• Journal of Power Electronics
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• v.17 no.3
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• pp.756-765
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• 2017

The control of the power conversion system (PCS) in a battery energy storage system has a challenge due to the existence of grid impedance. This paper studies an impedance model of an LCL-based PCS in the d-q domain. The feature of a PCS connected to a weak grid is unveiled by use of an impedance model and a generalized Nyquist criterion. It is shown that the interaction between grid impedance and the PCS destabilizes the cascaded system in certain cases. Therefore, this paper proposes a novel control method that adopts virtual resistors to overcome this issue. The improvement in the control loop leads the PCS to a more stable condition than the conventional method. Impedance measurement is implemented to verify the correctness of the theoretical analysis. Experimental results obtained from a down-scaled prototype indicate that the proposed control method can improve the performance of the PCS under a weak grid.

• Journal of Power Electronics
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• v.18 no.2
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• pp.511-521
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• 2018

Proportional capacitor current feedback active damping (CCFAD) has a limited valid damping region in the discrete time domain as (0, $f_s/6$. However, the resonance frequency ($f_r$) of an LCL-type filter is usually designed to be less than half the sampling frequency ($f_s$) with the symmetry regular sampling method. Therefore, ($f_s/6$, $f_s/2$) becomes an invalid damping region. This paper proposes an improved CCFAD method to extend the valid damping region from (0, $f_s/6$ to (0, $f_s/2$), which covers all of the possible resonance frequencies in the design procedure. The full-valid damping region is obtained and the stability margin of the system is analyzed in the discrete time domain with the Nyquist criterion. Results show that the system can operate stably with the proposed CCFAD method when the resonance frequency is in the region (0, $f_s/2$). The performances at the steady and dynamic state are enhanced by the selected feedback coefficient H and controller gain $K_p$. Finally, the feasibility and effectiveness of the proposed CCFAD method are verified by simulation and experimental results.

• Journal of Power Electronics
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• v.16 no.1
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• pp.297-309
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• 2016

Grid-connected inverters (GCIs) with an LCL output filter have the ability of attenuating high-frequency (HF) switching ripples. However, by using only grid-current control, the system is prone to resonances if it is not properly damped, and the current distortion is amplified significantly under highly distorted grid conditions. This paper proposes a synchronous reference frame equivalent proportional-integral (SRF-EPI) controller in the αβ stationary frame using the parallel virtual resistance-based active damping (PVR-AD) strategy for grid-interfaced distributed generation (DG) systems to suppress LCL resonance. Although both a proportional-resonant (PR) controller in the αβ stationary frame and a PI controller in the dq synchronous frame achieve zero steady-state error, the amplitude- and phase-frequency characteristics differ greatly from each other except for the reference tracking at the fundamental frequency. Therefore, an accurate SRF-EPI controller in the αβ stationary frame is established to achieve precise tracking accuracy. Moreover, the robustness, the harmonic rejection capability, and the influence of the control delay are investigated by the Nyquist stability criterion when the PVR-based AD method is adopted. Furthermore, grid voltage feed-forward and multiple PR controllers are integrated into the current loop to mitigate the current distortion introduced by the grid background distortion. In addition, the parameters design guidelines are presented to show the effectiveness of the proposed strategy. Finally, simulation and experimental results are provided to validate the feasibility of the proposed control approach.

• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.136-144
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• 2016

Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.