Energy & utilities
Power transformer
Insulation life is a temperature problem, and temperature follows load.
A transformer wears out when its paper insulation gets hot. The hot-spot temperature follows from load and ambient with a well-known thermal model. We use it to see cooling problems and to price a hot afternoon in lost life.
20 MVA, 69 / 12.47 kV, ONAN / ONAF
- Hot spot at nameplate
- 110 °C
- Aging at nameplate
- 1.00× normal
- Rating
- 20 MVA
- Peak load
- 107% of rating
Anatomy and nameplate
- 1Top-oil temperature. Anchor for the thermal model.
- 2Winding hot spot. Fiber-optic or calculated.
- 3Load current. Current transformer on the high side.
- 4Bushing tap. Capacitance and power factor.
- 5Dissolved gas. Online gas in oil.
- 6Fan and pump current. Cooling stage health.
- 7Oil level. Conservator level.
- 8Tap changer. Motor current and position count.
| Rating | |
|---|---|
| Rating | 20 MVA ONAF (15 MVA ONAN) |
| Voltage | 69 kV delta / 12.47 kV wye |
| Impedance | 8.0% |
| Tap changer | On-load, ±10%, 32 steps |
| Bushing BIL | 350 kV high side |
| Thermal | |
| Top-oil rise, rated | 45 °C |
| Hot-spot gradient, rated | 35 °C |
| Hot spot at nameplate, 30 °C ambient | 110 °C |
| Insulation | Thermally upgraded paper, 110 °C limit |
| Loss ratio R | 4.5 |
| Exponents n and m | 0.8 and 0.8 |
| Oil | 5,600 gal mineral oil |
The physics
The equations behind every curve on this page.
Top-oil rise
Δθ_TO = Δθ_TO,R·[(K²R+1)/(R+1)]^n
Oil warms with load squared, tempered by the loss ratio.
Hot-spot rise
Δθ_H = Δθ_H,R·K^(2m)
The winding runs hotter than the oil around it.
Aging factor
F_AA = exp(15000/383 − 15000/(θ_H + 273))
One at 110 °C. Many times more above it.
Heat and life
Load and weather set the hot spot. The hot spot sets the aging rate.
Winding hot-spot temperature against load
- 30 °C ambient
- 40 °C ambient
Heat in the winding rises faster than load, because losses go with current squared. Hot days leave less room for peaks.
θ_H = θ_A + Δθ_TO,R·[(K²R+1)/(R+1)]^n + Δθ_H,R·K^(2m)
Insulation ages faster as it gets hotter
- Aging factor
Paper insulation loses life on an Arrhenius curve. Twenty degrees over the limit uses up life many times faster.
F_AA = exp( 15000/383 − 15000/(θ_H + 273) )
A day on the load profile
A daily load shape and a hot afternoon, with healthy and weak cooling side by side.
A day on the load profile: healthy cooling versus fouled radiators
35 °C ambient
- Healthy cooling
- Fouled radiators, fans out
- Load (right axis)
- Life used per day, healthy
- 0.88 days
- Life used per day, fouled
- 3.15 days
Same load, same weather. Weak cooling lifts the hot spot over the limit at the evening peak, and the insulation pays for it.
Life used per day = (1/24) · Σ F_AA(θ_H, hour)
Failure modes
What breaks, what it looks like, what the twin does about it.
| Failure mode | The physics | Signals that show it | How the twin catches it |
|---|---|---|---|
| Cooling degradation | Fouled radiators or failed fans raise the oil rise. | Top-oil above the model at the same load. Fan current. | Solves for the oil rise that explains the gap. |
| Insulation aging | Heat breaks down paper on an Arrhenius curve. | Gas in oil. Furan content. Hot-spot history. | Adds up aging factor across every hour. |
| Bushing deterioration | Moisture and partial discharge raise the loss angle. | Tap power factor and capacitance. | Trends loss angle against temperature. |
| Tap changer wear | Contacts erode with each operation. | Motor current signature. Operation count. Gas. | Counts operations against contact life. |
| Overload | Load above nameplate heats the winding faster than the oil can follow. | Load above 1.0 per unit for long periods. | Shows the safe overload time for today’s weather. |
How we catch it early
A physics twin and a PINN, working on one power transformer.
The twin is a set of equations for this machine, tuned to its nameplate. Give it the flow, speed and conditions and it returns what every reading should be. It always gives the same answer for the same inputs.
A physics-informed neural network, or PINN, sits on top. It is trained on the plant’s own data and it is penalized whenever it breaks a physics rule. So it can only learn what the equations leave out: wear, fouling, friction. It cannot invent an answer that the machine could never produce.
Step 1
Measure
Flow, pressure, current, temperature, vibration. Whatever the asset already has.
Step 2
Physics twin
The equations of this machine, set to its nameplate. It says what the readings should be right now.
Step 3
Residual
Measured minus expected. Demand, weather and speed are already taken out.
Step 4
PINN
A small neural network that learns the cause of the gap, under the physics rules.
Step 5
Finding
A named cause, a date, and the kWh or hours at stake. An engineer reviews it.
loss = (measured − predicted)² + λ · (physics residual)²
The second term is the rulebook. It is zero when the network obeys the equations.
Why this beats black-box AI
A black-box model learns patterns from history. It needs examples of each failure, and it goes quiet when the pump runs at a point it has not seen. The twin starts from physics, so it works on day one. The PINN adds what physics cannot know about this particular machine.
That is also what makes the savings countable. The baseline is a calculation, not a guess, so the gap between baseline and meter is a number a customer can check.
What the twin checks on this asset
- Top-oil temperature against the thermal model
- Aging factor summed every hour
- Cooling stage current
- Bushing loss angle against temperature
| Fixed alarm | Black-box AI | Twin + PINN | |
|---|---|---|---|
| Needs failure history to learn | No | Yes, lots | No |
| Says what is wrong | No | Rarely | Yes, by name |
| Works at a flow it has never seen | No | Often fails | Yes, the equations still hold |
| Puts a number on the saving | No | No | Yes, in kWh and dollars |
| Lead time on slow wear | Late | Varies | Weeks to months |
| Every number can be traced | Yes | No | Yes, to an equation |
What the twin puts a number on
Energy and cost, from the equations.
Hot spot at nameplate, 30 °C
110 °C
Aging factor 1.0
Life used per day
0.88 days
Healthy cooling, 35 °C
With weak cooling
3.15 days
Same load and weather
What we do for you
We watch it. We catch it. We prove it.
Our reliability engineers run the twin on your power transformer, review every finding, and help your crew fix it. After the repair we compare the meter to the baseline and write the result in the ledger.