In this paper, we propose a wide-band oscillation suppression method for three-phase utility interactive inverters that adapts to changing oscillation modes. The proliferation of renewable energy sources, predominantly interfaced through power electronic converters like utility interactive inverters, has led to an increased risk of wide-band oscillations in modern power systems. These oscillations, stemming from dynamic interactions between multiple inverters and the grid impedance, can jeopardize system stability. Traditional mitigation methods, often based on impedance reshaping, are typically designed for a specific frequency band. Consequently, they fail when the grid condition changes, altering the dominant oscillation frequency (mode). Furthermore, reshaping the inverter’s output impedance over a broad frequency range to cover multiple potential oscillations can adversely affect its characteristics at other frequencies, potentially inducing new instabilities. Our method addresses these limitations by integrating a voltage feedforward path with a phase-corrected, phase-shift-free Finite Impulse Response (FIR) band-pass digital filter, enabling adaptive and minimally intrusive impedance reshaping targeted precisely at the evolving oscillation band.
The core structure of a grid-connected LCL-type utility interactive inverter equipped with the proposed oscillation suppression channel is considered. The standard control comprises a Phase-Locked Loop (PLL), a current controller in the synchronous reference frame (dq-frame), and an LCL filter. The novel suppression channel is added in parallel to the current control loop. It processes the d- and q-axis components of the point of common coupling (PCC) voltage. First, a custom-designed FIR band-pass filter extracts only the frequency components within the real-time oscillation band without introducing phase shift—a critical feature achieved by using a band-stop filter implementation. This filtered signal is then fed into a voltage feedforward transfer function block, \(K_{cv}(s)\). The output of this block is injected into the current controller’s output, effectively modifying the modulating signal to the PWM generator. This injection aims to reshape the output impedance of the utility interactive inverter at the specific frequencies where oscillation is detected.
The analytical foundation lies in the sequence impedance modeling of the utility interactive inverter. Using the harmonic linearization approach, which decouples the frequency coupling effects introduced by the PLL and synchronous frame control, we derive the positive-sequence \(Z_{11}(s)\) and negative-sequence \(Z_{22}(s)\) output impedances. For a standard inverter without the suppression channel, the positive-sequence impedance can be expressed as:
$$
Z_{11}(s, f_p) = \frac{L_1 L_2 C s^3 + (L_1 + L_2 + K_c C L_2)s^2 + (K_{\text{dq}} + K_c C \omega_1)s + K_c K_{\text{dq}} \omega_1}{1 + L_1 C s^2 + K_c C s + K_c C F_{\text{pll}}(s \pm j\omega_1)\left[\frac{1}{2}(D_0 \pm j Q_0) – \frac{1}{2}(A_0 \pm j B_0)\right]}
$$
where \(L_1, L_2, C\) are LCL filter parameters, \(K_c\) is the capacitor current feedback gain, \(K_{\text{dq}}\) is the decoupling coefficient, \(\omega_1\) is the fundamental frequency, \(F_{\text{pll}}(s)\) is the closed-loop PLL transfer function, and \(D_0, Q_0, A_0, B_0\) are steady-state operating point quantities. A similar expression governs \(Z_{22}(s)\). The “±” signs correspond to the frequency shift effect (\(f_p – f_1\) or \(f_n + f_1\)). According to the impedance-based stability criterion, an oscillation is likely when the magnitude of the grid impedance matches that of the inverter impedance at a frequency where the phase difference exceeds 180°. Therefore, to prevent this, the proposed method aims to reshape the inverter’s impedance by making its magnitude very large (ideally infinite) within the oscillation band, thereby avoiding the critical intersection point.
The design of the voltage feedforward transfer function \(K_{cv}(s)\) is crucial for effective wide-band reshaping. The goal is to make the denominator of the inverter’s sequence impedance approach zero at a target frequency \(f_p\), which pushes its magnitude to infinity. The required \(K_{cv}(s)\) for the positive-sequence channel is derived as:
$$
K_{\text{cvp}}(s) = \frac{1 + L_1 C (s + j\omega_1)^2 + K_c C (s + j\omega_1) + K_c C F_{\text{pll}}(s)[…]}{U_1 (1 – F_{\text{pll}}(s))}
$$
This direct form contains complex coefficients due to the frequency-shifting effects of the dq-transformation. To implement this as a real-coefficient transfer function applicable over a range around \(f_p\), we introduce a transformation factor \(\lambda_p = s / (2\pi|f_p – f_1|)\). This factor approximates the imaginary unit \(j\) at the specific offset frequency \(|f_p – f_1|\), allowing the derivation of a realizable \(K_{cv1}(s)\). To simplify implementation (reduce order), the high-order numerator is separated. The dominant part, \(K_{cv1d}(s)\), used for lower frequency oscillations, is given by:
$$
K_{cv1d}(s) = \frac{L_1 C (s^2 – \omega_1^2) + K_c C s + K_c C F_{\text{pll}}(s) [\frac{1}{2}(D_0 – jQ_0) – \frac{1}{2}(A_0 – jB_0)]}{U_1 (1 – F_{\text{pll}}(s))}
$$
This transfer function, when activated, successfully reshapes the utility interactive inverter’s impedance by increasing its magnitude significantly within a band centered on the configured \(f_p\), as shown in the following comparison table of impedance magnitude at the target frequency:
| Condition | Impedance Magnitude at \(f_p\) (dB) | Phase Margin at \(f_p\) (degrees) |
|---|---|---|
| Without Suppression | 7.0 | -5 |
| With \(K_{cv1d}(s)\) Feedforward | > 40 | > 60 |
To achieve adaptive and minimal-interference operation, the oscillation suppression channel must only reshape the impedance in the frequency band where oscillation is currently present. This requires precise extraction of the oscillatory components from the PCC voltage signals \(u_d\) and \(u_q\). A standard digital band-pass FIR filter introduces a constant group delay, causing a phase shift in the filtered signal. This phase shift would misalign the corrective injection from the \(K_{cv}(s)\) block, rendering it ineffective or even destabilizing. Therefore, we design a phase-shift-free band-pass filter using a band-stop approach: \(U_{\text{bp}} = U_{\text{original}} – U_{\text{bs}}\), where \(U_{\text{bs}}\) is the output of a band-stop FIR filter with the same cutoff frequencies. This yields the band-pass signal \(U_{\text{bp}}\) without the group delay.
Furthermore, the sampling frequency \(F_s\) of this digital filter impacts the stability of the overall system when placed in the feedback path. A low \(F_s\) can introduce additional phase lag that reduces stability margins. The following table illustrates the impact on the system’s phase margin at the crossover frequency when using different filter sampling rates:
| FIR Filter Sampling Frequency (\(F_s\)) | System Phase Margin | Stability Status |
|---|---|---|
| 5 kHz | -5° | Unstable |
| 10 kHz | 8° | Low Margin |
| 100 kHz | 45° | Stable |
| 1 MHz | 48° | Stable |
To enable the use of a lower, more practical sampling frequency without compromising stability, a phase lead compensator is added after the FIR filter. The compensator has the form:
$$
G_{\text{lead}}(s) = \frac{1 + aT_{\text{lead}}s}{1 + T_{\text{lead}}s}, \quad (0 < a < 1)
$$
where \(T_{\text{lead}} = 1/(2\pi f_c)\) and \(f_c\) is the center frequency of the oscillation band. The parameter \(a\) controls the amount of phase boost. With proper tuning (e.g., \(a=0.1\), \(f_c\)=300 Hz for a mid-frequency oscillation), this compensator can restore adequate phase margin even with \(F_s = 5\) kHz, making the system stable. The complete adaptive oscillation suppression algorithm for the utility interactive inverter is summarized as follows:
- Monitor: Continuously monitor the PCC voltage of the utility interactive inverter.
- Detect & Analyze: Use a real-time detection algorithm (e.g., FFT or Prony analysis) to identify the dominant oscillation frequency \(f_{\text{osc}}\) and its amplitude.
- Adapt:
- Set the center frequency \(f_p\) of the voltage feedforward transfer function \(K_{cv1d}(s)\) to \(f_{\text{osc}}\).
- Set the passband of the phase-shift-free FIR filter to \([f_{\text{osc}} – \Delta f, \; f_{\text{osc}} + \Delta f]\), where \(\Delta f\) is a design bandwidth (e.g., 20-50 Hz).
- Adjust the parameters of the phase lead compensator \(G_{\text{lead}}(s)\) if necessary, based on the new \(f_c = f_{\text{osc}}\).
- Suppress: The updated channel now selectively reshapes the utility interactive inverter’s impedance only around \(f_{\text{osc}}\), injecting a damping signal to suppress the oscillation.
The effectiveness of the proposed method is rigorously validated through electromagnetic transient (EMT) simulations and Real-Time Laboratory (RTLAB) hardware-in-the-loop experiments. The simulation parameters for the utility interactive inverter are: Power Rating = 1.5 MW, DC Voltage \(U_{dc}\) = 1200 V, Grid Voltage \(U_g\) = 575 V (LL), LCL Filter: \(L_1\) = 0.08 pu, \(L_2\) = 0.08 pu, \(C\) = 0.3 pu, Switching Frequency = 1980 Hz, Current Controller: PI with \(k_{p}\) = 0.8, \(k_{i}\) = 100, PLL: PI with \(k_{p,\text{pll}}\) = 30, \(k_{i,\text{pll}}\) = 700.
First, the adaptability to grid impedance changes is tested. A weak grid condition is simulated by varying the grid inductance \(L_g\). Without suppression, different \(L_g\) values excite oscillations at different frequencies. The proposed channel, with its filter band and feedforward center frequency updated accordingly, successfully suppresses all cases. In contrast, a conventional fixed virtual impedance method fails to maintain suppression when \(L_g\) changes significantly. The results are summarized below:
| Grid Inductance (\(L_g\)) | Dominant Oscillation Freq. (No Suppression) | Conventional Virtual Impedance Result | Proposed Adaptive Method Result |
|---|---|---|---|
| 2 mH | 575 Hz | Partial Suppression, then re-oscillation | Fully Suppressed |
| 6 mH | 330 Hz | Partial Suppression, then re-oscillation | Fully Suppressed |
| 10 mH | 225 Hz | Very Poor Suppression | Fully Suppressed |
The necessity of the phase-shift-free filter and the phase lead compensator is also verified. Replacing our custom filter with a standard FIR band-pass filter (which has group delay) results in failed oscillation suppression. Similarly, disabling the phase lead compensator while using a low sampling frequency (5 kHz) also leads to instability or poor damping. With the compensator enabled, stable and effective suppression is achieved even at 5 kHz.
The method’s minimal interference characteristic is confirmed by examining the impedance spectrum. When the suppression channel is tuned for a specific band (e.g., 250-310 Hz), the utility interactive inverter’s impedance is dramatically increased only within that band, leaving its impedance characteristics at other frequencies virtually unchanged. This is a key advantage over broad-spectrum reshaping techniques.
The scalability to multi-inverter systems is investigated. Simulations with 2, 3, and 4 parallel utility interactive inverters show that the method remains effective. As more inverters are connected, the aggregate system impedance magnitude decreases, and the phase margin at the resonant frequency reduces, making the system more prone to oscillation at a lower frequency. The adaptive channel, installed in each inverter or a central damping device, successfully suppresses oscillations triggered by varying \(L_g\) in all multi-inverter scenarios. The RTLAB experiments further validate the practical feasibility of the method. For a single utility interactive inverter system, when \(L_g\) changes from 15 mH to 20 mH, the system without suppression becomes highly oscillatory or even unstable. With the proposed adaptive suppression channel enabled, the PCC voltage is stabilized and remains sinusoidal under both grid conditions. The test was successfully repeated for a two-inverter system.
In conclusion, we have proposed and validated an adaptive wide-band oscillation suppression method for utility interactive inverters. The core innovation lies in the synergistic combination of an analytically designed wide-band impedance reshaping feedforward transfer function and a phase-corrected, phase-shift-free FIR filter. This combination allows the suppression channel to dynamically track and target the specific frequency band of the dominant oscillation mode, which may shift due to changes in grid impedance or control parameters. Consequently, the utility interactive inverter’s output impedance is reshaped precisely where it is needed, providing robust damping against evolving oscillations while minimizing unwanted alterations to the inverter’s dynamics at other frequencies. This ensures stable integration of utility interactive inverters into increasingly complex and variable grid environments. Future work will focus on extending this method to inverter control structures that include outer power or voltage control loops and on optimizing the real-time oscillation detection and parameter adaptation logic for field deployment.