Solar inverters have become the key interface between photovoltaic arrays and the utility grid. As penetration of renewable generation increases, the reliable operation of solar inverters under abnormal grid conditions has attracted significant attention. Among these conditions, unbalanced voltage sags occur more frequently than symmetrical faults. When an unbalanced fault happens, negative-sequence voltage components appear, and the positive-sequence voltage magnitude drops. These phenomena cause active power oscillations, current distortion, and a sharp rise in the peak output current of solar inverters. The excessive peak current may exceed the rating of switching devices, trigger overcurrent protection, and even lead to failure of low-voltage ride-through. Therefore, an effective peak current suppression strategy for solar inverters is essential.
In this article, I first analyze the mechanism that causes excessive peak current in solar inverters under unbalanced voltage sags. Then I propose a modified reference current algorithm that incorporates multiple adjustment parameters. Based on this algorithm, I develop an active and reactive power coordination control strategy. The proposed method effectively limits the peak current, expands the active power output capability, and maintains flexible power control. Simulation results in PSCAD/EMTDC verify the correctness and effectiveness of the proposed strategy.
1. Topology and Mathematical Model of Solar Inverters
The topology of a typical three-phase solar inverter is shown in the figure below. This topology is widely used in photovoltaic generation systems. It employs a three-phase three-wire configuration, so zero-sequence current does not exist. The output power can flow in both directions, and the DC voltage is controllable. The DC-side voltage is denoted by \(U_{dc}\), the output resistance and inductance are \(R\) and \(L\), and the photovoltaic array is connected to the AC ideal source through the solar inverter. The output current is nearly sinusoidal.
The mathematical model of the solar inverter can be expressed as
$$ u_i = R i_i + L \frac{d i_i}{d t} + e_i \tag{1} $$
where \(R\) and \(L\) are the resistance and reactance of the solar inverter, \(e_i\) is the grid-side voltage, \(u_i\) is the inverter-side voltage, and the subscript \(i\) represents the three phases \(a\), \(b\), and \(c\). After Clarke transformation, the model in the \(\alpha\beta\) stationary frame becomes
$$ \begin{cases} u_\alpha = R i_\alpha + L \frac{d i_\alpha}{d t} + e_\alpha \\ u_\beta = R i_\beta + L \frac{d i_\beta}{d t} + e_\beta \end{cases} \tag{2} $$
where \(u_\alpha\) and \(u_\beta\) are the inverter output voltage components in the \(\alpha\beta\) frame, \(i_\alpha\) and \(i_\beta\) are the output current components, and \(e_\alpha\) and \(e_\beta\) are the grid voltage components.
2. Mechanism of Excessive Peak Current in Solar Inverters under Unbalanced Faults
According to instantaneous power theory, the steady-state active and reactive powers of a solar inverter can be written as
$$ \begin{cases} p = 1.5 (u_\alpha i_\alpha + u_\beta i_\beta) \\ q = 1.5 (u_\beta i_\alpha – u_\alpha i_\beta) \end{cases} \tag{3} $$
Under unbalanced conditions, the grid voltage in the \(\alpha\beta\) frame can be decomposed into positive- and negative-sequence components:
$$ \begin{aligned} u_\alpha &= u_\alpha^+ + u_\alpha^- = U^+ \cos(\omega t + \delta^+) + U^- \cos(\omega t + \delta^-) \\ u_\beta &= u_\beta^+ + u_\beta^- = U^+ \sin(\omega t + \delta^+) + U^- \sin(\omega t + \delta^-) \end{aligned} \tag{4} $$
where \(u_\alpha^+\), \(u_\beta^+\) are positive-sequence voltage components, \(u_\alpha^-\), \(u_\beta^-\) are negative-sequence voltage components, \(\delta^+\) and \(\delta^-\) are the angles of the positive- and negative-sequence components, and \(U^+\), \(U^-\) are the corresponding voltage magnitudes:
$$ \begin{cases} U^+ = \sqrt{(u_\alpha^+)^2 + (u_\beta^+)^2} \\ U^- = \sqrt{(u_\alpha^-)^2 + (u_\beta^-)^2} \end{cases} \tag{5} $$
The output current of the solar inverter can be expressed in terms of active and reactive current components:
$$ \begin{cases} i_\alpha = i_{\alpha,\text{ref}}(p) + i_{\alpha,\text{ref}}(q) \\ i_\beta = i_{\beta,\text{ref}}(p) + i_{\beta,\text{ref}}(q) \end{cases} \tag{6} $$
During normal operation, solar inverters usually operate at unity power factor, so the reactive power reference is zero. From (3) to (6), the reference current can be derived as
$$ \begin{cases} i_{\alpha,\text{ref}} = i_{\alpha,\text{ref}}(p) = \frac{2 u_\alpha^+ P_{\text{ref}}}{3 U^+} \\ i_{\beta,\text{ref}} = i_{\beta,\text{ref}}(p) = \frac{2 u_\beta^+ P_{\text{ref}}}{3 U^+} \end{cases} \tag{7} $$
Equation (7) shows that the reference current depends on the positive-sequence voltage. When an unbalanced fault occurs, negative-sequence components appear, and the positive-sequence voltage decreases. If the reference active power remains unchanged, the reference current increases significantly. The peak current may become several times larger than the balanced condition. This can damage the switching devices, cause overcurrent protection actions, and lead to failure of low-voltage ride-through for solar inverters.
Moreover, the negative-sequence components cause second-order harmonic oscillations in the active and reactive powers. These oscillations affect the DC-link voltage stability and the lifetime of the DC capacitor. Neglecting losses, the DC capacitor balance equation can be written as
$$ C U_{dc} \frac{d U_{dc}}{d t} = P_{pv} – P_{\text{out}} \tag{8} $$
where \(C\) and \(U_{dc}\) are the DC-link capacitance and voltage, \(P_{pv}\) is the photovoltaic array output power, and \(P_{\text{out}}\) is the inverter output power. Under unbalanced faults, the second-order oscillation in \(P_{\text{out}}\) causes periodic fluctuations in the DC voltage, which degrades the reliability of solar inverters.
3. Proposed Reference Current Algorithm for Solar Inverters
Under unbalanced grid voltage, different control targets can be achieved by controlling the positive- and negative-sequence currents. Common control targets are summarized in Table 1.
| Target | Description | Active power oscillation | Reactive power oscillation | Output current |
|---|---|---|---|---|
| I | Symmetric three-phase current | Large | Large | No negative-sequence component |
| II | Constant reactive power | Large | Zero | Contains negative-sequence component |
| III | Constant active power | Zero | Large | Contains negative-sequence component |
Considering the influence of active power oscillations on the DC-link voltage, maximum power point tracking, conversion efficiency, and system stability, the second-order oscillation in active power should be eliminated. Therefore, target III is adopted. The reference current equation in the \(\alpha\beta\) frame for target III is
$$ \begin{bmatrix} i_{\alpha,\text{ref}} \\ i_{\beta,\text{ref}} \end{bmatrix} = \frac{1}{u_\alpha^2 + u_\beta^2} \begin{bmatrix} u_\alpha & u_\beta \\ u_\beta & -u_\alpha \end{bmatrix} \begin{bmatrix} P_{\text{ref}} \\ Q_{\text{ref}} \end{bmatrix} \tag{9} $$
To provide reactive power support during faults and to suppress the peak current, I introduce multiple adjustment parameters \(m\), \(n\), \(k_1\), and \(k_2\). The new reference current expression is given by
$$ \begin{aligned} i_{\alpha,\text{ref}} &= \frac{2(u_\alpha^+ – k_1 u_\alpha^-)}{3 (U^+ – k_1 U^-)} m P_{\text{ref}} + \frac{2(u_\beta^+ + k_2 u_\beta^-)}{3 (U^+ + k_2 U^-)} n Q_{\text{ref}} \\ i_{\beta,\text{ref}} &= \frac{2(u_\beta^+ – k_1 u_\beta^-)}{3 (U^+ – k_1 U^-)} m P_{\text{ref}} – \frac{2(u_\alpha^+ + k_2 u_\alpha^-)}{3 (U^+ + k_2 U^-)} n Q_{\text{ref}} \end{aligned} \tag{10} $$
where \(m\), \(n\), \(k_1\), and \(k_2\) are adjustment parameters in the range \([0,1]\). By adjusting these parameters, the peak current, power oscillations, and power references can be regulated. After inverse Clarke transformation, the three-phase current amplitudes are obtained as
$$ \begin{aligned} i_a &= \sqrt{A_1^2 + A_2^2} + 2 A_1 A_2 \cos(\delta – \theta) \\ i_b &= \sqrt{A_1^2 + A_2^2} + 2 A_1 A_2 \cos\left(\delta – \theta – \frac{2\pi}{3}\right) \\ i_c &= \sqrt{A_1^2 + A_2^2} + 2 A_1 A_2 \cos\left(\delta – \theta + \frac{2\pi}{3}\right) \end{aligned} \tag{11} $$
where
$$ \begin{aligned} A_1 &= \sqrt{\left(\frac{2 m P_{\text{ref}}}{3 U^+ (1 – k_1 \varepsilon)}\right)^2 + \left(\frac{2 n Q_{\text{ref}}}{3 U^+ (1 + k_2 \varepsilon)}\right)^2} \\ A_2 &= \sqrt{\left(\frac{2 m k_1 P_{\text{ref}}}{3 U^+ (1 – k_1 \varepsilon)}\right)^2 + \left(\frac{2 n k_2 Q_{\text{ref}}}{3 U^+ (1 + k_2 \varepsilon)}\right)^2} \\ \theta &= \arctan\left(\frac{n Q_{\text{ref}} (1 – k_1 \varepsilon)}{m P_{\text{ref}} (1 + k_2 \varepsilon)}\right) \\ \delta &= \arctan\left(\frac{n k_2 Q_{\text{ref}} (1 – k_1 \varepsilon)}{m k_1 P_{\text{ref}} (1 + k_2 \varepsilon)}\right) \\ \varepsilon &= \frac{U^-}{U^+} \end{aligned} \tag{12} $$
The maximum grid current can be expressed as
$$ i_{\max} = \sqrt{A_1^2 + A_2^2} = \frac{2}{3} \sqrt{\frac{(m P_{\text{ref}})^2 + (n Q_{\text{ref}})^2}{(U^+ (1 – k_1 \varepsilon))^2} + \frac{(m k_1 P_{\text{ref}})^2 + (n k_2 Q_{\text{ref}})^2}{(U^+ (1 + k_2 \varepsilon))^2}} \tag{13} $$
Equation (13) shows that the peak current of solar inverters depends on the four adjustment parameters, the active power \(P\), the reactive power \(Q\), and the voltage unbalance factor \(\varepsilon\). Proper selection of these parameters can effectively reduce the peak current.
4. Active and Reactive Power Coordination Control Strategy
For the reference current in (10), the instantaneous active and reactive powers can be decomposed as
$$ \begin{cases} p = P^+ + P^- + \tilde{P} \\ q = Q^+ + Q^- + \tilde{Q} \end{cases} \tag{14} $$
Substituting (3)–(5) and (10) into (14), the instantaneous active power can be written as
$$ \begin{aligned} P^+ &= \frac{U^+}{U^+ – k_1 U^-} m P_{\text{ref}} \\ P^- &= -\frac{k_1 U^-}{U^+ – k_1 U^-} m P_{\text{ref}} \\ \tilde{P} &= \frac{(1 – k_1) U^+ U^-}{(U^+ – k_1 U^-)^2} m P_{\text{ref}} \cos(2\omega t) + \frac{(1 – k_1) U^+ U^-}{(U^+ – k_1 U^-)^2} m P_{\text{ref}} \sin(2\omega t) + \frac{(1 – k_2) U^+ U^-}{(U^+ + k_2 U^-)^2} n Q_{\text{ref}} \cos(2\omega t) + \frac{(1 – k_2) U^+ U^-}{(U^+ + k_2 U^-)^2} n Q_{\text{ref}} \sin(2\omega t) \end{aligned} \tag{15} $$
Similarly, the instantaneous reactive power can be decomposed as
$$ \begin{aligned} Q^+ &= \frac{U^+}{U^+ + k_2 U^-} n Q_{\text{ref}} \\ Q^- &= \frac{k_2 U^-}{U^+ + k_2 U^-} n Q_{\text{ref}} \\ \tilde{Q} &= \frac{(1 – k_2) U^+ U^-}{(U^+ + k_2 U^-)^2} n Q_{\text{ref}} \cos(2\omega t) – \frac{(1 – k_2) U^+ U^-}{(U^+ + k_2 U^-)^2} n Q_{\text{ref}} \sin(2\omega t) – \frac{(1 – k_1) U^+ U^-}{(U^+ – k_1 U^-)^2} m P_{\text{ref}} \cos(2\omega t) + \frac{(1 – k_1) U^+ U^-}{(U^+ – k_1 U^-)^2} m P_{\text{ref}} \sin(2\omega t) \end{aligned} \tag{16} $$
From (15) and (16), if \(m=1\) and \(n=1\), then \(P^+ + P^- = P_{\text{ref}}\) and \(Q^+ + Q^- = Q_{\text{ref}}\). Thus, the output active and reactive powers can accurately follow the power references. When \(k_1=1\) and \(k_2=1\), the control strategy eliminates active power oscillations (target III). Adjusting \(k_1\) and \(k_2\) does not change the relationships \(P^+ + P^- = P_{\text{ref}}\) and \(Q^+ + Q^- = Q_{\text{ref}}\), but it changes the peak current and the power oscillations.
When \(m\) and \(n\) are adjusted, the output power references become
$$ \begin{cases} p = m P_{\text{ref}} \\ q = n Q_{\text{ref}} \end{cases} \tag{17} $$
Adjusting \(m\) and \(n\) reduces the active and reactive power references. According to (13), reducing the output power also reduces the peak current. Based on grid codes and practical requirements, I propose the following active and reactive power coordination control strategy for solar inverters:
- When an unbalanced fault occurs and the positive-sequence voltage drops between 0.9 and 1.0 p.u., the solar inverter remains at unity power factor. If the output current exceeds the maximum allowed current \(I_{\max}\), the parameters \(k_1\) and \(k_2\) are adjusted to keep the output current within the allowed range.
- When the positive-sequence voltage drops below 0.9 p.u., the solar inverter provides reactive power according to grid code requirements. The parameters \(k_1\) and \(k_2\) are still adjusted to limit the peak current. This ensures a relatively high active power output.
- If the voltage sag is severe and adjusting \(k_1\) and \(k_2\) cannot keep the peak current below \(I_{\max}\), the parameters are set to \(k_1=1\) and \(k_2=1\) to eliminate active power oscillations. Then \(m\) and \(n\) are adjusted to reduce the output power. The reactive power output is prioritized. If capacity remains, active power is output subject to the maximum peak current constraint.
The corresponding active power output can be calculated as
$$ P_{\text{ref}} = \frac{2}{3} \frac{U^+ I_{\max}^2 (1 + \varepsilon)^2 – n Q_{\text{ref}}}{2 m (1 + \varepsilon)} \tag{18} $$
The reactive current required by grid codes is
$$ i_{q,\text{ref}} = \begin{cases} 0, & U^+ > 0.9 \text{ p.u.} \\ 2(1 – U^+), & 0.9 \text{ p.u.} \ge U^+ \end{cases} \tag{19} $$
Since \(P_{\text{ref}} = \sqrt{S^2 – Q_{\text{ref}}^2}\), the active power that can be output by the solar inverter is determined by the inverter capacity and the maximum allowed current. Both active and reactive powers depend on the positive- and negative-sequence voltages. Therefore, a lookup table can be built relating \(k_1\) and \(k_2\) to the positive- and negative-sequence voltages. An improved particle swarm optimization (IPSO) algorithm can be used to minimize the active power oscillation while satisfying the current constraint:
$$ \min f = \tilde{P} \tag{20} $$
subject to
$$ I_{pv} \le I_{\max} \tag{21} $$
The proposed control strategy is summarized in Table 2.
| Condition | Control action | Objective |
|---|---|---|
| \(U^+ > 0.9\) p.u., \(I_{\text{peak}} \le I_{\max}\) | Unity power factor | Normal operation |
| \(U^+ > 0.9\) p.u., \(I_{\text{peak}} > I_{\max}\) | Adjust \(k_1, k_2\) | Limit peak current |
| \(U^+ \le 0.9\) p.u., \(I_{\text{peak}} \le I_{\max}\) | Provide reactive power, adjust \(k_1, k_2\) | Reactive support and peak current limit |
| \(U^+ \le 0.9\) p.u., \(I_{\text{peak}} > I_{\max}\) after \(k_1,k_2\) adjustment | Set \(k_1=1, k_2=1\), adjust \(m, n\) | Limit peak current, prioritize reactive power |
5. Simulation Verification
I established a simulation model of the photovoltaic generation system in PSCAD/EMTDC. The control strategy is shown in the previous section. The simulation parameters are listed in Table 3.
| Parameter | Value |
|---|---|
| Rated power \(P_{\text{rated}}\) | 0.5 MW |
| DC-side voltage \(U_{dc}\) | 800 V |
| DC-side capacitance \(C\) | 5700 μF |
| Grid-side filter inductance \(L\) | 1 mH |
| Switching frequency \(f\) | 6 kHz |
Under normal conditions, the solar inverter operates at unity power factor, and maximum power point tracking is based on the perturb and observe method. At \(t=2\) s, an unbalanced fault occurs. The active power reference is set to 0.5 MW, and the reactive power reference is 0. The solar inverter stops MPPT and adopts the proposed coordination control strategy. The maximum allowed peak current \(I_{\max}\) is set to 1.2 times the rated current.
5.1 Case 1: Voltage unbalance factor \(\varepsilon = 0.18\)
In this case, the positive-sequence voltage is 0.95 p.u., so the solar inverter does not need to provide reactive power. It remains at unity power factor. The peak current before control is about 1.3 times the rated current. The theoretical value from (13) is 1.28 times the rated current, which matches the simulation. Since the peak current exceeds the allowed maximum, \(k_1\) and \(k_2\) are adjusted. To minimize active power oscillation, \(k_1=0.645\) and \(k_2=0\). The peak current is limited to about 1.2 times the rated current, and the theoretical value is 1.19 times. The active power oscillation increases after 2.4 s, while the reactive power oscillation decreases.
5.2 Case 2: Voltage unbalance factor \(\varepsilon = 0.3\)
In this case, the positive-sequence voltage is 0.887 p.u. According to the grid code, the solar inverter must provide 0.226 p.u. of reactive current. The active power is 0.487 MW, and the reactive power is 0.113 Mvar, ensuring rated capacity output. The peak current before control is about 1.6 times the rated current, and the theoretical value is 1.61 times. To minimize active power oscillation, the parameters are \(k_1=0.163\) and \(k_2=0.264\). After control, the peak current is about 1.2 times the rated current, and the theoretical value is 1.19 times. The active power oscillation increases after 2.4 s, while the reactive power oscillation decreases.
5.3 Case 3: Voltage unbalance factor \(\varepsilon = 0.6\)
In this case, the voltage sag is severe. The peak current before control is about 3.6 times the rated current, and the theoretical value is 3.6 times. Adjusting \(k_1\) and \(k_2\) alone cannot keep the peak current within \(I_{\max}\). The positive-sequence voltage is 0.688 p.u., and the required reactive power is 0.624 p.u. The active power that can be output while keeping the peak current within \(I_{\max}\) is 0.15 p.u. Thus, the reactive power is 0.312 Mvar, and the active power is 0.0725 MW. After applying the coordination control strategy, the peak current is about 1.2 times the rated current, satisfying the grid requirement. The active power oscillation is essentially eliminated, and the reactive power oscillation is reduced.
Table 4 compares the simulation results with theoretical calculations.
| \(\varepsilon\) | \(U^+\) (p.u.) | Theoretical peak current before control (times rated) | Simulated peak current before control (times rated) | Adjusted parameters | Theoretical peak current after control (times rated) | Simulated peak current after control (times rated) |
|---|---|---|---|---|---|---|
| 0.18 | 0.95 | 1.28 | 1.30 | \(k_1=0.645, k_2=0\) | 1.19 | 1.20 |
| 0.30 | 0.887 | 1.61 | 1.60 | \(k_1=0.163, k_2=0.264\) | 1.19 | 1.20 |
| 0.60 | 0.688 | 3.60 | 3.60 | \(k_1=1, k_2=1, m=0.15, n=0.624\) | 1.20 | 1.20 |
For comparison, a previous method with \(\varepsilon=0.3\) outputs 0.41 MW while limiting the peak current to 1.5 times the rated current. The proposed strategy outputs 0.487 MW while limiting the peak current to 1.2 times the rated current. Thus, the proposed method expands the power output capability and strictly follows grid requirements.
6. Discussion
The proposed strategy provides a flexible way to suppress peak current in solar inverters. The four parameters \(m\), \(n\), \(k_1\), and \(k_2\) allow simultaneous adjustment of peak current, active power oscillation, reactive power oscillation, and power references. The lookup table approach ensures real-time implementation. The improved particle swarm optimization minimizes active power oscillation under the current constraint. The simulation results confirm that the proposed method works well for different voltage unbalance factors.
However, the method has some limitations. When the voltage unbalance factor is very high, the active power output may be significantly reduced to prioritize reactive power support. This is consistent with grid code requirements but may reduce the economic benefit of the solar inverter. Future work can focus on optimizing the parameter selection to further improve the active power output while maintaining the peak current limit.
7. Conclusion
I have proposed a peak current suppression strategy for solar inverters under unbalanced faults. The main contributions are as follows:
- A modified reference current algorithm with multiple adjustment parameters is developed. It can regulate the peak current and power oscillations of solar inverters.
- An active and reactive power coordination control strategy is proposed. It effectively solves the overcurrent problem, expands the active power output capability, and provides reactive power support according to grid codes.
- The parameter adjustment principle is established, and a lookup table based on the positive- and negative-sequence voltages is suggested for real-time implementation.
- Simulation results in PSCAD/EMTDC verify the correctness and effectiveness of the proposed strategy under different voltage unbalance factors.
The proposed strategy can be applied to solar inverters in photovoltaic generation systems to improve their reliability and fault ride-through capability under unbalanced grid conditions.
Appendix: Key Equations for Solar Inverters
For convenience, the key equations used in the proposed control strategy are summarized below.
$$ \begin{cases} u_\alpha = R i_\alpha + L \frac{d i_\alpha}{d t} + e_\alpha \\ u_\beta = R i_\beta + L \frac{d i_\beta}{d t} + e_\beta \end{cases} \tag{A1} $$
$$ \begin{bmatrix} i_{\alpha,\text{ref}} \\ i_{\beta,\text{ref}} \end{bmatrix} = \frac{1}{u_\alpha^2 + u_\beta^2} \begin{bmatrix} u_\alpha & u_\beta \\ u_\beta & -u_\alpha \end{bmatrix} \begin{bmatrix} P_{\text{ref}} \\ Q_{\text{ref}} \end{bmatrix} \tag{A2} $$
$$ i_{\max} = \frac{2}{3} \sqrt{\frac{(m P_{\text{ref}})^2 + (n Q_{\text{ref}})^2}{(U^+ (1 – k_1 \varepsilon))^2} + \frac{(m k_1 P_{\text{ref}})^2 + (n k_2 Q_{\text{ref}})^2}{(U^+ (1 + k_2 \varepsilon))^2}} \tag{A3} $$
$$ P_{\text{ref}} = \frac{2}{3} \frac{U^+ I_{\max}^2 (1 + \varepsilon)^2 – n Q_{\text{ref}}}{2 m (1 + \varepsilon)} \tag{A4} $$
$$ i_{q,\text{ref}} = \begin{cases} 0, & U^+ > 0.9 \text{ p.u.} \\ 2(1 – U^+), & 0.9 \text{ p.u.} \ge U^+ \end{cases} \tag{A5} $$
These equations form the foundation of the proposed peak current suppression strategy for solar inverters under unbalanced voltage sags.