In the context of the “dual-carbon” goals, renewable energy sources have experienced rapid development. However, the inherent randomness and intermittency of sources like photovoltaic and wind power generation weaken the ability of grid-connected points to actively support grid voltage amplitude and frequency, posing significant challenges to the security and stable operation of new power systems. The utility interactive inverter, serving as the power interface between distributed generation and the grid, plays a crucial role in converting stochastic and fluctuating renewable power into high-quality, stable AC power.
Traditional control methods for utility interactive inverters primarily include constant power control, constant voltage and frequency control, and droop control. Constant power control does not support grid frequency regulation. Constant voltage and frequency control methods maintain the inverter output at a constant voltage, widely used in off-grid operations. Droop control techniques enable inverters to emulate certain characteristics of synchronous machines, allowing utility interactive inverters to participate in primary frequency and voltage regulation of the grid, but they fail to provide system damping and inertia.
To enhance the support functions of utility interactive inverters, such as frequency and voltage regulation, virtual inertia and virtual damping have been introduced into control strategies, treating the inverter as a Virtual Synchronous Generator (VSG). This addresses frequency stability issues in high-penetration renewable energy grids. This method does not require a phase-locked loop; synchronization with the grid is achieved through its own algorithm. However, the voltage and angular frequency of distributed generation units employing traditional VSG control strategies are susceptible to power fluctuations and grid voltage disturbances, and their current control performance is relatively poor. To tackle these issues, this paper proposes an improved self-synchronizing voltage source control strategy for utility interactive inverters. Through balanced current control, the impedance characteristics between the internal potential of the self-synchronizing voltage source and the grid voltage are adjusted, enhancing current control capability under unbalanced grid conditions. Additionally, a DC-side voltage anti-collapse control is introduced to improve the stability of the DC-link voltage in photovoltaic self-synchronizing voltage source systems. The overall control strategy balances self-synchronizing characteristics with current performance, thereby improving the stability of renewable energy grid-connected systems.
Fundamental Principles of Self-Synchronizing Control
The main circuit topology of a utility interactive inverter based on a self-synchronizing voltage source is shown in the figure. In this configuration, $U_{dc}$ represents the DC-link voltage, $C_{dc}$ is the DC-side filter capacitor, $L$ is the filter inductance, $C_1$ is the filter capacitor, $R_C$ is the passive damping resistor in series with the filter capacitor, $R_g$ and $L_g$ are the equivalent grid resistance and inductance, respectively, $e_a$, $e_b$, $e_c$ are the three-phase grid voltages, $U_{od}$ and $U_{oq}$ are the d-axis and q-axis components of the grid-connected point voltage, and $I_{od}$ and $I_{oq}$ are the d-axis and q-axis components of the grid-connected point current.
Using instantaneous power theory, the actual output active power $P$ and reactive power $Q$ of the system are calculated as:
$$
P = 1.5 (u_{od} i_{od} + u_{oq} i_{oq})
$$
$$
Q = 1.5 (u_{od} i_{oq} – u_{oq} i_{od})
$$
The active power loop primarily emulates the rotor motion equation of a synchronous generator:
$$
\omega = \omega_0 + \frac{m}{J\omega_0 s + 1} (P_0 – P)
$$
$$
\frac{d\theta}{dt} = \omega
$$
where $\omega_0$ is the rated angular frequency when the utility interactive inverter’s given active power command is $P_0$, $m$ is the droop coefficient for power-angle control, $J$ is the virtual moment of inertia simulating synchronous generator units, and $s$ is the Laplace operator. The output phase angle $\theta$ of the self-synchronizing voltage source is obtained by integrating $\omega$.
The reactive power loop for the VSG is:
$$
E^* = U_0 + n (Q_0 – Q)
$$
where $U_0$ is the rated voltage, $n$ is the reactive power-voltage droop coefficient (typically set such that a 100% change in reactive power results in a voltage amplitude change within 2%), $Q_0$ is the rated reactive power, and $E^*$ is the output voltage amplitude command of the VSG.
Combining the amplitude information $E^*$ from the reactive power loop and the phase information $\theta$ from the active power loop, the voltage control signal $u_{ref}$ is generated, which serves as the modulation wave for PWM.
Improved Control Method Based on Self-Synchronizing Voltage Source
To address issues such as active support and grid current performance enhancement in grid-connected mode, an improved self-synchronizing voltage source control method for utility interactive inverters is proposed. Compared to traditional self-synchronizing control methods, the proposed approach incorporates a balanced current control loop based on a PIR regulator, thereby improving current control capability and disturbance rejection, and enhancing system stability.
Improved Control Scheme
The control block diagram of the proposed self-synchronizing voltage source method is illustrated. Key enhancements include the balanced current control and DC-side voltage anti-collapse control.
The proposed self-synchronizing voltage source control method can be effectively applied to photovoltaic grid-connected systems. To prevent DC-link voltage instability under power disturbances, a DC-side voltage anti-collapse control is introduced. This control acts as a PI controller with an upper limit of 0, where the reference input signal is $U_{dc\_min}$ (the minimum power point voltage from MPPT) and the output signal is the active power increment $\Delta P_{ref}$. When $U_{dc}$ is above $U_{dc\_min}$, the controller output is 0, and the photovoltaic source operates in the droop characteristic region. When the load increases beyond the MPP power of the photovoltaic source, the DC capacitor continues to discharge. Once $U_{dc}$ falls below $U_{dc\_min}$, the controller rapidly reduces $P$, stabilizing $U_{dc}$ at $U_{dc\_min}$. The proportional and integral coefficients $k_{pU_{dc}}$ and $k_{iU_{dc}}$ are designed to improve response speed and eliminate steady-state error, respectively.
Coordinate Transformation and Power Calculation
Voltages and currents are measured at various points: filter capacitor voltages $u_{Ca}$, $u_{Cb}$, $u_{Cc}$; bridge-side inductor currents $i_{La}$, $i_{Lb}$, $i_{Lc}$; grid-connected point voltages $u_{oa}$, $u_{ob}$, $u_{oc}$; and grid-connected point currents $i_{oa}$, $i_{ob}$, $i_{oc}$. These are transformed into dq components via single synchronous rotating coordinate transformation, yielding $U_{Cd}$, $U_{Cq}$, $I_{Ld}$, $I_{Lq}$, etc.
Let the discrete sequences of $U_{Cd}$ and $U_{Cq}$ be $U_{Cd}(n)$ and $U_{Cq}(n)$, and the discrete sequences of filter capacitor current dq components $I_{Cd}$ and $I_{Cq}$ be $I_{Cd}(n)$ and $I_{Cq}(n)$. The generic differential discretization equation for calculating filter capacitor currents is:
$$
I_{Cd}(n) = I_{Cd}(n-1) + \frac{C T_s}{N} \sum_{k=0}^{K} k_{n-k} U_{Cd}(n-k)
$$
$$
I_{Cq}(n) = I_{Cq}(n-1) + \frac{C T_s}{N} \sum_{k=0}^{K} k_{n-k} U_{Cq}(n-k)
$$
where $C$ is the value of filter capacitor $C_1$, $T_s$ is the inverter sampling frequency, $K$ is the number of discrete sequence points, and $n$ and $k$ are natural numbers.
From the discrete sequences $I_{Cd}(n)$ and $I_{Cq}(n)$, the filter capacitor current dq components $I_{Cd}$ and $I_{Cq}$ are obtained. The output current dq components $I_{od}$ and $I_{oq}$ are derived from the output current calculation equation:
$$
I_{od} = I_{Ld} – I_{Cd}
$$
$$
I_{oq} = I_{Lq} – I_{Cq}
$$
The average active power $P$ and average reactive power $Q$ are computed as:
$$
P = \left( \prod_h \frac{s^2 + \omega_h^2}{s^2 + 2Q_{pq}\omega_h s + \omega_h^2} \right) \cdot \frac{1.5}{\tau s + 1} \cdot (U_{Cq} I_{oq} + U_{Cd} I_{od})
$$
$$
Q = \left( \prod_h \frac{s^2 + \omega_h^2}{s^2 + 2Q_{pq}\omega_h s + \omega_h^2} \right) \cdot \frac{1.5}{\tau s + 1} \cdot (U_{Cd} I_{oq} – U_{Cq} I_{od})
$$
where $Q_{pq}$ is the quality factor of the power calculation equation, $\omega_h$ is the angular frequency of harmonics to be filtered out, $\tau$ is the time constant of the first-order low-pass filter, and $h$ is the harmonic order to be eliminated.
Angular Frequency Calculation and Three-Phase Terminal Voltage Command
Based on the average active power $P$ and the given active power command $P_0$ of the utility interactive inverter, the angular frequency $\omega$ of the self-synchronizing voltage source is obtained through the power-angle control equation, as shown in Equation (2). The parameter $J$ represents the rate of change of system frequency; a larger $J$ ensures smoother frequency changes but may introduce instability if too high. The droop coefficient $m$ is typically set such that a 100% change in active power results in a frequency change within 0.5 Hz. $P_0$ and corresponding $\omega_0$ define the droop curve’s position.
Based on the average reactive power $Q$ and the given reactive power command $Q_0$ of the utility interactive inverter, the terminal voltage amplitude command $E^*$ of the self-synchronizing voltage source is derived from the reactive power control equation, as in Equation (3). Using the vector angle $\theta$ and amplitude command $E^*$, the three-phase terminal voltage commands are synthesized:
$$
e_{aref} = E^* \sin(\theta)
$$
$$
e_{bref} = E^* \sin(\theta – 120^\circ)
$$
$$
e_{cref} = E^* \sin(\theta + 120^\circ)
$$
Balanced Current Control
From the three-phase terminal voltage commands $e_{aref}$, $e_{bref}$, $e_{cref}$ and the measured grid voltages $u_{oa}$, $u_{ob}$, $u_{oc}$, the current reference signals are obtained through balanced current control:
$$
i_{aref} = \frac{e_{aref} – u_{oa}}{s L_v + R_v}
$$
$$
i_{bref} = \frac{e_{bref} – u_{ob}}{s L_v + R_v}
$$
$$
i_{cref} = \frac{e_{cref} – u_{oc}}{s L_v + R_v}
$$
where $R_v$ is the virtual resistance and $L_v$ is the virtual inductance. These parameters simulate the total resistance and inductance between the utility interactive inverter output and the grid, establishing the voltage-current vector relationship between the internal potential terminal of the VSG control output and the grid-connected point. This enhances current control capability, and appropriately reducing virtual impedance can suppress unbalance.
The current reference signals $i_{aref}$, $i_{bref}$, $i_{cref}$ are transformed into dq coordinates to obtain $i_{dref}$ and $i_{qref}$. Combined with the measured bridge-side inductor current dq components $I_{Ld}$ and $I_{Lq}$, the control signals are derived via the current control equation:
$$
U_d = \left( K_p + \frac{K_i}{s} + \frac{K_{ri} s}{Q_i \omega_0 s + \omega_0^2} \right) (i_{dref} – I_{Ld})
$$
$$
U_q = \left( K_p + \frac{K_i}{s} + \frac{K_{ri} s}{Q_i \omega_0 s + \omega_0^2} \right) (i_{qref} – I_{Lq})
$$
where $K_p$ is the proportional control coefficient of the current loop, $K_i$ is the integral control coefficient, $K_{ri}$ is the resonant controller coefficient, and $Q_i$ is the quality factor of the quasi-resonant regulator. The quasi-resonant regulator primarily eliminates DC components in the system, with the quality factor considering gain and stability.
The control signals $U_d$ and $U_q$ are inversely transformed to obtain voltage control signals $u_a$, $u_b$, $u_c$, which generate PWM signals for the switches.
System Modeling and Stability Analysis
To further analyze the proposed control method, a small-signal model of the utility interactive inverter system is developed. The state-space equations are derived considering the self-synchronizing voltage source dynamics, balanced current control, and DC-link dynamics. The key state variables include the angular frequency $\omega$, voltage amplitude $E^*$, dq-axis currents, and DC-link voltage $U_{dc}$.
The linearized model around an operating point can be expressed in matrix form:
$$
\Delta \dot{x} = A \Delta x + B \Delta u
$$
where $\Delta x$ is the state vector, $\Delta u$ is the input vector, and $A$ and $B$ are system matrices. The eigenvalues of matrix $A$ determine system stability. Parameters such as virtual inertia $J$, droop coefficients $m$ and $n$, and current loop gains $K_p$, $K_i$, $K_{ri}$ are tuned to ensure all eigenvalues have negative real parts, indicating stable operation.
A comprehensive parameter sensitivity analysis is conducted to evaluate the impact of key parameters on system performance. For instance, increasing virtual inertia $J$ improves frequency stability but may slow down dynamic response. The balanced current control enhances damping, as evidenced by eigenvalue loci moving leftward in the complex plane.
| Parameter | Symbol | Typical Range | Effect on Stability |
|---|---|---|---|
| Virtual Inertia | $J$ | 0.1 – 10 kg·m² | Higher values improve frequency nadir but may cause overshoot. |
| Droop Coefficient (Active) | $m$ | 0.01 – 0.1 rad/kW | Affects power sharing and frequency regulation. |
| Droop Coefficient (Reactive) | $n$ | 0.01 – 0.1 V/kVar | Influences voltage support and reactive power distribution. |
| Virtual Resistance | $R_v$ | 0.1 – 1 Ω | Enhances damping and current limiting. |
| Virtual Inductance | $L_v$ | 1 – 10 mH | Affects current dynamics and harmonic rejection. |
| Current Loop Proportional Gain | $K_p$ | 0.5 – 2 | Higher gains improve response but may reduce stability margin. |
| Current Loop Integral Gain | $K_i$ | 5 – 50 | Eliminates steady-state error; too high causes oscillation. |
| Resonant Controller Gain | $K_{ri}$ | 10 – 100 | Supports harmonic compensation; optimal tuning required. |
The stability margins (gain margin and phase margin) are evaluated through frequency response analysis of the open-loop transfer functions. The proposed control method demonstrates robust stability across a wide range of grid impedances, including weak grid conditions with Short Circuit Ratio (SCR) as low as 1.5.
Simulation and Experimental Verification
To validate the effectiveness and superiority of the proposed self-synchronizing voltage source control method for utility interactive inverters, simulation models of both the traditional self-synchronizing control strategy and the proposed method are built in MATLAB/Simulink. Key parameters are listed in Table 2.
| Parameter | Value |
|---|---|
| Rated AC Voltage $U_0$ | 380 V |
| DC-link Voltage $U_{dc}$ | 650 V |
| Filter Inductance $L$ | 0.3 mH |
| Filter Capacitance $C_1$ | 200 μF |
| Active Power Command $P_0$ | 100 kW |
| Rated Angular Frequency $\omega_0$ | 314 rad/s |
| Passive Damping Resistor $R_C$ | 0.266 Ω |
| Reactive Power Command $Q_0$ | 0 |
| Sampling Frequency | 10 kHz |
| Active-Frequency Droop Coefficient $m$ | 0.025 rad/kW |
| Reactive-Voltage Droop Coefficient $n$ | 0.076 V/kVar |
| Current Loop Proportional Gain $K_p$ | 0.8 |
| Current Loop Integral Gain $K_i$ | 10 |
| Resonant Controller Gain $K_{ri}$ | 50 |
Steady-State Performance Analysis
The control capability of the proposed method under steady-state conditions is analyzed. Figure 1 shows the grid-connected voltage and current waveforms of the proposed method under weak grid conditions (SCR = 1.5). The results indicate that the proposed self-synchronizing voltage source control method ensures stable and symmetrical three-phase grid-connected point voltages and currents under steady-state conditions, with the system operating stably.
During transient processes caused by renewable energy uncertainty, the total power control response within the interconnected system can track reference commands well, with adjustment times not exceeding 2 seconds and overshoot within 10%, demonstrating strong robustness and tracking performance.
Performance Under Three-Phase Unbalance
Scenario: Phase A undervoltage with unbalance degree of 4%, resulting in Phase A voltage amplitude of 0.94 pu. Figure 2 compares the grid-connected point current waveforms of the proposed method and the traditional self-synchronizing control method when SCR = 1.5. Phase A grid voltage is set to 0.94 pu during 2.0–2.2 s. Through waveform comparison and unbalance degree calculation, under identical grid voltage conditions, the current unbalance degree of the traditional self-synchronizing control method is 5.68%, while that of the proposed method is 1.02%. Thus, the proposed self-synchronizing voltage source control method exhibits stronger capability in suppressing unbalance.
| Control Method | Current Unbalance Degree | Improvement |
|---|---|---|
| Traditional Self-Synchronizing Control | 5.68% | — |
| Proposed Self-Synchronizing Voltage Source Control | 1.02% | 82% reduction |
Disturbance Rejection Capability Analysis
A comparative analysis of disturbance rejection capability between the proposed method and traditional self-synchronizing control is conducted. Figure 3 shows grid current waveforms under voltage sag conditions using different control methods. Grid voltage sags by 50% during 1.5–1.7 s, with SCR = 1.5.
Waveform comparison reveals that the grid current peak of the traditional self-synchronizing control method approaches 800 A, whereas that of the proposed method is less than 500 A. Thus, the proposed method offers better current control capability compared to traditional self-synchronizing control.
| Control Method | Peak Grid Current (A) | Reduction |
|---|---|---|
| Traditional Self-Synchronizing Control | 800 | — |
| Proposed Self-Synchronizing Voltage Source Control | 500 | 37.5% reduction |
Experimental Results
The proposed control method is further validated through a hardware-in-the-loop experimental platform. Parameters are set according to Table 2. First, the steady-state performance of the proposed control method is verified, as shown in Figure 4. The grid-connected point voltage and current experimental waveforms are three-phase symmetrical, with the system operating stably.
The performance under three-phase unbalance is experimentally verified, as shown in Figure 5. Comparative analysis and unbalance degree calculation show that the grid current unbalance degree of the traditional method is 6.56%, while that of the proposed method is 1.33%. Therefore, the experimental waveforms of the proposed control method exhibit higher balance under identical grid conditions.
The disturbance rejection capability is experimentally validated, as shown in Figure 6. The grid current peak of the traditional self-synchronizing control method is 700 A, while that of the proposed method is 500 A. Compared to traditional self-synchronizing control, the proposed control method yields smaller grid-connected point current peaks. The proposed self-synchronizing voltage source control method for utility interactive inverters demonstrates superior performance in current control and disturbance rejection.
| Metric | Traditional Control | Proposed Control | Enhancement |
|---|---|---|---|
| Current THD at Rated Load | 4.2% | 2.1% | 50% reduction |
| Frequency Recovery Time after Step Load | 1.8 s | 1.2 s | 33% faster |
| Voltage Regulation under ±20% Load Change | ±3.5% | ±1.8% | 49% improvement |
| DC-link Voltage Ripple under Disturbance | 12 V | 5 V | 58% reduction |
Comparative Analysis with Other Advanced Methods
To place the proposed method in context, a comparative analysis with other advanced control strategies for utility interactive inverters is conducted. Key competitors include enhanced VSG with adaptive inertia, model predictive control (MPC), and sliding mode control (SMC).
| Control Strategy | Key Features | Advantages | Disadvantages | Suitability for High-Penetration Renewables |
|---|---|---|---|---|
| Traditional VSG | Emulates synchronous machine dynamics, provides inertia and damping. | Simple implementation, grid-friendly. | Poor current control under disturbances, parameter sensitivity. | Moderate |
| Enhanced VSG with Adaptive Inertia | Adjusts virtual inertia based on frequency deviation. | Improved frequency response, better stability. | Increased complexity, tuning challenges. | Good |
| Model Predictive Control (MPC) | Uses system model to predict future states and optimize control actions. | Fast dynamic response, handles constraints. | Computationally intensive, requires accurate model. | High (if computational resources available) |
| Sliding Mode Control (SMC) | Robust control via sliding surface, invariant to matched uncertainties. | Strong robustness, simple implementation. | Chattering issues, may require high switching frequencies. | Good |
| Proposed Self-Synchronizing Voltage Source Control | Combines self-synchronization with balanced current control and DC-voltage anti-collapse. | Excellent current quality, robust to unbalance and disturbances, stable DC-link. | Moderate complexity in parameter tuning. | Excellent |
The proposed method outperforms others in terms of current quality and disturbance rejection, making it particularly suitable for weak grids and unbalanced conditions. Its self-synchronizing capability eliminates the need for PLL, enhancing reliability. The integration of balanced current control and DC-voltage anti-collapse ensures comprehensive performance for utility interactive inverters in modern power systems.
Mathematical Formulations for Extended Analysis
To deepen the understanding, additional mathematical formulations are provided. The dynamics of the DC-link voltage can be expressed as:
$$
C_{dc} \frac{dU_{dc}}{dt} = P_{pv} – P_{ac}
$$
where $P_{pv}$ is the power from the photovoltaic source and $P_{ac}$ is the AC output power. Under the anti-collapse control, when $U_{dc} < U_{dc\_min}$, the active power reference is adjusted as:
$$
P_{ref} = P_0 – \Delta P_{ref}, \quad \Delta P_{ref} = \min\left(0, k_{pU_{dc}}(U_{dc\_min} – U_{dc}) + k_{iU_{dc}} \int (U_{dc\_min} – U_{dc}) dt\right)
$$
The impedance model of the utility interactive inverter with virtual impedance is:
$$
Z_v(s) = R_v + s L_v
$$
The current control loop transfer function $G_c(s)$ is:
$$
G_c(s) = K_p + \frac{K_i}{s} + \frac{K_{ri} s}{s^2 + Q_i \omega_0 s + \omega_0^2}
$$
The overall closed-loop transfer function from reference to output current can be derived, and bandwidth analysis shows improved tracking for harmonics up to the 13th order.
For frequency support, the equivalent inertia constant $H_{eq}$ provided by the utility interactive inverter is:
$$
H_{eq} = \frac{J \omega_0^2}{2 S_b}
$$
where $S_b$ is the base power. With proper tuning, the proposed method can provide inertia comparable to conventional generators, enhancing grid frequency stability.
Conclusion
This paper proposes an improved self-synchronizing voltage source control method for utility interactive inverters to enhance grid self-synchronizing characteristics and current performance. The balanced current control improves current control capability under unbalanced voltage conditions and system stability. The DC voltage anti-collapse control enhances DC-link voltage stability. Simulation and experimental results demonstrate that the proposed self-synchronizing voltage source control method offers better current control capability and disturbance rejection compared to traditional self-synchronizing control. The method effectively balances self-synchronization with high-quality current output, making it a robust solution for renewable energy integration in modern power systems. Future work may focus on adaptive parameter tuning for varying grid conditions and integration with energy storage systems for enhanced flexibility.
In summary, the utility interactive inverter equipped with the proposed control strategy not only supports grid frequency and voltage actively but also maintains superior current quality under disturbances, contributing significantly to the reliability and stability of high-penetration renewable energy grids. The comprehensive approach, combining self-synchronization, balanced current control, and anti-collapse mechanisms, sets a new benchmark for utility interactive inverter performance in challenging operating environments.