As a researcher dedicated to the reliable integration of renewable energy systems, I have focused my recent efforts on addressing one of the most pressing technical challenges for grid-connected solar inverters: the excessive peak current that occurs during asymmetric voltage sags. The growth of solar power generation has been remarkable, but it also brings new responsibilities for ensuring grid stability. This concern is particularly acute because unbalanced faults occur more frequently in actual power grid operations than their symmetrical counterparts, and the resulting current stress on power electronic devices can be catastrophic. My research is consequently oriented toward developing a control strategy that can effectively suppress peak currents in solar inverters under unbalanced voltage conditions, thereby ensuring fault ride-through capability and enhancing the overall reliability of photovoltaic generation systems.
In my investigation of the fault behavior of solar inverters, I first recognized that the standard control algorithms developed for balanced grid conditions are no longer satisfactory when an asymmetric fault occurs. The presence of a negative-sequence voltage component leads to significant power oscillations, current waveform distortion, and, most critically, a dramatic increase in the magnitude of the output current. The peak current during the fault can easily reach several times its nominal value, which may cause the switching devices to overheat, trigger overcurrent protection, or even permanently damage the inverter. Consequently, the photovoltaic system may fail to ride through the fault, adversely affecting the stability of the power system. My work addresses this issue through a comprehensive analytical framework and a practical control solution. To structure my presentation, the following sections describe the inverter topology, the mechanism of peak current generation, my proposed reference current algorithm, the coordinated control strategy, and the simulation validation that confirms the effectiveness of the approach. The content I present here is based on experiments and theoretical derivations from my own research, and I have made an effort to provide sufficient mathematical detail so that other researchers can reconstruct my arguments and extend them as necessary.
Let me begin my technical narrative by introducing the system topology that I used throughout this study. The grid-connected solar inverter considered in my work is a three-phase, three-wire voltage-source converter, which is the most commonly adopted configuration in photovoltaic power plants. Figure 1 illustrates the topology of the inverter system, where the photovoltaic array is connected to the DC bus, and the power is transferred to the AC grid through three inverter legs and an inductive filter. The system is characterized by its bidirectional power flow and controllable DC-link voltage. The electrical behavior of this inverter can be described by the voltage balance equation in the stationary reference frame. I will now present my mathematical model. The phase voltage equations in the abc reference frame are given by:
$$u_{i}=Ri_{i}+L\frac{di_{i}}{dt}+e_{i}$$
Here, \(R\) and \(L\) represent the equivalent resistance and inductance of the output side, while \(e_{i}\) is the grid phase voltage, \(u_{i}\) is the inverter output voltage, and the subscript \(i\) corresponds to the phases a, b, and c. When I apply the Clarke transformation to this model, I obtain the following equations in the αβ reference frame:
$$u_{\alpha}=Ri_{\alpha}+L\frac{di_{\alpha}}{dt}+e_{\alpha}$$
$$u_{\beta}=Ri_{\beta}+L\frac{di_{\beta}}{dt}+e_{\beta}$$
These equations form the foundation for the subsequent controller design in my work. It is important to note that under unbalanced conditions, the grid voltage and consequently the inverter output voltage both contain positive- and negative-sequence components. This necessitates a control strategy capable of handling these two rotating reference frames independently.
Mechanism of Peak Current in Solar Inverters
In order to develop an effective peak current suppression strategy for solar inverters, I first performed a thorough analysis of the mechanisms that lead to excessive current magnitudes under asymmetric voltage sags. The instantaneous power theory provides a convenient starting point. Under steady-state conditions, the active and reactive power delivered by the solar inverter can be expressed in the αβ reference frame as:
$$p=1.5(u_{\alpha}i_{\alpha}+u_{\beta}i_{\beta})$$
$$q=1.5(u_{\beta}i_{\alpha}-u_{\alpha}i_{\beta})$$
During an unbalanced fault, the grid voltage contains both positive- and negative-sequence components. Therefore, the α-axis and β-axis voltages can be decomposed as:
$$u_{\alpha}=u_{\alpha}^{+}+u_{\alpha}^{-}=U^{+}\cos(\omega t+\delta^{+})+U^{-}\cos(\omega t+\delta^{-})$$
$$u_{\beta}=u_{\beta}^{+}+u_{\beta}^{-}=U^{+}\sin(\omega t+\delta^{+})-U^{-}\sin(\omega t+\delta^{-})$$
where \(U^{+}\) and \(U^{-}\) represent the amplitudes of the positive- and negative-sequence voltages, respectively, while \(\delta^{+}\) and \(\delta^{-}\) are their respective phase angles. The positive- and negative-sequence voltage magnitudes can be computed as follows:
$$U^{+}=\sqrt{(u_{\alpha}^{+})^{2}+(u_{\beta}^{+})^{2}}$$
$$U^{-}=\sqrt{(u_{\alpha}^{-})^{2}+(u_{\beta}^{-})^{2}}$$
For the solar inverter output current, it is convenient to separate the contributions of active power and reactive power control. Thus, I represent the reference current as the sum of an active current component and a reactive current component:
$$i_{\alpha\_ref}=i_{\alpha\_ref}(p)+i_{\alpha\_ref}(q)$$
$$i_{\beta\_ref}=i_{\beta\_ref}(p)+i_{\beta\_ref}(q)$$
According to the technical regulations for photovoltaic power plants, the power factor of the inverter should not be less than 0.98 during normal operation. Therefore, I initially assumed that the solar inverter operates at unity power factor, which implies that the reactive power reference is set to zero. With this assumption, the reference currents that generate the desired active power can be derived as:
$$i_{\alpha\_ref}(p)=\frac{2P_{ref}}{3(U^{+})^{2}}u_{\alpha}^{+}$$
$$i_{\beta\_ref}(p)=\frac{2P_{ref}}{3(U^{+})^{2}}u_{\beta}^{+}$$
where \(P_{ref}\) is the active power reference. It becomes clear from these equations that, under balanced conditions, the reference current is directly proportional to the positive-sequence voltage. However, when an asymmetrical fault occurs, the positive-sequence voltage decreases while the negative-sequence component is no longer negligible. Since the reference power \(P_{ref}\) remains unchanged, the calculated reference currents increase significantly. The reason is evident in the denominator of the equation: the term \((U^{+})^{2}\) becomes smaller during a voltage sag. In severe cases, the calculated reference current can be several times larger than the pre-fault value, leading to current saturation, protection tripping, and potential damage to the semiconductor switches. This is exactly the problem of excessing output peak current that I aim to solve.
Yet, the effects of asymmetric faults on solar inverters are not limited to the amplification of current. The negative-sequence voltage also introduces power oscillations. When I consider the instantaneous power in the presence of negative-sequence components, the active and reactive powers contain a double-frequency ripple. This oscillation propagates to the DC-link capacitor and destabilizes the DC-link voltage. The impact on the capacitor voltage can be described by the following balance equation:
$$C U_{dc}\frac{dU_{dc}}{dt}=P_{pv}-P_{out}$$
Here, \(C\) and \(U_{dc}\) are the DC-link capacitance and voltage, while \(P_{pv}\) and \(P_{out}\) denote the solar array output power and the inverter output power. The double-frequency ripple contained in \(P_{out}\) leads to a periodic fluctuation of \(U_{dc}\), which in turn affects the control quality of the inverter and shortens the lifetime of the capacitor. Therefore, my control objectives are twofold: to limit the peak output current and to manage the power fluctuations appropriately.
Reference Current Generation with Positive- and Negative-Sequence Control
Having analyzed the origins of the problem, I now describe my approach to generating the reference currents for the solar inverter. The key idea is to use both the positive- and negative-sequence voltages in the calculation, thereby gaining the ability to control not only the output power but also the current peak value. In the literature, several control objectives are commonly proposed for grid-connected converters under unbalanced faults. The first objective is to produce three-phase balanced currents. This strategy eliminates the negative-sequence current, but the resulting active and reactive powers contain large oscillations. The second objective is to achieve constant reactive power, meaning that the double-frequency ripple in the reactive power is eliminated. However, in this case the active power exhibits a significant ripple. The third objective, which is the one I selected as the basis for my work, is to eliminate the active power oscillation. This is especially important for solar inverters because an oscillating active power directly impacts the DC-link voltage and the maximum power point tracking. By choosing the strategy that eliminates the active power ripple, I obtain the following reference current equation in the αβ reference frame:
$$\begin{bmatrix} i_{\alpha\_ref} \\ i_{\beta\_ref} \\ i_{\alpha\_ref} \\ i_{\beta\_ref} \end{bmatrix} = \frac{2}{3}\begin{bmatrix} u_{\alpha}^{+} & u_{\beta}^{+} & u_{\alpha}^{-} & u_{\beta}^{-} \\ u_{\beta}^{+} & -u_{\alpha}^{+} & u_{\beta}^{-} & -u_{\alpha}^{-} \\ u_{\alpha}^{-} & u_{\beta}^{-} & u_{\alpha}^{+} & u_{\beta}^{+} \\ u_{\beta}^{-} & -u_{\alpha}^{-} & u_{\beta}^{+} & -u_{\alpha}^{+} \end{bmatrix} \begin{bmatrix} P_{ref} \\ 0 \\ 0 \\ Q_{ref} \end{bmatrix} \frac{1}{D}$$
where \(D=(U^{+})^{2}-(U^{-})^{2}\). This formulation ensures that the active power output remains constant. However, my analysis of the resulting current waveforms revealed that this strategy alone may still produce an unacceptable peak current in the solar inverter.
The issue is that the reference current expression above does not take the current peak value explicitly into account. To address this limitation, I developed an improved reference current algorithm by introducing several adjustable parameters into the expression. The enhanced reference currents are formulated as:
$$i_{\alpha\_ref}^{1}=\frac{2P_{ref}}{3[(U^{+})^{2}-k_{1}(U^{-})^{2}]}m(u_{\alpha}^{+}-k_{1}u_{\alpha}^{-})$$
$$i_{\beta\_ref}^{1}=\frac{2P_{ref}}{3[(U^{+})^{2}-k_{1}(U^{-})^{2}]}m(u_{\beta}^{+}-k_{1}u_{\beta}^{-})$$
$$i_{\alpha\_ref}^{2}=\frac{2Q_{ref}}{3[(U^{+})^{2}-k_{2}(U^{-})^{2}]}n(u_{\beta}^{+}-k_{2}u_{\beta}^{-})$$
$$i_{\beta\_ref}^{2}=\frac{-2Q_{ref}}{3[(U^{+})^{2}-k_{2}(U^{-})^{2}]}n(u_{\alpha}^{+}-k_{2}u_{\alpha}^{-})$$
In these equations, the parameters \(m\), \(n\), \(k_{1}\), and \(k_{2}\) are adjustable coefficients that vary within the range [0, 1]. The parameters \(m\) and \(n\) are used to scale the active and reactive power references, respectively, while \(k_{1}\) and \(k_{2}\) regulate the influence of the negative-sequence voltage on the current reference. By tuning these parameters, I can adjust the output current peak value and the power fluctuations according to the requirements of the grid code. The total reference currents are then the sum of the active and reactive components:
$$i_{\alpha\_ref}=i_{\alpha\_ref}^{1}+i_{\alpha\_ref}^{2}$$
$$i_{\beta\_ref}=i_{\beta\_ref}^{1}+i_{\beta\_ref}^{2}$$
To evaluate the performance of this reference current algorithm, I derived an expression for the maximum current value of the three-phase output currents. By applying the inverse Clarke transformation, the three-phase currents can be written as:
$$i_{a}=A_{1}\cos(\omega t)-2\sqrt{A_{1}A_{2}}\cos(\delta-\theta_{1}-\theta_{2})+A_{2}\cos(\omega t+\delta-\theta_{1}-\theta_{2})$$
$$i_{b}=A_{1}\cos(\omega t-\frac{2\pi}{3})-2\sqrt{A_{1}A_{2}}\cos(\delta-\theta_{1}-\theta_{2}-\frac{2\pi}{3})+A_{2}\cos(\omega t+\delta-\theta_{1}-\theta_{2}-\frac{2\pi}{3})$$
$$i_{c}=A_{1}\cos(\omega t+\frac{2\pi}{3})-2\sqrt{A_{1}A_{2}}\cos(\delta-\theta_{1}-\theta_{2}+\frac{2\pi}{3})+A_{2}\cos(\omega t+\delta-\theta_{1}-\theta_{2}+\frac{2\pi}{3})$$
where the amplitudes \(A_{1}\) and \(A_{2}\) and the angles \(\theta_{1}\) and \(\theta_{2}\) are given by the following set of equations:
$$A_{1}=\frac{1}{1-\varepsilon^{2}}\sqrt{[\frac{mP_{ref}}{U^{+}}]^{2}+[\frac{nQ_{ref}}{U^{+}}]^{2}}$$
$$A_{2}=\frac{1}{1-\varepsilon^{2}}\sqrt{[\frac{m k_{1}P_{ref}}{U^{+}}]^{2}+[\frac{n k_{2}Q_{ref}}{U^{+}}]^{2}}$$
$$\theta_{1}=\tan^{-1}(\frac{nQ_{ref}(1-k_{2})}{mP_{ref}(1-k_{1})})$$
$$\theta_{2}=\tan^{-1}(\frac{n k_{2}Q_{ref}(1-k_{1})}{m k_{1}P_{ref}(1-k_{2})})$$
In the above equations, the parameter \(\varepsilon\) is defined as the ratio of the negative-sequence voltage to the positive-sequence voltage, i.e., \(\varepsilon=U^{-}/U^{+}\). From these expressions, the maximum output current among the three phases can be calculated as:
$$i_{max}=\frac{2}{3}(A_{1}+A_{2})$$
This is an important result because it establishes a direct mathematical relationship between the peak current and the control parameters. After substituting the expressions for \(A_{1}\) and \(A_{2}\), the maximum current becomes:
$$i_{max}=\frac{2}{3}\cdot\frac{2}{1-\varepsilon^{2}}\left(\sqrt{(\frac{mP_{ref}}{U^{+}})^{2}+(\frac{nQ_{ref}}{U^{+}})^{2}}+\sqrt{(\frac{m k_{1}P_{ref}}{U^{+}})^{2}+(\frac{n k_{2}Q_{ref}}{U^{+}})^{2}}\right)$$
This formulation confirms that the peak current of the solar inverter is influenced by the four adjusting parameters and the voltage unbalance degree. I can therefore achieve peak current limitation by appropriately selecting these parameters, which is the central idea of my proposed control strategy.
Power Oscillation Analysis
In addition to the peak current, I also need to consider the oscillations in the active and reactive power when evaluating the performance of my control strategy. By substituting the improved reference current expression into the instantaneous power theory, I can decompose the output power into its average and oscillating components. The instantaneous active power is derived as follows:
$$p=P^{+}+P^{-}+\tilde{P}$$
The individual terms in this equation are given by:
$$P^{+}=\frac{2mP_{ref}U^{+}}{3[(U^{+})^{2}-k_{1}(U^{-})^{2}]}\cdot\frac{2}{3}\cdot\frac{(U^{+})^{2}-k_{1}(U^{-})^{2}}{(U^{+})^{2}-k_{1}(U^{-})^{2}}$$
$$P^{-}=\frac{-2mP_{ref}k_{1}(U^{-})^{2}}{3[(U^{+})^{2}-k_{1}(U^{-})^{2}]}$$
The oscillating component \(\tilde{P}\) can be written as:
$$\tilde{P}=\frac{2mP_{ref}(1-k_{1})U^{+}U^{-}\cos(2\omega t)}{3[(U^{+})^{2}-k_{1}(U^{-})^{2}]}+\frac{2nQ_{ref}(1-k_{2})U^{+}U^{-}\sin(2\omega t)}{3[(U^{+})^{2}-k_{2}(U^{-})^{2}]}$$
Similarly, the instantaneous reactive power is decomposed as:
$$q=Q^{+}+Q^{-}+\tilde{Q}$$
The corresponding terms are:
$$Q^{+}=\frac{2nQ_{ref}U^{+}}{3[(U^{+})^{2}-k_{2}(U^{-})^{2}]}$$
$$Q^{-}=\frac{-2nQ_{ref}k_{2}(U^{-})^{2}}{3[(U^{+})^{2}-k_{2}(U^{-})^{2}]}$$
And the oscillating component \(\tilde{Q}\) is:
$$\tilde{Q}=\frac{2nQ_{ref}(1-k_{2})U^{+}U^{-}\cos(2\omega t)}{3[(U^{+})^{2}-k_{2}(U^{-})^{2}]}+\frac{2mP_{ref}(1-k_{1})U^{+}U^{-}\sin(2\omega t)}{3[(U^{+})^{2}-k_{1}(U^{-})^{2}]}$$
From these expressions, I observe that when \(m=1\) and \(n=1\), the average active and reactive power accurately track the reference values. When \(k_{1}=1\) and \(k_{2}=1\), the strategy reduces to the constant active power control mentioned earlier. The key insight is that adjusting \(k_{1}\) and \(k_{2}\) does not change the average power tracking, but it modifies the magnitude of the power oscillations and the current peak value. In contrast, adjusting \(m\) and \(n\) directly scales the power commands and therefore also reduces the peak current. These observations form the basis for my coordinated control strategy.
Coordinated Active and Reactive Power Control
My coordinated control strategy is designed to take full advantage of the flexible parameters in the reference current algorithm. It is organized as a multi-step procedure that depends on the severity of the voltage sag and the corresponding requirements of the grid code. I have summarized the decision-making process in Table 1.
| Voltage condition | Reactive power reference | Parameters adjusted | Control objective |
|---|---|---|---|
| 0.9 p.u. ≤ U+ ≤ 1.0 p.u. | No reactive power required | k1, k2 | Maintain unity power factor; limit peak current |
| U+ < 0.9 p.u. | Reactive current set by grid code | k1, k2 | Provide reactive support; operate at rated capacity |
| Severe sag, U+ < 0.9 p.u., k1/k2 insufficient | Reactive power prioritized | m, n (with k1=1, k2=1) | Limit peak current; maintain constant active power |
In the first situation, when the positive-sequence voltage drops only mildly, specifically to the range of 0.9 to 1.0 per unit, the solar inverter continues to operate at unity power factor. The main concern in this scenario is the increase in the output peak current caused by the voltage imbalance. If the computed peak current exceeds the maximum allowed value \(I_{max}\), I adjust the parameters \(k_{1}\) and \(k_{2}\) to keep the current within the safe boundary. In my research, I set the maximum allowable peak current to 1.2 times the rated current of the inverter, which is a conservative value compatible with standard overcurrent capabilities. This parameter adjustment is performed while minimizing the active power ripple to avoid unnecessary stress on the DC-link capacitor.
In the second situation, when the positive-sequence voltage falls below 0.9 per unit, the grid code requires the solar inverter to provide reactive power support. According to the German medium-voltage grid code, which I used as a reference in my work, the reactive current must satisfy the following relationship:
$$i_{q\_ref}=\begin{cases} 0 & U^{+}>0.9 \\ 2(1-U^{+}) & U^{+}<0.9 \end{cases}$$
Under this condition, the reactive power reference and the corresponding active power reference are determined by the grid requirements and the rated capacity of the inverter. The active power is then given by:
$$P_{ref}=\sqrt{S_{rated}^{2}-Q_{ref}^{2}}$$
Within this framework, I continue to adjust \(k_{1}\) and \(k_{2}\) to ensure that the peak current remains within the permissible range. Because the output power is now somewhat reduced, the current is typically easier to manage.
The third situation arises when the fault is so severe that adjusting \(k_{1}\) and \(k_{2}\) alone cannot limit the peak current adequately. In this case, because the voltage unbalance factor is substantial, using non-unity values of \(k_{1}\) and \(k_{2}\) would cause significant power oscillations that could threaten the DC-link voltage stability. Therefore, I reset \(k_{1}=1\) and \(k_{2}=1\), which restores the constant active power characteristic, and instead reduce the output power by adjusting \(m\) and \(n\). The principle I follow is to prioritize reactive power output to support the grid voltage. Once the required reactive power is established, the remaining capacity is used for active power output, provided that the peak current does not exceed its limit. By solving the peak current equation for the maximum active power under this constraint, I obtain:
$$P_{ref}=\frac{2U^{+}}{3(1+\varepsilon)}\sqrt{(\frac{I_{max}}{2})^{2}-(1-\varepsilon)(\frac{nQ_{ref}}{U^{+}})^{2}}$$
where the scaling factor \(n\) is chosen to meet the reactive power requirement. This formula provides a direct way to compute the allowable active power output in the third stage of my control strategy.
To facilitate rapid parameter selection during online operation, I employed a lookup table approach. Since the required reactive power and the inverter capacity constraints depend on the positive- and negative-sequence voltages, the parameters \(k_{1}\) and \(k_{2}\) can be precomputed for a range of voltage unbalance conditions. The lookup table is constructed offline by minimizing the active power ripple subject to the constraint that the output current peak remains within the maximum allowed value. I used an improved particle swarm optimization algorithm for this offline optimization. The objective function of the optimization, which I denote as \(f\), is:
$$f=\min(\tilde{P})$$
subject to:
$$I_{pv}\leq I_{max}$$
The improved particle swarm optimization converges quickly and accurately, making it well-suited for generating the lookup table. In real-time operation, the control system measures the grid voltage, extracts the symmetrical components, and then obtains the appropriate parameter values directly from the table. This ensures that the control latency is minimized and that the solar inverter can respond promptly to changing grid conditions.
The overall control structure that I designed is illustrated in Figure 3. It is based on the αβ reference frame and uses proportional-resonant (PR) controllers to regulate the injected current. The resonance frequency of the PR controller is set to the fundamental grid frequency of 50 Hz, which corresponds to an angular frequency of \(\omega_{0}=314\) rad/s, enabling zero steady-state error for sinusoidal current references. The control diagram comprises the following components:
1. The three-phase grid voltage \(u_{abc}\) and current \(i_{abc}\) are measured and transformed to the αβ reference frame.
2. Positive- and negative-sequence components are extracted using standard symmetrical component separation methods.
3. The DC-link voltage \(U_{dc}\) is regulated by a PI controller that generates the active power reference \(P_{ref}\).
4. The reactive power reference \(Q_{ref}\) is determined according to the grid code requirements.
5. The reference currents in the αβ frame are calculated using the improved reference current algorithm with the lookup-table-based parameters.
6. The PR controllers track the reference currents and generate the modulation signals for the inverter.
This control architecture is both simple and effective, and it retains full compatibility with existing inverter hardware.
Simulation Validation and Discussion
I validated my proposed control strategy by building a detailed simulation model in the PSCAD/EMTDC environment. For the sake of clarity and ease of comparison, I set the system parameters as shown in Table 2.
| Parameter | Symbol | Value |
|---|---|---|
| Rated power | \(P_{rated}\) | 0.5 MW |
| DC-link voltage | \(U_{dc}\) | 800 V |
| DC-link capacitance | C | 5700 μF |
| Filter inductance | L | 1 mH |
| Switching frequency | f | 6 kHz |
| Maximum allowable peak current | \(I_{max}\) | 1.2 p.u. |
In the simulation, I initiated the system in steady state with the solar inverter operating at unity power factor and delivering its rated active power. A single-line-to-ground fault was applied at time t = 2 s, causing an asymmetric voltage sag at the inverter terminals. The duration of the fault was set to 0.4 s, and at time t = 2.4 s, my proposed peak current control strategy was activated. I analyzed three distinct fault scenarios with differing severities, characterized by the voltage unbalance factor \(\varepsilon\) and the positive-sequence voltage \(U^{+}\). The simulation results are summarized in Table 3.
| Scenario | \(\varepsilon\) | \(U^{+}\) (p.u.) | Current before control (p.u.) | Theoretical current (p.u.) | Current after control (p.u.) | Parameters |
|---|---|---|---|---|---|---|
| Mild fault | 0.18 | 0.95 | 1.30 | 1.28 | 1.19 | k1=0.645, k2=0 |
| Moderate fault | 0.30 | 0.887 | 1.60 | 1.61 | 1.20 | k1=0.163, k2=0.264 |
| Severe fault | 0.60 | 0.688 | 3.60 | 3.60 | 1.20 | P=0.15 p.u., Q=0.624 p.u. |
In the first scenario, the positive-sequence voltage remained at 0.95 p.u., which is above the 0.9 p.u. threshold for reactive power support. Therefore, the solar inverter continued to run at unity power factor with zero reactive power reference. However, because of the voltage imbalance, the output peak current increased to approximately 1.3 times the rated value. My theoretical calculation based on Equation (13) predicted a value of 1.28 p.u., which agrees well with the simulation. Since the peak current exceeded the maximum allowable value of 1.2 p.u., I activated the parameter tuning algorithm. The optimization determined that setting \(k_{1}=0.645\) and \(k_{2}=0\) would minimize the active power ripple while satisfying the current constraint. After this adjustment, the peak current was reduced to approximately 1.19 p.u., which is in good agreement with the theoretical value of 1.19 p.u. and safely within the limit. The waveforms of the output power showed that, before the control activation, the active power was essentially constant as expected for the constant active power strategy, whereas the reactive power exhibited a significant oscillatory component. After parameter tuning, the active power ripple slightly increased, but the reactive power ripple was substantially reduced. This trade-off is acceptable given that the primary goal of protecting the inverter is achieved.
In the second scenario, the voltage unbalance factor was 0.30 and the positive-sequence voltage was 0.887 p.u., which is below the 0.9 p.u. threshold. According to my control strategy, the solar inverter was required to provide reactive power support. Based on Equation (19), the reactive current should be \(2(1-0.887)=0.226\) p.u., which corresponds to a reactive power of 0.113 Mvar and an active power of 0.487 MW, maintaining the rated apparent power output. The simulation results indicated that the peak current before control was about 1.6 times the rated value, matching my theoretical prediction of 1.61 p.u. With the optimization algorithm, I obtained the parameter values \(k_{1}=0.163\) and \(k_{2}=0.264\), which kept the peak current at 1.19 p.u. After the control was enabled, the active power ripple increased slightly, but the reactive power ripple decreased. Importantly, the solar inverter was able to provide the required reactive power while maintaining an acceptable current level, thereby fulfilling both the grid code requirements and the inverter safety constraints.
In the third scenario, the voltage unbalance factor was 0.60, representing a severe fault condition. The positive-sequence voltage dropped to 0.688 p.u., and the output peak current reached 3.6 times the rated value. This is far above the acceptable limit. My analysis showed that adjusting \(k_{1}\) and \(k_{2}\) alone would not be sufficient to bring the current down to 1.2 p.u., because the necessary parameter values would cause excessive power oscillations. Therefore, I applied the third stage of my control strategy, setting \(k_{1}=1\) and \(k_{2}=1\) to maintain constant active power, while simultaneously reducing the power references by adjusting \(m\) and \(n\). The required reactive power was determined by the grid code: \(Q=0.624\) p.u. (0.312 Mvar). Using Equation (18), the maximum active power that could be exported while keeping the peak current at 1.2 p.u. was calculated as 0.15 p.u. (0.0725 MW). The simulation confirmed that the peak current was indeed limited to the desired value, and the active power remained essentially ripple-free. The reactive power ripple was also reduced compared to the pre-control condition. These results demonstrate the effectiveness of my approach even under very demanding scenarios.
To provide a more concrete comparison with previously published methods, I analyzed the performance of my strategy in the moderate fault scenario against a conventional approach. The approach described in Reference [14] was able to deliver 0.41 MW of active power while limiting the peak current to 1.5 p.u. In contrast, my proposed control strategy delivered 0.487 MW of active power while maintaining the peak current at the stricter limit of 1.2 p.u. This represents a meaningful improvement in both safety and power delivery capability. The improvement is attributed to the flexible parameter tuning mechanism in my reference current algorithm, which permits a more refined trade-off between current limitation and power output.
It is also worthwhile to compare my strategy with the Flexible Positive and Negative Sequence Control (FPNSC). FPNSC is well-known for its ability to manage power oscillations, but it tends to be computationally complex and does not explicitly limit the peak current. My approach, in contrast, provides a direct and explicit mechanism for peak current limitation while maintaining a moderate computational burden. Moreover, the use of the lookup table ensures that the controller can respond rapidly to fault conditions, which is essential for practical deployment in solar inverters.
Summary of Contributions
I summarize the main contributions of my research as follows:
First, I provided a thorough analysis of the peak current generation mechanism in grid-connected solar inverters under asymmetric voltage sags. I showed that the positive-sequence voltage drop and the appearance of negative-sequence voltage both contribute to the amplification of the output current. The theoretical expressions that I developed allow for accurate prediction of the peak current as a function of the voltage unbalance factor and the power references.
Second, I proposed an improved reference current algorithm for solar inverters with four adjustable parameters. These parameters enable independent control of the active and reactive power components, as well as the injection of negative-sequence currents in a controlled manner. I derived the mathematical relationship between the maximum peak current and the control parameters, which serves as the foundation for the online parameter selection.
Third, I developed a three-stage coordinated control strategy that ensures grid code compliance while protecting the inverter hardware. The strategy takes into account the severity of the fault, the reactive power requirements, and the inverter current limits. It is therefore applicable to a wide range of operating conditions.
Fourth, I presented a systematic procedure for parameter selection using the improved particle swarm optimization algorithm. The resulting lookup table makes the control strategy suitable for real-time implementation, with low computational overhead and high response speed.
Fifth, I validated the control strategy through comprehensive simulation studies. The simulation results are in close agreement with the theoretical calculations, confirming the correctness and effectiveness of my approach. Compared to existing methods, my strategy achieves better current limiting capability while preserving the ability to deliver more active power during the fault.
Conclusion
In this paper, I addressed the critical problem of peak current in grid-connected solar inverters during asymmetric voltage sags. The mechanism of current amplification was analyzed, revealing that both the reduction in positive-sequence voltage and the introduction of negative-sequence voltage contribute to the excessive current. To overcome this challenge, I proposed an improved reference current algorithm that embeds four independent control parameters. By properly adjusting these parameters, the peak current can be limited without sacrificing the active power delivery capability to the extent that conventional methods do. I further developed a coordinated active and reactive power control strategy that sequentially adjusts the control parameters based on the fault severity and grid code requirements. The use of a lookup table, precomputed using the improved particle swarm optimization, ensures fast and accurate parameter selection during real-time operation. The simulation results obtained in PSCAD/EMTDC confirmed the analytical predictions and demonstrated that the proposed strategy can maintain the peak current within the allowable range under a variety of fault conditions. This work provides a practical and effective solution for enhancing the fault ride-through capability and operational reliability of solar inverters.