The Pennsylvania State University The Graduate School MODELING BATTERY-ULTRACAPACITOR HYBRID SYSTEMS FOR SOLAR AND WIND APPLICATIONS

Transcription

1 The Pennsylvania State University The Graduate School MODELING BATTERY-ULTRACAPACITOR HYBRID SYSTEMS FOR SOLAR AND WIND APPLICATIONS A Thesis in Energy and Mineral Engineering by Charith Tammineedi 2011 Charith Tammineedi Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2011

2 The thesis of Charith Tammineedi was reviewed and approved by the following: Jeffrey R. S. Brownson Assistant Professor of Energy and Mineral Engineering Thesis Advisor Ramakrishnan Rajagopalan Research Associate of Materials Research Institute Susan W. Stewart Research Associate of Aerospace Engineering and Architectural Engineering Yaw D. Yeboah Professor of Energy and Mineral Engineering Head of the Department of Energy and Mineral Engineering Signatures are on file in the Graduate School.

3 Abstract The purpose of this study was to quantify the improvement in the performance of a battery with the addition of an ultracapacitor as an auxillary energy storage device for solar and wind applications. The improvement in performance was demonstrated through simulation and modeling. A ceraolo battery model and a third order ultracapacitor ladder model were implemented in Matlab/Simulink. Sample battery load cycles for solar and wind applications have been obtained from literature and the corresponding C-rates were quantified. The C-rate for the solar load cycle was found to be 0.3C and 0.2C for the wind load cycle. The performance of the batteryultracapacitor system was checked for the sample solar and wind load cycles and compared with the performance of the battery system without an ultracapacitor. A reduction of 50.5% in battery RMS currents was found for the solar load cycle and 60.9% for the wind load cycle. This reduction in battery RMS currents was found to be directly proportional to the ultracapacitor contribution. Given the low C-rates for the sample load cycles it was deduced that the addition of an ultracapacitor will not significantly improve the battery life to justify the high initial costs. ii

4 Table of Contents List of Figures List of Tables List of Symbols Acknowledgments v vii viii x Chapter 1 Literature Review Introduction Lead Acid Batteries Lead Acid Chemistry Discharge Process Charge Process Lead Acid Battery Models Operating Conditions of Batteries in Solar PV systems Battery Aging in PV systems Sulfation Acid Stratification Ultracapacitors History Principle of operation - Simple Double Layer capacitor Classification and materials used Double Layer Capacitors Capacitors utilizing pseudo-capacitance Hybrid (Asymmetric) Capacitors Ultracapacitor Applications Ultracapacitor Cost considerations Ultracapacitor Modeling Classical Equivalent Circuit Model Transmission Line Model Justification for using Third Order UC Model iii

5 Chapter 2 Modeling Battery-ultracapaitor hybrid system Lead Acid Battery Model Ceraolo Battery Model Battery Capacity State of Charge(SOC) and Depth of Charge(DOC) Extracted Charge Main Branch Voltage (Em) Main Branch Resistance (R 1 ) Main Branch Capacitance (C 1 ) Terminal Resistance (R 0 ) Main branch Resistance (R 2 ) Parasitic branch Current (I p ) Thermal Model Component development in Simscape Third Order Ultracapacitor Modeling Energy Storage System Sizing Battery Sizing Ultracapacitor Sizing Simulation Environment Chapter 3 Results and Discussion Battery Modeling results Solar Load Cycle Battery response without ultracapacitor Battery response with ultracapacitor Ultracapacitor Response Wind Load cycle Battery response without ultracapacitor Battery response with ultracapacitor Ultracapacitor Response Impact of DC-DC converter block Initial System costs Chapter 4 Conclusions 46 Appendix A Model Implementation In Matlab 48 A.1 Battery and Ultracapacitor Models A.2 Storage System Costs: Wind Bibliography 52 iv

6 List of Figures 1.1 Ragone Plot - Lead Acid Battery Ragone Plot - Energy Storage options Characteristic Output of Large scale Wind systems[1] Characteristic Output of Large scale Solar systems[2] Solubility curve for lead sulfate in sulphuric acid[3] Thevenin Battery Model Non-Linear Battery Model Battery Currents in units of I 10 for European Conditions[4] State of Charge for different Classes of operating conditions[4] Maxwell BOOSTCAP ultracapacitors Ultracapacitor[5] Classical equivalent Circuit Model Ladder Model Comparison of accuracy of various orders[6] Working Order of Ultracapacitors Lead-acid Battery equivalent electric model Battery Stack building Third Order Ultracapacitor Model Ultracapacitor Order Reduction Methodlogy Measured vs Modeled Voltage (V) Solar Load cycle Solar C-Rate Solar Load cycle:battery Performance w/o ultracapacitor Solar Load cycle: Battery Performance with Ultracapacitor Solar Load cycle: Ultracapacitor Performance Solar Load cycle: Battery-Ultracapacitor currents Wind Load cycle Wind C-Rate Wind Load cycle: Battery Performance w/o ultracapacitor Wind Load cycle: Battery Performance with ultracapacitor Wind Load cycle: Ultracapacitor Performance Wind Load cycle: Battery-Ultracapacitor currents Solar Load cycle: Impact of DC-DC converter Solar Load cycle:battery Current Histogram w/o ultracapacitor Solar Load cycle:battery Current Histogram with ultracapacitor v

7 3.17 Wind Load cycle: Battery Current Histogram w/o ultracapacitor Wind Load cycle: Battery Current Histogram with ultracapacitor A.1 Battery Model in Matlab A.2 Ultracapacitor Model in Matlab vi

8 List of Tables 1.1 Classes of battery operating conditions Comparison battery and ultracapacitor characteristics[7] Classification of Ultracapacitors[8] Performance Characteristics of Ultracapacitor technologies[8] The specific capacitance of selected electrode materials[8] Ceraolo Model Parameters[9] Model Parameters of Maxwell 100F Scaled Ultracapacitor Model Parameters Battery and Ultracapacitor Sizing Energy Storage System Specifications Solar Load Cycle: Energy Storage System Performance Energy Storage System Specifications: WInd Wind Load Cycle: Energy Storage System Performance A.1 Energy Storage System Costs: Wind A.2 Energy Storage System Costs: Solar vii

9 List of Symbols Letters θ f Electrolyte freezing temperature Q Charge C Capacitance θ Electrolyte Temperature I avg Mean Discharge current(a) E m Main branch voltage E m0,k E constants for a battery R 1 Main branch resistance R 10 Emperical constant R 0 Terminal resistance A 0,R 00 Constants for a battery R 2 Main branch resistance R 20,A 21 and A 22 Empirical constants for a battery I p Current loss in the parasitic branch V P N Voltage at parasitic branch G p0 Constant V p0 Constant A P Constant θ a Ambient Temperature P s Internal Heat generation (W) C θ Thermal Capacitance ( J o C ) N Scaling Ratio ( o C) R knew New Resistance (Ω) N s Cells in series N p Cells in parallel V Voltage drop viii

10 Abbreviations & Acronyms PV CEC HEV EV EDLC RMS ESR EPR SOC DOC DoD Photovoltaic Classical Equivalent Circuit Hybrid Electric Vehicle Electric Vehicle Electric Double Layer Capacitor Root Mean Square Equivalent Series Resistance Equivalent Parallel Resistance State of Charge Depth of Charge Depth of Discharge ix

11 Acknowledgments I would like to first thank my advisor Dr. Jeffery Brownson for giving me this opportunity and introducing me to the beautiful world of solar energy. I would like to thank Dr. Ramakrishnan Rajagopalan for his valuable guidance throughout the course of this project and Dr. Susan Stewart for her valuable input. I would also like to thank Luke Witmer and Ramprasad Chandrasekharan for their considerable help in various aspects of this project. x

12 Dedication For my parents to whom I will forever be in debt for their constant love and support. xi

13 Chapter 1 Literature Review 1.1 Introduction The rapid deployment of stand-alone renewable energy systems such as wind and solar is limited by high life cycle costs. One main contributor to the high life cost is the battery bank which is used to store electricity generated from intermittent systems such as wind and solar. Energy Storage is an integral part of renewable energy systems such as wind and solar due to their intermittent nature. However this very intermittent nature of their output causes the battery to operate at conditions that it was not designed for. They often operate at deep-discharged and overcharged states and the continuous exposure to rapid charge/discharge profiles degrades the battery performance and reduces its lifetime[3, 10, 11]. The reduced battery lifetimes lead to frequent replacement thereby increasing the overall life cycle costs. Shown in Figure 1.1 is the Ragone the plot of the lead acid battery. It can be seen that the as the power demand increases the battery energy capacity decreases due to which the batteries need to be oversized for high power applications. This can be a problem for space constrained applications and additionally for high discharge rates (>18C) the battery lifetime is also reduced significantly[3]. It can be seen from Figure 1.2 that ultracapacitors have much higher than power densities and have the potential to complement traditional battery systems[12]. This configuration is mainly being considered by the automotive industry for HEV and EV applications because of the potential reduction in the size/volume of the overall energy storage system. The usage of ultracapacitors also decreases the current loads on battery systems thereby potentially improving battery lifetimes. It is this because of these advantages, that makes it worth investigating the battery-ultracapacitor configuration in the context of PV and wind systems. Previous studies have shown that a simple parallel combination of battery and ultracapacitor leads to improved energy storage system performance [13, 14]. It has been shown theoritically that peak power of the energy storage system can be enhanced, internal losses be reduced and discharge life of the battery be extended with the usage of ultracapacitors[13]. Experimental

14 Energy Density (Wh/Kg) 100 Area of Operation Power Density (W/Kg) Figure 1.1. Ragone Plot - Lead Acid Battery 1000 Fuel Cells 10h 1h 0.1h 100 Lithium-ion 36 sec Energy Density (Wh/Kg) Lead-Acid Double-Layer Capacitors Ultracapacitor 3.6 sec.36 sec 36 msec Electrolytic Capacitors Power Density (W/Kg) Figure 1.2. Ragone Plot - Energy Storage options

15 3 studies on battery-ultracapacitor hybrid systems have been conducted and demonstrated improved performance[14]. Battery-ultracapacitor hybrid have first been explored as an alternative to batteries subjected to pulsed loads in digital communication applications[15]. Studies have demonstrated that ultracapacitors are a good fit with fuel cell systems which have poor dynamic response [14, 16, 17, 18]. Battery-ultracapacitor hybrid systems are being explored as an alternative to traditional battery systems by the automotive community due to potential size reduction and potential improvement in battery lifetime due reduction in battery RMS values[18, 19]. Ultracapacitors are also being considered for use in renewable energy applications especially wind[20, 21, 22]. For PV applications some studies have directly integrated the ultracapacitors to the PV systems for improving efficiency and reliability[23, 24]. The characterization studies of large scale PV and wind output have revealed that ultracapacitors can share the load during high frequency power fluctuations and other high energy density devices can provide fill in power over lower frequencies as shown in Figure 1.3 and Figure 1.4 [1, 2]. 1.2 Lead Acid Batteries Renewable Energy Systems like Solar and Wind are intermittent in nature. For stand-alone applications they often require energy storage systems to provide the fill in power. Batteries have been traditionally used to provide the fill-in power for solar and wind systems The Lead Acid Battery is one of the widely used electrochemical energy storage systems. This can be attributed to its chemical and physical properties that makes it an efficient system and suitable for a variety of applications. A few of these properties are given below. ˆ The reactants are solids of low solubility which causes a stable voltage and higly reversible reactions ˆ Both electrodes contain only lead and lead compounds as active material that do not require conducting additives ˆ It has a high cell voltage of 2V ˆ Lead Acid technology is cheaper than most technologies and is the primary reason for being widely used in renewable systems where larger storage capacities are required Lead Acid Chemistry The reaction inside the lead acid battery consists of several steps before the actual charge transfer. The slowest step is what determines the overall rate of the reaction. It is thus essential to understand the individual steps to understand the overall response of the lead-acid battery and also the subsequent aging mechanisms at high discharge rates. The overall reaction of the leadacid battery can be given by,

16 4 Figure 1.3. Characteristic Output of Large scale Wind systems[1] Figure 1.4. Characteristic Output of Large scale Solar systems[2]

17 5 Pb + PbO H 2 SO 4 2 PbSO H 2 O where Pb and PbO 2 are the reactants and PbSO 4 is the product of the cell reaction. Lead sulfate is formed as a product at both electrodes since lead is the basic element in both the electrodes Discharge Process Reaction at Negative Electrode: During the discharge process the Pb atoms of the negative electrode are converted to Pb 2+ ions. This reaction can only take place on conductive sites i.e on fresh lead. Therefore the rate of this reaction is dependent on the surface area of the fresh lead available. Pb Pb e Given the concentration ranges of H 2 SO 4 in the battery it would have already dissociated into H + and HSO 4. Only about 1 percent of the H 2 SO 4 molecules dissociate into 2 H + and SO 4 [25]. The Pb 2+ then reacts with HSO 4 to form PbSO 4 (Lead Sulfate) which is termed the Deposition process. Pb 2+ + HSO 4 PbSO 4 + H + This reaction is function of the both Pb 2+ and sulfuric acid concentrations. The solubility of lead sulfate reaches a maximum value at 10% concentration of the acid and it only decreases with further increase in concentration of the acid as shown in the figure1.5. So the overall discharge reaction now becomes, Reaction at Positive Electrode: Pb + H + + HSO 4 PbSO H e PbO 2 + HSO H e + PbSO H 2 O It can be seen that at higher concentrations of sulfuric acid formation of lead sulfate is faster. It would be ideal if the formation of this lead sulfate is uniform throughout the negative electrode but this is not the case in reality as the concentration of the acid in the interior of the electrode decreases and so does the formation of lead sulfate in these areas. The formation of lead sulfate is higher at the electrode electrolyte interface due to the higher concentration of sulfuric acid in these areas. The penetration of lead sulfate through the electrode is a function of surface area, paste density and discharge rates. For the same paste density and surface area the penetration becomes solely the function of the discharge rate. At lower discharge rates(< 0.4C 1 ) the formation of lead sulfate is slower. This is due to the lower concentration of Pb 2+ ions at the beginning of the discharge. The transport of HSO 4 to the interior of the electrode is balanced by the formation of lead sulfate. Hence the lead sulfate forms in the interior of the cell as well as the interface and thereby leading to a more uniform distribution of lead sulfate throughout

18 6 Figure 1.5. Solubility curve for lead sulfate in sulphuric acid[3]. the electrode.for high rates of discharge the supersaturation level Pb 2+ is high and so is its dissolution rate. This leads to a much faster formation of lead sulfate. The transport of HSO 4 cannot keep up with lead sulfate production so the interior quickly runs out of HSO 4 ions and the replenishment is not allowed to happen. Now the formation of lead sulfate is mainly in the outer regions of the electrode leading to non-uniform distribution of lead sulfate Charge Process The charge process consists of the dissolution of PbSO 4 to Pb 2+ and SO 2 4 followed by the subsequent deposition of Pb 2+ to Pb. PbSO 4 Pb 2+ + SO 2 4 H + + SO4 2 HSO 4 Pb e Pb

19 7 The overall charge process of the negative electrode is given by, PbSO e + H + Pb + HSO 4 During the charging process the electrons flow through the grid metal to the active sites as the electrical resistance of the grid metal is smaller than that of discharged material. Along with the deposition of Pb there is also the competing reaction of hydrogen evolution.now for the charging process after the battery has been discharged at low discharge rates,the relative density of sulfuric acid is more due to more utilization of active material. It can be seen from Figure 1.5 that at low concentration of acid the dissociation of PbSO 4 to Pb 2+ and SO 2 4 takes place easily. The subsequent deposition of Pb 2+ to Pb is not impeded and can take place before the evolution of hydrogen. On the other hand when the battery is discharged at high rates the relative density of acid is higher which plays a key role during subsequent charging. The rate of dissociation of PbSO 4 is slow. The subsequent lower concentration of Pb 2+ impedes the deposition of lead which decreases the active material available for the next discharge cycle. The evolution of hydrogen starts earlier than expected. The lead sulfate keeps accumulating after every cycle and eventually completely cuts off access to the active material thereby leading to battery failure due to sulfation.

20 8 1.3 Lead Acid Battery Models Batteries in general exhibit complex, non-linear behavior as they are electrochemical systems that store and release energy through oxidation and reduction reactions. There exist models that are based on the electrochemistry of the system [26][27] and also Equivalent circuit models that consist of capacitors and resistances used to represent the charge storing capacity of the battery and the resistance to the flow of charge respectively[28][29]. The most commonly used electrochemical model is the Shepherds model[26]. The shepherds model is used in several forms with modifications made to suite specific battery types. The simplest of the equivalent circuit models for batteries is the Thevenin Battery Model [28]. C 0 R R 0 E 0 Figure 1.6. Thevenin Battery Model As shown in the figure it consists of a no-load voltage source, internal resistance R, a capacitor C with a resistance R 0 in parallel to it. The values of the various components remain constant throughout the simulation which is why this model is not very accurate. In reality the values of the components are a function of several battery conditions like State of Charge(SOC), Battery Storage Capacity, Rate of Discharge and Temperature[30]. C 0 R 1d R 1c R 2d E 0 R p R 2c Figure 1.7. Non-Linear Battery Model

21 9 A non-linear Electrical Model consists of components whose values vary non-linearly.the functional forms that model the non-linearity of the individual components can be determined empirically. Two such models were found in literature, the Salameh Model [30] and the Ceraolo Model [9, 31]. For the purpose of this study the equivalent circuit model approach was selected due to its compatibility with the chosen simulation environment, Simscape. The Ceraolo model, a rate-dependent third order model was selected because of its well documented validation work, accuracy and ease of implementation within the Matlab/Simulink environment. The implemented battery model is shown in Appendix A Operating Conditions of Batteries in Solar PV systems It is essential to understand the typical operating conditions of batteries in stand-alone systems to be able to design them properly. Additionally most of the aging processes are a function of these operating conditions and a good understanding is necessary to optimize battery life. The following classification has been made based on an intensive study of 30 stand-alone PV systems (under European conditions) that use batteries by the authors of [32, 4]. Table 1.1. Classes of battery operating conditions System Indicators Class 1 Class 2 Class 3 Class 4 Solar Fraction 100% % 50% < 50% Days of Autonomy Currents small small medium high Capacity throughput Based on the operating conditions they are divided into four classes. Where Class 1 is a system without a back up diesel generator and is designed to be highly reliable. Class 2, 3 and 4 are hybrid systems with increasing capacities of diesel power back-up. It can be seen in Figure 1.8 that for class 1 battery the normalized discharge rates are not very high and for classes 2, 3 the normalized discharge rates are relatively higher. For class 4, where battery size is relatively smaller, the normalized discharge currents are higher than classes 2 and 3. Due to the availability of diesel generator back-up, the days of autonomy for the battery for classes 2,3 and 4 do not have to be very high. As a result the smaller sized batteries are subjected to relatively larger number of charge/discharge cycles. Similarly it can be seen from Figure 1.9 that the battery depth of discharge is higher for classes 2 and 4. The class 3 battery has however been designed to operate at much higher states of charge even though the rates of discharge are similar to classes 2 and 3. From the capacity throughput values (defined as ratio of Ampere-hour discharged from the battery to the nominal capacity of the battery) it can be seen that the number of charge/discharge cycles is increasing progressively from class 1 to class 4 with class 4 battery being subjected to the most number of cycles (>1200 cycles). Given the lower discharge rates of class 1 and class 2 batteries, it can be theorized that they will not be facing the same

22 10 Figure 1.8. Battery Currents in units of I 10 for European Conditions[4]. Figure 1.9. State of Charge for different Classes of operating conditions[4].

23 11 aging problems as the batteries of class 3 and 4 which have higher discharge rates Battery Aging in PV systems Sulfation As elaborated in the sections above during the discharge process of a lead-acid battery lead sulfate is formed (P bso 4 ) is formed and during the subsequent charging process it gets dissociated into Pb 2+ and SO 2 4. However in reality the complete dissociation of lead sulfate never happens[11]. The remaining lead sulfate represents the loss in capacity for the immediate discharge cycle. As the number of cycles increases the lead sulfate that could not be dissolved keeps accumulating and the capacity loss keeps on increasing until the battery completely fails. The rate of dissolution of lead sulfate is directly proportional to its surface area. Hence it is essential to maximize the surface area of the lead sulfate during its formation. At high discharge rates the lead sulfate does not penetrate throughout the electrode but is formed preferentially on the areas closer to the free electrolyte. As a result the overall surface area of the lead sulfate formed is reduced. The size of the lead sulfate crystals also plays an important role in the dissolution of lead sulfate. For a given volume of lead sulfate formed, a large number of small sulfate crystals has a larger surface area than a fewer number of large sulfate crystals. Hence it is essential to keep the size of the sulfate crystals small. This can be done under high supersaturation of the electrolyte with P b 2+ ions. This occurs only at the beginning of a discharge after a complete charging when lead sulfate has been completely dissolved. With this as the background it has been proposed that after complete charging of the battery, if it is discharged under high discharge rates for a few seconds (such that the high supersaturation P b 2+ ions takes place), a large number of small crystals could be generated[10]. For more detailed explanation of this phenomena please refer the following references[10, 33, 34] Acid Stratification In lead-acid batteries the concentration of the sulfuric is not uniform. These exists a gradient with the upper part of the electrode being exposed more diluted sulfuric and lower part being exposed to more concentrated sulfuric acid. Due to this the active material in the upper part of the electrode is only partially utilized and it is overstressed in lower part of the electrode. Acid Stratification in itself is not an aging process but accelerates active material disintegration in the lower parts of the positive electrode and sulfation in the lower parts of the negative electrode[10, 25]. This is a serious issue in stationary applications like stand-alone systems. Forced agitation is used to partially solve the problem however the usage of immobilized electrolyte has proven to be more effective.

24 Ultracapacitors History The ultracapacitor also known as a supercapacitor or electric double layer capacitor are large capacitance devices, with capacitances upto of several thousand farads. The first patent for a capacitor based on high surface area carbon dates back to 1957 [35]. In 1969 the SOHIO Corporation made the first attempt to commercialize ultracapacitors [36]. Figure Maxwell BOOSTCAP ultracapacitors However it was not until the nineties that the interest in ultracapacitors was renewed in the context of hybrid electric vehicles. An ever increasing power requirement for automotive applications have rendered the standard battery design obsolete leading to the design of pulsed batteries and battery-ultracapacitor hybrid systems for high power applications[18, 19]. However with the increasing penetration of renewable energy technologies that require energy storage, the usage of ultracapacitors in these systems has also been investigated by few authors[24, 22]. Ultracapacitors are high power density devices. It can be seen from the Figure 1.2 that ultracapacitors fills the gap between batteries and conventional capacitors in terms of specific energy and specific power and due to this it lends itself very well as a complementary device to the battery. By combining ultracapacitors with batteries, which are typically low power devices, the battery performance can be improved in terms of the power density. Additionally they have high cycle life which makes them attractive for high power applications.

25 13 Table 1.2. Comparison battery and ultracapacitor characteristics[7] Available Performance Lead Acid Battery Ultracapacitor Energy Density (Wh/Kg) Power Density(W/Kg) <1000 < Cycle Life (cycles) 1000 > Efficiency Discharge Time hrs s Charge Time 1-5 hrs s Figure Ultracapacitor[5] Principle of operation - Simple Double Layer capacitor The storage of electric charge and energy in an ultracapacitor is electrostatic i.e non-faradaic. An electrode when immersed in an electrolyte results in the formation of an electrochemical double layer at the solid/electrolyte interface. Ultracapacitors store the electric energy in this electrochemical double layer also known as the Helmholtz Layer. The double layer capacitance is about µf/cm 2 [37] for an electrode in concentrated electrolyte solution and the corresponding electric field in the electrochemical double layer is very high and assumes values of up to 10 6 V/cm [38]. In order to achieve a higher capacitance the electrode surface area is increased by using porous electrodes with an extremely large internal effective surface(1000 to 2000m 2 /g)[37]. A single cell of an ultracapacitor (shown in figure 1.11) consists of two electrodes immersed in an electrolyte. The electrodes in the system are separated by a porous separator containing the

26 14 same electrolyte. The energy stored in an ultracapacitor is given by, E = CV 2 2 (1.1) where Q is the energy stored, C is the capacitance and V is the voltage. However the calculation of capacitance for an ultracapacitor is very complex. For an ideal double-layer capacitor there should not be any faradaic reactions between the electrode and electrolyte. The capacitance for such a capacitor is independent of the voltage. Another mode of storage has also been utilized by the ultracapacitors that involves faradaic reactions. Capacitance in such cases is termed pseudo-capacitance. Charge transferred in such cases is voltage dependent subsequently leading the capacitance to also be voltage dependent Classification and materials used Based on mode of storage they can be classified into double layer capacitors, pseudo-capacitance based Capacitors and hybrid ultracapacitors. Table 1.3. Classification of Ultracapacitors[8] Technology type Electrode materials Energy storage mechanisms Electric double-layer Activated carbon Charge Separation Advanced carbon Graphite carbon Charge transfer or intercalation Advanced carbon Nanotube forest Charge separation Pseudo-capacitive Metal oxides Redox charge transfer Hybrid Carbon/metal oxide Double-layer/ charge transfer Hybrid Carbon/lead oxide Double-layer/faradaic Table 1.4. Performance Characteristics of Ultracapacitor technologies[8] Eelctrode Materials Energy density Wh/kg Cell voltages Power density kw/kg Activated carbon Graphite carbon Nanotube forest Carbon/lead oxide Metal oxides Carbon/metal oxide Double Layer Capacitors This is the most commercialized of the several ultracapacitor technologies and is termed electric double layer capacitor(edlc). In the Double Layer Capacitor the energy is stored in the dou-

27 15 ble layer formed at the electrode/electrolyte interface. Carbon is mainly used as the electrode material for this type of ultracapacitor[39, 40]. The reasons for using carbon as the electrode material are i.) Low Cost ii.) High Surface area iii.) Availability and iv.) Established electrode production technologies. For carbon electrodes the energy stored is mainly capacitive with a minor contribution from pseudo-capacitance.for carbon electrodes both aqueous and organic electrolytes can be used with each configuration having its own advantage. A higher cell voltage can be obtained using an organic electrolyte(typically 2.7V) and thereby a higher energy density as energy stored is CV 2 /2. But the organic electrolytes have higher specific resistances thereby decreasing the maximum usable power. On the other hand the aqueous electrolytes typically limit the cell voltage to 1V. However they have higher conductances thereby leading to higher power densities and additionally the aqueous electrolytes cost less. The measured specific capacitances as shown in Table 1.5 for carbon materials are in the range of F/g for aqueous electrolytes and F/g for organic electrolytes. This disparity can be attributed to the larger sized ions present in the organic electrolytes. The cell voltage is mainly dependent on the breakdown voltage of the electrolyte. For the aqueous electrolyte the cell voltage is around 1V and for the organic electrolytes it is 2.7V[8] Capacitors utilizing pseudo-capacitance For capacitors based on pseudo-capacitance there exists a faradaic reaction between the electrode and the electrolyte. In other words the ions in the double-layer are transferred to the surface. The charge transferred is voltage dependent therefore the capacitance of the system also becomes voltage-dependent. Three types of electrochemical processes have been utilized for storing charge. They are Surface Adsorption of ions from electrolyte, redox reactions involving ions from the electrolyte, and the doping and undoping of active conducting polymer material in the electrode[8]. The main advantage is that they have much higher energy densities than the double layer ultracapacitors. This technology is mainly in the research phase and is not commercially available[41] Hybrid (Asymmetric) Capacitors This category of devices use carbon as one of the electrodes and the other electrode utilizes either a pseudocapacitance material or a faradaic material like that used in a battery and hence the term assymetric capacitors. Hybrid Capacitors employ materials like nickel oxide and lead oxide as the material in positive electrode and carbon cloth for negative electrodes. The discharge times are in the range of min, the peak power densities are aound 300W/kg and the energy densities are projected to be in the range of 10-20Wh/kg. The performance characteristics are closer to that of battery s than the ultracapacitor s.

28 16 Table 1.5. The specific capacitance of selected electrode materials[8] Material F/cm 3 Electrolyte Density F/g g/cm 3 Carbon cloth 35 organic KOH Aerogel carbon 84 KOH Carbon black 95 KOH Particulate from TiC 60 organic KOH Particulate from SiC 72 organic KOH Doped conducting polymers 315 organic Anhydrous RuO H 2 SO Hydrous RuO H 2 SO Ultracapacitor Applications The ultracapacitors lend themselves very well to pulsed loads i.e high peak power and low energy applications because of their high power densities and low energy densities. The ideal applications for ultracapacitors are those that demand energy for a duration in the range of 10 2 s < t < 10 2 s because batteries and traditional capacitors have to be oversized to meet the requirement[38]. Mentioned below are just a few of the potential applications for ultracapacitors. A more complete list of applications can be found in [38, 7]. ˆ Traditional electronic applications like mobile phones, cameras, TV satellite recievers, rechargable toys etc. ˆ UPS applications where the ultracapacitor provides power during short-duration interruptions and voltage sags and the batteries provide power during the longer interruptions. In cases of critical loads requiring fill-in power only for a few seconds, the ultracapacitor alone can be used to good effect. ˆ Power conditioning applications where brief bursts of energy are required to filter voltage sags on the system. ˆ It can be used to provide bursts of power in intermittent systems like solar and wind. It is especially useful in wind turbine systems where bursts of power are required for rotor blade adjustments. ˆ HEV and EV applications where ultracapacitors can be used to provide the bursts of power needed during acceleration and also absorb energy made available through regenerative braking. ˆ Cold start applications for diesel engines.

29 Ultracapacitor Cost considerations It must be noted that ultracapacitors are currently not in high volume production and hence the costs can be prohibitive for implementation in some of the applications mentioned above. With a steady increase in demand for ultracapacitors, automating the production facilities is a way to reduce production costs. However the cost of manufacturing also depends on material costs which are currently high for ultracapacitors. The major material costs for double layer capacitors are the carbon, the organic electrolyte, and the salt added to the electrolyte to provide the ions. The cost of carbon, the material used for electrodes, can be as high as $100/kg with an average in the range of $30-50/kg[18]. It is anticipated that the price of ultracapacitors can be in the range of 1-2 /F for small devices and /F for large devices with automated production and reduced material costs[18]. It must be noted that ultracapacitors cannot compete with batteries in terms of $/Wh because of their low energy densities but they can on a $/W basis. They are projected to compete with lithium-ion technologies on a cost level under high volume production and carbon prices less than $20/kg. 1.5 Ultracapacitor Modeling Ultracapacitors store energy electrostatically and the process is known as non-faradaic electrical energy storage. Ultracapacitors differ from traditional capacitors in its usage of electrodes which are porous in nature in the case of ultracapacitors. This usage of porous electrodes which are essential for obtaining high capacitances also complicate the behavior of the ultracapacitors making them a strong function of the frequency of operation. Many models are available for modeling the complex behavior of an ultracapacitor and the most widely used ones are based on porous electrode theory [42, 43, 44]. Models based on porous electrode theory accurately predict the ultracapacitor s performance by solving a series of governing equations. There also exist other equivalent circuit models that accurately predict the ultracapacitor s dependence on frequency by employing multiple time constants [45, 46, 47, 15]. The time constants in an electrical circuit can be generated by adding an resistor-capacitor branch and the values of which need to be determined from electrochemical impedance spectroscopy measurements.the simplest of this type of models is the Classical Equivalent Circuit Model as shown below Classical Equivalent Circuit Model It can be seen that the Classical Equivalent Circuit(CEC) model consists of three electrical components, The Capacitor C, Resistance in series ESR and Resistance in Parallel EP R. C is the charge storage capacity of the ultracapacitor, ESR is the internal series resistance and EP R is used to model the leakage current that also impacts long term storage performance of the ultracapacitor. The CEC model is sufficient for applications where the ultracapacitor is allowed to discharge slowly over a period of few seconds. The methodolgy for the parameter estimation is detailed in [45].

30 18 C ESR EPR Figure Classical equivalent Circuit Model Transmission Line Model One of the widely used equivalent circuit models is the Ladder Model[15, 48]. It employs multiple time constants by adding more RC blocks to the circuit. Addition of RC blocks improves the order of accuracy of the model however the determination of parameters becomes very laborious. It is therefore essential to determine the frequency of application and tailor the model as per the application. For instance A 5-stage ladder model that consists of 5 RC blocks can be employed for frequencies upto 10 khz. A methodology for automatically selecting the order of the model based on the application has also been proposed. L R 1 R 2 R 3 R n C 1 C 2 C 3 C n R p Figure Ladder Model Justification for using Third Order UC Model The plot shown in Figure 1.14 has been adopted from reference [6]. It compares the accuracy of the various orders of the Ladder Model with measurements on a 100F maxwell ultracapacitor. In order to determine which order model needs to be employed it is required to determine the frequency of the application. For the application in this study the frequency is taken to be 10 1 Hz as the magnitude of variation in time periods lesser than 5-10 seconds is insignificant for Solar and Wind systems [2, 1, 49]. Our application lies in the region where the third order model is reasonably accurate. Hence the reason for picking the third order model.

31 Imaginary Part Impedance (ohm) order 2-order order Frequency(Hz) Figure Comparison of accuracy of various orders[6] Ultracapacitor Working Order 2-Order 3-Order 4-Order 5-Order Range of Frequency for Solar and Wind Data Frequency(Hz) Figure Working Order of Ultracapacitors

32 Chapter 2 Modeling Battery-ultracapaitor hybrid system As mentioned before the approach taken to test the compatibility of battery-ultracapacitor systems was to develop a system scale model of the energy storage system which will then be then subjected varying load profiles that represent a renewable energy load requirement. So each component of the energy storage system, i.e. the battery and the ultracapacitor system were modeled and tested separately and then integrated to form the energy storage system that is the subject of study. 2.1 Lead Acid Battery Model Ceraolo Battery Model The Ceraolo Battery Model is a third order model. It is essentially an electric equivalent model in which the individual parameters of each electric component are determined empirically. The Ceraolo Model interpolates the battery behavior as seen from the terminals and does not model individual parts of the battery i.e. electrodes, electrode/electrolyte interface, electrolyte etc. Shown below is the generic electrical equivalent schematic of the Ceraolo Model. It can be seen that the network has two main branches the main branch which is composed of several R-C blocks and the parasitic branch. The parasitic branch models the irreversible parasitic reactions like the water electrolysis that draw current but do not participate in the main reaction. The complexity of the main branch can be increased by adding more R-C blocks depending on the type of application. The type of application is characterized by the speed of evolution of the electric quantities. However for most applications it is sufficient to include only one R-C block and still obtain good accuracy.

33 21 C R 2 p R 0 R 1 Main Branch Em R p Parasitic Branch Ep Figure 2.1. Lead-acid Battery equivalent electric model Battery Capacity The first and most important step is to accurately model the battery capacity. The battery capacity is not a constant and is strongly dependent on the discharge current I and the electrolyte temperature θ. At fixed discharge currents I the variation of capacity is given by C(I, θ) I,θ=const = C 0 (I)(1 + θ θ f ) ɛ (2.1) where, θ f is the electrolyte freezing temperature and can be assumed to be -40 and C 0 (I) is a function of discharge current I and is equal to the battery capacity at 0. From experimental results C 0 (I) was determined emperically to be, C 0 (I) = K c C (K c 1)( I I ) δ (2.2) K c and δ are emperical coefficients that are constant for a given battery and a reference current I. Eq.(2.3) gives accurate results for a wide range of currents around I and its value is unique for a given battery application. Now by combining Eq. 2.1 and 2.3 we have, θ θ f ) ɛ C(I, θ) = K cc 0 ( (K c 1)( I (2.3) I ) δ Eq. 2.1 and 2.3 are valid when electrolyte temperature and discharge current are constant. For transient currents the Ceraolo Model postulates that they are still valid given that instead of the actual current I a filtered value of this current I avg is used so that C(I, θ) now becomes C(I avg, θ). The value of I avg is equated to the value of the current flowing in the resistor(r1) in the main branch. This hypothesis has been experimentally confirmed by the authors of the model.

34 State of Charge(SOC) and Depth of Charge(DOC) In the Ceraolo Model the values of individual circuit elements need to be identified for different States of Charge (SOC). The State of Charge (SOC) of a battery is the ratio of the capacity remaining in the battery to the maximum capacity of the battery at a given temperature. Depth of Discharge (DOC) is the ratio of the capacity remaining in the battery to the maximum capacity of the battery with reference to the actual discharge regime. In other words State of Charge (SOC) is a measure of the fraction of charge remaining in the battery and the Depth of Charge (DOC) is a measure of usable fraction of charge remaining in the battery. SOC = 1 Q e C(0, θ) (2.4) Where, SOC State of Charge DOC Depth of Charge Q e Charge of battery (A secs) C Battery Capacity (A secs) θ Electrolyte Temperature( o C) I avg Mean Discharge current(a) DOC = 1 Q e C(I avg, θ) (2.5) Extracted Charge Q e is the extracted charge from the battery and can be calculated by integrating the current that is flowing in and out of the battery. Q e (t) = Q e initial + Where, Q e initial Charge extracted initially I m Main branch current(a) τ Integration time variable t time t 0 I m (τ)dτ (2.6) Main Branch Voltage (Em) Em is the open circuit voltage of a battery cell. temperature(θ) and state of charge(soc) of the cell. It can be seen that it is a function of E m = E m0 K E (273 + θ)(1 SOC) (2.7)

35 23 Where, E m Main branch voltage E m0,k E constants for a battery Main Branch Resistance (R 1 ) The resistance R 1 varies with the depth of discharge(doc) of the battery. It can be seen that the resistance increases exponentially as the DOC decreases. R 1 = R 10 ln(doc) (2.8) Where, R 1 Main branch resistance R 10 Emperical constant Main Branch Capacitance (C 1 ) The main branch capacitance C 1 is given by Where, C 1 Main branch capacitance τ 1 Main branch time constant(secs) C 1 = τ 1 R 1 (2.9) Terminal Resistance (R 0 ) The resistance R 0 is the resistance observed at the battery terminals. It is assumed to be constant at all temperatures[assumption] but is a function of State of Charge(SOC). R 0 = R 00 [1 + A 0 (1 SOC)] (2.10) Where, R 0 Terminal resistance A 0,R 00 Constants for a battery Main branch Resistance (R 2 ) It can be seen that the resistance R 2 increases with the increase in state of charge(soc) and is also dependent on the discharge rate. The resistance becomes significant during the charging and becomes relatively insignificant during discharging. R 2 = R 20 exp[a 21 (1 SOC)] 1 + exp (A22Im) I ) (2.11)

36 24 Where, R 2 Main branch resistance R 20,A 21 and A 22 Empirical constants for a battery Parasitic branch Current (I p ) Parasitic branch currenti p is the current lost during the charging of a battery. The behavior of the parasitic branch is strongly non-linear and the empirical equation matches the Tafel gassing -current relationship. It is imortant to note that R 2 = 0 and I P = 0 during the discharge. Hence R 2 and the whole parasitic branch can be omitted from the model while simulating the discharge alone. Where, I p Current loss in the parasitic branch V P N Voltage at parasitic branch G p0 constant V p0 constant A P constant I p = V P N G p0 exp( V P N V p0 + A P (1 θ θ f )) (2.12) Thermal Model A thermal model of the battery is required to compute the Electrolyte temperature. In reality the temperature of the electrolyte is not uniform but to avoid additional complexity the electrolyte temperature is assumed to be uniform throughout the battery. By developing a heat balance we have, C θ dθ dt = θ θ a R θ + P s (2.13) P s is the internal heat generation in the R 0 and R 2 components The electrolyte temperature can now be computed by Where, θ Electrolyte Temperature ( o C) θ a Ambient Temperature ( o C) P s Internal Heat generation(w) C θ Thermal Capacitance ( J o C ) P s = I 2 mr 2 + (I m I p ) 2 R 0 (2.14) θ(t) = θ init + t 0 ( P s (θ θa) R θ )dt (2.15) C θ