Microinverter Power System to Feed Grid-Isolated AC Loads Using Fuel Cells

Abstract

Microgrids based on fuel cells are used to produce energy due to their zero emissions, stand-alone operation, and compact size that facilitates mobility; making research in fuel cell applications essential to support their widespread adoption. This paper proposes two main contributions: the adaptation of a TMDSSOLARUINVKIT microinverter for integration into a microgrid powered by a fuel cell, and the design and implementation of adaptive controllers. The controllers ensure the proper operation of the microgrid and avoid the fuel cell starvation. The microgrid comprises a fuel cell emulator, a TMDSSOLARUINVKIT microinverter, and AC linear and nonlinear loads. The research methodology follows three steps. First, a hardware-in-the-loop approach is proposed to emulate the fuel cell using a real-time target machine and a power interface, utilizing a model derived from the fuel cell manufacturer’s specifications. Then, a detailed model of a flyback converter is obtained to design and implement a control system, consisting of two adaptive controllers, one for regulating the current of the fuel cell and another for controlling the DC-link voltage. The current controller adapts a proportional gain to ensure a desired cut-off frequency and the DC-link voltage controller adapts a proportional and integral gains due changes in the duty cycle, ensuring the proper operation in any operating condition. Finally, the functionality of the microgrid based on a fuel cell is validated through four experiments. The results confirm the effective operation of the controllers ensuring the safe operation of the fuel cell. One experiment is designed to demonstrate the capability of the proposed solution to meet the requirements of rural areas in Colombia.

Introduction

Currently, electric nanogrids based on fuel cells are a promising option to produce energy due to its zero emissions, production of heat, water as a residual component, and the compact size that facilitates its transportation. The hydrogen production supports the possibilities of operating fuel cells in stand-alone environments increasing the access to electrical energy. Among the current applications of Proton Exchange Membrane (PEM) fuel cells are replacing back-up generators, powering DC nanogrids and standalone AC renewable microgrids, powering the traction system of hybrid vehicles, and complementing variable sources as photovoltaic arrays (Leva and Zaninelli 2009; Saxena et al. 2021; Török et al. 2018; Arezki and Boudour 2014; Jian and Wang 2022; Benlahbib et al. 2020). The authors of Leva and Zaninelli (2009) provides a valuable overview of hybrid fuel cell technologies for microgrids. However, more research is needed to assess the cost and complexity of those systems and address the technical challenges that must be achieved for their implementation. As back-up generators for DC nanogrids, PEM fuel cells are commonly combined with a solar array and a battery pack. For example, the authors of Saxena et al. (2021) present an energy management system of a DC nanogrid composed by a PV panel, a battery, a fuel cell, and the load. In such a work each element has an associated converter and their respective controller. Moreover, the use of fuel cells as back-up systems is reported in Török et al. (2018), where diesel generators are replaced by fuel cells in back-up power to feed telecom systems to provide reliable communication during disasters or emergencies. In Török et al. (2018), the authors demonstrate the importance of stand-alone systems as back-up power where fuel cells or photovoltaic generators can be used to replace diesel generators. Another application can be found in remote communities where AC microgrids work as autonomous systems composed by PV generators, small wind generators, fuel cells, and AC loads. The renewable sources and the storage system require converters and their control systems. In that way, the authors of Benlahbib et al. (2020) propose a standalone hybrid microgrid composed by a wind generator emulator, a solar array emulator, batteries, and a fuel cell emulator. That work is focused on an experimental study of the standalone microgrid. Complementing PV arrays in sustainable power hybrid systems is another application of PEM fuel cells. The authors of Arezki and Boudour (2014) present a Simulink/Matlab simulation of a hybrid power system, which is composed by a PV generator with a power converter and an MPPT system interacting with a PEM fuel cell to power an isolated load, which is interfaced through a power inverter with a PWM control. Powering traction systems of hybrid vehicles is another current application of PEM fuel cells. The authors of Jian and Wang (2022) propose a fuel cell electric vehicle power system model which is validated by hardware-in-the-loop real-time emulation. The power sources of the system are a multi-stack fuel cell and a battery pack. The system is implemented in a MicroLabBox and a desk computer. Classical controllers, a rule-based energy management system, the converters, the batteries, and the fuel cells are emulated in the MicroLabBox; the desk computer has installed Matlab R2016b and dSPACE real-time interface (RTI-1202). In these processing devices, advanced control strategies can be easily implemented to increase the operation range of the system. Based on the last examples arises the necessity of investigating the associated control systems of microgrids, the integration of commercial platforms in the implementation of microgrids, and the implementation of emulators that saves hydrogen and prevents the damage of PEM fuel cells. This work implements a PEM fuel cell emulator to contribute to the first two topics.

One active research area in the use of PEM fuel cells concerns the control systems applied to operate and protect them. Several control systems have been proposed in this area covering classical control, robust control, rule-based energy management systems, and fuzzy control (Li et al. 2005, 2019; Matraji et al. 2013; Papadimitriou et al. 2016). In this way, the analysis of control and operation of an isolated power plant based on a fuel cell is presented in Li et al. (2005), where two control strategies are developed and simulated; the constant utilization control and the constant voltage control. That work is focused on the development of basic controllers and also establishes the relationship of the fuel cell internal voltage, the hydrogen fuel input, and the stack current using a small signal method, which is used to analyze the system. In Li et al. (2019) a robust control for a PEM fuel cell is proposed, where the control objective is to avoid the oxygen starvation during sudden load changes. That work proposes a cascade controller that consists of oxygen excess ratio tracking and compressor flow rate regulation. In that work, the sliding mode cascade controller was validated using a hardware-in-loop test bench, which consist of a commercial twin screw air compressor and a real-time fuel cell emulation system. The authors of Matraji et al. (2013) propose a robust nonlinear second order sliding mode controller in cascade to keep an optimum net power output. The controller performance is validated through hardware-in-the-loop, where the fuel cell and the controller are implemented in a real time emulation system. A commercial twin screw air compressor corresponds to the hardware part in the loop. In Papadimitriou et al. (2016) a fuzzy control scheme for a power generation system based on a fuel cell that is feeding an isolated load is presented. A laboratory setup is composed by a fuel cell, a battery, a power converter of two stages, a DSP platform, a step-up transformer, and AC domestic loads. Although a fuzzy controller design is described, there is not detail information to reproduce the reported results. As the last review shows, robust control systems are an appropriate option to increase the operating condition spectrum of systems; however, those control systems must be experimentally validated facing linear and nonlinear loads, and real power profiles, that is why this work validates the robust adaptive controllers facing different type of loads.

Commercial integration is another approach that has been reported by several authors (Thale et al. 2014; Tritschler et al. 2010). For example, a laboratory setup for emulating different sources as photovoltaic, fuel cell, and a battery is proposed in Thale et al. (2014). The authors produce the source emulator integrating the Texas Instruments platform TMS320F28027, which is a controlled flyback converter, with the National Instrument’s NIDAQ USB6008. That work demonstrates the advantage of integrate commercial platforms to produce a research and teaching instrument. A fuel cell generation system, which can be grid connected or power an isolated load, is presented in Tritschler et al. (2010). The fuel cell system integrates a proton exchange membrane fuel cell emulator, a boost converter, an inverter, a grid emulator, and an electric load. The fuel cell was emulated using a DC source, a Simulink model and a DSPACE environment; the electric grid was emulated using a power amplifier and an ARENE real time grid simulator. Commercial platforms offer a low-cost solution that supports the spread of fuel cells powering isolated AC loads. For the advantages exposed in Thale et al. (2014); Tritschler et al. (2010), this work adapts a TMDSSOLARUINVKIT microinverter for integration into a microgrid powered by a PEM fuel cell.

The literature review shows that one of the main efforts in the research of use fuel cell power systems has been the implementation of emulators because they are helpful saving hydrogen, avoiding the reduction of real fuel cell lifespan, and avoiding the purchase or damage of fuel cells. Also, the cost of the fuel cell stack could be prohibitive for some laboratory research. Among the implementation of emulators there are several approaches. Some authors are focused on the use of buck converters to emulate the power stage (Marsala et al. 2009; Trapp et al. 2011), others are focused on reproduce the steady state and dynamic behavior of the fuel cells (Lindahl et al. 2018; Restrepo et al. 2012), and others are concentrated on hardware-in-the-loop integration of several technologies (Gao et al. 2012, 2011; Pinto and Vega-Leal 2010).The use of buck converters to emulate the power stage is presented in Marsala et al. (2009); Trapp et al. (2011). An emulator of a PEM fuel cell is implemented using a DC/DC buck converter in Marsala et al. (2009). The fuel cell system, including its auxiliaries and related control system, is emulated using the buck converter and a DSPACE environment. That work is focused on emulating the characteristics of the PEM fuel cell, allowing its utilization as a stand-alone and low-cost system for design and experimental purposes. In Trapp et al. (2011), for an accurate reproduction, fuel cells are emulated using experimental data from their respective characteristic curves and a buck converter. Several authors have focused on demonstrate that it is possible to emulate both the steady state and dynamic behaviors of fuel cells to assess power interfaces or fuel cell loads. For example, the authors of Lindahl et al. (2018) proposed a fuel cell stack emulator which is composed by real fuel cell and a power amplifier. The emulator is used to maintain a one-to-one correspondence of cell and load currents. Such a work confirms that it is necessary to emulate fuel cells in order to increase the research results of this alternative source, without wasting hydrogen or decreasing the lifespan of bigger cells. Similarly, a real-time fuel cell emulator was designed in Restrepo et al. (2012) to estimate the oxygen excess ratio of real devices. The emulator was based on a model of a 1.2 kW NEXA fuel cell, where both the static and dynamic behaviors were successfully reproduced. Some authors have aimed for the integration of hardware-in-the-loop emulators. For example, a test of a hardware-in-the-loop emulator for fuel cells is reported in Pinto and Vega-Leal (2010). The authors tested real-time instrumentation software as well as modular electronic instrumentation. The behavior of the variables of the fuel cell emulator are shown using a LabVIEW interface and those results are compared with simulation results obtained with Simulink. In Gao et al. (2012, 2011) the authors propose a PEM fuel cell emulator to be used in hardware-in-the-loop applications. The emulator uses a multi-rate model of the fuel cell, which is implemented in DSPACE processors; the power stage is implemented with a DC/DC converter and a DC power source. At the end, the emulator is validated against experimental results obtained from a Ballard NEXA 1.2 kW stack. Due clear advantages of using fuel cells emulators, this work implements a hardware-in-the-loop system to emulate a fuel cell. The static behavior is achieved following the characteristic curves of a real fuel cell and the dynamic behavior reproducing a first order system.

Based on the results of the previous literature review, the two main contributions of this paper are the adaptation of a solar microinverter for integration into a microgrid powered by a fuel cell, and the design and implementation of adaptive controllers. The controllers ensure the proper operation of the microgrid and avoid the fuel cell starvation. The proposed solution has a control system formed by two loops, which are designed and implemented to ensure a safe and reliable operation. The first loop adaptively controls the fuel cell current and limits its slew-rate to avoid the oxygen starvation phenomenon. The second loop adaptively controls the voltage of the output capacitor and consequently regulates the DC-link voltage, which provides a safe operation for the stand-alone inverter. The generation system also integrates a commercial platform designed to be used with solar systems, thus adapting this device to interface fuel cells with stand-alone AC loads. To avoid the waste of hydrogen and the reduction of a fuel cell lifespan, the fuel cell is emulated. The emulator is constructed with a real-time target machine and a four-quadrant bipolar power supply, which reproduces both the steady-state and the dynamic behavior of a commercial fuel cell; in this case, a commercial PEM fuel cell stack of 100 W was selected to be emulated. The behavior of the emulator was validated comparing its experimental curves versus the curves reported in the user manual given by the fuel cell manufacturer. The whole fuel cell generation system is implemented and validated through experiments where the behavior of the emulator, the power conversion platform, the control system, and the load are observed and verified.

The remain of the paper is organized as follow. In Section 2 the fuel cell emulator is proposed and validated. Both steady-state and dynamic behaviors are verified comparing the emulator experimental curves versus the characteristic curves given by the manufacturer. Then, a detailed model of a flyback DC/DC converter is developed in order to design and implement the control system, which is formed by two adaptive controllers. That contribution is presented in Section 3. In Section 4, the fuel cell emulator, the flyback-based microinverter platform with its control system, and the AC load are integrated. In that section, the operation of the integrated fuel cell generation system is described in detail and the effectiveness of the control system is demonstrated. Finally, the conclusions of the work are presented in Section 5.

Emulation of the Fuel Cell System

The hardware-in-the-loop method was used to emulate the fuel cell (FC), where the emulator is constructed with two main components: (i) a behavioral model that is executed in a real-time machine, and (ii) a power interface that generates the emulated voltage to the load, which in the case of this work, is a four-quadrant power amplifier.

The behavioral model is formed by two parts: the characteristic curves that model the steady-state behavior, and a first-order system that models the dynamic behavior of the fuel cell. The fuel cell selected to illustrate the proposed solution is the H-100 PEM fuel cell (FCS-C100) from Horizon fuel cell technologies (Technologies 2024). The H-100 system includes the hydrogen control system and the air supply system (Blower), thus it provides a single voltage vs. current curve for the complete operation range, which is common in commercial fuel cell systems as reported in Ramos-Paja et al. (2009) and Ramos-Paja et al. (2010). The H-100 system provides a maximum power of 100 W, which occurs at a stack current of 8.2 A and stack voltage of 12 V. In those conditions, the stack consumes a hydrogen flow equal to 1000 ml/min with an efficiency of 40 % (Technologies 2024).

The steady-state behavior of the H-100 system is reported by the manufacturer with the voltage vs. current ($V_{\mathit{FC}}-I_{\mathit{FC}}$) curve reported in Technologies (2024). Similarly, the hydrogen consumption is reported with a $H_2$ vs. power ($H_2-P_{\mathit{FC}}$) curve available in the same datasheet. Using the data extracted from the datasheet curves and the Matlab curve-fitting toolbox, the polynomial model given in (1) is obtained to reproduce the $V_{\mathit{FC}}-I_{\mathit{FC}}$ relation at the fuel cell output. Similarly, using data extracted from both $V_{\mathit{FC}}-I_{\mathit{FC}}$ and $H_2-P_{\mathit{FC}}$ datasheet curves and the same curve-fitting toolbox, the second polynomial model given in (2) is obtained to reproduce the hydrogen consumption of the fuel cell.

1

$$\begin{array}{cc}\hfill V_{\mathit{FC}}=& -6.728\times {10}^{-5}·I_{\mathit{FC}}^7+0.00221·I_{\mathit{FC}}^6\hfill \\ \hfill & -0.03027·I_{\mathit{FC}}^5+0.2244·I_{\mathit{FC}}^4\hfill \\ \hfill & -0.9869·I_{\mathit{FC}}^3+2.571·I_{\mathit{FC}}^2-3.994·I_{\mathit{FC}}+18.63\hfill \end{array}$$

2

$$H_2=2.024\times {10}^{-12}·I_{\mathit{FC}}^8-6.792\times {10}^{-10}·I_{\mathit{FC}}^7+9.205\times {10}^{-8}·I_{\mathit{FC}}^6-6.486\times {10}^{-6}·I_{\mathit{FC}}^5+0.0002646·I_{\mathit{FC}}^4-0.006941·I_{\mathit{FC}}^3+0.1383·I_{\mathit{FC}}^2+6.192·I_{\mathit{FC}}+1.034$$Both polynomial models (1) and (2) were programmed on a real-time simulator as depicted in figure 1: the fuel cell current is measured and acquired using an Analog-to-Digital Converter (ADC), since the ADC only accepts values from 0 V to 10 V, the current measurement must be scaled by $0.5V/A$, thus inside the real-time simulator the current value is reconstructed (scaled) using the inverse factor $2.0A/V$. Then, the current value is processed by both polynomial models (1) and (2) to produce the fuel cell voltage and hydrogen consumption. Following the modeling procedure published in Ramos-Paja et al. (2009), the dynamic behavior of the fuel cell is represented using a first order filter with a time constant $\tau$ equal to 0.25 s. Finally, both fuel cell voltage and hydrogen consumption are transformed to analog signals using the on-board Digital-to-Analog Converters (DAC), but due to the DAC and power stage ranges, the fuel cell voltage is scaled between 0 V and 4 V, while the hydrogen consumption is scaled between 0 V and 10 V.

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Fig. 1

Fuel cell emulator

The power interface of the emulator is the four-quadrant power amplifier BOP50-20GL from Kepco, which can be controlled to impose the desired voltage (-50 V to 50 V) with an analog command between -10 and 10 volts. Therefore, to impose the desired fuel cell voltage, the DAC1 output is scaled. Figure 1 also shows the block diagram of the fuel cell emulator: the Speedgoat real-time simulator measures the fuel cell current using the analog interface of the device, and it processes the fuel cell model to produce both the fuel cell voltage and hydrogen consumption. Then, using the analog interface (DAC1), the voltage command is delivered to the BOP50-20GL, which imposes the correct output voltage to emulate the fuel cell behavior. In addition, the hydrogen consumption is provided using the DAC2. Finally, a Simulink client is used to program the fuel cell model into the real-time simulator, inspect the variables, and store data.

To test the performance of the fuel cell emulator, a current sweep from 0 A to 10 A was applied using a BK-Precision 8514 electronic load, as shown in Fig. 1. The testbench includes an oscilloscope to register the current, emulated voltage and hydrogen consumption, which are used to reconstruct the characteristic curves of the fuel cell. Figure 2(a) shows the $V_{\mathit{FC}}-I_{\mathit{FC}}$ curve provided by the manufacturer, Fig. 2(e) shows the $H_2-P_{\mathit{FC}}$ curve, and Fig. 2(e) shows the power vs. current ($P_{\mathit{FC}}-I_{\mathit{FC}}$) curve. Figure 2 also reports the experimental curves generated by the fuel cell emulator: $V_{\mathit{FC}}-I_{\mathit{FC}}$ curve is given in Fig. 2(b), $H_2-P_{\mathit{FC}}$ curve is given in Fig. 2(f), and curve $P_{\mathit{FC}}-I_{\mathit{FC}}$ is given in figure 2(d). Those results put into evidence the accurate reproduction of the steady-state behavior provided by the fuel cell emulator.

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Fig. 2

Steady-state curves of both the real fuel cell (datasheet data) and emulated fuel cell

To confirm the correct reproduction of the dynamic behavior, a new experiment was executed: Fig. 3 shows the emulated fuel cell voltage produced by current steps between 8.94 A, 1.1 A, and 5 A. The first change (from 8.94 to 1.10 A) exhibits a transition from 11.38 to 16.51 V, which corresponds to the $V_{\mathit{FC}}-I_{\mathit{FC}}$ characteristic described by the manufacturer. Moreover, the emulator exhibits a time response of one second, which corresponds to $4·\tau$, thus confirming the desired dynamic behavior. For the second current change (from 1.1 to 5 A), the voltage dropped to 13.27 V with a similar response time, which confirms the correct emulator performance. In conclusion, the previous experiments confirm the correct operation of the fuel cell emulator. Therefore, it is a suitable alternative to test power interfaces and controllers designed for fuel cells.

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Fig. 3

Dynamic performance of the fuel cell emulator

The emulated H-100 fuel cell enables to develop power systems up to 100 W, but fuel cell stacks with a wide range of power levels are available. For example, in Technologies (2024) are available fuel cell stacks of 12 W, 60 W, 100 W, 300 W, 500 W, 1 kW, 2 kW, 3 kW, 5 kW, 10 kW, 30 kW, 40 kW, 65 kW, 100 kW, and 120 kW. Therefore, the solution proposed in this paper can be designed for a wide range of power applications. Finally, multiple fuel cell systems can be connected in parallel to supply higher power requirements.

Modeling and Control of the Flyback-Based Interface for the Fuel Cell

Galvanic isolation is used to prevent the propagation into the fuel cell of the common-mode noise generated by inverters, which is the case of stand-alone AC load circuits. This is important, since long-time exposure to leakage current in that noise could significantly degrade the fuel cell (Khan et al. 2023) (Hong et al. 2021). In addition, fuel cells are sensitive to ground failures, hence the galvanic isolation is needed to ensure the safety connection of a fuel cell to any DC bus used to power an inverter.

One well-known DC/DC converter with galvanic isolation is the flyback topology. Such a converter has been used to implement stand-alone power sources with larger DC voltage; for example, this topology provides a compact solution for fuel cell-based vehicles (Shen et al. 2019). Moreover, the flyback converter provides high voltage conversion ratio due to the boosting factor of the high-frequency transformer, hence it is useful for high-boosting applications (Li et al. 2012). In addition, the flyback converter is able to provide high power density and low electromagnetic interference (Yau and Hung 2022). One example of fuel cell interfaces based on a flyback converters is reported in Yigeng and Yu (2014), where the flyback converter regulates the output voltage, but no prevention of the detrimental oxygen starvation phenomenon is discussed (Ramos-Paja et al. 2010).

Based on the previous discussion, this work is based on the Texas Instrument solar microinverter TMDSSOLARUINVKIT (Bhardwaj and Choudhury 2017), which has two stages. The first stage consists on a flyback converter feeding a DC-link, thus it provides both galvanic isolation and high voltage conversion ratio; while the second stage is a controlled inverter. One important contribution of this paper is to adapt the TMDSSOLARUINVKIT to interface fuel cells and isolated AC loads. Such an adaptation is focused on controlling the first stage of the microinverter to provide a safe operation to both the fuel cell and the inverter. Figure 4 shows the block diagram of the proposed fuel cell power system, where the first stage is formed by the flyback converter and the proposed first stage controller; the second stage is an inverter regulated with a classical controller for isolated AC loads; the electrical scheme and classical controller of the second stage are reported in Bhardwaj and Choudhury (2017).

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Fig. 4

Fuel cell power interface based on the TMDSSOLARUINVKIT hardware

Figure 4 also shows the circuital scheme of the first stage, where the connection between the fuel cell and the flyback converter includes a capacitor $C_{\mathit{FC}}$ to avoid any discontinuous current entering the fuel cell. The flyback converter includes a high-frequency transformer with a turn-ratio 1 : n, and the circuital model includes both the magnetizing and leakage inductances $L_m$ and $L_k$, respectively. The DC-link capacitor ($C_{\mathit{dc}}$) and second stage (stand-alone inverter) can be modeled with a general representation: the stand-alone inverter current consumption is modeled by the current source $i_{\mathit{dc}}$, which has both DC and AC components due to the inverter operation. It is important to highlight that the stand-alone inverter does not regulate the voltage at the DC-link, hence the first stage must to regulate that voltage.

The proposed control scheme have two control loops: first, a current controller must be designed to limit the current derivative of the fuel cell, which ensures that oxygen starvation phenomenon is not present (Ramos-Paja et al. 2010), thus providing a safe fuel cell operation; and second, a voltage controller must be designed to ensure a safe voltage level at the DC-link. In this scheme the voltage controller provides the reference to the current controller, which produces the duty cycle d for the PWM circuit that generates the activation signal u of the MOSFET. Finally, the fuel cell voltage changes depending on the power requested by the inverter (which depends on the AC load consumption), and the DC-link voltage exhibits a sinusoidal oscillation at 120 Hz due to the inverter operation (Trejos et al. 2012). Therefore, the behavior of both controllers must be adapted to those input (fuel cell) and output (DC-link) perturbations, hence both current and voltage controllers must be adaptive structures.

Dynamic Model of the First Stage

The first step is to develop a dynamic model of the first stage, where the input voltage is defined by the fuel cell ($v_{\mathit{FC}}$), and output voltage $v_{\mathit{dc}}$ must be regulated. The dynamic analysis is performed when the MOSFET control signal is $u=1$ and $u=0$, which produces the following dynamic equations for the magnetizing current $i_m$ (3), DC-link voltage $v_{\mathit{dc}}$ (4), leakage current $i_k$ (5), and MOSFET current $i_{\mathit{MOS}}$ (6). Such a system of differential equations forms a switched model.

3

$$\begin{array}{cc}\hfill \frac{d{i}_m}{\mathit{dt}}=& \frac{v_{\mathit{FC}}}{L_m}·u-\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}·\left(1,-,u\right)\hfill \end{array}$$

4

$$\begin{array}{cc}\hfill \frac{d{v}_{\mathit{dc}}}{\mathit{dt}}=& \frac{1}{C_{\mathit{dc}}}·\left[\frac{i_m}{n},·,\left(1,-,u\right),-,i_{\mathit{dc}}\right]\hfill \end{array}$$

5

$$i_k=\frac{i_m}{n}·\left(1,-,u\right)$$

6

$$i_{\mathit{MOS}}=i_m·u$$Taking into account that the control stage includes a PWM circuit, the switched model must be averaged within the switching period $T_{\mathit{sw}}$. This is performed by averaging the MOSFET control signal u within the switching period, which results in the duty cycle value d:

7

$$\begin{array}{c}\hfill d=\frac{1}{T_{\mathit{sw}}}·{\int }_0^{T_{\mathit{sw}}}udt\end{array}$$Therefore, the averaged model is the following one:

8

$$\begin{array}{cc}\hfill \frac{d{i}_m}{\mathit{dt}}=& \frac{v_{\mathit{FC}}}{L_m}·d-\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}·\left(1,-,d\right)\hfill \end{array}$$

9

$$\begin{array}{cc}\hfill \frac{d{v}_{\mathit{dc}}}{\mathit{dt}}=& \frac{1}{C_{\mathit{dc}}}·\left[\frac{i_m}{n},·,\left(1,-,d\right),-,i_{\mathit{dc}}\right]\hfill \end{array}$$

10

$$\begin{array}{cc}\hfill i_k=& \frac{i_m}{n}·\left(1,-,d\right)\hfill \end{array}$$

11

$$i_{\mathit{MOS}}=i_m·d$$Then, the steady-state duty cycle and magnetizing current are calculated from the averaged model as follows:

12

$$\begin{array}{c}\hfill d=\frac{1}{1+\frac{v_{\mathit{FC}}}{v_{\mathit{dc}}}·\left(n,+,\frac{L_k}{n·L_m}\right)}\end{array}$$

13

$$\begin{array}{c}\hfill i_m=\frac{n·i_{\mathit{dc}}}{1-d}\end{array}$$From the previous expression for $i_m$, and taking into account the MOSFET current given in (10), the average steady-state current of the MOSFET is given in (14), which also corresponds to the steady-state value of the fuel cell current.

14

$$\begin{array}{c}\hfill i_{\mathit{MOS}}=i_{\mathit{FC}}=i_m·d=\frac{n·i_{\mathit{dc}}·d}{1-d}\end{array}$$Finally, the voltage conversion ratio M(d) is calculated from equation (12) as given in expression (15). From this expression is observed that selecting a higher turn-ratio 1 : n of the transformer makes possible to increase the output voltage ($v_{\mathit{dc}}$) for the same duty cycle, thus providing the same dynamic range for higher voltage applications.

15

$$\begin{array}{c}\hfill M(d)=\frac{v_{\mathit{dc}}}{v_{\mathit{FC}}}=\frac{d}{1-d}·\left(n,+,\frac{L_k}{n·L_m}\right)\end{array}$$

Fuel Cell Current Controller

The design of the FC current controller is based on regulating the magnetizing current $i_m$. Therefore, the dynamic equation (8) is transformed to the Laplace domain:

16

$$\begin{array}{c}\hfill s·i_m=\left(\frac{v_{\mathit{FC}}}{L_m},+,\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}\right)·d-\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}\end{array}$$Then, the current controller is designed using a proportional gain $k_c$, which must to limit the current derivative to avoid the oxygen starvation phenomenon (Ramos-Paja et al. 2010), and also must to track the current reference $i_{\mathit{ref}}$. The control law of the current loop is given in (17), where the error between the reference and the magnetizing current is multiplied by $k_c$.

17

$$\begin{array}{c}\hfill d=k_c·\left(i_{\mathit{ref}},-,i_m\right)\end{array}$$Then, introducing such a control law into the dynamic equation (16) results into the closed-loop dynamic expression given in (18), which has the same form of a low-pass filter with a cut-off frequency ${\omega }_c$.

18

$$\begin{array}{c}\hfill \frac{i_m}{i_{\mathit{ref}}}=\frac{\left(\frac{v_{\mathit{FC}}}{L_m},+,\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}\right)·k_c}{s+\left(\frac{v_{\mathit{FC}}}{L_m},+,\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}\right)·k_c}=\frac{{\omega }_c}{s+{\omega }_c}\end{array}$$This current-loop provides a null steady-state error, and also enables to limit the current derivative of the magnetizing current by imposing a suitable cut-off frequency ${\omega }_c$, which can be defined to ensure a safe current derivative to the fuel cell, thus avoiding the oxygen starvation phenomenon. However, expression (18) reports that the cut-off frequency changes with both the fuel cell and DC-link voltages, hence the proportional gain $k_c$ must be adapted to those changes to ensure the desired ${\omega }_c$ value. The adaptive law for $k_c$ is obtained from equation (18) as follows:

19

$$\begin{array}{c}\hfill k_c=\frac{{\omega }_c}{\frac{v_{\mathit{FC}}}{L_m}+\frac{v_{\mathit{dc}}}{n·L_m+L_k/n}}\end{array}$$Therefore, this is an adaptive current controller that requires the following measurements: the fuel cell and DC-link voltages, and the magnetizing current $i_m$. However, measuring $i_m$ is not feasible in the TMDSSOLARUINVKIT platform (Bhardwaj and Choudhury 2017), hence it is estimated from the fuel cell current measurement combining expressions (12) and (14), as follows:

20

$$\begin{array}{c}\hfill i_m=i_{\mathit{FC}}·\left[1,+,\frac{v_{\mathit{FC}}}{v_{\mathit{dc}}},·,\left(n,+,\frac{L_k}{n·L_m}\right)\right]\end{array}$$

DC-Link Voltage Controller

The current-loop operation is modeled by a current source imposing the desired current to the flyback converter. This modeling approach is illustrated in Fig. 5, where the voltage controller provides the reference to a dependent current source (the current-loop), which imposes the leakage current at the output port of the flyback converter. In this case the current source has a gain $\frac{1-d}{n}$ calculated from equation (10), where $i_m=i_{\mathit{ref}}$ due to the action of the current controller.

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Fig. 5

Equivalent scheme of the DC-link and current-loop

Using the previous model is obtained the differential equation governing the DC-link voltage, given in (21), which is transformed to the Laplace domain as given in (22).

21

$$\begin{array}{cc}\hfill C_{\mathit{dc}}·\frac{d{v}_{\mathit{dc}}}{\mathit{dt}}=i_{C_{\mathit{dc}}}=& \frac{1-d}{n}·i_{\mathit{ref}}-i_{\mathit{dc}}\hfill \end{array}$$

22

$$\begin{array}{cc}\hfill v_{\mathit{dc}}=& \frac{1-d}{n·C_{\mathit{dc}}·s}·i_{\mathit{ref}}-\frac{1}{C_{\mathit{dc}}·s}·i_{\mathit{dc}}\hfill \end{array}$$Figure 5 also shows the proposed control loop for the DC-link voltage, where the equivalent model including the current loop is also present. The voltage controller is a PI structure, where the parameters must be adapted.

The DC-link voltage is defined in agreement with the ratings of the DC-link capacitor and inverter, hence the reference value $v_{\mathit{ref}}$ is always constant. Instead, the perturbations of the system occur in the current requested by the inverter ($i_{\mathit{dc}}$), thus the voltage controller must be designed to account for those perturbations. Based on the previous discussion, the transfer function between the DC-link voltage $v_{\mathit{dc}}$ and the inverter current $i_{\mathit{dc}}$ is:

23

$$\begin{array}{c}\hfill \frac{v_{\mathit{dc}}}{i_{\mathit{dc}}}=G_{\mathit{VL}}=\frac{\frac{-s}{C_{\mathit{dc}}}}{s^2+\frac{1-d}{n·C_{\mathit{dc}}}·k_p·s+\frac{1-d}{n·C_{\mathit{dc}}}·k_i}\end{array}$$The main problem of designing the PI parameters concerns the variation of the previous transfer function due to changes on the duty cycle. Therefore, the transfer function given in (23) is modified to isolate the controller parameters from the duty cycle, this my enclosing in two normalized parameters ${\alpha }_p$ and ${\alpha }_i$ both the PI parameters and the duty cycle. Both ${\alpha }_p$ and ${\alpha }_i$ are defined in equation (24). This strategy leads to the constant-parameters transfer function given in (25), which will be used to design the voltage controller. Then, the adaptive $k_p$ and $k_i$ values are extracted from ${\alpha }_p$ and ${\alpha }_i$ by reversing expression (24) using the value of the duty cycle present in the experimental platform at any moment, thus adapting $k_p$ and $k_i$ to any operation condition.

24

$${\alpha }_p=\frac{1-d}{n}·k_p\wedge {\alpha }_i=\frac{1-d}{n}·k_i$$

25

$$\begin{array}{cc}\hfill G_{\mathit{VL}}=& \frac{\frac{-s}{C_{\mathit{dc}}}}{s^2+\frac{{\alpha }_p}{C_{\mathit{dc}}}·s+\frac{{\alpha }_i}{C_{\mathit{dc}}}}\hfill \end{array}$$The strongest change on the DC-link current is modeled as a step-change with a magnitude $I_{\mathit{max}}$, which in the Laplace domain is expressed as $i_{\mathit{dc}}=\frac{I_{\mathit{max}}}{s}$. Therefore, the dynamic behavior of the DC-link voltage is obtained by multiplying such a $i_{\mathit{dc}}$ function by $G_{\mathit{VL}}$:

26

$$\begin{array}{c}\hfill v_{\mathit{dc}}=\frac{\frac{-s}{C_{\mathit{dc}}}}{s^2+\frac{{\alpha }_p}{C_{\mathit{dc}}}·s+\frac{{\alpha }_i}{C_{\mathit{dc}}}}·\frac{I_{\mathit{max}}}{s}\end{array}$$Contrasting the denominator of that expression with the canonical second-order function ($s^2+2·\rho ·{\omega }_n·s+{\omega }_n^2$), it is observed that $2·\rho ·{\omega }_n=\frac{{\alpha }_p}{C_{\mathit{dc}}}$ and ${\omega }_n^2=\frac{{\alpha }_i}{C_{\mathit{dc}}}$. The controller is designed to impose a desired damping ratio $\rho$, this depending on the desired balance between overshoot and rising time. In this way, the ${\alpha }_p$ parameter is calculated as given in (27). Finally, both ${\alpha }_p$ and ${\alpha }_i$ are obtained by solving simultaneously (26) and (27) for the desired damping ratio and maximum overshoot, i.e. $max\left(v_{\mathit{dc}}\right)-MO=0$. This solution can be calculated using numerical methods like Newton–Raphson, genetic algorithm, particle swarm optimization, etc.

27

$$\begin{array}{c}\hfill {\alpha }_p=2·\rho ·\sqrt{{\alpha }_i·C_{\mathit{dc}}}\end{array}$$Then, the voltage controller parameters $k_p$ and $k_i$ are adapted, in real time, using the calculated ${\alpha }_p$ and ${\alpha }_i$ values and the instantaneous duty cycle; those adaptive equations are calculated from (24), as follows:

28

$$\begin{array}{c}\hfill k_p=\frac{{\alpha }_p·n}{1-d}\wedge k_i=\frac{{\alpha }_i·n}{1-d}\end{array}$$Figure  6 shows the block diagram of the adaptive control structure. The control system requires the measurement of the DC-link voltage and both the fuel cell current and voltage; and the control system provides the duty cycle for the PWM circuit driving the MOSFETs. The first part corresponds to the adaptive current controller, which estimates in real time the magnetizing current $i_m$ using equation (20), where the static gain $G_m$ is given in (29). The current controller also calculates the adaptive gain $k_c$ using equation (19), where the static gain $G_{\mathit{kc}}$ is given in (30). Finally, the current controller generates the duty cycle by multiplying $k_c$ by the error between the estimated magnetizing current and the current reference $i_{\mathit{ref}}$ generated by the adaptive voltage controller.

29

$$\begin{array}{c}\hfill G_m=n+\frac{L_k}{n·L_m}\end{array}$$

30

$$\begin{array}{c}\hfill G_{\mathit{kc}}=n·L_m+\frac{L_k}{n}\end{array}$$

[See PDF for image]

Fig. 6

Block diagram of the adaptive control structure

The second part of the block diagram corresponds to the adaptive voltage controller, which calculates the adaptive parameters $k_p$ and $k_i$, in real time, using expression (28). Then, both parameters are used to implement an adaptive PI structure to process the voltage error, thus generating the $i_{\mathit{ref}}$ signal that ensures $v_{\mathit{dc}}=v_{\mathit{ref}}$ limiting the DC-link voltage up to the maximum overshoot MO, and at the same time, imposing the desired cut-off frequency ${\omega }_c$ for the current.

Calculation of the Controllers Parameters

The parameters of the control system must be calculated for the TMDSSOLARUINVKIT microinverter (Bhardwaj and Choudhury 2017), which has the electrical parameters reported in Table 1. Such a table includes the desired DC-link voltage ($v_{\mathit{ref}}=120V$), and the maximum perturbation in the DC-link is considered equal to the 50 % of the maximum power that can be provided by the fuel cell. Since the DC-link voltage is 120 V, such a perturbation corresponds to steps of $0.415A$ in the DC-link current. For this design it is defined an acceptable maximum deviation of 10 % from the desired DC-link voltage, even if the inverter of the experimental platform supports a larger deviation, but this value provides a safe margin. Finally, the control system is designed to impose a maximum current derivative of $20A/ms$ to the fuel cell, which corresponds to a change from 0 % to d100 % of the rated power in a half of a millisecond. This maximum derivative is defined to ensure a safe operation of the fuel cell based on the experiments reported in Ramos-Paja et al. (2010), but any other value can be defined depending on the particular fuel cell system.

Table 1. Electrical parameters of the first stage

Parameter	Value
$L_m$	$20\mu H$
$L_k$	$4\mu H$
n	5.4
$C_{\mathit{dc}}$	$103\mu F$
$v_{\mathit{ref}}$	$120V$
Maximum perturbation (power)	$50\%$ ($50W$)
Equivalent $I_{\mathit{max}}$	$0.415A$
Acceptable MO	$10\%$ ($12V$)
Maximum current derivative of the fuel cell ($m_{\mathit{fc}}$)	$20A/ms$

The calculation of $k_c$ is performed in real-time using expression (19), hence it requires the measurement of both the fuel cell and the DC-link voltages. In addition, the desired cut-off frequency ${\omega }_c$ must be defined to ensure the maximum current derivative of the fuel cell. From expression (18) it is observed that the current controller filters the reference current $i_{\mathit{ref}}$ to define the magnetizing current $i_m$, which defines the fuel cell current as given in expression (14).

Considering a step change of the reference current (i.e. the fastest change possible), the resulting magnetizing current is given in (31), where $\mathrm{\Delta }{I}_{m,max}$ is the step amplitude. Applying the inverse Laplace transformation leads to the time-domain waveform given in (32).

31

$$i_m=\frac{{\omega }_c}{s+{\omega }_c}·\frac{\mathrm{\Delta }{I}_{m,max}}{s}$$

32

$$i_m=\mathrm{\Delta }{I}_{m,max}·\left(1,-,e^{-t·{\omega }_c}\right)$$The average slope $m_{i_m}$ of the waveform given in (32) is calculated as the ratio between the half of the maximum current change ($\mathrm{\Delta }{I}_{m,max}/2$) and the time required to reach such a current ($t_m$):

33

$$\begin{array}{c}\hfill m_{i_m}=\frac{\mathrm{\Delta }{I}_{m,max}/2}{t_m}\end{array}$$Solving equation (32) for $i_m=\mathrm{\Delta }{I}_{m,max}/2$ results in $t_m=ln\left(2\right)/{\omega }_c$. Moreover, taking into account the relation between the fuel cell and magnetizing currents given in (14), the maximum change in the fuel cell current due to the maximum change in magnetizing current is $\mathrm{\Delta }{I}_{\mathit{fc}}=\mathrm{\Delta }{I}_{m,max}·d$, and the maximum derivative of the fuel cell current ($m_{\mathit{fc}}$) is calculated as $m_{\mathit{fc}}=m_{i_m}·d$. Then, replacing previous $t_m$, $\mathrm{\Delta }{I}_{\mathit{fc}}$ and $m_{\mathit{fc}}$ values into (33) results in the following expression for ${\omega }_c$:

34

$$\begin{array}{c}\hfill {\omega }_c=\frac{2·ln\left(2\right)·m_{\mathit{fc}}}{\mathrm{\Delta }{I}_{\mathit{fc}}}\end{array}$$For the experimental platform, the calculation of ${\omega }_c$ is performed by considering $m_{\mathit{fc}}=20A/ms$ (reported in Table 1) and a maximum change $\mathrm{\Delta }{I}_{\mathit{fc}}=10A$, i.e. from 0 to 100 % of the fuel cell current range. Then, using expression (34), the cut-off frequency for the experimental platform is ${\omega }_c=2.7krad/s$.

The calculation of the voltage loop parameters considers a maximum voltage deviation $MO=12V$ (reported in Table 1) and a damping ratio $\rho =0.707$ to provide a tradeoff between settling time and overshoot. Solving simultaneously expressions (26) and (27) for those $\rho$ and MO values results in the voltage controller parameters ${\alpha }_i=11.5A/\left(V,·,s\right)$ and ${\alpha }_p=0.0487A/V$.

The control system and power stage were implemented in the power electronics simulator PSIM to test the system safety before the experimental implementation. Figure 7(a) confirms the correct regulation of the DC-link voltage for a 50 % perturbation on the fuel cell power (50 W), where the DC-link voltage is constrained within the 10 % band. This simulation confirms the correct operation of the adaptive voltage controller.

[See PDF for image]

Fig. 7

Simulation of a the DC-link voltage regulation, b derivative limitation on the fuel cell current

The second simulation, reported in Fig. 7(b), considers a step change in the current reference ($i_{\mathit{ref}}$) to test the derivative limitation of the fuel cell current. The step current ($\mathrm{\Delta }{i}_{\mathit{ref}}$) has an amplitude of 16.6 A, which corresponds to a step change of 10 A in the fuel cell current as calculated from equation (14). The simulation confirms that the current derivative in the fuel cell is lower than the limit defined in Table 1, which confirms the correct operation of the adaptive current controller. It must be noted that the fuel cell current does change by 10 A since the voltage loop acts on the current reference to avoid a large change on the DC-link voltage. In any case, the current reference exhibits an instantaneous change at 120 ms, which enables to perform the desired test. Finally, the simulation results confirm the correct operation of the adaptive control system.

A final simulation was conducted to compare the proposed adaptive control system with a classical control approach. The classical control system consist in a cascade connection, similar to the one reported in Fig. 5, but considering static parameters for both the current and voltage loops, i.e. non-adaptive $k_c$, $k_p$, and $k_i$. The value of the parameters for the classical control system are calculated for the same $L_m$, $L_k$, n, $C_{\mathit{dc}}$, $v_{\mathit{ref}}$ values reported in Table 1, also considering the average fuel cell voltage $⟨v_{\mathit{FC}}⟩=14.5V$. Finally, it is adopted the same cut-off frequency ${\omega }_c=2.7krad/s$ previously calculated to define the maximum derivative of the fuel cell current ($m_{\mathit{fc}}$ in Table 1). From those parameters, the static estimation gain for the magnetizing current is calculated from (20) as $i_m=1.66·i_{\mathit{FC}}$, and the static current-loop gain is calculated from (19) as $k_{c,static}=1.5\times {10}^{-3}{A}^{-1}$; those static gains form the classical current loop. The parameters of the classical voltage loop are calculated from the same normalized values ${\alpha }_i=11.5A/\left(V,·,s\right)$ and ${\alpha }_p=0.0487A/V$ using expressions (12) and (28), which results in the static voltage-loop gains $k_{i,static}=1.56\times {10}^{2}A/\left(V,·,s\right)$ and $k_{p,static}=6.6\times {10}^{-1}A/V$. Then, the classical control system is implemented in PSIM, and a 50 % power perturbation is introduced (similar to Fig. 7(a)).

Figure  8 shows the performance comparison between the adaptive (proposed) and static (classical) control systems, where the adaptive control system ensured that the DC-link voltage is constrained within the 10 % band. Instead, the static (classical) controller provides a DC-link outside the acceptable band given in Table 1, thus not ensuring the required behavior, i.e. the operation below the safe band could produce a shut-down of the load.

[See PDF for image]

Fig. 8

Comparison of the DC-link voltage regulation using the adaptive and classical controllers

In fact, the simulation shows that both adaptive and static controllers have the same steady-state behavior before the power perturbation, this because the static gains of the classical controller were calculated for that operation condition. However, after the power perturbation, the adaptive controller is able to adjust the gains of both the current and voltage loops to ensure the desired behavior; instead, the static gains of the classical controller are fixed, thus making it impossible to adapt to the new operating condition, which results in a poor performance. Finally, the classical (static) control structure is slower than the proposed (adaptive) solution, which is caused by the fixed gains designed for a particular operating point. This can be quantified by calculating the relative error of both the adaptive $v_{\mathit{dc}}$ and the static $v_{\mathit{dc}}$ with respect to the reference value $v_{\mathit{ref}}$, which results in 1.76 % for the proposed solution and 5.67 % for the classical approach. Therefore, in the time interval of the simulation, the classical solution introduces an error three times higher than the one introduced by the proposed control system.

In conclusion, this simulation put into evidence the advantages of the proposed solution over a classical approach: the proposed solution is able to ensure the desired (safe) performance in any feasible fuel cell and load operating conditions; instead, the classical (static) solution is usually designed at a particular operating condition, hence it is not able to ensure the desired performance when the load power changes.

Comparison of Control Systems Applied to Generation Systems Based on Fuel Cells

Several control systems have been proposed to be applied in converters that interface fuel cell emulators with AC loads, those controllers respond to mitigate the problems arisen by each application. To discriminate the several proposed solutions, the next table compares the global stability guaranteed, type of control, protection, type of validation, validation scenarios, cost, and efficiency.

Table 2. Characteristics comparison of several solutions applied to generation systems based on PEM fuel cells

Refe-rences	Global stability guaranteed	Type of control	Protection of the fuel cell	Experimental validation	Validation scenarios	Cost	Efficiency [%]
Proposed solution	Yes	Fuel cell current and DC voltage adaptive controllers	Oxygen starvation	Yes	Variations in different loads	Medium	92-95
Li et al. (2005)	No	Constant voltage and constant fuel utilization control	N/R	No	Variations in one load	Low	N/R
Matraji et al. (2013)	Yes	Sliding mode controller of the oxygen excess ratio	Oxygen starvation	Yes	Variations in one load	High	N/R
Li et al. (2019)	Yes	Extended-state-observer-based cascade controller	Oxygen starvation	Yes	Variations in one load	High	N/R
Papadimitriou et al. (2016)	No	Fuzzy logic controller	N/R	Yes	Variations in one load	Medium	N/R

In Table 2, the comparison in columns “Global stability guaranteed” and “Type of control” shows that some works are focused on the design of controllers that guarantee the global stability of the controlled system. In the case of Matraji et al. (2013) and Li et al. (2019) the control has been applied to variables in the PEM fuel cell. Those works implements adaptive and robust controllers over the commercial TMDSSOLARUINVKIT microinverter, taken advantage over the functional converter and guaranteeing the global stability. Oxygen starvation elimination is the focus of some publications, column “Protection of the fuel cell” discriminates which works are developed to protect the PEM fuel cell. Although, most of the works validates their solutions using experimental benches, only the solution proposed here is validated during variations of linear or resistive loads, nonlinear or current and power programed loads, and nonlinear or commercial LEDs. Most of the revised works validate their proposed solution facing variations of the same type of load. In order to compare the cost, we qualify those works that use hydrogen as high-cost systems, those that use emulators as medium-cost systems and those that just simulate mathematical models, as low-cost systems. The main concern with solutions that are validated through simulation is the uncertainty of correct operation during the experimental validation. Also, as it is in column “Efficiency [%]” most of the papers do not report (N/R) the power efficiency during experimental validations; in this work, the efficiency of the first stage converter is reported in Table 2.

Implementation and Experimental Verification

The fuel cell power system formed by the emulator, the microinverter and the load, was experimentally implemented. Figure 9(a) shows the fuel cell emulator formed by the KEPCO BOP-50-20 L and the Speedgoat PC910 industrial computer, which operates as explained in Sect. 2. Moreover, figure 9(a) also shows a non-linear AC load formed by 20 led bulbs of 7 W each, which is used to test the system’s performance at different load conditions. The figure also depicts the Texas Instruments TMDSSOLARUINVKIT microinverter interfacing both the fuel cell emulator and the AC load, where a laptop is used to program the proposed control system. Finally, two oscilloscopes (RTE1204 and MDO3024) are used to register the current, voltage and power of the fuel cell emulator, and both the DC and AC sides of the microinverter. Figure 9(b) shows a detail of the connections in the TMDSSOLARUINVKIT platform, where the C2000 microcontroller is used to implement the adaptive first-stage controller proposed in Sect. 3. This figure also shows the fuel cell and load connections.

[See PDF for image]

Fig. 9

Test bench of the fuel cell generation system

Four test were carried out to validate the performance of the proposed solution. The first test evaluates the voltage regulation under fast current transients: the DC-link voltage is regulated at the desired 120 V, but the DC-link current is perturbed with a step change as observed in Fig. 10(a), where the current starts at 200 mA, then it is increased to 500 mA; this perturbation was performed using a non-linear load. Such a perturbation causes a transient in the DC-link voltage, which stabilizes after 54.8 ms with a maximum overshoot of 8 V (6.7 %). After the transient, the DC-link voltage remains at 120 V, thus confirming the correct operation of the proposed voltage controller. Figure 10(a) also shows the increment in the power requested by the inverter, from 24 to 60 W. Figure 10(b) shows the experimental signals at the fuel cell side, where the fuel cell current increases from 1.63 to 4.61 A with a stabilization time of 148 ms and an overshoot of 7.4 %. The fuel cell voltage changes from 15.5 to 14.14 V due to the $V_{\mathit{FC}}-I_{\mathit{FC}}$ characteristic curve, which increases the fuel cell power from 25.26 to 65.19 W. Finally, from the fuel cell and DC-link power measurement reported in Fig. 10, it is calculated that the controlled first-stage exhibits an efficiency of 95 % at 24 W and 92 % at 60 W.

[See PDF for image]

Fig. 10

DC-link voltage regulation for step changes on the power requested by the inverter

A second test was conducted by changing the current of a resistive (linear) AC load connected to the inverter: the AC load current is first increased in 60 % (from 1.19 to 1.9 A as observed in Fig. 11), which causes an increment in the ripple of the DC-link voltage, but the voltage controller ensures a correct regulation at the desired average value (120 V). The increment in the load power resulted in the elevation of the power provided by the fuel cell, but the first stage controller successfully regulates the microinverter to provide a safe operation of the second stage. Finally, after 6.5 s the AC load current is decreased to the original value, and again the DC-link voltage is correctly regulated. Therefore, this experimental data shows that the DC-link voltage is always stable and regulated around the desired value (120 V), thus demonstrating the correct adaptation of the control system to different AC load conditions.

[See PDF for image]

Fig. 11

DC-link regulation for changes on the AC load power. DC-link voltage (yellow) regulated at 120 V and AC load current (green)

A third experiment was designed to demonstrate the capability of the proposed solution to meet the requirements of rural areas in Colombia. This test uses the monthly-average daily load profile of the Vigia del Fuerte city (Antioquia - Colombia), which is located in the coordinates $6^{\circ }$35’22” North - ${76}^{\circ }$53’59” West (IPSE et al. 2023). The maximum power of the load profile is 25 kW, which must be scaled to 100 W to be in agreement with the maximum power of the fuel cell. The load profile was programmed into an electronic (non-linear) load to apply step-type changes in the DC-link power every 6 s to represent an hour of the load profile, thus providing a scaled-down load profile to test the small fuel cell power system.

Figure 12(a) shows that the programmed load profile starts at 12 W, and the load power is gradually increased to reach the maximum value (80.4 W); this behavior represents the consumption profile reaching night-time conditions in Vigia del Fuerte. Then, the load profile is decreased in a short time, which represents the consumption in the early hours of the day. The experimental data confirms the correct regulation of the DC-link voltage (120 V) provided by the first-stage controller, thus ensuring a safe operation of the second stage of the microinverter. Figure 12(b) presents the fuel cell voltage, current and power: as expected the fuel cell power has the same form of the load profile, but with higher values to account for the microinverter efficiency; in this experiment the efficiency is between 80 and 89 %. It is noted that both the fuel cell current and voltage change with the power requested, which is expected since the current controller only limits the current derivative. Therefore, this experiment confirms the correct operation of the fuel cell power system.

[See PDF for image]

Fig. 12

Example of operation with a load profile of an isolated area

A final experiment was conducted to evaluate the controller performance with non-linear loads that produce harmonic contents. The experiment uses a commercial non-linear AC load formed by 20 LED bulbs (SYLVANIA 2024), each consuming 7 W, which require 100 V RMS; therefore, the DC-link voltage is regulated at 150 V. Fig. 13 shows the AC current requested by the load, which has harmonic content due to the non-linear operation of the LED bulbs. Such a harmonic content is transferred to the DC-link current by means of the inverter; this is observed in the DC-link power, which exhibits discontinuities. However, despite such non-ideal waveforms, the first-stage controller successfully regulates the DC-link voltage to the desired value (150 V). In the middle of the test, an additional LED bulb was turned on, thus increasing the load current from 0.4 to 0.47 A RMS (increasing the power from 61.4 to 69.66 W), and the experimental data confirms the correct regulation of the DC-link voltage, thus ensuring a safe operation for the second stage even under fast changes of non-linear loads.

[See PDF for image]

Fig. 13

Operation feeding LED bulbs (non-linear load): DC-link voltage (blue) regulated to 150 V, AC load current (green) and DC-link power (red)

In conclusion, the proposed solution exhibits satisfactory performances with resistive (linear) loads, current and power programmed (non-linear) loads, and with commercial LEDs as (non-linear) loads.

Conclusions

A fuel cell generation system to power stand-alone linear and nonlinear AC loads was presented in this paper, which is based on two adaptive control loops. Several conclusions are derived from the work presented in this paper. First, the integration of commercial platforms, with self-developed platforms, and advance technical knowledge accelerates the design of fuel cell solutions for research and social development. Second, fuel cell emulators are confirmed as the way to carry out multiple research tests on fuel cells, also avoiding the waste of hydrogen and the degradation of a costly energy source; in this case the H-100 PEM fuel cell (FCS-C100). Third, advance control systems can be implemented in open power converter platforms, thus improving the operation of fuel cell generation systems, and guarantying the electric power supply to remote areas with the desired restrictions. In this case, a first loop adaptively controls the fuel cell current, and limits its slew-rate, to avoid the oxygen starvation phenomenon; a second loop adaptively controls the voltage of the output capacitor and consequently regulates the DC-link voltage, which provides a safe operation for the stand-alone inverter.

Power electronics laboratories allow to test the system performance with real electric profiles, which increase the knowledge over those electric systems and allow to test and compare several solutions. In this case, one experiment was carried out to test the proposed solution meeting the requirements of rural areas in Colombia using the monthly-average daily load profile of the Vigia del fuerte city in the province of Antioquia ($6^{\circ }$35’22” North - ${76}^{\circ }$53’59” West).

Finally, experimental tests include all the physical phenomena present in the analyzed devices for the specific environment, that situation required to solve all the implementation problems in the fuel cell generation system. From the last conclusion, it is observed that reproduce the experimental tests developed in this paper, over a real fuel cell, will waste hydrogen, degrade the real fuel cell, but will increase the knowledge over the power system and their solutions. It is worth noting that the four experimental tests reported in this paper confirm the correct operation of the proposed first-stage controller, thus ensuring a safe operation of both the fuel cell and the second stage of the microinverter.

Acknowledgements

This research was funded by Minciencias, Universidad Nacional de Colombia, Universidad del Valle, and Instituto Tecnológico Metropolitano under the research project "Dimensionamiento, planeación y control de sistemas eléctricos basados en fuentes renovables no convencionales, sistemas de almacenamiento y pilas de combustible para incrementar el acceso y la seguridad energética de poblaciones colombianas", (Minciencias code 70386), which belongs to the research program "Estrategias para el desarrollo de sistemas energéticos sostenibles, confiables, eficientes y accesibles para el futuro de Colombia", (Minciencias code 1150-852-70378, Hermes code 46771).

Funding

Open Access funding provided by Colombia Consortium.

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