DC High Voltage Generation and Measurement

Rectification looks like basic electronics until you need 200 kV.

Rectification looks like basic electronics until you need 200 kV of it with controlled ripple. Three technical reasons make a DC source indispensable in a high voltage laboratory. The first is dielectric. Under DC there is no steady-state capacitive current, so everything flowing in the steady state is conduction current through or across the insulation. That turns a simple microammeter into a diagnostic instrument: the leakage current is a direct photograph of dielectric quality, something impossible on AC where the capacitive component is orders of magnitude larger and buries the conduction.

The second reason is test power. Large-capacitance objects — long cables, power capacitors, generators — would demand an AC source able to supply C·ω·U, which for a few kilometres of cable easily reaches tens of amperes. On DC, once the charging transient is over, the source only has to supply the leakage current, in the microampere to few-milliampere range. A portable DC source weighing a few kilograms replaces, in that role, a resonant system weighing tonnes. The third reason is direct application: electrostatic precipitators, X-ray sources, HVDC transmission equipment and particle accelerators operate natively on DC and must be tested with the same nature of voltage. IEC 60060-1 defines the DC test value as the arithmetic mean voltage and imposes two simultaneous requirements on the generating system: ripple factor no greater than 3%, and mean value stability within ±1% for tests up to 60 s.

What you will be able to do

• Conceptually design half-wave and full-wave high voltage rectifier circuits, sizing diodes by peak inverse voltage and choosing the filter capacitor.

• Calculate the ripple factor of a DC test source, check it against the 3% limit of IEC 60060-1, and build and interpret the load characteristic U(I).

• Explain the Greinacher / Cockcroft-Walton multiplier cascade, derive its voltage drop and ripple expressions, and find the optimum number of stages.

• Measure high voltage DC with a precision resistive divider and a rod-rod gap under IEC 60052, respecting the uncertainty requirements of IEC 60060-2.

• Separate the capacitive, absorption and conduction components of leakage current, and compute the dielectric absorption ratio and polarisation index.

• Explain, in terms of space charge and field distribution, why DC withstand testing was abandoned for extruded cable and replaced by very low frequency testing.

Diodes in series, and the peak inverse voltage rule

Since an individual silicon diode blocks typically 1 to 6 kV, a high voltage rectifier column is a series stack of tens to hundreds of junctions, and that stack creates the first design problem: reverse voltage does not distribute itself uniformly. Stray capacitance and leakage differences make some diodes take more voltage than others, so the classic answer is grading — resistors in parallel with each diode against leakage differences, capacitors in parallel against recovery differences during commutation.

The sizing parameter is peak inverse voltage. In a half-wave rectifier with a filter capacitor, when the source reverses polarity the diode sees the capacitor voltage of roughly +Vmax in series with the negative source peak of −Vmax, so PIV = 2·Vmax. That rule reappears in every stage of a multiplier cascade, where conveniently no diode and no capacitor has to hold more than 2·Vmax regardless of stage count. Half-wave dominates high voltage circuits because the cost of each rectifier column makes a full bridge rare above a few tens of kilovolts, but it carries a silent penalty: the unidirectional secondary current contains a DC component that tends to saturate the supply transformer core.

Ripple is a calculation, not a hope

IEC 60060-1 defines the ripple amplitude as half the difference between the extreme values, δ = (Umax − Umin)/2, and the ripple factor as δ/Ū. The normative limit for DC test voltages is 3% unless the product committee says otherwise. Where the ripple is roughly sinusoidal, the standard allows estimating δ as the RMS of the AC component multiplied by √2, which is a useful shortcut when measuring with a capacitively coupled RMS voltmeter.

The engineering calculation starts from a charge balance. In the steady state the charge the capacitor gives up between two recharges is Q = I·Δt, where Δt is one period on half-wave and half a period on full-wave. Since ΔQ = C·ΔU, the design amplitudes are δV = I/(2·f·C) half-wave and δV = I/(4·f·C) full-wave. A worked case fixes the orders of magnitude: a 100 kV source running a leakage test at 1 mA, with a 100 nF filter capacitor at 60 Hz half-wave, produces roughly 167 V peak to peak, a ripple factor of about 0.08%. But if the object draws 10 mA, as a precipitator would, the ripple climbs to 1.7 kV peak to peak and the factor approaches 1%; at 30 mA the limit is broken. The designer's weapons, in usual order of cost: increase C, double the effective frequency by going full-wave or by using a switched converter at 15 to 100 kHz, or add cascaded RC and LC filters. The mean value itself also falls with current, and the U(I) load characteristic is the identity document of a DC test source: it shows the regulation and the maximum current that keeps the ripple factor legal.

The cascade multiplier and its cubic penalty

Transformers for very high direct voltages run into cost and insulation limits: producing 800 kV DC by direct rectification would need a transformer of roughly 570 kV RMS and a colossal rectifier column. The way out, proposed by Greinacher in 1919 and perfected by Cockcroft and Walton in 1932, is to multiply a modest alternating voltage. The doubler charges one capacitor to −Vmax on the negative half cycle through one diode, and on the positive half cycle the source in series with that capacitor charges the output capacitor to +2·Vmax through the other diode. Stack n identical cells and the no-load output is U0 = 2·n·Vmax, with the remarkable property that each capacitor and each diode holds at most 2·Vmax. The oscillating column on one side is pumped by the source every period; the smoothing column on the other accumulates the DC plateaus. The cascade is, in essence, a charge elevator.

Under load, every transferred charge packet leaves a deficit. The classical analysis for a half-wave cascade with all capacitors equal to C gives a total voltage drop ΔU = [I/(f·C)]·(2n³/3 + n²/2 − n/6) and a ripple amplitude δV = [I/(f·C)]·n·(n+1)/2. The message is in that 2n³/3 term: voltage drop grows with the cube of the stage count while the voltage gain grows only linearly. There is therefore an optimum number of stages beyond which adding cells reduces the loaded output voltage, and keeping only the cubic term gives n_opt ≈ √(Vmax·f·C/I). For Vmax = 100 kV, f = 50 Hz, C = 50 nF and I = 10 mA, n_opt is about 5. That is why industrial cascades at mains frequency rarely exceed four to six stages, and why modern sources migrated to high-frequency excitation in the tens of kilohertz, which multiplies f by three orders of magnitude and collapses both ΔU and δV in the same proportion. Two more refinements matter: the symmetrical cascade, with two oscillating columns in antiphase feeding one smoothing column, doubles the effective recharge frequency and cancels the transformer DC component; and closing a control loop from the measuring divider back to the excitation holds Ū constant under changing load.

Measuring DC: the resistive divider takes back the throne

On DC the natural divider is resistive, with a scale factor (R1 + R2)/R2, and its apparent banality hides three precision traps. The first is self-heating: the divider current dissipates U²/R1 in the high arm, resistance moves with temperature at typically 10 to 100 ppm/°C, and the scale factor drifts through the test. The classic compromise is a divider current around 0.5 to 1 mA at rated voltage, which at 300 kV means R1 = 600 MΩ dissipating 150 W along the column. The second trap is corona and surface leakage: a 600 MΩ resistor two metres long carries a mean surface gradient of 1.5 kV/cm, and without guard rings and equipotential shields those currents add to the column current and falsify the scale factor. The third is ripple, which the resistive divider passes: measuring Ū demands filtering at the instrument, and measuring the ripple itself demands a dedicated capacitive branch. IEC 60060-2 requires an approved DC measuring system to hold expanded uncertainty within 3% on Ū and to measure the ripple amplitude within 10% of the ripple itself.

The simplest and most informative instrument in a DC test is the microammeter in series with the object, and its position matters. On the grounded side it measures safely but adds the leakage of the whole bus; on the high side, with shielding and optical readout, it measures the object alone. Protection is mandatory: a spark gap or varistor in parallel, because object breakdown would send the discharge current through the instrument. As for the sphere gap, on DC it loses its poise. Dust particles are electrostatically attracted into the field between the spheres and trigger erratic breakdowns well below the expected voltage. The standardised answer in IEC 60052 is the rod-rod gap: two square-section steel rods of 10 to 25 mm, aligned, with spacing d between 250 and 2500 mm, for which breakdown in air follows U50 = 2 + 0.534·d with U50 in kV and d in mm, valid for absolute humidity between 1 and 13 g/m³ and giving about ±3% after atmospheric correction. At 500 kV, d works out to roughly 933 mm. The rod gap is the field standard that lets you check a suspect divider on site.

Leakage current is the first diagnostic tool you own

Apply a DC step to an insulation and the microammeter records a current that decays over minutes, and the decay is the diagnosis. The capacitive component charges the geometric capacitance, decays exponentially in seconds or less and carries no dielectric information. The absorption component feeds the slow polarisation mechanisms, dipolar and interfacial, and decays as a power law t^(−n) with n around 0.5 to 1 in Curie–von Schweidler behaviour, over minutes to hours. The conduction component is the final plateau, associated with real carrier migration through and across the insulation. That is the leakage proper, and it is what responds to moisture, contamination and ageing.

An insulation resistance tester is nothing more than a regulated DC source, typically 500 V to 15 kV, with a microammeter calibrated in ohms: R(t) = U/i(t). Since i decays, R rises, and the shape of that rise is the diagnosis. Two dimensionless indices remove the dependence on object size and applied voltage: the dielectric absorption ratio, DAR = R(60 s)/R(30 s), and the polarisation index, PI = R(10 min)/R(1 min). In dry, sound insulation absorption dominates for many minutes and PI is 2 or better; in wet or contaminated insulation conduction dominates early, the current settles fast and PI tends to 1. IEEE 43 practice for rotating machines recommends PI at 2.0 or above for class B, F and H insulation, and allows the criterion to be waived when R at one minute already exceeds 5 GΩ. Watch the interpretation traps: resistance roughly halves for every 10 °C of heating, so correct to a common temperature before comparing against history; use the guard terminal to divert surface leakage away from the instrument; and remember that modern epoxy-mica systems absorb so little that PI loses sensitivity.

Above the range of the insulation tester, the DC test source takes over. Apply the voltage in steps — 25, 50, 75 and 100% of the test level, one to five minutes each — recording the settled current at each plateau. In sound insulation the current rises roughly linearly with voltage; an upward inflection is the classic warning of internal ionisation or a forming leakage path, and stopping before breakdown is precisely the diagnostic value of the method. The DC method has one well-documented limit. DC withstand testing was standard for paper-insulated lead-covered cable, but on extruded XLPE and EPR it proved not merely ineffective but harmful: charge becomes trapped in the polymer bulk and at the interfaces with the semiconducting layers, and when the voltage is removed or the cable is re-energised on AC, the residual field of that space charge adds to the service field and can break a cable that would have survived untested. The DC field also distributes itself by resistivity rather than permittivity, stressing regions the service condition never stresses. IEEE Std 400.2 documents the evidence and establishes the replacement: very low frequency testing at typically 0.1 Hz, which keeps the source portable because reactive power at 0.1 Hz is 500 to 600 times lower than at power frequency, while reversing polarity every 5 s so space charge never accumulates.

Syllabus

• Why DC: conduction-only current, low source power for capacitive objects, and natively DC applications

• IEC 60060-1 DC requirements: mean value as the test value, ripple ≤ 3%, stability ±1% up to 60 s

• Rectifier columns: silicon avalanche diodes in series, static and dynamic grading

• Peak inverse voltage: why every diode must hold 2·Vmax

• Half-wave versus full-wave: recharge once or twice per period, and the DC component that saturates the supply transformer

• Ripple definition δ = (Umax − Umin)/2 and the ripple factor δ/Ū

• Design formulas: δV = I/(2·f·C) half-wave, δV = I/(4·f·C) full-wave

• Voltage drop and regulation; the load characteristic as the identity document of a DC source

• The Greinacher doubler and the Cockcroft-Walton cascade; U0 = 2·n·Vmax at no load

• Cascade equations: ΔU = [I/(f·C)]·(2n³/3 + n²/2 − n/6) and δV = [I/(f·C)]·n·(n+1)/2

• The optimum stage count n ≈ √(Vmax·f·C/I) and the migration to high-frequency excitation

• Symmetrical cascades and high-frequency inverter architectures

• Precision resistive dividers on DC: self-heating, corona and surface leakage, guard rings

• The series microammeter, its position in the circuit and its mandatory protections

• Rod-rod gaps for DC: U50 = 2 + 0.534·d, and why sphere gaps fail on DC

• Leakage current components: capacitive, absorption following Curie–von Schweidler, conduction

• Insulation resistance, DAR and PI; IEEE 43 practice and its interpretation traps

• Step-voltage leakage testing and the upward inflection as an early warning

• The historical DC to VLF transition in extruded cable testing

Laboratory work

Four stages on the DC bench, with the permit issued and under supervision. Stage one, assembly and inspection: build the half-wave circuit — test transformer, rectifier column, filter capacitor, resistive divider, microammeter — and check clearances, screen grounding and the discharge stick. The safety-critical point is that high voltage capacitors hold lethal charge, so a resistor-limited discharge followed by a visible solid ground precedes any approach, and the waiting time respects the circuit time constant. Stage two, ripple: energise to 30 kV into a known resistive load, measure Ū on the divider with a mean-reading voltmeter and 2δ on the capacitive branch with an oscilloscope, compute δ/Ū, compare against the prediction from δV = I/(2fC) and check the 3% limit. Stage three, load characteristic: vary the load over five points, record U against I, overlay the theoretical curve and discuss the discrepancies from diode drops, transformer impedance and divider leakage. Stage four, leakage as diagnosis: apply a step to a clean dry insulator and repeat with the same insulator humidified, recording i(t), computing DAR and PI in both states and discussing the contrast, then run the 25/50/75/100% step test and observe the linearity of i against U. The report delivers a dimensioned single-line diagram, a measurement table with uncertainties, the measured against theoretical U-I curve, the two i(t) plots with their indices, and a conformity analysis against IEC 60060-1.

Key takeaway

The ripple doubled when you connected the object. That is a signal, not a defect. Since δV = I/(2fC) is directly proportional to the current drawn, a leakage current equal to the divider current doubles the total current and doubles the ripple with nothing wrong. Check that the absolute value still conforms and that the object's leakage matches its history and nature. But if the ripple doubled while the mean current did not, suspicion changes: there may be a pulsating component in the leakage, recharging every half cycle, and that object deserves a partial discharge investigation.

Module 5 of the Atlas Energy Academy · Generating & Measuring · about 4 hours · Video series plus hands-on DC bench practice · Prerequisites: Module 4 — AC High Voltage Measurement