In modern uninterruptible power supply (UPS) systems, the demand for high reliability and efficient power distribution has led to the widespread adoption of parallel-connected voltage source inverters (VSIs). Among these, the three-phase four-wire inverter topology is particularly advantageous for handling both balanced and unbalanced loads, such as single-phase and three-phase configurations. Traditional control methods for parallel VSI systems often rely on frequency and voltage droop techniques to manage active and reactive power flow. While these approaches offer improved reliability and redundancy, they suffer from limitations like slow dynamic response and inadequate voltage regulation. To address these issues, we explore a distributed control strategy that leverages instantaneous current information from all parallel units, enabling superior transient performance, accurate load sharing, and seamless integration or removal of inverters during operation. This paper focuses on applying this distributed control strategy to parallel three-phase four-wire VSIs in UPS applications, ensuring equitable load current distribution, rapid response to load variations, and enhanced system stability.
The foundation of our approach lies in the parallel operation of multiple three-phase four-wire VSIs, where each inverter unit contributes to supplying power to common loads. A key challenge in such systems is achieving precise current sharing among inverters while minimizing circulating currents and maintaining voltage quality. Traditional centralized control methods require extensive communication networks and complex computations, which can increase costs and reduce robustness. In contrast, the distributed control strategy proposed here utilizes local measurements and minimal external synchronization, simplifying implementation and improving scalability. By employing a dual-loop control structure—comprising an outer voltage control loop and an inner current control loop—we ensure that each three-phase inverter operates in harmony with others, even under dynamic conditions. This strategy not only enhances the reliability of UPS systems but also facilitates modular expansion, making it ideal for critical applications where uninterrupted power is paramount.
The control structure for parallel three-phase four-wire VSIs involves interconnected loops that regulate output voltage and balance currents. Each three-phase inverter in the system is equipped with filters—typically consisting of resistors (R), inductors (L), and capacitors (C)—to smooth the output waveforms and mitigate harmonics. The voltage control loop employs a PID controller to maintain the output voltages (v_A, v_B, v_C) in sync with a common reference, ensuring consistency across all phases. This loop acts as a communication link between inverters, though it requires only a single synchronization signal, reducing dependency on complex inter-inverter data exchange. The current control loop, on the other hand, uses proportional control to adjust the inductor currents (i_A, i_B, i_C), enabling accurate load current distribution. By incorporating virtual impedance, this loop mimics series resistance, which helps in damping oscillations and preventing circulating currents. The overall control framework is designed to be cost-effective, as it avoids additional sensors or intricate communication systems, and can be implemented using analog or digital circuits. This makes the three-phase inverter system highly adaptable for various UPS scenarios, from industrial setups to data centers.
To mathematically model the parallel three-phase inverter system, we consider the average model of a single-phase equivalent, which can be extended to three phases due to symmetry. The dynamics of each VSI are described by differential equations governing the inductor current and capacitor voltage. For a system with n parallel inverters, the state-space representation captures the interactions between components. Let i denote the inductor current, v_C represent the capacitor voltage, u be the inverter output voltage modulated by pulse-width modulation (PWM), and V_dc signify the DC-link voltage. The system equations are as follows:
$$ L \frac{di}{dt} = u V_{dc} – v_C $$
$$ C \frac{dv_C}{dt} = i – \frac{v_C}{R_0} $$
where R_0 is the load resistance. Transforming these into state-space form, we define the state vector as [i, v_C]^T, leading to:
$$ \frac{d}{dt} \begin{bmatrix} i \\ v_C \end{bmatrix} = \begin{bmatrix} 0 & -\frac{1}{L} \\ \frac{1}{C} & -\frac{1}{R_0 C} \end{bmatrix} \begin{bmatrix} i \\ v_C \end{bmatrix} + \begin{bmatrix} \frac{V_{dc}}{L} \\ 0 \end{bmatrix} u $$
Applying Laplace transforms, we derive the transfer functions that relate the input voltage to the output current and voltage, which are essential for controller design. The transfer functions for the three-phase inverter system are:
$$ \frac{i}{u} = \frac{V_{dc} (s R_0 C + 1)}{L C R_0 s^2 + L s + R_0} $$
$$ \frac{v_C}{u} = \frac{V_{dc} R_0}{L C R_0 s^2 + L s + R_0} $$
These transfer functions highlight the system’s frequency response and stability characteristics, guiding the selection of controller parameters. For the voltage control loop, we implement a discrete-time PID controller to account for sampling effects and computational delays. The PID controller, designed using z-transform techniques, is expressed as:
$$ \text{PID}_k[z] = \frac{u[z]}{e[z]} = \frac{1.281z^2 – 2.364z + 1.091}{z^2 – 1.025z + 0.02455} $$
This controller ensures precise voltage regulation by minimizing errors between the reference and actual voltages. In the current control loop, we introduce a virtual impedance K, which acts as a proportional gain to balance currents among parallel three-phase inverters. The value of K is selected based on per-unit (p.u.) system calculations, with a base impedance Z_b defined as:
$$ Z_b = \frac{V_b^2}{S_b} $$
where V_b is the base voltage and S_b is the base power. Setting K to 0.1 p.u. provides an effective means of current sharing, analogous to adding series impedance to the filter inductors. This approach enhances the dynamic performance of the three-phase inverter system, allowing it to handle load transients and nonlinearities without instability.
Simulation studies were conducted to validate the proposed distributed control strategy for parallel three-phase four-wire inverters. The tests evaluated both steady-state and dynamic performance under various conditions, including balanced loads, unbalanced loads, and nonlinear loads. In steady-state operation, two parallel three-phase inverters demonstrated equal current sharing, as evidenced by the identical magnitudes and phases of their output currents. The DC-link currents remained positive and balanced, indicating no circulating power between inverters. Load voltages maintained symmetry and stability, confirming the effectiveness of the control strategy. The following table summarizes key performance metrics from the simulations, highlighting improvements in current distribution and system efficiency:
| Parameter | Steady-State Value | Dynamic Response |
|---|---|---|
| Current Sharing Error | < 2% | < 5% during transients |
| Voltage THD | < 3% | < 5% under nonlinear loads |
| Response Time | N/A | < 10 ms for step changes |
Under dynamic conditions, such as step load changes or the sudden connection/disconnection of inverters, the system exhibited rapid response and stable operation. For instance, when a three-phase inverter was paralleled at 0.05 seconds, the load current was immediately shared between units without significant overshoot or oscillation. This demonstrates the strategy’s capability to maintain uninterrupted power supply even during fault conditions or maintenance events. Additionally, simulations with nonlinear loads—common in UPS applications—revealed that the control strategy effectively managed harmonic currents, ensuring smooth operation and minimal distortion. The virtual impedance played a crucial role in damping oscillations and enhancing robustness, making the three-phase inverter system resilient to various disturbances.
In conclusion, the distributed control strategy for parallel three-phase four-wire inverters offers a robust solution for UPS applications, addressing critical issues like load current sharing, dynamic response, and circulating currents. By combining voltage and current control loops with virtual impedance, this approach ensures that each three-phase inverter operates efficiently and harmoniously within the system. Simulation results confirm that the strategy provides fast transient response, accurate current distribution, and high reliability under diverse operating conditions. Future work could focus on optimizing controller parameters for specific load profiles and extending the strategy to larger-scale systems with multiple three-phase inverters. Overall, this research contributes to the advancement of UPS technology, emphasizing the importance of distributed control in achieving resilient and scalable power solutions.