Unit 2 - Batteries PDF

3 Energy Source: Battery A basic requirement for electric vehicles (EVs) is a portable source of electrical energy, which is converted to mechanical energy in the electric motor for vehicle propulsion. Electrical energy is typically obtained through conversion of chemical ener...

3 Energy Source: Battery A basic requirement for electric vehicles (EVs) is a portable source of electrical energy, which is converted to mechanical energy in the electric motor for vehicle propulsion. Electrical energy is typically obtained through conversion of chemical energy stored in devices such as batteries and fuel cells. A flywheel is an alternative portable source in which energy is stored in mechanical form to be converted into electrical energy on demand for vehicle propulsion. The portable electrical energy source presents the biggest obstacle in commercialization of EVs. A near-term solution for minimizing the environmental pollution problem due to the absence of a suitable, high-energy-density energy source for EVs is perceived in the hybrid electric vehicles (HEVs) that combine propulsion efforts from gasoline engines and electric motors. A comparison of the specific energy of the available energy sources is given in Table 3.1. The specific energy is the energy per unit mass of the energy source. The specific energies are shown without taking containment into consideration. The specific energy of hydrogen and natural gas would be significantly lower than that of gasoline when containment is considered. Among the available choices of portable energy sources, batteries have been the most popular choice of energy source for EVs since the beginning of research and development programs in these vehicles. The EVs and HEVs commercially available today use batteries as the electrical energy source. The various batteries are usually compared in terms of descriptors, such as specific energy, specific power, operating life, etc. Similar to specific energy, specific power is the power available per unit mass from the source. The operating life of a battery is the number of deep discharge cycles obtainable in its lifetime or the number of service years expected in a certain application. The desirable features of batteries for EV and HEV applications are high specific power, high specific energy, high charge acceptance rate for recharging and regenerative braking, and long calendar and cycle life. Additional technical issues include methods and designs to balance the battery segments or packs electrically and thermally, accurate techniques to determine a battery’s state of charge, and recycling facilities of battery components. And above all, the cost of batteries must be reasonable for EVs and HEVs to be commercially viable. 42 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS Battery technology has been undergoing extensive research and development efforts over the past 30 years, yet there is currently no battery that can deliver an acceptable combination of power, energy, and life cycle for high-volume production vehicles. The small number of EVs and HEVs that were introduced in the market used batteries that were too expensive and have short calendar life, making the batteries the biggest impediment in commercializing EVs and HEVs. TABLE 3.1 Nominal Energy Density of Sources 3.1 BATTERY BASICS The batteries are made of unit cells containing the chemical energy that is convertible to electrical energy. One or more of these electrolytic cells are connected in series to form one battery. The grouped cells are enclosed in a casing to form a battery module. A battery pack is a collection of these individual battery modules connected in a series and parallel combination to deliver the desired voltage and energy to the power electronic drive system. The energy stored in a battery is the difference in free energy between chemical components in the charged and discharged states. This available chemical energy in a cell is converted into electrical energy only on demand, using the basic components of a unit cell, which are the positive and negative electrodes, the separators, and the electrolytes. The electrochemically active ingredient of the positive or negative electrode is called the active material. Chemical oxidation and reduction processes take place at the two electrodes, thereby bonding and releasing electrons, respectively. The electrodes must be electronically conducting and are located at different sites, separated by a separator, as shown in Figure 3.1. During battery operation, chemical reactions at each of the electrodes cause electrons to flow from one electrode to another; however, the flow of electrons in the cell is sustainable only if electrons generated in the chemical reaction are able to flow through an external electrical circuit that connects the two electrodes. The connection points between the  ENERGY SOURCE: BATTERY 43 electrodes and the external circuit are called the battery terminals. The external circuit ensures that most of the stored chemical energy is released only on demand and is utilized as electrical energy. It must be mentioned that only in an ideal battery does current flow only when the circuit between the electrodes is completed externally. Unfortunately, many batteries do allow a slow discharge, due to diffusion effects, which is why they are not particularly good for long-term energy storage. This slow discharge with open-circuit terminals is known as self- discharge, which is also used as a descriptor of battery quality. FIGURE 3.1 Components of a battery cell. (a) Cell circuit symbol; (b) cell cross-section. The components of the battery cell are described as follows: 1. Positive electrode: The positive electrode is an oxide or sulfide or some other compound that is capable of being reduced during cell discharge. This electrode consumes electrons from the external circuit during cell discharge. Examples of positive electrodes are lead oxide (PbO2) and nickel oxyhydroxide (NiOOH). The electrode materials are in the solid state. 2. Negative electrode: The negative electrode is a metal or an alloy that is capable of being oxidized during cell discharge. This electrode generates electrons in the external circuit during cell discharge. Examples of negative electodes are lead (Pb) and cadmium (Cd). Negative electrode materials are also in the solid state within the battery cell. 3. Electrolyte: The electrolyte is the medium that permits ionic conduction between positive and negative electrodes of a cell. The electrolyte must have high and selective conductivity for the ions that take part in 44 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS electrode reactions, but it must be a nonconductor for electrons in order to avoid self-discharge of batteries. The electrolyte may be liquid, gel, or solid material. Also, the electrolyte can be acidic or alkaline, depending on the type of battery. Traditional batteries such as lead-acid and nickel- cadmium use liquid electrolytes. In lead-acid batteries, the electrolyte is the aqueous solution of sulfuric acid [H2SO4(aq)]. Advanced batteries currently under development for EVs, such as sealed lead-acid, nickel- metal-hydride (NiMH), and lithium-ion batteries use an electrolyte that is gel, paste, or resin. Lithium-polymer batteries use a solid electrolyte. 4. Separator: The separator is the electrically insulating layer of material that physically separates electrodes of opposite polarity. Separators must be permeable to the ions of the electrolyte and may also have the function of storing or immobilizing the electrolyte. Present day separators are made from synthetic polymers. There are two basic types of batteries: primary batteries and secondary batteries. Batteries that cannot be recharged and are designed for a single discharge are known as primary batteries. Examples of these are the lithium batteries used in watches, calculators, cameras, etc., and the manganese dioxide batteries used to power toys, radios, torches, etc. Batteries that can be recharged by flowing current in the direction opposite to that during discharge are known as secondary batteries. The chemical reaction process during cell charge operation when electrical energy is converted into chemical energy is the reverse of that during discharge. The batteries needed and used for EVs and HEVs are all secondary batteries, because they are recharged during regeneration cycles of vehicle operation or during the battery recharging cycle in the stopped condition using a charger. All the batteries that will be discussed in the following are examples of secondary batteries. The major types of rechargeable batteries considered for EV and HEV applications are: • Lead-acid (Pb-acid) • Nickel-cadmium (NiCd) • Nickel-metal-hydride (NiMH) • Lithium-ion (Li-ion) • Lithium-polymer (Li-poly) • Sodium-sulfur (NaS) • Zinc-air (Zn-Air) The lead-acid type of battery has the longest development history of all battery technology, particularly for their need and heavy use in industrial EVs, such as for golf carts in sports, passenger cars in airports, and forklifts in storage facilities and supermarkets. Research and development for batteries picked up momentum following the resurgence of interest in EVs and HEVs in the late  ENERGY SOURCE: BATTERY 45 1960s and early 1970s. Sodium-sulfur batteries showed great promise in the 1980s, with high energy and power densities, but safety and manufacturing difficulties led to the abandonment of the technology. The development of battery technology for low-power applications, such as cell phones and calculators, opened the possibilities of scaling the energy and power of nickel- cadmium- and lithium-ion-type batteries for EV and HEV applications. The development of batteries is directed toward overcoming significant practical and manufacturing difficulties. Theoretical predictions are difficult to match in manufactured products due to practical limitations. Theoretical and practical specific energies of several batteries are given in Table 3.2 for comparison. The characteristics of some of the more important battery technologies mentioned above are given in the following. The theoretical aspects of the lead- acid battery will be discussed in detail first, followed by shorter descriptions of the other promising technologies. TABLE 3.2 Specific Energy of Batteries 3.2 LEAD-ACID BATTERY Lead-acid batteries have been the most popular choice of batteries for EVs. Lead- acid batteries can be designed to be high powered and are inexpensive, safe, and reliable. A recycling infrastructure is in place for them. However, low specific energy, poor cold temperature performance, and short calendar and cycle life are among the obstacles to their use in EVs and HEVs. The lead-acid battery has a history that dates to the middle of the 19th century, and it is currently a mature technology. The first lead-acid battery was produced as early as in 1859. In the early 1980s, over 100,000,000 lead-acid batteries were produced per year. The long existence of the lead-acid battery is due to the following: 46 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS • Relatively low cost • Easy availability of raw materials (lead, sulfur) • Ease of manufacture • Favorable electromechanical characteristics The battery cell operation consists of a cell discharge operation, when the energy is supplied from the battery to the electric motor to develop propulsion power, and a cell charge operation, when energy is supplied from an external source to store energy in the battery. 3.2.1 CELL DISCHARGE OPERATION In the cell discharge operation (Figure 3.2), electrons are consumed at the positive electrode, the supply of which comes from the negative electrode. The current flow is, therefore, out of the positive electrode into the motor-load, with the battery acting as the source. FIGURE 3.2 Lead-acid battery: cell discharge operation. The positive electrode equation is given by: A highly porous structure is used for the positive electrode to increase the PbO 2 (s)/electrolyte contact area, which is about 50 to 150 m2 per Ah of battery capacity. This results in higher current densities, as PbO2 is converted to PbSO4 (s). As discharge proceeds, the internal resistance of the cell rises due to PbSO4 formation and decreases the electrolyte conductivity as H2SO4 is consumed. PbSO4(s) deposited on either electrode in a dense, fine-grain form can lead to sulfatation. The discharge reaction is largely inhibited by the buildup of PbSO4, which reduces cell capacity significantly from the theoretical capacity.  ENERGY SOURCE: BATTERY 47 The negative electrode equation during cell discharge is: The electrons are released at the negative electrode during discharge operation. The production of PbSO4(s) can degrade battery performance by making the negative electrode more passive. The overall cell discharge chemical reaction is: 3.2.2 CELL CHARGE OPERATION The cell charge operation (Figure 3.3) is the reverse of the cell discharge operation. During cell charging, lead sulfate is converted back to the reactant states of lead and lead oxide. The electrons are consumed from the external source at the negative electrode, while the positive electrode releases the electrons. The current flows into the positive electrode from the external source, thereby delivering electrical energy into the cell, where it gets converted into chemical energy. The chemical reaction at the positive electrode during cell charging is: FIGURE 3.3 Lead-acid battery: cell charge operation. The chemical reaction at the negative electrode during cell charging is: The overall chemical reaction during cell charging is: Conventionally, lead-acid batteries are of flooded-electrolyte cells, where free acid covers all the plates. This imposes the constraint of maintaining an upright position for the battery, which is difficult in certain portable situations. Efforts in 48 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS developing hermetically sealed batteries faced the problem of buildup of an explosive mixture of hydrogen and oxygen on approaching the top-of-charge or overcharge condition during cell recharging. The problem is addressed in the valve-regulated-lead-acid (VRLA) batteries by providing a path for the oxygen, liberated at the positive electrode, to reach the negative electrode, where it recombines to form lead-sulfate. There are two mechanisms for making sealed VRLA batteries, the gel battery, and the AGM (absorptive glass microfiber) battery. These types are based on immobilizing the sulfuric acid electrolyte in the separator and the active materials, leaving sufficient porosity for the oxygen to diffuse through the separator to the negative plate.1 3.2.3 CONSTRUCTION FIGURE 3.4 Schematic diagram of a lead-acid battery showing through-partition connection. FIGURE 3.5 A lead-acid battery grid. Construction of a typical battery consists of positive and negative electrode groups (elements) interleaved to form a cell. The through partition connection in the battery is illustrated in Figure 3.4. The positive plate is made of stiff paste of the active material on a lattice-type grid, which is shown in Figure 3.5. The grid, made of a suitably selected lead alloy, is the framework of a portable battery to  ENERGY SOURCE: BATTERY 49 hold the active material. The positive plates can be configured in flat pasted or tubular fashion. The negative plates are always manufactured as pasted types. 3.3 ALTERNATIVE BATTERIES 3.3.1 NICKEL-CADMIUM BATTERY Nickel-cadmium (NiCd) and nickel-metal-hydride (NiMH) batteries are examples of alkaline batteries with which electrical energy is derived from the chemical reaction of a metal with oxygen in an alkaline electrolyte medium. The specific energy of alkaline batteries is lowered due to the addition of weight of the carrier metal. The NiCd battery employs a nickel oxide positive electrode and a metallic cadmium negative electrode. The net reaction occurring in the potassium hydroxide (KOH) electrolyte is: The practical cell voltage is 1.2 to 1.3 V, and the atomic mass of cadmium is 112. The specific energy of NiCd batteries is 30 to 50 Wh/kg, which is similar to that of lead-acid batteries. The advantages of NiCd batteries are superior low- temperature performance compared to lead-acid batteries, flat discharge voltage, long life, and excellent reliability. The maintenance requirements of the batteries are also low. The biggest drawbacks of NiCd batteries are the high cost and the toxicity contained in cadmium. Environmental concerns may be overcome in the long run through efficient recycling, but the insufficient power delivered by the NiCd batteries is another important reason for not considering these batteries for EV and HEV applications. The drawbacks of the NiCd batteries led to the rapid development of NiMH batteries, which are deemed more suitable for EV and HEV applications. 3.3.2 NICKEL-METAL-HYDRIDE (NiMH) BATTERY The nickel-metal-hydride battery is a successor to the nickel-hydrogen battery and is already in use in production HEVs. In NiMH batteries, the positive electrode is a nickel oxide similar to that used in a NiCd battery, while the negative electrode is a metal hydride where hydrogen is stored. The concept of NiMH batteries is based on the fact that fine particles of certain metallic alloys, when exposed to hydrogen at certain pressures and temperatures, absorb large 50 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS quantities of the gas to form the metal-hydride compounds. Furthermore, the metal hydrides are able to absorb and release hydrogen many times without deterioration. The two electrode chemical reactions in a NiMH battery are: At the positive electrode, At the negative electrode, M stands for metallic alloy, which takes up hydrogen at ambient temperature to form the metal hydride MHX. The negative electrode consists of a compressed mass of fine metal particles. The proprietary alloy formulations used in NiMH are known as AB5 and AB2 alloys. In the AB5 alloy, A is the mixture of rare earth elements, and B is partially substituted nickel. In the AB2 alloy, A is titanium or zirconium, and B is again partially substituted nickel. The AB2 alloy has a higher capacity for hydrogen storage and is less costly. The operating voltage of NiMH is almost the same as that of NiCd, with flat discharge characteristics. The capacity of the NiMH is significantly higher than that of NiCd, with specific energy ranging from 60 to 80 Wh/kg. The specific power of NiMH batteries can be as high as 250 W/kg. The NiMH batteries have penetrated the market in recent years at an exceptional rate. The Chrysler electric minivan “Epic” uses a NiMH battery pack, which gives a range of 150 km. In Japan, NiMH battery packs produced by Panasonic EV Energy are being used in Toyota EV RAV-EV and Toyota HEV Prius. The components of NiMH are recyclable, but a recycling structure is not yet in place. NiMH batteries have a much longer life cycle than lead-acid batteries and are safe and abuse tolerant. The disadvantages of NiMH batteries are the relatively high cost, higher self-discharge rate compared to NiCd, poor charge acceptance capability at elevated temperatures, and low cell efficiency. NiMH is likely to survive as the leading rechargeable battery in the future for traction applications, with strong challenge coming only from lithium-ion batteries.2 3.3.3 LI-ION BATTERY Lithium metal has high electrochemical reduction potential (3.045 V) and the lowest atomic mass (6.94), which shows promise for a battery of 3 V cell potential when combined with a suitable positive electrode. The interest in secondary lithium cells soared soon after the advent of lithium primary cells in  ENERGY SOURCE: BATTERY 51 the 1970s, but the major difficulty was the highly reactive nature of the lithium metal with moisture, restricting the use of liquid electrolytes. Discovery in the late 1970s by researchers at Oxford University that lithium can be intercalated (absorbed) into the crystal lattice of cobalt or nickel to form LiCoO 2 or LiNiO2 paved the way toward the development of Li-ion batteries.3 The use of metallic- lithium is bypassed in Li-ion batteries by using lithium intercalated (absorbed) carbons (LixC) in the form of graphite or coke as the negative electrode, along with the lithium metallic oxides as the positive electrode. The graphite is capable of hosting lithium up to a composition of LiC6. The majority of the Li-ion batteries uses positive electrodes of cobalt oxide, which is expensive but proven to be the most satisfactory. The alternative positive electrode is based on nickel oxide LiNiO2, which is structurally more complex but costs less. Performance is similar to that of cobalt oxide electrodes. Manganese-oxide-based positive electrodes (LiMn2O4 or LiMnO2) are also under research, because manganese is cheaper, widely available, and less toxic. The cell discharge operation in a lithium ion cell using LiCoO2 is illustrated in Figure 3.6. During cell discharge, lithium ions (Li+) are released from the negative electrode that travels through an organic electrolyte toward the positive electrode. In the positive electrode, the lithium ions are quickly incorporated into the lithium compound material. The process is completely reversible. The chemical reactions at the electrodes are as follows: At the negative electrode, FIGURE 3.6 Lithium-ion cell. 52 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS At the positive electrode, During cell charge operation, lithium ions move in the opposite direction from the positive electrode to the negative electrode. The nominal cell voltage for a Li-ion battery is 3.6 V, which is equivalent to three NiMH or NiCd battery cells. Lithium-ion batteries have high specific energy, high specific power, high energy efficiency, good high-temperature performance, and low self-discharge. The components of Li-ion batteries are also recyclable. These characteristics make Li-ion batteries highly suitable for EV and HEV and other applications of rechargeable batteries. 3.3.4 LI-POLYMER BATTERY Lithium-polymer evolved out of the development of solid state electrolytes, i.e., solids capable of conducting ions but that are electron insulators. The solid state electrolytes resulted from research in the 1970s on ionic conduction in polymers. These batteries are considered solid state batteries, because their electrolytes are solids. The most common polymer electrolyte is polyethylene oxide compounded with an appropriate electrolyte salt. The most promising positive electrode material for Li-poly batteries is vanadium oxide V6O13.1 This oxide interlaces up to eight lithium atoms per oxide molecule with the following positive electrode reaction: Li-poly batteries have the potential for the highest specific energy and power. The solid polymers, replacing the more flammable liquid electrolytes in other type of batteries, can conduct ions at temperatures above 60°C. The use of solid polymers also has a great safety advantage in case of EV and HEV accidents. Because the lithium is intercalated into carbon electrodes, the lithium is in ionic form and is less reactive than pure lithium metal. The thin Li-poly cell gives the added advantage of forming a battery of any size or shape to suit the available space within the EV or HEV chassis. The main disadvantage of the Li-poly battery is the need to operate the battery cell in the temperature range of 80 to 120°C. Li-poly batteries with high specific energy, initially developed for EV applications, also have the potential to provide high specific power for HEV applications. The other key characteristics of the Li-poly are good cycle and calendar life.  ENERGY SOURCE: BATTERY 53 3.3.5 ZINC-AIR BATTERY BATTERY Zinc-air batteries have a gaseous positive electrode of oxygen and a sacrificial negative electrode of metallic zinc. The practical zinc-air battery is only mechanically rechargeable by replacing the discharged product, zinc hydroxide, with fresh zinc electrodes. The discharged electrode and the potassium hydroxide electrolyte are sent to a recycling facility. In a way, the zinc-air battery is analogous to a fuel cell, with the fuel being the zinc metal. A module of zinc air batteries tested in German Mercedes Benz postal vans had a specific energy of 200 Wh/kg, but only a modest specific power of 100 W/kg at 80% depth-of- discharge (see Sections 3.4 and 3.5 for definitions of depth-of-discharge and specific power). With present-day technology, the range of zinc-air batteries can be between 300 to 600 km between recharges. Other metal-air systems have been investigated, but the work has been discontinued due to severe drawbacks in the technologies. These batteries include iron-air and aluminum-air batteries, in which iron and aluminum are, respectively, used as the mechanically recyclable negative electrode. The practical metal-air batteries have two attractive features: the positive electrode can be optimized for discharge characteristics, because the battery is recharged outside of the battery; and the recharging time is rapid, with a suitable infrastructure. 3.3.6 SODIUM-SULFUR BATTERY Sodium, similar to lithium, has a high electrochemical reduction potential (2.71 V) and low atomic mass (23.0), making it an attractive negative electrode element for batteries. Moreover, sodium is abundant in nature and available at a low cost. Sulfur, which is a possible choice for the positive electrode, is also a readily available and low-cost material. The use of aqueous electrolytes is not possible due to the highly reactive nature of sodium, and because the natures of solid polymers like those used for lithium batteries are not known. The solution of electrolyte came from the discovery of beta-alumina by scientists at Ford Motor Company in 1966. Beta-alumina is a sodium aluminum oxide with a complex crystal structure. Despite several attractive features of NaS batteries, there are several practical limitations. The cell operating temperature in NaS batteries is around 300°C, which requires adequate insulation as well as a thermal control unit. This requirement forces a certain minimum size of the battery, limiting the development of the battery for only EVs, a market that is not yet established. Another disadvantage of NaS batteries is the absence of an overcharge mechanism. At the top-of-charge, one or more cells can develop a high resistance, which pulls down the entire voltage of the series-connected battery 54 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS cells. Yet another major concern is safety, because the chemical reaction between molten sodium and sulfur can cause excessive heat or explosion in the case of an accident. Safety issues were addressed through efficient design, and manufactured NaS batteries have been shown to be safe. Practical limitations and manufacturing difficulties of NaS batteries have led to the discontinuation of its development programs, especially when the simpler concept of sodium-metal-chloride batteries was developed. 3.3.7 SODIUM-METAL-CHLORIDE BATTERY The sodium-metal-chloride battery is a derivative of the sodium-sulfur battery with intrinsic provisions of overcharge and overdischarge. The construction is similar to that of the NaS battery, but the positive sulfur electrode is replaced by nickel chloride (NiCl2) or a mixture of nickel chloride and ferrous chloride (FeCl2). The negative electrode and the electrolyte are the same as in a NaS battery. The schematic diagram of a NaNiCl2 cell is shown in Figure 3.7. In order to provide good ionic contact between the positive electrode and the electrolyte, both of which are solids, a second electrolyte of sodium chloraluminate (NaAlCl 4) is introduced in a layer between NiCl2 and beta-alumina. The NaAlCl4 electrolyte is a vital component of the battery, although it reduces the specific energy of the battery by about 10%.3 The operating temperature is again high, similar to that of the NaS battery. The basic cell reactions for the nickel chloride and ferrous chloride positive electrodes are as follows: The cells in a sodium metal chloride battery are assembled in a discharged state. The positive electrode is prefabricated from a mixture of Ni or Fe powder and NaCl(common salt). On charging after assembly, the positive electrode compartment is formed of the respective metal, and the negative electrode compartment is formed of sodium. This procedure has two significant advantages: pure sodium is manufactured in situ through diffusion in beta- alumina, and the raw materials for the battery (common salt and metal powder) are inexpensive. Although iron is cheaper than nickel, the latter is more attractive as the metallic component because of fewer complications and a wider operating temperature range.  ENERGY SOURCE: BATTERY 55 FIGURE 3.7 A sodium-nickel-chloride cell. Sodium chloride batteries are commonly known as ZEBRA batteries, which originally resulted from a research collaboration between scientists from the United Kingdom and South Africa in the early 1980s. ZEBRA batteries have been shown to be safe under all conditions of use. They have high potential for being used as batteries for EVs and HEVs. There are several test programs utilizing the ZEBRA batteries. 3.4 BATTERY PARAMETERS 3.4.1 BATTERY CAPACITY The amount of free charge generated by the active material at the negative electrode and consumed by the positive electrode is called the battery capacity. The capacity is measured in Ah (1 Ah=3600 C, or coulomb, where 1 C is the charge transferred in 1 s by 1 A current in the MKS unit of charge). The theoretical capacity of a battery (in C) is: where x is the number of moles of limiting reactant associated with complete discharge of the battery, n is the number of electrons produced by the negative electrode discharge reaction, and F=Le. L is the number of molecules or atoms in a mole (known as the Avogadro constant), and e0 is the electron charge. F is the Faraday constant. The values for the constants are: and 56 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS FIGURE 3.8 Battery cells connected in series. The theoretical capacity in Ah is: (3.1) where mR is the mass of limiting reactant (in kg), and M is the molar mass of limiting reactant (in g/mol). The cells in a battery are typically connected in series (Figure 3.8), and the capacity of the battery is dictated by the smallest cell capacity. Therefore, QTbattery=QTcell. 3.4.2 DISCHARGE RATE The discharge rate is the current at which a battery is discharged. The rate is expressed as Q/h rate, where Q is rated battery capacity, and h is discharge time in hours. For a battery that has a capacity of QT Ah and that is discharged over t, the discharge rate is QT/ t. For example, let the capacity of a battery be 1 Q=100 Ah. (1 Q usually denotes the rated capacity of the battery.) Therefore, and 3.4.3 STATE OF CHARGE The state of charge (SoC) is the present capacity of the battery. It is the amount of capacity that remains after discharge from a top-of-charge condition. The battery SoC measurement circuit is shown in Figure 3.9. The current is the rate of change of charge given by where q is the charge moving through the circuit. The instantaneous theoretical state of charge SoCT(t) is the amount of equivalent positive charge on the aaaaaaaa  ENERGY SOURCE: BATTERY 57 FIGURE 3.9 Battery SoC measurement. positive electrode.If the state of charge is QT at the initial time t, then SOCTt0)=QT. For a time interval dt, Integrating from the initial time t0 to the final time t, the expression for instantaneous state of charge is obtained as follows: (3.2) 3.4.4 STATE OF DISCHARGE The state of discharge (SoD) is a measure of the charge that has been drawn from a battery. Mathematically, state of discharge is given as follows: (3.3) 3.4.5 DEPTH OF DISCHARGE The depth of discharge (DoD) is the percentage of battery capacity (rated capacity) to which a battery is discharged. The depth of discharge is given by 58 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS (3.4) The withdrawal of at least 80% of battery (rated) capacity is referred to as deep discharge. FIGURE 3.10 (a) Steady-state battery equivalent circuit. (b) Battery open circuit voltage characteristics. 3.5 TECHNICAL CHARACTERISTICS The battery in its simplest form can be represented by an internal voltage Ev and a series resistance Ri, as shown in Figure 3.10a. The internal voltage appears at the battery terminals as open circuit voltage when there is no load connected to the battery. The internal voltage or the open circuit voltage depends on the state of charge of the battery, temperature, and past discharge/charge history (memory effects), among other factors. The open circuit voltage characteristics are shown in Figure 3.10b. As the battery is gradually discharged, the internal voltage decreases, while the internal resistance increases. The open circuit voltage characteristics have a fairly extended plateau of linear characteristics, with a slope close to zero. The open circuit voltage is a good indicator of the state of discharge. Once the battery reaches 100% DoD, the open circuit voltage decreases sharply with more discharge. The battery terminal voltage (Figure 3.11) is the voltage available at the terminals when a load is connected to the battery. The terminal voltage is at its full charge voltage VFC when the battery DoD is 0%. In the case of a lead-acid battery, it means that there is no more PbSO4 available to react with H2O to produce active material. Vcut is the battery cut-off voltage, where discharge of battery must be terminated.  ENERGY SOURCE: BATTERY 59 FIGURE 3.11 Battery terminal voltage. FIGURE 3.12 Battery SoD measurement. In order to predict the range of an EV, the SoC or DoD can be used. However, the question is which one will be more accurate? The SoC and DoD are related as The reliability of SoC depends on reliability of QT, which is a function of discharge current and temperature, among other things. It will be difficult to use SoC for general discharge currents, because it is hard to predict QT. On the other hand, the DoD can be expressed more accurately, because it is expressed as a fraction of QT, and it is easier to measure SoD (Figure 3.12). 3.5.1 PRACTICAL CAPACITY The practical capacity QP of a battery is always much lower compared to the theoretical capacity QT, due to practical limitations. The practical capacity of a battery is given as (3.5) where t0 is the time at which the battery is fully charged [SoD(t)=0], and tcut is the time at which the battery terminal voltage is at Vcut. Therefore, Vt(tcut)=Vcut. 60 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS FIGURE 3.13 Battery capacity measurement. FIGURE 3.14 Constant current discharge curves. 3.5.1.1 Capacity Redefined The practical capacity of a battery is defined in the industry by a convenient and approximate approach of Ah instead of coulomb under constant discharge current characteristics. Let us consider the experiment shown in Figure 3.13, where the battery is discharged at constant current starting from time t=0. Current is maintained constant by varying the load resistance RL until the terminal voltage reaches Vcut. The constant current discharge characteristics are shown qualitatively at two different current levels in Figure 3.14. The following data are obtained from the experiment: The results show that the capacity depends on the magnitude of discharge current. The smaller the magnitude of the discharge current, the higher the  ENERGY SOURCE: BATTERY 61 capacity of the battery. To be accurate, when the capacity of a battery is stated, the constant discharge current magnitude must also be specified. 3.5.1.2 Battery Energy The energy of a battery is measured in terms of capacity and discharge voltage. To calculate energy, the capacity of the battery must be expressed in coulombs. A measurement of 1 Ah is equivalent to 3600 C, while 1 V refers to 1 J (J for joule) of work required to move 1 C charge from the negative to positive electrode. Therefore, the stored electrical potential energy in a 12 V, 100 Ah battery is (12) (3.6×105)J=4.32 MJ. In general, the theoretical stored energy is: where Vbat is the nominal no load terminal voltage, and Q is the theoretical capacity in C. Therefore, using Equation 3.1, we have (3.6) The practical available energy is: (3.7) where t0 is the time at which the battery is fully charged, tcut is the time at which battery terminal voltage is at Vcut, v is the battery terminal voltage, and/is the battery discharge current. EP is dependent on the manner in which the battery is discharged. 3.5.1.3 Constant Current Discharge The battery terminal voltage characteristic is shown again in Figure 3.15, indicating the midpoint voltage (MPV) at t=1/2 tcut The extended plateau of the midpoint voltage can be represented by the straight-line equation Vt=mt+b, where m and b are the constants of the equation. We will replace the nonlinear terminal voltage characteristic of the battery by the extended plateau straight-line equation for simplicity. The energy of a battery with constant current dis- charge is Let the average battery terminal voltage over discharge interval 0 to tcut be. Therefore, 62 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS FIGURE 3.15 Midpoint voltage. where A1 and A are the areas indicated in Figure 3.15. We can assume that the areas A1 and A2 are approximately equal, A1 A2. However, m(l/2 tcut)+b=MPV (MPV is midpoint voltage). This gives Substituting, (3.8) An empirical relation often used to describe battery characteristics is Peukert’s equation. Peukert’s equation relating constant current with tcut is as follows: (3.9) where and n are constants. Substituting Peukert’s equation in the energy equation, 3.5.1.4 Specific Energy The specific energy of a battery is given by The unit for specific energy is Wh/kg. The theoretical specific energy of a battery is (3.10) If the mass of the battery MB is proportional to the mass of the limiting reactant of the battery mR, then SET is independent of mass. The specific energy of a lead- acid battery is 35 to 50 Wh/kg at Q/3 rate. Because EP varies with discharge rate, the practical specific energy SEP is also variable.  ENERGY SOURCE: BATTERY 63 FIGURE 3.16 Battery power characteristics. The term energy density is also used in the literature to quantify the quality of a battery or other energy source. Energy density refers to the energy per unit volume of a battery. The unit for energy density is Wh/liter. 3.5.2 BATTERY POWER Battery power characteristics are illustrated in Figure 3.16. The instantaneous battery terminal power is: (3.11) where Vt is the battery terminal voltage, and/is the battery discharge current. Using Kirchoff’s voltage law for the battery equivalent circuit of Figure 3.10a, (3.12) Substituting Equation 3.12 into Equation 3.11 yields: (3.13) Maximum power output is needed from the battery in fast discharge conditions, which occur when the electric motor is heavily loaded. Acceleration on a slope is such a condition, when the motor draws a lot of current to deliver maximum power required for traction. Using the maximum power transfer theorem in electric circuits, the battery can deliver maximum power to a DC load when the load impedance matches the battery internal impedance. The maximum power is: Because Ev and Ri vary with the state of charge, Pmax also varies accordingly. The performance of batteries to meet acceleration and hill climbing requirements can be evaluated with the help of rated power specifications, which are based on the ability of the battery to dissipate heat. Rated continuous power is the maximum power that the battery can deliver over prolonged discharge intervals without damage to the battery. These do not necessarily correspond to Pmax on the p—i curve of battery characteristics. The rated instantaneous power 64 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS is the maximum power that the battery can deliver over a short discharge interval without damage to the battery. 3.5.2.1 Specific Power The specific power of a battery is (3.14) where P is the power delivered by the battery, and MB is the mass of the battery. Typically, a lead-acid battery’s maximum specific power is 280 W/kg (which corresponds to Pmax) at DoD=80%. Similar to specific energy and energy density, power density refers to the power of the battery per unit volume, with units of W/ liter. 3.5.2.2 Battery Pack Design Batteries can be configured in series or in parallel configuration or in a combination thereof. Design depends on output voltage and discharge requirements. The series connection yields the required voltage, while the parallel connection delivers the desired capacity for the battery pack for minimum run time before recharging. The battery pack also includes electronics, which are typically located outside the battery pack. The electronic circuit of a multilevel battery pack controls charging and ensures reliability and protection against overcharge, overdischarge, short circuiting, and thermal abuse. 3.5.3 RAGONE PLOTS In lead-acid and other batteries, there is a decrease in charge capacity (excluding voltage effects) with increasing currents. This is often referred to as the Ragone relationship and is described by Ragone plots. Ragone plots are usually obtained from constant power discharge tests or constant current discharge plots. Consider the experiment of Figure 3.13, but this time, the current/is adjusted by varying RL such that the power output at the battery terminals is kept constant. The experiment stops when the battery terminal voltage reaches the cut-off voltage, i.e., Vt=Vcut. We assume that the battery is fully charged at t=0. The experiment is performed at several power levels, and the following data are recorded: power p(t)=Vti=P, time to cut-off voltage tcup, and practical energy EP= Ptcut. The plot of SP vs. SE on log-log scale is known as the Ragone plot. The Ragone plots of some common batteries are shown in Figure 3.17.  ENERGY SOURCE: BATTERY 65 FIGURE 3.17 Specific power vs. specific energy (Ragone plots) of batteries, gasoline engine, and fuel cell. To a first-order approximation, we can use a linear Ragone plot (on a log-log scale) according to the following relationship between specific power and specific energy: (3.15) where n and are curve-fitting constants. The above is an alternative approach of using Peukert’s equation to describe battery characteristics. The Ragone plots of several batteries, along with alternative energy sources and internal combustion (IC) engines, are given in Figure 3.17 to give an idea about the relative power and energy capacities of these different units. EXERCISE 3.1 The data given in Table 3.3 are collected from an experiment on a battery with mass 15 kg. The data are used to draw the Ragone plot shown in Figure 3.18. Using the data points (8,110) and (67.5,10), calculate the constants of Peukert’s equation, n and. Solution TABLE 3.3 Data from Constant Power Discharge Test 66 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS FIGURE 3.18 Ragone plot for Exercise 3.1. 3.6 TARGETS AND PROPERTIES OF BATTERIES The push for zero-emission vehicles led to numerous research and development initiatives in the United States, Europe, and Japan. The California legislative mandates in the early 1990s led to the formation of the U.S. Advanced Battery Consortium (USABC) to oversee the development of power sources for EVs. The USABC established objectives focusing on battery development for mid- term (1995 to 1998) and long-term criteria. The purpose of the mid-term criteria was to develop batteries with a reasonable goal, while the long-term criteria were set to develop batteries for EVs, which would be directly competitive with IC engine vehicles (ICEVs). At the advent of the 21st century and following the developments in the 1990s, intermediate commercialization criteria were developed. The major objectives for the three criteria are summarized in Table 3.4. The two most developed battery technologies of today are lead-acid and nickel-cadmium batteries. However, these batteries will not be suitable for EVs, because the former store too little energy, while the latter have cost and toxicity problems. The future of the other batteries is difficult to predict, because these are mostly prototypes, where system design and performance data are not always available. The status of the promising batteries described in the previous section is summarized in Table 3.5 from information obtained from recent literature.  ENERGY SOURCE: BATTERY 67 TABLE 3.4 USABC Objectives for EV Battery Packs TABLE 3.5 Properties of EV and HEV Batteries 3.7 BATTERY MODELING Peukert’s equation is a widely accepted empirical relation among capacity (Q), discharge current (I), and time (t) or among specific power (SP), specific energy (SE), and time (t). Peukert’s equation is used in developing a fractional depletiont model (FDM) of batteries. The FDM of a battery can be used to predict the range of an EV. The FDM can be developed using the constant current discharge 68 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS approach or the power density approach associated with the two forms of Peukert’s equation. 3.7.1 CONSTANT CURRENT DISCHARGE APPROACH Consider the constant current discharge experiment of Figure 3.13. The battery is discharged under constant current condition from 100% capacity until cut-off voltage is reached. The load resistance RL is varied to change the constant current level and also to maintain the current constant for each experiment. The I vs. tcut data are used to fit Peukert’s equation (Equation 3.9) with constant current: (3.16) where I is the constant discharge current; and , and n are curve-fitting constants, with n 1 for small currents and n 2 for large currents. EXAMPLE 3.1 Find the curve-fitting constants n and , for Peukert’s equation for the two measurements available from a constant current discharge experiment of a battery: (i) (t1,I1)=(10,18) (ii) (t2,I2)=(1,110) Solution Equation 3.16 is the Peukert’s empirical formula using the constant current discharge approach. Taking logarithm of both sides of Equation 3.16: Comparing with the equation for a straight line, y—mx+b, I vs. tcut curve is linear on a log-log plot, as shown in Figure 3.19. The slope of the straight line is  ENERGY SOURCE: BATTERY 69 FIGURE 3.19 Plot of Peukert’s equation using constant current discharge. Therefore, For the graph shown, The other constant can now be calculated from Peukert’s equation: 3.7.1.1 Fractional Depletion Model Using Peukert’s equation, we can establish the relationship between Q and I. The practical capacity of a battery is 70 ELECTRIC AND HYBRID VEHICLES: DESIGN FUNDAMENTALS Substituting into Peukert’s equation: Because 0