In recent years, the global energy crisis and environmental concerns have driven the rapid development of renewable energy sources, with solar power standing out as a promising solution due to its abundance and cleanliness. Photovoltaic (PV) systems, which convert solar energy into electricity, rely heavily on inverters to transform direct current (DC) into alternating current (AC) for various applications. Among the different types of solar inverter, off-grid inverters are particularly vital for standalone systems, such as in remote areas, emergency power supplies, and telecommunications, where grid connection is unavailable. These inverters must meet stringent dynamic and static performance requirements to ensure stability and efficiency. Traditional design methods for inverter control systems often involve sequential tuning of inner current loops and outer voltage loops, which can be cumbersome and may lead to suboptimal dynamic responses. To address this, I propose a pole assignment method for designing the control parameters of a dual-loop system in an off-grid PV inverter. This approach simplifies the design process by directly placing system poles at desired locations, ensuring robust performance. In this article, I will detail the design of a 10 kW off-grid full-bridge inverter, including core component parameter calculations, control strategy implementation with feedforward compensation, and simulation validation using PSIM software. The results demonstrate that this method achieves excellent dynamic and static characteristics, along with strong anti-interference capabilities.
The foundation of any PV system lies in the inverter, and understanding the various types of solar inverter is crucial for selecting the right technology. Generally, inverters can be categorized into grid-tied, off-grid, and hybrid types. Grid-tied inverters synchronize with the utility grid and feed excess power back, but they cannot operate independently during grid outages. Off-grid inverters, like the one discussed here, function autonomously to power AC loads without grid support, making them ideal for isolated applications. Hybrid inverters combine features of both, often incorporating energy storage for enhanced flexibility. Each of these types of solar inverter has distinct control requirements; for instance, off-grid inverters must maintain stable voltage and frequency under varying loads, which necessitates advanced control techniques. In my design, I focus on a single-phase full-bridge off-grid inverter, which is commonly used in residential and small-scale commercial systems due to its simplicity and efficiency. The control system employs a dual-loop structure with an inner current loop and an outer voltage loop, enhanced by feedforward compensation to improve response speed and reduce deviations. By applying the pole assignment method, I aim to optimize the system’s performance, ensuring it meets the demanding criteria for off-grid applications.
To begin the design process, I first outline the specifications for the 10 kW off-grid PV inverter. The input voltage range is set at 360–420 V DC, while the output is single-phase 220 V AC at 50 Hz frequency. The load power factor is 0.8 (inductive), and the total harmonic distortion (THD) of the output voltage must be less than 5%. The switching frequency is chosen as 20 kHz to balance efficiency and filtering requirements. Key components include the input capacitor, switching devices (IGBTs or MOSFETs in a full-bridge configuration), output LC filter, and control circuitry. The LC filter, composed of an inductor (L) and capacitor (C), is critical for smoothing the output waveform and attenuating high-frequency harmonics. Proper design of these components ensures minimal distortion and stable operation under various load conditions.
The design of the filter inductor involves limiting the voltage drop across it to within 3% of the output voltage RMS value, with a current ripple factor of 0.2. The inductance can be derived from the following equations, which account for the worst-case scenario during modulation. The voltage across the inductor is given by:
$$ V_L = L \frac{di}{dt} = L \frac{\Delta i_L}{D T_s} = V_{dc} – V_{out} $$
where Δi_L is the peak-to-peak current ripple, D is the duty cycle, T_s is the switching period, V_dc is the input DC voltage, and V_out is the output AC voltage. The duty cycle for a sinusoidal pulse width modulation (SPWM) system is expressed as:
$$ D = m_a \sin(\omega t) $$
where m_a is the modulation index. The output voltage relates to the input as V_out = V_dc D. Substituting and solving for the current ripple:
$$ \Delta i_L = \frac{m_a \sin(\omega t) T_s V_{dc} (1 – m_a \sin(\omega t))}{L_i} $$
By differentiating Δi_L with respect to sin(ωt) and setting it to zero, the maximum current ripple is found at sin(ωt) = 1/(2m_a). Thus, the maximum ripple is:
$$ \Delta i_{L_{\text{max}}} = \frac{V_{dc} T_s}{4 L_i} $$
Rearranging for inductance:
$$ L_i = \frac{V_{dc}}{4 f_s \Delta i_{L_{\text{max}}}} $$
where f_s is the switching frequency. The maximum current ripple is related to the trip current and output power:
$$ \Delta i_{L_{\text{max}}} = 2 I_{\text{trip}} \frac{P_O}{V_O} $$
Given V_out = 311 V (peak), f_s = 20 kHz, I_Lmax ≈ 79.2 A, and P_O = 10 kW, the calculated inductance is L = 300 μH. For the filter capacitor, the cutoff frequency f_c of the LC filter is set to 10% of the switching frequency to achieve effective filtering:
$$ f_c = \frac{1}{2\pi \sqrt{LC}} = 0.1 f_s $$
Solving for capacitance:
$$ C = \left( \frac{10}{2\pi f_s} \right)^2 / L $$
Substituting values, C ≈ 20 μF. These parameters form the basis of the power stage design, ensuring low harmonic distortion and stable operation.
| Parameter | Value | Description |
|---|---|---|
| Input Voltage Range | 360–420 V DC | DC input from PV panels |
| Output Voltage | 220 V AC (RMS) | Single-phase AC output |
| Output Frequency | 50 Hz | Standard grid frequency |
| Rated Power | 10 kW | Maximum output power |
| Load Power Factor | 0.8 (inductive) | Simulates typical loads |
| THD | < 5% | Voltage distortion limit |
| Switching Frequency | 20 kHz | PWM switching rate |
| Filter Inductance (L) | 300 μH | Output filter inductor |
| Filter Capacitance (C) | 20 μF | Output filter capacitor |
The control strategy for the off-grid inverter is pivotal for maintaining output voltage quality under dynamic loads. I employ a dual-loop control system with an inner current loop and an outer voltage loop, complemented by feedforward compensation. This structure enhances the system’s ability to reject disturbances, such as load changes, and improves transient response. The inner current loop samples the inductor current, while the outer voltage loop regulates the output voltage. Feedforward control is added to compensate for load current disturbances, accelerating the response and reducing steady-state error. The overall control block diagram illustrates how the reference voltage V_ref is compared to the actual output voltage, with the error processed by a voltage controller to generate a current reference for the inner loop. The current controller then produces the modulation signal for the SPWM block, which drives the full-bridge switches.
In the pulse width modulation (PWM) system, the modulation wave V_r is compared with a triangular carrier wave V_c to generate switching signals. When V_r > V_c, switches T1 and T4 are on, resulting in V_ab = V_D; otherwise, T2 and T3 are on, giving V_ab = -V_D. The duty cycle D in one carrier period T_c is:
$$ D = \frac{T_k}{T_c} = \frac{1}{2} \left(1 + \frac{V_r}{V_{cm}}\right) $$
where V_cm is the peak carrier voltage. The average output voltage V_ab over T_c is:
$$ V_{ab} = \frac{T_k \cdot V_D – (T_c – T_k) \cdot V_D}{T_c} = (2D – 1) V_D $$
Substituting D, the relationship simplifies to:
$$ V_{ab} = \frac{V_D}{V_{cm}} V_r $$
This linear model connects the modulation wave to the inverter output, forming the basis for control design. The LC filter dynamics are described by:
$$ L \frac{di_L}{dt} = V_{ab} – V_o – r i_L $$
$$ C \frac{dV_o}{dt} = i_L – i_o $$
where r is the equivalent series resistance of the inductor, i_L is the inductor current, V_o is the output voltage, and i_o is the load current. Combining this with the PWM model, the open-loop system transfer function can be derived. However, as shown in the Bode plot from PSIM simulations, the open-loop system has a low phase margin (around 2°), indicating poor stability. Thus, closed-loop control is essential.
For the dual-loop controller, I use proportional-integral (PI) regulators for both voltage and current loops. The transfer functions are:
$$ G_v(s) = k_{1p} + \frac{k_{1i}}{s} $$
$$ G_i(s) = k_{2p} + \frac{k_{2i}}{s} $$
where k_{1p}, k_{1i} are the voltage controller gains, and k_{2p}, k_{2i} are the current controller gains. The closed-loop transfer function from reference voltage V_ref to output voltage V_o, considering the feedforward path for load current i_o, is:
$$ V_o(s) = \frac{(k_{1p} s + k_{1i})(k_{2p} s + k_{2i})}{s D(s)} V_{\text{ref}}(s) – \frac{s^2 (sL + r)}{LC D(s)} I_o(s) $$
The characteristic equation D(s) is:
$$ D(s) = s^4 + \frac{rC + C k_{2p}}{LC} s^3 + \frac{1 + k_{1p} k_{2p} + C k_{2i}}{LC} s^2 + \frac{k_{1p} k_{2i} + k_{2p} k_{1i}}{LC} s + \frac{k_{1i} k_{2i}}{LC} $$
To design the controller gains, I apply the pole assignment method, which allows direct placement of closed-loop poles at desired locations for specific dynamic responses. The dominant poles are chosen as complex conjugates with damping ratio ζ = 0.707 and natural frequency ω_n = 2500 rad/s, ensuring a balance between response speed and overshoot. Non-dominant poles are placed at -mζω_n and -nζω_n with m = 8 and n = 10 to minimize their impact. The desired characteristic equation is:
$$ D(s) = (s^2 + 2\zeta\omega_n s + \omega_n^2)(s + m\zeta\omega_n)(s + n\zeta\omega_n) $$
Expanding and comparing coefficients with the actual D(s), I solve for the controller gains:
$$ k_{1p} = \frac{LC(2 + m + n)\zeta\omega_n}{C} – r $$
$$ k_{1p} k_{2p} + C k_{2i} = LC \omega_n^2 [1 + (mn + 2m + 2n)\zeta^2] $$
$$ k_{1p} k_{2i} + k_{2p} k_{1i} = LC (2mn\zeta^2 + m + n) \zeta \omega_n^3 $$
$$ k_{1i} k_{2i} = LC m n \zeta^2 \omega_n^4 $$
Substituting the values, I obtain k_{1p} = 0.01, k_{1i} = 150, k_{2p} = 0.3, and k_{2i} = 2000. The Bode plot of the closed-loop system now shows sufficient phase margin, confirming stability and good dynamic performance.
To validate the design, I built a simulation model in PSIM 2021a, a powerful tool for power electronics simulations. The model includes the full-bridge inverter, LC filter, load, and control blocks implementing the dual-loop PI controllers with feedforward. Simulation tests assess performance under steady-state and transient conditions. In steady-state operation with a 10 kW inductive load (power factor 0.8), the output voltage and current waveforms are nearly sinusoidal, with a THD of only 0.02667%, well below the 5% limit. The output voltage RMS is 220.34 V, active power is 10.335 kW, and power factor is 0.80039, meeting all specifications. This demonstrates the effectiveness of the pole assignment method in optimizing control parameters for various types of solar inverter, particularly off-grid systems where voltage quality is critical.
For dynamic performance, I conducted tests under load and input voltage variations. In the load突变 test, a 20 Ω resistor is connected in parallel at 0.2 s and disconnected at 0.6 s. The output voltage remains stable with minimal deviation, and the current adjusts quickly, showcasing the system’s robustness. Similarly, when the input voltage changes between 360 V, 400 V, and 420 V at different time intervals, the output voltage maintains consistency, proving the controller’s ability to reject input disturbances. These results highlight the advantages of using feedforward compensation and pole assignment in designing reliable off-grid inverters.
| Test Condition | Output Voltage (V RMS) | THD (%) | Active Power (kW) | Power Factor |
|---|---|---|---|---|
| Steady-State (10 kW load) | 220.34 | 0.02667 | 10.335 | 0.80039 |
| Load Step Change | ~220 (stable) | < 0.05 | Varies with load | Maintained |
| Input Voltage Variation | ~220 (stable) | < 0.05 | ~10 | 0.8 |
In conclusion, the pole assignment method offers a systematic approach to designing control parameters for off-grid PV inverters, simplifying the process and ensuring optimal dynamic and static performance. By combining dual-loop control with feedforward compensation, the system achieves high stability, low distortion, and strong anti-interference capabilities, as verified through PSIM simulations. This design is applicable to various types of solar inverter, emphasizing the importance of advanced control techniques in enhancing renewable energy systems. Future work could explore real-time implementation and adaptation to changing environmental conditions, further improving the versatility of off-grid solutions.