Frequency Assessment

Summary

This short paper addresses several equations used to interpret the severity of the ac-voltage frequency deviations on the power system. As demonstrated in this paper, each equation can lead to very different conclusions.

Introduction

A variety of means are available for the measurement of synchronous power frequency. These include, and are not necessarily limited to, the following:

• Measured time interval between zero crossings of an ac input signal.
• Measured output frequency of a phase-locked-loop operating on an ac input signal.
• Use of a frequency-to-voltage converter, with an input derived from either the ac input signal or from a phase-locked-loop.
• FFT analysis of digitally sampled ac input waveform.

Rapid progress in electronic measurement technology of ac waveforms has opened the way for a variety of measurement application techniques.

This paper does not provide a specific recommended approach to ac frequency measurements, rather it outlines and compares a few methods to assess the level of samples acquired in a specific interval such as the 10-s interval specified in the EN 50-160.

Table 1: Frequency values used for the case study

 Assessment method

This demonstration assumes one sample per 200 ms (every 10 cycles for 50-Hz system) for the sampling rate. The assessment is normally required in each 10-s window which contains 50 samples of the frequency measured on the power system. The values in Table 1 are plotted in Figure 1 and are used for the case study to understand each approach to assess the frequency level in a 10-s interval.

Figure 1: Frequency used for the case study

Equation to assess the 10-s interval

At least seven equations can assess the level in the 10-s interval. The following sections briefly explain each equation.

1. The frequency average over 10 s

The average of the frequency values Fr_n sampled in the 10-s interval is probably the first equation used during the past 50 years using the following equation:



2. The rms of the frequency over 10 s

Similar to the average, the rms assessment uses the squared values before to apply the average. This rms is obtained with the following equation:



3. The rms of the frequency deviation

In this case, each frequency value is expressed as the percent deviation from the nominal frequency. This is obtained using the following equation:



Using this approach, the sampled data is represented using a new scale as shown in figure 2.



Figure 2: Deviation of the frequency sampled

The rms frequency deviation based on the deviation calculation is then obtained using the following equation:



4. The rms of the over frequency

The frequency can be either under frequency or over frequency. When the actual frequency is below the nominal frequency, the over frequency is considered to be 0. In this concept, negative over frequency can not occur. Applied to this case study, the over frequency component of the power system is shown in the Figure 3:



Figure 3: Over frequency component of the actual frequency recorded.

The rms frequency deviation assessment uses the following equation where all negative values of (Fr-50) becomes equal to zero.



5. The rms of the under frequency

The under frequency is the percent deviation between the nominal frequency and the actual frequency measured. When the actual frequency exceeds the nominal frequency, the under frequency becomes zero. In this concept, negative under frequency can not occur. Applied to this case study, the under frequency component of the power system is illustrated in the Figure 4:



Figure 4: Under frequency component of the power system

The rms under frequency deviation assessment uses the following equation where all positive values of (Fr - 50) becomes equal to zero.



6. The average of the over frequency

The average over frequency deviation assessment uses the following where all negative values of (Fr-50) become equal to zero.



7. The average of the under frequency

The average under frequency deviation assessment uses the following equation where all positive values of (Fr - 50) become equal to zero.

Results

This case study demonstrates the effect of each equation used to assess the frequency level in a 10-s interval. The results can be found in Table 2.

Table 2: Frequency of a 50-Hz power system assessed in 10-s interval

The rms of the values and the average of the values lead to opposite conclusions in this case study. While the average of the values shows a result below the nominal frequency, the rms of the values exceeds the nominal frequency. Furthermore none of the two equations reflects the severity of the minimum and the maximum recorded.

The rms of the values and the rms of the deviation gives also different results. In this example, the rms of the values gives 0.52% deviation from the nominal frequency while the rms of the deviation is 60% higher with 0.82% deviation.

Both the rms frequency and the rms deviation hide the low-frequency values. In this case study, the under-frequency values reached about 10 times the severity in amplitude of the rms frequency and lasted about twice the duration of the over frequency.

The over frequency and under frequency show values which better reflect the severity. During the 10-s interval, part of the time was under frequency and part of the time was over frequency and this is well reflected in the over frequency and under frequency assessment method.

Conclusions

The equation to use is function of the monitoring objectives.

Frequency is used to drive some motor driven clocks connected on the power system. The precision of the frequency is not so important as long as the frequency is reduced or increased for adjusting the clock. In this case the average of value is the most appropriate factor to use. However, with the evolution of crystal clock, this factor is not so important in many countries.

The ac power frequency is used today for synchronous motors in many industrial processes. In some cases, the over frequency could affect as much as the under frequency. Some controls may be instantaneously affected by the slow frequency variation. In this case, the average over frequency and under frequency or the rms over frequency or under frequency can apply.

Finally the rms of the values recorded is useless in the frequency application.