**5. Traceability of harmonic voltage and its uncertainty**

#### **5.1 Determination of harmonic voltage**

When Eq. (3.1.1) expresses a non-sinusoidal voltage signal and Eq. (3.1.3) denotes the sampling data under the sampling model of Eq. (3.1.2), the DC voltage, fundamental voltage, and harmonic voltage components can be obtained after calculation according to Eq. (3.3.7). These are expressed as follows:

$$V\_0 = a\_0 \,\prime \tag{5.1.1}$$

$$V\_1 = \sqrt{a\_1^2 + b\_1^2} \tag{5.1.2}$$

$$
\varphi\_{V1} = \arctan(b\_1 \, / \, a\_1) \, / \, \tag{5.1.3}
$$

$$V\_k = \sqrt{a\_k^2 + b\_k^2} \,\,\,\,\,\tag{5.1.4}$$

arctan( / ) *Vk k k b a* , (5.1.5)

where φ*V*1, φ*Vk* are the phase angles (against a reference time point) of the fundamental and harmonics, respectively, and *k* = 2,3,…*w*.

The experimental determination of the technical specifications of the NIM harmonic power standard equipment is discussed next, beginning with harmonic voltage.

#### **5.2 Frequency characteristic**

The frequency characteristic of the standard equipment can be initially determined by adopting the existing National AC Voltage Primary Standard for thermo-converters. In this process, the stable sinusoidal signals are exported at the selected frequency points that correspond to the fundamental, 10th, 20th, 30th, 40th, 50th, and 60th orders. Their amplitudes are set to correspond to the full range. Such signals are connected in parallel to the AC Voltage Standard and the harmonic power standard equipment (DVM or/and RVD). The experimental results show the differences than the AC Voltage Standard and its uncertainties.

This frequency characteristic is a special frequency attribute. The principal difference is that in the sampling measurement for high frequencies, harmonic discrete division is adopted (see Section 3.6). A similar case exists for the current discussed in Section 5.1 and the phase shift mentioned in Section 7.4, but this is not discussed for simplification.
