Scalability and performance study of an innovative battery based on electric-circuit models

Scalability and performance study of an innovative battery based on electric-circuit models 1st Petra Alexandra Reisz Power and Renewable Gas Systems AIT Austrian Institute of Technology GmbH Vienna, Austria https://orcid.org/0009-0005-4574-0250 2nd Klara Maggauer Integrated Energy Systems AIT Austrian Institute of Technology GmbH Vienna, Austria [email protected] 3rd Fei Haojie Centre of Polymer Systems Tomas Bata University in Zl´ ın Zl´ ın, Czech Republic [email protected] 4th Thaiskang Jamatia Centre of Polymer Systems Tomas Bata University in Zl´ ın Zl´ ın, Czech Republic [email protected] 5th Viera Pechancova Centre of Polymer Systems Tomas Bata University in Zl´ ın Zl´ ın, Czech Republic [email protected] Abstract—In this article, we present a performance study and benchmarking approach for low technology readiness level (TRL) batteries, based on an interpretation of circuit-based battery model parameters. We show that when these parameters are tailored to the underlying cell, they can be a predictor of battery efficiency and dissipated power losses under different operating conditions and state of charge. We then consider electrical circuit parameters in a typical use case scenario (i.e. with a typical charge/discharge rate and battery cell capacity). It is then shown how in this scenario the expected efficiency and power losses can be forecasted. We additionally derive a forecast for the scaling of the battery parameters with its coulombic capacity, and validate this by comparing the results of pulse discharge measurements from two commercial lithium iron phosphate batteries with different capacities. Finally, we use our new methodology to predict the performance of a particular low TRL battery. The example which is taken in this article is a cell which uses a solid-state electrolyte made from bacterial cellulose, and is developed in scope of the EU project TwinVECTOR. It is currently being produced and developed on laboratory scale at the Tomas Bata University in Zl´ ın. Index Terms—Battery Technology, Battery Modeling, Renewable Technology Development, Electric Circuit Battery Models I. INTRODUCTION Batteries play an increasingly important part of today’s global energy system. In the energy sector, battery storage was the fastest growing commercially available energy technology in 2023. Its deployment shows Moore’s Lawlike behavior [1]. A total of 42 GW of battery storage capacity was installed globally in 2023. Electric vehicle (EV) battery deployment showed a 40% increase in 2023 [1]. In this regard, lithium ion batteries (LIBs) represent one of the most important technologies for achieving carbon neutrality. This technology has evolved significantly over the past decade, resulting in significant cost reductions, higher energy densities, and longer lifetimes [2], [3]. According to [3] LIB costs could be further reduced, despite recent metal price spikes. However, technology development is needed This study has received support from the Horizon Europe project TwinVECTOR, funded by the European Union (Grant Agreement No. 101078935). in order to reduce environmental impacts, potential material scarcity, and to improve safety [4], [5]. New battery technologies that are both affordable and sustainable over their entire life cycle are crucial for achieving the goals of the European Green Deal [6]. To examine the environmental impacts of certain technologies, the method of life cycle analysis (LCA) is a state of the art approach, which is gaining importance. It plays a vital part in the analysis of the effects of sustainability of a certain technology, irrespective of the exact application sector [7]–[11]. In [11], a method for cradle-to-gate LCA for a non-commercial, laboratory-scale produced battery cell using the promising technology of bacterial cellulose electrolyte [12], [13] is represented. In order for a technology to successfully enter the market it is however not sufficient to only consider the environmental impact of a product through every (or some) phase of its life. A performance benchmark and prediction might be crucial as well. This paper will therefore provide an approach to: 1) Examine the performance of battery technologies from low TLR onwards. For laboratory scale products, this usually means capacities of a few milli-Ampere-hours (mA h). 2) Estimate properties when scaling the technology to higher cell capacity. As a first step, the underlying model is introduced alongside with literature recommendations. II. MODEL DESCRIPTION In order provide a theoretical backbone for performance indicators and prediction, a fundamental model is introduced in this section. In battery modeling, circuit-based models have been demonstrated to be accurate and effective in capturing both dynamic and power dissipating or solely power dissipating behavior of batteries [14]–[18]. In this article, we build our theory from a sub-type of electric equivalent circuit models, namely the one with a single resistor-capacitor (RC) element. In the following, it is referenced as “ECM”. A graphical representation is shown in Figure 1.979-8-3315-9515-9/25/$31.00 ©2025 IEEE 2025 IEEE International Conference on Environment and Electrical Engineering and 2025 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe) | 979-8-3315-9515-9/25/$31.00 ©2025 IEEE | DOI: 10.1109/EEEIC/ICPSEUROPE64998.2025.11169054 Authorized licensed use limited to: Tomas Bata University in Zlin. Downloaded on October 29,2025 at 07:46:19 UTC from IEEE Xplore. Restrictions apply. V R1 R0 Voc Vbat C1 Fig. 1: Graphical representation of the ECM. Taken from [19]. A. ECM equations According to the ECM approach, the terminal voltage of the battery (Vbat from Figure 1) is given as Vbat =Voc(SoC)−R0(SoC)·I−v1(1) where v1denotes the transient voltage on the RC-element. It is modeled by the first order differential equation dv1 dt =−1 τ·v1+1 C1 I(2) and the time constant τfrom (1) is given by the product of the resistor’s and capacitance’s value by: τ=R1·C1(3) The parameters from Figure (1) and in equations (1), (2) are given as a function of the state of charge (SoC) of the battery. By SoC, the Coulombic State of Charge is meant, defined by the quotient of the stored amount charge in the battery CapAh (in A h) divided by the maximal capacity of the battery Cap0 (this can degrade with time [20]–[22]). SoCAh := CapAh Cap0 (4) Note that the only directly observable/measurable quantity from Figure 1 is Vbat, representing the amount of voltage at the battery’s terminal at its given state and operating conditions. These conditions are governed primarily by the battery current I, which is measurable as well. The used convention for the equations (1), (2) and in this work is is the following: •I > 0when discharging •I < 0when charging. For more on this approach it is referred to the literature [14]–[17], [19], [23]. B. Parameter description and acquisition In [19] a method is proposed for determining the values Voc, R0, R1, C1as a function of the state of charge of the battery. The aforementioned parametrization is based on a set of automated pulse discharge measurements and subsequent (adaptive) polynomial fitting of the acquired data. After executing the procedure, the following performance indicators of the battery are available: •Voc(SoC) = pn1(SoC): A value of the open-circuit voltage that can be delivered by the respective battery cell in Volts (V) at the state of charge SoC. The functional dependence is fitted by a polynomial pn1of degree n1. This value represents a theoretical maximum of the measurable voltage across the battery terminals under no-load conditions. •R0(SoC) + R1(SoC) = pn2(SoC) + pn3(SoC) : A value of the internal resistance of the respective battery cell in Ohms (Ω) if it is at the state of charge SoC. The functional dependence is fitted by a polynomial pn2of degree n2for R0, for R1by a polynomial pn3of degree n3. Both are given in Ohms (Ω). These values enable to model the amount of Joule heating power losses PJ. It can be derived with using Joule’s law of electric heating, resulting in (5): PJ= (R1+R0)·I2:= Rt·I2(5) •C1(SoC) = pn4(SoC) : A value of the capacitance of the respective battery cell in Farads (F) if it is at the state of charge SoC. The functional dependence is fitted by a polynomial pn4of degree n4. Together with R1it builds a resistor-capacitor element. This RC element captures the fact that batteries have a non-instantaneous, transient response in terms of their voltage to some requested or charged current. The inertia of the battery voltage is expressed according to electric circuit models by the time constant τ. This behavior is governed by (2). •R1(SoC): see above points. After introducing the theory, in the following sections its application based interpretation is presented. The outcome of the interpretation are explicit equations that give an indication and prediction on the battery performance. III. PERFORMANCE BENCHMARK As it is discussed in the previous section and in its referred literature, the parameters of the ECM model fully determine the battery’s behavior at its certain state. In this section, we derive an application-based interpretation, which can guide the development of a low TRL battery. We apply this to a laboratory scale battery using bacterial cellulose with polymer as solid electrolyte. The technology is being developed within the EU Project TwinVECTOR [24]. In the following, the aforementioned cell is referred as ”TwinVECTOR battery”. As a first step, we obtain its ECM parameters (see Section II) with the pulse discharge measurements following the methodology in [19], [23]. A. Theory We focus on energy-related applications, with the following key performance indicators (KPIs): •The maximal deliverable voltage (at discharging) and minimal required applied voltage (at charging). For this, the Voc curve is examined. •The dissipated power, determining the efficiency under given operating conditions. The former is given as PJ from (5). For this, the product of the resistances R0+ R1:= Rtis examined. This determines the total internal resistance of the battery cell at its given state. As we are concerned here only with the above KPIs, in the following this paper focuses on the parameters Voc and Rt=R0+R1. In this consideration, the capacitance C1can be neglected, since it does not result in dissipated power, nor does it affect the maximal deliverable or minimal required applied voltage. Model-wise, this means that C1from Figure 1 is set to be infinitely large. The voltage across its plates will therefore remain at 0 V. This means that the circuit from Figure 1 will effectively act as a voltage source Voc with a Authorized licensed use limited to: Tomas Bata University in Zlin. Downloaded on October 29,2025 at 07:46:19 UTC from IEEE Xplore. Restrictions apply. resistor Rtconnected across it with the capacitor acting as an open circuit. From a mathematical point of view, C17→ ∞ would mean that the first order differential equation (2) has a vanishing right-hand-side. Therefore the battery terminal voltage responses immediately to currents, and only power losses are incorporated. In energy sector applications and simulations, the timescale is usually discretized in larger timesteps (order of tens of minutes, or hours). Considering that τfrom (3) typically takes tens of seconds [19], [25], neglecting the transient phase would not matter in this case. Moreover, in many use case scenarios, the efficiency is the actual KPI of interest rather than the response time of the battery voltage. A further advantage of neglecting C1is numerical. The ordinary differential equation for v1(2) has no analytical solution for non-zero right-hand side and arbitrary current. Numerical methods (explicit or implicit) must be used. Both lead to necessary restrictions of the simulation time step size (usually below a few seconds) or to the numerical solution of an equation (e.g. with Newton’s method) in each simulation step [26]. By neglecting C1this problem does not arise as (6) below gives an analytical expression for the battery voltage at any current. Considering solely R1, R0and Voc from Figure 1, the equation for the battery terminal voltage simplifies to (6): Vbat =Voc −R0I−v1 =Voc −R0I−R1I =Voc −RtI (6) Since the right-hand-side of the differential equation (2) representing the transient part vanishes. It can have the homogeneous solution being not explicitly dependent on time: v1=R1·I(7) B. Measurement and parameter extraction For the TwinVECTOR battery, we obtained the parameter values from the pulse discharge measurement as it is described in [19]. They are shown in Figure 2. There are several points of difference in the pulse discharge measurement results and method compared to a commercial LFP battery cell (hereafter referred to as “1.2Ah LFP battery”), which is shown in [19]. The following difficulties and their solutions were encountered: •As is typical for laboratory-scale technologies, the TwinVECTOR battery could be only produced at small scale, with a determined 12 mA h capacity. •This results in possible current pulses of only a few mA. This very much constrains the performance of the solver when obtaining the parameters of the ECM model. For better understanding of the requirements and working principle of the solver, it is referred at this point to the description of MATLAB’s “BatteryPulseSequence” object, building the fundament of the underlying parameter extraction procedure [19], [27]. •In order to smooth the SoC-resistance or SoC −Voc dependencies, lower degree (here degree 6) polynomial fitting is done via the NumPy library [28]. The resulting Rtand Voc curves are shown in Figure 2. Their interpretation follows below. 0.0 0.2 0.4 0.6 0.8 1.0 SoC 0.5 1.0 1.5 2.0 2.5 3.0 R 1+ R 0= Rt [ ] Data points, pulse disch. measurement R 1+ R 0 Polynomial fit (a) Rt 0.0 0.2 0.4 0.6 0.8 1.0 SoC 2.4 2.6 2.8 3.0 3.2 3.4 Voc [V] Data points, pulse disch. measurement Voc polynomial fit (b) Voc Fig. 2: Rtand Voc curve, TwinVECTOR Battery. Both the data-points from pulse discharge measurement with subsequent parameter extraction (orange) and fitted functional dependency (blue line) are shown. C. Interpretation - deriving efficiency Comparing the values of Rt=R1+R0shown in Figure 2, which are of the order of 1 Ω, with those of [19], [25], which are a few tens of milliohms, the significantly higher value of the TwinVECTOR battery’s resistance becomes apparent. However, we show in the following that the small coulombic capacity and therefore small possible currents need to be taken into account as well. To calculate the battery efficiency, one examines the relation between the actual and theoretically possible (when discharging) or necessary (when charging) battery power. 1) Discharging: To get an expression for the efficiency at discharging ηd, the actual delivered battery power Pdis related to the theoretically deliverable battery power Pth. This results in the expression: ηd=Pd Pth =Vbat ·I Voc ·I(8) The equation (8) holds since Vth represents the upper limit of the deliverable voltage at the respective battery state, and therefore its product with the delivered current represents the theoretically possible value of delivered power at this discharging current. The relation from (8) can be further simplified using (6): ηd=Vbat ·I Voc ·I=(Voc −Rt·I)I Voc ·I= 1 −RtI Voc −RtI(9) For discharging, I > 0holds. Therefore, ηdfrom (9) is always less than 1 if the discharging procedure remains Authorized licensed use limited to: Tomas Bata University in Zlin. Downloaded on October 29,2025 at 07:46:19 UTC from IEEE Xplore. Restrictions apply. within physically reasonable operating conditions. With “reasonable” the following requirements are meant: 1) 0< Vbat < Voc: the battery voltage does not exceed the theoretical upper limit given by Voc at discharging. 2) Voc ·I > Rt·I2⇔Pth > PJ. The dissipated ohmic power does not exceed the theoretically deliverable power. The latter is given by the theoretical upper limit of the deliverable voltage Voc times the delivered current I. Therefore the derived mathematical expression for the discharging efficiency stays in the range [0,1]. 2) Charging: For the charge efficiency ηc, the actual power charged into the battery Pcis related to the theoretical minimum power Pth required for charging. This gives the following expression: ηc=Pth Pch =Voc ·I Vbat ·I(10) Furthermore, (10) can be combined with (6) to give: ηc=VocI (Voc −Rt·I)I=Voc Voc +Rt· |I|(11) Using the absolute value of the charging current removes the negative sign in (11), since I < 0for charging. 3) Simplifying expressions: If one defines the quotient of the voltage falling on the resistances R0+R1=Rtwith no-load voltage at a certain state (Voc) as f: f:= Voc Rt· |I|(12) the expression for the momentous efficiency becomes by simplifying (9) at discharging: ηd= 1 −1 f−1(13) and by simplifying (11) for charging ηc=1 1 + f(14) With the derived relations (13) and (14) the efficiency prediction at a certain battery state of charge and (dis)charging current is enabled. Note that fis an explicit function of SoC (since Voc and Rtare) and I. D. Application With (13) and (14), one is able to calculate efficiency values at different SoC values when knowing the (dis)charging current. To apply the derived expressions in practice, the expected discharging efficiency of the low TRL (TwinVECTOR) battery is compared with that of the commercial 1.2 Ah LFP battery. For both batteries a discharging current Id corresponding to a C-rate of C= 0.5(units in 1/hours) is taken into account. For the TwinVECTOR battery, with the determined cell capacity of 12 mA h and C=0.5 the discharging current amounts to: Id= 12 mA h ·0.5 h−1= 6 mA (15) For the 1.2Ah LFP battery, with the determined cell capacity of 1.2 A h and C=0.5 the discharging current amounts to: Id= 1.2 A h ·0.5 h−1= 0.6 A (16) 0.2 0.4 0.6 0.8 1.0 SoC 0.9800 0.9825 0.9850 0.9875 0.9900 0.9925 0.9950 0.9975 1.0000 for TwinVECTOR battery, at C = 0.5 for LFP battery, at C = 0.5 Fig. 3: Discharging efficiency according to (13). Comparing TwinVECTOR battery with commercial 1.2 A h LFP cell. The plot of ηdfrom (13) for the representative current corresponding to C= 0.5over the SoC range is shown in Figure 3. The comparative curve of the resistance over SoC between the cells is also shown in Figure 4. The latter graph is evaluated in more detail in the following section. What can be seen from the two figures is that, although the resistance is higher, the dependence of the efficiency on f makes it easier to achieve higher efficiencies for small battery sizes. This is due to the fact that the “loss voltage” RtI remains small compared to the open circuit voltage, whose profile is similar for lithium-ion based batteries, as it ranges for this technology between 2.6 V and 4.2 V [29]. In summary, this subsection shows that looking at cell internal resistance alone is not enough to paint a complete picture of performance in application. One must also consider: •What is the allowable (or typical) applied C-rate of the underlying cell? •How does the product of the internal resistance and typical operating current values compare to the no-load voltage of the cell (see (13) and (14))? IV. SCALING AND PERFORMANCE PREDICTION In Section III a benchmark of the low TRL battery in comparison to a commercial LFP battery is presented. However, the question arises: what could be expected if the technology is kept (i.e. same electrolyte and electrodes, structure and geometry) but the fabrication capabilities allow bigger cells to be produced? In this section, a theory for approximating the to be expected properties with increasing cell size is derived. This results in a formula which allows to estimate the scaling of Rtwith cell capacity. Then this scaling theory is validated by comparing two commercial LFP batteries with different capacities. A. Derivation of scaling law We derive a scaling of the resistance of the same battery technology under the following assumptions: 1) The cell’s nominal Coulombic capacity Cap0scales proportionally with its volume V:Cap0∝V 2) The cell’s volume can be calculated as product of its base area Atimes its length l:V=A·l. The base area Authorized licensed use limited to: Tomas Bata University in Zlin. Downloaded on October 29,2025 at 07:46:19 UTC from IEEE Xplore. Restrictions apply. is rectangular for prismatic and pouch cells and it is circular for cylindrical cells. 3) By using the same technology (electrodes and electrolyte materials), the specific resistivity of the cell ρ remains the same even with larger cell sizes.. With the above assumptions we can predict how the total resistance of the cell changes to R′ twhen its volume is increased from Vto V′and its capacity therefore from Cap0 to Cap′ 0. The factor n, by which the capacity is increased is: n=Cap′ 0 Cap0 =V′ V(17) where the second equality follows from assumption 1. To increase the volume of the cell by a factor of n, the width and depth of the base (for pouch and prismatic cells) or the radius (for cylindrical cells) are scaled by a factor of nx. The parameter xdepends on the geometry of the cell. Additionally, the length of the cell is increased by a factor of nαx, where αis another geometric parameter. Since the area Adepends on the square of the radius (for cylindrical cells) or the product of the two enclosing dimensions (for prismatic and pouch cells), it scales by a factor of n2x. Consequently, the total volume, which is the product of area and length, follows the scaling relation: CapAh Cap′ Ah =V V′=A·l (An2x)·(lnαx)=1 n(2+α)x(18) Thus, from (17) the following condition arises: 1 n(2+α)x≡1 n(19) As (2 + α)x= 1 needs to be fulfilled. Knowing the scaling factors for the geometry (x, α), the expected change in the resistance can be approximated: Rt R′ t =ρ·A l·ρl·nαx A·n2αx −1 (20) A natural case is that α= 1, which implies when the cell’s geometry has been scaled proportionally in all dimensions. In this case, the length increases by the same factor as the characteristic width or radius, ensuring a uniform expansion of the cell. Putting these values in (20) the assumption α= 1 and resulting value of x= 1/3from condition in (19) leads to: Rt R′ t =1 n1/3(21) As a second example, suppose the increase in the radius (or enclosing faces) is proportionally greater than the increase in length, for example following a 7:6 ratio. Then it means that α= 6/7and the value of xfrom (19) equals x= 7/20. With these slightly different proportions in the geometry change, the scaling of the resistance given by (20) modifies to: Rt R′ t =1 n2/5(22) The open-circuit voltage is assumed to stay the same with the increase of the cell size, as the same electrodes are used. This is because Voc is a result of a thermodynamic equilibrium, 0.0 0.2 0.4 0.6 0.8 1.0 SoC 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Rt [ ] Rt , TwinVECTOR, scaled Rt , TwinVECTOR unscaled Rt 1.2 Ah LFP cell Fig. 4: Expected behavior of the TwinVECTOR Battery’s resistance if it was scaled up to a capacity of 1.2 A h and the latter is characterized by the molar Gibbs energy ∆g, which is an intensive property, and therefore its magnitude is independent of the size of the system [30]. B. Observation and application in practice We compare pulse discharge measurement results of two batteries, both Li-Ion technology with polymer electrolytes. The results for the first 1.2Ah LFP battery are taken from [19]. For the second, we use pulse discharge measurement data from [31]. This second battery has a capacity of 10.006 Ah, so we refer to it as “10 Ah cell”. A comparison of the expected scaling according to the derivation in the previous subsection for the different geometry proportions (α= 1 or α= 6/7) is shown in Figure 5. The “Observation” point on the graph represents the average of the polynomial fit on the two batteries (1.2Ah LFP and 10Ah) evaluated over 100 equally spaced SoC values in the interval [0.05,0.99]). To estimate the resistance (and therefore the expected performance) of the TwinVECTOR battery as if it were scaled to the capacity of the 1.2Ah LFP battery, the relation derived in the previous subsection can be used. Using the relation from (20) with the choice of α= 6/7, the expected resistance of the low TRL TwinVECTOR battery can be scaled: n=1.2 A h 12 mA h = 100 =⇒R′ t(SoC) = Rt(SoC)·1002/5(23) With the scaling in (23) the TwinVECTOR technology can now be compared “fairly” to the commercial 1.2Ah LFP battery. The results are shown in Figure 4. As can be seen, the expected performance of the TwinVECTOR battery is still lower than that of the commercial technology at equal capacity. This lower performance, even when scaled, is a result of it being low TRL, and further improvements are being done as part of the project especially related to the electrolyte. V. DISCUSSION AND OUTLOOK A. Benefits This paper presents a methodology to: 1) Compare and benchmark the behavior of low TRL batteries based on the interpretation of ECM model parameters at its current state and size. Authorized licensed use limited to: Tomas Bata University in Zlin. Downloaded on October 29,2025 at 07:46:19 UTC from IEEE Xplore. Restrictions apply. 0 20 40 60 80 100 n = Cap 0 / Cap 0 2 4 6 8 10 Scaling factor R / R 0 Scaling n 1/3 Scaling n 2/5 Observation Identity Fig. 5: Scaling behaviour of battery internal resistance based on two geometric assumptions and observation. “Identity” indicates what would be observed if internal resistance scaled proportionally to the volume. 2) Estimate the performance of the same technology when production is possible for larger cell size and capacity. We have partially validated these theoretical considerations with real-world observations. The presented methodology enables research institutes and laboratories to examine their product and make assumptions how the technology would perform once it is scaled up to a commercialized level. It is highly resource efficient, since the derived equations do not require any further measurements in addition to the pulse discharge sequence which is described more detailed in [19]. B. Outlook and future work The derived scaling models and efficiency considerations are rather theoretical at this stage. They would benefit from validation with further measurements. We propose in future work to: •Compare battery cells at their laboratory scale with their commercialized and higher capacity scale (for validation of relations presented in Section IV). •Compare battery cells with identical technologies (same electrodes and electrolytes) in terms of their resistance (for validation of relations presented in Section IV). •Measure cell efficiencies for different C-rates and compare it with different size and technology batteries (for validation of relations presented in Section III). Further application of the presented theory includes: •Using the efficiency related equations for estimating the round-trip efficiency of the underlying cell. 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