As the penetration of renewable energy sources increases, power electronic converters are widely used to interface photovoltaic (PV) systems with the grid. However, the declining proportion of traditional synchronous generators reduces system inertia, threatening frequency stability. Grid-forming control technology provides an effective solution by simulating the inertia characteristics of synchronous machines through inverter control systems. In photovoltaic inverters, matching control utilizes the energy stored in the DC-link capacitor to emulate rotor inertia without requiring power reserve, making it particularly suitable for power-constrained sources like PV. To test such grid-forming inverters, a test platform must simultaneously emulate both AC grid characteristics and DC-side power source dynamics. Conventional grid simulators typically focus only on AC-side characteristics, ignoring the impact of the DC-side power source. This paper proposes an innovative AC-DC dual-port operation condition emulation test platform that synchronously simulates AC-side grid voltage, frequency, impedance, and DC-side PV generation dynamics. The method provides a comprehensive testing environment for grid-forming PV inverters. Throughout this article, we will repeatedly emphasize the importance of understanding various types of solar inverter — from traditional string and central inverters to modern grid-forming inverters — and how our proposed emulation method addresses their unique testing requirements.
Introduction
The rapid integration of renewable energy sources has led to a significant increase in the number of power electronic converters connected to the grid. These converters, which include various types of solar inverter such as string inverters, central inverters, microinverters, and hybrid inverters, are essential for converting DC power from PV panels into AC power suitable for grid connection. However, as the share of converter-based generation grows, the overall system inertia decreases because these devices lack the rotating mass of synchronous generators. This reduction in inertia can cause larger frequency deviations during disturbances, potentially leading to instability.
Grid-forming (GFM) inverters have been proposed to address this challenge. Unlike grid-following inverters, GFM inverters can actively regulate voltage and frequency, providing synthetic inertia and damping to support grid stability. Among the many control strategies for GFM inverters, matching control has emerged as a promising approach for photovoltaic applications. Matching control establishes a relationship between the DC-link voltage and the rotor speed of a synchronous machine, allowing the inverter to use the DC capacitor’s stored energy to emulate inertia. This method does not require power reserve, thus maintaining high energy efficiency while providing grid support.
To validate the performance of such grid-forming PV inverters, comprehensive testing under realistic operating conditions is necessary. Traditional testing methods often employ a physical grid simulator that focuses solely on AC-side characteristics, such as voltage amplitude, frequency, and impedance. However, for grid-forming inverters that employ matching control, the DC-side dynamics are equally important because the control directly couples the DC voltage with the AC frequency. Therefore, a test platform must emulate both the AC grid and the DC power source (e.g., a PV array). Unfortunately, existing grid simulators are typically designed for AC-side emulation only, ignoring the DC-side behavior. This paper presents a novel AC-DC dual-port operation condition emulation method that simultaneously simulates the AC grid and the DC PV source, enabling accurate testing of grid-forming PV inverters.
Our proposed platform consists of an AC grid simulator (a DC/AC converter) and a DC power source simulator (a DC/DC converter) sharing a common DC voltage source. The AC simulator replicates grid voltage, frequency, and line impedance, while the DC simulator mimics the power characteristics of a PV panel, including constant power operation under maximum power point tracking (MPPT). This configuration forms a complete power loop, allowing the external DC source to supply only the losses of the three converters, thus reducing power rating requirements. Additionally, the DC/DC converter employs a dual active bridge (DAB) topology, whose high-frequency transformer naturally blocks zero-sequence current paths, enhancing system performance.
Throughout this discussion, we will refer to different types of solar inverter to contextualize our work. For instance, string inverters are commonly used in residential and commercial installations, while central inverters dominate utility-scale PV plants. Microinverters offer module-level MPPT, and hybrid inverters integrate battery storage. Grid-forming capability can be added to any of these types, but the testing requirements vary. Our proposed method is particularly relevant for any types of solar inverter that adopt grid-forming control, especially those using matching control on the DC side.
Principle of Grid-Forming Control and Matching Control
Grid-forming inverters are designed to behave as voltage sources behind an impedance, similar to synchronous generators. The most well-known concept is the virtual synchronous generator (VSG), which mimics the swing equation of a synchronous machine. The VSG control consists of two primary loops: active power–frequency (P–f) and reactive power–voltage (Q–V). The P–f loop is governed by:
$$
\omega = \omega_0 – \frac{1}{J s + D_p} (p – P_0)
$$
where $\omega$ is the angular frequency, $\omega_0$ is the rated angular frequency, $J$ is the virtual inertia, $D_p$ is the damping coefficient, $p$ is the measured active power, and $P_0$ is the power reference. The Q–V loop determines the voltage amplitude:
$$
U = U_0 – D_q (q – Q_0)
$$
where $U$ is the voltage amplitude, $U_0$ is the rated voltage, $D_q$ is the droop coefficient, $q$ is the measured reactive power, and $Q_0$ is the reactive power reference.
While VSG control works well for energy storage systems where the DC side has a stiff voltage source (e.g., batteries), it is less suitable for PV inverters because PV power is limited and variable. Operating a PV inverter with VSG control requires reserving power margin (e.g., operating below the maximum power point), which reduces energy yield.
Matching control solves this problem by establishing a direct relationship between the DC-link voltage $u_{dc}$ and the angular frequency $\omega$. The control law is:
$$
\omega = \omega_0 – \frac{1}{D_p} (u_{dc}^2 – u_{dcref}^2)
$$
Here, $u_{dcref}$ is the reference DC voltage. The DC capacitor energy $\frac{1}{2}C_{dc}u_{dc}^2$ emulates the kinetic energy of a synchronous machine rotor. Consequently, when grid frequency changes, the DC voltage adjusts automatically, causing the inverter to inject or absorb active power accordingly. The reactive power–voltage loop remains similar to VSG:
$$
U = U_0 – D_q (q – Q_0)
$$
This control structure inherently couples the AC and DC sides, making it essential to test the inverter under simultaneous AC and DC disturbances. This requirement motivates our AC-DC dual-port emulation method. The types of solar inverter that implement matching control are often advanced grid-forming inverters, but the principle can be applied to any inverter topology — two-level, three-level, or multilevel — as long as the DC bus is accessible for control.
Proposed AC-DC Dual-Port Operation Condition Emulation Platform
System Architecture
Our proposed test platform is illustrated conceptually. It comprises three main components: an AC grid simulator (DC/AC converter), a DC power source simulator (DC/DC converter), and a common external DC voltage source. The AC simulator connects to the AC terminals of the inverter under test (IUT), while the DC simulator connects to the DC bus of the IUT. The external DC source supplies the common power loop, but its power rating only needs to cover the total losses of all converters, as the active power circulates through the IUT and the simulators.
The AC simulator uses a two-level voltage source converter (VSC) topology, but for higher power or voltage levels, multilevel topologies can be employed without changing the control structure. The DC simulator adopts a dual active bridge (DAB) topology, which provides galvanic isolation and bidirectional power flow capability. The high-frequency transformer in the DAB naturally blocks zero-sequence current paths, preventing unwanted zero-sequence circulation within the test platform.
This architecture is flexible and can accommodate various types of solar inverter. For example, a string inverter typically has a low DC voltage (300–500 V) and requires a step-up transformer on the AC side; our platform can emulate the AC grid impedance accordingly. For central inverters with higher DC voltage (800–1500 V), the DC simulator must be rated for higher voltage and power. The control parameters are software-configurable, enabling rapid reconfiguration for different inverter specifications.
DC-Side Emulation Control
The DC-side simulator emulates a photovoltaic array operating under MPPT. In practice, MPPT algorithms adjust the operating point on a timescale of seconds to minutes. For testing grid-forming inverters, we are interested in dynamic phenomena within a few seconds; therefore, the PV source can be approximated as a constant power source over short intervals. The equivalent circuit is a controlled current source with power $P_{pv}$ determined by the MPPT setpoint.
The control block diagram of the DAB converter is shown conceptually. The DAB measures its output voltage $u_{dc\_sim}$ and output current $i_{dc\_sim}$ to compute the instantaneous power $p_{sim} = u_{dc\_sim} i_{dc\_sim}$. This measured power is compared with the power reference $P_{pv}^*$ (e.g., from a MPPT simulation). The error is fed into a PI controller, which generates the phase shift angle $d$ for the DAB modulation. The DAB then regulates the power flow accordingly. The transfer function of the PI controller is:
$$
d = \left( K_p + \frac{K_i}{s} \right) (P_{pv}^* – p_{sim})
$$
where $K_p$ and $K_i$ are proportional and integral gains. The DAB topology ensures that the power can be transferred bidirectionally with high efficiency, and its transformer isolation prevents zero-sequence current from flowing into the DC bus of the IUT.
This DC emulation method is suitable for all types of solar inverter that require a controlled DC input. For example, microinverters often have a dedicated DC/DC converter per panel; our platform can emulate the output of that converter. However, in our test scenario, we directly connect the DC simulator to the inverter’s DC bus, which is representative of a central inverter or string inverter without additional DC/DC stages.
AC-Side Emulation Control
The AC grid simulator must replicate a three-phase ideal voltage source $u_s$ in series with a line impedance $Z_{line}(s) = s L_{line} + R_{line}$. To implement this in a digital controller, we employ a virtual impedance method combined with voltage and current control loops. The reference voltage at the point of common coupling (PCC) is computed as:
$$
u_{gref} = u_s – i_g Z_{line}(s)
$$
However, the derivative term $s L_{line}$ amplifies high-frequency noise. To avoid this, we replace the ideal impedance with a low-pass filtered version:
$$
u_{gref} = u_s – i_g \frac{s L_{line} + R_{line}}{1 + T s}
$$
where $T$ is the low-pass filter time constant. The filtered virtual impedance transfer function is:
$$
G_{VI}(s) = \frac{s L_{line} + R_{line}}{1 + T s}
$$
The control system then regulates the inverter output voltage $u_g$ to follow $u_{gref}$. A proportional-resonant (PR) controller is used for both voltage and current loops to achieve zero steady-state error at the fundamental frequency. The PR controller transfer function is:
$$
G_{PR}(s) = K_p + \frac{2 K_i \omega_c s}{s^2 + 2 \omega_c s + \omega_0^2}
$$
where $K_p$ is the proportional gain, $K_i$ is the resonant gain, $\omega_c$ is the cutoff frequency, and $\omega_0$ is the resonant frequency (50 Hz). The outer voltage loop compares $u_{gref}$ with the measured $u_g$ to generate a current reference $i_{gref}$ for the inner current loop. The inner current loop then controls the inductor current to track $i_{gref}$. This cascaded structure provides fast dynamic response and high bandwidth.
| Parameter | Symbol | Value | Rationale |
|---|---|---|---|
| Line inductance | $L_{line}$ | 10 mH | Typical low-voltage distribution network ($L/R \approx 10$) |
| Line resistance | $R_{line}$ | 1 $\Omega$ | Typical distribution network |
| Low-pass filter time constant | $T$ | 0.01 s | Suppresses derivative noise; phase lag < 5° at 50 Hz |
| Virtual impedance transfer function | $G_{VI}(s)$ | $\frac{s\cdot 0.01 + 1}{1+0.01s}$ | Filtered version of $Z_{line}$ |
The AC simulator can flexibly change the virtual impedance and source voltage to represent different grid strengths. For weak grids, the short-circuit ratio (SCR) is low, and $L_{line}$ is relatively large. The simulation parameters can be adjusted in software without hardware modifications, making the platform suitable for testing various types of solar inverter under diverse grid conditions.
Simulation Verification and Results
To validate the proposed emulation method, we built a simulation model in PLECS. The system parameters are summarized in the table below.
| Parameter | Symbol | Value | Remarks |
|---|---|---|---|
| DC capacitance | $C_{dc}$ | 2200 $\mu$F | Based on voltage ripple constraint (Eq. 7 in original paper) |
| Line inductance | $L_{line}$ | 10 mH | As above |
| Line resistance | $R_{line}$ | 1 $\Omega$ | As above |
| Inertia coefficient | $J$ | 0.1 kg·m² | Time constant ≈ 0.5 s |
| Active damping coefficient | $D_p$ | 5 N·m·s/rad | From stability criterion |
| Low-pass filter time constant | $T$ | 0.01 s | As above |
| Rated DC voltage | $u_{dc}$ | 750 V | — |
| DC voltage reference | $u_{dcref}$ | 750 V | — |
| Rated active power | $P_n$ | 20 kW | — |
| AC grid voltage amplitude | $U_0$ | 311 V (peak) | — |
| AC grid frequency | $f_0$ | 50 Hz | — |
The DC capacitance was calculated to limit voltage ripple to 5% of rated under a 10% power step. The line impedance represents a typical weak grid condition.
AC Frequency Fluctuation Scenario
We emulated a grid frequency ramp from 50 Hz to 51 Hz at a rate of 0.4 Hz/s, representing a large load increase or generation loss. The inverter under test (IUT) employed matching control. The simulation results show that as the grid frequency increased, the DC voltage rose from 750 V to about 810 V (8% rise). The active power output dropped from 20 kW to approximately 17.5 kW. Key performance metrics are listed in the table.
| Metric | Value | Specification |
|---|---|---|
| Transient frequency response time | 245 ms | — |
| Settling time | 680 ms | — |
| Active power regulation deviation | ±1% | Within typical standard |
| DC voltage overshoot | 8% | Acceptable for capacitor rating |
The inverter successfully injected virtual inertia by reducing active power output, helping to stabilize frequency. The response demonstrates that the proposed emulation platform can accurately reproduce coupled AC-DC dynamics.
DC Power Variation Scenario
We simulated a step change in PV input power from 20 kW to 15 kW at t = 1 s, emulating a sudden cloud cover. The DC simulator adjusted its output accordingly. The inverter under test maintained DC voltage regulation and the output active power tracked the input power change within 0.08 s (dynamic response time). The DC voltage recovered to 750 V ± 2% after the transient. The results are summarized below.
| Metric | Value | Requirement |
|---|---|---|
| Dynamic response time | 0.08 s | < 0.5 s (typical grid-forming standards) |
| DC voltage recovery | 750 V ± 2% | — |
| Active power tracking error | < 1% steady-state | — |
These results confirm that the DC simulator can accurately emulate PV power variations and that the inverter’s matching control maintains proper operation.
Zero-Sequence Current Suppression Analysis
One advantage of using DAB topology for the DC simulator is its inherent zero-sequence blocking capability. We compared the zero-sequence current in a conventional Buck-Boost DC simulator (without isolation) versus the DAB simulator under the same AC frequency disturbance. The conventional topology produced zero-sequence current peaks up to 3 A, while the DAB topology reduced them to below 0.1 A. This suppression prevents unwanted zero-sequence circulation in the test platform, which could otherwise distort the test results or cause equipment damage.
| Topology | Peak Zero-Sequence Current |
|---|---|
| Conventional Buck-Boost | 3 A |
| Dual Active Bridge (DAB) | < 0.1 A |
This feature is particularly beneficial when testing sensitive types of solar inverter that may be vulnerable to zero-sequence harmonics.
Discussion on Applicability to Various Types of Solar Inverter
The proposed AC-DC dual-port emulation method is not limited to a single class of inverters. It can be adapted to test a wide range of types of solar inverter in the context of grid-forming control. Below we discuss several common types and how our platform can accommodate them.
- String Inverters: These are widely used in residential and commercial systems with power ratings from a few kW to tens of kW. They typically operate at a DC voltage of 300–500 V and require galvanic isolation on the AC side (through a transformer) or the DC side. Our AC simulator can emulate the grid impedance seen at the inverter’s AC terminals, and the DC simulator can emulate the combined output of multiple PV strings. Matching control can be implemented in the inverter’s firmware.
- Central Inverters: Used in utility-scale PV plants, central inverters have power ratings from 500 kW to several MW. Their DC voltage ranges from 800 V to 1500 V. The proposed platform can be scaled by using higher-power converters (e.g., multilevel topologies for the AC simulator). The DAB DC simulator must be rated for the corresponding voltage and power. The control software can be reconfigured for different power levels.
- Microinverters: These are module-level inverters with power typically below 2 kW and operate at low DC voltage (30–50 V). Testing microinverters with our platform would require a DC simulator that can provide low voltage and high current. Additionally, microinverters often have their own MPPT; the DC simulator should emulate a single PV panel. The AC simulator can represent the local household grid. While microinverters are usually grid-following, emerging designs include grid-forming capabilities where our platform would be valuable.
- Hybrid Inverters: These integrate PV and battery storage. The DC side has both a PV input and a battery port. Our platform can emulate the PV source on the PV port and the battery on the battery port (or emulate the combined DC bus). For grid-forming hybrid inverters, the control strategies often involve coordination between the two sources. Our dual-port emulation can independently control each source’s power to test the overall system response.
- Grid-Forming Inverters (Any Type): The core contribution of this paper is to provide a realistic emulation environment for any types of solar inverter that adopt grid-forming control, especially those using matching control. Since matching control requires simultaneous AC and DC dynamics, only a platform like ours can properly test them. Traditional single-port simulators would fail to reproduce the coupling effects.
The flexibility of software-defined parameters (grid impedance, source power profile, frequency/voltage disturbances) makes the platform adaptable to different inverter specifications. Future work will include hardware-in-the-loop experiments to further validate the method across different types of solar inverter and grid conditions.
Conclusion
This paper presented a full-condition emulation method for grid-connection testing of grid-forming photovoltaic inverters. The proposed AC-DC dual-port platform simultaneously simulates the AC grid characteristics (voltage, frequency, impedance) and the DC-side PV generation dynamics, which is essential for testing inverters employing matching control. The system uses a DC/AC converter for grid emulation with virtual impedance, and a DAB DC/DC converter for PV power emulation with constant power control. Both converters share a common external DC source, minimizing power losses. The DAB’s isolation effectively blocks zero-sequence currents.
Simulation results demonstrated the platform’s effectiveness under AC frequency fluctuations and DC power variations. The inverter under test responded correctly, providing virtual inertia via DC voltage modulation. The platform also suppressed zero-sequence current compared to non-isolated designs. The methodology is applicable to various types of solar inverter, including string, central, micro, and hybrid inverters, by adjusting software parameters and hardware ratings. This work provides a robust and flexible testing solution for the emerging grid-forming inverter technology, which is critical for the stable integration of high-penetration renewable energy systems.