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Battery Life Estimation of Mobile Embedded Systems


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Abstract

Since battery life directly impacts the extent and duration of
mobility, one of the key considerations in the design of a mobile
embedded system should be to maximize the energy delivered
by the battery, and hence the battery lifetime. To facilitate
exploration of alternative implementations for a mobile
embedded system, in this paper we address the issue of developing
a fast and accurate battery model, and providing a
framework for battery life estimation of Hardware/Software
(HW/SW) embedded systems.
We introduce a stochastic model of a battery, which can
simultaneously model two key phenomena affecting the battery
life and the amount of energy that can be delivered by
the battery: the Rate Capacity effect and the Recovery effect.
We model the battery behavior mathematically in terms
of parameters that can be related to physical characteristics
of the electro-chemical cell. We show how this model can be
used for battery life estimation of a HW/SW embedded system,
by calculating battery discharge demand waveforms using
a power co-estimation technique. Based on the discharge
demand, the battery model estimates the battery lifetime as
well as the delivered energy. Application of the battery life
estimation methodology to three system implementations of
an example TCP/IP network interface subsystem demonstrate
that different system architectures can have significantly different
delivered energy and battery lifetimes.

Introduction

As the need for mobile computation and communication
increases, there is a strong demand for design of Hardware/
Software (HW/SW) Embedded Systems for mobile applications.
Maximizing the amount of energy that can be delivered
by the battery, and hence the battery life, is one of the
most important design considerations for a mobile embedded
system, since it directly impacts the extent and duration of the
system's mobility. To enable exploration of alternative implementations
for a mobile system, it is critical to develop fast
and accurate battery life estimation techniques for embedded
systems. In this paper, we focus on developing such a battery
model, and provide a framework for battery-life estimation of
HW/SW embedded systems.

Motivation : Exploration For Battery
Efficient Architectures


In this section, we present the effect of system architectures
on the delivered energy and the lifetime of battery. Our investigations
motivate the need for fast and accurate battery life
estimation techniques that can used for system level exploration.
We analyze the performance of an example TCP/IP network
inteface subsystem with respect to the delivered energy
and the lifetime of the battery. The subsystem consists
of the part of the TCP/IP protocol stack performing the
checksum computation (Figure 1). CreafePacket receives a
packet, stores it in a shared memory, and enqueues its starting
address. IP-Chk periodically dequeues packet information,
erases specific bits of the packet in memory, and coordinates
with Chksum to verify the checksum value. Figure 1
shows a candidate architecture for the TCP/IP system where
Createpacket and Packet-Queue are software tasks mapped
to a SPARC processor, while IP-Chk and Chksum are each
mapped to dedicated hardware. Packet bits are stored in a
singl

Battery Background

A battery cell consists of an anode, a cathode, and electrolyte
that separates the two electrodes and allows transfer of electrons
as ions between them. During discharge, oxidation of
the anode (Li for LiIon battery) produces charged ions (Li+),
which travel through the electrolyte and undergo reduction at
the cathode. The reaction sites (parts of the cathode where reductions
have occurred) become inactive for future discharge
because of the formation of an inactive compound. Rate Capacity
Effect (dependency of energy delivered by a battery
on magnitude of discharge current) and Recovery Effect (recovery
of charged ions near cathode) are two important phenomena
that affect the delivered energy and the lifetime of a
battery. A short description of the physical phenomena responsible
for these effects follows.
The lifetime of a cell depends on the availability and reachability
of active reaction sites in the cathode. When discharge
current is low, the inactive sites (made inactive by previous
cathode reactions) are distributed uniformly throughout the
cathode. But, at higher discharge current, reductions occur at
the outer surface of the cathode making the inner active sites
inaccessible. Hence, the energy delivered (or the battery lifetime)
decreases since many active sites in the cathode remain
un-utilized when the battery is declared discharged.

Notations and Definitions

A battery cell is characterized by the open-circuit potential
(Vw), i.e., the initial potential of a fully charged cell under
no-load conditions, and the cut-off potential (V,,) at which
the cell is considered discharged. Two parameters are used
to represent the cell capacity: the theoretical and the nominal
capacity. The former is based on the amount of energy stored
in the cell and is expressed in terms of ampere-hours. The
latter represents the energy that can be obtained from a cell
when it is discharged at a specific constant current (called the
rated current, C,-&d). Battery data-sheets typically represent
the capacity of the cell in terms of the nominal capacity.
Finally, to measure the cell discharge performance, the following
two parameters are considered : Battery Lifetime and
Delivered Specific Energy. Battery Lifetime is expressed as
seconds elapsed until a fully charged cell reaches the V,,
voltage. Delivered Specific Energy is the amount of energy
delivered by the cell of unit weight, i.e., expressed as watthour
per kilogram.
In the next section, we describe our basic stochastic
battery-model that captures the Recoveg: Effect, and a descriution
of an extension of the model to incorporate the Rate
CadaciQ Effect.

Battery Models

The fine-grained electro-chemical phenomena underlying the
cell discharge are represented by the accurate model, based
on PDE (Partial Differential Equations) [14], which involve
a large number of parameters depending on the type of cell.
The set of results that can be derived through the PDE model
is limited since as the discharge current and the cut-off potential
decrease, the computation time becomes exceedingly
large. Hence, the accurate PDE model cannot be used for
system-level exploration of a mobile embedded system. In
the following section, we present a more tractable parametric
model that captures the essence of the recovery mechanism.

Stochastic Battery Model

We model the battery behavior mathematically in terms of
parameters that can be related to the physical characteristics
of an electro-chemical cell [15, 161. The proposed stochastic
model focuses on the Recovery Effect that is observed when
Relaxation Times are allowed in between discharges.

Generating System Current Discharge
Profiles


In this section, we briefly describe the techniques that we
used to generate system-level current discharge profiles.
Please note that, while the focus of this paper is accurate and
efficient estimation of the lifetime and delivered energy of the
battery, system current discharge profiles are required as inputs
to the battery models presented earlier, hence we include
a description of how they can be generated.
We adapted the system-level power estimation framework
presented in [9] for our purpose. It consists of a discreteevent
co-simulation environment, power models for various
system components (including processors, synthesized hardware,
system-level buses, and memories), and speedup techniques
that enable efficient power estimation for complex
systems. As shown in [9], co-simulation (of the various
system components) is necessary in order to obtain accurate
power estimates. This is especially important in the
context of battery life estimation, since we need accuracy
in the current (hence, power) waveforms, not just the average
power or total energy. To estimate the power dissipation
in a programmable processor component, we use an
instruction-set simulator enhanced with an instruction-level
power model [ 181.

Experimental Results & Application

In this section, we demonstrate how our proposed battery life
estimation technique can be used to evaluate different system
implementations and select a battery-optimal implementation.
We report results obtained by applying the proposed
battery life estimation methodology on three system implementations,
SYSI, SYS2 and SYS3, of the TCPAP network
interface subsystem, shown in Figure 1. In the first implementation
(SYSI), the incoming packets are processed in a
pipelined manner; for example, while Chksum is processing
one packet, CreatePacket starts writing the next packet
to memory. Figure 8(a) shows the arrival and processing of
packets over time for SYS1. The cumulative current profile
for this system is shown in Figure 8(b), with the total current
(in mA) plotted over time (in ms). Alternative ways of processing
the packets lead to the second (SYS2) and the third
(SYS3) implementations, as shown in Figures 8© and 8(e)
respectively. The corresponding current profiles are shown in
Figures 8(d) and 8(f) respectively.

Conclusion and Future Work

We have presented a stochastic model of battery and a framework
for estimating the battery life as well as the delivered
energy for system-level design space exploration of battery-
powered mobile embedded systems. The model proposed is
fast enough to enable iterative battery life estimation for system
level exploration. At the same time, it is very accurate,
as validated using an accurate PDE model. In future, we will
use the developed framework for exploring how system architectures
can be made battery-efficient and for suggesting
the optimum battery configuration for any HW/SW embedded
system.