The main purpose of understanding the properties of different frequency de-tection techniques and their tuning methods was to compare and analyse the methods in order to identify the best technique to detect frequency in a weak electrical grid. Essentially the chosen method has to adhere to the requirements of frequency detection declared in section 5.2.
As part of the theoretical investigation of each method, the bandwidth for vary-ing design parameters were studied. In this section, all the frequency detection methods are compared so that they all share the same bandwidth, for an
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ased comparison. Step and ramp frequency variations will be simulated using a voltage waveform with harmonic distortion. The frequency trending during loading will also be simulated using the weak grid model for cases with and without source impedance.
5.6.1 Test cases
For testing a set of four bandwidths corresponding to the optimum designs of the SRF-PLL, the DFT with Hamming window, the DFT with Blackman win-dow and the DSOGI-FLL was considered. The bandwidths of the candidate frequency detection techniques were made equivalent as the basis of compari-son. The bandwidths were calculated using (5.3.14), (5.4.22) and (5.5.20) for the SRF-PLL, the generalised modified DFT and the DSOGI-FLL respectively. The test cases and the design parameters for all methods for each case are listed in Table 5.6. These test cases will be evaluated for different frequency and voltage variations in the following sections. However, note that the SRF-PLL for very high bandwidths (ts <50 ms) produces a large ripple rendering the significant ripple effects of other methods unobservable. Therefore, for the two higher bandwidths, SRF-PLL results were not included.
Case Bandwidth SRF-PLL DFT(Hamming) DFT(Blackman) DSOGI
rad/s ms rad/s ms ms
Table 5.6:Test cases for the optimum design of each method along with other methods adjusted to the same bandwidth.
5.6.2 Comparison for a Step Change In Frequency
Firstly, the three methods are compared under the same bandwidth for a step change in frequency. Fig.5.28 presents the simulation results for the three fre-quency detection techniques discussed.
From the step response for each test case presented in Figs.5.28a to 5.28d, one can see that all methods have approximately the same rise time, confirming that their respective bandwidths are aligned for each test case. For all test cases,
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(a)Case 1 (b)Case 2
(c)Case 3 (d)Case 4
Figure 5.28:Comparison of frequency detection techniques for Case 1,2,3,4 for a step change in frequency
one can see that the DFT with either Hamming or Blackman window has the fastest settling time with the minimum steady state ripple. Between, the two windowing techniques, the DFT with Hamming is slightly faster. The DSOGI-FLL exhibits midway performance between the DFT and the SRF-PLL, with regards to both settling time and harmonic attenuation. Therefore, for a step change in frequency, the DFT displays superior qualities over the other two.
5.6.3 Comparison for a Ramp Change In Frequency
Next, all methods are compared with the same test cases for a ramp frequency variation. Fig.5.29 shows the simulation results obtained.
When the frequency variation is changed from a step to a ramp, the perfor-mance ordering of the methods change dramatically under the same bandwidth comparison. The SRF-PLL, which is a type II system that produces a zero steady state error for a ramp, always settles at the actual ramp during the given settling time. Also, the SRF-PLL overestimates the ramp (ROCOF) within the settling
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(a)Case 1 (b)Case 2
(c)Case 3 (d)Case 4
Figure 5.29:Comparison of frequency detection techniques for Case 1,2,3,4 for a ramp change in frequency
time. On the other hand, the increase in bandwidth (i.e. decrease in settling time) causes a larger ripple. The results confirm over and over again that the SRF-PLL is unable to fulfil the requirements of the proposed energy storage control system.
In the case of the DFT, the delay dependence on the window length is appar-ent in all test cases. Without any closed loop mechanism, the DFT techniques will always have a delay in estimating a ramp. Nevertheless, the error (due to ripple) of the ramp estimation is excellent with minimal steady state ripple.
The DSOGI-FLL for a given bandwidth is able to track the ramp with low error, while also being closer to the actual ramp than the other techniques. Although the FLL suffers from non-zero steady state error for a ramp, compared to the DFT, the corresponding steady state error is lower for all bandwidths. Hence, we can state that for the estimation of ramp changes frequency, the DSOGI-FLL displays better overall performance.
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5.6.4 Comparison of Frequency Trending for Load Changes
Having compared the methods for step and ramp changes in frequency, the most important frequency variation in the context of this research is approached next. Our preliminary interest lies on estimating the frequency trend followed by changes in loading. The shape of a typical oscillatory speed trend occurring as a consequence of loading/shedding was explained in Chapter 3. Using the weak grid simulation model, a worst-case weak grid voltage profile was cre-ated, to be processed using the frequency detection techniques. This voltage contains the effects of the AVR, effects of the impedance in addition to the fre-quency variation. The methods are tested for two sets of cases i.e. when there is a comparable source impedance and when there is not, both in the presence of AVR effects.
(a)Case 1 (b)Case 2
(c)Case 3 (d)Case 4
Figure 5.30:Comparison of frequency detection techniques for Case 1,2,3,4 for a load change frequency trend without source impedance
For the case without the source impedance, there exists no instantaneous volt-age glitch, but the amplitude of the voltvolt-age is regulated by the AVR. A rated load (i.e. R = 20Ω) is used to create the frequency drop. Fig.5.30 presents the simulation results that estimates the characteristic frequency trend after
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ing.
The results obtained for the detected frequency closely resembles that observed for a ramp. The DSOGI-FLL provides a slightly better estimation with less over-all delay that that of the DFTs. A DFT with a Hamming over a Blackman win-dowing can also be recommended for higher bandwidths to minimise delay.
Next, a source impedance was introduced to the weak grid simulation as found in section 3.3.3 in chapter 3 , i.e. Ls = 22.5mH and Rs = 0.9Ω. With the volt-age waveform representing the complete worst-case weak grid voltvolt-age profile, the consequences of the instantaneous voltage glitch on frequency detection can now be observed. Fig.5.31 presents the results of the frequency estimation from the voltage profile. The results clearly exhibit an initial dip in the detected frequency, which was not present in the case without impedance in Fig.5.30.
(a)Case 1 (b)Case 2
(c)Case 3 (d)Case 4
Figure 5.31:Comparison of frequency detection techniques for Case 1,2,3,4 for a load change frequency trend with source impedance
All frequency detection techniques tested experience the initial dip in the esti-mated frequency. This is both due to the sudden change in voltage amplitude and the sudden phase shift in the voltage. A phase shift necessarily creates a change in frequency during that cycle despite the method used. This directly
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explains how the voltage glitch affects the DFT. The modified DFT processes the instantaneous phase difference in order to calculate the instantaneous fre-quency, meaning a phase jump directly affects the value calculated. While a similar manifestation of the phase jump occurs in the SRF-PLL and the DSOGI-FLL, these methods use the amplitude of the voltage in the frequency estima-tion algorithm. In SRF-PLL, it is replicated in the d-axis voltage prior to the loop-filter, whereas in the DSOGI-FLL, it is replicated in the QSG amplitude.
Since the voltage glitch/phase shift is self-recovering, the frequency dip in the estimation is self-recovering as can be seen in all test cases. The recovery time has a close relationship with the settling time chosen (i.e. bandwidth). For a given case, all four estimations recover the initial dip and follows the fre-quency trend. Hence, the recovery time is not helpful in distinguishing a better technique for the worst-case.
Consider the maximum dip experienced by the different techniques. The DSOGI-FLL dip is the smallest, whereas the SRF-PLL produces a similar dip if one ex-amines closely ignoring the ripple. The DFT methods make a larger dip because the dip settles quickly in the DFT algorithm. According to the fundamentals, the area under the frequency curve is equal to the phase difference. However, the area of the dip is equal to the phase-shift and is the same across all methods.
Hence, the dip height is inversely proportional to the dip duration.
Reviewing all methods for the worst-case voltage profile, one can see that none of the methods is capable of detecting the estimated frequency from the ini-tial erratic dip. Technically, the spurious frequency dip can cause the energy storage control to falsely activate early as it exploits the real time frequency to trigger the energy storage control. All methods erratically crosses the threshold frequency i.e.49 Hz, before the actual frequency crosses the threshold for the rated load. In the worst case, the initial dip can mimic a non existent frequency drop that is not necessary to be recovered by the energy storage. Due to this, the energy storage may respond and supply active power unnecessarily.
5.6.5 Comparison of Methods for Frequency Trending Using Optimum Bandwidths
In addition to the same bandwidth comparison, this section presents all the methods with their best parameters. Fig.5.32 shows the frequency response for a rated loading using all methods with their best parameters.
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(a)Without Impedance (b)With Impedance
Figure 5.32:Comparison of frequency detection techniques with their opti-mum parameters, for a load change in frequency with and without source impedance
According to Figs.5.32a and 5.32b, one is unable to take advantage of the ramp settling provided by the SRF-PLL due to its long settling time. Both DSOGI-FLL and DFTs estimate the frequency with a similar delay with similar ripple amplitude. Hence, with their optimum parameters, both DSOGI-FLL and the DFTs provide similar performance. The difference between the DSOGI-FLL and the DFTs can only be seen in the presence of source impedance in Fig. 5.32b.
The erratic dip of the DFT is three times as larger than that of the DSOGI-FLL.
In order to use the proposed energy storage control in weak grids, this erratic dip should either be eliminated or mitigated. A smoothing technique to flatten the dip is proposed in the next section.