Part 6 · Chapter 21

Insulation Diagnostics and Condition Monitoring

The previous chapters built a toolbox: partial discharge for the local fault, tan δ for the global condition, and many more besides. This closing chapter of the diagnostics part asks how those separate readings are combined into a single verdict — is this machine healthy, and how long will it stay that way? — and how that verdict is watched, trended and acted upon across an asset's whole life. The story moves from one-off pass/fail testing toward continuous condition-based maintenance, where insulation resistance, dielectric response, dissolved-gas analysis and online sensors together form a health picture far richer than any one test alone.

High-Voltage Engineering Prof. Mithun Mondal Reading time ≈ 45 min
i What you'll learn
  • Why high-voltage practice has moved from pass/fail type tests toward trended diagnostics and condition-based maintenance.
  • Insulation resistance and the three insulation currents, and how the polarization index \(\mathrm{PI}\) and dielectric absorption ratio \(\mathrm{DAR}\) read dryness and cleanliness.
  • Dielectric-response methods — PDC, the recovery voltage method and frequency-domain spectroscopy — and how they estimate moisture in oil-paper insulation.
  • Dissolved gas analysis (DGA): the key fault gases, what each one signals, and the rate-of-generation idea.
  • Interpreting DGA with the Rogers / IEC ratios and the Duval triangle, and reading furan (2-FAL) as the marker of paper ageing through the degree of polymerization.
  • How online sensors and the fusion of many indicators build an asset health index that guides run / refurbish / replace decisions.
Section 21-1

From Test to Diagnosis

A withstand test asks a blunt question: does the insulation survive a defined overvoltage, yes or no? It is a gate — pass and the apparatus ships, fail and it does not. That is exactly what is wanted when a new machine leaves the factory. But the great population of high-voltage plant in service — transformers, bushings, cables, switchgear and rotating machines, much of it decades old — cannot be answered with a single gate. What an asset owner needs is not a verdict at one instant but a trajectory: how the insulation is ageing, what is driving the decline, and how much useful life remains. That is the realm of diagnostics and condition monitoring.

The shift is one of philosophy. Reactive maintenance runs equipment to failure, which is cheap until the failure is catastrophic. Time-based preventive maintenance services everything on a fixed calendar, which is safer but wasteful, since healthy units are disturbed needlessly while a sick one may fail between visits. Condition-based maintenance threads between the two: each asset is measured, its condition trended, and intervention is timed to the evidence. The diagnostic tests of this part — partial discharge, tan δ, and the methods below — are the instruments that make condition-based maintenance possible, because each turns an invisible internal state into a number that can be watched.

A diagnostic is a trend, not a verdict. The power of a condition measurement lies less in any single reading than in its change over time. A tan δ of 0.004 is unremarkable; a tan δ that has crept from 0.002 to 0.004 over three years is a warning. Almost every method in this chapter is most valuable when repeated and plotted — the slope, not the point, tells the story.
Section 21-2

Insulation Resistance, the PI and DAR

The simplest and oldest diagnostic is the insulation resistance (IR) test: a DC voltage (commonly \(500~\mathrm{V}\) to \(5~\mathrm{kV}\)) is applied with a megohmmeter and the resulting current — hence the resistance — is read. What makes it diagnostic rather than a simple ohm reading is the way the current changes with time. When DC is suddenly applied to insulation, three currents flow together:

The three insulation currents
\[ i(t) = \underbrace{i_C(t)}_{\text{capacitive charging}} \;+\; \underbrace{i_A(t)}_{\text{dielectric absorption}} \;+\; \underbrace{i_L}_{\text{conduction / leakage}} \]
i t → i_C (charging) i_A (absorption) i_L (leakage) wet (flat → PI≈1) 1 min 10 min
The three insulation currents after DC is applied — for dry, clean insulation the absorption current keeps decaying so the total current falls (resistance rises); for wet or dirty insulation leakage dominates and the current stays flat, giving \(\mathrm{PI}\approx 1\)

The capacitive current charges the geometric capacitance and dies away in seconds. The absorption (polarization) current decays much more slowly, over minutes, as the dielectric's slow polarization mechanisms settle. The conduction current is the small steady leakage that remains. In dry, clean insulation the absorption current keeps falling for many minutes, so the measured resistance keeps rising; in wet or contaminated insulation a large, constant leakage swamps the decaying terms, and the resistance is high from the start but never climbs. Two simple ratios capture exactly this behaviour:

Time-ratio indices (IEEE 43)
\[ \mathrm{DAR} = \frac{R_{60\,\mathrm{s}}}{R_{30\,\mathrm{s}}} \qquad\qquad \mathrm{PI} = \frac{R_{10\,\mathrm{min}}}{R_{1\,\mathrm{min}}} \]
🔑
A ratio cancels the geometry
\[ \mathrm{PI} = \frac{R_{10}}{R_{1}} = \frac{i_{1\,\mathrm{min}}}{i_{10\,\mathrm{min}}} \]

Because it is a ratio of the same object's resistance at two times, the polarization index is independent of size, geometry and absolute resistance level. A high \(\mathrm{PI}\) (a current that keeps falling) means a healthy, dry dielectric; \(\mathrm{PI}\approx 1\) (a flat current) signals moisture or contamination. The reading is otherwise strongly temperature-dependent and is corrected to a reference temperature before trending.

As a rough guide for machine windings, a polarization index above about \(2\) indicates dry insulation, while a value near \(1\) calls for drying or cleaning before the machine is returned to service. The same logic — watch how the charging settles, not just where it starts — underlies the more sophisticated dielectric-response methods that follow.

Section 21-3

Dielectric Response and Moisture

The polarization index reads the dielectric's slow response at two coarse instants. Dielectric-response methods generalise this into a full curve, and from that curve they extract one prize above all others for oil-paper insulation: the moisture content of the paper, which governs both its dielectric strength and the rate at which it ages. Three methods are in use, two in the time domain and one in the frequency domain.

In the polarization–depolarization current (PDC) method, a DC voltage is applied for a long time while the slow polarization current is recorded; the supply is then removed and the specimen short-circuited, and the depolarization current is recorded as the stored polarization relaxes. The shapes of these two slow currents encode the conductivity of the oil and the moisture and ageing of the paper. The older recovery voltage method (RVM) works similarly but measures the voltage that re-appears across an initially charged, then briefly shorted, specimen, mapping out a "polarization spectrum" whose central time constant was once used as a moisture indicator.

tan δ log f → 1 mHz 1 Hz 1 kHz dry wet / aged
Frequency-domain spectroscopy — sweeping tan δ from millihertz to kilohertz spreads the single loss number into a curve; moisture and conductivity lift the low-frequency loss sharply, separating a wet, aged insulation from a dry one far better than a single-frequency reading

The modern favourite is frequency-domain spectroscopy (FDS), also called dielectric frequency response. Here the loss tangent and capacitance are measured across a wide band — typically from a few millihertz up to a kilohertz — turning the single tan δ point of Chapter 20 into a full spectrum. Moisture and ionic conduction dominate at the lowest frequencies, lifting the loss steeply there, while the bulk geometry sets the high-frequency end. By fitting the measured curve against a library of oil-paper responses, the moisture in the solid insulation can be estimated without taking the apparatus apart. This is the diagnostic descendant of the tan δ measurement: the same loss angle, now read as a function of frequency to separate the causes that a single number blends together.

Section 21-4

Dissolved Gas Analysis

For oil-filled apparatus — above all the power transformer — the single most powerful diagnostic is dissolved gas analysis (DGA). Its principle is beautifully direct: whenever oil or paper is stressed beyond a threshold, by local overheating or by electrical discharge, the molecules break apart and release characteristic gases, which dissolve in the oil. A small oil sample, degassed and run through a gas chromatograph, then reveals — in parts per million — a chemical fingerprint of whatever fault is at work, often long before any electrical symptom appears.

The diagnostic gases fall into a few families. Hydrogen \((\mathrm{H_2})\) accompanies almost any disturbance and is especially associated with partial discharge. The light hydrocarbons — methane \((\mathrm{CH_4})\), ethane \((\mathrm{C_2H_6})\), ethylene \((\mathrm{C_2H_4})\) — appear in a sequence that climbs with temperature, ethylene marking the hotter thermal faults. Acetylene \((\mathrm{C_2H_2})\) is the alarm gas: it forms only in the intense heat of arcing, so its presence in any quantity signals a high-energy electrical fault. Finally, the carbon oxides — carbon monoxide \((\mathrm{CO})\) and carbon dioxide \((\mathrm{CO_2})\) — come from the cellulose of the paper, so they report on the involvement and overheating of the solid insulation.

energy / temp partial discharge → H₂ (+ CH₄) thermal < 300 °C → CH₄, C₂H₆ thermal 300–700 °C → C₂H₄ rising arcing / > 700 °C → C₂H₂ (alarm) paper involved → CO, CO₂
The fault-gas ladder — as the energy of a fault climbs from partial discharge through thermal heating to arcing, the dominant gas shifts from hydrogen through the hydrocarbons to acetylene; carbon oxides flag involvement of the cellulose paper

Just as important as which gases are present is how fast they are growing. A modest but steadily rising concentration is more worrying than a high but stable one, since the rate of generation (in ppm per day) measures how active the fault is right now. Standards such as IEEE C57.104 set both absolute concentration levels and rate-of-change limits, escalating the response from routine sampling, through increased surveillance, to removal from service as the total combustible gas and its growth rate climb.

Key gasChiefly indicatesSource
Hydrogen \((\mathrm{H_2})\)partial discharge / coronaoil & paper
Methane, ethane \((\mathrm{CH_4,\,C_2H_6})\)low-temperature overheatingoil
Ethylene \((\mathrm{C_2H_4})\)high-temperature overheatingoil
Acetylene \((\mathrm{C_2H_2})\)arcing (high-energy discharge)oil
CO, CO\(_2\)cellulose (paper) overheatingpaper
Section 21-5

Interpreting DGA: Ratios and the Duval Triangle

A list of gas concentrations is raw data; turning it into a fault diagnosis takes an interpretation scheme. The key-gas method simply reads off the dominant gas. More robust are the ratio methods — the Rogers ratios and the IEC 60599 scheme — which take the quotients of selected gas pairs, because ratios are less sensitive than absolute amounts to the size of the fault and the volume of oil. Three ratios do most of the work:

IEC / Rogers diagnostic ratios
\[ R_1 = \frac{\mathrm{C_2H_2}}{\mathrm{C_2H_4}} \qquad R_2 = \frac{\mathrm{CH_4}}{\mathrm{H_2}} \qquad R_5 = \frac{\mathrm{C_2H_4}}{\mathrm{C_2H_6}} \]

The pattern of these three places the fault into a category: a partial discharge, a low-energy or high-energy electrical discharge, or a thermal fault of low, medium or high temperature. A large \(R_1\) (acetylene present) points to arcing; a large \(R_5\) (ethylene over ethane) points to a hot thermal fault; \(R_2\) helps separate discharge from heating. The ratio schemes are powerful but have a known weakness: some gas combinations fall outside every defined code, leaving no diagnosis.

The Duval triangle was devised to close that gap. It uses just the three hydrocarbon gases — \(\mathrm{CH_4}\), \(\mathrm{C_2H_4}\) and \(\mathrm{C_2H_2}\) — expressed as percentages of their sum, so every possible sample maps to exactly one point inside an equilateral triangle. The triangle is partitioned into zones, and the zone containing the point names the fault. Because every point lands somewhere, the triangle always returns an answer.

Duval triangle coordinates
\[ \%\mathrm{CH_4}=\frac{\mathrm{CH_4}}{S},\quad \%\mathrm{C_2H_4}=\frac{\mathrm{C_2H_4}}{S},\quad \%\mathrm{C_2H_2}=\frac{\mathrm{C_2H_2}}{S}, \qquad S=\mathrm{CH_4+C_2H_4+C_2H_2} \]
100% CH₄ 100% C₂H₄ 100% C₂H₂ PD T1 T2 T3 DT D1 D2 sample → T3
The Duval triangle (schematic) — the three hydrocarbon gases as percentages fix one point inside the triangle; its zone names the fault (PD, thermal T1–T3, discharge D1–D2, mixed DT). The plotted sample, high in ethylene and low in acetylene, lands in T3 — a hot thermal fault above 700 °C

Ratios and triangle are best used together and alongside the gas trend: a consistent diagnosis from several schemes, confirmed by a rising generation rate, is far stronger evidence than any one method alone. This is the recurring theme of the chapter — no single indicator is trusted on its own.

Section 21-6

Oil Quality and Furan Analysis

Dissolved gases report on active faults; the quality of the oil itself reports on the slow ageing of the insulation system. Routine oil tests measure the breakdown voltage (which falls with moisture and particles), the water content by Karl Fischer titration, the acidity or neutralization number (which rises as the oil oxidises), the interfacial tension (which falls with the same oxidation), and the oil's own dissipation factor. Together these say whether the oil is still a sound dielectric and heat-transfer medium, or whether it should be reconditioned or replaced.

But the oil can be changed; the paper cannot. The cellulose of the solid insulation is the true life-limiting element of a transformer, and as it ages its long molecular chains break, measured by the degree of polymerization (DP) — about \(1000\)–\(1200\) when new, falling toward \(150\)–\(200\) at end of life, where the paper has lost most of its mechanical strength. DP can be measured directly only on a paper sample, which usually means cutting into the machine. The elegant alternative is furan analysis: as cellulose degrades it releases furanic compounds, chiefly 2-furaldehyde (2-FAL), into the oil, where it can be measured from the same kind of sample as DGA. An empirical correlation then turns the 2-FAL concentration into an estimate of DP — and hence of remaining paper life — without opening the tank.

Furan–DP correlation (Chendong)
\[ \log_{10}\!\big(\text{2-FAL [ppm]}\big) = 1.51 - 0.0035\,\mathrm{DP} \qquad\Longrightarrow\qquad \mathrm{DP} = \frac{1.51 - \log_{10}(\text{2-FAL})}{0.0035} \]

The carbon-oxide ratio from the DGA helps too: a \(\mathrm{CO_2/CO}\) ratio that drifts low can corroborate accelerated paper degradation. As always, furan, DP and the carbon oxides are read together and over time — the paper's ageing is a slow trend, and it is the trajectory toward the end-of-life DP that an asset owner is really tracking.

Section 21-7

Online and Continuous Monitoring

Everything so far is, in its classic form, an offline test — the apparatus is sampled or de-energised, measured, and the result trended visit by visit. The modern direction is to bring the measurement online, with permanent sensors that watch the asset continuously and stream their readings to a monitoring system. Several of the diagnostics map naturally onto sensors:

transformer bushing tap → C, tan δ HFCT / UHF → PD gas sensor → DGA (H₂…) fibre optic → temperature monitor + data fusion health index → run / refurbish / replace
An online monitoring architecture — bushing-tap, partial-discharge, gas and fibre-optic sensors feed a monitor that fuses the streams into a health index, turning continuous data into a maintenance decision

The bushing tap gives a continuous reading of capacitance and tan δ, catching a developing bushing fault — historically a leading cause of transformer failure. High-frequency current transformers and UHF antennas pick up partial discharge while the unit stays energised. Online gas sensors track hydrogen, and increasingly the full gas suite, between laboratory samples. Fibre-optic probes read winding and hot-spot temperature directly, where once it could only be inferred. Fed into a monitoring platform, these streams move the asset from periodic snapshots to a living record — the difference between checking a patient yearly and wearing a continuous monitor. The cost is justified on the most critical, most expensive or most loaded units, where an unexpected failure is least affordable.

Section 21-8

The Asset Health Index

The chapter's recurring lesson is that no single test tells the whole story. Partial discharge finds local defects but misses diffuse ageing; tan δ weighs the bulk but cannot locate a fault; DGA reads active faults but not mechanical strength; furan reads paper life but not an incipient discharge. The art of diagnostics is data fusion — combining many indicators, each with its blind spot, into a verdict more reliable than any one of them.

In practice this is formalised as an asset health index: each diagnostic is scored against limits and trends, the scores are weighted by how strongly each predicts failure, and the weighted aggregate places the asset on a scale from healthy to end-of-life. The index is not a precise physical quantity but an engineering judgement made repeatable, and its real output is a decision — continue in service, increase surveillance, refurbish, or replace — and a ranking of a whole fleet so that limited maintenance budgets flow to the units that most need them. This is where high-voltage diagnostics meets asset management: the physics of the earlier chapters becomes, in the end, a defensible plan for keeping the lights on.

DiagnosticReadsBlind to
Partial discharge (Ch 19)localised defects, voidsdiffuse ageing
Tan δ / FDS (Ch 20–21)bulk loss, moisturefault location
Insulation resistance / PIdryness, surface cleanlinessdeep internal faults
DGAactive thermal / electrical faultsmechanical strength
Furan / DPpaper ageing, remaining lifesudden incipient faults
Section 21-9

Worked Examples

1 Polarization index

Problem. A motor winding reads insulation resistance \(R_{1\,\mathrm{min}} = 200~\mathrm{M}\Omega\) and \(R_{10\,\mathrm{min}} = 1000~\mathrm{M}\Omega\). Find the polarization index and judge the insulation.

Solution. Apply \(\mathrm{PI} = R_{10}/R_{1}\):

Working
\[ \mathrm{PI} = \frac{1000}{200} = 5 \]

A \(\mathrm{PI}\) of 5 — the resistance climbs five-fold over ten minutes, so the absorption current keeps decaying. The insulation is dry and clean. Had the resistance been flat (\(\mathrm{PI}\approx 1\)), moisture or contamination would be indicated.

2 DGA by the IEC ratios

Problem. A transformer oil sample gives \(\mathrm{H_2}=60\), \(\mathrm{CH_4}=120\), \(\mathrm{C_2H_6}=40\), \(\mathrm{C_2H_4}=240\), \(\mathrm{C_2H_2}=8\) (all ppm). Compute the three ratios and classify the fault.

Solution. Form \(R_1, R_2, R_5\):

Working
\[ R_1 = \frac{8}{240}\approx 0.03,\qquad R_2 = \frac{120}{60} = 2.0,\qquad R_5 = \frac{240}{40} = 6.0 \]

Negligible acetylene (\(R_1\) small) rules out arcing; a high ethylene-to-ethane ratio (\(R_5>4\)) with \(R_2>1\) points to a high-temperature thermal fault, above 700 °C (T3).

3 The same sample on the Duval triangle

Problem. Using only \(\mathrm{CH_4}=120\), \(\mathrm{C_2H_4}=240\), \(\mathrm{C_2H_2}=8\) ppm from Example 2, find the Duval coordinates and confirm the zone.

Solution. Sum \(S = 120+240+8 = 368\); take percentages:

Working
\[ \%\mathrm{CH_4}=\frac{120}{368}=33\%,\quad \%\mathrm{C_2H_4}=\frac{240}{368}=65\%,\quad \%\mathrm{C_2H_2}=\frac{8}{368}=2\% \]

High ethylene, very low acetylene — the point falls in the T3 zone, agreeing with the ratio method. Two independent schemes giving the same answer is exactly the corroboration the chapter argues for.

4 Paper life from furan

Problem. The oil of an in-service transformer contains \(\text{2-FAL} = 1~\mathrm{ppm}\). Estimate the degree of polymerization of the paper.

Solution. Invert the Chendong correlation with \(\log_{10}(1)=0\):

Working
\[ \mathrm{DP} = \frac{1.51 - \log_{10}(1)}{0.0035} = \frac{1.51}{0.0035} \approx 430 \]

A DP near 430 — the paper is well into mid-life (new paper sits near \(1000\)–\(1200\), end-of-life near \(200\)). Worth trending: if 2-FAL keeps rising, DP is falling toward the end-of-life threshold.

5 Gas generation rate

Problem. Total dissolved combustible gas rises from \(500~\mathrm{ppm}\) to \(800~\mathrm{ppm}\) over \(30\) days. Find the generation rate and comment.

Solution. Divide the increase by the interval:

Working
\[ \text{rate} = \frac{800-500}{30} = \frac{300}{30} = 10~\mathrm{ppm/day} \]

Ten ppm per day is a brisk, sustained increase — by the IEEE C57.104 framework this calls for escalated surveillance: shorten the sampling interval, run the ratio and triangle interpretation, and prepare to act if the rate holds. The rate, not the absolute 800 ppm, is what raises the alarm.

Review

Chapter Summary

Test → diagnosis

Pass/fail testing gives way to trended condition-based maintenance: watch the slope, not the single point.

IR, PI & DAR

The decay of the absorption current is read as \(\mathrm{PI}=R_{10}/R_{1}\); high means dry, \(\approx 1\) means wet or dirty.

Dielectric response

PDC, RVM and FDS spread the loss across time or frequency to estimate moisture in oil-paper insulation.

DGA

H₂ for PD, hydrocarbons climbing with heat, C₂H₂ for arcing, CO/CO₂ for paper; the generation rate matters most.

Ratios & Duval

IEC/Rogers ratios and the Duval triangle of CH₄–C₂H₄–C₂H₂ percentages place the fault in a zone.

Furan & health index

2-FAL estimates paper DP and remaining life; fused with all indicators it builds the asset health index.

Practice

Problems

For each item, first identify what it tests — the diagnostic philosophy, an index, a dielectric-response idea, the DGA gases, a ratio or triangle interpretation, or paper ageing — then apply it. Difficulty rises down the list.

  1. Distinguish reactive, time-based preventive and condition-based maintenance, and say where the diagnostic tests of this part fit.
  2. Name the three currents that flow when DC is applied to insulation, and explain which one makes the polarization index diagnostic.
  3. A winding gives \(R_{1\,\mathrm{min}}=150~\mathrm{M}\Omega\) and \(R_{10\,\mathrm{min}}=180~\mathrm{M}\Omega\). Find the \(\mathrm{PI}\) and state the likely condition.
  4. Explain why frequency-domain spectroscopy reveals moisture more clearly than a single-frequency tan δ reading.
  5. For each of the following, name the gas chiefly expected: partial discharge; a 200 °C hot spot; arcing; overheated paper.
  6. A sample gives \(\mathrm{H_2}=100\), \(\mathrm{CH_4}=40\), \(\mathrm{C_2H_4}=10\), \(\mathrm{C_2H_2}=1\), \(\mathrm{C_2H_6}=20\) ppm. Compute \(R_1,R_2,R_5\) and suggest the fault type.
  7. A sample has \(\mathrm{CH_4}=50\), \(\mathrm{C_2H_4}=20\), \(\mathrm{C_2H_2}=30\) ppm. Find the Duval percentages and say which broad region (thermal or discharge) the point lies in.
  8. Oil shows \(\text{2-FAL}=4~\mathrm{ppm}\). Estimate the paper DP and comment on the remaining life.
  9. Explain why the rate of gas generation can be more important than the absolute concentration, and how online sensors change this picture.
  10. Argue why an asset health index, rather than any single test, is the right basis for a fleet's maintenance decisions, and explain how partial discharge and tan δ contribute complementary information to it.
Tip: this chapter has no single master equation — its master idea is fusion over time. Each method reads one facet: the polarization index reads dryness from the decay of a current; dielectric response spreads the loss across frequency to find moisture; DGA reads active faults from fault gases, sorted by ratios and the Duval triangle; furan reads paper ageing through \(\mathrm{DP}\). None is trusted alone. Combine them, trend them, and weight them into a health index, and the separate physics of the whole course becomes one defensible verdict on whether an asset should run, be refurbished, or be retired.