I have been studying single-phase solar inverters because they are a critical interface between distributed photovoltaic sources and the ac grid. In my view, the most demanding technical issue in this area is not only maximum power point tracking or current regulation, but also the intrinsic second-order ripple power that appears when an inverter delivers single-phase ac power. For solar inverters, this ripple power can degrade photovoltaic energy harvesting, increase thermal stress, and force the use of large electrolytic capacitors if no active decoupling method is used. I therefore focus my work on active power decoupling for single-phase solar inverters with boost and power-decoupling capabilities, and I investigate model predictive control and virtual oscillator control as practical ways to improve steady-state behavior, transient response, parameter robustness, and grid-distortion adaptability.
In my analysis, the instantaneous output power of a single-phase solar inverter operating at unity power factor can be written as
$$p_o = v_o i_o = V_o\sin(\omega t)\,I_o\sin(\omega t) = \frac{1}{2}V_oI_o – \frac{1}{2}V_oI_o\cos(2\omega t).$$
This expression contains a constant term and a second-order ripple term. If I include the filter inductor voltage drop, the output power becomes
$$p_o = \frac{1}{2}V_oI_o – \frac{1}{2}V_oI_o\cos(2\omega t) + \omega L_f I_o^2\sin(2\omega t).$$
For solar inverters, the dc side should ideally see a constant power equal to the average ac power. If the ripple power is not buffered, it propagates into the photovoltaic source and reduces the effectiveness of maximum power point tracking. I summarize the two main families of solutions in my study as passive power decoupling and active power decoupling.
Passive power decoupling uses a large capacitor or an LC network on the dc bus. If I assume that a dc-link capacitor stores the entire ripple energy, the required capacitance can be approximated by
$$C_b = \frac{P_r}{\omega \Delta V_{ave} V_{ave}}.$$
For a 1 kW solar inverter with a 380 V dc bus and a 2% voltage ripple, the capacitance can easily reach hundreds of microfarads. In practice, electrolytic capacitors are often selected, but their lifetime at high temperature is much shorter than that of photovoltaic modules. This reduces the reliability of solar inverters and conflicts with the high-power-density target of modern distributed generation.
Active power decoupling avoids the large electrolytic capacitor by transferring the ripple power to a small film or ceramic capacitor through an auxiliary circuit. The decoupling capacitor is allowed to have a large voltage swing, so its capacitance can be much smaller. I classify active power decoupling topologies into parallel, series, and differential structures. I also classify the decoupling cells into buck, boost, buck-boost, full-bridge, and half-bridge types. Among these, a boost-type dc-side active power decoupling circuit is attractive for solar inverters because the photovoltaic voltage is usually lower than the peak grid voltage.
In my research, I use a single-phase solar inverter topology with both boost and power-decoupling capabilities. The front-end circuit behaves as a rotating buck-boost converter, and the rear-end circuit is a full-bridge inverter with an output filter inductor. A dc bus capacitor is placed at the input of the H-bridge for high-frequency filtering and partial power decoupling. The topology can be summarized by the following relationships:
$$v_{Cb}=v_{dc}+v_{Cd}=\frac{v_{dc}}{1-d},$$
$$v_{Cd}=\frac{d}{1-d}v_{dc}.$$
Here, \(v_{dc}\) is the photovoltaic input voltage, \(v_{Cd}\) is the decoupling capacitor voltage, \(v_{Cb}\) is the dc bus voltage, and \(d\) is the duty ratio of the front-end switch. This topology provides boost capability and allows the decoupling capacitor voltage to swing widely, which is exactly what I want for high-density solar inverters.
I have found that the control algorithm is the decisive factor in achieving good active power decoupling. Existing control strategies can be broadly grouped into four categories: power-balance-based control, harmonic-suppression-based control, virtual-impedance-based control, and automatic-power-decoupling-based control. I compare them in the following table because this comparison shaped my own control design.
| Control strategy | Main control loops | Decoupling performance | Dynamic response | Parameter-drift robustness | Adaptability to distorted grid | Control complexity | Dependence on topology |
|---|---|---|---|---|---|---|---|
| Power-balance-based | Decoupling capacitor voltage loop plus ac-side loop | Good | Moderate | Weak | Weak | Moderate | Moderate |
| Harmonic-suppression-based | Ripple current or voltage loop plus ac-side loop | Good | Slow | Good | Moderate | Moderate | Moderate |
| Virtual-impedance-based | Emulated capacitor, inductor, or LC resonator plus ac-side loop | Excellent | Slow | Good | Moderate | Moderate | High |
| Automatic-power-decoupling-based | Direct dc input voltage or current loop plus ac-side loop | Excellent | Fast | Strong | Strong | Simple | Moderate |
My own approach belongs to the automatic power decoupling family. In this family, I do not directly control the ripple port. Instead, I control the dc input voltage or current so that the dc-side power is nearly constant. The ripple power is then automatically buffered by the passive components. This is especially attractive for solar inverters because the photovoltaic source should not be disturbed by second-order ripple, and because the control structure can remain relatively simple.
I first studied open-loop power decoupling. In an ideal grid, if the decoupling capacitor absorbs the entire second-order ripple, its voltage reference can be written as
$$v_{Cd}=V_d+B\sin(2\omega t+\theta).$$
The dc bus capacitor voltage then contains a similar ac component:
$$v_{Cb}=v_{dc}+v_{Cd}=V_b+B\sin(2\omega t+\theta).$$
If I calculate the ripple power of \(C_d\) and \(C_b\), the sum must match the second-order output ripple. However, this open-loop method introduces an inherent fourth-order power term:
$$p_{ripple,4} = \omega(C_d+C_b)B^2\sin(4\omega t+2\theta).$$
I also observed that when the grid voltage is distorted, the ac power contains fourth-, sixth-, and eighth-order ripple components. An open-loop reference based only on the second-order ripple cannot compensate these components well. Moreover, the reference depends on the capacitance, so parameter drift directly degrades decoupling. For solar inverters operating over a wide power range, this is a serious limitation.
I then examined a proportional-integral control method based on automatic power decoupling. In this method, a dc input voltage outer loop generates an input current reference, and an input current inner loop tracks it. The ac side uses a dc bus voltage outer loop and an output current inner loop. Although this method is simple and can handle distorted grid conditions better than open-loop decoupling, I found three main drawbacks:
| Issue | Consequence in solar inverters |
|---|---|
| PI controllers are used in cascaded loops | Transient response is slow, especially when the photovoltaic operating point changes. |
| Controller design depends on circuit parameters | Inductance and capacitance drift can detune the controller and weaken decoupling. |
| Small-signal design is valid near one operating point | Wide input-power variation and distorted grid voltage can make the controller ineffective. |
Because of these issues, I decided to combine continuous control set model predictive control with automatic power decoupling. Continuous control set model predictive control has a fixed switching frequency, which is beneficial for inductor design in solar inverters. It also avoids the variable switching frequency of finite control set model predictive control. I proposed an input-current continuous control set model predictive control algorithm for the front-end decoupling circuit.
In my input-current continuous control set model predictive control method, I predict the inductor current and input current using a discrete-time model. For the front-end circuit, I write
$$v_L = L_d\frac{di_{Ld}}{dt},$$
$$v_L =
\begin{cases}
v_{dc}, & S_1=1,\ S_2=0,\\
-v_{Cd}, & S_1=0,\ S_2=1.
\end{cases}$$
Using forward Euler discretization, the inductor current prediction is
$$i_{Ld}(k+1)=i_{Ld}(k)+\frac{d(k)T_s}{L_d}v_{dc}(k)-\frac{(1-d(k))T_s}{L_d}v_{Cd}(k).$$
I also predict the input current with a factor \(k_s\) to account for the different high-frequency behavior of the capacitor current:
$$i_{in}(k+1)=i_{in}(k)+\frac{k_sT_s}{L_d}\left[d(k)v_{dc}(k)-(1-d(k))v_{Cd}(k)\right].$$
I choose the cost function
$$f_{cost}=\left[i_{in}(k+1)-i_{in,ref}(k+1)\right]^2.$$
Minimizing this cost gives the optimal duty ratio for the front-end switch. In a compact form, I obtain
$$d(k)=\frac{L_d\left[i_{in,ref}(k+1)-i_{in}(k)\right]+k_sT_sv_{Cd}(k)}{k_sT_s\left[v_{Cd}(k)+v_{dc}(k)\right]}.$$
I use a second-order Lagrange interpolation to estimate the next-step reference:
$$i_{in,ref}(k+1)=3i_{in,ref}(k)-3i_{in,ref}(k-1)+i_{in,ref}(k-2).$$
The duty ratio must satisfy
$$0<d(k)<1.$$
I analyzed the effect of inductance mismatch on stability. If the real inductance is \(L_d\) and the controller inductance is \(L_{ctr}\), the discrete transfer function from reference to input current contains the factor \(L_{ctr}/L_d\). The stability condition can be expressed as
$$L_d>0.5L_{ctr}.$$
This means that my input-current continuous control set model predictive control method remains robust when the inductance is reduced by up to about 50%. This is a major advantage for solar inverters because magnetic components can vary with temperature, saturation, and manufacturing tolerance.
For the ac side of the solar inverter, I used a phase-locked loop based on a second-order generalized integrator, a moving average filter for the dc bus voltage feedback, and grid voltage feedforward. I introduced these blocks because the dc bus voltage ripple caused by power decoupling can propagate into the output current reference and create odd harmonics. I summarize the harmonic transfer mechanism as follows:
| Source of ripple | Frequency component | Effect on output current | Effect on dc-side power |
|---|---|---|---|
| Single-phase ac power | Second order | Odd harmonics if voltage feedback is not filtered | Second-order ripple |
| Dc bus voltage ripple | Second and fourth order | Third, fifth, and higher odd harmonics | Fourth and sixth order |
| Distorted grid voltage | Third, fifth, seventh order | Current distortion if no feedforward or PLL filtering is used | Fourth, sixth, eighth order |
I tested the input-current continuous control set model predictive control algorithm in simulation, hardware-in-the-loop experiments, and a 1 kW prototype. The main parameters I used are listed below.
| Parameter | Value |
|---|---|
| Rated power | 1 kW |
| Rated input voltage | 182.5 V |
| Average dc bus voltage | 380 V |
| Peak output voltage | 311 V |
| Sampling frequency | 40 kHz |
| Decoupling circuit switching frequency | 40 kHz |
| H-bridge switching frequency | 20 kHz |
| Grid frequency | 50 Hz |
| Decoupling capacitor \(C_d\) | 160 \(\mu\)F |
| Dc bus capacitor \(C_b\) | 80 \(\mu\)F |
| Decoupling inductor \(L_d\) | 100 \(\mu\)H |
| Output filter inductor \(L_f\) | 4 mH |
In the ideal-grid steady-state test, I compared open-loop decoupling, automatic-power-decoupling PI control, and my input-current continuous control set model predictive control method. The input voltage peak-to-peak ripple was about 18 V for open-loop control, 12 V for PI control, and 6.1 V for my method. The input current peak-to-peak ripple was about 0.77 A, 0.35 A, and 0.18 A, respectively. I concluded that my method gives the best steady-state decoupling performance among these three.
In the dynamic test, I stepped the input voltage reference from 182.5 V to 210 V. My method recovered in about 5 ms, while the automatic-power-decoupling PI method needed about 20 ms. This confirmed that continuous control set model predictive control improves the transient response of solar inverters without requiring aggressive linear controller tuning.
I also tested parameter drift. When the decoupling capacitor was reduced by 62.5%, the input voltage peak-to-peak ripple in my method increased only slightly, while the open-loop and PI methods degraded significantly. When the decoupling inductor was reduced by 40%, my method again showed much stronger robustness. I summarize the observed trends in the following table.
| Condition | Open-loop decoupling | Automatic-power-decoupling PI | Input-current CCS-MPC |
|---|---|---|---|
| \(C_d\) reduced by 62.5% | Large ripple increase | Noticeable ripple increase | Small ripple increase |
| \(L_d\) reduced by 40% | Large ripple increase | Moderate ripple increase | Very small ripple increase |
| Step change of input voltage | Not optimized | About 20 ms | About 5 ms |
| Distorted grid | Poor decoupling | Good decoupling | Good decoupling with lower THD |
Although the input-current continuous control set model predictive control method performed well, I noticed that the input current reference is generated by an outer PI voltage loop. This means that the inner predictive controller is still constrained by the outer loop bandwidth. For solar inverters, the photovoltaic input voltage may change over a wide range, and the outer loop tuning may not remain optimal at every operating point. Therefore, I developed a second method: input-voltage continuous control set model predictive control.
In this method, I removed the cascaded current inner loop and designed a single-loop predictive controller for the front-end decoupling circuit. I chose a cost function that simultaneously minimizes input current ripple and input voltage tracking error:
$$f_{cost}=\left[i_{in}(k+1)-i_{in}(k)\right]^2+\left[v_{dc}(k+1)-v_{dc,ref}\right]^2.$$
By minimizing this cost, I derived the duty ratio
$$d(k)=\frac{L_d\left[v_{dc}(k+1)-v_{dc,ref}\right]+k_sT_sv_{Cd}(k)}{k_sT_s\left[v_{Cd}(k)+v_{dc}(k)\right]}.$$
I use Lagrange interpolation for the next-step input voltage:
$$v_{dc}(k+1)=3v_{dc}(k)-3v_{dc}(k-1)+v_{dc}(k-2).$$
This single-loop method has a simpler control structure than the input-current method. It does not require a dc input voltage PI outer loop, so the predictive controller can fully use its fast dynamic response. In my simulation tests, the input voltage ripple was about 2.4 V, or 1.3% of the rated value, in both ideal and distorted grids. The input current ripple was about 0.07 A in the ideal grid. Compared with the input-current method, the input-voltage method reduced input voltage ripple from 6.1 V to 2.4 V and input current ripple from 0.18 A to 0.07 A.
I also compared the dynamic responses. With a step from 182.5 V to 210 V, the input-voltage continuous control set model predictive control method reached steady state in less than 2 ms, while the input-current method took about 5 ms. This confirmed that removing the outer PI loop allows the model predictive controller to act directly on the input voltage and improves both decoupling and transient performance.
| Feature | Input-current CCS-MPC | Input-voltage CCS-MPC |
|---|---|---|
| Control structure | Cascaded: PI voltage outer loop + predictive current inner loop | Single predictive voltage loop |
| Input voltage peak-to-peak ripple | About 6.1 V | About 2.4 V |
| Input current peak-to-peak ripple | About 0.18 A | About 0.07 A |
| Dynamic response to input voltage step | About 5 ms | Less than 2 ms |
| Robustness to inductor drift | Strong | Strong |
| Distorted-grid decoupling | Good | Excellent |
I validated the input-voltage continuous control set model predictive control method on a 6 kW solar inverter prototype as well. The dc bus average voltage was 400 V, the ripple amplitude was 36 V, the decoupling capacitor was 725 \(\mu\)F, the dc bus capacitor was 290 \(\mu\)F, the decoupling inductor was 300 \(\mu\)H, and the output filter inductor was 1 mH. Compared with passive decoupling, which would require about 2986 \(\mu\)F, my active method reduced the required capacitance by about 66%. The prototype tests showed stable operation at the maximum power point and a smooth transition when the input voltage reference was stepped from 200 V to 220 V.
At this stage, I had improved the front-end decoupling control substantially. However, I still needed to address the rear-end inverter control. Active power decoupling intentionally creates a large voltage ripple on the decoupling capacitor and the dc bus capacitor. This ripple can affect the ac output current if the inverter control uses a conventional dc bus voltage outer loop and an output current inner loop. The voltage ripple can modulate the current reference and generate odd harmonics. A phase-locked loop can also propagate grid voltage harmonics into the current reference. I therefore proposed a virtual oscillator control method for the rear-end inverter of the solar inverter.
Virtual oscillator control is a time-domain control method. It does not require a phase-locked loop, and it can synchronize a solar inverter with the grid through a nonlinear oscillator dynamic. In my implementation, I use a unified virtual oscillator control structure. The voltage vector is defined as
$$\mathbf{v}=V_p(t)e^{j\theta(t)}.$$
The derivative of the voltage vector is
$$\frac{d\mathbf{v}}{dt}=j\omega_0\mathbf{v}+\eta(\mathbf{i}_{0}-\mathbf{i})e^{j\phi}.$$
Here, \(\omega_0\) is the nominal angular frequency, \(\eta\) is a positive design parameter, \(\mathbf{i}_0\) is the output current reference vector, \(\mathbf{i}\) is the measured output current vector, and \(\phi\) determines the power-angle relationship. When \(\phi=\pi/2\), the oscillator behaves with a voltage-reactive power and frequency-active power droop-like characteristic. When \(\phi=0\), it behaves with a voltage-active power and frequency-reactive power characteristic.
To improve synchronization and reduce the effect of grid voltage distortion, I add grid voltage feedforward:
$$\mathbf{v}_s=\mathbf{v}+\mathbf{v}_o,$$
$$\frac{d\mathbf{v}}{dt}=j\omega_0\mathbf{v}+\eta(\mathbf{i}_{o,ref}-\mathbf{i}_o)e^{j\phi}.$$
For a single-phase solar inverter, I use a second-order generalized integrator to generate the orthogonal component. The active power reference for the rear-end inverter can be generated from the dc bus voltage and the input power:
$$P_0=p_{in}\frac{v_{Cb}}{V_b}.$$
Because active power decoupling keeps the photovoltaic input power nearly constant, \(P_0\) contains a second-order component due to the dc bus voltage ripple. I analyzed the small-signal relationship between power reference disturbance and output current. Using a synchronous reference frame aligned with the grid voltage, I write
$$\frac{d}{dt}\begin{bmatrix} I_d \\ I_q \end{bmatrix}
=
\begin{bmatrix}
-\frac{R}{L} & \omega \\
-\omega & -\frac{R}{L}
\end{bmatrix}
\begin{bmatrix} I_d \\ I_q \end{bmatrix}
+
\frac{1}{L}
\begin{bmatrix}
V_{a}\cos(\theta_s)-V_{rms} \\
V_{a}\sin(\theta_s)
\end{bmatrix}.$$
I also express the active and reactive powers as
$$\begin{bmatrix} P \\ Q \end{bmatrix}
=
V_a
\begin{bmatrix}
\cos(\theta_s) & \sin(\theta_s) \\
\sin(\theta_s) & -\cos(\theta_s)
\end{bmatrix}
\begin{bmatrix} I_d \\ I_q \end{bmatrix}.$$
From the small-signal model, I found that the output current is much less sensitive to \(P_0\) and \(Q_0\) disturbances than in a conventional voltage-current dual-loop control structure. This is important for solar inverters because it means that the large dc bus voltage ripple caused by active power decoupling does not need a moving average filter or a dedicated harmonic compensation loop on the ac side. I can therefore simplify the rear-end control and reduce the computational burden.
I combined input-voltage continuous control set model predictive control on the front end with virtual oscillator control on the rear end. I call this combined method ICMV in my work. The control structure has the following features:
| Feature | ICMV method |
|---|---|
| Front-end decoupling | Input-voltage continuous control set model predictive control |
| Rear-end inverter | Virtual oscillator control with grid voltage feedforward |
| Phase-locked loop | Not required |
| Dc bus ripple filtering | Not required on the ac current reference |
| Grid voltage harmonic compensation | Provided by feedforward and oscillator synchronization |
| Dynamic response | Less than 2 ms in my tests |
| Distorted-grid output current | Maintained with low THD |
I tested ICMV in simulation and hardware-in-the-loop experiments. In an ideal grid, the input voltage ripple remained about 2.4 V, the input current was nearly constant, and the output current THD was about 3.10%. The dc bus voltage ripple was about 26 V, but it did not significantly degrade the output current. When the grid frequency changed from 50 Hz to 49.5 Hz and then to 50.5 Hz, the solar inverter remained synchronized without a phase-locked loop, and the power factor remained close to unity. When the input voltage reference was stepped from 182.5 V to 210 V, the transient response was smooth and completed within 2 ms.
Under a distorted grid with 10% third harmonic, 10% fifth harmonic, and 5% seventh harmonic, the input voltage ripple stayed around 2.9 V, and the output current THD was about 3.84%. Without virtual oscillator control, a conventional inverter control with an unfiltered phase-locked loop produced much higher output current distortion, about 5.93%. This showed me that virtual oscillator control with grid voltage feedforward can reduce the effect of grid distortion without requiring a dedicated harmonic compensator for each harmonic order.
I also compared the harmonic spectra under distorted-grid conditions. The input voltage THD and input current THD in the ICMV method were close to those of the input-voltage continuous control set model predictive control method alone. The output current THD was also similar, but the ICMV method removed the phase-locked loop and eliminated the need for a moving average filter in the dc bus voltage feedback path. For solar inverters, this is attractive because it reduces control complexity and avoids phase-locked-loop-related instability.
| Quantity under distorted grid | Input-current CCS-MPC | Input-voltage CCS-MPC | ICMV |
|---|---|---|---|
| Input voltage THD | About 4.08% | About 0.41% | About 0.42% |
| Input current THD | About 4.94% | About 0.39% | About 0.40% |
| Output current THD | About 3.83% | About 3.83% | About 3.84% |
| Phase-locked loop | Required with notch | Required with notch | Not required |
| Dc bus ripple filter | Moving average filter | Moving average filter | Not required |
Across my studies, I found that the automatic power decoupling principle is a strong foundation for solar inverters because it directly regulates the dc input power and lets the passive components buffer the ripple. Continuous control set model predictive control makes this principle more effective by providing a fixed switching frequency, fast transient response, and good robustness to inductance variation. Input-voltage continuous control set model predictive control further simplifies the front-end control by removing the cascaded voltage outer loop. Virtual oscillator control then simplifies the rear-end control by removing the phase-locked loop and reducing sensitivity to dc bus voltage ripple.
In my view, the main contributions of my work can be summarized as follows. I proposed an input-current continuous control set model predictive control method for a single-phase solar inverter with boost and power-decoupling capabilities. I showed that it improves steady-state decoupling, dynamic response, parameter-drift robustness, and distorted-grid adaptability compared with open-loop decoupling and automatic-power-decoupling PI control. I then proposed an input-voltage continuous control set model predictive control method with a single control loop, which avoids the outer PI voltage loop and further improves decoupling performance. Finally, I proposed a combined input-voltage continuous control set model predictive control and virtual oscillator control method, which reduces the impact of dc bus voltage ripple on the ac output current and avoids the phase-locked loop.
For practical solar inverters, I believe the following design guidelines follow from my results:
| Design aspect | Guideline from my study |
|---|---|
| Decoupling capacitor | Allow a large voltage swing to reduce capacitance and avoid electrolytic capacitors. |
| Dc bus capacitor | Use it for high-frequency filtering and partial ripple buffering, but do not rely on it alone. |
| Decoupling inductor | Design for acceptable current ripple and saturation margin, considering dc bias. |
| Front-end control | Prefer single-loop input-voltage predictive control for faster response and simpler structure. |
| Rear-end control | Prefer virtual oscillator control to avoid phase-locked loop and reduce ripple sensitivity. |
| Grid distortion | Use grid voltage feedforward and virtual oscillator synchronization instead of many harmonic resonators. |
| Parameter drift | Continuous control set model predictive control remains robust for moderate inductance reduction. |
I also noted several limitations that should be addressed in future work. First, the common-mode current and its suppression were not the main focus of my study. For solar inverters without transformers, common-mode voltage and leakage current are important safety and electromagnetic compatibility issues. Second, I applied my control methods to one boost and power-decoupling topology, but the principles may be extended to other active power decoupling topologies. Third, the front-end decoupling control and the rear-end inverter control were still designed somewhat independently. A unified control algorithm that coordinates both stages could further improve stability and transient performance.
I can express the general power balance condition that my control methods aim to satisfy as
$$p_{in}=P_{dc}=\frac{1}{2}V_oI_o,$$
$$p_{ripple}=p_o-P_{dc}.$$
For a distorted grid, the ripple power is not limited to the second order. I represent it as
$$p_{ripple}=P_2\cos(2\omega t+\theta_2)+P_4\cos(4\omega t+\theta_4)+P_6\cos(6\omega t+\theta_6)+\cdots.$$
My automatic power decoupling approach does not require me to calculate each \(P_h\) and \(\theta_h\) explicitly. Instead, I keep the dc input power constant, and the passive network absorbs the ripple components automatically. This is why the method is robust when the grid voltage contains harmonics and when the photovoltaic input power varies over a wide range.
For the front-end decoupling inductor design, I used the current ripple constraint
$$\Delta i_{Ld,max}=\frac{v_{dc}v_{Cd}}{4L_df_s(v_{dc}+v_{Cd})}.$$
For the output filter inductor of the solar inverter, I used the voltage-drop and ripple constraints
$$L_f \leq \frac{0.05V_o}{\omega I_o},$$
$$L_f \geq \frac{V_{rms}}{8f_s(0.3I_{o,rms})}.$$
These equations helped me choose practical passive components while keeping the switching frequency fixed and the output current ripple acceptable.
In my experimental comparisons, I also observed that the proposed methods maintain better performance when the input voltage reference is far from the nominal operating point. The automatic-power-decoupling PI method showed larger input current ripple when the input voltage reference changed from 182.5 V to 210 V under a distorted grid. In contrast, both continuous control set model predictive control methods kept the ripple low. The input-voltage method with virtual oscillator control gave the smoothest output current transition and did not require a moving average filter or a phase-locked loop.
I summarize the control evolution in my work as follows:
| Stage | Front-end method | Rear-end method | Main improvement |
|---|---|---|---|
| Baseline | Open-loop power decoupling | Conventional voltage-current control | Simple but sensitive to parameters and grid distortion |
| Improved baseline | Automatic-power-decoupling PI | Conventional voltage-current control with moving average filter and PLL notch | Better distorted-grid decoupling but slow dynamics |
| My first proposed method | Input-current CCS-MPC | Conventional control with moving average filter, PLL notch, and feedforward | Fixed switching frequency, faster dynamics, stronger parameter robustness |
| My second proposed method | Input-voltage CCS-MPC | Conventional control with moving average filter, PLL notch, and feedforward | Single-loop front-end control, better decoupling and faster dynamics |
| My third proposed method | Input-voltage CCS-MPC | Virtual oscillator control with grid feedforward | No PLL, no dc ripple filter, simpler rear-end control, good distorted-grid behavior |
From my perspective, the most important conclusion is that active power decoupling for solar inverters should not be treated only as a topology problem. The control algorithm determines whether the passive components are used effectively, whether the photovoltaic source sees a clean dc current, and whether the ac output current remains acceptable under grid distortion. By combining continuous control set model predictive control with automatic power decoupling, I obtained a fixed switching frequency, fast transient response, and strong robustness. By adding virtual oscillator control, I removed the phase-locked loop and reduced the influence of dc bus voltage ripple on the ac current.
I also want to emphasize that the proposed methods are not limited to ideal grid conditions. In my simulations and hardware-in-the-loop tests, I injected third, fifth, and seventh harmonics into the grid voltage. The input-voltage continuous control set model predictive control method kept the input voltage ripple near 1.3% and the input current ripple very small. The combined ICMV method kept the output current THD near 3.84%, which is within typical grid-code limits. This is achieved without designing individual resonant controllers for each harmonic, which makes the method attractive for practical solar inverters.
In terms of computational burden, the continuous control set model predictive control method requires a prediction model and a modulator, but it avoids a large search over switching states. The virtual oscillator control method uses a time-domain oscillator and a small-signal-stable feedback law, and it does not require a phase-locked loop. For a digital signal processor, these features are beneficial because they reduce the number of control blocks and avoid the tuning of many resonant controllers.
I conclude my study with the following statements. First, the second-order ripple problem in single-phase solar inverters is unavoidable, but it can be managed efficiently with active power decoupling. Second, automatic power decoupling is a robust principle because it regulates the dc input power rather than trying to cancel every ripple harmonic explicitly. Third, continuous control set model predictive control is well suited to the front-end decoupling circuit because it provides a fixed switching frequency and fast dynamic response. Fourth, input-voltage continuous control set model predictive control is superior to input-current continuous control set model predictive control in my tests because it removes the cascaded voltage outer loop. Fifth, virtual oscillator control is a promising rear-end control method for solar inverters with active power decoupling because it avoids the phase-locked loop and reduces the effect of dc bus voltage ripple.
For future work, I plan to investigate common-mode current suppression in transformerless solar inverters, extend the proposed control methods to other active power decoupling topologies, and develop a unified control framework that coordinates the front-end decoupling circuit and the rear-end inverter. I also plan to study the interaction between multiple solar inverters connected to a weak grid, because the virtual oscillator control method may provide advantages in that scenario. Finally, I intend to explore online parameter estimation to further improve robustness when the decoupling inductance and capacitance drift over the lifetime of a solar inverter.
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