The global transition towards sustainable energy systems has placed distributed photovoltaic (PV) generation at the forefront of modern power infrastructure. Solar inverters serve as the critical interface, converting the variable DC output from PV panels into grid-compliant AC power. Their performance, reliability, and cost directly impact the viability and efficiency of solar energy deployment. This article delves into the comprehensive optimization of component configuration and control strategies for two-stage single-phase grid-connected solar inverters. A primary focus is the elimination of DC voltage sensors, which are traditionally used for maximum power point tracking (MPPT) and DC-link voltage regulation, to reduce system cost and enhance immunity to electromagnetic interference (EMI) without compromising performance.
The proliferation of distributed generation, particularly in urban environments, often leads to the formation of PV-rich microgrids. These microgrids aggregate the output of numerous distributed solar inverters, mitigating the impact of individual source variability on the main grid and enhancing overall supply reliability. Within such architectures, the two-stage inverter topology—comprising a front-end DC-DC boost converter followed by a DC-AC inverter—is prevalent for low-to-medium power applications. This topology offers distinct advantages: the boost stage decouples the PV voltage from the DC-link voltage, allowing for a wider MPPT operating range and improved energy harvest under partial shading or varying irradiance conditions.
The conventional control paradigm for these solar inverters relies heavily on sensor measurements. Typically, voltage sensors are deployed to measure the PV array voltage (\(u_{pv}\)) and the DC-link voltage (\(u_{dc}\)). The PV voltage and current (\(i_{pv}\)) are used to compute instantaneous power for MPPT algorithms. Simultaneously, the DC-link voltage is measured and regulated via a Proportional-Integral (PI) controller to a fixed reference value, ensuring stable input conditions for the inverter stage. The grid current is then controlled to follow a reference derived from the measured PV power. While effective, this approach has drawbacks. The sensors and their associated signal conditioning circuits increase the bill of materials (BOM) and system complexity. More critically, they introduce potential points of failure and are susceptible to noise and EMI, which can degrade control precision and system reliability. In a microgrid with numerous distributed solar inverters, the cumulative cost and reliability concern become significant.
This article proposes a novel sensorless control strategy that removes the need for the \(u_{pv}\) and \(u_{dc}\) voltage sensors. The strategy is based on the intrinsic relationships between controller internal signals (modulation index and duty cycle) and the physical voltages in the system. By reconstructing and indirectly controlling these voltages, the proposed method maintains high-performance MPPT and high-quality grid current injection while achieving a more cost-effective and robust design for distributed solar inverters.
System Topology and Conventional Control Analysis
The standard two-stage single-phase grid-connected system for solar inverters is depicted in Figure 1 (conceptual). It consists of a PV array, an input capacitor \(C_1\), a boost converter (inductor \(L\), switch \(S_1\), diode \(D\)), a DC-link capacitor \(C_2\), and a full-bridge inverter connected to the grid via an LCL or L filter (\(L_{ac}\)).
Conventional Control Principle: The control structure is typically divided into two loops:
- MPPT & Boost Control: Measures \(u_{pv}\) and \(i_{pv}\) to compute PV power (\(P_{pv} = u_{pv} \cdot i_{pv}\)). An MPPT algorithm (e.g., Perturb and Observe) adjusts the duty cycle \(d\) of the boost converter to force the PV operating point to the maximum power point.
- DC-Link Regulation & Grid Current Control: Measures \(u_{dc}\) and regulates it to a constant reference \(U_{dc\_ref}\) using a PI controller. The output of this PI controller, often interpreted as a power or current compensation term, is used to shape the grid current reference. Assuming ideal lossless conversion and a stable DC-link voltage, the power balance in steady-state over a grid period relates PV power to grid power:
$$ P_{pv} = P_g = \frac{1}{2} \hat{U}_g \hat{I}_g $$
where \(\hat{U}_g\) and \(\hat{I}_g\) are the amplitudes of the grid voltage and current, respectively. Therefore, the grid current amplitude reference is generated as:
$$ \hat{I}_{g\_ref} = \frac{2 P_{pv}}{\hat{U}_g} = \frac{2 u_{pv} i_{pv}}{\hat{U}_g} $$
A Phase-Locked Loop (PLL) extracts the grid voltage phase \(\theta_g\) and amplitude \(\hat{U}_g\). The instantaneous grid current reference is then \(i_{g\_ref}(t) = \hat{I}_{g\_ref} \cdot \sin(\theta_g)\). A current controller (e.g., PR or PI in dq-frame) forces the actual grid current \(i_g\) to track \(i_{g\_ref}\).
The reliance on direct voltage measurements is clear in this standard approach for solar inverters.
Proposed DC Voltage Sensorless Control Strategy
The proposed strategy for solar inverters eliminates the \(u_{pv}\) and \(u_{dc}\) sensors by exploiting relationships between control signals and system voltages.
1. Relationship Between DC-Link Voltage and Modulation Index
For a sinusoidal pulse-width modulation (SPWM) controlled single-phase full-bridge inverter, the fundamental component of the output AC voltage is related to the DC-link voltage and the modulation index. The amplitude of the output voltage at the inverter terminals before the filter is \(M \cdot u_{dc}\), where \(M\) is the modulation index (ratio of the amplitude of the sinusoidal reference wave to the carrier wave amplitude). Considering the voltage drop across the filter inductance and aligning with the grid voltage, the average DC-link voltage \(U_{dc\_avg}\) over a switching period relates to the peak grid voltage \(\hat{U}_g\) approximately as:
$$ \hat{U}_g \approx M \cdot U_{dc\_avg} $$
Therefore,
$$ U_{dc\_avg} \approx \frac{\hat{U}_g}{M} $$
This is a key insight. Instead of measuring \(u_{dc}\) and controlling it to a fixed voltage reference \(U_{dc\_ref}\), we can control the modulation index \(M\) to an equivalent reference \(M_{ref} = \frac{\hat{U}_g}{U_{dc\_ref}}\). The amplitude \(M\) of the SPWM modulating signal is inherently available within the inverter’s digital controller. By regulating \(M\) to \(M_{ref}\), the DC-link voltage is indirectly regulated to the desired value. This removes the need for the DC-link voltage sensor in solar inverters.
2. Relationship Between PV Voltage, DC-Link Voltage, and Boost Duty Cycle
For a continuous conduction mode (CCM) boost converter, the ideal steady-state relationship between input and output voltage is:
$$ U_{pv} = (1 – D) \cdot U_{dc\_avg} $$
where \(D\) is the steady-state duty cycle. Combining this with the previous equation, we get:
$$ U_{pv} = (1 – D) \cdot \frac{\hat{U}_g}{M} $$
This equation shows that the PV voltage can be estimated using the known/grid-measured \(\hat{U}_g\), the controlled modulation index \(M\), and the duty cycle \(D\) commanded to the boost converter. The duty cycle \(D\) is a direct output of the boost converter’s controller and is readily available without any additional sensor. Therefore, the PV voltage sensor in the solar inverter can also be eliminated.
3. Control Strategy Implementation
The complete sensorless control structure for the solar inverter is shown in the block diagram below and can be summarized in the following table:
| Control Objective | Traditional Method | Proposed Sensorless Method |
|---|---|---|
| DC-Link Voltage Control | Measure \(u_{dc}\), compare with \(U_{dc\_ref}\), use PI controller. | Use modulation index \(M\). Regulate \(M\) to \(M_{ref} = \hat{U}_g / U_{dc\_ref}\). No direct measurement. |
| PV Voltage for MPPT | Directly measure \(u_{pv}\). | Estimate \(U_{pv} = (1-D) \cdot \hat{U}_g / M\). Use only \(i_{pv}\) sensor and controller signals \(D, M\). |
| Grid Current Reference Generation | \(\hat{I}_{g\_ref} = 2 u_{pv} i_{pv} / \hat{U}_g\) | Substitute estimated \(U_{pv}\): \(\hat{I}_{g\_ref} = \frac{2 (1-D) i_{pv}}{M}\) |
The implementation steps are as follows:
- Grid Synchronization: A standard PLL measures grid voltage \(u_g(t)\) to obtain \(\hat{U}_g\) and \(\theta_g\).
- DC-Link Voltage Indirect Control: The error between the reference modulation index \(M_{ref}\) and the actual \(M\) (easily obtained from the normalized modulating signal) is processed through a PI controller. The output of this PI controller generates a compensating current amplitude \(\hat{I}_{gb}\). This compensates for system losses and any power imbalance, ensuring precise regulation of the equivalent DC-link voltage.
- Grid Current Reference Calculation: The primary grid current amplitude reference is calculated using the sensorless formula: \(\hat{I}_{g\_ref}’ = 2 (1-D) i_{pv} / M\). The total reference amplitude is then \(\hat{I}_{g\_ref} = \hat{I}_{g\_ref}’ + \hat{I}_{gb}\). The instantaneous reference is \(i_{g\_ref}(t) = \hat{I}_{g\_ref} \cdot \sin(\theta_g)\).
- Current Control: A current controller (e.g., Proportional-Resonant) generates the SPWM modulating signal to force \(i_g\) to track \(i_{g\_ref}(t)\). The amplitude \(M\) of this modulating signal is fed back for the indirect DC-link control loop.
4. MPPT Algorithm Using Only PV Current
With the PV voltage estimated as \(U_{pv\_est} = (1-D) \cdot \hat{U}_g / M\), the PV power can be estimated as \(P_{pv\_est} = U_{pv\_est} \cdot i_{pv} = \frac{(1-D) \cdot \hat{U}_g \cdot i_{pv}}{M}\). However, for the Perturb & Observe (P&O) MPPT algorithm, only the trend of power change relative to current change is needed. Observing the relationship \(\hat{I}_{g\_ref}’ \propto P_{pv\_est}\), we can use \(\hat{I}_{g\_ref}’\) as a proxy for PV power. The MPPT logic can be performed by perturbing the boost converter’s duty cycle \(D\) and observing the resulting change in \(\hat{I}_{g\_ref}’\) and \(i_{pv}\).
The algorithm can be described as follows:
- If an increase in \(D\) causes \(\hat{I}_{g\_ref}’\) to increase, the operating point is on the left side of the MPP (positive dP/dI slope).
- If an increase in \(D\) causes \(\hat{I}_{g\_ref}’\) to decrease, the operating point is on the right side of the MPP (negative dP/dI slope).
The duty cycle is adjusted accordingly to climb the power curve. This allows effective MPPT using only the \(i_{pv}\) current sensor, completing the sensorless scheme for the solar inverter’s DC side.
Simulation Verification and Results Analysis
The proposed sensorless control strategy for solar inverters was modeled and simulated in MATLAB/Simulink to validate its performance. The system parameters are listed in the table below:
| Parameter | Symbol | Value |
|---|---|---|
| PV Array Maximum Power | \(P_{mpp}\) | 1.2 kW |
| DC-Link Voltage Reference | \(U_{dc\_ref}\) | 400 V |
| Grid Voltage (RMS) | \(U_g\) | 220 V |
| Grid Frequency | \(f_g\) | 50 Hz |
| Boost Inductor | \(L\) | 1 mH |
| Input Capacitor | \(C_1\) | 220 µF |
| DC-Link Capacitor | \(C_2\) | 220 µF |
| Grid-Side Inductor | \(L_{ac}\) | 20 mH |
| Switching Frequency | \(f_{sw}\) | 20 kHz |
MPPT Performance: The simulation started with the PV array under standard test conditions. The proposed current-sensor-only MPPT algorithm successfully tracked the maximum power point. Figure 2 shows the PV power converging rapidly to the rated 1.2 kW, demonstrating that the MPPT functionality is fully preserved in the sensorless solar inverter.
Grid Connection Performance: After the MPPT stabilized, the inverter was connected to the grid. Figure 3 shows the waveforms of the grid voltage (\(u_g\)) and the injected grid current (\(i_g\)). The current is sinusoidal and perfectly in phase with the grid voltage (unity power factor). The Total Harmonic Distortion (THD) of the grid current was analyzed to be below 3%, meeting standard grid codes such as IEEE 1547, proving that the power quality is not degraded by the removal of voltage sensors in the solar inverter.
DC-Link Voltage Behavior: Figure 4 shows the waveform of the DC-link voltage (\(u_{dc}\)). As expected in a single-phase system, it contains a second-harmonic (100 Hz) ripple due to the pulsating instantaneous power flow. However, its average value is maintained stable at the intended level corresponding to \(M_{ref}\). The indirect control loop successfully regulates this average voltage without direct measurement, confirming the core principle of the proposed strategy for solar inverters.
Comparative Analysis: The table below summarizes a qualitative comparison between the conventional and proposed solar inverter designs.
| Aspect | Conventional Solar Inverter | Proposed Sensorless Solar Inverter |
|---|---|---|
| Required Voltage Sensors | PV Voltage (\(u_{pv}\)), DC-Link Voltage (\(u_{dc}\)) | None on DC side |
| Required Current Sensors | PV Current (\(i_{pv}\)), Grid Current (\(i_g\)) | PV Current (\(i_{pv}\)), Grid Current (\(i_g\)) |
| MPPT Accuracy | High (direct measurement) | High (indirect estimation/current-based algorithm) |
| Grid Current THD | Low (dependent on control) | Low (identical current control loop) |
| Cost | Higher (more sensors, isolation, circuits) | Lower (reduced component count) |
| Reliability / EMI Robustness | Potentially lower due to more signal paths | Higher due to fewer vulnerable measurement nodes |
| Control Complexity | Standard | Slightly increased software complexity, no extra hardware. |
Conclusion and Future Directions
This article has presented a comprehensive optimization approach for distributed solar inverters, with a focal point on a novel DC voltage sensorless control strategy. By leveraging the fundamental relationships between the modulation index, boost converter duty cycle, and system voltages, the proposed method successfully eliminates all DC voltage sensors traditionally required for MPPT and DC-link regulation in two-stage single-phase solar inverters. The strategy reconstructs the necessary voltage information from readily available controller signals, thereby reducing hardware cost, simplifying system assembly, and enhancing overall robustness against electromagnetic interference.
Simulation results confirm that the sensorless solar inverter maintains excellent performance: accurate and fast maximum power point tracking, high-quality sinusoidal grid current injection with low THD, and stable regulation of the DC-link voltage’s average value. These attributes are achieved without sacrificing the core functionalities expected from modern grid-tied solar inverters.
The optimization contributes significantly to making distributed PV systems more economical and reliable, which is crucial for their widespread adoption in microgrids and utility networks. Future research directions could include:
- Extending the sensorless concept to three-phase solar inverter topologies or inverters with more complex filtering requirements.
- Developing advanced MPPT algorithms explicitly designed for the single-current-sensor paradigm to improve dynamic response under rapidly changing irradiance.
- Investigating the integration of this sensorless solar inverter with energy storage systems within a microgrid framework, focusing on coordinated power management without additional voltage sensing.
- Practical implementation and long-term field testing to validate reliability under real-world noise and disturbance conditions.
The pursuit of such intelligent, cost-optimized designs is essential for driving the next generation of efficient and resilient solar energy conversion systems.