In the context of global carbon reduction goals, renewable energy sources such as photovoltaic and wind power have garnered significant attention. Due to their relatively small scale, wide distribution, and large numbers, these are termed distributed generation (DG) units. To manage the diversity and dispersion of DG, microgrids—integrated systems comprising DG, loads, energy storage devices, and converters—have emerged as a viable solution. Solar inverters play a crucial role in these systems, converting DC power from photovoltaic arrays into AC power for grid connection or local consumption. However, traditional control strategies for solar inverters often rely on communication links, which reduce system reliability and hinder scalability. Moreover, in islanded mode, maximum power point tracking (MPPT) algorithms can lead to overvoltage and overcharging issues. To address these challenges, this paper proposes a novel droop control method for single-phase solar inverters that inherently achieves MPPT functionality without complex algorithms, while retaining the advantages of communication-free operation and plug-and-play capability.
The core innovation lies in reformulating the traditional droop control equations by incorporating the derivative of the photovoltaic array’s P-V characteristic curve, denoted as \( \frac{dp_{pv}}{dv_{pv}} \). This approach enables direct adjustment of the photovoltaic array output voltage by controlling the inverter’s output power, thereby facilitating maximum power point tracking. In grid-connected mode, the method ensures efficient MPPT; in islanded mode, it allows adaptive power sharing among multiple solar inverters based on load demand, provided the load capacity does not exceed the system’s rating. The proposed strategy eliminates the need for dedicated MPPT controllers, enhances reliability, and supports seamless transition between operational modes. Throughout this discussion, the term “solar inverters” will be emphasized to underscore their pivotal role in modern energy systems.
Photovoltaic arrays exhibit non-linear power-voltage (P-V) characteristics that vary with irradiation and temperature. A typical P-V curve for a commercial solar panel (e.g., 1Soltech-1STH-215-P) under standard test conditions (1000 W/m², 25°C) can be modeled mathematically. The output current \( i_{pv} \) and voltage \( v_{pv} \) of a photovoltaic array are related as follows:
$$ i_{pv} = N_p I_{sc} \left[1 – \exp\left(\frac{v_{pv}}{N_s a V_t} – \frac{V_{oc}}{a V_t}\right)\right] $$
where \( N_p \) and \( N_s \) represent the number of parallel and series-connected cells, respectively; \( I_{sc} \) is the short-circuit current; \( V_{oc} \) is the open-circuit voltage; \( a \) is the diode ideality factor; and \( V_t = \frac{NkT}{q} \) is the thermal voltage, with \( k \) as Boltzmann’s constant, \( q \) as the electron charge, and \( T \) as the temperature. The power output is \( p_{pv} = v_{pv} \cdot i_{pv} \). The P-V curve always features a unique maximum power point (MPP), where the derivative \( \frac{dp_{pv}}{dv_{pv}} = 0 \). To the left of the MPP, \( \frac{dp_{pv}}{dv_{pv}} > 0 \), and to the right, \( \frac{dp_{pv}}{dv_{pv}} < 0 \). For stability and enhanced load-bearing capacity, solar inverters should operate on the right side of the MPP, where power output increases as voltage decreases.
The proposed droop control method, termed \( f-\frac{dp_{pv}}{dv_{pv}} \) droop control, integrates this derivative into the frequency regulation loop. The control equations are:
$$ f = f^* – m \frac{dp_{pv}}{dv_{pv}} $$
$$ U = U^* – n Q $$
where \( f^* \) is the rated grid frequency, \( f \) is the inverter output reference frequency, \( U^* \) is the no-load voltage amplitude, \( U \) is the reference voltage amplitude, \( m \) is the active power droop coefficient, \( n \) is the reactive power droop coefficient, and \( Q \) is the inverter output reactive power. The derivative \( \frac{dp_{pv}}{dv_{pv}} \) is computed in real-time using a first-order low-pass filter to process \( i_{pv} \) and \( v_{pv} \). The filter’s transfer function is \( F(s) = \frac{1}{Ts + 1} \), with a cutoff frequency set to 1000 Hz. The filtered currents and voltages, \( i_f \) and \( v_f \), are derived as:
$$ i_f(s) = \frac{1}{Ts + 1} \cdot i_{pv}(s) $$
$$ v_f(s) = \frac{1}{Ts + 1} \cdot v_{pv}(s) $$
In the time domain, the derivatives are approximated as:
$$ \frac{di_f}{dt} = \frac{i_{pv} – i_f}{T}, \quad \frac{dv_f}{dt} = \frac{v_{pv} – v_f}{T} $$
Thus, \( \frac{di_{pv}}{dv_{pv}} \approx \frac{i_{pv} – i_f}{v_{pv} – v_f} \), leading to:
$$ \frac{dp_{pv}}{dv_{pv}} = i_{pv} + v_{pv} \frac{i_{pv} – i_f}{v_{pv} – v_f} $$
This calculation is implemented as shown in the following block diagram, which is integrated into the control loop of the solar inverters.
The control principle operates in two modes. In grid-connected mode, the solar inverters adjust their output frequency based on \( \frac{dp_{pv}}{dv_{pv}} \). If \( \frac{dp_{pv}}{dv_{pv}} > 0 \), the frequency decreases, reducing inverter output power and allowing the photovoltaic array voltage to rise, shifting the operating point toward the MPP. Conversely, if \( \frac{dp_{pv}}{dv_{pv}} < 0 \), the frequency increases, boosting output power and lowering the voltage, again moving toward the MPP. At steady state, \( \frac{dp_{pv}}{dv_{pv}} = 0 \), and all solar inverters synchronize to the grid frequency \( f^* \), with \( p_{pv} \approx P_{\text{max}} \). In islanded mode, the solar inverters operate autonomously. When load demand is below the total capacity, the system stabilizes at a point where \( \frac{dp_{pv}}{dv_{pv}} < 0 \), ensuring robust load sharing. If multiple solar inverters have similar P-V characteristics, they achieve proportional power sharing without communication, as their frequencies synchronize to a common value \( f \neq f^* \). This inherent adaptability makes the method ideal for decentralized microgrids with multiple solar inverters.
To validate the proposed method, a simulation model was built in MATLAB/Simulink with two parallel solar inverters, reflecting real-world conditions from a large-scale grid-connected photovoltaic plant in Jiangsu, China. The environmental parameters were set to a constant temperature of 13.5°C and irradiance varying between 412 W/m² and 796 W/m². The photovoltaic array consisted of 11 series-connected cells based on the 1Soltech-1STH-215-P model. Key system parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Rated Voltage Amplitude \( U^* \) | 311 V |
| Rated Frequency \( f^* \) | 50 Hz |
| Filter Inductance \( L_f \) | 3 mH |
| Filter Capacitance \( C_f \) | 40 μF |
| DC-link Capacitance \( C_{DC} \) | 2000 μF |
| Active Droop Coefficient \( m \) | \( 2 \times 10^{-5} \) |
| Reactive Droop Coefficient \( n \) | \( 5 \times 10^{-3} \) |
The photovoltaic cell parameters under standard test conditions are listed in Table 2.
| Parameter | Value |
|---|---|
| Maximum Power \( P_{\text{max}} \) | 213.15 W |
| Open-Circuit Voltage \( V_{oc} \) | 36.3 V |
| Short-Circuit Current \( I_{sc} \) | 7.84 A |
| Voltage at MPP \( V_{mp} \) | 29 V |
| Current at MPP \( I_{mp} \) | 7.35 A |
For the array of 11 series cells, the maximum power outputs at irradiances of 796 W/m², 604 W/m², and 412 W/m² (at 13.5°C) were approximately 1880 W, 1434 W, and 977 W, respectively, as derived from the P-V curves. The simulation tested both grid-connected and islanded modes. In grid-connected mode, irradiance was varied as a disturbance: initially constant at 796 W/m² for both solar inverters from 0 to 0.4 s, then slowly decreased to 604 W/m² and 412 W/m² for inverters 1 and 2, respectively, from 0.4 to 0.5 s, and held constant thereafter. The results demonstrated excellent MPPT performance, with power outputs matching the theoretical maxima and steady-state fluctuations within ±0.5%. Frequency regulation was precise, with deviations within ±0.03 Hz, showcasing the stability of the solar inverters under dynamic conditions.
In islanded mode, the load was initially set to 3200 W, with irradiances of 796 W/m² and 604 W/m² for the two solar inverters. At 0.4 s, the load suddenly dropped to 2400 W, and from 0.8 to 0.9 s, the irradiance for inverter 2 increased from 604 W/m² to 796 W/m². The solar inverters adapted seamlessly: before 0.4 s, output powers were 1850 W and 1400 W, summing to near the load demand; after load reduction, they settled at 1450 W and 950 W, respectively; and after irradiance equalization, both converged to approximately 1200 W, achieving perfect power sharing. This confirms that the proposed droop control enables solar inverters to autonomously adjust output based on load and environmental changes, without communication.
To further highlight the advantages, Table 3 compares the proposed method with other MPPT techniques from literature, focusing on key metrics such as MPPT efficiency, grid support functions, mode transition capability, communication requirements, and computational load. The comparison underscores the superiority of the \( f-\frac{dp_{pv}}{dv_{pv}} \) droop control for solar inverters in modern microgrid applications.
| Method | MPPT Efficiency | Voltage/Frequency Support | Seamless Grid-Island Transition | Communication Required | Computational Load |
|---|---|---|---|---|---|
| Proposed \( f-\frac{dp_{pv}}{dv_{pv}} \) Droop | Excellent (98.93%) | Yes | Yes | No | Low |
| Constant Voltage + Incremental Conductance (CV+IC) | Good | No | No (grid-only) | Yes | Moderate |
| Hybrid Particle Swarm Optimization (HPSO) | Excellent | No | No (grid-only) | No | High |
| Improved Variable Step Perturb & Observe (IVSPO) | Good | No | No (grid-only) | No | Moderate |
| Neural Network Improved Perturb & Observe (NNIPO) | Good | No | No (grid-only) | No | High |
The mathematical foundation of the control method can be extended to analyze stability. Consider small-signal models of the solar inverter system. The power output of a photovoltaic array near the MPP can be linearized as \( \Delta p_{pv} = \left. \frac{dp_{pv}}{dv_{pv}} \right|_{\text{op}} \Delta v_{pv} \), where the operating point derivative influences dynamics. Combining this with the inverter’s power balance equation \( p_{pv} = p_{ac} + C_{DC} v_{pv} \frac{dv_{pv}}{dt} \), where \( p_{ac} \) is the AC output power, and applying the droop law \( \Delta f = -m \Delta \left( \frac{dp_{pv}}{dv_{pv}} \right) \), we derive a transfer function for closed-loop response. For stability, the droop coefficient \( m \) must be chosen such that the system poles lie in the left-half plane. A detailed eigenvalue analysis confirms that for typical solar inverter parameters, the system remains stable under wide variations in irradiance and load.
Moreover, the reactive power control loop in solar inverters follows the standard \( U-Q \) droop, which ensures voltage regulation and VAR sharing. Since the focus is on active power and MPPT, the reactive loop operates independently, but interactions are minimal due to decoupling in single-phase systems via orthogonal signal generation. The overall control structure for a single-phase solar inverter includes a power calculation block, the \( \frac{dp_{pv}}{dv_{pv}} \) estimator, and droop controllers feeding a voltage source inverter with PWM modulation. This design is scalable to multiple units, as each solar inverter relies only on local measurements, promoting redundancy and fault tolerance.
Practical implementation considerations for solar inverters include sensor accuracy, filter time constants, and anti-islanding protection. The derivative computation requires precise current and voltage sensing, but modern sensors with high resolution suffice. The low-pass filter cutoff must be high enough to track irradiance changes (typically below 10 Hz) but low enough to reject switching noise. For anti-islanding, the droop control inherently shifts frequency in islanded mode, which can be detected by standard relays. Additionally, the method complements energy storage systems; when storage is present, the solar inverters can operate in MPPT mode continuously, with storage absorbing excess power. However, the proposed method reduces storage needs by enabling power curtailment via droop action, lowering system costs.
Future work could explore three-phase extensions, integration with battery management systems, and hardware-in-the-loop testing. The \( f-\frac{dp_{pv}}{dv_{pv}} \) droop principle can also apply to other renewable sources with non-linear characteristics, such as fuel cells. For solar inverters specifically, advancements in wide-bandgap semiconductors could enhance efficiency when switching at higher frequencies dictated by the control algorithm.
In conclusion, this paper presents a novel droop control method for single-phase solar inverters that integrates MPPT functionality directly into the frequency regulation loop. By utilizing the derivative of the photovoltaic array’s P-V curve, the method enables efficient maximum power point tracking in grid-connected mode and adaptive power sharing in islanded mode, without communication links. Simulations under realistic conditions validate its effectiveness, showing high MPPT efficiency, stable frequency regulation, and seamless mode transitions. Compared to existing MPPT techniques, the proposed approach offers significant advantages in reliability, scalability, and grid support, making it well-suited for decentralized microgrids dominated by solar inverters. As the world transitions to cleaner energy, such innovative control strategies will be vital for optimizing the performance and integration of solar power systems.