The three-phase grid tied inverter serves as the critical power conversion interface for integrating renewable energy sources, such as photovoltaic and wind power systems, into the utility grid. As the penetration of such “double-high” (high penetration of renewables, high proportion of power electronics) grids rapidly increases, these grid tied inverters face increasingly stringent performance requirements. They must not only achieve high-quality power conversion with stable output but also possess fast dynamic response capabilities and strong robustness to handle grid fluctuations, parameter uncertainties, and complex operational conditions. Among various control strategies for the grid tied inverter, current loop control is paramount as it directly determines the tracking accuracy of the grid-connected current and overall power quality.
Deadbeat current predictive control has garnered significant attention due to its inherent advantages of fast dynamic response, high control precision, and relatively simple system design. However, its performance is highly dependent on the accuracy of the system model. In practical implementations of a grid tied inverter, factors such as component aging, temperature variations, and manufacturing tolerances lead to parameter drift (e.g., in filter inductances and capacitances). Furthermore, the digital control system inevitably introduces computational and pulse-width modulation (PWM) update delays, typically amounting to two sampling periods. These modeling errors and delays can severely degrade the current tracking performance, introduce steady-state errors, and even threaten system stability if not properly addressed. Therefore, developing a control strategy that enhances the robustness of the deadbeat controller against model mismatches and disturbances is of great practical importance for reliable grid tied inverter operation.
This work proposes a composite control strategy for an LCL-type grid tied inverter, centered on an improved deadbeat predictive current controller augmented with a feedforward disturbance compensation loop. The compensation is provided by a Sliding Mode Disturbance Observer (SMDO), whose key parameters are optimized using a Genetic Algorithm (GA). The strategy aims to decouple the controller’s performance from precise model knowledge, thereby improving the grid tied inverter’s resilience to parameter variations and unmodeled dynamics. First, an improved deadbeat predictive control law is derived, incorporating a prediction scheme based on Newton’s interpolation method to estimate future state variables and actively compensate for the two-sample computational delay. Second, an SMDO is designed to estimate the lumped disturbance—encompassing parameter mismatches, grid voltage harmonics, and measurement errors—in real-time. This estimated disturbance is then fed forward to the current controller for compensation. Finally, to overcome the inefficiency and suboptimal performance associated with manual tuning of the SMDO’s gains, a GA is employed to automatically search for the optimal parameter set that minimizes a defined performance index, such as Total Harmonic Distortion (THD). This results in a GA-SMDO-based disturbance compensation scheme that significantly enhances the robustness and power quality of the grid tied inverter.
System Modeling and Improved Deadbeat Predictive Control
The topology of a three-phase two-level grid tied inverter with an LCL filter is considered. The inverter bridge is fed by a DC source \(U_{dc}\), and the AC side is connected to the grid through an LCL filter composed of \(L\), \(C_f\), and \(L_g\). The equivalent series resistances of the filter components are generally small and are neglected in the derivation for simplicity. The inverter bridge is modeled as a gain \(K_{PWM}\). The primary control objective for this grid tied inverter is to force the grid-side current \(i_g\) to accurately track its reference \(i_g^*\), which is typically generated by an outer power or DC-link voltage control loop.
The continuous-time state-space model of the LCL filter in the stationary \(\alpha\beta\) frame can be expressed by relating the inverter-side current \(i_L\), grid-side current \(i_g\), and the capacitor voltage \(u_c\). Using the coupling relationship between the three energy storage elements, the dynamics can be formulated with \(i_L\) and \(i_g\) as state variables. For a given phase \(x\) (where \(x\) represents \(\alpha\) or \(\beta\)), the relationship is:
$$
\frac{di_{Lx}}{dt} = \frac{1}{L}(u_{inv_x} – u_{c_x}), \quad \frac{di_{gx}}{dt} = \frac{1}{L_g}(u_{c_x} – u_{g_x}), \quad u_{c_x} = L \frac{di_{Lx}}{dt} + L_g \frac{di_{gx}}{dt}
$$
Combining these equations allows us to express the derivative of the grid-side current. Applying the forward Euler discretization method with a sampling period \(T_s\) yields the discrete-time model crucial for digital implementation in the grid tied inverter:
$$
\begin{aligned}
i_{Lx}(k+1) &= i_{Lx}(k) + \frac{T_s}{L} \left( u_{inv_x}(k) – u_{c_x}(k) \right) \\
i_{gx}(k+1) &= i_{gx}(k) + \frac{T_s}{L_g} \left( u_{c_x}(k) – u_{g_x}(k) \right)
\end{aligned}
$$
To derive a direct control law for \(u_{inv}\) based on the grid current reference, a coupling coefficient \(\lambda\) is introduced. This coefficient establishes a functional relationship between the increments of the inverter-side current and the grid-side current between consecutive sampling instants:
$$
\frac{i_{Lx}(k+1) – i_{Lx}(k)}{i_{gx}(k+1) – i_{gx}(k)} = \lambda
$$
The value of \(\lambda\) influences system stability and performance. Analysis using the Jury stability criterion indicates that the system remains stable for \(0.1 \leq \lambda \leq 0.7\). Through simulation, \(\lambda = 0.7\) is selected as it provides an optimal balance, yielding low THD and minimal tracking error. Substituting this relationship into the discretized equations and solving for the inverter voltage needed at time \(k\) to make \(i_g(k+1)\) equal to its reference \(i_g^*(k+1)\) gives the basic deadbeat control law for the grid tied inverter:
$$
u_{inv_x}(k) = \frac{L}{\lambda T_s} \left[ i_{gx}^*(k+1) – i_{gx}(k) \right] + \frac{L_g}{T_s} \left[ i_{gx}^*(k+1) – i_{gx}(k) \right] + u_{g_x}(k)
$$
To address the inevitable two-sample period delay (\(k \rightarrow k+2\)) in a practical digital control system (comprising sampling, computation, and PWM update), the control law must be advanced. This is achieved by predicting the required voltage for the \((k+1)\)-th instant such that the current at \((k+2)\) tracks its reference. This requires predictions of \(i_g(k+1)\) and \(u_g(k+1)\). Newton’s interpolation method is employed for this purpose. Using a third-order Newton polynomial based on present and past samples, the predictions are obtained:
$$
\begin{aligned}
\hat{i}_{g_x}(k+1) &= \frac{3}{4}i_{g_x}(k) – \frac{3}{2}i_{g_x}(k-1) + \frac{1}{4}i_{g_x}(k-2) \\
\hat{u}_{g_x}(k+1) &= 3u_{g_x}(k) – 3u_{g_x}(k-1) + u_{g_x}(k-2)
\end{aligned}
$$
The final improved deadbeat predictive control law for the grid tied inverter, compensating for the two-step delay, becomes:
$$
\begin{aligned}
u_{inv_x}(k+1) = & \frac{L}{\lambda T_s} \left[ i_{gx}^*(k+2) – \hat{i}_{gx}(k+1) \right] \\
&+ \frac{L_g}{T_s} \left[ i_{gx}^*(k+2) – \hat{i}_{gx}(k+1) \right] + \hat{u}_{g_x}(k+1)
\end{aligned}
$$
This forms the core current controller, denoted as \(u_0\), for the grid tied inverter.
Sliding Mode Disturbance Observer Design for the Grid Tied Inverter
While the improved deadbeat controller handles delays, its performance remains sensitive to model inaccuracies. To enhance robustness, a feedforward compensation loop based on a Sliding Mode Disturbance Observer (SMDO) is designed. The lumped disturbance \(d(t)\) is defined to include all mismatches between the nominal model and the actual grid tied inverter system: parameter variations (\(\Delta L, \Delta L_g\)), grid voltage harmonics/unbalance (\(\Delta u_g\)), and other unmodeled dynamics or measurement noise.
The system model in the \(\alpha\beta\) frame, including disturbance, is rewritten as:
$$
\dot{x} = A x + B u_s + d
$$
where \(x = [i_{g\alpha}, i_{g\beta}]^T\), \(u_s = [u_{inv\alpha}-u_{g\alpha}, u_{inv\beta}-u_{g\beta}]^T\), \(A\) and \(B\) are system matrices based on nominal parameters, and \(d\) represents the lumped disturbance vector. It is assumed that the disturbance varies slowly relative to the observer dynamics, i.e., \(\dot{d} \approx \zeta(t)\), where \(\|\zeta(t)\|\) is bounded.
The SMDO is constructed to estimate this disturbance \(d(t)\). The observer structure is defined as:
$$
\begin{aligned}
\dot{\hat{x}} &= A \hat{x} + B u_s + \hat{d} + u_{smo} \\
\dot{\hat{d}} &= h u_{smo}
\end{aligned}
$$
Here, \(\hat{x}\) and \(\hat{d}\) are the estimates of the state and disturbance, respectively. \(u_{smo}\) is the sliding mode control term to be designed, and \(h > 0\) is the observer gain governing the disturbance estimation dynamics. Defining the estimation errors as \(e_x = x – \hat{x}\) and \(e_d = d – \hat{d}\), the error dynamics are:
$$
\begin{aligned}
\dot{e}_x &= A e_x + e_d – u_{smo} \\
\dot{e}_d &= \zeta(t) – h u_{smo}
\end{aligned}
$$
The goal is to force the state estimation error \(e_x\) to zero in finite time, upon which the equivalent control will reveal the disturbance. A sliding surface is chosen as \(s = e_x\). A power rate reaching law is adopted for its fast convergence and ability to mitigate chattering:
$$
\dot{s} = -k |s|^\mu \text{sign}(s)
$$
where \(k > 0\) is the switching gain, and \(0 < \mu < 1\) is the power exponent. From the error dynamics, \(\dot{s} = \dot{e}_x = A e_x + e_d – u_{smo}\). To satisfy the reaching law, the sliding mode control term \(u_{smo}\) is designed as:
$$
u_{smo} = A e_x + k |e_x|^\mu \text{sign}(e_x)
$$
Under the condition that \(k \geq \| e_d \| / |e_x|^\mu\) and with an appropriate choice of \(h\), the sliding mode \(s = e_x = 0\) will be reached in finite time. Once on the sliding surface (\(\dot{e}_x = e_x = 0\)), the equivalent control \(u_{smo,eq}\) satisfies \(0 = e_d – u_{smo,eq}\), implying \(u_{smo,eq} = e_d\). Furthermore, from the \(\dot{e}_d\) dynamics and the average behavior of the sliding mode, it can be shown that \(\hat{d}\) will converge to \(d\). The estimated disturbance \(\hat{d}\) is obtained by integrating \(\dot{\hat{d}} = h u_{smo}\):
$$
\hat{d} = \int h u_{smo} \, dt
$$
This estimated disturbance is then used for feedforward compensation. The final control voltage \(u_m\) sent to the PWM modulator of the grid tied inverter is the sum of the nominal deadbeat control output \(u_0\) and the negative of the estimated disturbance:
$$
u_m = u_0 – \hat{d}
$$
This structure effectively cancels out the lumped disturbance, making the grid tied inverter’s current loop behave as if it were the nominal, disturbance-free system.
Genetic Algorithm-Based Parameter Optimization for the SMDO
The performance of the SMDO—its convergence speed, estimation accuracy, and chattering magnitude—heavily depends on the proper selection of three key parameters: the observer gain \(h\), the switching gain \(k\), and the power exponent \(\mu\). Manual tuning of these parameters is often time-consuming and may not yield optimal performance. To systematically and efficiently find the best parameter set, a Genetic Algorithm (GA) is employed.
The GA is a population-based metaheuristic optimization algorithm inspired by natural selection. It operates on a population of candidate solutions (individuals), each represented by a chromosome encoding the parameters \([h, k, \mu]\). The algorithm evolves the population over successive generations to find individuals that maximize a fitness function, which quantifies the performance of the grid tied inverter controller using that specific parameter set.
The optimization process is structured as follows:
1. Fitness Function Definition: The fitness function must reflect the control objectives. A common and effective choice for a grid tied inverter is to minimize the Total Harmonic Distortion (THD) of the grid current under steady-state operation with a parameter mismatch. Therefore, the fitness function \(F\) for an individual can be defined as \(F = 1 / (THD + \epsilon)\), where \(\epsilon\) is a small constant to prevent division by zero. A higher fitness value corresponds to lower THD.
2. Initialization: An initial population of \(N\) individuals is randomly generated within predefined bounds for each parameter. Based on preliminary analysis, effective bounds were identified as: \(h \in (0, 2)\), \(k \in (0, 2)\), and \(\mu \in (0, 1)\).
3. Evaluation: For each individual in the population, the parameters \([h, k, \mu]\) are used to configure the SMDO within a simulation model of the grid tied inverter. The simulation is run under a defined test condition (e.g., steady-state with a 20% inductance mismatch), and the resulting grid current THD is calculated to evaluate the fitness.
4. Genetic Operators: The population evolves through selection, crossover, and mutation.
- Selection: Individuals are selected for reproduction based on their fitness. Techniques like tournament selection or roulette wheel selection ensure that fitter individuals have a higher chance of passing their genes to the next generation.
- Crossover: Selected pairs of parents exchange parts of their chromosomes to create offspring. This combines promising parameter combinations from different individuals.
- Mutation: With a small probability, random changes are introduced into an offspring’s chromosome. This injects genetic diversity into the population, helping to explore new areas of the parameter space and avoid convergence to local optima.
5. Termination: Steps 3 and 4 are repeated for a predetermined number of generations. The individual with the highest fitness found during the entire run is selected as the optimal parameter set.
For this grid tied inverter application, a GA was run with a population size of 10, 5 generations, a crossover probability of 0.9, and a mutation probability of 0.4. The test condition involved a significant mismatch in the grid-side inductance \(L_g\). The optimization results yielded an optimal parameter set that significantly improved performance over a wide range of manual guesses. The following table summarizes the performance of several candidate sets, with the GA-optimized set highlighted:
| Set | \(h\) | \(k\) | \(\mu\) | THD (%) | Fitness (1/(THD+0.01)) |
|---|---|---|---|---|---|
| Manual 1 | 1.24 | 1.08 | 0.59 | 3.30 | 30.21 |
| Manual 2 | 0.83 | 0.76 | 0.59 | 2.90 | 34.36 |
| GA-Optimized | 0.529 | 0.686 | 0.421 | 2.57 | 38.91 |
| GA Candidate 3 | 0.525 | 0.631 | 0.408 | 2.58 | 38.76 |
The effectiveness of the GA-SMDO compensation is further validated by testing the grid tied inverter controller under varying levels of grid-side inductance mismatch. The results clearly demonstrate that the controller with the optimized SMDO maintains significantly lower grid current THD across a wide mismatch range compared to the controller without disturbance compensation.
| Actual \(L_g\) (mH) | THD without SMDO (%) | THD with GA-SMDO (%) | Improvement |
|---|---|---|---|
| 0.9 (150% nominal) | 6.45 | 2.57 | 60.2% reduction |
| 0.8 (133% nominal) | 4.77 | 2.09 | 56.2% reduction |
| 0.7 (117% nominal) | 3.93 | 1.55 | 60.6% reduction |
| 0.6 (Nominal) | 1.13 | 0.99 | 12.4% reduction |
| 0.5 (83% nominal) | 0.91 | 0.59 | 35.2% reduction |
Simulation and Experimental Verification
The proposed GA-SMDO-based improved deadbeat control strategy for the grid tied inverter was validated through comprehensive simulations in MATLAB/Simulink and experiments on a 3-kW T-type three-level inverter prototype. The system parameters for both simulation and experiment are listed below:
| Parameter | Symbol | Value |
|---|---|---|
| Rated Power | \(S\) | 6.5 kVA |
| DC Link Voltage | \(U_{dc}\) | 700 V |
| Grid Voltage (phase-to-phase, RMS) | \(U_g\) | 380 V |
| Grid Frequency | \(f_g\) | 50 Hz |
| Inverter-side Inductance | \(L\) | 5 mH |
| Grid-side Inductance | \(L_g\) | 0.6 mH |
| Filter Capacitance | \(C_f\) | 6.65 μF |
| Switching / Sampling Frequency | \(f_s / f_{sample}\) | 10 kHz |
Simulation Results: The simulations evaluated three key scenarios: steady-state operation with parameter mismatch, a sudden step increase in current reference, and a sudden step decrease in current reference. In all cases, a 20% increase in the actual grid-side inductance (\(L_g = 0.72\) mH) was introduced to create a model mismatch, while the controller used the nominal value of 0.6 mH.
1. Steady-State Performance: The grid tied inverter was commanded to inject 10 A (RMS) per phase. Without the SMDO, the grid current exhibited visible distortion, with a THD of 6.45%. Upon activating the GA-SMDO-based compensation at t=1.04s, the current waveform became nearly sinusoidal, and the THD dropped significantly to 2.57%. The three-phase currents remained balanced and in phase with the grid voltages.
2. Dynamic Response to Current Step Increase: The current reference was stepped from 10 A to 15 A (RMS) at t=1.04s. With the proposed control, the grid tied inverter’s output current tracked the new reference within approximately 720 μs (less than one fundamental cycle). The THD during the new steady state was 2.03%. The voltage and current maintained proper synchronization throughout the transient.
3. Dynamic Response to Current Step Decrease: The current reference was stepped down from 10 A to 5 A (RMS). The grid tied inverter achieved reference tracking within 652 μs. The steady-state THD after the step was 2.86%.
These simulation results consistently demonstrate that the GA-SMDO-enhanced controller for the grid tied inverter effectively suppresses the negative effects of parameter mismatch, yielding low THD in steady-state and very fast dynamic response during transients.
Experimental Results: The control algorithm was implemented on a TMS320F28335 digital signal processor, controlling a 3-kW T-type three-level grid tied inverter hardware prototype. The experiments mirrored the simulation conditions, with an intentional mismatch between the actual and modeled grid-side inductance.
1. Steady-State: Without the SMDO, the measured grid current THD was 7.21%. After enabling the disturbance observer, the THD improved to 3.57%, and the current waveform quality was visibly enhanced.
2. Current Step Change (10A to 15A): The grid tied inverter’s current followed the reference with a settling time of about 1.13 ms, and the steady-state THD was measured at 2.97%.
3. Current Step Change (10A to 5A): The settling time was approximately 0.98 ms, with a post-transient THD of 4.05%.
The experimental waveforms confirmed the simulation trends. While the absolute THD values and settling times differed slightly due to non-ideal hardware characteristics (e.g., dead-time effects, sensor noise, component nonlinearities), the consistent directional improvement validates the practical effectiveness of the proposed GA-SMDO-based control strategy for a real-world grid tied inverter. The phase current remained synchronized with the grid voltage under all tested conditions.
Conclusion
This work has presented a robust and high-performance control strategy for an LCL-type grid tied inverter. The core of the strategy is an improved deadbeat predictive current controller that incorporates Newton interpolation for accurate state prediction and explicit two-step delay compensation. To address the critical vulnerability of model-based predictive control to parameter inaccuracies and external disturbances, a Sliding Mode Disturbance Observer (SMDO) was integrated to provide real-time feedforward compensation. Furthermore, a Genetic Algorithm was successfully applied to automate the tuning of the SMDO’s key parameters (\(h\), \(k\), \(\mu\)), overcoming the limitations of manual trial-and-error and ensuring optimal observer performance.
Both simulation and experimental results on a 3-kW prototype confirm the superiority of the proposed GA-SMDO-based approach. Under significant parameter mismatch, the strategy dramatically reduced the grid current THD—from 6.45% to 2.57% in simulation and from 7.21% to 3.57% in experiment during steady-state operation. Moreover, the grid tied inverter exhibited excellent dynamic performance, tracking step changes in current reference within approximately one millisecond while maintaining low harmonic distortion and stable grid synchronization. The proposed composite control strategy significantly enhances the robustness, power quality, and dynamic response of the grid tied inverter, making it a highly suitable solution for modern renewable energy systems operating under non-ideal and variable grid conditions.