###### Abstract  
Three microbial fuel cells (MFCs) with different volumes (S-, M-, and L-MFCs) were operated at individual flow (phase I) and serially connected flow modes (phase II for forward flow and phase III for reverse flow) at the same flow rate. The three MFCs showed different voltages and power generation according to the hydraulic and electric connection modes. The M- and L-MFCs showed a similar voltage at hydraulic series-forward flow mode (phase II). The principal component analysis (PCA) and Pearson correlation showed that voltage generation and power density were affected by volume, hydraulic retention time (HRT), chemical oxygen demand (COD) loading rate, removed COD, and internal resistances. When they were connected electrically in series and parallel, the stack showed relatively lower voltage loss (28-30%) compared to the voltage losses of the other stacks (43-94%). These results suggest an easy way to connect MFCs with different volumes can be a new option to avoid voltage reversal and minimize energy loss. hydraulic connection; electric connection; series; parallel; stack; voltage loss +
Footnote †: 2021: 11, 1019. [[https://doi.org/10.3390/app11031019](https://doi.org/10.3390/app11031019)]([https://doi.org/10.3390/app11031019](https://doi.org/10.3390/app11031019))  
cell voltage and MPDs in a submerged-exchangeable MFC stack system consisting of six MFCs [14]. Several approaches have been used to prevent voltage imbalance and reversal, and many methods can be used to prevent voltage reversal. First, the active bypass method can stop voltage reversal by bypassing the excessive current and voltage from superior cells to inferior cells and equalizes the voltage in a stacked system [15]. A serially stacked MFC stack using the cell balance system maintains the cell voltage of individual MFCs [16; 17]. On the other hand, this method is not suitable for small-scale MFCs and requires complicated systems such as voltage controllers, magnets, and switches [9; 15]. Second, the passive bypass method using semiconductor diodes can equalize the voltage and control voltage reversal in a stacked system [15]. This method cannot prevent voltage reversal completely, and the energy loss of the diodes can be high [9]. Finally, the charged and discharged method can avoid voltage reversal and minimize the energy loss in a stack system [18]. An MFC stack using a capacitor produced a stable MPD regardless of the variable performance of individual MFCs [18]. On the other hand, this method also requires complicated systems, such as a capacitor, controller, and switches. Therefore, a novel and more straightforward method to overcome the voltage imbalance and voltage reversal needed for practical applications. The electricity production of an MFC stack system is affected by the electric connection method (in series and parallel), hydraulic flow modes (in series and parallel), reactor configuration, and operating conditions [19]. In particular, the parallel electrode connection system in hydraulically series flow mode achieved the highest MPD of 420 mW/m\({}^{2}\) (12.8 W/m\({}^{3}\)) [19]. Therefore, the hydraulic flow modes can be a significant issue for the practical applications of a stacked MFC system. The novel MFC stack consisted of four units operating in hydraulic parallel flow mode showed a uniform power generation for all individual MFCs [6]. However, in the case of hydraulic parallel flow mode considerable cost may arise due to the large number of inflow pumps for fuel supply. In contrast, in the case of hydraulic series flow mode, a voltage imbalance can occur because the chemical oxygen demand (COD) loading rate and COD removed are different according to the position of each MFC unit in an MFC stack. The electricity generation of an MFC is also affected by the COD loading rate (CLR) and COD removed. In particular, an MFC using a pure culture was reported to show good linear relationships between power generation and CLR when using an identical influent source [20].