The codes are ready and I need to make them work like in the paper attached here. Feel free to ask more questions or if you need more files.
%Battery charge/discharge power, current DOD and battery capacity as input function DOD_new = DOD_fcn(DOD,power,capacity) %matrices for DOD model Ad = [1 0; 0 0]; Ac = [0 0; 0 1]; 1Bd = [1;0]; Bc = [0;1]; %Calculates the new DOD using the DOD model if power <= -0.01="" dod_new="Ad*DOD" -="" bd.*(power/capacity);="" elseif="" power="">= 0.01 DOD_new = Ac*DOD + Bc.*(power/capacity); else DOD_new = [0;0]; end lable at ScienceDirect Journal of Power Sources 257 (2014) 325e334 Contents lists avai Journal of Power Sources journal homepage: www.elsevier .com/locate/ jpowsour A holistic aging model for Li(NiMnCo)O2 based 18650 lithium-ion batteries Johannes Schmalstieg a,c,*, Stefan Käbitz a,c, Madeleine Ecker a,c, Dirk Uwe Sauer a,b,c a Electrochemical Energy Conversion and Storage Systems Group, Institute for Power Electronics and Electrical Drives (ISEA), RWTH Aachen University, Jägerstrasse 17/19, 52066 Aachen, Germany b Institute for Power Generation and Storage Systems (PGS), E.ON ERC, RWTH Aachen University, Germany c Jülich Aachen Research Alliance, JARA-Energy, Germany h i g h l i g h t s � Extended accelerated aging tests on lithium-ion batteries including storage and cycling. � Detailed analysis of temperature and voltage dependencies of calendar cell aging. � Detailed analysis of influence of cycle depth and SOC range on cycle aging. � Lifetime prediction based on identified main aging phenomena. � Comprehensive verification measurements for aging model. a r t i c l e i n f o Article history: Received 5 December 2013 Received in revised form 21 January 2014 Accepted 4 February 2014 Available online 13 February 2014 Keywords: Lithium-ion Calendar aging Cycle aging Lifetime prognosis Battery model * Corresponding author. Electrochemical Energy Con Group, Institute for Power Electronics and Electrical University, Jägerstrasse 17/19, 52066 Aachen, Germa fax: þ49 241 80 92203. E-mail address:
[email protected] (J. Schma http://dx.doi.org/10.1016/j.jpowsour.2014.02.012 0378-7753/� 2014 Elsevier B.V. All rights reserved. a b s t r a c t Knowledge on lithium-ion battery aging and lifetime estimation is a fundamental aspect for successful market introduction in high-priced goods like electric mobility. This paper illustrates the parameteri- zation of a holistic aging model from accelerated aging tests. More than 60 cells of the same type are tested to analyze different impact factors. In calendar aging tests three temperatures and various SOC are applied to the batteries. For cycle aging tests especially different cycle depths and mean SOC are taken into account. Capacity loss and resistance increase are monitored as functions of time and charge throughput during the tests. From these data physical based functions are obtained, giving a mathe- matical description of aging. To calculate the stress factors like temperature or voltage, an impedance based electric-thermal model is coupled to the aging model. The model accepts power and current profiles as input, furthermore an ambient air temperature profile can be applied. Various drive cycles and battery management strategies can be tested and optimized using the lifetime prognosis of this tool. With the validation based on different realistic driving profiles and temperatures, a robust foundation is provided. � 2014 Elsevier B.V. All rights reserved. 1. Introduction Lithium-ion batteries are a key technology for current and future energy storage, whether they are used for mobile or sta- tionary application. As the batteries’ portion of cost is quite high for many applications, battery lifetime is a critical point for profit- ability. However, performing real life aging tests for every single version and Storage Systems Drives (ISEA), RWTH Aachen ny. Tel.: þ49 241 80 96911; lstieg). application is an expensive and time consuming process which cannot be done in every case. Lifetime prediction using aging models can overcome this challenge as they have to be done only once per cell type. Different approaches are used for modeling of lithium-ion bat- teries. The most realistic models are physico-chemical ones which simulate mostly single aging effects. However, these models are very slow and complex to parameterize. Therefore they are not suitable for aging prediction on a long time scale. In contrast neuronal network models have a very high computation speed, but they are usually not able to extrapolate aging for conditions that were not included in the learning set. Using physical based func- tions fitted to accelerated aging tests is a compromise between fast 0 20 40 60 80 100 35 40 45 50 SOC /% te m pe ra tu re /° C Fig. 2. Test matrix of calendar aging tests. 100 J. Schmalstieg et al. / Journal of Power Sources 257 (2014) 325e334326 models on the one and realistic models on the other hand. These mathematical functions allow to reproduce the factors influencing aging, such as temperature or storage voltage, and extrapolating from a fixed set of tests to a wide range of applications. For an aging prediction a lot of different aging factors have to be accounted. These factors are e.g. temperature, storage voltage and time for calendar aging and in addition cycle depth, SOC range, current rate and charge throughput for cycle aging [1,2]. Some studies have already published simulations dealing with a few of these factors, either calendar life [3e6] or cycle life [7]. Completely parameterized models including all of these factors and consid- ering both calendar and cycle life are still missing. This paper shows an accelerated aging test set including more than sixty cells of a commercial high-energy 18650 system with NMC cathode material. Both capacity loss as well as resistance in- crease are addressed. Calendar and cycle aging are considered separately. A holistic aging model including an impedance based electric-thermal model is presented. Finally the comparison be- tween simulation results and verification measurements at nine different conditions will be shown. 2. Experimental The tested battery was the Sanyo UR18650E, an 18650 round cell which is manufacturer rated with 2.05 Ah minimum and 2.15 Ah typically. The cathode active material is Li(NiMnCo)O2 (NMC) and the anode consists of graphite. It is a high energy cell with a maximum discharge rate of 3C and 165 Wh kg�1 energy density. Voltage limits are 2.5 V for discharging and 4.2 V for chargingwith a proposed end of discharge voltage of 3.0 V and end of charge voltage of 4.1 V. An OCV curve of the cell is shown in Fig. 1. A detailed analysis of the cell, the aging tests and the occurring processes can be found from Ecker et al. [8]. 2.1. Calendar aging matrix A list of all tested calendar aging test conditions can be found in Fig. 2. As the temperature dependency with an Arrhenius equation is already described by some authors [1,9], only three different temperatures are tested to verify this dependency. More attention was given to the voltage dependency, which is highly resolved with 10 different conditions. Each combination of temperature and voltage in the calendar aging test consists of three cells to get some statistics. All cells were held at a constant voltage (float conditions) during the tests. Every seven weeks a measurement of the cells capacity and inner resistance was performed. 2.2. Cycle aging matrix Themain focus of the cycle aging tests was the influence of cycle depth and mean SOC. A diagramwith all cycle aging test conditions 0 20 40 60 80 100 3.4 3.6 3.8 4 4.2 SOC /% vo lta ge /V Fig. 1. OCV curve for a new cell (Sanyo UR18650E), measured at 35 �C. can be found in Fig. 3. All cycling tests were done at a current rate of 1C and a cell temperature of 35 �C. Temperature was logged using a sensor mounted on the surface of the cell. The mean SOC was set by a constant voltage charge using the OCV curve of the cell. Cycling was done Ah based around this point, with a reset of the mean SOC every 100 cycles. If a test had 0 or 100% SOC as limit, these points were used to set the cycle range. Checkups measuring the capacity and the inner resistance of the cell were made every 3 weeks. 2.3. Checkups All capacity and resistance measurements were done at 35 �C. The capacity measurement starts with a standard charge which is a 1C charge up to 4.2 V followed by a CV charge until current was below C/50. After that the capacity was measured during the 1C discharge down to 2.5 V. The inner resistance was measured at SOC steps of 10%, starting from90% SOCdown to 10% SOC. Every stepwas reached Ah based by discharging 1/10 of nominal capacity starting from a completely charged battery in the first step. At each step a pulse power characterizationprofile (PPCP) is applied to the battery. The PPCP consists of an 18 s 2C discharge followed by a 40 s rest period. After that a 10 s 1C charge is applied, again followed by a 40 s rest period. A voltage response to this PPCP is shown in Fig. 4. From this profile various inner resistances are calculated, a 2,10 and 17 s resistance for the discharge and a 2 and 10 s resistance for the charge. For the aging calculation the 10 s discharge resistance at 50% SOC is used. This resistance is calculated as the difference be- tween the voltage before the discharge pulse and 10 s after the beginning of the discharge pulse divided by the current. All other resistances are calculated in a similar way. 3. Calendar aging In the calendar aging tests, cells were stored at different tem- peratures and voltages. Each test condition was performed with 3 0 20 40 60 80 100 0 20 40 60 80 average SOC /% ΔD O D /% Fig. 3. Test matrix of cycle life tests performed on a 2.05 Ah cell. All cycle life tests were done at 1C and a cell temperature of 35 �C. −20 0 20 40 60 80 3.6 3.7 3.8 3.9 4 vo lta ge /V time /s Fig. 4. Voltage reaction of a new cell to a PPCP. The two voltages used for calculating the 10 s discharge resistance are marked red. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 5. a) Normalized capacity over time and b) normalized resistance over time for calendar aging tests at 50 �C. For each SOC the average on three cells under tests is shown. The capacities for cells under same conditions have a great uniformity, while resistance increase varies a bit. J. Schmalstieg et al. / Journal of Power Sources 257 (2014) 325e334 327 cells to demonstrate the reproducibility of the experiment. The results show a very similar aging for cells tested under the same conditions, the measured capacities show an especially great uni- formity [8]. Only the