# Grid Impedance Estimation with Large SCR Disturbances based on Grid-Forming Converter

Wentao Liu, Anant Narula, Massimo Bongiorno, Jan R Svensson

► To cite this version:

Wentao Liu, Anant Narula, Massimo Bongiorno, Jan R Svensson. Grid Impedance Estimation with Large SCR Disturbances based on Grid-Forming Converter. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0327. hal-05073814

HAL Id: hal-05073814

https://utc.hal.science/hal-05073814v1

Submitted on 19 May 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Grid Impedance Estimation with Large SCR Disturbances based on Grid-Forming Converter

Wentao Liu¹, Anant Narula¹, Massimo Bongiorno¹ and Jan R. Svensson²

¹CHALMERS UNIVERSITY OF TECHNOLOGY, SE-412 96, Göteborg, Sweden

²HITACHI ENERGY, SE-721 82, Västerås, Sweden

Tel.: +46-317721000.

E-Mail: [wentaol@chalmers.se](mailto:wentaol@chalmers.se), [anant.narula@chalmers.se](mailto:anant.narula@chalmers.se), [massimo.bongiorno@chalmers.se](mailto:massimo.bongiorno@chalmers.se), [jan.r.svensson@hitachienergy.com](mailto:jan.r.svensson@hitachienergy.com)

URL: [https://www.chalmers.se/en/departments/e2/](https://www.chalmers.se/en/departments/e2/)

## Keywords

«Estimation technique», «Power system stability», «Grid-forming converter», «Converter control».

## Abstract

Grid-Forming (GFM) converters face significant synchronization challenges when suddenly exposed to ultra-weak grid conditions, primarily due to the lack of prior knowledge about grid impedance. This paper proposes a passive method for estimating grid impedance during large disturbances caused by a substantial reduction in the grid short-circuit ratio (SCR). The proposed method relies solely on local measurements, specifically the point of common coupling (PCC) voltage and output power. By dynamically adjusting the active power reference based on these estimates, GFM converters can maintain synchronization even under extremely low SCR conditions, well below 1. This method has been validated through experimental results.

## Introduction

Grid-Forming (GFM) control is emerging as a promising alternative to grid-following control for grid-connected converters, particularly in renewable energy applications [1]. GFM control offers notable advantages, such as enhanced stability in weak grid conditions and robust voltage and frequency support during grid faults and frequency disturbances [2]. Despite these benefits, existing conventional fault ride-through control strategies often assume adequate power transfer capability in the connected grid network. However, GFM converters face challenges like loss of synchronization (LOS) when subjected to

ultra-weak grid conditions, such as sudden tripping of a primary transmission line that significantly limits the grid transmission capability. To mitigate the risk of LOS, an accurate estimation of the grid impedance is crucial, as it directly reflects the remaining power transmission capabilities of the grid.

The existing grid impedance estimation methods are generally classified into three categories: active, quasi-passive and passive approaches. Active methods estimate online grid impedance by injecting non-fundamental frequency signals, such as 75 Hz [3] or 630 Hz [4], into the grid and analyzing the response of the grid. While these methods are effective and do not rely on natural grid disturbances, the additional signal injection may deteriorate power quality and conflict with grid codes [5]. Moreover, active estimations are suitable only for steady-state conditions, facing challenges during transient events.

Quasi-passive methods, on the other hand, estimate grid impedance by introducing controlled variations in the converter's active and reactive power references. For instance, some approaches use multiple steady-state operating points to determine impedance [6], however, this estimation condition is hard to obtain during the grid SCR drops. Another approach measures the step responses of active and reactive power during the PQ tracking process [7], but this typically assumes a constant grid frequency, which may not hold under fluctuating grid conditions.

Passive methods, in contrast, rely on naturally occurring disturbances or the system's normal steady-state operation, eliminating the need for additional signal injection as well. This category can be further divided into two subsets based on the presence or absence of disturbances. The first
<figure><img src="image_2.png" /><figcaption>Fig. 1: Diagram of grid-forming (GFM) converter with its control structure.</figcaption></figure>

subset, purely passive methods, includes observer-based [8] and Kalman filter-based [9] approaches. These methods estimate impedance using system state information during steady-state operation, avoiding any disruption to the grid. However, the tuning of observer and Kalman filter parameters is quite challenging. The second subset focuses on leveraging naturally occurring disturbances, such as sudden short-circuit ratio drops. For instance, [10] estimates impedance using the angle-increasing information generated by the active power control loop of a GFM controller during a grid event. While effective, these methods often assume a fixed grid frequency, limiting their applicability in grids with variable frequency.

Above all, there remains a research gap in the grid impedance estimation during large grid short-circuit ratio (SCR) drops, particularly when the SCR falls well below 1. To address this challenge, this paper proposes a passive method for grid impedance estimation based solely on local measurements, including power and voltage at the point of common coupling (PCC). Using the estimated grid impedance, the GFM controller can effectively adjust its active power reference ensuring synchronization under ultra-weak grid conditions.

# Fundamentals

## Basic GFM Control

To operate a GFM converter as a reliable voltage source behind an output inductor, this work adopts the virtual admittance-based GFM controller as described in [2] with the implementation depicted in Fig. 1. Measurements of active power ($P_s$), reactive power ($Q_s$) and output voltage ($u_s$) are fed into Active Power Loop (APL) Control and AC Voltage Control (AVC)

<table><caption>Table I: SYSTEM PARAMETERS</caption><thead><tr><th>Items</th><th>SI</th><th>p.u.</th></tr></thead><tbody><tr><td>Apparent Power S<sub>b</sub></td><td>1000 VA</td><td>1</td></tr><tr><td>Line voltage (RMS) U<sub>b</sub></td><td>100 V</td><td>1</td></tr><tr><td>Line frequency f<sub>g</sub></td><td>50 Hz</td><td>1</td></tr><tr><td>DC-side voltage U<sub>dc</sub></td><td>300 V</td><td>3</td></tr><tr><td>Rated current I<sub>b</sub></td><td>10 A</td><td>1</td></tr><tr><td>Filter inductance L<sub>f</sub></td><td>5 mH</td><td>0.157</td></tr><tr><td>Filter capacitance C<sub>sh</sub></td><td>30 μF</td><td>0.094</td></tr><tr><td>Grid inductance, SCR = 4</td><td>8 mH</td><td>0.251</td></tr><tr><td>Grid inductance, SCR = 0.8</td><td>40 mH</td><td>1.256</td></tr></tbody></table>

modules, which generate virtual-back electromotive force (EMF) vector $u_{EMF}$ based on respective limiter algorithms: Active Power Limiter and Voltage Limiter [2]. $P_{ref}$ is the active power reference and $P_{ref\_lim}$ is the limited value of $P_{ref}$. The virtual admittance-based current control module produces the final PWM signals. For more details on the GFM implementation, please refer to [2].

The voltage vectors at Bus 1 (PCC) and Bus 2 are expressed as $U_s \angle \theta_1$ and $U_g \angle \theta_2$, respectively. The power angle between the two Buses is represented by $\delta = \theta_1 - \theta_2$. The power flow through the grid impedance ($Z_g = R_g + jX_g$) is regulated by the difference between the two voltage vectors.

## LOS under an Ultra-Weak Grid

The steady-state active and reactive power transfer between Bus 1 and Bus 2 are expressed in equations (1) and (2), respectively.

$$P_s = \frac{U_s^2 R_g - U_s U_g R_g \cos \delta + U_s U_g X_g \sin \delta}{R_g^2 + X_g^2} \quad (1)$$

$$Q_s = \frac{U_s^2 X_g - U_s U_g R_g \sin \delta - U_s U_g X_g \cos \delta}{R_g^2 + X_g^2} \quad (2)$$

where $R_g$ and $X_g$ are the equivalent grid resistance and inductance. To simulate ultra-weak grid conditions, two equivalent parallel lines are considered, as shown in Fig. 1. The pre-disturbance grid equivalent impedance is given by $R_g + jX_g = (R_{g1} + jX_{g1}) \parallel (R_{g2} + jX_{g2})$. A low SCR is induced by tripping one of the transmission lines. Additionally, the grid SCR can be defined as

$$SCR = \frac{1}{Z_{g\_pu}} = \frac{1}{\sqrt{R_g^2 + X_g^2 / Z_b}} \quad (3)$$

where $Z_{g\_pu}$ is the per unit value of grid impedance, and $Z_b$ is the base value of the system. The larger the SCR value, the smaller the grid
impedance and the higher the power transmission capability, and vice versa.

Referring to the system parameters utilized in the lab, as listed in TABLE I and the R/X ratio = 0.1, the pre-disturbance grid transmission lines are set as, $L_{g1}$ = 40 mH and $L_{g2}$ = 10 mH. With an initial SCR of 4 and stable $U_s$, the power angle ($P-\delta$) curve in (1) is represented by the blue dashed line in Fig. 2(a). The blue point “a” indicates the steady-state operating point with $P_{ref}$ injection into the grid at a power angle of $\delta_0$. After tripping of $L_{g1}$, SCR falls to 0.8 and the increased grid equivalent impedance reduces the maximum transmission capability of the grid ($P_{max_new}$) corresponding to the peak of the red curve. Ignoring the phase jump at the transient moment, the operating point shifts from point “a” to point “b”, resulting in $P_s < P_{ref}$. To increase $P_s$, APC continuously increases the GFM frequency to expand $\delta$, as indicated by the brown arrows. However, since $P_{max_new}$ is always less than $P_{ref}$, the APL experiences uncontrollable frequency acceleration, eventually leading to LOS.

Suppose the GFM converter can quickly determine the value of $P_{max_new}$ during the SCR drop transient and select an appropriate new active power reference $P_{ref_new}$ as shown in Fig. 2(b). In this case, the GFM converter can stably operate at a new steady-state operating point “c”. According to (1), $P_{max_new}$ is mainly determined by grid impedance. Therefore, accurately estimating the post-disturbance grid impedance is crucial.

# Methodology

## Relationship between P and Q

Based on the grid structure in Fig. 1 and parameters listed in TABLE I, the transient waveforms of $P_s$ and $Q_s$ at Bus 1, when the system enters an ultra-weak grid condition, are illustrated in Fig. 3. It is important to note that the current limitation is disregarded here for explanatory purposes. In the subsequent experimental verification, the current limitation will be enabled. The grid SCR decreases from 4 to 0.8 at 1.5 s, while the active power reference, indicated by the dashed black line, remains constant and exceeds the maximum active power (marked in blue) following the transient event. As a result, the converter fails to reach the equilibrium point. The orange curve illustrates significant variations in $Q_s$, which, together with the changes in $P_s$, offers additional insights. Moreover, the PCC voltage, marked in green in Fig. 3, decreases

<figure><img src="image_3.png" /><figcaption>Fig. 2: Diagram of $P-\delta$ curves with SCR reduction. (a). Maintaining a constant active power reference $P_{ref}$. (b). Adjusting the active power reference to a new value $P_{ref_new}$.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3: Waveforms of active power, reactive power, and PCC voltage magnitude when SCR decreases from 4 to 0.8.</figcaption></figure>

slightly due to the droop control with a coefficient of $K_D$ = 0.01 p.u.

Assuming that the grid impedance remains constant after the SCR reduction, $R_g$ and $X_g$ for the post-disturbance grid structure are updated as new, unknown constants. By applying the parameter definitions in (6), the power equations in (1) and (2) can be reformulated as

$$P_s = \alpha U_s^2 - U_s U_g (\alpha \cos \delta - \beta \sin \delta) \quad (4)$$

$$Q_s = \beta U_s^2 - U_s U_g (\alpha \sin \delta + \beta \cos \delta) \quad (5)$$

$$\left\{ \begin{array}{l} \alpha = R_g / |Z_g|^2 \\ \beta = R_g / |Z_g|^2 \\ |Z_g| = \sqrt{R_g^2 + X_g^2} \end{array} \right. \quad (6)$$

From (4) and (5), $P_s$ and $Q_s$ are functions of the power angle $\delta$ and grid impedance. However, the $\delta$ is difficult to obtain in real-time operation. Noting the symmetry of the formulations of (4) and (5), by eliminating $\delta$, the relationship between $P_s$ and $Q_s$ can be further derived as
$$ (P_s - \alpha U_s^2)^2 + (Q_s - \beta U_s^2)^2 = \left( \frac{U_g U_s}{|Z_g|} \right)^2 \quad (7) $$

## Grid impedance estimation

From (7), it is seen that if the voltage magnitudes of both two buses remain constant, the trajectory of $P_s$ and $Q_s$ forms a circle with a centre at $(\alpha U_s^2, \beta U_s^2)$ and a radius of $U_g U_s / |Z_g|$. However, as noted, the voltage magnitude at Bus 1 is not constant during the transient, which causes variations in the circle centre and radius during the transient process. To mitigate its impact and account for the units, equation (7) is further reformulated.

$$ \left( \frac{P_s Z_b}{U_s^2} - \alpha Z_b \right)^2 + \left( \frac{Q_s Z_b}{U_s^2} - \beta Z_b \right)^2 = \left( \frac{U_g Z_b}{U_s |Z_g|} \right)^2 \quad (8) $$

$$ Z_b = \frac{U_b^2}{S_b} \quad (9) $$

where $U_b$, $S_b$, and $Z_b$ are the base values of system voltage, power and impedance, respectively. Those base values used in this work are listed in TABLE I. Equation (8) describes a circle, referred to as the quasi-power circle $C_{qp}$, with a constant centre $(\alpha Z_b, \beta Z_b)$ and a stable radius. By recording an adequate number of points of $(P_s Z_b / U_s^2, Q_s Z_b / U_s^2)$, it is possible to obtain the parameters of $C_{qp}$ through an appropriate fitting algorithm. Additionally, as the power angle gradually increases due to the inertia provided by the GFM controller, the instantaneous power ($P_{ins}$, $Q_{ins}$) at Bus 2 is close to the corresponding steady-state power ($P_s$, $Q_s$) at each operating instant during the transient [11]. Consequently, the power trajectory points are utilized for the circle $C_{qp}$ fitting.

$$ \left\{ \begin{aligned} P_{traj} &= P_{ins} Z_b / U_s^2 \\ Q_{traj} &= Q_{ins} Z_b / U_s^2 \end{aligned} \right. \quad (10) $$

Fig. 4 plots the trajectory of ($P_{traj}$ and $Q_{traj}$) labelled in black. It is observed that, after the SCR reduction, the operating point shifts from the initial point of (1, 0) to around (0.4, 0) and continuously moves along the path indicated by the purple arrows. The trajectory delineates a circular pattern on the plane, as described by (9). Hence, if the circle can be fitted using the prominent segment, exemplified by the red curve in Fig. 4, the centre of this circle can be calculated which is directly correlated with the grid impedance. Therefore, accurate circle fitting is crucial by utilizing real-time measurements.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Quasi-power circle fitting based on the trajectory of $P_{traj}$ vs $Q_{traj}$.</figcaption></figure>

Additionally, as illustrated in the enlarged subfigure shown in Fig. 4, the transient process after the SCR drop can be divided into two stages. Stage I consists of both power jumps and oscillations which can be regarded as electromagnetic transients. The fluctuations in converter output power during this stage can be stabilized in a short period owing to the effective design of the GFM controller. In contrast, Stage II is characterized by the absence of significant power oscillations, the output power can be considered as steady-state operating points.

## Quasi-Power Circle Fitting

Note that upon entering ultra-weak grid conditions, the substantial increase in grid equivalent impedance results in a sudden reduction of converter output active power, as depicted in the $P_s$ curves shown in Fig. 3(a). Hence, the abrupt drop in $P_s$ can be an initial signal that prompts changes in the grid structure [11]. When the reduction of $P_s$, denoted as $\Delta P_s$, exceeds a predetermined threshold $\Delta P_{th}$, the measurement acquisition is triggered, and the time stamp is set as $t_0$. Using the recorded measurement of $U_s$, $P_{ins}$, and $Q_{ins}$, the quasi-power points ($P_{traj}$, $Q_{traj}$) can be calculated based on (11). Next, using a sliding window, the sum of squares error between pre- and post-filtering values of ($P_{traj}$, $Q_{traj}$) can be calculated as

$$ E_{stage1} = \sum \left[ \left( P_{traj} - P_f \right)^2 + \left( Q_{traj} - Q_f \right)^2 \right] \quad (12) $$

where $P_f$ and $Q_f$ are the sliding window filtered values of $P_{traj}$ and $Q_{traj}$, respectively. When $E_{stage1}$ falls below a predefined threshold $E_{th}$, the transient instant $t_1$ starts to enter Stage II. After time $t_1$, the algorithm records a bunch of ($P_{traj}$, $Q_{traj}$) points which are noted as

$$ \left\{ \begin{aligned} x_k &= P_{traj}(k) \\ y_k &= Q_{traj}(k) \end{aligned} \right. \quad (11) $$
where the subscript k represents the k-th recorded data in the time domain and $x_k$ and $y_k$ can form a set of coordinates. Considering that N sets of coordinates are recorded, two matrices X and Y can be designed as follows

$$X = \begin{bmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ \vdots & \vdots & \vdots \\ x_n & y_n & 1 \end{bmatrix}_{n \times 3} \quad Y = \begin{bmatrix} -x_1^2 - y_1^2 \\ -x_2^2 - y_2^2 \\ \vdots \\ -x_n^2 - y_n^2 \end{bmatrix}_{n \times 1} \quad (12)$$

The relationship between X and Y is

$$Y = X\lambda + \varepsilon \quad (13)$$

where $\lambda$ is a three-element column vector containing the required parameters of the fitted circle $C_{qp}$ and $\varepsilon$ represents the error term. To minimize the sum of squared residuals, i.e., $\|\varepsilon\|^2$, the least squares method can be adopted. Hence, $\lambda$ can be estimated by

$$\lambda = (X^T X)^{-1} (X^T Y) \quad (14)$$

Based on the estimated $\lambda = [\lambda_1, \lambda_2, \lambda_3]^T$, the fitted circle centre and radius can be calculated as

$$\begin{cases} x_{c\_est} = -\lambda_1/2, & y_{c\_est} = -\lambda_2/2 \\ r_{c\_est} = \sqrt{\lambda_1^2 + \lambda_2^2}/4 - \lambda_3 \end{cases} \quad (15)$$

Since the actual centre of the quasi-power circle is $(\alpha Z_b, \beta Z_b)$, with both coordinates being positive. Considering the grid transmission line is typically inductive (i.e., $X_g > R_g$), the estimated circle centre satisfies the following restraint.

$$y_{c\_est} > x_{c\_est} > 0 \quad (16)$$

where $x_{c\_est}$ and $y_{c\_est}$ denote the x-axis and y-axis coordinates of the centre of the fitted circle, respectively. Utilizing (6), (8) and (9), the grid impedance can be ultimately estimated as

$$\begin{cases} R_{g\_est} = x_{c\_est} Z_b / \sqrt{x_{c\_est}^2 + y_{c\_est}^2} \\ X_{g\_est} = y_{c\_est} Z_b / \sqrt{x_{c\_est}^2 + y_{c\_est}^2} \\ Z_{g\_est} = \sqrt{R_{g\_est}^2 + X_{g\_est}^2} \end{cases} \quad (17)$$

To alleviate the real-time computational burden associated with least square calculations and memory usage, the Recursive Least Square (RLS) method is employed [12]. Combine the estimated grid impedance with equation (8) and assuming a nominal grid voltage magnitude, the maximum active power transfer capability ($P_{max}$) of the new grid line structure can be calculated as

$$P_{max} = \frac{R_{g\_est}}{|Z_{g\_est}|^2} U_s^2 + \frac{1}{|Z_{g\_est}|} U_s \quad (18)$$

By adjusting the $P_{ref}$ to a new value slightly smaller than $P_{max}$, thereby creating an angle stability margin, the system can maintain stability after a large SCR drop disturbance.

## Experimental Validation

To validate the proposed grid impedance estimation method, the corresponding experiments are conducted utilizing the same system parameter listed in TABLE I. The grid-side voltage is generated by a controllable AC voltage source and the structure of the grid transmission line is configured as shown in Fig. 1. For the safety of the two-level GFM converter, it is operated with an effective current limitation, as referenced in [2], and the limited active power reference $P_{ref\_tim}$ is recorded instead of $P_{ref}$. Specifically, before the SCR drop disturbance, the system operates with two parallel lines (Line 1 consisting of a 40 mH inductor and Line 2 consisting of a 10 mH inductor). At one certain moment, Line 2 is tripped, leaving only Line 1 in operation. The system's transient performances with and without the active power reference adjustment are recorded and shown in Fig. 5 and Fig. 6, respectively.

In Fig. 5, at about 1.5 seconds, Line 2 tripped. The increased grid impedance results in a reduction of the converter's output current, as shown in Fig. 5(b), along with a noticeable drop in the active power curve in Fig. 5(d). The large difference between the output active power $P_s$ and its reference $P_{ref\_lim}$ prompts the APL to accelerate the converter frequency, as seen in the frequency curve in Fig. 5(c). As the power angle increases, both $P_s$ and $Q_s$ in Fig. 5(d) exhibit a similar upward trend as depicted in Fig. 3. Despite the dynamic reduced $P_{ref\_lim}$ being lower than the constant value of 1 p.u., the system is still unable to maintain synchronization following a large SCR drop. Therefore, it is crucial to provide a correct new active power reference $P_{ref\_new}$ in time during the transient period.

It is worth noting that the converter voltage magnitude remains stable during the transient process from 1.5s to 1.9s, which meets the requirement of the proposed grid impedance estimation method. With the estimated grid impedance, the active power reference can be
<figure><img src="image_6.png" /><figcaption>Fig. 5: Experimental transient of entering an ultra-weak grid condition without active power reference correction. (a). PCC voltage, (b) GFM converter output current, (c) frequency of GFM converter, and (d) limited active power reference, measured active and reactive power.</figcaption></figure>

correctly updated and the corresponding results are plotted in Fig. 6.

Similarly, at around 1.5 s, the power system enters an ultra-weak grid condition with SCR = 0.8. Unlike in Fig. 5, the estimation algorithm detects the active power drop when it exceeds the preset threshold $ΔP_{th} = 0.1$ p.u. The proposed grid impedance estimation then initiates, following the process outlined in Fig. 4. As the power angle increases, more and more useful quasi-power points ($P_{traj}$, $Q_{traj}$) are measured and the centre of the fitting circle gradually converges to a stable value, as depicted in Fig. 6(e). Based on equation (17), the grid impedance is estimated to be (0.95 + j12.97) Ω, which closely matches the actual value of the applied 40 mH inductor. Using equation (18), $P_{max}$ is calculated to be 0.81 p.u. based on the estimated grid impedance and is shown as a black dashed line in Fig. 6(d). To maintain angle stability, the new active power reference is set below $P_{max}$ (specifically, 0.85 × $P_{max}$ is selected in this work) and updated at 1.7 seconds, as indicated by the green curve in Fig. 6(d). Due to the activated current limiting control in the GFM controller [2], the active power limited reference is automatically reduced to safely ride through the transient. After the transient process, the system reaches a new steady-state point corresponding to the newly

<figure><img src="image_7.png" /><figcaption>Fig. 6: Experimental results of entering an ultra-weak grid condition with grid impedance estimation-based active power reference correction. (a). PCC voltage, (b) GFM converter output current, (c) frequency of GFM converter, (d) limited active power reference, measured active and reactive power, (e) fitted circle centre, and (f) real and estimated grid impedance.</figcaption></figure>

calculated $P_{ref_new}$. Overall, the experimental results verified the correctness and accuracy of the proposed grid impedance estimation and the capability of maintaining stability with an updated selected active power reference after a significant SCR drop disturbance.

## Conclusion

In this article, a novel passive grid impedance estimation method using local measurements from the connected Grid-Forming (GFM) converter under ultra-weak grid conditions is proposed. When the system experiences a significant drop in grid short-circuit ratio (SCR), the GFM converter risks losing synchronization due to the mismatched active power reference, which could be adjusted based on the prior knowledge of grid impedance. To address this
issue, we present an easily implementable passive
grid impedance estimation approach that utilizes
a fixed-centred quasi-power circle, leveraging the
correlation of active power and reactive power
variations of the PCC during transients. This
allows for the correct selection of a new active
power reference, enabling the GFM converter to
maintain synchronization while transitioning to a
new steady state. Experimental results
demonstrate the method's effectiveness and
accuracy.

References

[1]. R. Rosso, X. Wang, M. Liserre, X. Lu, and S. Engelken: Grid-forming converters: Control approaches, grid-synchronization, and future trends—A review, IEEE Open J. Ind. Appl., Vol. 2, pp. 93–109, 2021.

[2]. A. Narula, P. Imgart, M. Bongiorno, M. Beza, J. R. Svensson, and J.-P. Hasler: Voltage-Based Current Limitation Strategy to Preserve Grid-Forming Properties Under Severe Grid Disturbances, IEEE Open J. Power Electron., Vol. 4, pp. 176–188, 2023.

[3]. N. Mohammed, M. Ciobotaru, and G. Town: Fundamental grid impedance estimation using grid-connected inverters: A comparison of two frequency-based estimation techniques, IET Power Electron., Vol. 13, no. 13, pp. 2730–2741, 2020.

[4]. D. K. Alves, R. L. A. Ribeiro, F. B. Costa, T. O. A. Rocha, and J. M. Guerrero: Wavelet-based monitor for grid impedance estimation of three-phase networks, IEEE Trans. Ind. Electron., Vol. 68, no. 3, pp. 2564–2574, Mar. 2021.

[5]. M. K. De Meerendre, E. Prieto-Araujo, K. H. Ahmed, O. Gomis-Bellmunt, L. Xu, and A. Egea-Àlvarez: Review of local network impedance estimation techniques, IEEE Access, Vol. 8, pp. 213647–213661, 2020.

[6]. N. Mohammed, T. Kerekes, and M. Ciobotaru: An online event-based grid impedance estimation technique using grid-connected inverters, IEEE Trans. Power Electron., Vol. 36, no. 5, pp. 6106–6117, May 2021.

[7]. J. Sun, J. Yu, J. Qiu, and Y. Wang: Transient-responses-based grid impedance estimation for grid-forming converters, CEECT 2022, pp. 741–745.

[8]. R. Fantino, C. A. Busada, and J. A. Solsona: Grid impedance estimation by measuring only the current injected to the grid by a VSI with LCL filter, IEEE Trans. Ind. Electron., Vol. 68, no. 3, pp. 1841-1850, March 2021.

[9]. N. Hoffmann and F. Fuchs: Minimal invasive equivalent grid impedance estimation in inductive-resistive power networks using

extended Kalman filter, IEEE Trans. Power Electron., Vol. 29, no. 2, pp. 631–641, Feb. 2014.

[10]. Zhao, S., Sul, SK.: Real-time grid parameter estimation with grid-forming converters for robust synchronous power control. J. Power Electron., 159–170, 2024.

[11]. B. Pepper and D. Campos-Gaona: Impedance Estimation for Transient Stability Enhancement of Virtual Synchronous Machines, PEDG 2024, pp. 1-6.

[12]. A. Suárez, C. Blanco, P. García, Á. Navarro-Rodríguez and J. Manuel Cano Rodríguez: Grid impedance estimator for active multisource AC grids, IEEE Trans. Smart Grid, Vol. 14, no. 3, pp. 2023–2033, May 2023.