, and the obvious guess was that the loops were the obstacle. That guess was wrong, and the real answer is worse.
Hazen-Williams needs a roughness coefficient C, and C is derived from the pressure drop it is supposed to predict. Worse, the industry does not agree that it changes at all:
DIPRA (ductile iron assn) C = 140, "maintained over
the life of the pipe"
Michigan State "constant head loss is an
INCORRECT assumption"
Hudson 1966, seven cities C = 62 to 118 at age 50
On one 200 mm pipe, 500 m, 50 L/s at age fifty, that is a head loss of 5.58 m against 25.24 m — a factor of 4.52. DIPRA sells ductile iron; the association publishing the contrary evidence sells PVC. Two trade bodies, opposite claims, both cited in practice.
⚠ That is not uncertainty in a measurement. It is a disagreement about the law. No instrument settles it, because the two sides are not measuring different things — they are asserting different physics.
Same pipe, same physical uncertainty about how rough it is:
Darcy-Weisbach, epsilon +/-30% x1.14 Hazen-Williams, C 62 to 118 x3.29
The choice of law sets how wide the answer is, before anything is measured. Two formulas for one pipe, agreeing to 4.6% on the central figure and differing by 2.9x in how much they admit they do not know.
This page inverts a feeder because a feeder has a constant that means something: conductor resistivity is a property of copper, published to four figures, the same in every handbook. C is not that kind of number, and no page here will pretend otherwise.
The one branch that survives is narrow: a new transmission line, radial, on Darcy-Weisbach, where the spread is 15% rather than 62% and the inversion is x1.31. That is buildable, and it is not a national water network.
PhysWall was developed and architected by Gadi Zion.
Built on PhysWall — the same engine reads antenna bandwidth, conductor loss, bit erasure and heat limits. It answers what the measurement implies, and refuses when the measurement cannot say.⚠ Check this instead of believing it. Every number here reproduces from a source that is named, and the claims that turned out wrong are still printed next to what replaced them. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. How to check each one →