In my research, I focus on enhancing the performance of power electronic converters, particularly those used in renewable energy systems. Among the various configurations, LCL-type voltage source inverters are widely adopted for grid-connected solar applications due to their excellent harmonic attenuation and voltage utilization. However, the control of these inverters faces challenges such as parameter sensitivity in traditional model predictive control (MPC) and poor adaptability of fixed-gain disturbance observers. To address these issues, I propose a model-free predictive power control strategy based on an adaptive linear extended state observer (ALESO-MFPPC). This work is especially relevant for different types of solar inverters, including string inverters, central inverters, and microinverters, where robust and fast control is essential for maximum power point tracking and grid compliance.
The LCL inverter topology I consider consists of a full-bridge switching network, a compensation inductor, a resonant capacitor, and an output inductor feeding an equivalent load. I model the system in the synchronous rotating dq frame to decouple the active and reactive power loops. Figure 1 illustrates a typical LCL resonant inverter circuit, which is a common topology among various types of solar inverters.
To avoid reliance on precise physical parameters, I adopt an ultra-local model for output power prediction. The ultra-local model approximates the system dynamics as:
$$ \dot{P}_o = \alpha u_{in} + f_u $$
where \(P_o\) is the output active power, \(\alpha\) is a constant input gain, \(u_{in}\) is the control input derived from the inverter voltage, and \(f_u\) represents the lumped disturbance including unmodeled dynamics and parameter variations. Discretizing this model using forward Euler gives:
$$ P_o(k+1) = P_o(k) + T_s \left[ \alpha u_{in}(k) + f_u(k) \right] $$
The cost function for the model-free predictive power controller is:
$$ g = \left| P^* – P_o(k+1) \right|^2 $$
By applying the deadbeat principle, I compute the optimal phase-shift angle \(\theta(k)\) as:
$$ \theta(k) = 2 \arccos\left( \frac{\pi}{4 U_{DC}} \sqrt{\frac{ P^* – P_o(k) – f_u(k) }{ \alpha T_s }} \right) $$
This approach significantly reduces sensitivity to circuit parameters, making it suitable for various types of solar inverters operating under diverse grid conditions.
To estimate the lumped disturbance \(f_u\), I design a linear extended state observer (LESO) with fixed bandwidth. The observer dynamics in continuous time are:
$$ \begin{cases} \dot{\hat{P}}_o = \alpha u_{in} + \hat{f}_u + l_1 (P_o – \hat{P}_o) \\ \dot{\hat{f}}_u = l_2 (P_o – \hat{P}_o) \end{cases} $$
The observer gains are selected as \(l_1 = 2\gamma_0\) and \(l_2 = \gamma_0^2\), where \(\gamma_0\) is the observer bandwidth. However, fixed gains lead to performance degradation under non-linear parameter drift and digital control delays. To overcome this, I propose an adaptive linear extended state observer (ALESO) that uses a forgetting factor recursive least squares (FFRLS) algorithm to online tune the observer bandwidth. The FFRLS update equations are:
$$ \begin{aligned} \hat{\theta}(k) &= \hat{\theta}(k-1) + \mathbf{K}(k) \varepsilon(k) \\ \mathbf{K}(k) &= \frac{\mathbf{P}(k-1) \phi(k)}{\lambda + \phi^T(k) \mathbf{P}(k-1) \phi(k)} \\ \mathbf{P}(k) &= \frac{1}{\lambda} \left[ \mathbf{I} – \mathbf{K}(k) \phi^T(k) \right] \mathbf{P}(k-1) \end{aligned} $$
where \(\lambda\) is the forgetting factor, \(\phi(k) = [\tau(k-1), y(k-1)]^T\) is the information vector, and \(\tau(k)\) is the adaptive reinforcement factor. The ALESO dynamics become:
$$ \begin{cases} \dot{\hat{P}}_o = \alpha u_{in} + \hat{f}_u + \tau l_1 (P_o – \hat{P}_o) \\ \dot{\hat{f}}_u = \tau l_2 (P_o – \hat{P}_o) \end{cases} $$
Using Jury stability criterion, I derive the stability condition for the discrete-time ALESO as:
$$ 0 < \tau < \frac{2}{T_s (\beta_1 + 2\beta_2)} $$
This adaptive mechanism ensures fast convergence and high disturbance rejection across a wide operating range, which is critical for all types of solar inverters that experience fluctuating solar irradiance and grid impedance changes.
I built a low-power experimental platform (Figure 2) to validate the proposed ALESO-MFPPC strategy. The system parameters are summarized in Table I.
| Parameter | Value |
|---|---|
| Compensation Inductance \(L_r\) | 150 μH |
| Resonant Capacitance \(C_p\) | 1.4 μF |
| Output Inductance \(L_p\) | 64 μH |
| DC Input Voltage \(U_{DC}\) | 24 V |
| Switching Frequency \(f_s\) | 20 kHz |
| Rated Power \(P\) | 100 W |
Steady-state experiments were conducted at 80 W output power. Table II compares the current total harmonic distortion (THD) among three control methods.
| Control Strategy | THD (%) |
|---|---|
| MPPC | 4.53 |
| LESO-MFPPC | 4.14 |
| ALESO-MFPPC | 3.65 |
The results show that the proposed ALESO-MFPPC achieves the lowest harmonic distortion, which benefits grid-connected types of solar inverters that must meet strict THD standards.
Dynamic performance was evaluated by stepping the power reference from 50 W to 100 W. The settling times are summarized in Table III.
| Control Strategy | Settling Time (ms) |
|---|---|
| MPPC | 32 |
| LESO-MFPPC | 16 |
| ALESO-MFPPC | 10.2 |
Clearly, ALESO-MFPPC provides the fastest transient response, which is crucial for types of solar inverters during sudden irradiance changes.
Parameter mismatch robustness was tested by halving the inductance value. The recovery times are given in Table IV.
| Control Strategy | Recovery Time (ms) |
|---|---|
| MPPC | 142 |
| LESO-MFPPC | 128 |
| ALESO-MFPPC | 119 |
Even under severe parameter variations, the adaptive observer maintains superior recovery performance, making it ideal for field-deployed types of solar inverters where component aging is inevitable.
In summary, I have developed a model-free predictive power control strategy that combines an ultra-local model with an adaptive linear extended state observer. The method eliminates the need for accurate system parameters, adapts its bandwidth online, and significantly improves both steady-state and dynamic performance. Experimental results confirm that the proposed approach is well-suited for various types of solar inverters, including those in residential and commercial photovoltaic systems. Future work will extend the strategy to multi-objective optimization and grid fault ride-through scenarios.