Abstract:
Grid-connected inverters play a crucial role in transmitting power from distributed production systems and renewable sources to the grid. However, these inverters often generate current harmonics due to high-frequency switching and DC link ripple. To address these issues, various filters, including the LCL filter, are employed. Yet, in situations with variable network impedance and LCL filter resonance in weak networks, instability can occur. This paper focuses on improving the power quality of grid-connected Fuel Cell using LCL filters, primarily through a current sensor and virtual impedance shaping. The paper divides the output impedance of the Fuel Cell power optimization system into an active and passive part. It neutralizes the active component by introducing a series virtual impedance and counteracts its adverse effects with parallel virtual impedance. The design process for both series and parallel virtual impedance is elaborated, and the system's sensitivity is thoroughly analyzed. To validate the proposed approach, extensive simulations have been carried out using MATLAB software. The simulations demonstrate the robust and precise performance of the control system in effectively injecting the maximum power generated by the Fuel Cell into the grid. Additionally, they showcase the high-quality current being injected into the grid and the system's capacity to maintain stability, even in a weak network environment.


Introduction
The rapid reduction of fuel reserves and the harmful effects of burning fossil fuels cannot be ignored. The fact that fossil fuels cause environmental concerns such as greenhouse gas emissions, atmospheric effects, and public health has drawn the attention of researchers to replace fossil fuels with renewable energy sources that are sustainable, environmentally friendly, and clean. Renewable energy sources include: fuel cell, wind turbines, geothermal, fuel cells, Among the renewable sources, fuel cells are a suitable option for various applications due to their simple use, high reliability, low maintenance cost, and being silent (Yuan,2020).
The production voltage level of the fuel cell for applications connected to the grid is low. Therefore, a DC-DC converter is used to increase the output voltage level of the fuel cell. A DC-AC converter is also used to connect the fuel cell to the network. In practical applications, LCL-type grid-tied inverters have been widely utilized due to their superior harmonic mitigation capabilities and compact size.
For an LCL-filtered grid-connected inverter, active damping based on network current feedback can ensure the desired bandwidth and good robustness. However, the performance of the inverter is seriously jeopardized by non-ideal conditions at the point of common coupling (PCC), including network voltage distortions and variable network impedance (Zhu, 2019). Active damping based on network current feedback may not work well for wide variations in network impedance. Therefore, in (Xu,2018), the robustness of this control method is discussed, and its relationships with system parameters are extracted and established through mathematical equations.
Impedance shaping based on virtual impedance is an effective and enhanced method to control grid-connected inverters in weak and distorted networks (Zhu, 2019, Chen, 2017). In (Wang, 2015), an impedance shaping strategy with parallel and series virtual impedances is proposed. In fact, shaping parallel virtual impedance is equivalent to the voltage feed-forward strategy at the PCC, ensuring system robustness against network disturbances (Zhu, 2019, Wang, 2015).
In a majority of the previously discussed methods, the initial step involved the introduction of a specific control approach, after which impedance shaping of the inverter output was examined within the framework of that approach. This approach resulted in a lack of generality. To address this limitation, the present paper introduces an impedance shaping method that is rooted in a tangible physical concept for a Fuel Cell power injection system. For this purpose, a series virtual impedance has been designed using network current feedback to eliminate the active component. In the feedback path, a high-pass filter has been used to avoid undesirable effects of the series virtual impedance at lower frequencies gain and system phase margin. Since the use of series virtual impedance may jeopardize the control system's stability around the resonance frequency due to changes in LCL filter parameters, a parallel virtual impedance has been employed using voltage feedback at the PCC to address this issue. Finally, a systematic and uncomplicated design of control system parameters has been put forth for enhancing the Fuel Cell power injection system. This proposed design has been compared to existing methods in terms of the passive performance of the grid-connected inverter.

System modeling and passive performance characteristics
Figure 1 depicts the schematic of the Fuel Cell power injection system connected to the grid, incorporating an LCL filter. In this figure, the inductor L1 is on the inverter side, the inductor L2 is on the grid side, and the C signifies the filter capacitor. The network at the PCC is characterized as an ideal voltage source Vg coupled to a network impedance Zg. The inductance of power lines and transformers, as well as the capacitance of power factor correction circuits, are typically indicative of Zg (C. Zou,2014), which is identified by Cg and Lg. Within the components of the filter and network impedance, there are parasitic resistances that provide a degree of passive damping for system stability. Since considering them complicates the analysis and design of control parameters, in most research, parasitic resistances are ignored in the analysis and control parameter design (Akhavan, 2020, Rodriguez-Diaz, 2019)-( Harnefors, 2007). To implement closed-loop control, the network current, denoted as ig, is measured. The PCC voltage, VPCC, is measured for synchronizing the current with the grid voltage through the phase locked loop (PLL), where θ represents the tracking angle. The angle θ is combined with the reference current magnitude I* to form the reference current signal, iref. Subsequently, the errors are transmitted to the current controller Gc for the generation of modulation signals VM. Lastly, power-switching gates signal are produced through a pulse width modulation (PWM) modulator.

Figure 1. Configuration of grid-connected Fuel Cell power optimization system with LCL filter
Simulation results
The power conditioning system of the Fuel Cell has been simulated and evaluated for a 5 kW output power. The output voltage of the Fuel Cell is boosted using a boost converter. The energy produced by the system is then injected into the grid using an inverter connected to an LCL filter. The power conditioning system of the Fuel Cell is analyzed with and without the presence of virtual impedances, both series and parallel.

(a) (b)
Figure 2- (a) Output voltage and current of the grid-connected Fuel Cell in the presence of virtual impedances (b) Grid voltage and current with and without the presence of virtual impedances
Conclusion
In this study, an approach for the enhancement of grid-connected Fuel Cell power conditioning systems is presented. The utilization of an LCL filter and a tailored control method is employed to improve the quality of the injected current. In parallel, stability and passive system performance are ensured through the application of an advanced virtual impedance shaping technique. The inverter output impedance is partitioned into two essential components, one passive and the other active, connected in series. To nullify the active component, a virtual series impedance is employed, guided by grid current feedback. To mitigate any potential adverse influences on the system's low-frequency loop gain and phase margin, a high-pass filter modification is incorporated into the feedback function. Simultaneously, a parallel virtual impedance is introduced through PCC voltage feedback, augmenting system stability and passive performance. The proposed control methodology has been applied to the Fuel Cell’s power conditioning system, linked to the grid. Comprehensive evaluations have been carried out under stable conditions and simulated disturbances arising from perturbing the amount of fuel. The simulation results consistently affirm the high quality of the injected current into the grid. Notably, the system retains its stability and passive performance, even when confronted with substantial variations in the network impedance. These results underscore the effectiveness and resilience of the approach in optimizing Fuel Cell power conditioning system performance in grid-connected scenarios.