Measurement and Instrumentation

How a power system is measured and tested: quantities read through instrument transformers, the condition of insulation, and the resistance of an electrode or a site's soil to earth. The area carries 6–9 of 80 questions across three subtopics: instrument transformers and metering, insulation testing, and ground resistance testing.

What the problems look like

Short calculations and judgment calls, often from a one-line or a test record. Recurring shapes — a CT or VT ratio referral; a burden total; a meter multiplier or two-wattmeter reading; a miswired meter to diagnose; an insulation resistance reading to correct and judge; a polarization index; a current-versus-time record; a four-pin soil survey; a fall-of-potential test; and a rod or grid resistance to earth. A few are NEC Article 250 lookups.

By exam day you should be able to —

• refer quantities through a CT or VT: I_s = I_p/N, V_s = V_applied/N, and meter multiplier = CT ratio × VT ratio;
• total a burden: Z = VA/I_s² at rated secondary current, lead resistance on the loop, VT burdens summed in volt-amperes (exact when their power factors match);
• read a two-wattmeter set: P = W₁ + W₂, and for a balanced load tan φ = √3(W₁ − W₂)/(W₁ + W₂);
• correct an insulation resistance reading, R(40 °C) = k·R(T), and form PI = R₁₀ min/R₁ min;
• apply the absorption decay I_A = K·t⁻ⁿ to a test current;
• turn a four-pin reading into resistivity, ρ = 2πaR for shallow pins, and place the fall-of-potential probe at 62%;
• compute a rod's resistance, R = ρ/(2πl)·[ln(8l/d) − 1], and a grid's lower limit, (ρ/4)·√(π/A).

Where people lose points

• Trace the drawing before the nameplate. Find which conductor the CT is on, which secondaries reach the instrument and the polarity marks; a reversed CT subtracts. A VT's secondary voltage follows the voltage across its primary leads, line-to-neutral or line-to-line.
• Burden bookkeeping. On a single CT or VT circuit, lead resistance is the loop, twice the one-way run. The CT's winding resistance stays out of a burden compared with a rating and joins the loop when the question asks what voltage the CT must develop. Burdens on a VT are in parallel, so their volt-amperes add.
• Scale once, with both ratios. A transformer-rated meter needs the CT ratio and the VT ratio; instruments scaled in primary units already include theirs. A watthour meter responds to real power, so its reading takes no power factor.
• Correct to 40 °C, then compare. Pick the coefficient by insulation family (thermoplastic k = 0.5^((40 − T)/10); thermosetting has two exponential forms, each with its own temperature range) and multiply. A winding hotter than 40 °C corrects upward. Choose the row of the minimum table by winding type and vintage.
• Polarization index as defined. Ten-minute reading over one-minute reading, with no temperature correction.
• After the first minute, only the absorption current decays. Subtract the conduction-plus-leakage floor before applying the power law. A total current that stays flat for ten minutes points to a wet or contaminated winding.
• Four-pin dimensions. In ρ = 2πaR, a is the spacing between adjacent pins, and the short form holds only for pins driven to l ≤ 0.1a; deeper pins need the general form.
• Electrode tests. Measure the 62% from the electrode under test. In the rod relation, length appears twice and ρ belongs to the soil the rod occupies. Electrodes far enough apart not to interact combine as parallel resistances; closer ones read higher. The 25-ohm figure in the 250.53(A)(2) Exception decides whether a single rod, pipe or plate electrode needs a supplement; a metal water pipe is covered separately in 250.53(D)(2).

Have these at your fingertips

PI, the 40 °C correction, ρ = 2πaR and the rod relation, plus where they sit in the Handbook. Under Insulation Testing: Insulation Resistance Theory (the current components and I_A = K·t⁻ⁿ), Characteristics of the Measured Direct Current (the test-voltage and recommended-minimum tables), Effect of Temperature, and Insulation Polarization Index (PI). Ground Resistance Testing holds both four-pin arrays and the driven-rod method; Substation Grounding Resistance holds the grid limits. Burden and accuracy-class relations are not printed in the Handbook, so carry them in. Grounding of instrument transformers, meters and relays is in NEC 250, Part IX (250.170 to 250.178). The exam supplies NFPA 70-2020 (NEC) and opens one chapter of a standard at a time.

Going deeper

• Instrument transformers (CTs and VTs) on the PE Power exam — ratios, burden, accuracy classes
• Grounding and ground resistance testing on the PE Power exam — soil surveys, electrode tests and Article 250
• The PE Power handbook and code books — what is supplied
• General Applications — grounding design

Part of the PE Electrical: Power exam. Practice with exam-real problems — Castor, the AI tutor, walks any one you miss. → Start practicing Or take the free PE Power practice exam first.