Battery Lifetime Modelling

Transcription

1 Risø-I-2440 Battery Lifetime Modelling Simulation model for improved battery lifetime for renewable based energy systems for rural areas. Anton Andersson Department of Applied Physics and Electronics Umeå University Sweden Risø National Laboratory Roskilde Denmark January 2006

2 Author: Anton Andersson Title: Battery Lifetime Modelling Department: VEA, VES Risø-I-2440 January 2006 Abstract: In a renewable energy hybrid system, different power sources are combined to generate electricity for remote off-grid applications. To ensure stability and power quality, renewable energy is often compensated with a storage unit. The lead acid battery is, by far, the most common storage method since it is a well-studied science, available at a low cost and has a high availability. However, lead acid batteries are commonly agreed to be a weak link in the system since the lifetime is unsure and the investment cost significant. In order to be able to predict performance and lifetimes of batteries in hybrid systems, research cooperation has been performed between institutes in Europe that has resulted in a battery simulation tool. This report details the work that has been done to improve and tune the model for more accurate lifetime and performance estimations. The model predicts that active mass degradation is the main ageing mechanism that contributes to the reduction in capacity in hybrid systems. In the model, a new theory is implemented to simulate the effect of high and low discharge currents. The new approach is to simulate the changes in PbSO 4 crystal structure at the electrodes. The improved battery model will be implemented in IPSYS, a newly developed simulation tool for hybrid systems. Risø National Laboratory Information Service Department P.O.Box 49 DK-4000 Roskilde Denmark Telephone bibl@risoe.dk Fax

3 Acknowledgements Thanks to: Henrik Bindner for encouraging supervision, Oliver Gehrke for sharing your excellent computer skills, Tom Cronin for a splendid helpdesk, Julia Schiffer for your admirable battery and computer skills, Risø for providing a suburb research environment, Anders Lundin for supervision, My parents for never ending support and to my Eleonora!

4 TABLE OF CONTENTS 1 BACKGROUND Introduction Hybrid systems Photovoltaic panels Wind turbines Diesel generator Energy storage Inverter Controller IPSYS (Integrated Power Systems) IPSYS simulation example AIM WITH PROJECT LEAD ACID BATTERIES Major stress factors of the batteries Major damage mechanisms Battery controller Battery model Batteries simulated Battery model input Test runs METHODS Improved code Varying time steps Improved design with object-oriented programming, OOP Vectorizing Global Variables Current factor Definition of Current factor Current factor used in the initial model New approach for the current factor in the improved model Mathematics behind the model Parameters New test series Test series for model valuation Test series for validation of model response RESULT AND DISCUSSION Simulation validation CRES simulations ISPRA simulations Simulation response for different control strategies CONCLUSIONS REFERENCES APPENDIX 52

5 1 BACKGROUND 1.1 Introduction Technologies for stand alone energy systems in remote areas are steadily developing and expanding worldwide. Environmental issues and rising fuel costs have turned interest for integration of renewable energy towards these systems. At the same time new technologies have proven reliability for solar photovoltaic and small wind turbines. Consequently, renewable energy has steadily and beyond doubt become an acceptable energy source. Battery storage is often necessary in autonomous power supplies with continuous power demand. It often improves both economics and performance of the system. To be able to understand the operation characteristics of batteries, knowledge in several different topics are necessary. Battery science connects topics such as chemistry, physics and energy engineering in a genuine mixture. None of the topics can independently of one another explain and describe the battery fully. This makes battery simulations difficult, but at the same time very interesting and necessary. Battery operation is the key for optimal performance of small-scale off-grid hybrid systems. However, it is commonly agreed that batteries contribute to a significant investment cost and are the weakest link in the system. The aim with this project is to improve an existing battery model to be able to accurately predict lifetime and performance of the batteries used in renewable based rural energy systems. This project will in detail explain the steps made to improve the model, which has resulted in a model that performs faster calculations and more accurate simulations. The intension with the improved battery model is, in the future, to implement it into the larger hybrid simulation platform IPSYS. Experience has shown a need for complete system simulations, to be able to predict the performance and cost of energy systems. 1

6 1.1.1 Hybrid systems There are several different definitions of a hybrid system. The car company Toyota have a welldefined all-embracing description A hybrid system combines different power sources to maximize each one's strengths, while compensating for each other's shortcomings [1]. Off-grid power, locally produced electricity, supplies many people and applications around the world with electricity. For remote areas such as isolated communities, islands and developing countries, these systems are vital for survival. Examples of usage are rural health clinics, communication and water supply maintenance [2]. Numerous sites around the world are today powered by conventional diesel generators. By integrating renewable energy sources into these local systems, it is possible to produce environmentally friendly energy at a reasonable cost. Each kwh produced by renewable energy will save the same amount of energy generated from conventional fossil systems. Environmental awareness is something that has become very important during the past few years. Renewable energy hybrid systems consist of several components interacting together to meet the power demand. This interface between the mix of power generation results in a unique system of design issues that strongly depends on local conditions, such as wind speeds and solar radiation. The term renewable penetration is a measure of the amount of renewable energy used in the system. The following presents a short survey over the components that together build up a hybrid system [3],[4] Photovoltaic panels Solar power is one of the first things that come to people s minds when the topic of renewable energy is discussed. A solar cell consists of semiconductors that transform sunlight directly into DC electricity. The concept with semiconductors and no moving parts make the PV panels highly reliable which leads to low maintenance cost. The photovoltaic (PV) panel consists of several individual cells that are connected in series or in parallel to produce the desired voltage. One solar cell normally produces a direct current with a voltage of V. By connections of several cells in series the voltage is increased to 12 or 24 V. The panels are easily assembled into differently sized arrays to meet the demands of any given size load. PV panels are rated in terms of peak watts (Wp) which is a combined measurement of both panel size and panel efficiency. It states the amount of power delivered by a panel during solar radiation of 1 kw/m 2 at 20 C. A Panel rated at 150 Wp will produce 150 W during these conditions [2]. The efficiency of regular silicon solar cells is about %. Today higher efficiencies are available (>20%) but then the price is very high. New techniques such as chemical vapour deposition make it possible to construct multi-junction solar panels. Each junction is designed to absorb a specific wavelength of radiation. Consequently less energy is lost by heat radiation and higher efficiency is achievable [5]. The power from the PV panel equals the product between the current and voltage. Depending on different solar radiation intensities the power output from the PV panel can fluctuate. Consequently, the photovoltaic panels and the load will only have a single operation point at any given conditions 2

7 since they have different current-voltage relations [6]. Smaller independent PV systems with a consumption power of less than 200 W are almost always designed as DC system with storage in lead acid batteries. For larger systems, greater than 1000 W consumer power, the system is converted by an inverter to an AC system. The combination of solar energy and wind power is considered beneficial over the year. The wind turbine complements the solar cells during winter and bad weather [7] Wind turbines Wind turbines are a promising alternative energy resource for remote locations with good wind conditions. The wind is a powerful energy source, since the kinetic energy of the wind is proportional to the cube of the wind velocity. Accordingly, the power production of a wind turbine is highly variable. To be able to ensure useful power production, wind turbines normally are combined with another energy source. The turbines used in independent systems are usually smaller then the wind turbines used in regular grids. This section will generally focus on wind turbines of the size <15 kw. A wind turbine operating performance is characterized by its power curve. An example is showed in Figure 1. Figure 1 Power curve for the 11 kw Gaia wind turbine. Risø National Laboratory has during the last three and a half years performed tests on a modified 11 kw wind turbine produced by the Danish company Gaia-Wind. The turbine has been modified to ensure stable operation in hybrid systems. The intensions with the tests have been to demonstrate that the wind turbines can operate in a proper way in the combined system. The Gaia turbine operates on the horizontal axis, down wind and free yawing principle. The rotor consists of two stall regulated blades that work in the range of m/s with a fixed rotor speed of 56 rpm. The generator is of asynchronous induction type that needs reactive power for magnetization. This reactive power is provided by the diesel generator [3]. Smaller wind turbines are often designed as permanent magnet machines. These wind turbines produce an AC current with a frequency that is proportional to the rotor speed. By power electronics it is possible to convert the power into DC current. The voltage is also proportional to the rotation speed of the rotor [2]. 3

8 1.1.4 Diesel generator For small independent grids containing wind turbines, the power production is often secured by diesel engines directly coupled to synchronous generators. The diesel generator operates also as a source of reactive power. This implies that the system always has to have at least one diesel generator operating. Many remote communities are today powered with diesels systems only. High fuel costs have turned interest to new alternatives. An attractive solution for many locations, with sufficient wind resources, is to reduce running cost by implementation of wind turbines [6]. At the test site at Risø National Laboratory a 48 kw / 60 kva diesel generator is connected to the Gaia wind turbine. When the wind turbine s power production falls short of the power demand the diesel generator steps in to complement and secure power. [6] Energy storage Batteries are used in renewable energy systems to store excess energy for later usage. Energy storage often improves both economics and performance of the system. The explanation of this is that the batteries can provide the extra energy to ride out load peaks or low wind or sun conditions. Power is ensured without a start of a diesel generator. By far the most common storage technique is lead acid batteries. This is due to a proven technology, low cost and high availability. The theory of lead acid batteries will be discussed in more detail in the chapter 1.3. There are many circumstances that need reconsidering when dimensioning the size of the storage. However, there are two main design philosophies; storage with the capacity to ensure power for one or two hours, to ride out power peaks, or a larger capacity to secure power for several days. The design is done by carefully considering and weighting circumstances as wind conditions, diesel prices and investment cost of the batteries. The smaller size storage is dimensioned after autonomy, which means discharge time or capacity at a continuous load [7] Inverter Several components, such as PV panels, batteries or small wind turbines, operate with DC current. An inverter converts DC into AC power. There are several different classes of AC current, examples are, square wave, modified sine wave and sine wave. The square wave current is only suitable for resistive load but it is the least expensive form. A modified sine wave inverter constructs a sine wave by combining small steps. Some electronic equipment does not operate properly with this modified wave. For these cases, a sine wave inverter is the only feasible method [2] Controller For effective usage of renewable resources and to be able to regulate the system a controller is necessary. The controller operates as the brain of the system; assesses system condition and performance, controls factors such as frequency and voltage. The complexity of the controller depends on the complexity of the system, since several components need to be measured and supervised. For this project the lifetime of the batteries is an essential question. A decent batterycharging algorithm is vital for continuous operation and a long battery lifetime. Furthermore, the controller should have a low and high voltage disconnect to protect the batteries against over discharge and overcharge. 4

9 1.2 IPSYS (Integrated Power Systems) This chapter gives an overview of the simulation package, IPSYS [6]. Experience has shown that hybrid systems need to be carefully designed. This is not an easily performed task since the systems often consist of several components which make the configuration complex. The wind energy department, Risø National Laboratory, has recently developed a simulation and supervisory tool to perform the design and control of these autonomous power systems. IPSYS operates as a platform where different system configurations, in the evaluation phases, can be designed and evaluated. The ability to simulate energy systems opens up possibilities to investigate different mixes of energy generation and as a result provide energy at a lower cost. As a side effect it can be a push forward for exploitation of local renewable energy resources. To satisfy investors a technical and economical analysis needs to be done over the proposed system configuration. To be able to perform these calculations correctly the system needs either to be running or at least simulated. With the IPSYS concept it is possible to simulate how an existing diesel system should cooperate with different new system configurations. Performance estimations can be carried out as a result of different operating strategies. By simulating a wide range of configurations it is possible to show that the project can be an economically profitable deal. An additional key feature of IPSYS is that it can operate as a supervisory controller, to apply control signals to operate the interaction between renewable and conventional energy generations. IPSYS is designed to perform accurate calculations in terms of fuel consumptions, power flows and voltage levels. These calculations are performed under the condition that there exists an energy balance for the included modules [6] IPSYS simulation example This section will illustrate the potential of the simulation package IPSYS. At numerous places around the world there are communities that maintain their energy from conventional autonomous diesel generators. Several of these locations are directly suitable for implementation of sun or wind energy. The installation of the wind turbines triggers several questions that need to be answered. Available wind resources are modelled in IPSYS by integration with WAsP (Wind atlas and application program) [6]. The power system simulated in this example has a fluctuating load with an average value of 25 kw and a reactive power consumption of 10 kvar. The hybrid system consists of two Gaia 11 kw wind turbines and three diesel generators. The diesel generators individually supply a power between 5-35 kw and a maximum reactive power of 60 kvar. Figure 2 presents the simulation result. Figure 2(a) shows running status of the diesel generator. Diesel generator 1 runs continuously while the other two run at 18 % and 0 % respectively of the simulated period. Figure 2(b) presents the voltage fluctuations at the defined busbars. Figure 2(c) illustrates the different powers. The grey line indicates that some excess energy must be dumped to keep the power balance in the system. The fourth and last Figure 2(d) presents the total diesel consumption. 5

10 (a) (b) (c) (d) Figure 2 IPSYS output plot. From top to bottom: Diesel generator status, busbar voltages, active power, fuel consumption for diesel generators. By analysing the simulation results it is possible to see that an implementation of battery storage in the system configuration could save diesel runtime. In a hybrid system the diesel generators are configured with a minimum runtime. A small load peak can trigger the diesel generator to run for a defined period of time. The load peaks that trigger diesel generator 2 to start in Figure 2(c) could instead be levelled out by the capacity of the battery storage. The implementation of battery storage would then compensate diesel generator 3 fully and save fuel consumption for the remaining two diesel generators. 6

11 2 AIM WITH PROJECT During this project, studies will be undertaken on lead acid batteries that operate in hybrid systems. A lead-acid battery model developed in cooperation between Fraunhofer-Institute and Risø national laboratory will be improved and used as a simulation tool to identify and map major damage mechanisms that cause battery ageing. The goal is to produce a simulation tool that can accurately predict the lifetime and performance of batteries by analyzing the current profiles from a hybrid system. The improved model will in a later project be implemented in a larger hybrid simulation platform IPSYS. The original MATLAB battery model requires further development, in order to shorten its simulation time and to improve battery lifetime predictions. The current model severely over predicts the lifetime of the simulated batteries and is in strong need of improvement. The current model does take into account several important physical properties, one among which is the effect of a low charge on the crystal distribution on the electrode s surface. In order to achieve an improved model a complete understanding of the current model is essential. Consequently, a review of the mathematics and the functions used in the model is undertaken. The parts of the model that need improvements must be identified. Furthermore, the model requires reconstruction to yield faster calculations and enable a later translation and implementation in IPSYS. This project will follow-up the request for more validation of the battery model, stated in earlier projects. The simulation results from the improved model will be analyzed in search of control strategies that will improve the battery lifetime in a hybrid system. Both old and new current profiles will be simulated in order to get an enhanced validation and complete understanding of the model. Even though some of the tested batteries are of the same type and brand, their performances may differ. By comparing simulation results it maybe achievable to understand the spread in performance between identical batteries. In summary the project aims are: Review of model mathematics, MATLAB implementation and used parameters. Identification of areas needing improvements and implement improvements. Enhancing the validation of the model by analyzing old and new current profiles. Analyzing simulation results in search of control strategies for improved battery lifetime. 7

12 3 LEAD ACID BATTERIES The unpredictable nature of renewable energy sources implies that in most autonomous cases, storage of energy is required to meet the power demand and ensure stability and power quality [8]. Lead acid batteries have been a successful solution for more than a century. The French physicist Raymond Gaston Planté performed initial research in Even though the lead acid battery suffers from a poor energy-to-weight ratio it is the most commonly used rechargeable battery today. The explanation for this is that the battery provides high-quality performance and has fairly satisfactory life characteristics. This has resulted in the battery being available in many different designs and sizes at a low price, in fact it is the least expensive storage battery and the battery type is sold in growing numbers [9]. A normal sized battery consist of six cells with a combined voltage of around 12 V and a capacity of Ah. The overall chemical reaction that occurs is: disch arg e Pb + PbO2 + 2 H 2SO4 2PbSO4 + 2H ch arg e 2 O This will result in a cell voltage of 2.0 V depending on the acid concentration. Looking upon the different electrodes; at the negative electrode Pb is oxidized to Pb 2+ during discharge. The Pb(II) ions then react with sulfate ions from the acid and form lead sulfate. Pb disch arg e 2 Pb + + 2e ch arg e Pb 2+ + SO 2 4 disch arg e PbSO ch arg e At the positive electrode PbO 2 reacts during discharge with the incoming electron and a proton from the acid to form Pb 2+ and water. The Pb 2+ reacts with sulfate from the acid to form lead sulfate. disch arg e + _ 2+ PbO2 + 4 H + 2e Pb + 2H ch arg e 2 O Pb 2+ + SO 2 4 disch arg e PbSO ch arg e For charging, the reaction is reversed. As the cell approaches full capacity the electrode reactions are pushed to the left, converting the majority of PbSO 4 into Pb and PbO 2. The lifetime of a battery is counted in cycles. A complete cycle is equivalent to a full discharge and charge, and varies widely depending on brand and model. A SLI (Starting, Lightning, Ignition) battery is designed for shallow cycles and is not designed to survive deep discharges. A typical lifetime for the shallow cycle cell design is about 300 cycles while a battery design for deep discharges can withstand cycles to an 80 % depth of discharge [2]. There are several different lead acid batteries on the market. Examples are flooded, SLA (sealed lead-acid) and VRLA (valve-regulated lead-acid) types. Flooded batteries are the most widespread type, with a liquid electrolyte, for example used in most vehicles. Market needs have driven the development of two new kinds of lead acid systems SLA and VRLA. The difference from flooded batteries is that the electrolyte is absorbed in a gel which makes it possible for the battery to operate in different orientations without spillage [8]

13 3.1.1 Major stress factors of the batteries There are several factors that influence the performance characteristics of a battery. One such factor is the discharge rate which states the current that has been applied and duration. Other examples are the amount of time the battery has been at low state of charge, the time between full charges, and the battery temperature. The temperature is a very important parameter since it strongly affects the chemical activity in the battery Major damage mechanisms Corrosion of positive grid At the positive electrode, oxidation transforms Pb into PbO and PbO 2. A thin layer with lower conductivity starts to grow around the positive electrodes as the battery ages. This layer with lower conductivity will increase electrical resistance, as the layer grows in thickness. It will also develop mechanical stresses within the structure. The battery will suffer from capacity losses through an increase in internal resistance. There are three main factors that affect corrosion: battery voltage, acid concentration and temperature. For least damage, the battery voltage should be kept at float voltage, for definition see appendix 1. Both low and high voltages increase the corrosion speed. Increased acid concentration will also increase the corrosion speed. Different acid concentrations have different densities and will react differently to gravity. Stratification will appear where several different concentration layers are formed. High concentration layers are formed close to the bottom and intensify the corrosion. The temperature also affects the corrosion speed. Lead acid batteries have an optimum operation temperature at 25 C. A temperature of 8 C would decrease the battery lifetime by half [8]. Hard/irreversible sulphation Sulfate crystals are formed at both the positive and the negative electrode throughout discharge. To achieve a continuous cycle these crystals are dissolved during charging. However, during certain operation conditions, lead sulphate crystals can aggregate into larger crystals. These crystals may be hard to dissolve and form particularly if the battery is not operated properly. This chemical response is called hard or irreversible sulphation and occurs for instance if the battery is stored during a long time in discharged condition. Least damage is caused to the battery if it is stored under float charge, when the voltage is charged with a slightly higher voltage than the battery voltage and a small current. This procedure prevents self discharge [8]. The sulfate crystals create mechanical stresses within the electrode structure since they have a larger volume than the PbO 2 or Pb atoms. Active material will be lost in the formations of the crystals, resulting in capacity losses [10]. Higher discharge currents have a positive impact on the battery lifetime compared to low discharge currents, a relation that can be surprising. The explanation lies in the crystal structure of the electrodes. Under ideal conditions a fully charged battery does not have any sulfate crystals left after recharging. This is not the case for a regular battery under normal conditions. During a discharge with a small current a small number of crystals with a large radius are formed. These crystals will gradually grow over a long time to become large and difficult to dissolve. A charging for a longer time is necessary after a discharge with a small current. A large discharging current, on the other hand, results in small crystals in large quantities with a large surface area. Experiments have showed that large crystals surfaces are easer to dissolve [11]. 9

14 Active mass degradation Degradation [8] is a loss of active material due to the reconstruction process during charging and discharging. It is a change in the mechanical structure of the electrodes that will reduce the porosity and thereby the surface area that is essential for ion transport. The loss in area will affect the chemical reaction and reduce the diffusion of the electrolyte. This process cannot be restored in an attempt to fully charge the battery. The active material can, by repeated cycles, become crystalline and finally break loose from the electrode. Shedding As a consequence of both corrosion and active mass degradation, mechanical stress can result in material detaching from the battery structure. This process is called shedding [8] and results in a loss of active material. For example overcharging can cause shedding. Electrolyte stratification It can be discussed if electrolyte stratification [8] is a separate damage factor or simply an accelerator for the corrosion discussed previously. During the chemical processes that occur during charge and discharge of the battery, the concentration of the electrolyte fluctuates. Gravity will affect the different electrolyte concentrations. Higher density electrolyte will sink towards the bottom and an electrolyte gradient will be built up. By overcharging a battery, bubbles are formed which mix the electrolyte and the problem with stratification can be overcome Battery controller The battery controller supervises the charging algorithm. A common approach is to divide the charging into three steps. The standard charging method is called an IUIa charge [8]. During charging the battery is charged with a constant current. This current is called the bulk current. The charging continues until the voltage reaches the upper voltage limit point, in this case 2.4 V. At the end of the first step the voltage increases up to that level where gassing occurs. This part is called the I phase. In the next phase, the U phase, the voltage is kept constant meanwhile the current lowered. The current drops down to a constant value and the Ia phase begin. The voltage can increase until it reaches an earlier defined safety point [12]. A good quality controller should also operate as a deep discharge protection. Otherwise during deep discharges a thin PbSO 4 layer is formed at the surface of the battery plates and, as mentioned earlier, this layer can be hard to dissolve resulting in degradation that reduces the capacity dramatically [12]. To prevent acid stratification [8], the controller should allow some periods of over charging. Acid stratification occurs mostly in PV systems where the charging procedure is a slow process. During overcharge hydrogen and oxygen bubbles are formed that will force the electrolyte to blend. This procedure is optimised if it is allowed to occur during 1-2 h each month. If it occurs too often then the battery lifetime will be decreased due to corrosion. The acid stratification will be discussed in more detailed later. 10

15 3.2 Battery model The following text presents an overview of the battery model used in this project. Mathematical simulations make the development of new technology both faster and more reliable. By using the power of the computer it is possible to save both time and cost from expensive experiments. The main goals with the development of the battery model are optimization of systems and minimizing cost of storage by simulating major damage mechanisms. A good knowledge in energy storage is a key factor for a successful development. The original battery model was developed at Fraunhofer-Institute, Freiburg and used for lifetime estimations of batteries in photo-voltaic systems. In order to be able to perform estimations of current profiles from wind systems, improvements of the model have been done, partly at Risø, (European Union Benchmarking research project)[8]. Simulations of battery lifetime in hybrid systems are essential to be able to make relevant cost estimations of the system. The batteries constitute a significant part of the investment cost and it is commonly agreed that the weakest part of renewable based rural energy systems is the batteries. A large part of this project has been to review the model, with the ambition to understand how the different functions of the model interact in order to predict performance and lifetime of the simulated battery. The mathematics behind the model will be discussed in more detail in chapter 3.0. This section will provide an overview of the structure of the model. There are several different methods to develop a lifetime model. The models used for this project combine a performance model with an ageing model. Figure 3 A strongly simplified flowchart of the FhG/Risø battery model. Figure 3 provides a simplified flowchart of the calculations in the model. [8] 11

16 The input into the model is a current profile containing the information used by the battery model to determine how the battery ages in the system. Another input is the battery specific parameters that describing the type of battery simulated. Some of these parameters are defined by the battery manufacturer others are established through a parameter fitting methodology. The performance model is primarily constituted of two parts; charge transfer and the battery voltage. The charge transfer, SOC (state of charge), is calculated by a time integral of the current input. For this battery simulation tool, and for most other battery models, the voltage is calculated by the Shepherd Equation. The voltage is calculated with respect to the current profile, discussed in more detail in chapter The voltage is used as a control parameter and it is the voltage model parameters that are used in order to simulate the ageing mechanism. These calculations are performed at every model timestep according to the current input and various weighting factors. If the battery capacity falls below 80 % of its nominal capacity 1 the battery life-time expires. The main assumption in the battery model is that degradation and corrosion are assumed to be calculated separately. Thereby, the ageing model can be built by a corrosion part and an active mass degradation part. The degradation embraces damage mechanisms such as hard/irreversible sulfation, shedding, electrolyte stratification and active mass degradation. Some of these damage mechanisms are simulated indirectly by using parameters and data from earlier performed battery tests. The output from these calculations results in different factors that combined simulates the reduction in capacity. By subtracting the reduction from the nominal capacity the remaining capacity is achieved which is a measurement of battery lifetime Batteries simulated As mentioned above the batteries, if not treated correctly, can be a weak link in the system. Testing has been performed on the two types of lead acid batteries that are used extensively in renewable energy systems. As a validation of the performance of the battery model tests were carried out in three laboratories CRES, JRC ISPRA and GENEC. The batteries are manufactured by BAE and known as OGI 50 and OPz 50. Both are of the type 6 cells and an output voltage of 12 V. The rated capacities of both batteries are 50 Ah. The OGi battery has a positive electrode made by a round-grip plate in a corrosionresistance Pd alloy and the negative electrode made by a flat plate based on antimony alloy. The OPz battery has a positive electrode consisting of a tubular plate with a woven polyester gauntlet of Pd alloy. The negative electrode corresponds to an antimony grid equivalent to the one used for the OGi battery. [14],[15] 1 For definition see appendix 1 12

17 3.2.2 Battery model input The battery model uses a current input in order to calculate battery voltage output. Depending on what system the battery is connected to, the current input profile will differ. In the case of the wind charge of the battery the profile has a wide distribution range compared with a PV charge. During the development of the battery model several different batteries have been subjected to test current profiles. These tests are then used for calculations, evaluation and calibration of the performance of the battery model. The present model has been tested against two different current profiles; the wind and the photovoltaic (PV). The wind and PV profiles are constructed to represent the operating conditions for batteries used in hybrid systems. Wind profile A wind block consists of 1 h discharge to reach 90 % SOC, followed by 50 wind profiles and a capacity test. One profile has the duration of hours and is produced by multiples of I 10 to ensure comparability. [8] Figure 4 Current profile for wind simulations. PV profile The photovoltaic profile is shown in Figure 5. The magnitude of the current is smaller than for the wind profile. Consequently, the PV profile will have a smaller effect on the lifetime of the batteries compared with those tested with the wind profile, which is also the case in reality. Figure 5 Current profile from PV simulations. The PV blocks are constructed by an I 10 discharge for two hours until a SOC of 80 % is reached. This is followed by 35 PV profile cycles, a discharge for three hour to reach a SOC of 50% continued by additional 35 PV profiles. The final part is made by a charge of a three hours charge to a SOC of 80 % continued by 35 PV profiles. [8] 13

18 Capacity tests Each test file consists of numerous blocks followed by a capacity tests. The capacity tests consist of three capacity measurements. The first one is a residual capacity test designed to measure the capacity left in the battery after each block. The second one is a solar capacity measurement, designed to replicate the typical charge from a photovoltaic system. The third measurement is to estimate the true capacity of the battery and is followed by an IUIa charge described earlier. [8] Test runs This section presents the test results of the simulations with the initial MATLAB model [15]. From Figure 6(a) it is possible to see that the model over predicts the lifetime of the test battery, since the remaining capacity (blue) does not fit the capacity test of the test battery (red stars). Instead the simulation stops when the battery remaining capacity reaches 80 % of the rated capacity (630 days). (a) (b) (c) Figure 6 Simulation results from the initial model. OPz Battery. Wind current profile from CRES. From top to bottom: (a) Remaining capacity (blue), State of charge, SOC (F, green) and test battery capacity (red stars). (b) Modelled voltage (U cell, blue). (c) Test current (I blue), Modelled controlled current (I batt, green), Initial discharge current (I cf, red) 14

19 In Figure 6(a) it can be seen that the capacities start at 150 %. This is explained by the actual capacity of the battery being larger than the nominal capacity defined by the battery manufacturer. 2 The manufacturer deliberately under predicts the capacity of the battery to ensure that under all circumstances the actual capacity is greater than the nominal capacity. Figure 6(b) presents the simulated voltage calculated by the Shepherd equation, described in detail in chapter 4.3. The bottom diagram, Figure 6(c), shows the test current in blue and the modeled current in green. After 210 days the controller steps in to restrict the charging current to save the battery. The controller is currently extracted from the improved model and later simulations will not show this behavior. Figure 7 is an enlargement of the model voltage compared with test. It is possible to see that the modelled voltage does not follow the peaks of the test voltage. It needs to be mentioned that this is a lifetime model and not designed to perform accurate calculations of the voltage. Most noticeable is the over prediction of voltage swings. An additional observation is that the voltage fits better during charge than discharge. Figure 7 Difference between the modelled voltage and the simulated voltage. The battery model was made for PV systems with currents in the range of I 10 or less. By including the wind profile the currents increase. This affected the simulations and made the model over predict lifetime of the batteries. The model includes simple control strategies, such as cut off. The over voltage controller steps in at voltage of 2.45 V/cell. 2 For definition of the different capacities see appendix 1 15

20 Figure 8 presents the coefficients that result to a decline in capacity Initial discharge capacity coefficient (C d, green). Capacity reduction from degradation (C deg, red). Capacity reduction from corrosion process (C k, light blue ). Internal resistance (rd total = ρ d,total, mauve). Increase in internal resistance from the corrosion process (r k =ρ k, yellow). Figure 8 shows the contribution of various capacity factors to the total capacity. The degradation (C deg ) contributes to the largest reduction in capacity while the corrosion coefficient (C k ) contributes only to a small extent for this OPz battery. The total capacity coefficient (Cd total ) is derived by subtracting the different reductions in capacity (C deg, C k ) from the initial discharge capacity coefficient (C d ). From the result of the benchmarking project there was an appeal for more test data to validate the operating mechanism in the model and a request to validate the model in full scale system testing. 16

21 4 METHODS 4.1 Improved code Varying time steps The original model was programmed to calculate data with a constant time step of 300 s. Such a constraint is not valid for the newly assembled datasets from ISPRA since the data was sampled at different frequencies. Modifications have been made so that the model can cope with data files with varying time steps, both in calculations and presentation of simulation result. Each time step is calculated individually by (Eq1) t = timevector( i + 1) timevector( i) Eq 1 The code for graphical presentation has been rebuilt to incorporate a varying time step. The improved model presents the simulation results as a function of a cumulative summation of the time steps. Through this approach it is possible to get a continuous timescale measured in days that starts at zero and continues until the battery is considered dead. Furthermore, computer memory is saved by only displaying every twentieth simulation value. This resolution still guarantees sufficient data for representative figures. To facilitate further use and analysis of simulation results all figures are auto saved with proper filenames in (jpg)-format into a user defined directory Improved design with object-oriented programming, OOP An important step to improve the structure of the model is to evolve the OOP (object-oriented programming) technique. The OOP technique was used in the initial model but not in full extent. This section will try to provide the reader with a short survey of this programming theory. OOP is about programming abstract data types (ADT), and their relationship. By this method it is possible to break up the program into separate fractions that will result in a better organised program. The modules of OOP are called classes. A class is an expansion of the principle of struct used in the traditional C-language. Each class can be seen as a blueprint to objects, like a car factory using the blueprint to produce cars of a certain brand. An object can be described as an exclusive variable that both stores data and is able to satisfy the requests sent to it. The function that answers the requests inside the object is called a method. Each object has its own user defined methods. A good program consists of a web of interacting objects, sending information telling each other what to do. By this communication it is possible to build up system complexity but at the same time hide behind the simplicity of the object. A proper OOP structure will contribute to an easier translation into IPSYS and C++ [17]. The initial MATLAB model consisted of one single large battery object that contained all mathematical methods used for the simulation. The large battery object in turn consisted of smaller 17

22 structures such as voltage and degradation. This made foreseeable difficult but it also implied that a method could by a simple mistake easily change variables outside its scope, since it had access to all variables. To improve the structure the large battery object was divided into smaller objects. The structures used in the initial model were upgraded to objects and corresponding methods were moved from the large object into the object it belonged to. By restricting the methods to only be able to write to the variables that belong to the same objects, data were encapsulated and secured for manipulation from the outside by another object. To improve understanding, all methods were renamed with a name that expressed what purpose their functions have to fill. Furthermore, since the battery model has its origin in Germany some variables had to be translated into English. To ensure that the variables are defined and used in the right object a variable overview graph was constructed using the DOT software [18]. The overview prevented the variables from being defined in the wrong objects, which would lead to unnecessary communication between the objects, and thereby use unnecessary CPU power. The structure was optimised by moving the variables into the objects where they were utilized. The principle is shown schematically in appendix 2 where also the new variable structure is shown Vectorizing Calculation speed can be increased by replacing traditional if and for statements with inbuilt vector functions that MATLAB offers. One example of this principle was implemented in the part of the code that calculates the dynamic timestep. The initial code was: for i=1:data_length % Main program loop. Each iteration is one timestep. if (i<data_length) dt=(data(i+1,1)-data(i,1))*24; % calculates timestep from days to hours. end if (i==data_length) dt=0.0001; end end This was replaced with the single statement: dt_series=[diff((data(:,1)-data(1,1))*24);0.0001]; Vectorizing followed by removal of unnecessary statements improved calculation speed dramatically and as a side effect improved the readability of the code Global Variables The initial model uses global variables, which are variables initial declared and accessed from any part of the program. In the improved model this element is replaced. The definitions of variables are instead moved into the objects where they are used. Furthermore, these variables are now write protected to secure their value. 18

23 4.2 Current factor Definition of Current factor The first battery model in MATLAB made poor predictions since it underestimated the battery lifetime dramatically. Especially for the wind profiles, where higher currents are present, it could be seen that the deep discharge factor, a factor implemented in an attempt to simulate the effects that result by deep discharging a battery, had a strong impact that reduced the predicted lifetime. This had not been seen earlier since the original model from Fraunhofer-Institute used smaller PVcurrents. In reality it is the opposite. A high discharge current has a positive impact on battery lifetime; this will be explained in further detail later. A factor called the current factor (CF) had been implemented in the initial model to be able to deal with high currents that otherwise would have had an unbalanced effect on the lifetime. The factor was designed to reduce the rate of capacity degradation at high currents. For the calculations an average period of 36 hours and a tuning constant C was used, see chapter for mathematic definition. These parameters are arbitrary numbers and do not have a physical basis. After some consulting it was decided that the current factor needed to be redefined and a new approach needed for the improved model. During discharge, Pb at the negative electrode and PbO 2 at the positive electrode will oxidise to Pb 2+. A large discharge current will result in that a large number of Pb 2+ ions are formed. The opposite relation pertains to a small discharge current. If a seed PbSO 4 crystal is present the reaction Pb 2+ + SO 2-4 PbSO 4 will begin and thereby lower the concentration of Pb 2+. If a seed crystal is not present the ion concentration of Pb 2+ must be high compared with the saturation concentration in order for the reaction to take place. As soon as a crystal is present the PbSO 4 molecules will aggregate into larger crystals. This reaction will decrease the Pb 2+ ion concentration and the production of PbSO 4 will cease. Consequently, new PbSO 4 molecules are formed at the initial state of the discharge. A small discharge current will result in a smaller number of PbSO 4 molecules. Furthermore, a small discharge current implies a long period of discharge, ensuring that the crystals will have time to arrange into large structures. The opposite occurs for a large discharge current. A large number of crystals are formed, but since the discharge time is reduced by the battery capacity only small PbSO 4 structures are able to build up [11]. A comparison of the crystals surface area can be made. The high discharge current with its large number of small crystals, will have a larger surface area than the crystals from a lower discharge current. Experiments have shown that when the battery is charged a larger surface area is easier to dissolve than a smaller surface area. Consequently a large discharge current is optimal for a battery. A small discharge current will result in longer charges to dissolve the large crystals. Additionally there is a risk that crystals are not dissolved and that the battery would age by sulfation. This theory can be used to define a new current factor. Poor recharging affects the size and number of crystals present on the electrodes of the batteries. If a battery is not properly charged the surface of a single crystal increases but the total number of crystals decreases. The result is that the total crystal surface area decreases, which makes later charges more difficult. In an attempt to simulate the influences of poor charging a factor was implemented that keep track on the number of poor charges. A bad charge is defined to occur when the SOC does not reach 99 % [11],[19]. 19

24 4.2.2 Current factor used in the initial model For calculations of the current-factor, in the initial model [8], a running discharge current average is required. It was calculated by summing the discharge Ah-throughput over the past 36 h, Q 36h in (Eq 2), and dividing by the sum of the time steps as these discharges occurred, T 36h in (Eq 3). The average discharge current is expressed by (Eq 4). Q 36 h = t I disch arg e past 36h t Eq 2 T 36 h = t t past 36h Eq 3 I average disch arg e = Q T 36h 36h Eq 4 This average discharge current was then used in (Eq 5) to achieve the current factor that gets the value 1 for small currents and 0.1 for large current values. C N is the nominal battery capacity. currentfactor = I C C N average discharg e Eq 5 In the above expression a constant C is introduced. By changing the magnitude of C the current factor can be tuned. A value of C equal to 0.1 will result in a current factor of size 1 for a current of I 10. All higher currents will result in a current factor < 1. Accordingly, if C is set to 0.01 the current factor will equal 1 for a current of I 100 and all higher currents will result in smaller values. This will reduce the impact on the aging mechanism and the simulated battery lifetime will be increased. This is something that is not physically explained and needs to be reworked in the improved model. 20