The rapid integration of renewable energy sources, such as wind and solar power, alongside the proliferation of DC loads like electric vehicle charging stations, has placed stringent demands on the performance of grid-connected power conversion systems. As the critical interface in modern hybrid AC/DC power supply systems, the on-grid inverter must exhibit exceptional dynamic response, precise control accuracy, and high-quality output current with low harmonic distortion. Traditional linear control methods, while simple, often struggle with the complexities of higher-order systems and achieving zero steady-state error for AC signals. Finite Control Set Model Predictive Control (FCS-MPC) has emerged as a powerful alternative for on-grid inverter control, prized for its rapid dynamic response, inherent robustness, and ability to handle multiple control objectives within a single cost function.
However, the superior performance of FCS-MPC is intrinsically tied to the accuracy of its underlying mathematical model. In practical applications, the parameters of an on-grid inverter’s passive components, particularly the LCL filter inductances, are susceptible to variation due to factors like thermal drift, aging, and manufacturing tolerances. This parameter mismatch between the controller’s model and the physical plant degrades prediction accuracy, leading to suboptimal switching decisions, increased current harmonics, and potentially system instability. This vulnerability represents a significant challenge for the reliable deployment of MPC in on-grid inverters.
This work addresses this fundamental limitation by proposing a novel, data-driven Model-Free Predictive Current Control (MFPCC) strategy for on-grid inverters. The core objective is to diminish the controller’s dependency on precise system parameters while maintaining, or even enhancing, dynamic and steady-state performance. The strategy synthesizes several advanced techniques: a weighted average current method for system order reduction, an ultra-local model for structural simplification, a Linear Extended State Observer (LESO) for real-time disturbance estimation, and a Recursive Least Squares (RLS) algorithm for continuous online model identification. The proposed approach aims to provide a robust control solution for on-grid inverters operating under realistic conditions of parameter uncertainty.
The standard topology for a three-phase two-level voltage source inverter with an LCL filter is considered. The LCL filter is preferred for its superior high-frequency harmonic attenuation compared to a simple L filter. The mathematical model of the system in the continuous-time domain is derived from Kirchhoff’s laws:
$$
\begin{aligned}
L_1 \frac{d\mathbf{i}_{g1}}{dt} &= \mathbf{v}_o – \mathbf{v}_c \\
L_2 \frac{d\mathbf{i}_{g}}{dt} &= \mathbf{v}_c – \mathbf{v}_s \\
C \frac{d\mathbf{v}_{c}}{dt} &= \mathbf{i}_{g1} – \mathbf{i}_{g}
\end{aligned}
$$
where $\mathbf{i}_{g1} = [i_{g1a}, i_{g1b}, i_{g1c}]^T$ is the inverter-side current, $\mathbf{i}_{g} = [i_{ga}, i_{gb}, i_{gc}]^T$ is the grid-side current, $\mathbf{v}_o = [v_{oa}, v_{ob}, v_{oc}]^T$ is the inverter output voltage, $\mathbf{v}_c = [v_{ca}, v_{cb}, v_{cc}]^T$ is the capacitor voltage, and $\mathbf{v}_s = [v_{sa}, v_{sb}, v_{sc}]^T$ is the grid voltage. The inherent resonance peak of the third-order LCL filter can challenge system stability. To mitigate this, a weighted average current method is employed for active damping and model reduction. A virtual current $\mathbf{i}_w$ is defined as a weighted sum of the two inductor currents:
$$
\mathbf{i}_w = m \mathbf{i}_{g1} + n \mathbf{i}_{g}
$$
with the weights $m = L_1/(L_1+L_2)$ and $n = L_2/(L_1+L_2)$. This manipulation transforms the original third-order system dynamics between $\mathbf{v}_o$ and $\mathbf{i}_w$ into an equivalent first-order system, effectively suppressing the resonant oscillation. The simplified continuous-time model, incorporating parasitic resistances $R_1$, $R_2$ and measurement errors $\mathbf{E}$, is:
$$
\frac{d\mathbf{i}_w}{dt} = \frac{1}{L} (\mathbf{v}_o – \mathbf{v}_s – R\mathbf{i}_w) + \mathbf{E}
$$
where $L = L_1 + L_2$ and $R = R_1 + R_2$. The conventional Model Predictive Current Control (MPCC) for an on-grid inverter discretizes this model using the forward Euler method:
$$
\mathbf{i}_w(k+1) = \mathbf{i}_w(k) + \frac{T_s}{L} \left( \mathbf{v}_o(k) – \mathbf{v}_s(k) \right)
$$
where $T_s$ is the sampling period and $k$ denotes the current sampling instant. The control algorithm evaluates all possible voltage vectors $\mathbf{v}_o^j$ (where $j \in \{0,1,…,7\}$ for a two-level inverter) generated by the inverter’s eight switching states. For each candidate, it predicts the future current $\mathbf{i}_w^j(k+1)$ using the model above. The optimal vector is selected by minimizing a cost function, typically the absolute error between the predicted current and its reference $\mathbf{i}_w^*$:
$$
g^j = \lambda_a |i_{wa}^* – i_{wa}^j(k+1)| + \lambda_b |i_{wb}^* – i_{wb}^j(k+1)| + \lambda_c |i_{wc}^* – i_{wc}^j(k+1)|
$$
where $\lambda_a, \lambda_b, \lambda_c$ are weighting coefficients, often set to 1 for balanced three-phase operation. The switching state corresponding to the voltage vector that minimizes $g^j$ is applied during the next sampling interval. The critical flaw here is the explicit dependence on the parameters $L$ and $R$ in the prediction model. Any mismatch between the nominal value $L$ used in the controller and the actual plant value $L^*$ directly corrupts the prediction, leading to performance deterioration in the on-grid inverter.
The proposed data-driven MFPCC strategy fundamentally rethinks the prediction model to circumvent parameter dependency. The first step is to reformulate the system dynamics into an ultra-local model format. The simplified model is rearranged as:
$$
\frac{d\mathbf{i}_w}{dt} = \frac{1}{L} \mathbf{v}_o + \left( -\frac{\mathbf{v}_s + R\mathbf{i}_w}{L} + \mathbf{E} \right)
$$
This can be abstracted into the standard first-order ultra-local model form:
$$
\dot{\mathbf{i}}_w = \alpha \mathbf{u} + \hat{\mathbf{F}}
$$
For the on-grid inverter system, we define $\alpha = 1/L$ as a system gain, $\mathbf{u} = \mathbf{v}_o$ as the control input (the inverter output voltage), and $\hat{\mathbf{F}} = (-\mathbf{v}_s – R\mathbf{i}_w)/L + \mathbf{E}$ as a lumped term encompassing all unknown or perturbed dynamics, including grid voltage, resistance effects, parameter mismatches ($L \ne L^*$, $R \ne R^*$), and unmodeled nonlinearities. The key advantage is that the complex, parameter-dependent physical model is replaced by this simple input-output relation. Discretizing this model yields the prediction equation:
$$
\mathbf{i}_w(k+1) = \mathbf{i}_w(k) + T_s \left( \alpha \mathbf{u}(k) + \hat{\mathbf{F}}(k) \right)
$$
While this reduces explicit parameter dependence, the gain $\alpha$ and disturbance $\hat{\mathbf{F}}$ remain unknown. To estimate the disturbance term $\hat{\mathbf{F}}(k)$ in real-time, a Linear Extended State Observer (LESO) is designed. Considering a single phase (e.g., phase-a) for clarity, the LESO treats $\hat{F}_a$ as an extended state. Its discrete-time formulation is:
$$
\begin{aligned}
e_{iw_a}(k) &= \hat{i}_{w_a}(k) – i_{w_a}(k) \\
\hat{i}_{w_a}(k+1) &= \hat{i}_{w_a}(k) + T_s \left( \hat{F}_a(k) + \alpha u_a(k) \right) – l_{01} e_{iw_a}(k) \\
\hat{F}_a(k+1) &= \hat{F}_a(k) – l_{02} e_{iw_a}(k)
\end{aligned}
$$
Here, $\hat{i}_{w_a}$ is the estimated current, $i_{w_a}$ is the measured current, and $l_{01}$, $l_{02}$ are observer gains. These gains are tuned by placing the observer’s poles for desired bandwidth. A common design sets $l_{01} = 2\omega_o T_s$ and $l_{02} = \omega_o^2 T_s$, where $\omega_o$ is the observer bandwidth. The LESO dynamically provides accurate estimates $\hat{\mathbf{F}}(k)$ which are then used to compensate the prediction model, significantly improving its accuracy against disturbances and slow parameter variations in the on-grid inverter.
The final step is to eliminate the remaining parameter dependency: the gain $\alpha$. This is achieved using a data-driven online identification technique, the Recursive Least Squares (RLS) algorithm with a forgetting factor. The ultra-local model is expressed as an AutoRegressive with eXogenous input (ARX) model:
$$
i_w(k) + a_1 i_w(k-1) = b_0 u(k-1) + b_1 u(k-2) + T_s \hat{F}(k-1)
$$
Setting $a_0=1$, this can be written in the standard linear regression form $\mathbf{y}(k) = \boldsymbol{\varphi}^T(k) \boldsymbol{\theta}(k)$, where:
$$
\begin{aligned}
\mathbf{y}(k) &= i_w(k) \\
\boldsymbol{\varphi}(k) &= [-i_w(k-1), u(k-1), u(k-2)]^T \\
\boldsymbol{\theta}(k) &= [a_1, b_0, b_1]^T
\end{aligned}
$$
The RLS algorithm then online updates the parameter vector $\hat{\boldsymbol{\theta}}(k)$ using the latest measurements:
$$
\begin{aligned}
\mathbf{e}(k) &= \mathbf{y}(k) – \boldsymbol{\varphi}^T(k) \hat{\boldsymbol{\theta}}(k-1) \\
\mathbf{K}(k) &= \frac{\mathbf{P}(k-1)\boldsymbol{\varphi}(k)}{\lambda + \boldsymbol{\varphi}^T(k)\mathbf{P}(k-1)\boldsymbol{\varphi}(k)} \\
\hat{\boldsymbol{\theta}}(k) &= \hat{\boldsymbol{\theta}}(k-1) + \mathbf{K}(k) \mathbf{e}(k) \\
\mathbf{P}(k) &= \lambda^{-1} \left( \mathbf{I} – \mathbf{K}(k)\boldsymbol{\varphi}^T(k) \right) \mathbf{P}(k-1)
\end{aligned}
$$
Here, $\mathbf{K}(k)$ is the gain matrix, $\mathbf{P}(k)$ is the covariance matrix, and $\lambda$ (typically $0.95 < \lambda \leq 1$) is the forgetting factor that allows the algorithm to track time-varying parameters. With the updated parameters $\hat{\boldsymbol{\theta}}(k) = [\hat{a}_1, \hat{b}_0, \hat{b}_1]^T$, the one-step-ahead current prediction for the on-grid inverter is computed as:
$$
i_w(k+1) = -\hat{a}_1 i_w(k) + \hat{b}_0 u(k) + \hat{b}_1 u(k-1) + T_s \hat{F}(k)
$$
This prediction model is entirely data-driven. The parameters $\hat{a}_1, \hat{b}_0, \hat{b}_1$ are continuously adapted based on input-output data, and the disturbance $\hat{F}(k)$ is provided by the LESO. Therefore, the controller no longer requires prior knowledge of $L$, $R$, or $C$. The complete MFPCC algorithm for the on-grid inverter executes the following steps at each sampling instant $k$:
- Measurement & Estimation: Sample grid-side and inverter-side currents $\mathbf{i}_g(k)$, $\mathbf{i}_{g1}(k)$. Compute the weighted average current $\mathbf{i}_w(k)$. Update the RLS algorithm to obtain $\hat{\boldsymbol{\theta}}(k)$. Obtain the disturbance estimate $\hat{\mathbf{F}}(k)$ from the LESO.
- Prediction: For each of the 7 unique voltage vectors $\mathbf{v}_o^j$ (excluding redundant zero vectors), calculate the predicted current $\mathbf{i}_w^j(k+1)$ using the data-driven model: $\mathbf{i}_w^j(k+1) = -\hat{a}_1 \mathbf{i}_w(k) + \hat{b}_0 \mathbf{v}_o^j(k) + \hat{b}_1 \mathbf{v}_o^{j}(k-1) + T_s \hat{\mathbf{F}}(k)$.
- Optimization: Evaluate the cost function $g^j$ for each prediction using the same absolute error criterion as traditional MPCC.
- Actuation: Apply the switching state corresponding to the voltage vector $\mathbf{v}_o^{j*}$ that minimizes $g^j$.
The performance of the proposed MFPCC strategy was rigorously evaluated and compared against the conventional MPCC through detailed simulations and Hardware-in-the-Loop (HIL) experiments. The system parameters for the three-phase on-grid inverter are summarized in the following table:
| Parameter | Symbol | Value |
|---|---|---|
| Grid Phase Voltage (RMS) | $V_s$ | 220 V |
| DC-Link Voltage | $V_{dc}$ | 800 V |
| Inverter-side Inductance | $L_1$ | 2.0 mH |
| Grid-side Inductance | $L_2$ | 1.0 mH |
| Filter Capacitance | $C$ | 0.5 μF |
| Sampling / Control Frequency | $f_s$ | 100 kHz |
| LESO Bandwidth | $\omega_o$ | 55,000 rad/s |
| RLS Forgetting Factor | $\lambda$ | 1.0 |
Under nominal parameters (i.e., controller model matches the plant), both strategies demonstrated excellent dynamic performance. When the current reference for the on-grid inverter was stepped from 0 A to 70 A, both controllers achieved stable tracking within 2 ms. Similarly, during a step-down from 70 A to 30 A, the dynamic response was swift and stable for both methods. The steady-state performance, however, revealed the advantage of the data-driven approach. The conventional MPCC produced a grid current with a Total Harmonic Distortion (THD) of 1.28%, while the proposed MFPCC strategy achieved a significantly lower THD of 0.45%. This improvement stems from the higher prediction accuracy of the online-adapted, disturbance-compensated model, leading to more optimal switching decisions for the on-grid inverter.
The core test of robustness involved introducing severe parameter mismatch. The controller’s nominal inductance value $L$ was deliberately set to a fraction or multiple of the actual plant inductance $L^*$. The performance was quantified using the Integral of Time multiplied by Absolute Error (ITAE) index:
$$
\text{ITAE} = \int_{0}^{T} t \, |e(t)| \, dt
$$
The following analysis summarizes the robustness comparison:
| Control Strategy | Parameter Condition ($L/L^*$) | Steady-State Performance | Robustness Indicator (ITAE) |
|---|---|---|---|
| Conventional MPCC | 1.0 (Nominal) | Stable, THD=1.28% | Baseline Value |
| 0.75 | Stable, degraded waveform | Increased by ~40% | |
| 0.5 | Unstable, loses tracking | N/A (Diverges) | |
| Proposed MFPCC | 1.0 (Nominal) | Stable, THD=0.45% | ~65% of MPCC baseline |
| 0.75 | Stable, minimal degradation | Nearly unchanged | |
| 0.5 | Stable, maintains tracking | Minor increase (~15%) |
The results are conclusive. The conventional MPCC for the on-grid inverter is highly sensitive to parameter mismatch. When $L$ is half its true value, the system becomes unstable. In contrast, the proposed MFPCC strategy maintains stable operation across the tested range from $L = 0.5L^*$ to $L = 1.5L^*$, with only a minor increase in ITAE. This demonstrates exceptional robustness. The RLS algorithm’s convergence was also verified; it successfully identified the model parameters online and remained stable even during reference step changes, ensuring the adaptive capability of the on-grid inverter controller.
HIL experiments conducted on a real-time platform confirmed the simulation findings. The MFPCC strategy provided lower current THD (2.11% vs. 3.56% for MPCC) under nominal conditions. Crucially, when the controller inductance was instantaneously changed to 50% of its correct value during operation, the conventional MPCC failed immediately, producing distorted, uncontrolled current. The MFPCC-controlled on-grid inverter, however, showed virtually no transient disturbance and continued to operate stably, visually validating its parameter-agnostic nature.
This work has presented a comprehensive data-driven Model-Free Predictive Current Control strategy designed to solve the critical problem of parameter sensitivity in on-grid inverter applications. By integrating a weighted average current for resonance damping, an ultra-local model for structural simplification, a Linear Extended State Observer for lumped disturbance estimation and compensation, and a Recursive Least Squares algorithm for continuous online model identification, the proposed controller successfully decouples performance from precise knowledge of LCL filter parameters. The strategy significantly enhances the operational robustness of the on-grid inverter against inevitable parameter variations due to aging, temperature, and manufacturing tolerances. Comparative simulation and HIL results confirm that, while matching the excellent dynamic response of traditional MPCC, the MFPCC strategy delivers superior steady-state current quality (lower THD) and, most importantly, maintains stable, high-performance operation under significant parameter mismatch conditions where conventional MPCC fails. This makes the data-driven MFPCC a highly promising control approach for reliable and efficient grid integration of renewable energy sources.