Experimental study on current distribution in parallel-connected solid oxide fuel cell strings

Abstract

To increase the power generated by solid oxide fuel cells (SOFCs), multiple cells have to be connected into a stack. Nonuniformity of cell performance is a worldwide concern in the practical application of stack, which is known to be unavoidable and caused by manufacturing and operating conditions. However, the effect of such nonuniformity on SOFCs that are connected in parallel has not been discussed in detail so far. This paper provides detailed experimental data on the current distribution within a stack with nonuniform cells in parallel connection, based on the basics of electricity and electrochemistry. Particular phenomena found in such a parallel system are the “self-discharge effect” in standby mode and the “capacity-proportional-load sharing effect” under normal operating conditions. It is believed that the experimental method and results proposed in this paper can be applied to other types of fuel cell or even other energy systems.

Graphical abstract

Keywords

solid oxide fuel cells (SOFCs) / stack / nonuniformity / parallel connection / current distribution

1 Introduction

Solid oxide fuel cell (SOFC), showing outstanding characteristics of environmental benignity, no precious metals involved, high electrical efficiency and fuel flexibility compared to conventional energy generation systems, has drawn more and more attention in recent years [1–4]. Additionally, high quality heat produced by SOFC as a by-product is able to be utilized for cogeneration and increase the total efficiency to more than 80% [5,6]. These advantages make an SOFC system suitable for wide-range of applications such as residential power systems, auxiliary power units, power plants, and electric vehicles [7–10]. However, it is usually not possible for a single SOFC to generate sufficient power applicable to real-world applications. Therefore, it is of great significance to investigate the design and fabrication of stacks. Table S1 in Electronic Supplementary Material has summarized some recent publications related to SOFC stacks [11–18].

A typical SOFC stack involves a quantity of cells or repeating units [19–23]. Generally, there are two common methods to connect cells together: serially or in parallel [24–27]. The serial connection of cells can increase the output voltage to a user-friendly value and minimize the power losses caused by connecting wires. But the whole serial stack will be severely impacted once one or more cells failed. In comparison, connecting cells in parallel is able to enhance current to some required value and increase the reliability of stack. However, more cells involved in a parallel stack also goes along with a higher connection loss for system due to the higher current. To combine the strengths of the two connections, Sandhu et al. [6] suggested mixed series and parallel configurations, which could meet the requirements both on output current/voltage and safety during operation.

It is generally considered optimal to have identical cells connected in a stack. In practice, however, not all the cells behave the same. There are many likely causes for cells to be “nonuniform,” including initial compositional inhomogeneities, operating parameters maldistributions [28–30], etc. The voltage distribution in serial stack with nonuniform cells and its impact on stack failure have been investigated (Table S1). For instance, Virkar et al. [31,32] developed a model for serial stacks in which one of the cells has a higher resistance than the others and simulation results indicated that such kinds of cells would operate under lower voltages and even a negative voltage, resulting in stack degradation. Negative voltage was the case that a voltage drop across the cell became greater than its open circuit voltage (OCV). Although the output power of parallel configuration has been proved higher than that of serial connection when the internal resistance of one cell increased [33], to the best of the authors’ knowledge, the number of publications on current distribution in a parallel stack is low. Especially, it is of great interest to know if the stack will fail when the cells are nonuniform.

In this paper, the influence of cell nonuniformity on current distribution within different parallel configurations and under different working conditions is discussed. Novel flat-chip reversible cell strings with different current–voltage characteristics, including the important descriptor—OCV, are adopted. To overcome the problem of simultaneously and independently acquire the current flowing through each string in the stack, the same shunt is connected in series with each string and the voltage over which is recorded by an advanced electrochemical workstation with multi-channel auxiliary electrometer. The measuring setup is first proved to have little impact on measurements. Then, the effects of operation mode, the number and power generating capacity of cell string on current distribution within parallel configuration are described in detail. Finally, two special but common situations, oxygen deficit and cell leakage, are surveyed. This paper provides the basis for future SOFC stack development.

2 Experimental

2.1 Flat-chip SOFC fabrication

Anode-supported flat-chip SOFC cells made by Zhejiang Zhentai Energy Technology Co., Ltd. were used for the fabrication of the stack [34–36]. Each cell has chip geometry with symmetric double-sided cathodes, showing good thermal and mechanical properties. More importantly, such kind of cell can be reversibly operated in fuel cell and electrolysis modes. The material for anode was a porous cermet comprised of nickel and yttria-stabilized zirconia (Ni/YSZ), while the electrolyte and cathode were dense YSZ and a composite of silver and ceria (Ag/SDC). The thicknesses of anode, cathode and electrolyte were 1.2 mm,10 μm, and 10 μm, respectively. Silver paste and wires were utilized as current collectors. The active area was 2 × (25 mm × 50 mm). To discuss the effect of nonuniformity, different grades of cells were deliberately picked from the said company.

2.2 Stack assembly

The mixed series and parallel configuration were adopted in this research to ensure the safety of experiment. Each four cells were connected in series individually to form a single cell string and then the five cell strings were placed in one furnace. To measure the current flowing through each cell string, five 5 A/50 mV shunts were used and connected in series. Fig.1 presents a schematic diagram of the arrangement for cells, shunts, and their connection with test setup. Five thermocouples recorded the center temperature of each string separately at an interval of one minute. Specifically, each thermocouple was placed in the middle of each cell string and all thermocouples were adjusted to the same height. The furnace was heated to 670 °C. Hydrogen and air/nitrogen were introduced to the anode and cathode of the cells at a total flow rate of 800 and 4000 cm³/min, respectively.

2.3 Characterizations

The voltage over shunt, OCV, electrochemical impedance spectroscopy (EIS), and linear sweep voltammetry (LSV) curves were conducted using a Gamry Reference 3000AE electrochemical workstation, which featured eight additional electrometers and was ideal for stack testing [37,38]. Distribution of relaxation time (DRT) was calculated from the EIS data by employing the DRTools [39], and the regularization parameter is 10⁻³. Before performing DRT analysis, Kramer–Kronig tests were carried out to ensure the quality of data. The goodness of fit {\chi }^2 value was within 10⁻⁶ while the residuals of real and imaginary data were within ± 0.1% over the measured frequency range of 10 kHz to 0.1 Hz [28]. Both the constant current and constant voltage tests were evaluated by an electronic load. It is worth noting that the relative standard deviation (RSD) was used to show the uniformity of cell strings, which is expressed as

(1)\mathrm{R}\mathrm{S}\mathrm{D}=\frac{\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{（x_i-\overline{x}）}^2}{n-1}}}}{\overline{x}}\times 100\mathrm{\%},

where n is the total number of cell strings measured, x_i is the measured data, and \overline{x} is the arithmetic mean of the measured data.

3 Results and discussion

3.1 Shunt and extra cable configurations in testing parallel systems

Under ideal conditions, identical connections are expected to provide an equal additional resistance between the cell strings. A test was first conducted to determine the effect of adding shunt and extra cables into the system. As shown in Fig.2(a) and Fig.2(b), the difference in EIS and LSV curves between each cell string with and without shunt was insignificant. The increment of ohmic resistance R₀ (ΔR₀) for the five cell strings (S1–S5) was similar (Fig.2(c)) since the same shunt and cables was adopted. Besides, the increment value (~10 mΩ) was very small relative to the total impedance of cell string, which might be the reason for the little change in the performance of S1–S5 as the shunts were connected. By contrast, the increment of polarization resistance R_p (ΔR_p) oscillates around 0 with small value. This is largely associated with the process of dynamic balance between multi-physics inside the furnace. All the results suggest that shunt and extra cables has little impact on the performance of cell strings and the following string current tests are the acceptable operation.

3.2 Effect of different OCVs on cell strings in parallel configuration

When there is no direct current (DC) bias, OCV is one of the important parameters to characterize the performance of SOFC. According to the Nernst equation, the OCV value is affected by SOFC temperature and reaction gas concentration [40,41]. Although the initial quality of cell itself can be ensured through strict screen material and advanced production craft, cell status as well as temperature and gas composition distribution inside SOFC system still vary with position and time. It is difficult to guarantee only cells of the same OCV being configured together to form the parallel arrangement, especially at different aged times. Thus, it is necessary to study what would happen when the OCVs of cell strings in parallel configuration are different.

Fig.3(a) shows the OCVs of the five carefully matched cell strings of S1–S5 in a new stack. Their OCV values ranged between 4.59 and 4.73 V (Fig.3(a)), and the RSD was 0.76%. When S4 that has the highest OCV is connected in parallel with other single strings, the current in the stack can be monitored through the voltage of the shunt in series in each cell string, as shown in Fig.3(b). In general, the voltage over Shunt 4 was positive while those over Shunt 1, Shunt 2, Shunt 3, and Shunt 5 were negative. However, the absolute values of both in paired configuration were close. This could be explained by Kirchhoff’s law as shown in Eq. (2) and clockwise direction in Fig.3(e) is the detour direction as a reference.

(2)\begin{array}{rl}& \mathrm{\Delta }\mathrm{O}\mathrm{C}\mathrm{V}={\mathrm{O}\mathrm{C}\mathrm{V}}_4-{\mathrm{O}\mathrm{C}\mathrm{V}}_x=i(R_{\mathrm{S}4}+R_4+R_x+R_{\mathrm{S}x}),\\ & x=1,2,3,5,\end{array}

where ΔOCV is the OCV difference between S4 and S1, or S2, S3, and S5; OCV_x is the OCV value of cell string Sx; i is the current flowing in the closed loop; R_S4 and R_Sx are resistances of Shunt 4 and Shunt x, respectively; and R₄ and R_x are internal resistances of S4 and Sx, respectively. Since S4 has the highest OCV, it could be seen from Eq. (2) that the voltage over Shunt 4 is positive as expected in Fig.3(e). Base on the methodology as described in Section 2, the positive and negative results suggest that when S4 is connected with other cell strings, the current goes out from the cathode of S4, flows through other strings, and finally returns to the anode of S4. In contrast, the current goes into the cathode of S1, S2, S3, and S5 which would possibly consume power. That means S4 serves as cells and S1, S2, S3, and S5 are more like loads. In addition, the data show that a relatively high current flows through both strings early in the parallel operation at 300 s, then the current decreases quickly and reaches a steady state within 200 s. As expected, the current drops to zero immediately after disconnected operation at 2000 s. The calculation indicates that the current value varies as the OCV difference between paired strings (ΔOCV) changes (Fig.3(c)) and the plots of current at 300 s and 2000 s vs. ΔOCV both yields a straight line (Fig.3(d)). All the results show that when the OCV of parallel strings is different, there is a current inside the stack loop (hereafter called parallel current, i_p) and the value of current is proportional to ΔOCV of the parallel strings. In addition, the string with a relatively high OCV charges the one with a low OCV, as illustrated in Fig.3(d). “Negative” current exists in parallel configurations (Fig.3(f)).

3.3 Multiple parallel strings

Multiple parallel strings could be encountered in real-world applications. Tests having a different number of cell strings in parallel were performed. The strings in Fig.2 are connected into five configurations: S4, S4–S2, S4–S2–S3, S4–S2–S3–S1, and S4–S2–S3–S1–S5, which are designated by 1P, 2P, 3P, 4P, and 5P in Fig.4, respectively. As can be seen from Fig.4(a), the parallel current flows in each cell string, which is consistent with the result in Fig.3. But unlike the equal value in paired parallel, currents passing through different cell strings are no longer even when the number of strings is greater than two. It is worth noting that they all obey the Kirchhoff’s current law no matter how many strings are in the test. That is, the total current entering a junction is equal to the total current leaving it. In addition, the output OCV of parallel configuration is between the highest and lowest OCV of the single string, and is closer to the one which has a small impedance. Ohm’s law can partly explain this phenomenon (Fig.3(f)). Combining the OCV and current distribution results, the conclusions can be drawn that the strings with OCVs higher than the total OCV will be discharged while those having a lower OCV will become the loads; the greater the OCV difference between the single string and parallel configuration, the higher is the parallel current distributed. Although the OCV of each string changes in different aging time periods, the above rule is verified, as shown in Fig.4(b) and Fig.4(c).

EIS and DRT were conducted to explore the effect of parallel current on the performance of relatively new multiple parallel strings (t = 0 h). All the resistances obtained from Fig.4(d) and Fig.4(e) shown by scatters in Fig.4(f) decrease as more strings are connected and seem to be in inverse proportion to the number of strings in the parallel configuration. More importantly, the measured values agree well with the result calculated from the record of single strings in Fig.2(a) by using parallel-resistance formula (dashed line), which might be caused by the fact that the small OCV difference makes the parallel current small. These results suggest that reversible cells or SOFC strings with varying OCVs within a reasonable range can be parallel-connected to operate in a satisfactory manner.

3.4 Effect of different power cell strings on current distribution

Apart from OCV, another performance indicator which is frequently mentioned regarding the assembly of SOFC module is the nominal power. Fig.2(b) and Fig.5(a) demonstrate that the five new cell strings do not have exactly the same power. That is, at different cell voltages, the discharge power generating capabilities of different cell strings vary. When it is necessary to provide power to external loads, attention should also be paid to the effect of cell nonuniformity on the discharge capacity of the parallel SOFC module. A module was configured with S1, S2, S3, S4, and S5 into a 5-string system (5P) and discharged in different modes. Fig.5(c) shows the current distribution within the galvanostatic parallel module, in which the current drawing from each of the cell strings at each step of 0.5–8 A is measured by the voltage over shunt as discussed earlier. The discharge load power sharing from S1 to S5 is shown in Fig.5(e). The error between the algebraic sum of each string current and theoretical setting value is less than 0.5%. In addition, the data show that the variation of load sharing is almost in consistent with that of the power ratio determined by LSVs (Fig.5(b)). It is worth noting that the deviation for extremely low current range might be caused by the measurement accuracy of different instruments and/or the OCV difference between the strings. Compared with the constant current mode, the error between the algebraic sum of each string current and theoretical setting value under potentiostatic mode is slightly larger (< 1%), whereas the variation of load sharing is also corresponding to the actual capacity recorded by LSV.

Tab.1 compares the measured values around 3 V in different test modes, which clearly indicates that although the value of current drawn from each cell string changes with different test instruments and test conditions, the results of load sharing in the three cases are almost the same. This suggests that the common LSV method could effectively reveal the string current distribution within parallel module, and the output of cells is likely proportional to their own capacity.

3.5 Oxygen deficit

Although the previous experiments proved that cell string tended to deliver power in proportion to their capacity, the test conditions adopted were ideal where the cells were relatively new and the gas supply was excessive. It would be of interest to explore how those cell strings shared the load considering the fact that the operating conditions became deteriorate. Taking gas supply as an example, the performance of SOFC parallel module was further explored during stand-by and discharge when oxygen decreased. Nitrogen was mixed with air to gradually reduce the partial pressure of oxygen (pO₂) at cathode to 10% and 5%, as shown in Fig.6. Compared with that in the air condition (Fig.3(a)), the OCV of all the five cell strings decreases with the decrease of pO₂ (Fig.6(a)), and the distribution also changes significantly when pO₂ reaches 5% (Fig.6(b)). The RSD are 0.47% and 3.6% at pO₂ = 10% and pO₂ = 5%, respectively. According to Fig.4(a) and the insets of Fig.6(e) and Fig.6(f), the parallel current exists when there is no load, and its value is positively correlated with the OCV difference as well as the RSD value of cell strings in parallel module, which is consistent with the discussion before. Similarly, the string discharged currents were positively correlated with single string power, i.e., a string with a high-power generating capacity delivers a relatively high current. However, when the reaction gas supply is insufficient, load sharing deviates from the power ratio measured by LSV. Additionally, as pO₂ decreases, the deviation became larger (Tab.2). The reduction of available oxygen content could also be achieved through the increase of discharge current, which could also be seen from Fig.6(e) and Fig.6(f): when the current is further increased, the deviation of load sharing is greater. These results suggest that the string current still correlate positively with the string capacity in gas deficiency, but the string capacity defined by LSV could no longer be used to accurately evaluate the value of load sharing for each string. New methods need to be developed in the future.

3.6 Cell leakage

In practical application, cell leakage is one of the common faults occurring in the SOFC system. Some may wonder whether similar results would be observed with cells that leak. Multiple thermal cycles were performed to accelerate the destruction of cell strings to investigate the performance change of the five-string parallel module. During one thermal cycle, the furnace cooled from 670 °C to room temperature and then heated back at a rate of 5 °C, in which cells would suffer from the thermal stress caused by the thermal expansion coefficients mismatch of the cell components and even start to crack [42]. Figure S1 shows that hydrogen inlet pressure declines, string temperature rises, and the power of S2 drops sharply after thermal cycling, all of which demonstrate that cell leakage has occurred.

When the five strings were connected in parallel, the changes in the OCV and parallel current was first studied, as shown in Fig.7(b). In the early stage, shunt voltages were related to OCV for each single string before parallel (Fig.7(a)), where S2 and S3 with OCVs greater than that of parallel module discharged while S1, S4, and S5 acted as the role of load as already discussed. Among them, S5 had the greatest OCV difference with parallel configuration but a low parallel current, which might be caused by the oscillation of the OCV after cell leakage. Different from the ideal parallel module, the state of each cell string is relatively unstable. As can be seen in Fig.7(b), the voltage of the shunt connected in series with S2 drops significantly in the first 20 h, and even changes from positive to negative. Although the total OCV of 5P also declines, it is clear that S2 decreases more. The decrease of OCV was possibly associated with the re-oxidation of anode in cells of S2 after module leakage. The parallel OCV remained stable after 100 h.

The five-string parallel module was then discharged at a constant voltage of 2.8 V. Fig.7(c) shows that initially the load sharing of S2 is lower than that of the nominal string capacity measured by LSV. This result might be caused by the re-oxidation of S2 in the static stage. However, the current drawn from S2 increases gradually over time and after 100 h, its capacity characterized by LSV is almost restored, as shown in Tab.3. For the last 100 h, the leak of cells develops and generates a large amount of heat, which further improves the performance of S2. All the results demonstrate that when there is a certain degree of cell leakage in the parallel system, some cells are re-oxidized in standby mode, thus changing the parallel current distribution. However, re-oxidized cells are reduced during discharge operation, again achieving the load sharing result related to string capacity characterized by LSV. In other words, a certain degree of cell leakage has little impact on the load sharing behavior of the parallel module.

4 Conclusions

This paper investigated the characteristics of SOFC stacks formed by nonuniform cell strings in parallel. Primary results obtained from the experimental study emphasize that nonuniform cell strings in the parallel configuration perform differently. When there is no DC bias, the existence of “parallel current” is initially realized within the parallel module through paired-parallel tests. Such current rises to a maximum at the beginning of the parallel operation, and then reaches a stable value after several hundred seconds. In particular, the stable current flowing in the loop is shown to be a linear function of the difference in OCV between cell strings. The cell string with a lower OCV experiences “negative current.” Then, the results are proven to be applicable to a stack of multiple cell stings in a larger number. In terms of discharge operation mode, the analysis reveals that the cell strings with nonuniform power generating capacities deliver different currents when connected in parallel and the load sharing of each cell string is in proportion to their nominal capacity under normal operating conditions. In addition, although the current distribution is found to change with respect to the changes of gas supply such as oxygen deficit and cell leakage and time, a cell with a lower OCV still experiences a negative current in a standby mode while a cell of higher capacity delivers a larger current in discharge mode. Accurate modeling considering more factors is the goal in future research.

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