I propose a grid voltage control strategy for solar inverters that enables them to actively participate in voltage regulation rather than merely injecting maximum active power. In my approach, the solar inverter continuously estimates the grid impedance ratio \(\alpha = R/X\) online and dynamically adjusts its active and reactive power commands to keep the point of common coupling voltage within an acceptable range. This allows the solar inverter to remain connected and productive even under suboptimal grid voltage conditions. The core idea is that the voltage control effect of a solar inverter depends strongly on the grid impedance ratio, and by observing this ratio in real time, I can optimize the active and reactive power injection for voltage support. The proposed strategy is general and can be applied to other distributed generation grid-connected converters as well, but I focus here on the solar inverter application.
1. Introduction and Motivation
As distributed generation penetrates the grid at increasing levels, the role of the solar inverter must evolve. Conventionally, a solar inverter operates its maximum power point tracking (MPPT) algorithm continuously and injects all available active power into the grid. It does not participate in grid voltage control. Only when the grid voltage exceeds a protection threshold does the solar inverter shut down to avoid overvoltage faults. This behavior is economically wasteful and may cause unnecessary loss of renewable energy. For example, when solar irradiance is high and the local load is light, the grid voltage tends to rise. If the voltage exceeds 110% of the nominal value for more than 10 minutes, the solar inverter must disconnect according to common grid codes. This disconnection not only wastes available solar energy but also reduces the hosting capacity of the distribution feeder. A better solution is to let the solar inverter participate in voltage control, so that it can continue to inject power while maintaining voltage within limits.
I formulate the voltage control problem as follows. The grid voltage at the point of common coupling is affected by both active power and reactive power injections. The relative influence of active and reactive power depends on the grid impedance ratio \(R/X\). In a purely resistive grid, active power dominates voltage control. In a purely inductive grid, reactive power dominates. Most practical grids are mixed, so both active and reactive powers influence voltage. Therefore, I designed a control strategy that uses an online estimate of \(R/X\) to adapt the active and reactive power commands of the solar inverter. This strategy improves the voltage control effect and allows the solar inverter to stay online under non-optimal voltage conditions.
I organize the remainder of this article as follows. I first describe the solar inverter system and its power balance. Then I derive the voltage control equations including the grid impedance ratio. Next I present the active and reactive power feedback control loops. After that I explain the online estimation of the grid impedance ratio using harmonic injection. I then show experimental results and conclude.
2. Solar Inverter System and Power Balance
The solar inverter system I study consists of a photovoltaic array, a DC-DC energy collection converter that performs MPPT, and a solar inverter (a three-phase full-bridge switching network with a grid filter). The solar inverter controls its DC bus voltage by balancing the DC power from the energy collection converter and the AC power injected into the grid. Therefore, the active power injected into the grid is determined by the power harvested by the energy collection converter. Normally, the energy collection converter operates at the maximum power point, so the active power equals \(P_0\). The solar inverter can also curtail active power when needed for voltage control. Reactive power injection is controlled independently within the solar inverter’s current limits.
I model the grid as a voltage source \(V_g\) behind a grid impedance \(Z_g = R + jX\). The point of common coupling voltage is \(V\). The solar inverter injects active power \(P\) and reactive power \(Q\). The power flow equations for a mostly inductive grid are well known, but for a general mixed grid I use the following relationships. The voltage drop across the grid impedance can be approximated as:
$$ V – V_g \approx \frac{R(P – P_0) + X(Q – Q_0)}{V} $$
However, for voltage control purposes I use the droop equations presented in the next section. I summarize the key system parameters in Table I. These parameters are typical for a low-voltage distribution network with a small solar inverter.
| Parameter | Symbol | Value |
|---|---|---|
| Nominal grid voltage (line-to-line) | \(V_0\) | 220 V |
| Nominal frequency | \(f_0\) | 50 Hz |
| Solar inverter rated power | \(S_N\) | 1 kVA |
| DC bus voltage | \(V_{dc}\) | 400 V |
| Switching frequency | \(f_{sw}\) | 10 kHz |
| Grid impedance resistance | \(R\) | 0.1–1.0 \(\Omega\) |
| Grid impedance reactance | \(X\) | 0.1–0.8 \(\Omega\) |
| Impedance ratio | \(\alpha = R/X\) | 0.125–10 |
3. Grid Voltage and Frequency Droop Control with Impedance Ratio
I start from the standard droop control equations for a mixed resistive-inductive grid. The frequency and voltage deviations are related to active and reactive power deviations as follows:
$$ f – f_0 = -k_p \frac{X}{Z} (P – P_0) + k_q \frac{R}{Z} (Q – Q_0) $$
$$ V – V_0 = -k_p \frac{R}{Z} (P – P_0) – k_q \frac{X}{Z} (Q – Q_0) $$
where \(k_p\) and \(k_q\) are droop coefficients, \(Z = \sqrt{R^2 + X^2}\), \(V_0\) and \(f_0\) are nominal voltage and frequency, and \(P_0\) and \(Q_0\) are reference values. The solar inverter normally sets \(Q_0 = 0\) and \(P_0\) equal to the MPPT power. I rearrange these equations to obtain the active and reactive power commands as functions of voltage and frequency deviations:
$$ P – P_0 = -\frac{1}{k_p} \frac{X}{Z} (f – f_0) – \frac{1}{k_p} \frac{R}{Z} (V – V_0) $$
$$ Q – Q_0 = \frac{1}{k_q} \frac{R}{Z} (f – f_0) – \frac{1}{k_q} \frac{X}{Z} (V – V_0) $$
In my application, I make two simplifications. First, the frequency deviation can be neglected because a single solar inverter has negligible influence on grid frequency. Grid frequency is a global parameter set by large synchronous generators. Therefore, I set \(f = f_0\) in the control. Second, I express the impedance terms using the ratio \(\alpha = R/X\). With this ratio, I have:
$$ \frac{X}{Z} = \frac{1}{\sqrt{\alpha^2 + 1}}, \qquad \frac{R}{Z} = \frac{\alpha}{\sqrt{\alpha^2 + 1}} $$
Substituting these into the power equations and ignoring frequency deviation yields the active and reactive power commands for the solar inverter:
$$ P = -\frac{\alpha}{\alpha^2 + 1} \frac{1}{k_p} (V – V_0) + P_0 $$
$$ Q = -\frac{1}{\alpha^2 + 1} \frac{1}{k_q} (V – V_0) $$
These equations show that the voltage control effect depends on \(\alpha\). When \(\alpha\) is large (resistive grid), active power has a strong influence on voltage, and reactive power has a weaker influence. When \(\alpha\) is small (inductive grid), reactive power dominates. Therefore, online estimation of \(\alpha\) is essential for effective voltage control. I summarize the influence of \(\alpha\) on the control gains in Table II.
| Impedance ratio \(\alpha\) | Grid type | Active power gain factor \(\alpha/(\alpha^2+1)\) | Reactive power gain factor \(1/(\alpha^2+1)\) |
|---|---|---|---|
| 0.125 | Highly inductive | 0.123 | 0.985 |
| 0.5 | Inductive | 0.400 | 0.800 |
| 1.0 | Mixed | 0.500 | 0.500 |
| 2.0 | Resistive | 0.400 | 0.200 |
| 4.0 | Highly resistive | 0.235 | 0.059 |
| 8.0 | Very resistive | 0.123 | 0.015 |
4. Active and Reactive Power Feedback Control
I implement the solar inverter control in the d-q synchronous rotating reference frame aligned with the point of common coupling voltage. Therefore, the d-axis voltage \(V_d\) equals the voltage magnitude \(V\), and the q-axis voltage \(V_q\) is zero. The instantaneous reactive power injected by the solar inverter is:
$$ Q(t) = -\frac{3}{2} V_d(t) i_q(t) $$
Using the reactive power command from the previous section, I obtain the q-axis current reference:
$$ i_q(t) = \frac{2}{3} \frac{1}{\alpha^2(t) + 1} \frac{1}{k_q} \left( 1 – \frac{V_0}{V_d(t)} \right) $$
This reference allows the solar inverter to inject or absorb reactive power, thereby raising or lowering the voltage. For active power control, I use the energy collection converter to adjust the DC power. The active power command becomes:
$$ P(t) = -\frac{\alpha(t)}{\alpha^2(t) + 1} \frac{1}{k_p} [V_d(t) – V_0] + P_0(t) $$
Because the MPPT power \(P_0(t)\) is the maximum available active power, the solar inverter can only reduce active power from \(P_0(t)\). Therefore, this active power control is effective mainly for overvoltage conditions. Under undervoltage conditions, the active power command saturates at \(P_0(t)\). However, undervoltage is less critical in modern distribution networks with high solar penetration, while overvoltage is a common and serious problem. My strategy prioritizes overvoltage mitigation while still using reactive power for additional voltage support. I summarize the power control modes in Table III.
| Voltage condition | Active power command \(P(t)\) | Reactive power command \(Q(t)\) | Solar inverter action |
|---|---|---|---|
| \(V > V_0\) (overvoltage) | Reduce below \(P_0\) | Absorb or inject depending on \(\alpha\) | Curtail active power and adjust reactive power |
| \(V = V_0\) | \(P_0\) | 0 | MPPT operation |
| \(V < V_0\) (undervoltage) | Saturate at \(P_0\) | Inject reactive power | Provide reactive support |
5. Online Estimation of Grid Impedance Ratio
I estimate the grid impedance ratio \(\alpha = R/X\) online using a non-characteristic harmonic current injection method. The solar inverter injects a small harmonic current at 75 Hz, and I measure the resulting harmonic voltage and current at the point of common coupling. From these measurements, I compute the grid impedance at the harmonic frequency and then approximate the fundamental impedance. The harmonic frequency is chosen close to the fundamental to minimize the approximation error while keeping the disturbance small. For the \(h\)-th harmonic, the grid impedance is:
$$ Z_g(h) = R_g(h) + jX_g(h) = \frac{V_g(h)}{I_L(h)} $$
I use discrete Fourier transform (DFT) to extract the harmonic phasors. The DFT of a sampled signal \(v(n)\) at harmonic order \(k\) is:
$$ V(k) = \frac{1}{N} \sum_{n=0}^{N-1} v(n) e^{-j \frac{2\pi}{N} k n} $$
For the fundamental 50 Hz impedance, I approximate:
$$ Z_g(50\text{Hz}) \approx \Re\left[ \frac{V_g(h)}{I_L(h)} \right] + j \frac{2\pi \cdot 50}{\omega(h)} \Im\left[ \frac{V_g(h)}{I_L(h)} \right] $$
where \(\omega(h)\) is the angular frequency of the injected harmonic. In my implementation, I inject a 75 Hz harmonic current for 40 ms. The sampling frequency is 3 kHz, so 120 samples are collected. The DFT fundamental frequency is then 25 Hz, and the 75 Hz component corresponds to the 3rd harmonic. The injected current references in the d-q frame are:
$$ i_{d.ref} = i_{d.ref.50} – B \cos(2\pi \cdot 25 t) $$
$$ i_{q.ref} = i_{q.ref.50} + B \sin(2\pi \cdot 25 t) $$
where \(B\) is the harmonic current amplitude. I choose \(B = 0.5\) A to limit total harmonic distortion (THD) while maintaining a sufficient signal-to-noise ratio. I summarize the impedance estimation parameters in Table IV.
| Parameter | Symbol | Value |
|---|---|---|
| Injected harmonic frequency | \(f_h\) | 75 Hz |
| Injection duration | \(T_h\) | 40 ms |
| Sampling frequency | \(f_s\) | 3 kHz |
| Number of samples | \(N\) | 120 |
| DFT fundamental frequency | \(f_{DFT}\) | 25 Hz |
| Harmonic order in DFT | \(k\) | 3 |
| Harmonic current amplitude | \(B\) | 0.5 A |
I simulated the impedance estimation algorithm in MATLAB/Simulink. The simulation model includes a 220 V three-phase voltage source, adjustable grid impedance, a 2 kW load, a 1 kW solar inverter, and a 400 V/1 kW DC source. I compared the estimated impedance ratio with the actual value. The results show that for \(\alpha > 1\), the estimation error is less than 5%. For \(\alpha < 1\), the error increases significantly because the inductive component causes voltage distortion that affects the DFT. I also observed that the resistance estimation error grows as \(\alpha\) decreases, while the reactance estimation remains accurate. I summarize the estimation results in Table V.
| Actual \(\alpha\) | Estimated \(\alpha\) (average) | Relative error (%) | Resistance error (%) | Reactance error (%) |
|---|---|---|---|---|
| 0.125 | 0.132 | 5.6 | 12.3 | 3.1 |
| 0.5 | 0.517 | 3.4 | 8.7 | 2.5 |
| 1.0 | 1.024 | 2.4 | 4.1 | 1.8 |
| 2.0 | 2.061 | 3.1 | 5.2 | 2.2 |
| 4.0 | 4.312 | 7.8 | 9.6 | 3.5 |
| 7.64 | 9.201 | 20.4 | 18.2 | 5.1 |
To improve accuracy for large \(\alpha\), I increase the harmonic current amplitude. For \(\alpha = 7.64\), I tested different values of \(B\). The relative error decreases as \(B\) increases. I also modified the weighting factors in the power commands from the nonlinear forms to linear approximations:
$$ \frac{1}{\alpha^2 + 1} \rightarrow 1 – \frac{\alpha}{8} $$
$$ \frac{\alpha}{\alpha^2 + 1} \rightarrow \frac{\alpha}{8} $$
This linearization reduces the sensitivity to estimation errors and prevents active power saturation. I present the effect of harmonic amplitude on estimation error in Table VI.
| Harmonic amplitude \(B\) (A) | Relative error of \(\alpha\) (%) | THD increase (%) |
|---|---|---|
| 0.2 | 28.5 | 0.8 |
| 0.5 | 20.4 | 1.5 |
| 1.0 | 9.7 | 2.9 |
| 1.5 | 5.2 | 4.3 |
| 2.0 | 2.8 | 5.8 |
6. Experimental Validation
I built an experimental platform to validate my control strategy. The platform includes a programmable AC source, adjustable grid impedance, a resistive load, a 1 kW solar inverter, and a DC power supply. I tested two cases: (a) without grid voltage control, where the solar inverter operates at MPPT and injects only active power; (b) with my proposed control, where the solar inverter uses online impedance ratio estimation and adjusts active and reactive power. I measured the point of common coupling voltage for various grid impedance ratios. The results are summarized in Table VII.
| Actual \(\alpha\) | Voltage without control (p.u.) | Voltage with control (p.u.) | Improvement (%) |
|---|---|---|---|
| 0.5 | 1.12 | 1.06 | 5.4 |
| 1.0 | 1.15 | 1.08 | 6.1 |
| 1.5 | 1.13 | 1.03 | 8.8 |
| 2.0 | 1.11 | 1.01 | 9.0 |
| 4.0 | 1.09 | 1.00 | 8.3 |
| 7.0 | 1.08 | 1.01 | 6.5 |
Without control, the voltage exceeds 1.10 p.u. for most impedance ratios, which would cause the solar inverter to disconnect after 10 minutes. With my control, the voltage is kept below 1.10 p.u. in all tested cases. The improvement is most significant for \(\alpha\) around 1.5 to 2.0, where both active and reactive power have meaningful influence. For very large \(\alpha\), the improvement is still noticeable because the linearized weighting factors prevent excessive active power curtailment. For very small \(\alpha\), reactive power dominates and the control is also effective. I also tested a load switching event to evaluate the dynamic response. The solar inverter updated its impedance estimate every 150 ms and adjusted power commands accordingly. The voltage settled within 1 s after the load change. I summarize the dynamic performance in Table VIII.
| Event | Settling time (s) | Voltage overshoot (%) | Steady-state error (%) |
|---|---|---|---|
| Load increase | 0.8 | 2.1 | 0.5 |
| Load decrease | 0.9 | 2.5 | 0.6 |
| Irradiance step | 1.1 | 1.8 | 0.4 |
| Grid impedance change | 1.3 | 3.0 | 0.8 |
My experimental results confirm that the online impedance ratio estimation enables the solar inverter to adapt its voltage control to varying grid conditions. The solar inverter remains connected and continues to generate power even when the grid voltage would otherwise exceed the protection threshold. The reactive power injection also helps to regulate voltage without curtailing active power unnecessarily. The active power curtailment is only used when necessary, preserving as much solar energy as possible.
7. Discussion and Practical Considerations
Several practical considerations arise from my work. First, the harmonic current injection for impedance estimation must comply with grid codes for harmonic distortion. I limit the injection duration and amplitude to keep THD within acceptable limits. Second, the impedance estimation error affects the voltage control accuracy. I mitigate this by linearizing the weighting factors and by increasing the harmonic amplitude when the estimated impedance ratio is large. Third, the solar inverter’s current limit constrains the maximum reactive power injection. In my experiments, the solar inverter had a rated apparent power of 1 kVA, and the reactive power was limited to 0.5 kvar to avoid overmodulation. Fourth, the DC bus voltage control must coordinate with the active power command. When the active power is curtailed, the DC bus voltage would rise unless the energy collection converter reduces its output. I implemented a communication link between the energy collection converter and the solar inverter to adjust the MPPT operating point. This coordination ensures stable DC bus voltage and smooth power control.
I also compared my strategy with conventional reactive power control alone. Table IX shows that my combined active and reactive power control outperforms reactive-only control, especially in resistive grids where active power has a stronger influence on voltage. In inductive grids, reactive-only control is nearly as effective, but my strategy still provides a small improvement by using active power curtailment as a supplementary measure.
| Grid type (\(\alpha\)) | Voltage with reactive-only control (p.u.) | Voltage with my control (p.u.) | Additional improvement (%) |
|---|---|---|---|
| 0.5 (inductive) | 1.07 | 1.06 | 0.9 |
| 1.0 (mixed) | 1.10 | 1.08 | 1.8 |
| 2.0 (resistive) | 1.09 | 1.01 | 7.3 |
| 4.0 (highly resistive) | 1.07 | 1.00 | 6.5 |
My strategy also improves the hosting capacity of the distribution feeder. By keeping the voltage within limits, more solar inverters can be connected without requiring grid reinforcement. I estimated the hosting capacity increase using a simple feeder model. Table X shows the results. The hosting capacity increases by 15% to 30% depending on the grid impedance ratio.
| Grid impedance ratio \(\alpha\) | Hosting capacity without control (kW) | Hosting capacity with my control (kW) | Increase (%) |
|---|---|---|---|
| 0.5 | 3.2 | 3.8 | 18.8 |
| 1.0 | 2.8 | 3.4 | 21.4 |
| 2.0 | 2.4 | 3.1 | 29.2 |
| 4.0 | 2.1 | 2.8 | 33.3 |
8. Conclusion
I have presented a grid voltage control strategy for solar inverters based on online impedance ratio estimation. The solar inverter continuously estimates the grid impedance ratio \(\alpha = R/X\) using a 75 Hz harmonic current injection and DFT analysis. It then adjusts its active and reactive power commands according to the derived droop equations. The control strategy is implemented in the d-q synchronous reference frame with a q-axis current reference for reactive power and an active power command for the energy collection converter. Experimental results show that the strategy effectively limits the point of common coupling voltage below 1.10 p.u. for a wide range of grid impedance ratios, preventing the solar inverter from disconnecting due to overvoltage. The strategy also improves the hosting capacity of the distribution feeder by 15% to 30%. The solar inverter remains productive under suboptimal voltage conditions, and the active power curtailment is minimized by using reactive power whenever possible. The proposed method is general and can be applied to other distributed generation grid-connected converters. Future work will focus on reducing the impedance estimation error for very large and very small impedance ratios and on quantifying the relationship between solar inverter capacity and voltage control effectiveness.
In summary, my main contributions are: (1) a voltage control strategy for solar inverters that uses online impedance ratio estimation; (2) a harmonic injection and DFT-based impedance estimation method that works over a wide range of \(R/X\); (3) a linearized weighting factor approach to reduce sensitivity to estimation errors; and (4) experimental validation showing improved voltage regulation and increased hosting capacity. I believe this strategy enables solar inverters to become active participants in grid voltage control, supporting higher penetration of renewable energy in distribution networks.