Comparison of Transient Response based on Simulation

estimation, they have all been simulated by the PSCAD/EMTDC software in the simple grid configuration shown in Fig. 2-1, with the same parameters and conditions as listed in Table 3-1 and described in section 3.3.2. To limit the amount of results, only the amplitudes of the PNS Virtual Flux components, found by vector summation of the αβ-quantities will be compared. The PNS grid voltage components, |vg+| and |vg-|, imposed in the simulation model will be used as a reference to evaluate the transient response of the estimated Virtual Flux.

The simulations are, as expected, resulting in identical transient response for the structures from Fig. 3-4 and Fig. 3-5. Therefore, only results from the structure in Fig.

3-4 with DSOGI-based sequence separation of estimated Virtual Flux signals will be shown in the figures, labeled as |χ⁺|VF-PNS. Simulation results obtained with the structure proposed in [107] and shown in Fig. 2-7 will also be shown in the figures, labeled as

|ψ⁺|PNS-VF,LP2, to represent a configuration with sequence separation of voltage followed by individual estimation of PNS Virtual Flux components. It can be noted that the simulations showed identical transient response in the positive and negative sequence amplitudes resulting from DSOGI-VF estimation, labeled as |χ⁺|DSOGI-VF in the figurer as for DSOGI-based sequence separation of measured voltages. Thus, results from DSOGI-based synchronization to measured voltage are not included in the figures.

3.4.1.1 Comparison of transient response to unbalanced voltage sags for different PNS Virtual Flux Estimation methods

The resulting amplitudes of the PNS-VF components compared to the amplitude of the PNS voltages imposed to the simulation model are shown in Fig. 3-13 for the case when the voltage sag listed in Table 3-1 occurs. The figure shows that the PNS components of the Virtual Flux estimated by the structure from Fig. 3-4, plotted by blue lines in Fig. 3-13 have a significant overshoot and a settling time in the range of 30-40 ms. The method proposed in [107], plotted by green dashed lines, shows a slightly more damped response, due to the higher damping factor of the second order low-pass-filter from (2.11), and the speed of response is slightly increased by using un-filtered input signals together with the phase-shifted signals when carrying out the sequence separation. However, the speed of response for the estimation methods in Fig. 3-4 and Fig. 3-5 can also be improved in a similar way by using un-filtered signals instead of the band-pass filtered signals in the sequence separation, and the damping can be increased by increasing the gain parameter k in Fig. 3-1. However, the overshoot and relatively long settling time of these methods is mainly a consequence of the conventional approach of cascading 2^nd order filters used for both sequence separation and Virtual Flux estimation.

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58 NTNU 2012

A faster and more damped response of both the positive and negative sequence amplitudes is clearly achieved with the proposed DSOGI-VF estimation method from Fig. 3-6 as plotted by red dashed lines in Fig. 3-13. The observed rise time of about 5 ms, and the settling time around 20 ms, is in accordance with the characteristics of the SOGI-QSG as discussed in section 3.1.1.2. This is because the DSOGI-VF estimation method effectively reduces the positive and negative sequence Virtual Flux estimation to a second order system, as long as the grid frequency is constant.

As mentioned, the DSOGI-VF estimation shows exactly the same amplitude response as DSOGI-based sequence separation of measured voltages according to [52], as long as the parameters for the flux estimation are accurately identified and the input signals are purely sinusoidal. This is the case for both voltage-based and voltage-sensor-less operation of the DSOGI-VF estimation, since the sequence separation of the measured currents has the same dynamic response as the DSOGI-VF estimation, and since the subtraction of the current induced fluxes corresponds to an arithmetic operation without introducing additional dynamics.

3.4.1.2 Comparison of transient response in case of grid frequency variations for different Virtual Flux estimation methods

Fig. 3-14 shows the results when the estimation methods compared in Fig. 3-13 are exposed to a step in the grid frequency from 50 to 60 Hz during the unbalanced conditions. Although an unrealistic frequency change for real grid conditions, this case gives useful illustration of the properties of the different estimation methods.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

0.5 0.6 0.7 0.8 0.9 1 1.1

Positive sequence [pu]

|v_g⁺| |^+|_VF-PNS ^|^+|_PNS-VF,LP2 ^|^+|_DSOGI-VF

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-0.1 0 0.1 0.2 0.3 0.4

Time [s]

Negative sequence [pu]

|v_g^-| |^-|_VF-PNS ^|^-|_PNS-VF,LP2 ^|^-|_DSOGI-VF

Fig. 3-13 Transient response of PNS Virtual Flux amplitudes for different estimation methods when exposed to an unbalanced drop in grid voltage

3.4 Evaluation and Comparison of Methods for Virtual Flux Estimation under Unbalanced Conditions

Jon Are Suul 59

From the curves in Fig. 3-14, it can be clearly seen how the filter-based method for sequence separation and Virtual Flux estimation based directly on (2.11) is unable to estimate the correct amplitude when the grid frequency is different from the nominal frequency. This is because the filter will result in a gain unequal to unity and a phase shift unequal to −90° for signals with angular frequencies unequal to the nominal value ωb used in the design of the filter. As mentioned in [107], it is also possible to make the implementation of this estimation structure frequency-adaptive either by introducing a correction factor based on the deviation from the nominal grid frequency, or by updating the parameters of the digital implementation according to the variations in the grid frequency. This will however be more complicated than for the SOGI-QSG that is based on a structure specifically designed to be frequency-adaptive.

Since all the methods for Virtual Flux estimation and sequence separation based on SOGI-QSGs will be explicitly frequency-adaptive, the estimation method from Fig. 3-4 is reaching a new steady state after a transient period of about 120 ms. The settling time is however mainly influence by the dynamics of the grid frequency tracking and its interaction with the VF estimation.

The DSOGI-VF estimation from Fig. 3-6 shows a faster response and a significantly lower maximum deviation from the real grid voltage amplitude compared to what can be obtained with the methods from Fig. 3-4 and Fig. 3-5. This improvement in the dynamical response is mainly because cascaded operation of sequence separation and Virtual Flux estimation is avoided, since the reduced settling time of the DSOGI-VF estimation makes the FLL operate on signals that are reaching steady-state faster than for the cases with cascaded structures.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

0.4 0.5 0.6 0.7 0.8 0.9

Positive sequence [pu]

|v_g⁺| |^+|_VF-PNS ^|^+|_PNS-VF,LP2 ^|^+|_DSOGI-VF

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

-0.1 0 0.1 0.2 0.3 0.4

Time [s]

Negative sequence [pu]

|v_g⁺| |^+|_VF-PNS ^|^+|_PNS-VF,LP2 ^|^+|_DSOGI-VF

Fig. 3-14 Amplitudes of estimated PNS-VF components for different VF estimation methods when exposed to a step in the grid frequency

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60 NTNU 2012

3.4.2 Comparative Summary of Characteristics and Implementation