With the rapid advancement of renewable energy technologies and the expanding scale of power grids, AC power supply is transitioning from centralized to distributed systems. Distributed energy resources are poised to play an increasingly significant role in future electricity supply. A typical AC microgrid structure comprises photovoltaic generation, wind power, energy storage units, and AC/DC loads, operating in either islanded or grid-connected modes, with energy provided by distributed sources and storage units. In this context, DC-DC sources are widely utilized in distributed energy systems, and when integrated into AC microgrids via DC-AC converters, challenges arise in proportional power distribution and output voltage sharing among inverters due to parameter variations. This can lead to circulating currents, severely impacting system stability and reliability. Therefore, designing parallel single phase inverter systems that ensure safe mode switching and enhanced stability is crucial.
We propose an intelligent power allocation strategy for single phase inverters in distributed energy access to AC microgrids, aiming to improve the stability of parallel and grid-connected inverter systems. In grid-connected operations, inverters require phase-locking to the reference voltage for SPWM modulation, controlling the output AC signal to match the grid’s phase and frequency. Traditional methods often involve communication between inverters for parallel control, which introduces delays, instability, and inefficiencies. Our approach eliminates the need for communication lines, employing potential difference current sharing and SOGI-PLL for phase synchronization, enabling intelligent power distribution without inter-inverter communication.
The system topology for the single phase inverter parallel and grid-connected operation is illustrated in the block diagram. It consists of control modules, main power modules, instantaneous sampling modules, RMS sampling modules, auxiliary power modules, and transformers. Each single phase inverter is a full-bridge type, generating SPWM waves via MCU modulation based on grid voltage sampling. PI closed-loop control stabilizes the output waveform, facilitating parallel and grid-connected operation. Key parameters include a DC input voltage of 50V, AC output voltage of 24V at 50Hz, with filtering components such as 470μH inductors and 1μF capacitors.
In parallel single phase inverter systems, multiple inverters operate together to increase system capacity. However, circulating currents due to imperfect current sharing can cause failures. To mitigate this, we use potential difference current sharing, which minimizes circulating currents by ensuring similar output voltages. Additionally, the circulating current phenomenon is analyzed mathematically. For a single phase inverter, the mathematical model is derived using KCL and KVL laws. The output voltage \( U_{o1} \) for one inverter can be expressed as:
$$ L \frac{dI_L}{dt} = U_Q – U_{o1} – I_L r $$
$$ C \frac{dU_{o1}}{dt} = I_L – I_{o1} $$
where \( U_Q \) is the inverter bridge output voltage, \( r \) is the equivalent resistance, \( L \) is the inductance, and \( C \) is the capacitance. Applying Laplace transform, the transfer function \( G(s) \) for the LC filter is:
$$ G(s) = \frac{U_{o1}(s)}{U_Q(s)} = \frac{r_1}{LC r_1 s^2 + (L + r r_1 C) s + (r + r_1)} $$
For the parallel system, with two single phase inverters, the equivalent model includes impedances \( Z_1 \) and \( Z_2 \), and the circulating current \( I_h \) is given by:
$$ I_h = \frac{1}{2} (I_{o1} – I_{o2}) = \frac{U_{o1} – U_{o2}}{2jX} $$
where \( X \) is the inductive reactance. This shows that circulating current is proportional to the voltage difference between inverters and inversely proportional to impedance. By controlling output voltages to be equal, circulating currents are reduced.
To achieve arbitrary current ratio distribution in parallel single phase inverters, we implement a voltage-current loop cyclic control strategy. The control flowchart involves setting a reference output voltage \( U_{ref} \) and current ratio \( K_{ref} \). The system samples the output voltage \( U_o \) and branch currents \( I_{o1} \) and \( I_{o2} \). If \( U_o \) does not match \( U_{ref} \), voltage PI control adjusts the modulation index; if the current ratio deviates from \( K_{ref} \), current PI control is applied. This cycle continues until both conditions are met, enabling proportional current sharing.
For grid connection, synchronization is critical. We employ a SOGI-PLL for accurate phase and frequency detection of the grid voltage. The SOGI generates orthogonal signals \( U_\alpha \) and \( U_\beta \) from the single-phase input \( U \):
$$ U = U_g \sin(\omega t + \phi) $$
$$ U_\alpha = U_g \sin(\omega t + \phi) $$
$$ U_\beta = -U_g \cos(\omega t + \phi) $$
The transfer functions for the orthogonal signal generator are:
$$ D(s) = \frac{U_\alpha(s)}{U(s)} = \frac{k \omega s}{s^2 + k \omega s + \omega^2} $$
$$ Q(s) = \frac{U_\beta(s)}{U(s)} = \frac{k \omega^2}{s^2 + k \omega s + \omega^2} $$
where \( k \) is the gain coefficient. Bode analysis shows that smaller \( k \) values improve filtering but slow response; we choose \( k = 1 \) for balance. The locked phase signal serves as the SPWM reference, ensuring the single phase inverter output matches the grid.
In grid-connected mode, intelligent power allocation is achieved through open-closed loop alternating control without communication. The bus current is set with upper and lower limits. Inverter 1 sets the total current \( I_{oset} \), and if the sampled current \( I_o \) is outside limits, closed-loop control adjusts the modulation index \( M \). Once within limits, the system switches to open loop. Inverter 2 automatically adjusts its current to maintain the total, allowing proportional distribution based on a set ratio \( K \). This minimizes oscillations and harmonic interference.
We validated the control strategy using MATLAB/Simulink simulations. The model parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| DC Side Voltage | 50 V |
| AC Side Voltage | 24 V |
| Grid Frequency | 50 Hz |
| Sampling Frequency | 1 kHz |
| Filter Inductance | 470 μH |
| Filter Capacitance | 1 μF |
Simulation results for SOGI-PLL show orthogonal signals \( U_\alpha \) and \( U_\beta \) with a phase difference of \( \pi/2 \). With PI controller parameters \( K_P = 0.1 \) and \( K_I = 0.5 \), the grid-connected output voltage peaks at 23.95 V, with an error less than 0.21%. The THD under PI control is below 0.25%, confirming stability and effectiveness. Parallel operation of two single phase inverters demonstrates accurate phase tracking and dynamic response. For instance, at a total current of 3 A, currents are distributed in a 1:2 ratio, and at 2.7 A, in a 1:1.5 ratio, verifying proportional power allocation.
An experimental prototype was built to test the single phase inverter system. The platform includes a 50 V DC input, 24 V AC output at 50 Hz, with a 10 Ω resistive load. Efficiency and THD measurements are shown in Table 2 for inverter 1 in islanded mode.
| Parameter | Value |
|---|---|
| Output Voltage | 24.01 V |
| Output Current | 2.41 A |
| Output Frequency | 49.9 Hz |
| Efficiency | 92.3% |
Load regulation tests, summarized in Table 3, show minimal voltage variation and low THD across different resistances, with efficiency up to 92.25%.
| Load Resistance (Ω) | Output Voltage (V) | THD (%) | Efficiency (%) |
|---|---|---|---|
| 0 | 24.01 | 0.04 | 0 |
| 10 | 24.02 | 0.08 | 90.75 |
| 20 | 24.02 | 0.08 | 92.25 |
In parallel operation, the total output current is 4.71 A, with small voltage differences minimizing circulating currents. For grid connection, the single phase inverter outputs synchronize closely with the grid voltage, as seen in waveform comparisons. Efficiency tests show inverter 1 reaches 93.3% and inverter 2 reaches 92.3% at 50 W output. Power allocation tests set a current ratio of 2:1; inverter 1 branch current is 2.6 A, and inverter 2 is 1.3 A, with errors under 2%. Waveforms indicate some distortion due to grid harmonics, but the ratio is maintained, proving intelligent distribution.
In conclusion, our strategy for single phase inverter parallel and grid-connected systems effectively addresses circulating currents and enables intelligent power allocation. The use of potential difference current sharing and SOGI-PLL ensures stable operation with high efficiency and low THD. Experimental results confirm the feasibility, with the single phase inverter system achieving proportional current sharing in grid-connected mode without communication, enhancing microgrid reliability and performance. Future work could explore scalability to larger systems and integration with other renewable sources.