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Peek-Frank: central claims

Source: F. W. Peek Jr., Dielectric Phenomena in High Voltage Engineering, 2nd ed., McGraw-Hill, 1920 (one PDF, 325 pages). Peek worked for General Electric, which had a commercial interest in transmission equipment.

Source gap note. The text is OCR on 324 of 325 pages; equations and tables are often garbled, so the load-bearing pages were read from page images. After QE, deep reads cover Chapters III-V (PDF pp.60-189), the end of VI and VII (pp.196-227), VIII-IX (pp.227-251) and the appendices (pp.277-311), including the corona-loss data appendix, transcribed. Still digest only: front matter and Chapters I-II (pp.1-59), the oil material of Chapter VI on pp.189-195, the design cases of Chapter X (pp.252-276) and the index. The loss law's constant is printed A = 241 on p.237 and 244 on p.242; the fit chain gives 241 (20,500/85). The primary papers Peek cites for the energy-limited-breakdown figures (Hayden and Steinmetz, A.I.E.E. 1910) and the 100,000-cycle loss check (Alexanderson) were not read, so those two items rest on Peek's account of them. Nothing here rests on [memory] alone.

  1. Peek's law of visual corona. The surface gradient at which a wire starts to glow rises as the wire gets thinner, g_v = g_o(1 + 0.301/sqrt(r)) kV/cm peak with g_o about 30 kV/cm, and in general g_v = g_odelta(1 + 0.301/sqrt(delta*r)) for relative air density delta, independent of spacing, conductor material and humidity. The constants are group-averaged fits (the "Sigma-Delta" method, with 9 of 19 points discarded), with variants 31(1+0.308/sqrt r) for cylinders and 27.2(1+0.54/sqrt R) for spheres.

  2. The energy-storage distance. Air has a constant strength g_o, but rupture needs a finite energy, so the gradient must stay at or above g_o over a distance 0.301*sqrt(r) cm from the wire; Peek attributes this to ionization by collision (electrons chiefly) but states that the form of the rupturing energy "has not been considered", and does not derive 0.301 or the square-root form from ion physics.

  3. Empirical corona-loss law for transmission lines. Loss above the disruptive voltage e_o is p = (244/delta)(f+25)sqrt(r/s)(e-e_o)^2 x 10^-5 kW/km, e_o = 21.1 m_o r delta ln(s/r) kV, with irregularity factors, a storm rule e_o x 0.8, and altitude and weather rules. A worked 100-mile line (e_o = 52.0 kV) recomputes correctly, and the book compares calculated with measured losses on the Leadville line and the Au Sable line (15 kW/mile calculated vs 15-20 measured, "preliminary rough measurements"). Corona is expected to be an economic rather than a physical limit on line voltage. The law was fitted by Peek's group-averaging method to single-phase test lines (stated on p.20 and p.286: Line A and Line B are single-phase); the constant is the product of an indoor frequency fit (f+25) and an outdoor 12-test fit, and the deep reader's refits show the outdoor data do not themselves fix the -25. The one out-of-sample check in the book is Alexanderson's 100,000-cycle measurement on two parallel wires (about five points, a GE test; Peek: 'a good check', 'complete conclusions cannot be drawn from this small amount of data'), which supports the frequency scaling of the slope but not the onset voltage.

  4. Strength of air at small gaps, and in thin films. Where the gap is shorter than the energy distance the gradient needed for breakdown is far above 30 kV/cm (196 kV/cm at 0.0025 cm for a free sphere gap; sphere-gap average 27.23(1+0.54/sqrt(deltaR))), and entrapped air films in solid insulation break down at the gradient of a free gap of the same thickness (161 kV/cm at 0.0025 cm). The appendix gives a Paschen table (minimum about 350 V at px = 0.05 cm Hg cm).

  5. Time lag: impulse voltages break insulation at far higher voltage than 60 cycles. Rupture requires a minimum energy and hence a minimum time ("dielectric spark lag"). In Peek's 1915 half-sine impulse tests (55 to 900 kc) needle-gap impulse ratios run from 1.00 to 2.34, oil and solids 2-3.3, rising further at low air density (up to 5.8), while sphere gaps stay within about 5 percent (so serve as impulse voltmeters), and rain lowers 60-cycle insulator flashover 36-40 percent but impulse flashover only 2-3 percent. The minimum-energy idea also has a measured form in the book: Hayden and Steinmetz (A.I.E.E. 1910, GE) found that gaps set to 30 kV at 60 cycles do not spark over at a 100 kV transient unless the circuit supplies 0.45 J (1.5 A) in air or 1.04 J (4 A) in oil, and Peek states that the disruptive energy of oil is about 30 times that of air. These are circuit energies from another investigation, not an energy stored in Peek's 0.301*sqrt(r) zone, and the figures plot current, not time.

  6. D.c. versus a.c. In air and oil, direct-current breakdown equals the a.c. peak (1.41 x the a.c. effective value), with exceptions in the book's own tables (thin wires in cylinders, long needle gaps; Whitehead's compiled positive d.c. corona 4-6 percent lower). In solid insulation (varnished cambric) d.c. strength is 1.27 to 2.59 times the a.c. peak, rising with thickness and time, which Peek ascribes to a.c. dielectric heating.