**10. Conclusion**

172 Modern Metrology Concerns

The commercial programmable signal generator not only provides sinusoidal fundamental waveform voltage and current signals, but also enables the modification of these waveforms to include harmonic components for the calibrations of harmonic meters. It is specified as a

The performance of the programmable signal generator is also verified using the harmonic power standard equipment. The generator is programmed to produce the set of IEC signals

The measured results are compared with the set values of the signal generator. The fiducial harmonic errors of voltage, current, and power from the DC to the 7th order harmonics are

However, a small non-linearity effect in the current output is observed. Larger errors are generated at the DC, 2nd, 4th, and 6th order harmonic currents. This result may be indicative of a non-linearity effect. Given the square of the fundamental component that produces the DC and 2nd order harmonic components, the cross term of the fundamental and 5th order harmonic component produces the 4th and 6th harmonic components. A similar but less noticeable phenomenon can also be observed in the voltage output. The

> Order Voltage/(V/V) Current/(A/A) Power/(W/VA) 0 79.5 –**237.0** 0.0 1 -12.9 -6.6 -19.5 2 12.1 **26.3** 0.0 3 8.7 7.1 0.0 4 4.9 **32.7** 0.0 5 -9.8 –6.3 -4.6 6 6.2 **51.3** 0.0 7 11.0 6.9 0.0

Although the harmonic power standard equipment is designed for harmonic power measurements, it can also be used to measure power/energy under sinusoidal waveform conditions. A comparison against the National Primary Power Standard of the NIM is

zero lead. The errors of the harmonic power standard equipment are no more than –18.6 W/VA at all the test conditions. This result is in agreement with previous findings within

Bilateral comparisons with the power standards of the National Metrology Institute of Germany PTB and USA NIST are also carried out using a traveling transfer standard under the test conditions 120 V, 5 A, 50 Hz, power factors of unity, 0.5 lag and lead, and zero lag

= 1, 0.5 lag, 0.5 lead, zero lag, and

= 1, and 5th harmonic 10 V, 1.2 A, and cos

= 1.

shown in Table 9.2.1 They basically confirm the specifications of the signal generator.

occurrence of the non-linearity effect should be confirmed through other tests.

Table 9.2.1. Fiducial harmonic errors of the signal generator at the IEC signal

**9.3 Comparison with the national energy standard** 

conducted under test conditions of 100 V, 5 A, 50 Hz, cos

the evaluated uncertainties of the calibration/experiment.

and lead. The agreement is within 4 μW/VA at all the test points.

**9.2 Test on the commercial programmable signal generator** 

0.02% device (a standard source).

of fundamental 50 Hz 100 V, 3 A, and cos

The harmonic power standard equipment of the NIM is introduced. It is based on the digital sampling technique, which does not require synchronous sampling. It features a special algorithm that compensates for the leakage effect caused by asynchronous sampling. When applied to power measurements with harmonic components of up to the 60th order, computation time is less than 2 seconds even without a large computer memory.

We propose a new concept of uncertainty expression that is related to the fundamental, and define it as the fiducial harmonic uncertainty. This concept is designed to evaluate harmonic measurements. A characterizing waveform signal is reported for the universality of the harmonic uncertainty claim of the NIM standard.

The harmonic power standard operates at fundamental frequencies ranging from 45 to 65 Hz with harmonic components of up to the 60th order, voltage range from 60 to 500 V, current range from 0.1 to 50 A, and any power factor from zero lag through unity to zero lead. The evaluated uncertainties (*k* = 2) of the harmonic voltages relative to the fundamental voltage, harmonic currents relative to the fundamental current, and harmonic power to the fundamental apparent power are 30 μV/V, 36 μA/A, and 42 μVA/W, respectively. These parameters may indicate the function of the principles and the methods described in this chapter, but will not be a limit for the future work.
