In this study, I investigate a robust control strategy for islanded photovoltaic power generation systems, with a particular focus on solar inverters. The primary objective is to maintain stable output voltage under fluctuating load conditions while ensuring high dynamic performance and disturbance rejection. The proposed approach combines maximum power point tracking (MPPT) for the photovoltaic array, hybrid energy storage for DC-link voltage stabilization, and a sliding mode controller (SMC) designed on the basis of state feedback precise linear decoupling for the solar inverter. Through comprehensive simulations in Matlab/Simulink, I verify that the proposed control architecture effectively suppresses DC bus voltage fluctuations and maintains the output voltage of solar inverters within acceptable limits. This paper elaborates on the system topology, the mathematical modeling, the exact linearization process, the design of the SMC law, and the simulation results under various operating scenarios.
The growing global energy demand and the depletion of conventional fossil fuels have accelerated the adoption of renewable energy sources. Among them, solar energy has proven to be economically viable and environmentally friendly. In particular, solar inverters play a critical role in converting the DC power generated by photovoltaic (PV) arrays into high-quality AC power for standalone or grid-connected applications. For islanded microgrids, the voltage and frequency stability of solar inverters are essential to ensure reliable operation. However, the inherent nonlinearity, strong coupling between d-q axes, and sensitivity to parameter variations make the control of solar inverters a challenging task.
Conventional linear controllers such as PI regulators often fail to provide satisfactory performance under severe load transients or significant parameter uncertainty. Therefore, advanced nonlinear control techniques are needed. In this work, I adopt feedback linearization to exactly decouple the nonlinear dynamics of the solar inverter, and then design a sliding mode controller based on the decoupled linear model. The SMC provides excellent robustness against model uncertainties and external disturbances. The hybrid energy storage system (HESS), composed of a supercapacitor and a battery, is employed to smooth the DC-link voltage fluctuations caused by intermittent PV power. The overall control strategy ensures that the solar inverter delivers stable voltage and frequency to the load even when the PV output power varies rapidly.
System Topology and Configuration
The islanded photovoltaic power generation system studied in this work is illustrated conceptually as follows: a PV array is connected to a Boost converter, which performs maximum power point tracking and boosts the PV voltage to a suitable DC bus level. The output of the Boost converter feeds a three-phase solar inverter. The inverter output is filtered by an LC filter and then connected to the load. On the DC side, a hybrid energy storage system—consisting of a supercapacitor and a battery—is integrated through bidirectional DC/DC converters. This configuration allows the HESS to absorb or release power to maintain a stable DC-link voltage, thereby isolating the solar inverter from PV output power fluctuations.
The control architecture of the entire system can be divided into four main parts: (1) MPPT control of the PV Boost converter; (2) bidirectional DC/DC converter control for the supercapacitor and battery; (3) voltage and current double-loop control for the solar inverter; and (4) sliding mode current control based on exact linearization. Each part is designed to fulfill specific functions, and together they guarantee stable operation of the islanded system.
Boost Converter and MPPT Control
For the PV array, I utilize the Perturb and Observe (P&O) algorithm, which is widely used due to its simplicity and effectiveness. The MPPT controller adjusts the duty cycle of the Boost converter to track the maximum power point (MPP) of the PV array under varying irradiance and temperature. The output voltage of the PV array, \(U_{pv}\), and its current \(I_{pv}\) are sampled. The MPPT algorithm generates the reference voltage \(U_{pv}^\ast\) and the PV output power \(P_{pv}\). The error between \(U_{pv}\) and \(U_{pv}^\ast\) is processed by a PI controller, whose output modulates the PWM signal driving the Boost switch.
The key equations of the Boost converter in continuous conduction mode are given by:
\[
U_{dc} = \frac{U_{pv}}{1-D}
\]
\[
I_{dc} = I_{pv}(1-D)
\]
where \(D\) is the duty cycle, \(U_{dc}\) is the DC bus voltage, and \(I_{dc}\) is the DC bus current. The MPPT controller ensures that the PV array always operates at the maximum power point, thus maximizing the power extracted from the solar panels.
Hybrid Energy Storage Control
To stabilize the DC bus voltage, I employ a hybrid energy storage system (HESS) comprising a supercapacitor and a battery. The supercapacitor handles high-frequency power fluctuations, while the battery manages low-frequency power variations. The control structure for the supercapacitor is shown as follows: the raw PV power \(P_F\) is passed through a low-pass filter to obtain the low-frequency component \(P_L\). The high-frequency component is \(P_H = P_F – P_L\). The reference current for the supercapacitor is calculated by dividing \(P_H\) by the supercapacitor voltage \(u_{sc}\):
\[
i_{sc}^\ast = \frac{P_H}{u_{sc}}
\]
The error between \(i_{sc}^\ast\) and the measured supercapacitor current \(i_{sc}\) is processed by a PI controller to generate the PWM signals for the bidirectional converter. On the other hand, the battery converter operates in a voltage-stabilizing mode. The DC bus voltage reference \(u_{dc}^\ast\) is compared with the actual DC bus voltage \(u_{dc}\). The error is passed through a PI regulator to produce the battery current reference \(i_b^\ast\). Then the error between \(i_b^\ast\) and the battery current \(i_b\) is regulated by another PI controller.
The power balance at the DC bus can be expressed as:
\[
P_{pv} = P_{load} + P_{sc} + P_{bat} + P_{loss}
\]
where \(P_{pv}\) is the PV output power, \(P_{load}\) is the load power, \(P_{sc}\) is the supercapacitor power, \(P_{bat}\) is the battery power, and \(P_{loss}\) represents converter losses. By controlling \(P_{sc}\) and \(P_{bat}\), the DC bus voltage \(u_{dc}\) can be regulated tightly. This is crucial for the proper operation of the solar inverter, as a stable DC input voltage ensures a clean AC output.
Mathematical Modeling of the Solar Inverter
For the three-phase solar inverter with an LC filter, I derive the dynamic equations in the abc reference frame using Kirchhoff’s voltage and current laws. Let \(u_{oA}, u_{oB}, u_{oC}\) be the capacitor voltages (which are also the load voltages), \(i_A, i_B, i_C\) be the inductor currents, and \(i_{oA}, i_{oB}, i_{oC}\) be the load currents. The filter resistance is \(R\), the filter inductance is \(L_f\), and the filter capacitance is \(C_f\). The inverter output voltages are denoted as \(u_A, u_B, u_C\). The voltage equation for phase A is:
\[
u_A = R i_A + L_f \frac{di_A}{dt} + u_{oA}
\]
Similarly for phases B and C. The capacitor current equation for phase A is:
\[
i_A = C_f \frac{du_{oA}}{dt} + i_{oA}
\]
Applying the Park transformation (abc to dq) with a reference frame rotating at the angular frequency \(\omega_0\), the system dynamics become:
\[
u_d = R i_d + L_f \frac{di_d}{dt} – \omega_0 L_f i_q + u_{od}
\]
\[
u_q = R i_q + L_f \frac{di_q}{dt} + \omega_0 L_f i_d + u_{oq}
\]
\[
i_d = C_f \frac{du_{od}}{dt} – \omega_0 C_f u_{oq} + i_{od}
\]
\[
i_q = C_f \frac{du_{oq}}{dt} + \omega_0 C_f u_{od} + i_{oq}
\]
In matrix form, the current dynamics are:
\[
\frac{d}{dt}
\begin{bmatrix}
i_d \\
i_q
\end{bmatrix}
=
\begin{bmatrix}
-\frac{R}{L_f} & \omega_0 \\
-\omega_0 & -\frac{R}{L_f}
\end{bmatrix}
\begin{bmatrix}
i_d \\
i_q
\end{bmatrix}
+
\begin{bmatrix}
\frac{u_d – u_{od}}{L_f} \\
\frac{u_q – u_{oq}}{L_f}
\end{bmatrix}
\]
It is evident from the above equations that the d-axis and q-axis currents are cross-coupled through the terms \(\omega_0 L_f i_q\) and \(\omega_0 L_f i_d\). Conventional PI controllers would require decoupling networks to compensate for this interaction. Moreover, the system is nonlinear due to the presence of the product of state variables and the dependence on load currents. Therefore, I apply state feedback exact linearization to fully decouple the system, transforming it into a set of independent first-order linear systems.
State Feedback Precise Linear Decoupling
The objective of feedback linearization is to find a nonlinear state transformation and a nonlinear feedback control law that renders the system linear in a new set of coordinates. For the solar inverter current dynamics, I define the state vector as:
\[
x = \begin{bmatrix} i_d \\ i_q \end{bmatrix}
\]
and the input vector as:
\[
u = \begin{bmatrix} u_d \\ u_q \end{bmatrix}
\]
The output vector is chosen as:
\[
y = \begin{bmatrix} h_1(x) \\ h_2(x) \end{bmatrix}
=
\begin{bmatrix} i_d \\ i_q \end{bmatrix}
\]
Thus we have a two-input, two-output nonlinear system described by:
\[
\dot{x} = f(x) + g_1(x) u_1 + g_2(x) u_2
\]
\[
y_1 = h_1(x), \quad y_2 = h_2(x)
\]
where
\[
f(x) =
\begin{bmatrix}
-\frac{R}{L_f} x_1 + \omega_0 x_2 – \frac{u_{od}}{L_f} \\
-\omega_0 x_1 – \frac{R}{L_f} x_2 – \frac{u_{oq}}{L_f}
\end{bmatrix}
\]
\[
g_1(x) =
\begin{bmatrix}
\frac{1}{L_f} \\
0
\end{bmatrix}, \quad
g_2(x) =
\begin{bmatrix}
0 \\
\frac{1}{L_f}
\end{bmatrix}
\]
To check the relative degree condition, I compute the Lie derivatives. For output \(h_1(x)=x_1\), we have:
\[
L_f^0 h_1(x) = x_1
\]
\[
L_{g_1} h_1(x) = \frac{1}{L_f}, \quad L_{g_2} h_1(x) = 0
\]
Similarly for \(h_2(x)=x_2\):
\[
L_{g_1} h_2(x) = 0, \quad L_{g_2} h_2(x) = \frac{1}{L_f}
\]
The decoupling matrix \(A(x)\) is therefore:
\[
A(x) =
\begin{bmatrix}
\frac{1}{L_f} & 0 \\
0 & \frac{1}{L_f}
\end{bmatrix}
\]
Since the matrix \(A(x)\) is nonsingular for all \(x\), the system has a vector relative degree \((1,1)\), and the sum of relative degrees equals the system order \(n=2\). This confirms that the system is exactly linearizable via state feedback.
I introduce a new input vector \(v\) defined by:
\[
v = b(x) + A(x) u
\]
where
\[
b(x) =
\begin{bmatrix}
L_f h_1(x) \\
L_f h_2(x)
\end{bmatrix}
=
\begin{bmatrix}
-\frac{R}{L_f} x_1 + \omega_0 x_2 – \frac{u_{od}}{L_f} \\
-\omega_0 x_1 – \frac{R}{L_f} x_2 – \frac{u_{oq}}{L_f}
\end{bmatrix}
\]
Then the system becomes:
\[
\begin{bmatrix}
\dot{y}_1 \\
\dot{y}_2
\end{bmatrix}
=
\begin{bmatrix}
v_1 \\
v_2
\end{bmatrix}
\]
This is a set of two decoupled integrators. The control objective is to make the actual outputs \(i_d\) and \(i_q\) track their references \(i_d^\ast\) and \(i_q^\ast\). However, the exact linearization relies on the accurate model parameters. In practice, parameter mismatch and unknown disturbances may degrade the performance. Hence, I integrate sliding mode control, which is known for its robustness, into the decoupled linear framework.
Sliding Mode Controller Design
The overall control system for the solar inverter employs a voltage and current double-loop structure. The outer voltage loop uses a PI controller to regulate the d-axis and q-axis output voltages \(u_{od}\) and \(u_{oq}\) to their references \(u_{od}^\ast\) and \(u_{oq}^\ast\). The outputs of the voltage PI controllers, along with the capacitor current decoupling terms, generate the current references \(i_d^\ast\) and \(i_q^\ast\). The inner current loop uses sliding mode controllers to track these references. The SMC design for the current loop is detailed below.
Define the tracking errors as:
\[
e_1 = i_d^\ast – i_d
\]
\[
e_2 = i_q^\ast – i_q
\]
To improve steady-state accuracy and eliminate reaching phase issues, I use an integral sliding surface with a nonlinear exponential term. The sliding surface is defined as:
\[
s_i = c_{i1} e_i – c_{i2} \int_0^t e_i d\tau – f_i(t)
\]
where \(i=1,2\), \(c_{i1}>0\), \(c_{i2}>0\), and \(f_i(t)=e_i(0)e^{-pt}\) with \(p>0\). The function \(f_i(t)\) ensures that the initial tracking error lies on the sliding surface, thus eliminating the reaching phase and providing global robustness.
To reduce chattering, I adopt a saturation function instead of the sign function. The reaching law is:
\[
\dot{s}_i = -k_i s_i – \varepsilon_i \,\text{sat}(s_i)
\]
where \(k_i>0\), \(\varepsilon_i>0\), and \(\text{sat}(\cdot)\) is defined as:
\[
\text{sat}(s) =
\begin{cases}
1, & s > \Delta \\
\frac{s}{\Delta}, & |s| \le \Delta \\
-1, & s < -\Delta
\end{cases}
\]
Differentiating the sliding surface gives:
\[
\dot{s}_i = c_{i1} \dot{e}_i – c_{i2} e_i + e_i(0) p e^{-pt}
\]
Combining with the reaching law, I solve for \(v_i\):
\[
v_i = \frac{1}{c_{i1}} \left[ c_{i2} e_i – k_i s_i – \varepsilon_i \text{sat}(s_i) – e_i(0) p e^{-pt} \right]
\]
Thus the control signals for the decoupled system are:
\[
v_1 = \frac{c_{12} e_1 – k_1 s_1 – \varepsilon_1 \text{sat}(s_1) – e_1(0) p e^{-pt}}{c_{11}}
\]
\[
v_2 = \frac{c_{22} e_2 – k_2 s_2 – \varepsilon_2 \text{sat}(s_2) – e_2(0) p e^{-pt}}{c_{21}}
\]
Finally, the actual inverter output voltage commands in the dq frame are obtained from the inverse feedback linearization law:
\[
u_d = u_{od} + L_f v_1 + R i_d – \omega_0 L_f i_q
\]
\[
u_q = u_{oq} + L_f v_2 + R i_q + \omega_0 L_f i_d
\]
These voltages are then transformed back to the abc frame using the inverse Park transformation and fed to the PWM modulator of the solar inverter. The complete control block diagram is summarized in the following table:
| Control Loop | Controller Type | Inputs | Outputs |
|---|---|---|---|
| MPPT | Perturb & Observe | \(U_{pv}, I_{pv}\) | \(U_{pv}^\ast, P_{pv}\) |
| Supercapacitor | PI + low-pass filter | \(P_F, u_{sc}, i_{sc}\) | PWM signals |
| Battery | PI (dual loop) | \(u_{dc}^\ast, u_{dc}, i_b^\ast, i_b\) | PWM signals |
| Voltage outer loop | PI + decoupling | \(u_{od}^\ast, u_{oq}^\ast, u_{od}, u_{oq}\) | \(i_d^\ast, i_q^\ast\) |
| Current inner loop | Sliding mode | \(i_d^\ast, i_q^\ast, i_d, i_q\) | \(u_{d}, u_{q}\) |
Simulation Results and Analysis
To validate the effectiveness of the proposed control strategy for solar inverters, I built a comprehensive simulation model in Matlab/Simulink. The system parameters are listed below:
| Parameter | Symbol | Value |
|---|---|---|
| Ambient temperature | \(T\) | 25 °C |
| Filter inductance | \(L_f\) | 2 mH |
| Filter capacitance | \(C_f\) | 50 μF |
| Filter resistance | \(R\) | 0.1 Ω |
| Angular frequency | \(\omega_0\) | 314 rad/s |
| DC bus voltage | \(u_{dc}\) | 600 V |
| Supercapacitor capacitance | \(C_{sc}\) | 5 F |
| Battery nominal voltage | \(U_{bat}\) | 240 V |
| Switching frequency | \(f_{sw}\) | 10 kHz |
| Sliding surface gains | \(c_{11}, c_{12}, c_{21}, c_{22}\) | 20, 5, 20, 5 |
| Reaching law gains | \(k_1, k_2, \varepsilon_1, \varepsilon_2\) | 100, 100, 1, 1 |
| Boundary layer | \(\Delta\) | 0.01 |
| Exponential parameter | \(p\) | 10 |
In the simulation, the irradiance varies according to the following schedule:
| Time (s) | 0–2 | 2–4 | 4–6 | 6–8 | 8–10 |
|---|---|---|---|---|---|
| Irradiance (W/m²) | 420 | 380 | 410 | 450 | 420 |
The PV output power waveform follows the irradiance profile. As the irradiance changes, the maximum power point also changes, and the MPPT controller tracks it accordingly. The Boost converter output voltage is shown to vary slightly, but the hybrid energy storage system effectively compensates for these fluctuations. The inverter input-side DC voltage remains nearly constant at 600 V, with a small ripple that is acceptable for stable operation of solar inverters.
The line voltage and line current RMS waveforms are presented under varying load conditions. The three-phase load is changed at t = 4 s, 6 s, 8 s, and 10 s. At t = 6 s, the load resistance decreases from 28 Ω to 20 Ω, representing a load increase. The simulation results show that the line voltage experiences a small transient dip but recovers within one fundamental period (20 ms). The line current increases correspondingly. This demonstrates the fast dynamic response of the sliding mode controller.
Load Step Response
With the load change at t = 6 s, the system output voltage and current transient waveforms reveal that the voltage deviation is small and the recovery is quick. The sliding mode controller provides strong robustness against this external disturbance. The frequency deviation is kept within ±0.2 Hz, satisfying the standard requirement for islanded microgrids.
In addition, to show the advantage of the proposed SMC over conventional PI control, I compared the performance under the same load step. The SMC-based solar inverter yields a smaller overshoot, shorter settling time, and lower steady-state error. The following table summarizes the comparison:
| Controller Type | Overshoot (%) | Settling Time (ms) | Voltage THD (%) |
|---|---|---|---|
| Conventional PI | 5.2 | 45 | 3.8 |
| Proposed SMC with exact linearization | 1.8 | 15 | 1.2 |
These results clearly demonstrate the superior performance of the proposed method for solar inverters. The exact linearization removes the cross-coupling between d and q axes, simplifying the controller design, and the sliding mode component ensures robustness against parameter uncertainties and load disturbances.
Discussion
For solar inverters operating in island mode, voltage stability is crucial. The method I propose addresses two key challenges: (1) the DC-link voltage fluctuations caused by intermittent PV power, and (2) the AC-side voltage regulation under load transients. The hybrid energy storage control effectively filters the power fluctuations and maintains the DC bus voltage. The feedback linearization technique provides a systematic approach to decouple the complex nonlinear dynamics of solar inverters, enabling the use of linear control techniques in the equivalent linear system. By replacing the linear controller with a sliding mode controller, I preserve the benefits of robust nonlinear control while avoiding the complexity of nonlinear system inversion.
One practical consideration is the chattering phenomenon inherent in sliding mode control. To mitigate this, I employ a saturation function with a boundary layer. The thickness of the boundary layer is chosen as a trade-off between chattering suppression and tracking accuracy. A smaller boundary layer reduces steady-state error but may cause more chattering; a larger boundary layer smooths the control signal but degrades accuracy. In simulations, a boundary layer of 0.01 works well for the given system.
Another important aspect is the accuracy of the state feedback linearization. The controller relies on the model parameters \(L_f\), \(R\), and \(C_f\). If these parameters drift due to temperature or aging, the exact cancellation of nonlinearities may not be achieved, leading to performance degradation. However, the sliding mode component provides an extra layer of robustness, because the sliding surface is designed based on the tracking error, and the reaching law forces the states to converge to the sliding surface even in the presence of matched uncertainties. Therefore, the proposed controller maintains satisfactory performance for a reasonable range of parameter variations.
The integration of solar inverters with energy storage is becoming increasingly important for standalone renewable systems. The ability to maintain stable AC output under fluctuating DC input and variable loads is essential for power quality. The proposed control architecture can be extended to other types of inverters, such as those used in microgrids with multiple distributed generation units. Moreover, the sliding mode control design can be adapted for grid-connected operation by modifying the outer loop references to achieve power dispatch.
Conclusion
In this paper, I have presented a sliding mode control strategy for solar inverters based on state feedback precise linear decoupling. The proposed approach consists of a hybrid energy storage system for DC-link voltage stabilization and a double-loop voltage-current controller for AC voltage regulation. The current inner loop uses a sliding mode controller designed after exact linearization of the inverter dynamics. The simulation results demonstrate the effectiveness of the proposed strategy under varying irradiance and load conditions. The key conclusions are:
- The hybrid energy storage control, combining a supercapacitor and a battery, effectively smooths the DC bus voltage fluctuations caused by PV output power variations, ensuring stable input voltage to solar inverters.
- The state feedback exact linearization successfully decouples the d-axis and q-axis current dynamics of the three-phase solar inverter, transforming the nonlinear coupled system into two independent first-order linear systems.
- The sliding mode controller, designed on the basis of the decoupled system, provides excellent robustness against load disturbances and model uncertainties. The use of an integral sliding surface with an exponential term eliminates the reaching phase and reduces steady-state error.
- The proposed controller enables fast voltage recovery, small overshoot, and low harmonic distortion, outperforming conventional PI control for solar inverters in islanded operation.
- The overall system maintains frequency deviation within ±0.2 Hz under load steps, complying with the requirements for standalone microgrids.
Future work will focus on experimental validation of the proposed control strategy and its extension to parallel operation of multiple solar inverters for higher power applications. Additionally, model predictive control could be combined with sliding mode control to further enhance the transient performance.
Overall, the combination of feedback linearization and sliding mode control offers a powerful solution for the high-performance control of solar inverters in autonomous power systems. The method not only ensures stable operation under severe conditions but also provides a systematic design procedure that can be readily applied to similar power conversion systems.