# Battery Efficiency and Aging Measurements for Multilevel Battery Energy Storage Systems -DC vs. 100Hz

Paul Aspalter, Markus Franta, Markus Vogelsberger, Hans Ertl

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Paul Aspalter, Markus Franta, Markus Vogelsberger, Hans Ertl. Battery Efficiency and Aging Measurements for Multilevel Battery Energy Storage Systems -DC vs. 100Hz. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0051. hal-05077118

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# Battery Efficiency and Aging Measurements for Multilevel Battery Energy Storage Systems – DC vs. 100Hz

Paul Aspalter, Markus Franta, Markus Vogelsberger, Hans Ertl

TU Wien, Inst. of Energy Systems & Electrical Drives

Gusshausstraße 27

Vienna, Austria

E-Mail: paul.aspalter@tuwien.ac.at

URL: https://www.tuwien.at/en/etit/esea

***Index Terms***—Battery impedance measurements, Energy Storage, Efficiency, Lifetime, Multi-level systems.

***Abstract***—Batteries in single phase DC/AC converters can be subject to second harmonic currents. This work examines the difference in battery round trip efficiency due to these currents, by calculation, simulation and physical measurements with batteries. Furthermore, batteries have been aged 1000 cycles of DC and DC+AC current to show no significant difference in aging.

## I. INTRODUCTION

With the share of renewables in the energy grid constantly growing, the need for energy storage systems also increases. This requires not only hourly, daily or seasonal energy storage on a grid level, but also the provision of ancillary services like frequency regulation, voltage support or even black start capabilities [1]. That is because many renewable energy sources are interfacing with the power grid through grid following inverters, which often cannot provide such services. Battery electric storage systems (BESS) could be a promising solution for this issue [2]. However, many of the currently available BESS do not scale well for high power applications, because they are operated at a low voltage level (≤ 1500V). Many publications, e.g. [3], [5], [6] suggest BESS in the medium or even high voltage range to improve overall system efficiency. Especially modular multilevel converter (MMC) or cascaded H-bridge converters (CHB) are considered as they scale well and batteries could be directly integrated into the converter cells. In such systems, the AC/DC converter and batteries are a combined unit and offer advantages like many output voltage levels, which decreases efforts to meet grid codes, low semiconductor blocking voltages, good scalability/modularity, etc.

Notable disadvantages are a high hardware and control complexity, as well as a the issue of reliability due to the component count, as it has been addressed in previous work by the author [4].

In this paper however the focus lies in the effect of the battery current spectrum. Typical BESS only impose a DC current on the batteries while MMC or CHB systems can also have a 100Hz component, as will be explained later. In the literature it is contradictory stated that this has negative [7] or positive [8], [9] effect on the lifetime of the battery. Broader studies show, that it depends on the battery impedance spectrum [10]. In [7] it is concluded that, in order to not drastically accelerate the aging process of batteries, low frequency current components (e.g. twice mains frequency) have to be avoided. The work in [8] claims that 100Hz current components do age batteries a lot slower than pure DC currents. In [9] no negative effect of a DC current with superimposed 10% or 15% 120Hz current could be observed. For this work the results in [8], [9] are not applicable, because the current waveforms differ strongly to those relevant for this work, which will be explained later. In [11] the current waveform is the same as in this work, as it also investigates single phase DC/AC converts (e.g. uninterruptible power supply), however, it uses lead acid batteries and only determines the aging after 35 cycles. Lithium iron phosphate batteries (LFP) were tested with comparable current waveforms in [12]. Due to their chemical properties LFP-batteries are often preferred for BESS, this work however, uses lithium cobalt oxide (LCO) batteries. Second life usage of electric vehicle batteries [13], which often are LCO, would be an ideal aspiration to lessen negative impacts like rare earth metal mining.
Similar to [12], this paper therefore investigates the efficiency of a single charge and discharge cycle but for an LCO-battery instead. A single cycle is simulated with a model based on electrochemical impedance spectroscopy (EIS) data, which is then verified by measurements. Furthermore, what sets this work apart from [12] is, that in this work the batteries were tested with a high cycle count to specifically investigate the effect of a CHB application on the lifetime of the battery.

## II. BATTERY CURRENT SPECTRUM

In a symmetrical three phase system, where the voltage and current phasors are constant, the power flow is constant. If the three phase system is connected to a DC voltage source, e.g. by an inverter, only a DC current is flowing in the DC source, due to the average of the pulsed DC link currents being constant. In a single phase system, however, the power flow pulsates in a sinusoidal shape between zero and double the mean power, at double the grid frequency. Therefore, the average of the pulsed DC link currents is not constant and if this power is supplied by a DC source at constant voltage, it would be loaded with a DC current and a sinusoidal current of the same amplitude as DC current and double the grid frequency. This issue is a fundamental advantage of three-phase systems requiring no $2f_{grid}$-energy storage, if constant power is to be supplied. Single-phase systems however need $2f_{grid}$-energy storage solutions like capacitor banks or resonant circuits, if constant power is to be supplied.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Comparison of the current spectrum of the DC source. At the top the current spectrum and a three phase two level converter is shown. The bottom depicts a CHB based converter.</figcaption></figure>

Consequently, looking at two possible three phase DC/AC topologies, a typical two level converter and a CHB converter in Fig. 1, the current spectrum in the battery is different. The three-phase converter (top) shows only a DC current flowing through the battery, while the CHB tpye (bottom) shows the current spectrum typical for a single phase system. This is because, fundamentally, a CHB converter cell is a single phase DC/AC converter, as can already be seen in the topology of the converter cell itself. Even though the whole CHB BESS is a three phase system, it's batteries experience the current spectrum of a single phase system, if no additional measures are taken.

Because the aforementioned solutions to eliminate the second current harmonic in the battery, e.g. capacitor banks or resonant circuit, require space, increase costs and/or reduce lifetime of the system, it would be ideal if they are not necessary, due to the fact that battery can provide these pulsating currents. However, with this the serious questions arise of the impact of such currents on the battery efficiency and in especial on the battery life time. As mentioned in the introduction, these are the fundamental questions addressed by this work.

## III. BATTERY EFFICIENCY SIMULATION

To simulate the effects of the current waveforms and have a hypothesis about the expected result, a simulation model of the batter is necessary. Three different types of cell modeling can be distinguished. The most accurate is a electrochemical model, which simulates the chemical reaction inside the battery. As this model has a very complex structure, requires many parameters and is not suitable for large electric circuit simulations, an equivalent circuit diagram model is usually used. The least accurate model is the analytical model, where only simplified formulas are used to describe the battery [14].

### A. Applied Battery Model

<figure><img src="image_3.png" /><figcaption>Fig. 2. Extended Thevenin equivalent circuit model of a battery cell used in this paper.</figcaption></figure>

The extended Thevenin model, depicted in Fig. 2, is chosen as equivalent circuit for the battery, as it
suitable for dynamic simulations [15]. $U_{EM}$ in the model stands for the open-circuit voltage in the battery. It is determined by measuring the so called open-circuit-voltage curve. In this curve the battery is discharged with current pulses and a certain time is waited between the pulses until the cell is at rest again, where the voltage is measured. The $R_0$ resistor, the DC resistance of the cell, is responsible for the voltage drop on the cell as soon as it is loaded. Two time elements are used to model the dynamic behavior of the cell at different time instants. The first element, $R_1C_1$, describing the diffusion resistance and the diffusion capacitance, has a time constant $\tau_1$ of 1 and 10 seconds [16]. The second time element, $R_2C_2$, simulates a slightly slower effect in the cell, with a $\tau_2$ of 100 to 1000 seconds, which models the concentration polarization resistance and the concentration polarization capacitance [16]. The passive components can only be determined by EIS measurements, which are explained in the next section.

Since DC and 100Hz AC current are not correlated the following consideration can be made with the model from Fig. 2: For pure DC current the losses in the battery can be described as in Eq. (1).

$$P_{DC} = I^2 \cdot (R_0 + R_1 + R_2) \quad (1)$$

In a CHB system, as in Fig. 1, the AC component of the current has the same amplitude and its associated losses can be added to $P_{DC}$. With the assumption of $R_1 >> 1/\omega C_1$ and $R_2 >> 1/\omega C_2$ for $\omega = 200\pi rad/s$ the time elements do not create any losses and the $P_{DC+AC}$ can be simply written as in Eq. (2).

$$P_{DC+AC} = I^2 (R_0 + R_1 + R_2) + \frac{1}{2} I^2 R_0 \quad (2)$$

With Eq. (2) it is expected that the losses are higher in the battery of the CHB converter-cell. If the ratio of $R_0$ to $R_1 + R_2$ is described as $n = (R_1 + R_2)/R_0$, then the ratio of the losses can be described as in Eq. (3).

$$\frac{P_{DC+AC}}{P_{DC}} = 1 + \frac{1/2}{1 + n} \quad (3)$$

This already confirms that with a linear battery model, the losses due to the additional AC current have to be higher.

## B. Impedance Measurement

To determine the impedance spectrum, the system is excited with a periodic current or voltage signal, often in the sinusoidal form. The system reacts to a

voltage excitation with a phase-shifted current, while a current excitation generates a phase-shifted voltage. The complex impedance of the system can be calculated by analyzing the phase shift and the amplitudes of the signals [17].

By sweeping the frequency, the complex impedance is determined in multiple points and builds up a spectrum. This spectrum provides detailed information about the frequency-dependent properties of the system and is essential for understanding its dynamic behavior. As the cells are usually temperature-dependent, as indicated on the circuit elements in Fig. 2, care should be taken to ensure that the temperature is kept constant during a measurement [17].

For valid EIS measurements, linearity and time invariance must be ensured. To ensure linearity, the AC signal should be kept low, usually in the range of 5 to 20mV for LIB. In order to maintain the time invariance, the cell must come to rest again after each measurement, for which a defined time is waited [18].

EIS is used in a variety of battery research approaches. Firstly, it enables the characterization of electrochemical processes such as charge transfer and mass transport. Secondly, EIS is used to assess the SoC and state of health (SoH) of the battery, as will be done later in this work. This is important for lifetime monitoring and performance optimization. Thirdly, EIS identifies degradation mechanisms and sources of failure by revealing losses of active material or increases in internal resistance. Fourth, EIS supports the investigation and optimization of material properties of electrodes and electrolytes, which contribute to the development of improved battery materials. Finally, and as used in this paper, EIS data helps to develop and refine electrochemical models that simulate and predict the behavior of the battery under different operating conditions. In this case it is used to determine the circuit elements from Fig. 2.

Three different LIB cells from Samsung were chosen as candidates for this research. The selection is based on necessary parameters for future work, which are not described here. For two out of three types the EIS data had too big of a variance, from cell to cell, to be used for this research. Because of this the third type, summarized in Tab. I, was selected.
<table><caption>TABLE I
SPECIFICATIONS OF SELECTED BATTERY [19], [20]</caption><thead><tr><td>Parameter</td><td>Value</td><td>Unit</td></tr></thead><tbody><tr><td>Manufacturer</td><td>Samsung</td><td>-</td></tr><tr><td>Model</td><td>INR21700-30T</td><td>-</td></tr><tr><td>Nominal voltage</td><td>3.6</td><td>V</td></tr><tr><td>Permissible voltage</td><td>2.5 to 4.2</td><td>V</td></tr><tr><td>Capacity</td><td>3000 @1C</td><td>mAh</td></tr><tr><td>Rated charge current</td><td>4</td><td>A</td></tr><tr><td>Max. continuous discharge</td><td>35</td><td>A</td></tr><tr><td>Cell chemistry</td><td>lithium cobalt oxide</td><td>-</td></tr></tbody></table>

Figure 3 shows the EIS measurements of a Samsung INR21700-30T cell for different SoCs, recorded with a BTC1 by BRS Messtechnik. The cell was loaded with a sinusoidal current of an 100mA amplitude and a frequency from 0.1Hz to 1kHz, at a temperature of 30°C.

<figure><img src="image_4.png" /><figcaption>Fig. 3. EIS curves for different SoCs of a Samsung INR21700-30T battery cell as Nyquist plot. Each point of a curve has a different frequency, starting from 0.1Hz and ending at 1kHz (right to left). The imaginary part of the impedance is plotted with a negative sign as usual for battery EIS data.</figcaption></figure>

As expected, it is clearly visible in Fig. 3 that with decreasing SoC the impedance in the low frequency region increases significantly as the amount of free charge carriers in the electrolyte decreases. Furthermore, the dashed black line represents the impedance of the cell at 100Hz, for the different SoCs, as it is the relevant frequency for this work. For the simulation model, the EIS data was recorded in 5% granularity of SoC.

The circuit elements are then retrieved from the data by parameter fitting and implemented as look-up-table where the abscissa is the SoC. This is shown exemplary in Fig. 2 for $U_{EM}$. Results of the simulation can be found together with the measurement results in the later chapter.

## IV. MEASUREMENT SETUP

Figure 4 shows the measurement setup. The battery is charged or discharged with the desired current, DC or DC+AC, by a power amplifier OPA549. An analog output channel of the DAQ system sets the desired current waveform $i^*$ by output putting the target voltage of the shunt. Furthermore, four differential analog input channels of the DAQ were used to measure the battery voltage $U_{Batt}$, battery current $I_{Batt}$, battery temperature $T_{Batt}$ and temperature inside the battery safe enclosure $T_{Amb}$. Voltage and current of the battery are measured in four wire principle, where the sense leads do not conduct the load current.

<figure><img src="image_5.png" /><figcaption>Fig. 4. Schematic of the testbench.</figcaption></figure>

The DAQ system, a National Instruments USB-6259, is sampling the 16Bit ADCs with 5kS to show enough detail of the 100Hz signal component. For accuracy, the voltage and current measurement were gain and offset corrected with a calibrated Keithly DMM6500. A Python script on the notebook is logging the analog-in data of the DAQ. Additionally, it is using the current measurement to correct the $i^*$ signal of the analog output to reach the desired output current within mA accuracy.

With the testbench from Fig. 4 the battery cell is continuously cycled. Typically, a battery is charged in a controlled current - controlled voltage (CCCV) method. The charge current is kept constant, until a voltage of 4.2V is reached, from which on the cell is kept at 4.2V until the current drops below a threshold,
for the tested battery, the threshold is 100mA. Due to the OPA 549 being configured as a controlled current source, the battery is charged until a voltage of 4.2V is reached. Then the cell is discharged with the same current amplitude down to a voltage off 3V, from which it is charged again. A complete cycle consists of the charge period from 3V to 4.2V and the discharge period, where it is discharge back to 3V. This way the battery never enters the CV region during charging. While this is different to typical battery charging, the aim of this research is to investigate the battery for applications in a BESS, which would operate as power plant on the grid. In this application the system is operated in a desired load point, resulting in defined battery current.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Voltage and current of the batteries during a section of the cycle.</figcaption></figure>

Two cells are cycled, in the above described manner, with a DC current of 4A. Those measurement series will therefore, from now on be called *DC-battery*. Two additional cells are cycled with the DC current and a superimposed 100Hz current with also an amplitude of 4A (this series are called *AC-battery*). A section of the measured signals can be seen in Fig. 5.

At irregular intervals of the cycling the capacity was measured with the gold standard method by CCCV charging and CC discharging. The CCCV charge process was limited to 0.667C (2A) with a 4.2V voltage limit and 100mA cut off point. The cell is then discharged at a continuous rate of 0.667C (2A) to a cut off voltage of 2.7V. During the discharge process the current is integrated to determine the capacity of the battery as the charge extracted from the battery.

## V. RESULTS

For both methods, *DC-battery* and *AC-battery*, one cell each was aged with 1000 cycles. After that an additional control measurement series *B* was done with

two cells with close to 200 cycles each. An overview of the tested cells can be found in Tab. III. Two results can be retrieved from the conducted measurements. Firstly, the single cycle results such as round trip efficiency, average loss and temperature rise. Secondly, the change of capacity across the cycles. The first point was also simulated in Matlab Simulink with the methodology described in section III.

### A. Single cycle results

Figure 6(a) shows the battery voltages and currents for the *DC-battery* simulated and measured. For the *AC-battery*, only the average values are shown. The four cycles are synchronized at the point where it switches from charge to discharge, therefore, only one current curve is displayed. Looking at the temperature trace first, Fig. 6(b), both measured batteries have the exact same timeline, just with a different offset. This is a first indicator of higher losses and can be seen in a higher ambient temperature with the AC measurement as well. Due to the battery being in a small, roughly 4 liter, enclosure (see Fig. 4) the losses of the battery change the equilibrium point of the ambient temperature.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Battery voltage and current during a full cycle (a), simulated and measured. (b) shows the temperature during the measurements.</figcaption></figure>

Furthermore, the measured voltage curves start later and end sooner. This is due to the impedance being higher than determined for the model. One reason for this could be the higher battery temperature. While the
*DC-battery* had an average temperature of 35°C and the *AC-battery* of 38°C, the simulation model is based on 30°C data.

As described by Eq. (3) it is expected that the losses are higher in the *AC-battery*. This is confirmed by the data in Tab. II, which is the summary of the single cycle simulation and measurement from Fig. 6(a).

<table><caption>TABLE II
COMPARISON OF CYCLE ENERGY AND RELATIVE LOSSES</caption><thead><tr><td>Cycle</td><td>E-in[Wh]</td><td>E-out[Wh]</td><td>Losses[%]</td><td>Ratio</td></tr></thead><tbody><tr><td>DC sim</td><td>11.50</td><td>11.07</td><td>3.73</td><td>1.305</td></tr><tr><td>AC sim</td><td>11.32</td><td>10.77</td><td>4.87</td><td>1.305</td></tr><tr><td>DC meas</td><td>10.67</td><td>10.25</td><td>3.92</td><td>1.13</td></tr><tr><td>AC meas</td><td>10.24</td><td>9.78</td><td>4.44</td><td>1.13</td></tr></tbody></table>

E-in describes the energy of the charge cycle, vice versa for E-out. The losses are given relative as the energy difference between input and output divided by the input. Finally, a ratio is given off relative AC losses to DC losses. Again, it seems as if the impedance is higher in the measurement than in the simulation which can be seen in the relative losses and the transferred energy. Input and Output energy of the *AC-battery* are slightly lower than of the *DC-battery*, in simulation and measurement, which is due to the start and endpoint of the cycle being defined by voltages. The discharge is started as soon as a cell voltage of $U_{Bat} > 4.2V$ is measured and then switched again to charging with the condition $U_{Bat} < 3V$. Due to the *AC-battery* having a superimposed sinusoidal voltage, this results in the transition conditions being met earlier. The sinus has an amplitude of 30mV, as can be seen in Fig. 5, which is enough to create this detectable difference.

## B. Aging measurements

With the voltage and current being completely recorded at 5k samples per second, every test cycle, it is possible to derive information which gives hints about aging of the batteries. These are summarized in Tab. III and a timeline over the cycles can be seen in Fig. 7.

Figure 7(a) shows that the relative losses are slightly increasing over the observed lifetime. Some outliers are visible but this is due to the cycling tests being started, because of a performed CCCV capacity measurement or other reasons. Otherwise the steady increase in losses is a first sign of aging. While, as described before, it is clearly visible that the *DC-Battery* experiences

<table><caption>TABLE III
AGING OVERVIEW WITH REGARDS TO CELL CAPACITY</caption><thead><tr><td>Cell</td><td>DC-bat</td><td>AC-bat</td><td>DC-bat B</td><td>AC-bat A</td></tr></thead><tbody><tr><td>cylces</td><td>1008</td><td>1008</td><td>181</td><td>190</td></tr><tr><td>Cap<sub>0</sub> [mAh]</td><td>3100</td><td>3075</td><td>3080</td><td>3074</td></tr><tr><td>Cap<sub>end</sub> [mAh]</td><td>2750</td><td>2760</td><td>2900</td><td>2950</td></tr><tr><td>decline</td><td>11.3%</td><td>10.2%</td><td>5.8%</td><td>4%</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Extracted data from each cycle. (a) shows the relative energy loss over one cycle. (b) plot shows the transferred charge during the cycle, as well as the by CCCV method determined capacity. The (c) plot shows the average temperature lift, over ambient, in one cycle. (d) is the legend for all three plots.</figcaption></figure>
lower relative losses, the aging trend is similar to the *AC-Battery*. A first indicator that the batteries age similar, regardless of the application.

In Fig. 7(c) the temperature difference between the battery and enclosure is shown. For the *DC-battery* the temperature rise is significantly higher for the first 13 cycles compared to the later ones. This is because at first the batteries were tested with typical spring contacted battery holders. Those had comparatively high contact resistances which produced additional losses that heated the battery. Furthermore, the first few cycles of each battery (first 28 of the *DC-battery*, first 18 of the *AC-battery*), were done without an enclosure. After the addition of the enclosure a slight and expected temperature rise is visible. For the *AC-battery* a strong decline in temperature is visible from cycle 85 onward. This is due to the temperature probe attached to the battery slowly detaching due to bad application.

Capacity, measured in Ah, of a battery is often used to quantize the SoH or aging of a battery. Figure 7(b) shows the transferred charge of each cycle. It is determined by averaging the amount of charge during charging with the amount during discharging. Since the start and stop voltage of each cycle is the same, the downward trend is visible in both batteries. DC (blue) and AC (orange) therefore clearly show aging of the battery. The transferred charge of the *AC-battery* is below the *DC-battery*, again, because of the superimposed sinusoidal voltage, as described before. To verify the battery capacity, it was determined at irregular intervals by a typical CCCV charge and CC discharge measurement, as also described before. Here a similar downward trend can be observed. The offset is, again, due to this method using more of the batteries voltage range. At the top, the CV region at 4.2V is added and the battery is discharged to 2.7V instead of 3V. The capacity degradation expectancy stated by the manufacturer is 40% after 250 cycles. However, this is with a discharge current of 35A (8.75C) and 4A (1.333C) charge current. This explains why the observed aging in the measurements is much lower.

To make Fig. 7(b) better comparable, the data was set in relation to the initial value at the beginning of the lifetime. Both batteries show approximately the same degrading rate, or it could even be said that the *DC-battery* aged stronger. In Fig. 8 the x-axis was changed from cycle to total transferred charge. Since an AC cycle has fewer transferred charge, than a DC

cycle, this is done to show the aging in relation to the moved charge.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Relative capacity shown in relation to the transferred charge.</figcaption></figure>

### C. *Comparison to the literature*

The work in [8] also tested batteries with a 100Hz sinusoidal current. However, it had only a small DC bias current, meaning its not as representative for a CHB application, as is this work. An aging trend shown in [8] demonstrates that the 100Hz cell has a significantly lower aging rate than a battery tested with DC current, if plotted over moved charge. However, the authors in [8] included the charge transferred by the 100Hz signal, which in average is 0. Here the question is, if ions moving at 0Hz, from one electrode to the other, has the same effect as no movement. This is confirmed by Fig. 7 and Fig. 8, where the aging shows no significant differences for both cases, since the moved charge from electrode to electrode is the same in both tests, it would confirm the theory.

Results from [7] and [11] suggest that batteries age faster due to 100Hz current. While [11] cannot be compared because lead acid batteries were used, the findings from [7], which also uses LCO cells, are contradictory to the findings of this work.

### D. *Additional verification measurements*

To not only rely on data from one cell per measurement series, for both the *DC-battery* and *AC-battery* measurement series an additional cell *B* was tested. Due to time constraints, those two cells were
only tested with close to 200 cycles. However, the trends in Fig. 7(a) and Fig. 7(b) for the first 200 cycles are pretty much equal to the first measurement series further improving the plausibility of the measurement results.

Furthermore, to use an additional parameter as indicator for aging, the EIS measurement was repeated for the *DC-battery* after 109 cycles and 257 cycles and for the *AC-battery* after 134 cycles and 262 cycles. The measurements were performed as described in III-B. Figure 9 shows the Nyquist plot of the measurements for a SoC of 50%. A sign of bad aging, as described in [7] would be a significant increase in the impedance. However, the *DC-battery* shows a slight improvement and the *AC-battery* even shows a significant improvement.

<figure><img src="image_10.png" /><figcaption>Fig. 9. Comparison of the impedance spectrum at 50%SoC.</figcaption></figure>

In [7] it is concluded that batteries are not to be loaded with AC currents due to significant aging. The authors there saw a drop in SoH of over 40% after only 10 cycles if the battery is tested with a current typical for MMC DC links! However, this paper did not use a capacity measurement to confirm this drastic result and only evaluated the SoH with the change of the DC resistance. Since the here presented work could not confirm such strong aging effects at all, it is believed that the impedance measurements seem to be faulty in [7]. Furthermore, Fig. 9 shows that the impedance of the cycled cells even improved, which further contradicts the result of [7]. Also the work in [10] cannot confirm accelerated aging due to superimposed AC currents.

However, it has to be noted that [10] did test the batteries at frequencies of 1Hz, 1kHz and 30kHz and not 100Hz.

### E. Possible Improvements

To conclude this section, it has to be noted that the lack of temperature control of the cell is a drawback of this study. Figure 7(c) shows quite big changes in temperature, mostly due to the test not being conducted in a temperature controlled room. To improve the results and eliminate the variable of cell temperature the measurement series should be repeated with temperature control. However, the authors still believe that the conclusion would be the same as the difference in cell temperature was only 0.5K on average.

## VI. CONCLUSION

The current waveform experienced in DC supplies of single phase systems, as found in CHB based converters, creates additional losses in a battery, compared to pure DC current, which does transmit the same amount of energy. This has been anticipated due to the existing cited literature [7], [8], [10], [12] and analytical calculations. It was then confirmed by simulations, using a equivalent circuit model of which the parameters were determined through measurements on physical battery cells. These simulations were then replicated in measurements and show the same result. Slightly higher losses occur due to the additional AC current, which increases the operation temperature slightly. Finally, 1000 cycle tests, of a *DC-battery* each, cannot confirm the significantly faster aging, as stated in [7]. It can be said that the two measurement series show a comparable aging profile or it could even be suggested that the *AC-battery* ages slightly better. The result of this work specifically addresses and suggests that batteries can be used in CHB converters without the need to eliminate the second current harmonic. This significantly simplifies the design of such converts in e.g. multi-level medium voltage BESS.

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