4.3 Frequency Detection Requirements
4.3.1 The Effect of Frequency Detection Time Delay
In order to observe the effects of time delay in frequency detection, the ideal frequency signal was modified with varying time delays. A time delay can be approximated by a first order lag according to control theory [87]. The modified control block diagram is shown in Fig.4.8. As can be seen, the first order lag of Td (frequency detection delay) is placed before the proportional ES controller to impose the effect of the frequency detection delay at the most appropriate point.
Figure 4.8:Block diagram of the proposed ES control system with frequency detection delay
Delay in frequency detection causes a delay in activating the ES. This condition directly influences the way the active power is supplied. The ideal frequency signal in the ES control is now replaced by the delayed signal, allowing the effect of the delay Td to be seen in the frequency recovery. The frequency re-covery achieved during rated load disturbance with the ES support for vary-ing frequency detection delays of 10ms, 20ms and 40ms are shown in Fig.4.9a.
These values represent typical delays associated with common frequency
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tection methods [6, 57, 59, 68, 70]. Fig.4.9a also shows a reference frequency recovery with no frequency detection delay. The active power supplied from the ES, corresponding to the delays considered is shown in Fig.4.9b.
(a)Frequency recovery
(b)Active power
Figure 4.9:The effect of frequency detection delay Td(ms)on frequency recov-ery and active power supplied by the ES control during the rated load disturbance, KES =30
The Figs.4.9a and 4.9b show the consequences of having a frequency detec-tion delay on the recovered frequency and the ES usage. According to Fig.4.9a, when the delay is increased, the recovered frequency experiences more under damped oscillations with larger initial oscillations. However, the time taken for the frequency to settle at the final steady state is approximately the same.
Therefore, it can be concluded that the first order delay decreases the damp-ing factor of the system for a fixed proportional gain KES. The reason for the appearance of oscillations can be explained as follows.
A delay in the detected frequency delays the detection of crossing the frequency threshold. During this delay, the actual frequency drops further. Therefore, the ES supplies power trying to catch up. During this time, due to the supplied
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ergy, the frequency reduces its drop rate down to zero. Yet, the ES still supplies power. During the next phase, the frequency starts to rise due to extra energy.
After realising this, the ES reduces the supplied power during which time, the frequency stops rising and starts decreasing again but to a lesser extent creating exponentially damped oscillations in the frequency response. This scenario is illustrated in zoomed images of Figs.4.9a and 4.9b.
This phenomenon can also be viewed in a different perspective. The oscillations occur due to the high rate of injecting energy (i.e. injected power) proportional to the frequency drop. If the constant of proportionality KES is decreased, one might be able to reduce the oscillations. Therefore, when the frequency detec-tion delay is increased, KES needs to be limited to mitigate frequency oscilla-tions. In extreme cases where KES is too high, the ES may switch on and off rapidly. On the other hand, understandably, the maximum frequency drop in the recovered frequency increases with increased frequency detection delay as shown in Fig.4.10d. This may be of concern that a larger initial frequency dip crossing 47.5 Hz may start load-shedding, hence, reducing the effectiveness of the frequency support technique.
In Fig.4.10a, the peak active power response from the ES is seen to be increasing with respect to the time delay. Due to the exponential damping of the frequency oscillations, the initial peak active power is significantly high. Moreover, the damped oscillations in the frequency and the active power supplied has a cou-pled effect on each other (P = τω = KES2πδω.ω). The energy supplied during the frequency oscillations aids in damping the frequency oscillations, while the frequency triggers the ES to supply active power demand.
Another important characteristic measure of the ES control system is the total energy supplied during the frequency support period (the period during which the frequency falls below the threshold). The integrated power over the time of the load disturbance transient, calculated for various frequency detection de-lays are shown in Fig.4.10b. As seen in the figure, the time delay has a negligible effect on the total energy supplied. In fact, with increasing time delay, the total energy spent decreases slightly.
This result can be explained with the peak active power supplied and the time taken for ES control to bring the system above the threshold. According to the results, longer frequency detection delays were found to be associated with larger initial peaks and shorter settling times. This means that the frequency recovery is over assisted as a result of the frequency oscillations; thus, is able to
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(a)Peak active power (b)Total energy injected
(c)ES active time (d)Maximum initial frequency drop Figure 4.10:ES usage with different frequency detection delays Td (for the
rated load disturbance, KES =30)
achieve the threshold with a subsequently shorter time, resulting in a marginal reduction in total energy supplied. Also, the ES active times of delivering active power support are relatively consistent under increasing detection delays as can be seen in Fig.4.10c.