Measurement and Instrumentation study guide

What this area covers

Measurement and Instrumentation asks whether you can trust a number. It covers instrument transformers and the multipliers they bring, how accurate a metering or relaying chain is, the classic wattmeter connections for three-phase power, how the meter itself disturbs the circuit, and what different meters actually report when the waveform is not a clean sine. This area accounts for 6–9 questions on the exam. The arithmetic is light; the usual errors are in connections, ratios and definitions.

The ideas everything else rests on

Every secondary reading needs its multiplier. A meter on the secondary of a current transformer and a voltage transformer sees scaled-down quantities. Primary power is the meter reading times the CT ratio times the VT ratio. A current-only reading takes just the CT ratio, a voltage-only reading just the VT ratio. Write the ratios as fractions with units, such as 600 A to 5 A, so the direction of scaling is never in doubt.

Accuracy classes are promises over a range. A metering-class instrument transformer is accurate near rated current and burden, which is what revenue metering needs. A relaying-class CT trades that fine accuracy for the ability to reproduce many times rated current during a fault without saturating badly. Both depend on staying within the rated burden, so adding a long lead run or an extra device can quietly move a CT out of its class.

Two wattmeters measure three-wire power. In a three-wire system, two wattmeters measure total real power whatever the load balance or power factor: P = W1 + W2. For a balanced load, the difference between the readings also reveals the power factor angle. With the first meter on line a current and the a-to-b voltage, the second on line c current and the c-to-b voltage, and positive sequence,

$$\tan\theta = \sqrt{3}\,\frac{W_2 - W_1}{W_1 + W_2}$$

At 0.5 power factor one meter reads zero, and below that one reads negative, which must be subtracted, not ignored. More generally, Blondel's theorem says a system with n wires needs n minus 1 measuring elements.

Meters load the circuit they measure. A voltmeter draws current through its internal resistance; across a high-resistance source, that current changes the very voltage being read. An ammeter adds series resistance. The size of the error comes from comparing the meter's resistance with the Thevenin resistance of the circuit at the measuring point.

Average-responding is not true RMS. Many simple meters rectify and average the waveform, then scale the result by the form factor of a sine wave. On a sine wave the answer is right. On a distorted current, such as the input of a rectifier or a variable-frequency drive, it can be badly off. A true-RMS meter computes the heating value directly and stays correct.

How to study it

1. Work meter-multiplier problems for single-phase and three-phase installations, with CTs and VTs on both sides of a transformer.
2. Check the primary values you find against the Three-phase power calculator, going from line voltage, current and power factor to kW, kVA and kVAR.
3. Derive the two-wattmeter readings for balanced loads at several power factors, including below 0.5, and confirm that the sum always equals the total power.
4. Use the Symmetrical components calculator to see how an unbalanced set of currents breaks into sequences, which is what many protective and power-quality meters report.
5. Finish with loading errors and waveform effects: a voltmeter across a divider, and the reading of an average-responding meter on a square wave and on a pulsed current.

Mistakes that cost points

• Inverting a ratio. Multiply secondary readings by the ratio to reach primary values. Dividing instead leaves the answer off by the square of the ratio.
• Dropping the sign of a negative wattmeter. Below 0.5 power factor one reading is negative, and the total is the algebraic sum.
• Applying the two-wattmeter power factor formula to an unbalanced load. The sum still gives total power; the angle formula only holds when the load is balanced.
• Trusting an average-responding meter on distorted waveforms. The sine-wave scaling no longer applies.

References worth having

• IEEE Std C57.13 (requirements for instrument transformers)
• ANSI C12.1 (code for electricity metering)