1c Discharge to Nominal Continuous Discharge

Battery Capacity

Battery capacity (AH) is defined as a product of the current that is drawn from the battery while the battery is able to supply the load until its voltage is dropped to lower than a certain value for each cell.

From: Distributed Generation Systems , 2017

Photovoltaic

Ziyad Salameh , in Renewable Energy System Design, 2014

Battery storage sizing

The battery storage system is sized independent of the photovoltaic array. The equipment load is converted from watt-hours to amp-hours at the system DC voltage in order to size the battery bank. The battery system is sized for the worst case and should be assumed to carry the entire load for a fixed number of days. The days of storage to use is a subjective judgment arrived at by considering "actual conditions" and how much they may vary from "average conditions" at the location. Generally, this is a site-specific variable and typical storage periods range from 3 to 10 days.

Battery capacity, in units of amp-hours, is temperature-dependent and manufacturers' ratings should be corrected for temperature in order to serve the load as intended. Once the required number of amp-hours has been determined, batteries or cells can be selected and the battery bank designed using manufacturers' information and desired depth of discharge. The total number of batteries needed is the product of the number of series batteries (to build up the voltage) and the number of parallel batteries (to build up the capacity). In summary, battery storage sizing is accomplished as follows:

1.

Determine load amp-hours requirement

2.

Correct amp-hours for temperature

3.

Determine the number of batteries (cells) required

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Solar Hybrid Systems and Energy Storage Systems

Ahmet Aktaş , Yağmur Kirçiçek , in Solar Hybrid Systems, 2021

3.1 Battery capacity

Battery capacity is defined as the total amount of electricity generated due to electrochemical reactions in the battery and is expressed in ampere hours. For example, a constant discharge current of 1 C (5 A) can be drawn from a 5 Ah battery for 1 hour. For the same battery a discharge current of 0.1 C (500 mA) can be withdrawn from the battery for 10 hours. For a given cell type the behavior of cells of different capacities with the same C ratio value is similar. The energy that a battery can deliver in the discharge process is called the capacity of the battery. The unit of the capacity is "ampere hour" and is briefly expressed by the letters "Ah." The label value of the battery is called rated capacity. The capacity of a battery depends on the following factors:

To the number and size of plates in a cell: Essentially, the number of plates or the large size means that the amount of active substance that stores energy increases. The battery's ability to store or deliver energy will increase if the active ingredient in the battery plates is excessive.

To the density of the electrolyte: If a high-density electrolyte is put in a battery, the capacity will increase to a certain extent. However, increasing density also means that the battery life is shorter. Therefore the electrolyte density cannot be increased as desired.

The two factors described earlier are related to the structure of the battery and are assigned to a battery that has been manufactured. Also, the capacity of a battery depends on its age. As the battery is used, the capacity decreases to a certain extent as a result of pouring the active substance from the plates, aging and wearing out of the elements forming the battery.

Electrolyte temperature: The capacity of a battery varies depending on the electrolyte temperature. Capacity increases as the temperature rises. Excessive heat causes wear on lead grates for lead–acid batteries. The worn grill rods come out and break. Therefore despite the capacity-increasing effect, batteries should not be exposed to excessive heat. Fig. 5.24 shows the relationships between the discharge voltage of a battery, discharge current, and discharge capacity [45].

Figure 5.24. Peukert curve based on discharge graph.

The top curves in Peukert curve indicate the voltage per cell when a battery is discharged within a certain current and time. The capacity curve shows how much of the rated capacity of the battery discharged with a certain current and time should yield. The discharge current curve explains how many amperes it must be discharged to achieve a certain capacity in a given time. The values apply to a new 100-Ah battery cell with full capacity at rated temperature. For a battery group the cell voltage values on the left should be multiplied by the number of cells, and for the batteries other than 100 Ah, the current and capacity values on the right should be taken into account.

The higher the batteries are discharged, the lower the battery capacity. For this reason the charge and discharge curves of the batteries are exponential, not linear, as seen in the graphic. The next equation is given in the Peukert law.

(5.2) $C_p={I_B}^{k}t$

C _p (Ah) is capacity according to Peukert, I _B (A) is battery discharge current, t is discharge time, and k is Peukert constant. Battery manufacturers can give their capacity values in the sales catalogs, and the k value is approximately between 1.1 and 1.3.

According to the Peukert curve, this curve is used for a battery that is less than 10 hours discharge time. In the case of discharges over 10 hours, the discharge capacity is determined by dividing the battery capacity Ah by the current value drawn. For example, if a 100-Ah battery is discharged with 10 A, its voltage drops to 13 V immediately at the start of discharge, and after supplying energy for 10 hours, its voltage becomes 11.3 V.

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Battery Life Analysis

Shahin Farahani , in ZigBee Wireless Networks and Transceivers, 2008

6.1 Battery Discharge Characteristics

Battery capacity is measured in milliamps × hours (mAH). For example, if a battery has 250  mAH capacity and provides 2   mA average current to a load, in theory, the battery will last 125 hours. In reality, however, the way the battery is discharged has an impact on the actual battery life. Discharging a battery at the manufacturer-recommended rate normally helps the battery deliver close to its nominal capacity. But the result cannot simply be extrapolated linearly to other discharge profiles.

In many short-range wireless sensor networks, although the average current consumption of a device is low, the instantaneous current can be high. For example, in Figure 6.1, a transceiver with sleep current of 1   μA and peak active current of 20   mA wakes up every 2 seconds and stays active for 5   ms. The average current consumption is only 50   μA, but the peak current of 20   mA can have an adverse effect on the battery's actual capacity, especially if there is not enough time between the periods of high current discharge to let the battery rest and recover.

Figure 6.1. An Example of Current Profile of a Device in a ZigBee Network

This can be explained by the relaxation phenomena (or recovery effect) [1]. When a battery is discharged at a high and sustained rate, the battery reaches its end of life even if there are still active materials left in the battery. However, if the discharge rate is not continuous and there are cutoffs or very low-current periods, the transport rate of active materials catches up with the depletion of the materials, giving the battery a chance to recover the capacity lost at the high discharge rate.

The actual capacity of a battery for a specific use-case scenario can be determined experimentally. Battery manufacturers might be able to provide an estimate for the actual battery capacity if the application's current profile (e.g., Figure 6.1) is provided. The ratio of the battery's actual capacity to its nominal capacity is called the battery efficiency factor.

One way to avoid high current discharge periods, if possible, is to use a sufficiently large capacitor to supply the current to the transceiver when the node is active. While the device is in sleep, the battery charges the capacitor, and when the device becomes active and requires a high discharge rate, this capacitor will provide current to the device. In this way, the battery would not experience high discharge rate periods and the battery efficiency can be improved.

Another characteristic of a battery is its self-discharge rate. A battery, even when not in use, loses its capacity over time due to internal leakage. Battery manufacturers quantify this leakage as self-discharge per month. For example, a 300   mAH battery with self-discharge per month of 0.5% loses 1.5   mAH of its capacity after one month. The battery shelf life is defined as the longest time a battery can be stored before its capacity falls below 80% of its nominal.

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Fuel Cells

Hamdi Abdi , ... Mohammad Salehimaleh , in Distributed Generation Systems, 2017

5.5.2.2 UltraCapacitor and Battery

As mentioned in the previous sections, the FC cannot respond to transient loads like the starting current properly. Therefore, when a system encounters a load current transient, the battery or ultracapacitor supplies the difference between the steady state FC power and the transient load power, then the FC power is changed following a safe profile to restore the battery charge and supply the new steady state load power [20].

In Fig. 5.29 after the DC-DC boost converter an ultracapacitor unit has been connected in parallel with the system. A supercapacitor is an energy storage device that acts like a battery. The ultracapacitor works in a system that needs high power in a short time. Thus, it can be modeled by a capacitor in series with a resistor as shown in Fig. 5.31.

Fig. 5.31. Circuit model of an ultracapacitor unit.

To reach the higher voltage, several ultracapacitors or batteries must be connected in series together to make a unit. Then, for example in the Fig. 5.29, this unit is connected in parallel with the high DC voltage bus. The Thevenin equivalent of a battery small signal model and its equations are presented in Fig. 5.32 [20]:

Fig. 5.32. Small signal model of a battery.

Because batteries are connected in series together, their voltages and resistances are added together. Each battery has specifications that are supplied by its manufacturer. If the voltage and resistance of each battery cell are considered equal to V_BC and R_BC , respectively, the following equations calculate the small signal parameters:

(5.46) $V_B=N_S\times V_{BC}$

(5.47) $R_B=N_S\times R_{BC}$

where N_S is the number of battery cells connected in series together. To obtain the capacitance in the small signal model, the maximum voltage must be used. Battery capacitance is written based on amperes per hour.

(5.48) $V_{\max ,B}=\sqrt{2}{V}_B$

(5.49) $V_C=V_{\max ,B}-V_B$

(5.50) $C_B=\frac{3600C_{AH}}{V_C}$

Battery capacity (AH) is defined as a product of the current that is drawn from the battery while the battery is able to supply the load until its voltage is dropped to lower than a certain value for each cell. For instance, if a battery injects 6  amp for 10   h before its voltage drops to its critical margin, then its nominal capacity is 60   AH.

Example 5.8

Calculating the number of required batteries in a system. Assume in Fig. 5.29 that the system needs a battery bank with 96   kW power for helping the FC during transient loads. The input voltage of the inverter is 48   V. The specifications of the battery cell are assumed as

$V_{BC}=2\mathrm{V},R_{BC}=0.04\mathrm{\Omega },I_{BC}=2000\mathrm{A}$

The input voltage of the inverter is 48   V while the manufacturer mentioned that the voltage of each cell is 2   V. So, these cells should be in series to reach 48   V for the battery. From the Eq. (5.46),

$V_B=N_S\times V_{BC}\Rightarrow N_S=\frac{V_B}{V_{BC}}\Rightarrow \frac{48}{2}$

$\Rightarrow N_S=24$ , therefore 24 battery cells must be connected in series. Now the number of parallel cells can be achieved as

$P=N_S\times N_P\times V_{BC}\times I_{BC}\Rightarrow N_P=\frac{P}{V_{BC}\times I_{BC}\times N_S}\Rightarrow \frac{96000}{2\times 2000\times 24}$

$\Rightarrow N_S=1$ , so the number of all cells is equal to 24.

$V_{\max ,B}=\sqrt{2}{V}_B\Rightarrow \sqrt{2}\times 48=68\mathrm{V}$

$R_B=N_S\times R_{BC}\Rightarrow 24\times 0.04=0.96\Omega$

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Solar PV DC nanogrid dynamic modeling applying the polynomial computational method for MPPT

Maged F. Bauomy , ... Adel A. Shaltout , in Advances in Clean Energy Technologies, 2021

2.5.2.1.1 Battery capacity

The battery capacity is the main terminology to study battery modeling, as it functions in discharge current and electrolyte temperature, which will function in the state of battery charge. The equation of battery capacity is illustrated in Eq. (2.31) [27, 31].

(2.31) $C\left(I,\theta \right)=\frac{K_{\mathrm{c}}{C}_{0^{⁎}}}{1+\left(K_{\mathrm{c}}-1\right){\left(I/I^{⁎}\right)}^{\delta }}{\left(1+\frac{\theta }{-{\theta }_{\mathrm{f}}}\right)}^{\varepsilon }$

Where the electrolyte freezing temperature is represented by θ _f, which can be assumed to be −   40°C, the no-load capacity is represented by C _0⁎ at 0°C in Ampere-seconds, the nominal current is represented by I*, which is the ratio of the nominal capacity C _n, and the nominal discharge time is t _n. Finally, there are some empirical coefficients K _c, δ, and ɛ that are constant.

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Emergency supply equipment

In Electrical Systems and Equipment (Third Edition), 1992

2.4.2 Ambient temperature

Since battery capacity and performance is reduced by low temperature, a minimum electrolyte temperature of 5°C is maintained as a general rule. However, in nuclear power stations, where reduced capacity could affect the safe shutdown of a reactor, a minimum temperature of 15°C is maintained by thermostatically controlled heaters of the totally-enclosed tubular type.

Whilst batteries are capable of operating in an ambient temperature of 35°C, with occasional excursions to 40°C, these high temperatures are avoided, as they lead to greater evaporation of water from the electrolyte and a significant reduction in service life.

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SECONDARY BATTERIES – LITHIUM RECHARGEABLE SYSTEMS | Electrolytes: Solid Sulfide

R. Kanno , in Encyclopedia of Electrochemical Power Sources, 2009

Sulfur electrode

The battery capacity of the lithium-ion system is mainly determined by the specific capacities of positive electrodes in the range of 150–200  mAh   g⁻¹, which are limited by the extent of lithium intercalation into transition metal oxides. Batteries based on the lithium/elemental sulfur redox couple might be a promising candidate for high-capacity batteries. Sulfur has a theoretical specific capacity and specific energy of 1672   mAh   g⁻¹ and 2600   Wh   kg⁻¹, respectively. However, high insulation caused high electronic resistivity, which makes only poor charge–discharge characteristics. The loss of active material in liquid electrolytes caused low active material utilization and poor rechargeability. The Li/S batteries with solid polymer electrolytes showed reversible discharge capacities of less than 30% of the theoretical capacity even at higher operating temperatures around 100   °C. On the contrary, all solid-state batteries using ceramic electrolyte showed good cycle performance; mechanically milled mixtures of S and CuS showed high reversible capacities more than 650   mAh   g⁻¹ at room temperature. All solid-state cells with the direct reversible reaction between S and Li₂S were obtained using composite electrode with sulfur and AB. Figure 10 shows the charge–discharge characteristics of the Li–Al/SE/S cell. Nano-composite of sulfur and AB was fabricated by gas phase mixing and showed a reversible specific capacity of ∼400   mAh   g⁻¹ at a current density of 0.13   mA   cm⁻².

Figure 10. Charge–discharge curves of all solid-state batteries with acetylene black/sulfur composite electrodes prepared by gas–solid mixing. The current density was 0.13   mA   cm⁻² with cutoff voltages of 0.5 and 2.7   V.

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Battery Management and Battery Diagnostics

Angel Kirchev , in Electrochemical Energy Storage for Renewable Sources and Grid Balancing, 2015

20.2.3 Battery Capacity

The battery capacity corresponds to the quantity of the electric charge which can be accumulated during the charge, stored during the open circuit stay, and released during the discharge in a reversible manner. It is obtained by integration of the discharge current starting from a completely charged battery and terminating the discharge process at certain voltage threshold often denoted as cutoff voltage or U _{cut_off} , reached in the moment t _{cut_off} . In this case it is denoted as discharge capacity or C _d and for the case of the lead-acid battery electrochemistry it can be expressed as

(20.5) $C_d=\underset{0}{\overset{t_{cut\_off}}{\int }}I\mathit{dt}=-\frac{2F}{M_{\mathrm{Pb}{\mathrm{O}}_2}}(m_{\mathrm{Pb}{\mathrm{O}}_2}^{initial}-m_{\mathrm{Pb}{\mathrm{O}}_2}^{cut\_off})=-\frac{2F}{M_{\mathrm{Pb}}}\left(m_{\mathrm{Pb}}^{initial}-m_{\mathrm{Pb}}^{cut\_off}\right)$

Equation (20.5) shows that the battery capacity is proportional to the quantity of the active materials which can be converted electrochemically until the battery voltage reaches the voltage threshold U _{cut_off} . The sign of the discharge capacity is negative; however, in practice its value is considered as a modulus. When the battery is discharged with constant current its capacity is given by the formula C _d   =   I·t_d, where t_d is the discharge duration. When the latter is expressed in hours, the typical unit for battery capacity is the Ampere-hour.

The discharge capacity of a new battery (i.e., before the notable beginning of the battery degradation) is a function of the temperature and the discharge current profile. A basic step in the development of each battery management algorithm is the estimation of the dependence of the discharge capacity on the current and temperature. Usually, it is done by subjecting one or several identical batteries or cells on several charge/discharge cycles at constant temperature using galvanostatic discharge with different discharge currents and a fixed complete recharge regime. The procedure is repeated at several different temperatures. During the development of such kind of design of experiments, one should be aware of the typical battery cycling degradation rate. For batteries where the aging rate in deep cycling mode is rapid (for example, cars flooded lead-acid batteries with thin plates and Sb-free grids) the number of such characterization deep cycles should be lower and the limited number of experimental points per battery could be compensated by the testing of larger number of batteries.

The dependence of the discharge capacity on the discharge current often follows the Peukert equation [2]:

(20.6a) $C_d=K·I^{1-n}$

where K and n are empirical constants. The coefficient n depends strongly on the design of the electrodes. For example, lead-acid batteries with thick plates have value of n in the range of 1.4 [3], while for designs with thinner plates n is in the range 1.20–1.25 [4]. For technologies like the lithium ion batteries, where the plates are very thin (in the range of 0.2–0.3   mm), the value of n is close to 1 [5]. In this case the Peukert equation and the corresponding experimental data can be presented using the duration of the discharge t _d instead of the capacity:

(20.6b) $t_d=K·I^{-n}$

When the experimental data t _d (I) are plotted in double logarithmic coordinates the Eqn (20.6b) is transformed into a straight line with a slope equal to the coefficient n. The Peukert equation illustrates one same trend for almost all types of primary and rechargeable batteries—the higher the discharge current, the lower the capacity. From the electrochemical point of view, the latter corresponds to a smaller quantity of active materials converted into discharge products. In the battery technology, the extent of this conversion is denoted as 'active materials utilization.' The decreased active materials utilization at high discharge currents can be ascribed very often to diffusion effects. For example, in the case of the lead-acid battery discharge (Eqns (20.1a) and (20.1b)) the sulfuric acid necessary to convert PbO₂ and Pb into PbSO₄ should diffuse from the volume of the electrolyte to the geometrical surface of the electrode and then inside its porous volume. At high discharge currents, the electrolyte from the volume of the cell located between the battery plates does not have enough time to diffuse inside the volume of the plates where it is rapidly depleted due to the electrochemical reactions. This results in the development of local concentration gradients and the appearance of diffusion polarization [6]. The latter causes rapid decrease of the cell discharge voltage. Logically, we can achieve higher capacities at higher currents only in battery technologies employing cell designs with thinner plates, where the diffusion is faster.

The Peukert equation features different range of validity for each different battery technology—for very high and very low discharge current it is no longer valid. It should be noted that a precise BMS algorithm should also rely on a set of n and K parameters measured for the particular type of battery used in the energy system, i.e., the couple of 'battery plus BMS' behaves as a key and a keyhole.

Equation (20.6b) can be used to explain the term 'rated capacity' and 'rated current,' both used often in battery practice. Here 'rated' corresponds to the choice of current to match a given discharge duration (or desired autonomy), or vice versa—how long will we run the battery at the applied discharge current. Thus, the current corresponding to a 20-h-long discharge is denoted as 20-h-rated current or I ₂₀ (or I _20h ). When the latter is multiplied by 20   h, the product is denoted as 20-h-rated capacity C₂₀ (C_20h).

Another term related to the battery capacity is the 'nominal capacity' (or nameplate capacity) denoted as C _n . The definition of C _n is often related to a certain application or battery testing standard. For example, the nominal capacity of starting, lighting, and ignition lead-acid battery typically coincides with the 20-h-rated capacity C_20h. The nominal capacity can be used to express the density of the charge and discharge current as a C rating presented as the ratio between the nominal capacity and the 'target' discharge or charge duration (the latter is different from real duration of the charge or the discharge). Thus, for current intended to charge or discharge the battery for 10   h, the current density is expressed as C_n/10   h. Higher currents like C_n/1   h are denoted as 1   C, C_n/30   min as 2   C, C_n/15   min as 4   C, etc. When the current is expressed in this way, it allows applying the same testing conditions to batteries with different sizes and to compare the obtained results in a reliable way. The convenience of such approach is related to the great difference between the battery testing capabilities of the laboratory which is charged with the development of the BMS and the actual size of the energy storage installation. Usually the mainstream battery testing benches are designed to test cells in the voltage range 0–5   V and the current range ±5–50   A (the higher the current, the more expensive the equipment). In many real-world battery installations for renewable energy storage and grid support the typical DC voltage range is 400   V and currents may reach 500–1000   A in the case when huge battery cells are employed making evident that the BMS will actually extrapolate the laboratory behavior of smaller cells and batteries in order to control and predict the operation of a large-size energy storage plant.

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Lead Alloys and Grids. Grid Design Principles

Detchko Pavlov , in Lead-Acid Batteries: Science and Technology (Second Edition), 2017

4.11 Copper-Stretch-Metal Negative Grids

High-capacity batteries have tall cells (resp. tall plates). With increase of cell height the electrical resistance of the grids increases. As a result of this the plates undergo lower depth of discharge at the bottom of the cell, which leads to a substantial potential difference between the top and bottom parts of the plates. Moreover, the higher grid resistance causes increased heat generation in the cell and hence increased energy loss. In an attempt to resolve these problems, the standard lead grids were replaced with copper grids for the negative plates. Copper has a specific electrical conductivity σ  =   59.6   ×   10⁶  S   m⁻¹ and that of lead is 10 times lower, σ  =   5.0   ×   10⁶  S   m⁻¹. Plates taller than 45–50   cm are produced with copper-stretch-metal (CSM) grids.

Copper strips are expanded to form grids with diamond-shaped structure of the grid wires. The expanded copper strip is then cut into individual grids. Top lead bars with lugs and bottom bars are cast, and the grids are covered with a thin layer of lead. Such a CSM grid design is presented in Fig. 4.65 [97]. The thus produced grids are then subjected to the subsequent technological procedures of pasting, curing, and formation.

Figure 4.65. Copper-stretch-metal grid as basic material and after coating with a lead layer [97].

Negative pales with CSM grids ensure much more uniform proceeding of charge and discharge processes throughout the whole plate surface, which contributes to higher utilization of the active material. When conventional negative pales with lead grids are discharged at high currents, the local current density in the upper parts of the plates is much higher than that in the bottom parts. This nonhomogeneity of current density may lead to sulfation of the bottom parts of the negative plates. It has been established that plates with CSM grids have about 17% lower electrical resistance than standard lead plates, which increases battery power output [104].

During charge, the copper grids ensure much more uniform current density distribution over the plate surface, and thus improve substantially the charge acceptance of the negative plates, which results eventually in improved energy performance of the battery. However, manufacture of negative plates with CSM grids involves a greater number of technological procedures and is therefore more expensive. The higher production costs of plates with CSM grids are worthwhile for the manufacture of batteries with high power and high capacity.

CSM grids are not suitable for positive plates because the corrosion will quickly "eat up" the lead layer covering the grid and copper ions will diffuse to the solution and thus reduce the charge efficiency and accelerate greatly the self-discharge processes.

With this brief description of the CSM grid technology, we will complete the overview of the most common grid alloys and grid design principles, and will continue further with the plate production processes.

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Biofuel cells as sustainable power sources for implantable systems

S. Kerzenmacher , in Implantable Sensor Systems for Medical Applications, 2013

6.1.2 The search for sustainable alternatives

The limited battery capacity of early implantable pacemaker models has sparked researchers to develop alternative solutions for a sustainable power supply within the human body. A relatively crude example from the early 1970s is the piezo-electric aorta clamp shown in Fig. 6.2 , which was intended to generate electricity from the pulsating movement of a blood vessel. Other examples are implantable glucose fuel cells (for a detailed historical overview see, e.g. Kerzenmacher et al, 2008b) or nuclear batteries, which indeed found their way into commercial products such as the Alcatel nuclear pacemaker (Parsonnet, 1972) . However, these research activities lost their momentum when the powerful lithium-iodine batteries (Greatbatch et al., 1971; Jeffrey and Parsonnet, 1998) allowed for pacemaker lifetimes of up to 10 years, which at that time appeared to be sufficient in most cases.

6.2. Piezo-electric converter (aorta clamp).

(Source: Reprinted from Lewin et al. (1968) with permission.)

Nevertheless, the majority of pacemaker patients would benefit from device lifetimes beyond 10 years, as Kindermann et al. concluded in their 2001 study (Kindermann et al., 2001). Furthermore, there is an increasing number of active implantable systems currently under development or already on the market (see for instance Receveur et al., 2007 and references therein). Unlike cardiac pacemakers, these devices are often intended for treating patients of all ages. Without a sustainable, autonomous power supply, this translates into a life of regular surgical procedures to replace spent batteries. This not only has a significant negative effect on the quality of life of patients, but poses also a major cost factor. Over the last decade, the search for an autonomous power supply for implantable systems thus has regained considerable interest.

Among the currently considered alternative approaches are mechanical generators (based on piezo-electric, electrostatic and inductive mechanisms) and thermoelectric generators (for a more detailed overview see, e.g. Rasouli and Phee, 2010; Wei and Liu, 2008). Both share the drawback of being highly dependent on ambient conditions, either the presence of a temperature gradient or body movement. Examples for mechanical energy harvesting generators are (i) a device of 11   mm by 11   mm in size with a projected power output of 80   μW (Miao et al., 2006), and (ii) a mechanical energy harvester directly integrated into a pacemaker lead. The latter generates about 1   μW of electrical energy from the pressure pulses resulting from heart motion. It is envisioned that with further material optimizations enough power for indefinite pacemaker operation can be generated (Roberts et al., 2008). While this harvester can be integrated into a pacemaker lead, other applications may require additional intra-body wire connections. Regarding thermoelectric generators, Yang et al. highlighted in a theoretical and conceptual study that these generators will have to be placed in close vicinity to the skin (Yang et al, 2007). This means that, compared to implantable fuel cells, there will be a significantly lower degree of freedom in the choice of implantation site. In some cases, it may thus be inevitable to have additional intra-body leads between the thermoelectric generator and the implantable system.

Probably the most elegant concept is to use the body's own glucose as inexhaustible and continuous source of chemical energy, continuously transformed into electricity by means of an implantable fuel cell (Barton et al, 2004; Heller, 2006; Kerzenmacher et al, 2008b). In principle, these devices promise a theoretically unlimited lifetime as long as sufficient oxygen and glucose are available from body fluids. Their main advantages over thermoelectric and mechanical harvesters are the continuous generation of electricity, independent from non-constant and difficult to control ambient factors such as movement and temperature gradient. Furthermore, the essentially two-dimensional nature of the fuel cell (meaning that its thickness is small compared to its geometric area, much like a membrane) allows for its adaption to arbitrarily shaped implants. This can be of significant advantage for applications where the battery puts constraints on the shape and size of the implantable system.

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