We present a comprehensive investigation into a grid voltage control strategy for solar inverters, which traditionally operate with maximum power point tracking (MPPT) and do not participate in voltage regulation. As the penetration of distributed generation increases, solar inverters must assume a more active role in maintaining grid stability. The proposed strategy enables the solar inverter to continue injecting power even under suboptimal grid voltage conditions by dynamically adjusting its active and reactive power outputs based on an online estimation of the grid impedance ratio. This approach not only prevents overvoltage faults but also avoids unnecessary disconnection, thereby improving the overall efficiency and reliability of photovoltaic systems.
Photovoltaic Distributed Generation System
The system under study consists of photovoltaic panels, an energy harvesting converter implementing MPPT, and a solar inverter comprising a three-phase full-bridge switching network and a grid filter. The output power of the solar inverter depends on solar irradiance and the MPPT algorithm. The solar inverter controls the current injected into the grid to regulate its DC‑link voltage. Thus, the active power injected is determined by the energy collected by the front‑end converter. The proposed control strategy not only manages the active and reactive power of the solar inverter but also performs online estimation of the grid impedance ratio, which is used to dynamically set the power references.
Grid Voltage and Frequency Control Principles
In a resistive grid, voltage is primarily influenced by active power, whereas in an inductive grid, reactive power dominates. Traditional droop control equations are given for two extreme cases:
$$ R \ll X: \begin{cases} f – f_0 = -k_p (P – P_0) \\ V – V_0 = -k_q (Q – Q_0) \end{cases} $$
$$ X \ll R: \begin{cases} f – f_0 = +k_p (Q – Q_0) \\ V – V_0 = -k_q (P – P_0) \end{cases} $$
For a mixed grid where both R and X are significant, a generalized droop model can be derived:
$$ f – f_0 = -k_p \frac{X}{Z} (P – P_0) + k_q \frac{R}{Z} (Q – Q_0) $$
$$ V – V_0 = -k_p \frac{R}{Z} (P – P_0) – k_q \frac{X}{Z} (Q – Q_0) $$
These equations can be rearranged to express the required active and reactive power adjustments in terms of frequency and voltage 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 practical solar inverter applications, frequency deviations can be neglected because the inverter’s capacity is too small to influence the grid frequency, which is a global parameter set by large generators. Only the local voltage magnitude is considered. Let the grid impedance ratio be defined as:
$$ \alpha = \frac{R}{X} $$
Then we have:
$$ \frac{X}{Z} = \frac{1}{\sqrt{\alpha^2 + 1}} $$
$$ \frac{R}{Z} = \frac{\alpha}{\sqrt{\alpha^2 + 1}} $$
Substituting these into the voltage control equations and ignoring frequency terms yields the practical droop laws 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 both active and reactive power references depend on the online estimated impedance ratio α.
Active and Reactive Power Control Implementation
The control of the solar inverter is performed in a synchronous rotating d‑q reference frame synchronized with the point of common coupling (PCC) voltage. Hence, the voltage magnitude V equals the d‑axis component Vd, and Vq = 0. The instantaneous reactive power injected by the solar inverter is:
$$ Q(t) = -\frac{3}{2} V_d(t) i_q(t) $$
By combining this with the reactive power droop law, the q‑axis current reference becomes:
$$ i_{q,ref}(t) = \frac{2}{3} \frac{1}{\alpha(t)^2 + 1} \frac{1}{k_q} \left[1 – \frac{V_0}{V_d(t)}\right] $$
The solar inverter can both supply and absorb reactive power, thus it can either raise or lower the voltage at the PCC.
The active power injected by the solar inverter is normally equal to the MPPT power P0. However, under overvoltage conditions we can reduce the power drawn from the DC link by communicating with the energy harvesting converter. The active power reference is:
$$ P(t) = -\frac{\alpha(t)}{\alpha(t)^2 + 1} \frac{1}{k_p} \left[V_d(t) – V_0\right] + P_0(t) $$
Since the solar inverter can only reduce its active power below P0, this strategy only corrects overvoltage. Undervoltage is not the main focus as it is generally mitigated by load‑side reactive compensation. The proposed control effectively limits overvoltage to below 110% of the nominal value, allowing the solar inverter to remain grid‑connected.
Online Estimation of Grid Impedance Ratio
Accurate knowledge of the impedance ratio α is crucial for the droop controller. In low‑voltage distribution networks, α can vary widely (from 2 to 8). We adopt a non‑characteristic harmonic current injection method for online estimation. The solar inverter injects a 75 Hz harmonic current into the grid (the corresponding d‑q references contain a 25 Hz component). The injection lasts for 40 ms, and the voltage and current at the PCC are sampled at 3 kHz, yielding 120 samples. A discrete Fourier transform (DFT) with a base frequency of 25 Hz is performed to obtain the 3rd harmonic (75 Hz) components:
$$ V(3) = \frac{1}{N} \sum_{n=0}^{N-1} v(n) e^{-j\frac{2\pi}{N}3n} \quad (N=120) $$
$$ I_L(3) = \frac{1}{N} \sum_{n=0}^{N-1} i_L(n) e^{-j\frac{2\pi}{N}3n} $$
The grid impedance at 75 Hz is:
$$ Z_g(75\, \text{Hz}) = \frac{V(3)}{I_L(3)} = R_g(75) + jX_g(75) $$
To approximate the 50 Hz impedance, we use:
$$ Z_g(50\, \text{Hz}) \approx \Re\left[Z_g(75)\right] + j \frac{2\pi\cdot 50}{2\pi\cdot 75} \Im\left[Z_g(75)\right] $$
The impedance ratio is then computed as:
$$ \alpha = \frac{R_g(50)}{X_g(50)} $$
We validated this method through simulations and experiments. The table below summarizes the relative error of the online estimation under different actual α values from a simulation study:
| Actual α | Relative error of α estimation (%) | Relative error of R (%) | Relative error of X (%) |
|---|---|---|---|
| 0.5 | 45.2 | 88.5 | 2.3 |
| 1.0 | 8.7 | 12.4 | 1.8 |
| 2.0 | 4.1 | 5.6 | 1.5 |
| 4.0 | 3.2 | 4.1 | 1.2 |
| 8.0 | 22.5 | 28.0 | 1.6 |
The simulation shows that the estimation is most accurate for α between 1 and 5. For small α (highly inductive), the resistance estimation becomes poor; for large α (highly resistive), the reactance estimation remains good but the resistance error increases due to larger voltage drop across the resistor. In experiments, we observed a similar trend. To improve accuracy at high α, we increased the injected harmonic current amplitude. For example, when α = 7.64, injecting 0.5 A gave a relative error of 28%, while injecting 1.5 A reduced the error to below 10%.
Overall Grid Voltage Control Strategy for Solar Inverter
The complete control block diagram integrates the online impedance ratio estimator, the droop‑based active and reactive power controllers, and the current control loops. The impedance ratio estimator is triggered periodically (e.g., every 150 ms) or when a significant voltage change is detected. The harmonic injection lasts 40 ms, and the DFT computation updates α. This value feeds into the power reference calculations. The solar inverter then adjusts its output currents accordingly. The flowchart can be summarized as follows:
- Measure Vd and compute voltage deviation ΔV = Vd – V0.
- If ΔV > threshold, trigger impedance estimation (if not already recent).
- With the latest α, compute Pref and Qref using the modified droop equations.
- Limit Pref to ≤ P0 (only curtailment possible).
- Convert to d‑q current references via id,ref = (2/3)·(Pref/Vd) and iq,ref as derived earlier.
- Inner current controllers regulate id and iq.
Because the impedance ratio estimation can have significant errors at very high α, we introduced a linearization of the weighting factors:
$$ \frac{1}{\alpha^2+1} \rightarrow 1 – \frac{\alpha}{8} $$
$$ \frac{\alpha}{\alpha^2+1} \rightarrow \frac{\alpha}{8} $$
This reduces the sensitivity of the power reference to estimation errors when α is large. Experimental results confirmed that this modification preserves voltage control effectiveness.
Experimental Validation
We built a laboratory setup consisting of a 220 V three‑phase voltage source, programmable grid impedance (Rg and Xg), a 2 kW load, and a 1 kW solar inverter fed by a 400 V/1 kW DC source. Two sets of experiments were performed for each grid impedance ratio: one without the proposed voltage control (the solar inverter runs at MPPT) and one with the control active. The table below shows the PCC voltage (pu) for different α values:
| Grid impedance ratio α | Voltage (pu) without control | Voltage (pu) with control | Improvement (%) |
|---|---|---|---|
| 0.5 | 1.18 | 1.07 | 48.2 |
| 1.0 | 1.15 | 1.06 | 42.5 |
| 2.0 | 1.12 | 1.05 | 36.3 |
| 4.0 | 1.09 | 1.04 | 25.0 |
| 6.0 | 1.07 | 1.03 | 19.4 |
| 8.0 | 1.06 | 1.02 | 16.7 |
Without the proposed strategy, the voltage frequently exceeded 1.10 pu for α below 4, triggering protection disconnection. With the proposed control, the voltage remained below 1.10 pu in all tested cases. The relative improvement (reduction of overvoltage magnitude) was greater for smaller α (about 40% improvement) and still significant for larger α (about 20% improvement). The solar inverter therefore remained connected and continued to deliver power, albeit at a slightly reduced level during overvoltage events.
Conclusions
We have developed a grid voltage control strategy for solar inverters that relies on online estimation of the grid impedance ratio. By dynamically adjusting the active and reactive power injections according to the estimated R/X ratio, the solar inverter effectively mitigates overvoltage conditions without disconnecting from the grid. The impedance estimation method based on harmonic injection and DFT provides sufficient accuracy over a wide range of grid conditions, especially when the impedance ratio is moderate. Experimental results demonstrate that the proposed method can keep the PCC voltage below 110% of the nominal value, enabling continuous operation of the solar inverter even under high solar irradiance and light load. Future work will focus on a deeper theoretical analysis of the estimation error versus grid impedance characteristics and on the quantitative relationship between solar inverter capacity and voltage control effectiveness.