Study of degradation of a battery using MATLAB Simulink Objective: To model a battery in MATLAB Simulink and study what effect does various factors such as temperature, high currents, age has on its performance and longevity. Background Lithium-ion batteries always undergo degradation over time, starting with the initial charge and persisting beyond. Although lithium-ion battery degradation is inevitable, it is not permanent. However, the degradation rate of lithium-ion batteries might vary considerably for each cycle, depending on the working conditions. Undoubtedly, the degradation of the battery will occur most rapidly when it is subjected to harsh conditions, such as elevated temperatures, high current rates, or low temperatures combined with high charging current rates. Lithium-ion batteries undergo continuous degradation, even during periods of inactivity, because of time and thermodynamics. This phenomenon is known as "calendar aging", which arises from the chemical composition of a lithium-ion battery, as there are inherent chemical side reactions that occur continuously. In the end, it is these secondary reactions that lead to the deterioration of the battery and hinder its ability to retain its maximum capacity over time. Lithium-ion batteries experience ongoing deterioration, even when not in use, because of the influence of time and thermodynamics. This phenomenon is referred to as "cycling-based degradation" which occurs from the chemical makeup of a lithium-ion battery, as there are inherent chemical side reactions that occur continuously. Ultimately, it is these subsequent responses that result in the degradation of the battery and impede its capability to maintain its peak performance over a period. While it may seem beneficial, rapid charging leads to expedited deterioration of lithium-ion batteries. This is because charging a lithium-ion battery too quickly increases the likelihood of lithium plating. Lithium plating results in more pronounced deterioration compared to the solid electrolyte interphase (SEI). Similar to the production of solid electrolyte interphase (SEI), lithium plating also depletes the lithium inventory. However, lithium plating occurs at a far faster rate. Lithium plating refers to the process in which the anode accumulates solid lithium metal. Due to its high reactivity and significant resistance, lithium engages in side reactions and contributes to a rise in internal resistance. Consequently, this results in both lower learning ability (LLI) and increased resistance, ultimately leading to diminished performance. Elevated temperatures consistently pose a significant risk when dealing with lithium-ion batteries. In addition to inducing potentially hazardous outcomes, high temperatures also accelerate the deterioration of batteries, leading to a reduction in their overall lifespan. Subjecting lithium-ion batteries to elevated temperatures has a dual impact: Firstly, it hastens the inevitable process of calendar aging. Additionally, it accelerates the degradation of the battery during regular charge and discharge cycles. What is the cause? Elevated temperatures accelerate the occurrence of chemical side reactions in the electrolyte, leading to a greater deterioration of the electrolyte. Here's a look at how battery degeneration manifests itself in the real world, what it implies for end users, and its repercussions. 1. A prominent consequence of a deteriorated battery is reduced capacity. This phenomenon is readily seen in the daily lives of the majority of individuals. Over the course of a few years, it is likely that you have observed a significant decrease in the longevity of your phone battery compared to when it was new. The reason for this is because a deteriorated lithium-ion battery has a reduced capacity to store energy compared to its initial state. 2. In addition to having less capacity, a degraded lithium-ion battery also experiences a decrease in power capability. This means that the battery takes longer to absorb and release electrical energy and does so with less efficiency compared to its previous state. The deteriorated battery generates additional heat during operation due to the heightened internal resistance. It is important to note that when there is an increase in heat generation, the battery will deteriorate more quickly, thereby initiating a cycle of degradation. 3. As a lithium-ion battery deteriorates and becomes less efficient, the controls of the Battery Management System (BMS) may likewise deteriorate. The reason behind this is because the pre-made software installed on current BMSS is typically designed to handle a battery as if it were brand new, even though batteries that have degraded behave in a significantly different manner. Consequently, the current Battery Management Systems (BMSs) will operate with imprecise data, which will become more inaccurate as the degradation of the system progresses. 4. At elevated temperatures, side reactions can occur, producing gases that cause the battery to expand. These gases increase the pressure and create pockets of resistance in the battery, causing the battery's performance and lifespan to deteriorate quickly. Battery swelling can happen in any type of battery cell however it is more commonly seen in pouch cells due to their lack of a solid structure. Modelling When developing and selecting rechargeable energy storage systems, a simulation model can be a valuable tool for evaluating the system's performance over both short and long periods of time. This study presents the development of a cycle life model that is based on the relationship between cycle life and several parameters such as operating temperature, constant discharge current rates, depth of discharge, and constant fast charging. Below is a table that provides a concise overview of the derived equations and their corresponding coefficients. The equations and coefficients have been derived using the least square fitting approach. The relationships mentioned have been incorporated into MATLAB Simulink to create a comprehensive cycle life model that accurately represents the anticipated working conditions. Relationships Cycle life versus working temperature CL = a.T³-b.T² + c.T+d Cycle life versus constant discharge current rates CL(Id) = e.efla) +g.e(h.la) Cycle life versus depth of discharge CL(DoD)=i.e..DoD) +k.d(1.DoD) Cycle life versus constant Coefficients a b C d 0.0039 e 1.95 f 67.51 g 2070 h 4464 i -0.1382 j -1519 k -0.4305 1 6.009.e9 -0.011879 6.009.e9 -0.01879 m n 0 P 5963 -0.6531 321.4 0.03168 charge current rates CL(Ich)=m.en.Ich + 0.e(p.Ich) Table 1. Summary of the extracted relationships at different working conditions Battery Aging Model SOC <SOC (%)> Temperature (deg. C) Deph-of-discharge (DOD) Ta DOD* Discharge current Idis⭑ Charge current Icharge* Current Degradation Model + Battery <Voltage (V)> <Current (A)> <SOC (%)> <Cell Temperature (oC)> <Age (Equivalent Full Cycles)> <Maximum Capacity (Ah)> Continuous powergui Scope Figure 1. Battery Degradation Model This model demonstrates the impact of aging, specifically caused by cycling, on the performance of a Lithium-Ion battery model with a voltage of 12.8 V and a capacity of 40 Ah. The battery undergoes a series of discharge-charge cycles at different temperatures, depths of discharge (DOD), and charge and discharge rates for a total of 2500 hours. Block Parameters: Battery Battery (mask) (link) Implements a generic battery model for most popular battery types. Temperature and aging (due to cycling) effects can be specified for Lithium-Ion battery type. Block Parameters: Battery Battery (mask) (link) Implements a generic battery model for most popular battery types. Temperature and aging (due to cycling) effects can be specified for Lithium-Ion battery type. Parameters Discharge Temperature Aging Type: Lithium-Ion Temperature Simulate temperature effects Use a preset battery: 12.8V 40Ah (LiFeMgPO4) Aging Simulate aging effects Nominal voltage (V) 12.6 Rated capacity (Ah) 40 Initial state-of-charge (%) 100 Battery response time (s) 90 Parameters Discharge Temperature Aging Determined from the nominal parameters of the battery Maximum capacity (Ah) 40 Cut-off Voltage (V) 10.5 Fully charged voltage (V) 13.8 Nominal discharge current (A) 20 Internal resistance (Ohms) 0.015 Capacity (Ah) at nominal voltage 30.14 Exponential zone [Voltage (V), Capacity (Ah)] [13.1 0.5] Display characteristics Discharge current [11, 12, 13,...] (A) [0.15 1.3 3.25] Units Ampere-hour Plot < OK Cancel Help Apply OK Cancel Help Apply Block Parameters: Battery Battery (mask) (link) Implements a generic battery model for most popular battery types. Temperature and aging (due to cycling) effects can be specified for Lithium-Ion battery type. × Block Parameters: Battery Battery (mask) (link) Implements a generic battery model for most popular battery types. Temperature and aging (due to cycling) effects can be specified for Lithium-Ion battery type. Parameters Discharge Temperature Initial cell temperature (deg. C) 25 Nominal ambient temperature T1 (deg. C) 20 Second ambient temperature T2 (deg. C) 0 Discharge parameters at T2 Maximum capacity (Ah) 36 Initial discharge voltage (V) 13 Aging Voltage at 90% maximum capacity (V) 11.7 Exponential zone [Voltage (V), Capacity (Ah)] [12.67 4] Thermal response and Heat loss Thermal resistance, cell-to-ambient (deg. C/W) 0.6411 Thermal time constant, cell-to-ambient (s) 4880 Heat loss difference [charge vs. discharge] (W) 0 OK Cancel Help Apply Parameters Discharge Temperature Initial battery age (Equivalent full cycles) 0 Aging model sampling time (s) 30 Aging Aging characteristics at ambient temperature Tal Ambient temperature Ta1 (deg. C) 23 Capacity at EOL (End Of Life) (Ah) 40*0.9 Internal resistance at EOL (Ohms) 0.0126*1.2 Charge current (nominal, maximum) [Ic (A), Icmax (A)] [20, 26] Discharge current (nominal, maximum) [Id (A), Idmax (A)] [20, 80] Cycle life at 100% DOD, Ic and Id (Cycles) 1500 Cycle life at 25% DOD, Ic and Id (Cycles) 10445 Cycle life at 100% DOD, Ic and Idmax (Cycles) 1017 Cycle life at 100% DOD, Icmax and Id (Cycles) 1460 Aging characteristics at ambient temperature Ta2 Ambient temperature Ta2 (deg. C) 45 Cycle life at 100% DOD, Ic and Id (Cycles) 982 OK Cancel Help Apply The four figures above depict the different characteristics employed in the battery model utilized in the simulation. The MATLAB's 12.8V 40 Ah Li-ion library model uses default settings for some of its parameters, while others are selected based on data from research papers, which are cited in the references. Results 14.5 14 13.5 13 20 15 10 -15 -20 <Voltage (V)> <SOC (%)> <Age (Equivalent Full Cycles)> 150H <Current (A)> 106 60- 28 27 26 25 100 50 <Cell Temperature (OC)> <Maximum Capacity (Ah)> 43.2 43.1 0.5 1.5 3.5 10° 43 42.9 42.8 42.7 42.6 42.5 0.5 10° This image shows the various parameters of the battery when simulated for near constant DoD of 20% and 50% over the 2500 hrs cycle at 25-degree Celsius ambient temperature with 20A charging and discharging currents. We observe that the battery capacity only drops to 42.5 from 43.2 Ah, also the internal temperature of the cell hovers near 30-31 degrees Celsius. The age of the battery is just 150 cycles. Effect of DoD Now we'll increase the DoD to ensure an extensive and a harsh usage of the battery to contrast its effect. 14 13 12 11 10 9 200 150 100 50 <Voltage (V)> <Current (A)> 60 50 <SOC (%)> 600 500 400 300 200 100 <Age (Equivalent Full Cycles)> <Cell Temperature (OC)> <Maximum Capacity (Ah)> 43.5 42.5 42 41.5- 41 40.5 35 0.5 1.5 2.5 3 3.5 0.5 1 1.5 25 <106 3.5 10° x10° In this run the DoD was allowed to go high as 90% and the results are clearly visible. Now the battery has aged quit a lot reaching 600 cycles in the same 2500hrs of simulation. The battery capacity has also dropped to 40.5 Ah compared to 42.5 Ah in the previous case. The internal cell temperature has risen upto 70 degrees which is concerning. This encapsulates the effect DoD has on the performance of the battery. Effect of Temperature In this run the ambient temperature was initially at 25 degrees, then was dropped down to 0 degrees and then increased to 45 degrees. 15 <Voltage (V)> 14.5 14 13.5 13 + 12.55 <Current (A)> 25 20 15 10 -10 -15 -20 100 95 90 85 80 70 60 <SOC (%)> 160 140- 120 100 80 60 40 20 아 <Age (Equivalent Full Cycles)> <Cell Temperature (OC)> <Maximum Capacity (Ah)> 43.5 43 42.5 42 41.5 41 25 20 15 40.5 40 39.5 10 39 3.5 0 0.5 1.5 3.5 0 0.5 25 3.5 106 106 <10%