In regions with abundant renewable energy resources, such as deserts and Gobi areas, the integration of large-scale photovoltaic (PV) systems is crucial for achieving carbon neutrality goals. However, these areas often lack conventional power sources like hydro or thermal plants, leading to weak grid conditions. As the penetration of renewable energy increases, grid strength diminishes, necessitating active support from grid-connected equipment. Grid-forming (GFM) solar inverters are promising solutions due to their ability to provide voltage and frequency support, mimicking synchronous generators. However, GFM solar inverters face challenges in delivering stable power support during grid frequency and voltage disturbances due to irradiation fluctuations. While energy storage systems can mitigate these issues, they involve high hardware costs. Therefore, power reserve-based GFM solar inverters have gained attention.
Power reserve control in solar inverters involves预留部分有功出力 to respond to grid disturbances. However, accurate power reservation is difficult under resource fluctuations, and imbalances between AC and DC power during irradiation and grid disturbances can cause DC transient overvoltage or undervoltage. This paper addresses these challenges by proposing a precise active power reserve control method for GFM solar inverters without additional sensors. We analyze the behavior model of PV arrays, estimate maximum power without extra irradiation or temperature sensors, and introduce a dual-loop, dual-update cycle method for online correction of the reserve power coefficient. Additionally, a DC voltage stabilization switching strategy is developed for extreme conditions. The proposed method ensures accurate online power reservation under irradiation and temperature variations, enabling solar inverters to provide active support and maintain DC voltage stability under dual disturbances. Validation is performed using an RT-LAB hardware-in-the-loop platform.
The main circuit topology of a grid-forming solar inverter without energy storage is shown in the figure below. It consists of a PV array connected to a DC-link capacitor, followed by a three-phase inverter with output filters. The inverter interfaces with the grid through inductors. The switching signals are generated via space vector modulation.
Grid-forming solar inverters employ control strategies that emulate synchronous generator characteristics. The active power control loop provides inertia and primary frequency response, while the reactive power control loop offers voltage support. The active power loop equation is:
$$ J \omega_n \frac{d\omega}{dt} = P_{\text{ref}} – P_e – D_p \omega_n (\omega – \omega_g) – K_d (\omega – \omega_g) $$
where \( J \) is the virtual inertia, \( \omega_n \) is the rated angular velocity, \( \omega_g \) is the grid angular velocity, \( P_{\text{ref}} \) is the active power reference, \( P_e \) is the output active power, \( D_p \) is the frequency-active power droop coefficient, and \( K_d \) is the damping coefficient. In maximum power point tracking (MPPT) mode, the solar inverter uses fixed DC voltage control, and the power reference is given by:
$$ P_{\text{ref}} = (U_{\text{dc}} – U_{\text{dcref}}) G_{\text{dc}}(s) $$
where \( U_{\text{dc}} \) is the DC voltage, \( U_{\text{dcref}} \) is the reference from the MPPT algorithm, and \( G_{\text{dc}}(s) \) is the DC voltage regulator. The reactive power control loop implements voltage-reactive power droop:
$$ E_m = \frac{1}{K_{iq} s} \left[ D_q (U_n – U_m) + (Q_{\text{ref}} – Q_e) \right] $$
where \( U_n \) is the nominal voltage, \( U_m \) is the measured voltage, \( Q_{\text{ref}} \) is the reactive power reference, \( Q_e \) is the output reactive power, \( D_q \) is the droop coefficient, and \( K_{iq} \) is the integral gain. The output of these loops generates the internal voltage reference for the inverter.
In active power reserve mode, the solar inverter operates with a reduced power output to preserve a reserve capacity for frequency response. The power reference is set as:
$$ P_{\text{ref}} = (1 – m) P_{\text{max0}} $$
where \( m \) is the reserve coefficient (0 ≤ m ≤ 1), and \( P_{\text{max0}} \) is the initial maximum power from MPPT. The reserve capacity is \( P_{\text{reserve}} = m P_{\text{max0}} \). During reserve operation, the MPPT algorithm is paused, and the power reference remains fixed. However, if irradiation or temperature changes, the actual maximum power shifts, leading to inaccuracies in reserve power. This can cause DC voltage instability during grid disturbances.
To estimate the maximum power of PV arrays without additional sensors, we utilize the behavioral model of solar cells. The output current of a PV array is expressed as:
$$ I_{\text{pv}} = n_0 \left[ k_1 – k_2 \left( \exp\left( \frac{k_3 U_{\text{pv}}}{k_4} \right) – 1 \right) \right] $$
where \( n_0 \) is the number of parallel cells, \( U_{\text{pv}} \) is the array voltage, and \( k_1 \) to \( k_6 \) are parameters dependent on irradiation \( S_{\text{Lx}} \) and temperature \( T_m \). The output power is \( P_{\text{pv}} = U_{\text{pv}} I_{\text{pv}} \). The parameters are calculated as follows:
| Parameter | Expression |
|---|---|
| \( k_1 \) | \( \frac{U_{\text{pv}}}{m_0} \) |
| \( k_2 \) | \( \left(1 – \frac{I_m}{I_{\text{sc}}}\right) \exp\left( \frac{U_m}{U_{\text{oc}} – U_m} \ln\left(1 – \frac{I_m}{I_{\text{sc}}}\right) \right) \) |
| \( k_3 \) | \( I_{\text{sc}} \) |
| \( k_4 \) | \( I_{\text{sc}} \left( \frac{S_{\text{Lx}}}{1000} – 1 \right) + a (T_m – 25) \) |
| \( k_5 \) | \( \frac{U_{\text{oc}} – U_m}{\ln\left(1 – \frac{I_m}{I_{\text{sc}}}\right)} \) |
| \( k_6 \) | \( b (T_m – 25) – R_s k_4 \) |
Here, \( I_{\text{sc}} \), \( I_m \), \( U_{\text{oc}} \), and \( U_m \) are short-circuit current, maximum power current, open-circuit voltage, and maximum power voltage per cell, respectively; \( a \) and \( b \) are correction coefficients; \( R_s \) is series resistance; and \( m_0 \) is the number of series cells. The maximum power point \( P_{\text{max}} \) is found by solving \( \partial P_{\text{pv}} / \partial U_{\text{pv}} = 0 \), which involves transcendental equations. To avoid iterative solutions, we precompute numerical relationships between \( P_{\text{pv}} \), \( U_{\text{pv}} \), and \( S_{\text{Lx}} \) for different temperatures, stored in lookup tables. Using measured \( P_{\text{pv}} \) and \( U_{\text{pv}} \), and temperature data from the station controller, we estimate \( S_{\text{Lx}} \) and then \( P_{\text{max}} \). This approach eliminates the need for local irradiation sensors and reduces computational burden.
Based on the time-scale differences between irradiation (seconds) and temperature (minutes) variations, we propose a dual-loop, dual-update cycle method for online correction of the reserve coefficient. The table update loop refreshes lookup tables periodically (e.g., every minute) using temperature data from the station. The reserve coefficient correction loop updates \( m \) frequently (e.g., every 0.1 seconds) based on real-time irradiation estimates. The steps are:
- Update lookup table 1 ( \( P_{\text{pv}} \)-\( U_{\text{pv}} \)-\( S_{\text{Lx}} \) ) and table 2 ( \( P_{\text{max}} \)-\( S_{\text{Lx}} \) ) using temperature \( T_m \).
- For correction: measure \( U_{\text{dc}} \) and \( P_{\text{pv}} \), find the closest values in table 1 to estimate \( S_{\text{Lx}} \).
- Use \( S_{\text{Lx}} \) in table 2 to get \( P_{\text{max}} \).
- Calculate the reserve coefficient: \( m = 1 – \frac{P_{\text{backup}} + D_p \Delta \omega_{g,\text{max}}}{P_{\text{max}}} \), where \( P_{\text{backup}} \) is the required reserve capacity, and \( \Delta \omega_{g,\text{max}} \) is the maximum frequency deviation.
The accuracy of this method is quantified by the reserve capacity deviation rate \( \sigma_{\text{err}} \):
$$ \sigma_{\text{err}} = \frac{\max | P_{\text{real}} – P_{\text{cmd}} |}{P_{\text{cmd}}} \times 100\% $$
In tests, traditional methods show \( \sigma_{\text{err}} = 125\% \), while the proposed method reduces it to 5%, demonstrating precise power reservation.
For extreme conditions with insufficient solar resources, we implement a DC voltage stabilization switching strategy. If \( P_{\text{max}} < P_{\text{backup}} \), the solar inverter switches to DC voltage control mode to maintain stability. The DC voltage reference \( U_{\text{st}} \) is set near the open-circuit voltage \( U_{\text{oc}} \), and the power output is minimized. Hysteresis comparison prevents frequent switching. The control mode switching logic is:
- MPPT mode: \( S_1 = 0 \), power reference from MPPT.
- Active power reserve mode: \( S_1 = 2 \), and if \( P_{\text{max}} \geq P_{\text{backup}} \), \( S_2 = 1 \) (precise reserve); else, \( S_2 = -1 \) (DC voltage control).
The proposed control strategy is validated through RT-LAB hardware-in-the-loop experiments. The platform includes an OP5707 simulator and a solar inverter controller. Parameters are listed below:
| Parameter | Value |
|---|---|
| Rated Power | 500 kW |
| DC Voltage Reference | 700 V |
| AC Voltage (line-to-line) | 270 V |
| Filter Inductance \( L_f \) | 150 μH |
| Filter Capacitance \( C_f \) | 100 μF |
| Droop Coefficient \( D_p \) | 32,000 |
| Virtual Inertia \( J \) | 0.138 |
Experiments under varying irradiation and temperature show that the solar inverter maintains DC voltage stability and provides accurate frequency response. For instance, when irradiation drops from 1000 W/m² to 800 W/m², the reserve coefficient \( m \) adjusts from 0.21 to 0.42, and the output power decreases accordingly. During grid frequency dips of 0.5 Hz, the solar inverter increases power by 100 kW without DC undervoltage. In extreme low-irradiation scenarios, the DC voltage control mode prevents shutdowns. The results confirm the effectiveness of the dual-loop method and switching strategy.
In conclusion, the proposed active power reserve control for grid-forming solar inverters enables precise power reservation under source and grid disturbances without additional sensors. The dual-loop online correction method handles rapid irradiation and slow temperature changes, while the DC voltage stabilization ensures reliability in extreme conditions. This approach enhances the stability of solar inverters in weak grids and supports renewable energy integration. Future work could explore integration with energy storage systems for extended support.