The NPL Reference Flickermeter is used in the calibration of flickermeters at NPL. To test the correct operation of the flickermeter under test, when certain voltage waveforms (see Flicker Waveform Library) are applied its Pst readings are compared to those of the NPL Reference Flickermeter. The design of NPL Reference Flickermeter is based on that given in [1] and other supporting publications [2],[3].

For certain waveforms the response of the IEC standard Flickermeter is known or calculable. This document provides results of simulations when these waveforms are applied to the NPL Reference Flickermeter and is evidence of its correct operation.

For a complete description of the NPL Reference Flickermeter see Design of NPL Flickermeter.

Results of Flickermeter Simulations
Simulated signals

Simulated 50 Hz signals with rectangular and sinusoidal modulation are used for the results in the following sections.

For rectangular modulation the simulated signal can be given by the following equation.

(1)

where f_c is the carrier frequency (50 Hz), is the relative voltage change, f_F is the modulation frequency and v(t) is the signal level at time t. sign(x) indicates multiplying by a value of +1 if the x is greater than zero and –1 if x is less than zero. If x is zero and decreasing the resulting value is -1 and +1 otherwise. For sinusoidal modulation the simulated signal can be represented as follows.

(2)   

Filter Charging

All results are obtained after allowing the filters in blocks 3 and 4 to charge, so that the output of the model is periodic.  To illustrate this, a typical output of block 4 is shown in Figure 1.  The data where the output is steadily decreasing from an initial high value as shown in Figure 1, is rejected. The theoretical considerations of this document are based on assumptions which rely on the filters being in steady state condition. For the comparisons with simulation in this document, a charge time of 120 seconds is used, to ensure steady state condition is reached in the filters and the scaling reference voltage. This time is a little longer than commonly used for measuring Pst and is reduced to 20 seconds in real flicker tests to bring the flickermeter design closer to that used in practise by commercial flickermeters. This results in a small error in flicker readings for some waveforms, which is included in the measurement uncertainty.

Figure 1 – Typical flicker meter output (8.8 Hz, sinusoidal modulation); data up to a time of 120 seconds is rejected when calculating the maximum perceptibility

Block 4 Output

The flickermeter model was run with simulated 50 Hz signals with sinusoidal and rectangular modulation to test the output of block 4 of the model, before the flicker readings are classified in block 5.

Performance with modulation depths from IEC61000-4-15

The flickermeter model was run with simulated 50 Hz signals with sinusoidal and rectangular modulation at the modulation frequencies and depths given in Tables 1 and 2 of section 4.1 of IEC61000-4-15.  The resulting max perceptibility at the various modulation frequencies and depths is shown in Figure 2.  The output is normalised to 1 for a modulation depth (dV/V) of 0.25 % with sinusoidal modulation at a modulation frequency of 8.8 Hz.

Figure 2 – Max perceptibility output at points given in IEC 61000-4-15

The maximum value from Figure 2 for sinusoidal modulation is 1.025 2 (at the 1 Hz point) and the minimum value is 0.986 8 (at the 15 Hz point).  According to IEC 61000-4-15, the output should be equal to 1 for all points.  However, it is stated in [3] that the dV/Vs given in Table 1 of IEC 61000-4-15 will give a perceptibility output of 1 within the range –2.5 % to +1.3 % for the dV/V values.  This would indicate that the model is working correctly as the deviations from 1 of the max perceptibility values given in Figure 2 are within this range.

Performance with modulation depths calculated from calculations given in [3].

The dV/Vs required to give a max perceptibility output of 1 at the modulation frequencies in Table 1 of IEC61000-4-15 for sinusoidal modulation can be calculated using the theoretical frequency response of the various filters in Blocks 3 and 4.

The gain of the filters in Blocks 3 and 4 is not included in the calculated responses given below. A scaling factor, S, is required to give a maximum perceptibility output of 1 for a dV/V of 0.25 % at a modulation frequency, f_F of 8.8 Hz.  This is the modulation frequency at which we are most sensitive to flicker from an incandescent light bulb. S is given by equation (3), the derivation of which is given in [3].

(3)   

where,

 is the magnitude frequency response of the block 3 high pass filter,

 is the magnitude frequency response of the block 3 low pass butterworth filter,

 is the magnitude frequency response of the block 3 weighting filter,

 is the magnitude frequency response of the block 4 variance estimator,

w_F = 2pf_F,

and d(w_F) is the dV/V = 0.0025.

The formulas for the magnitude frequency responses of all the filters are also given in [3].  Using these formulas and setting w_F to 2p8.8 rad/s gives a scaling factor, S, of 1238353.904.  This normalises the flickermeter output so that a max perceptibility of 1 is obtained for a dV/V of 0.25 % at a modulation frequency of 8.8 Hz. It is then possible to calculate the dV/V required to give a max perceptibility of 1 for each of the frequencies given in Table 1 of IEC 61000‑4‑15 using equation (4), below.

(4)   

The flickermeter model was run with simulated 50 Hz signals with sinusoidal modulation at the dV/Vs calculated using equation (4) at the modulation frequencies given in Table 1 of IEC 61000‑4‑15.  The results of the simulation are shown in Figure 3.

Figure 3 – Max perceptibility output at points calculated from equations in [1].

It can be seen in Figure 3 that the output agrees with that predicted within ± 0.04 %.  The deviation from 1 can be explained at low frequencies by the fact that some of the assumptions involved in the derivation of equations (3) and (4) break down at lower frequencies [3]. As the exact values are not easy to calculate, this deviation is included in the measurement uncertainty.

Calculation of Pst based on Theoretical Filter Responses

Based on the assumptions given in [3], it is further possible to calculate the expected Pst readings for given modulation depths for higher frequency sinusoidal modulations and for rectangular modulation at 4000 Changes Per Minute (CPM).

(5)  

This must then be multiplied by the scaling factor, S, to give the normalised instantaneous perceptibility value, p_F5(t),

(6)   

It can be seen that the instantaneous perceptibility then follows a repetitive cosine wave of frequency 2w_Ft. The flicker level exceeded for a given percentage of the test time can therefore be determined from the flicker level exceeded for the same percentage of one cycle of a cosine waveform. For a given percentage, P, any values of p_F5(t) where 2w_Ft is in the range

(7)   

will exceed those where 2w_Ft = . Therefore substituting  for 2w_Ft in equation (6) will give the flicker level exceeded for P % of the test time. The percentiles (P0.1, P0.7, etc.) from [1] and therefore the Pst value can be calculated.

Calculation of Pst for Rectangular Modulation at 4000 CPM

The above calculations are valid for sinusoidal modulation. It is stated in [3] that for a flicker frequency of w_F = 2p33 rad/s, the filter responses for sinusoidal and rectangular modulation are related by a gain factor of  to a good approximation.

This assumption, together with equations (3) and (6), is used to calculate the dV/V % value for a maximum perceptibility of 1 at 33 Hz or 4000 CPM, which is used in Table 2 of IEC 61000‑4‑15. The dV/V % value is given as 1.67 %. A more accurate dV/V % value is calculated as 1.671358 from the above. This value was applied to the NPL Reference Flickermeter and the resulting maximum perceptibility reading was 0.999901. The square root maximum perceptibility is 0.999950, an error of -50 ppm.

Dividing the d in equation (6) by the factor , given above, gives the instantaneous perceptibility for rectangular modulation for a flicker frequency of w_F = 2p33 rad/s as shown in equation (8),

(8) 

The value of d given in [1] for a Pst of 1 for rectangular modulation at a modulation frequency of 4000 CPM is 2.4 %. The required percentile values can then be calculated.

The resultant calculated Pst value is 1.024250, somewhat higher than the value of 1 given in [1]. The value obtained from simulation is 1.024107. This provides confidence in the NPL Flickermeter readings and is evidence that the filters and classification methods are working correctly.

Pst Results

The flickermeter model was tested with simulated 50 Hz signals with rectangular modulation at the modulation frequencies and depths given in Table 5 of IEC 61000‑4‑15.

The filters were charged with a modulated voltage for 120 seconds, before starting the test.

The resulting Pst values given by the NPL Flickermeter are shown below.

Changes per minute	dV/V (%)	Pst Reading	Error (%)
1	2.724	1.002	0.2
2	2.211	1.009	0.9
7	1.459	1.006	0.6
39	0.906	1.013	1.3
110	0.725	1.004	0.4
1620	0.402	0.987	–1.3
4000	2.4	1.024	2.4

Table 1 – Pst results

IEC 61000-4-15 states that a flickermeter should read a value of 1 ± 0.05, for the points in Table 5. However, as was explained above, the points were obtained using a flickermeter simulation based only approximately on the implementation described in [1] and therefore some deviation from these values is expected.

References

[1]    IEC 61000–4–15, Electromagnetic Compatibility (EMC) – Testing and measurement techniques – Flickermeter – Functional and design specifications, Published by The International Electrotechnical Commission, Amendment 1, 2003.

[2]    Flicker Simulation and Minimisation, W. Mombauer, 10^th Int. Conf. On Electr.Distrib. (CIRED), Brighton/UK 1989, IEE Conf. Publ. No. 305.

[3]    Calculating a New Reference Point for the IEC Standard Flickermeter, W. Mombauer, European Trans. On Electrical Power, Vol. 8, Part 6, December 1998, pp 429–436.