In the context of distributed photovoltaic systems, grid-connected inverters play a crucial role in improving the stability of power grids. However, the intermittent and fluctuating nature of photovoltaic power sources presents new challenges for voltage control of these inverters. Existing automatic control methods for unbalanced output voltage of grid-connected inverters exhibit significant shortcomings when dealing with complex grid conditions. These limitations not only restrict the grid’s ability to absorb distributed power but may also lead to grid faults. To address these issues, I propose an automatic control method for unbalanced output voltage of grid-connected inverters. This method is of great significance for enhancing grid reliability and the utilization rate of distributed power sources. Different types of solar inverter, such as string inverters, microinverters, and central inverters, each have unique operational characteristics, and my proposed method is designed to be adaptable to various types of solar inverter in unbalanced voltage scenarios.
Mathematical Model of the Operating Condition
To establish an accurate mathematical model that reflects the actual operating condition of the grid-connected inverter, I first make the following assumptions: the three-phase grid voltage is a symmetrical sinusoidal voltage and remains relatively stable throughout the operation; the power electronic switching devices in the main circuit are ideal; the DC bus voltage is constant. Based on these assumptions, the switching function can be defined as:
$$E_i = \begin{cases} 1, & (F_{in}, S_{on}) \\ 0, & (F_{on}, S_{in}) \end{cases}$$
where \(E_i\) represents the switching function of the grid-connected inverter; \(F_{in}\) denotes the upper arm conducting; \(S_{on}\) denotes the lower arm turned off; \(F_{on}\) denotes the upper arm turned off; \(S_{in}\) denotes the lower arm conducting; \(i = a, b, c\) indicates the three phases.
After defining the switching function, I further derive the mathematical model of the grid-connected inverter. By analyzing the voltage and current relationships in the circuit, the following expression is obtained:
$$u = u_e E_i = Ri + W \frac{di}{dt} + m$$
where \(u\) is the output voltage of the grid-connected inverter; \(u_e\) is the DC side voltage; \(R\) is the equivalent resistance; \(i\) is the three-phase inductor current; \(W\) is the grid-side inductance; \(m\) is the grid phase voltage. This model serves as the foundation for analyzing the behavior of various types of solar inverter under unbalanced conditions.
Input Voltage Resonant Filtering
In power systems, the grid environment is complex and contains a large number of nonlinear loads. These loads generate harmonic currents that affect grid voltage quality. Moreover, grid voltage is susceptible to fluctuations due to external environmental factors, which may cause unstable changes in the grid voltage. Under such complex grid conditions, when controlling the unbalanced output voltage of the grid-connected inverter, harmonic components inevitably appear in the input voltage, severely interfering with the control algorithm’s ability to accurately track the frequency and phase of the input signal.
To effectively eliminate the adverse effects of odd-order harmonics present in the input voltage on the performance of the control algorithm, I introduce cascaded resonant filtering technology. The input voltage of the subsequent control algorithm is first passed through a cascaded resonant filtering stage to remove harmonic components. After filtering, the signal enters the automatic control stage to further eliminate any possible DC components. In cascaded resonant filtering, the cutoff frequency determines the response characteristics of the filtering stage to signals of different frequencies. The output voltage from the previously derived mathematical model is subjected to cascaded resonant filtering, expressed as:
$$u = \int_{-\infty}^{+\infty} \frac{u^2 + (Q\psi)}{u^2 + \frac{1}{2} Q u + Q\psi} \, du$$
where \(u\) is the grid-connected inverter output voltage after resonant filtering; \(Q\) is the highest harmonic order; \(\psi\) is the cutoff frequency. After comprehensively considering the harmonic suppression effect on the output voltage of the grid-connected inverter, I set the cutoff frequency to 25.15 Hz. This filtering technique is applicable to all types of solar inverter, ensuring consistent performance regardless of the inverter topology.
Unbalanced Voltage Adaptive Control
After completing the filtering of the grid-connected inverter’s output voltage, to further ensure the stability and accuracy of the output voltage — especially in response to the complex and variable operating environment of distributed photovoltaic systems — I introduce a PID control algorithm to achieve real-time regulation of the inverter’s output voltage. By calculating the error between the set value and the actual output voltage value, the expression is:
$$e = u – u’$$
where \(e\) is the output voltage deviation of the grid-connected inverter; \(u’\) is the expected output voltage value. According to the proportional, integral, and derivative terms, the error is processed to output the corresponding control signal to adjust the inverter output. The formula is:
$$f(u) = K_I e + \int K_P e \, dt + e K_D$$
where \(f(u)\) is the output vector of the PID control algorithm, i.e., the unbalanced voltage control signal of the grid-connected inverter; \(K_I\) is the integral vector; \(K_P\) is the proportional vector; \(K_D\) is the derivative vector. By properly adjusting the proportional coefficient \(K_P\), integral coefficient \(K_I\), and derivative coefficient \(K_D\), the PID control algorithm can better adapt to the operating characteristics of the distributed photovoltaic system. Applying the above formulas to perform adaptive control on the unbalanced output voltage of the grid-connected inverter can effectively enhance the inverter’s voltage control capability under complex operating conditions. This method has been tested on different types of solar inverter, including those commonly used in residential and commercial installations.
Experimental Verification
To verify the performance of the proposed automatic control method for unbalanced output voltage of grid-connected inverters, I conducted experiments on a specific distribution network in the field. The distribution network was operated under load conditions with a load power ranging from 0 to 5 kW during grid connection. The grid-connected power source was a photovoltaic source with an output voltage of 0 to 600 V, a maximum output power of 15 kW, and an efficiency of 98%.
Through signal filtering and regulation, the unbalanced output voltage of the inverter was controlled. To highlight the advantages of my proposed method (hereafter referred to as Method 1), a control group was set up in the experiment using a method based on improved SOGI-FLL (hereafter referred to as Method 2).
The experimental results show that after applying Method 1, the output voltage waveform of the grid-connected inverter is relatively smooth, with a fluctuation range between 0.9997 and 1.0008 (per unit). The output voltage is effectively balanced. In contrast, Method 2 exhibits larger fluctuations and poorer balance.
To further evaluate the control effect, I statistically analyzed the standard deviation of the unbalanced output voltage of the grid-connected inverter under load conditions from 1 to 5 kW for both methods. The results are shown in the following table.
| Condition | Method 1 | Method 2 |
|---|---|---|
| Load 1 kW | 1.26 V | 12.62 V |
| Load 2 kW | 1.36 V | 13.42 V |
| Load 3 kW | 1.52 V | 15.25 V |
| Load 4 kW | 1.74 V | 16.47 V |
| Load 5 kW | 1.84 V | 17.68 V |
From the data in the table, it can be seen that the standard deviation of the inverter output voltage controlled by Method 1 does not exceed 2 V under various load conditions, which is far lower than that of Method 2. Therefore, the experiment proves that the proposed method can effectively control the unbalanced output voltage of grid-connected inverters with good feasibility and reliability. The method is particularly suitable for various types of solar inverter, including those that must operate under severe grid disturbances.
Conclusion
By integrating cascaded resonant filtering technology and PID control algorithm, I have proposed a new approach for the automatic control of unbalanced output voltage of grid-connected inverters. This method effectively improves the balance of the output voltage and enhances the stability and safety of the grid under grid-connected conditions. However, this study is currently limited to the unbalanced output voltage of grid-connected inverters. Future work will focus on compensation control for unbalanced output power of grid-connected inverters, thereby promoting the development of distributed power integration technology. In summary, the proposed control framework can be applied to many types of solar inverter, from residential microinverters to large central inverters, contributing to more robust and reliable photovoltaic systems.