A smoothing technique to mitigate the effect of spurious frequency dip pro-duced by frequency detection techniques is explained in this section. The ini-tial frequency dips are a consequence of the source impedance as illustrated in Fig.5.33 for a DSOGI-FLL and a DFT with Hamming for the four test cases.
The proposed smoothing technique uses a combination of filters; the rapid fre-quency variation during the initial dip period is cut-off, while the slowly vary-ing frequency is allowed through. It is of paramount importance not to delay the detected frequency too much after the initial dip. To achieve this, a heavy filter was incorporated throughout the duration of the initial erroneous dip. Im-mediately after recovering to the normal pattern of the frequency detection, a
CHAPTER 5: COMPARISON OF METHODS FORACCURATEFREQUENCY TREND
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(a)DSOGI-FLL (b)DFT Hamming
Figure 5.33:Initial frequency dip produced by a DSOGI-FLL and a DFT with Hamming window
faster filter was appointed to let the correctly measured frequency pass through with minimal delay.
It is mandatory to identify a clear reliable trigger for the point at which the dip begins to form, in order to sustain the independence of the energy storage con-trol. Since a voltage glitch essentially creates a rapid change in magnitude, the instantaneous time derivative of the magnitude of input voltage may be used as an accurate indication of the glitch occurrence. Figs.5.34b and 5.34c show the derivative of voltage magnitude calculated as a by product of the DSOGI-FLL and the DFT, for the rated load disturbance. One can see a clear fluctuation in the rate of change of magnitude of the DSOGI-FLL, corresponding to the instance of glitch shown in Fig.5.34a. However, the DFT does not show such rapid variation in the rate of change of magnitude.
In the DSOGI-FLL, the magnitude variation is immediately detected by the QSG and can be used as reliable trigger. But, in the DFT, the magnitude change can only be detected after at least half of the window length has passed. This is mainly because the Hamming and Blackman windows give prominence to the centre of the window. During this time, the magnitude drops slowly to its low-est value and rises again slowly. Therefore, an effect (i.e. glitch) that only lasts for 1 ms in the 3-phase voltage is spread out during a 12 ms period in the DFT magnitude output. Therefore, the derivative of the voltage magnitude calcu-lated by the generalised DFT with Hamming windowing as shown in Fig.5.34, does not show distinguishable characteristics to that of the DSOGI-FLL, that is necessary if it is to be employed as a trigger. However the author would like to recommend the use of the generalised DFT in energy storage control, if other
CHAPTER 5: COMPARISON OF METHODS FORACCURATEFREQUENCY TREND
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(a)VPCC
(b)DSOGI-FLL d(Vmag/dt)
(c)DFT d(Vmag/dt)
Figure 5.34:Time derivative of the voltage magnitude obtained using DSOGI-FLL (middle); using DFT (bottom) for the rated load with the cor-responding VPCC(top)
CHAPTER 5: COMPARISON OF METHODS FORACCURATEFREQUENCY TREND
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suitable provisions can be made to avoid the spurious frequency dip.
Therefore, during this study, the DSOGI-FLL was chosen as the suitable tech-nique to detect the frequency avoiding spurious frequency dips. This is justified as for the optimum parameters, both techniques perform similarly for the weak grid conditions defined in this study.
The significant variation in the rate of change of magnitude is set as the trig-ger of the smoothing technique. It is important to note that the rate of change of magnitude is independent of the load change - see Fig.5.35; and is funda-mentally defined by the total source impedance, which is fixed for a particular power system. The smoothing technique triggering condition was set as,
d(Vmag)
dt ≥1×104 (5.7.1)
In this smoothing technique, the knowledge of the frequency dip duration is essential. This is crucial for a smooth variation of the output when the two filters are interchanged. The duration of the dip is largely dependant on the frequency detection method used and its tuning parameters. For a DSOGI-FLL, the initial dip was found to last a period slightly less than the settling time. In this case, the duration of the depth was set as 30ms considering the settling time of the optimum DSOGI-FLL.
Figure 5.35:Time derivative of the voltage magnitude obtained using the DSOGI-FLL for rated and half rated loads
The heavy filter fsH used immediately after the trigger indicating the glitch until the end of the dip is,
fsH(s) = 1
0.033s+1 (5.7.2)
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And the faster filter fsL which was used before and after the initial dip duration is given by,
fsL(s) = 1
0.001s+1 (5.7.3)
The value for the faster filter was chosen such that its time constant was in-significant (<10%) relative to the settling time. The time constant of the heavy filter was chosen by trial and error considering the frequency dip for a rated load.
Fig.5.36 shows the effective smoothing achieved by filtering for rated and half-rated loads. As can be seen, the smoothing technique has visibly alleviated the erratic initial dip. Considering the benefits of mitigating the inaccurate activa-tion of energy storage over the slight delay(≈1 ms) caused by the fast filter, the proposed smoothing technique can be declared acceptable in the energy storage control algorithm.
(a)rated load (b)half-rated load
Figure 5.36:DSOGI-FLL frequency detection with the smoothing technique