The integration of distributed generation sources, such as photovoltaic (PV) systems, into the power grid has increased significantly in recent years. Traditionally, solar inverters operate using maximum power point tracking (MPPT) algorithms to inject as much active power as possible into the grid, without actively participating in grid voltage regulation. This passive approach can lead to voltage instability, especially in grids with high penetration of renewable energy. When grid voltage exceeds protective thresholds, solar inverters typically disconnect to avoid overvoltage faults, resulting in energy waste and reduced system reliability. To address this issue, this article proposes a novel grid voltage control strategy for solar inverters that leverages online estimation of grid impedance ratio. By dynamically adjusting the active and reactive power injection based on real-time impedance observations, the strategy enhances voltage control performance, allowing solar inverters to remain connected and contribute to grid stability even under suboptimal voltage conditions. The methodology is not limited to solar inverters but is also applicable to other distributed generation grid-connected converters.
The core principle underlying this strategy is that the effectiveness of grid voltage control depends heavily on the grid impedance ratio, defined as R/X, where R is the resistive component and X is the reactive component of the grid impedance. In resistive-dominated grids, voltage is primarily influenced by active power, while in inductive-dominated grids, reactive power plays a key role. For mixed impedance grids, both active and reactive power must be coordinated. The proposed control strategy continuously monitors the grid impedance ratio using an online estimation technique and adjusts the power outputs of the solar inverter accordingly. This approach mitigates overvoltage issues, prevents unnecessary disconnections, and improves overall grid power quality.
A typical PV distributed generation system consists of PV panels, a DC-DC converter for MPPT, and a grid-connected solar inverter with a three-phase full-bridge topology and an output filter. The solar inverter controls the current injected into the grid to maintain DC-link voltage stability, balancing the power from the PV panels and the grid. In conventional setups, the solar inverter operates at the MPPT point, injecting maximum active power with zero reactive power. However, this can exacerbate voltage fluctuations. The proposed system modifies this by incorporating grid voltage control loops that adjust both active and reactive power based on the online-estimated impedance ratio. This enables the solar inverter to act as a grid-supporting device, enhancing voltage regulation without compromising energy yield significantly.
The foundation of grid voltage and frequency control in distributed generation systems is the droop control method. The standard droop equations vary depending on the grid impedance characteristics. For grids where the reactance dominates (X >> R), the frequency and voltage droop equations are:
$$ f – f_0 = -k_p (P – P_0) $$
$$ V – V_0 = -k_q (Q – Q_0) $$
Conversely, for grids where resistance dominates (R >> X), the equations become:
$$ f – f_0 = +k_p (Q – Q_0) $$
$$ V – V_0 = -k_q (P – P_0) $$
In these equations, \(f\) and \(V\) are the measured grid frequency and voltage magnitude, \(f_0\) and \(V_0\) are their nominal values, \(P\) and \(Q\) are the active and reactive power outputs of the solar inverter, \(P_0\) is the active power at the MPPT point, \(Q_0\) is the reactive power reference (typically zero), and \(k_p\) and \(k_q\) are droop coefficients. For mixed impedance grids, a generalized form of the droop equations can be derived. By considering the grid impedance \(Z = R + jX\) and its ratio \(\alpha = R/X\), the voltage and frequency deviations can be expressed as:
$$ f – f_0 = -k_p \frac{X}{Z} (P – P_0) + k_q \frac{R}{Z} (Q – Q_0) $$
$$ V – V_0 = -k_p \frac{R}{Z} (P – P_0) – k_q \frac{X}{Z} (Q – Q_0) $$
Since grid frequency is a global parameter largely unaffected by distributed generators like solar inverters, we focus on voltage control and assume frequency deviations are negligible. Solving for \(P\) and \(Q\) yields the control 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 the active and reactive power references depend on the voltage deviation \((V – V_0)\) and the impedance ratio \(\alpha\). The terms \(\frac{\alpha}{\alpha^2 + 1}\) and \(\frac{1}{\alpha^2 + 1}\) act as weighting factors that determine the contribution of active and reactive power to voltage control. For accurate control, real-time knowledge of \(\alpha\) is essential, which necessitates online impedance estimation.
The control of active and reactive power in a solar inverter is implemented in the d-q synchronous reference frame aligned with the grid voltage at the point of common coupling (PCC). In this frame, the grid voltage vector is represented as \(V_d\) (magnitude) and \(V_q = 0\). The instantaneous reactive power \(Q(t)\) is given by:
$$ Q(t) = -\frac{3}{2} V_d(t) i_q(t) $$
where \(i_q(t)\) is the q-axis current. Substituting into the reactive power control equation, the q-axis current reference is derived:
$$ i_q(t) = \frac{2}{3} \frac{1}{\alpha(t)^2 + 1} \frac{1}{k_q} \left(1 – \frac{V_0}{V_d(t)}\right) $$
This allows the solar inverter to inject or absorb reactive power to regulate voltage. For active power control, the reference is obtained from the droop equation, but it is limited by the available power from the PV panels. The active power reference \(P(t)\) is:
$$ P(t) = -\frac{\alpha(t)}{\alpha(t)^2 + 1} \frac{1}{k_p} (V_d(t) – V_0) + P_0(t) $$
Here, \(P_0(t)\) is the maximum available power from the MPPT algorithm. If the grid voltage is below nominal (under-voltage), the required \(P(t)\) might exceed \(P_0\), causing saturation at \(P_0\). In such cases, the solar inverter primarily uses reactive power for voltage support. Over-voltage conditions are more critical for solar inverters, as they often lead to disconnection; thus, the control strategy prioritizes reducing active power to mitigate over-voltage, while utilizing reactive power as needed.
Online estimation of the grid impedance ratio is a critical component of this control strategy. The impedance ratio \(\alpha\) can vary widely in low-voltage distribution grids, typically ranging from 2 to 8, due to changes in load conditions and network topology. Various methods exist for grid impedance estimation, including offline, online, passive, and active techniques. Among these, an active steady-state online estimation method that injects a non-characteristic harmonic current has proven effective for solar inverters. Specifically, injecting a 75 Hz harmonic current (1.5 times the fundamental frequency) and performing discrete Fourier transform (DFT) analysis on the voltage and current signals enables accurate estimation of the impedance at the fundamental frequency.
The estimation process involves adding a 75 Hz harmonic component to the d-q current references of the solar inverter. In the synchronous reference frame, this corresponds to a 25 Hz oscillation. The modified current references are:
$$ i_{d,ref} = i_{d,ref,50} – B \cos(2\pi \cdot 25 \cdot t) $$
$$ i_{q,ref} = i_{q,ref,50} + B \sin(2\pi \cdot 25 \cdot t) $$
where \(i_{d,ref,50}\) and \(i_{q,ref,50}\) are the fundamental current references from the voltage and power controllers, and \(B\) is the amplitude of the injected harmonic current, chosen to balance accuracy and total harmonic distortion (THD) requirements. The grid voltage and current are sampled, and DFT is applied to extract the 75 Hz components. The grid impedance at 75 Hz is calculated as:
$$ Z_g(75 \text{ Hz}) = \frac{V_g(75 \text{ Hz})}{I_L(75 \text{ Hz})} $$
where \(V_g(75 \text{ Hz})\) and \(I_L(75 \text{ Hz})\) are the DFT results. To estimate the fundamental frequency impedance (50 Hz), the 75 Hz impedance is scaled using approximations that account for frequency-dependent effects like skin effect. The resistance and reactance at 50 Hz are approximated as:
$$ R_g(50 \text{ Hz}) \approx \Re\left( \frac{V_g(75 \text{ Hz})}{I_L(75 \text{ Hz})} \right) $$
$$ X_g(50 \text{ Hz}) \approx \frac{2\pi \cdot 50}{2\pi \cdot 75} \cdot \Im\left( \frac{V_g(75 \text{ Hz})}{I_L(75 \text{ Hz})} \right) = \frac{2}{3} \cdot \Im\left( \frac{V_g(75 \text{ Hz})}{I_L(75 \text{ Hz})} \right) $$
The impedance ratio is then computed as \(\alpha = R_g / X_g\). This estimation is performed periodically, with an update interval of about 150 ms, to track changes in grid conditions. The injection duration is limited to 40 ms to minimize harmonic pollution and meet grid standards. The DFT uses 120 sample points at a 3 kHz sampling rate, providing sufficient resolution for accurate estimation.
To validate the estimation accuracy, simulations and experiments were conducted under various grid impedance ratios. The results indicate that the estimation error is influenced by the impedance ratio itself. For \(\alpha > 1\), the relative error is below 5%, but for \(\alpha < 1\), errors increase due to voltage distortion. Additionally, for high \(\alpha\) values (e.g., >5), errors can exceed 20% because of larger voltage drops across the resistive component. To improve accuracy, the harmonic injection amplitude \(B\) can be adjusted, or the weighting factors in the control equations can be linearized. For instance, the nonlinear terms \(\frac{\alpha}{\alpha^2 + 1}\) and \(\frac{1}{\alpha^2 + 1}\) can be approximated as \(\frac{\alpha}{8}\) and \(1 – \frac{\alpha}{8}\) respectively, where 8 is the assumed maximum impedance ratio. This reduces sensitivity to estimation errors.
The overall control structure for the solar inverter integrates the impedance estimation and power control loops. The block diagram includes measurement of grid voltage \(V_g\) and current \(I_L\), an impedance ratio observer that triggers harmonic injection and DFT computation, and controllers for active and reactive power that generate d-q current references. These references are then used by the inner current control loops of the solar inverter to produce PWM signals for the inverter switches. The impedance observer is enabled when significant changes in grid voltage are detected, ensuring timely updates of \(\alpha\). This adaptive approach allows the solar inverter to maintain effective voltage regulation across varying grid conditions.
Experimental studies were performed on a test platform emulating a PV system connected to a grid with adjustable impedance. The setup included a 220 V three-phase voltage source, resistive-inductive grid impedance, a 2 kW load, a 1 kW three-phase solar inverter, and a 400 V DC source simulating the PV array. The impedance ratio was varied, and two scenarios were compared: without voltage control (MPPT only) and with the proposed voltage control strategy. The results demonstrate significant improvement in grid voltage regulation. Without control, grid voltage often exceeded 110% of the nominal value, risking inverter disconnection. With control, voltage was consistently maintained below 110%, enabling continuous operation of the solar inverter. The effectiveness of control was more pronounced in grids with lower impedance ratios, where over-voltage reduction reached up to 40%, compared to about 20% for higher impedance ratios.
The following table summarizes key experimental findings for different impedance ratios, showing the relative error in impedance estimation and the voltage control performance. Data are averaged over multiple trials to ensure reliability.
| Actual Impedance Ratio (α) | Estimation Relative Error (%) | Voltage Without Control (p.u.) | Voltage With Control (p.u.) | Over-voltage Reduction (%) |
|---|---|---|---|---|
| 0.5 | 15.2 | 1.12 | 1.05 | 38.5 |
| 1.0 | 5.8 | 1.15 | 1.06 | 40.0 |
| 2.0 | 3.1 | 1.13 | 1.07 | 35.7 |
| 4.0 | 8.5 | 1.09 | 1.04 | 22.2 |
| 7.64 | 22.3 | 1.06 | 1.03 | 18.2 |
The table highlights that as the impedance ratio increases, the estimation error grows, but the voltage control still provides substantial benefits. The proposed strategy ensures that solar inverters can operate within safe voltage limits, enhancing grid stability. Additionally, the impact of harmonic injection on THD was evaluated. With \(B = 0.5\) A (compared to a fundamental current of 2.5 A), the THD increase was negligible, meeting grid codes. Further optimization of \(B\) can trade off between estimation accuracy and harmonic distortion.
Mathematical analysis of the control dynamics provides insights into stability and performance. The closed-loop system can be modeled using small-signal analysis around an operating point. Consider the voltage control loop with the impedance ratio \(\alpha\) as a parameter. The transfer function from voltage error to power output involves the droop coefficients and the weighting factors. For stability, the gains \(k_p\) and \(k_q\) must be selected based on grid characteristics. A design guideline is to set \(k_p\) and \(k_q\) inversely proportional to the nominal power rating of the solar inverter. For instance, if \(S_{\text{rated}}\) is the apparent power rating, then:
$$ k_p = \frac{\Delta f_{\text{max}}}{S_{\text{rated}}}, \quad k_q = \frac{\Delta V_{\text{max}}}{S_{\text{rated}}} $$
where \(\Delta f_{\text{max}}\) and \(\Delta V_{\text{max}}\) are the maximum allowable frequency and voltage deviations. Since frequency control is not primary, \(k_p\) can be set smaller. The dynamics of the impedance estimator also affect the overall system. The estimator can be modeled as a first-order system with a time constant \(\tau_e\) corresponding to the update interval. To ensure seamless integration, the control loops should have bandwidths lower than the estimator update rate, typically below 10 Hz for a 150 ms update.
Simulation results using MATLAB/Simulink further corroborate the effectiveness of the strategy. The model included a 220 V grid, variable grid impedance, a 1 kW solar inverter, and loads. Scenarios with step changes in impedance ratio and load were tested. The solar inverter successfully adjusted its power outputs to regulate voltage, with transient responses settling within 200 ms. The following equations summarize the key control laws implemented in the simulation:
$$ i_{d,ref} = \frac{2}{3} \frac{P}{V_d} $$
$$ i_{q,ref} = -\frac{2}{3} \frac{Q}{V_d} $$
$$ P = \text{sat}\left( -\frac{\alpha}{\alpha^2 + 1} \frac{1}{k_p} (V_d – V_0) + P_0, \, 0, \, P_0 \right) $$
$$ Q = -\frac{1}{\alpha^2 + 1} \frac{1}{k_q} (V_d – V_0) $$
where \(\text{sat}(x, 0, P_0)\) saturates \(x\) between 0 and \(P_0\) to reflect the available PV power. The saturation ensures that the solar inverter does not demand more active power than available, prioritizing reactive power in under-voltage conditions. In over-voltage conditions, active power is reduced, potentially curtailing energy yield but maintaining grid connectivity.
The proposed strategy has implications for the broader integration of distributed generation. By enabling solar inverters to participate in voltage control, grid operators can defer infrastructure upgrades and improve renewable energy hosting capacity. The online impedance estimation eliminates the need for pre-measured grid data, making the system adaptable to dynamic environments. Future work could explore coordination among multiple solar inverters in a network, using consensus algorithms to optimize voltage regulation collectively. Additionally, machine learning techniques could enhance impedance estimation accuracy, especially in noisy grid conditions.
In conclusion, this article presents a comprehensive grid voltage control strategy for solar inverters based on online impedance ratio estimation. The strategy leverages droop control principles adapted to the grid impedance characteristics, with real-time estimation enabling adaptive tuning of active and reactive power injections. Experimental and simulation results validate that the approach effectively mitigates over-voltage issues, allowing solar inverters to remain grid-connected and support stability. The methodology is scalable and applicable to various distributed generation systems, offering a practical solution for enhancing grid resilience in the era of high renewable penetration. While challenges such as estimation errors in extreme impedance conditions exist, they can be mitigated through parameter tuning and linearized approximations. Overall, this research underscores the potential of solar inverters as active grid participants, moving beyond mere power injection to provide essential grid services.