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Estimating the Lifetime of Wireless Sensor Network Nodes through the Use of Embedded Analytical Battery Models


The operation of Wireless Sensor Networks ( WSN s) is subject to multiple constraints, among which one of the most critical is available energy. Sensor nodes are typically powered by electrochemical batteries. The stored energy in battery devices is easily influenced by the operating temperature and the discharge current values.

Therefore, it becomes difficult to estimate their voltage/charge behavior over time, which are relevant variables for the implementation of energy-aware policies. Nowadays, there are hardware and/or software approaches that can provide information about the battery operating conditions. However, this type of hardware-based approach increases the battery production cost, which may impair its use for sensor node implementations.

The objective of this work is to propose a software-based approach to estimate both the state of charge and the voltage of batteries in WSN nodes based on the use of a temperature-dependent analytical battery model. The achieved results demonstrate the feasibility of using embedded analytical battery models to estimate the lifetime of batteries, without affecting the tasks performed by the WSN nodes.


Figure 1. Example of a discharge profile based

Figure 1. Example of a discharge profile based

The main advantage of the methodology proposed in this paper is related to the deployment of a temperature-dependent battery model, which can be used to predict the behavior of the battery in low-power WSN nodes regardless of the associated hardware. The proposed methodology assumes that there is a cyclical operation pattern for the WSN nodes (e.g., a duty cycle), so that the discharge profile can be used as input parameter to compute the battery behavior over time (open-loop computation). Figure 1 depicts an example of a discharge profile based on a MICA2DOT WSN node.


Figure 2. Kinetic Battery Model (KiBaM)

Figure 2. Kinetic Battery Model (KiBaM)

KiBaM is one of the first high-accuracy analytical battery models that was proposed in the early nineties. It is based on an intuitive approach to model the behavior of high-capacity Lead-Acid batteries over time. This model uses a two-tank analogy to describe the battery charge and discharge processes, as shown in Figure 2.


Figure 3. Voltage tracking comparison using a constant discharge current (30 mA)

Figure 3. Voltage tracking comparison using a constant discharge current (30 mA)

Note that the original KiBaM voltage model represents a linear battery discharge curve, V × t. This type of approximation induces significant errors with respect to the lifetime analysis of any device connected to the battery. On the other hand, the T-KiBaM + TVM model offers a higher precision when estimating the behavior of the battery voltage curve over time. For instance, at T = − 5C (Figure 3a), analyzing the voltage level at 2.4 V, the relative error to the experiment of KiBaM is 37.53%, while in T-KiBaM is 0.73%.


This section presents the experimental results obtained when implementing the T-KiBaM model in multiple WSN-compatible MCUs. The objective is to check if analytical battery models, embedded in a low computational capacity hardware, can be used to track both the battery SoC and the voltage level of the battery itself over time. First, we present the basic characteristics of each MCU used in this work. Then, a discussion is included regarding the selected metrics used for the experimental evaluations. Finally, the results obtained from the experimental assessment are presented.


Figure 4. Node activity description. (a) Active mode only; (b) Active and inactive modes

Figure 4. Node activity description. (a) Active mode only; (b) Active and inactive modes

The node executes the T-KiBaM algorithm at the end of its task to update the state of charge of its battery. Although it may play a significant role in energy consumption, the node initialization process is not considered in these analysis, since it runs only once during its entire life cycle. Figure 4 depicts a schematic summarizing the node activities in the two presented scenarios.

Figure 9. Results using different time steps for voltage tracking

Figure 9. Results using different time steps for voltage tracking

Finally, the voltage level estimation provided by the T-KiBaM model is evaluated over time, using different time steps (Scenario 1). Again, a comparison of the experimental and analytical results is performed, using the results provided by the ATmega328P MCU at the time steps mentioned above. Figure 9 depicts the behavior of the estimation of the voltage curve at each update of the T-KiBaM model, under a continuous discharge current of 30 mA, at − 5C.


Estimating the battery lifetime is a complex task since many factors can influence the battery behavior, e.g., technology, operating temperature and discharge current. Analytical battery models may assist in this task, achieving results close to reality. However, two problems may arise within the WSN context. Firstly, the implementation of complex analytical models upon low-capacity hardware platforms is not an easy task, due to low processing capability, memory constraints and the high accuracy required to represent low varying analog values.

Secondly, the execution of this type of analytical models by real-world nodes will influence its energy consumption, and therefore, the required effort to estimate the network lifetime may reduce the lifetime of the network itself. The study performed in this paper evaluated the cost of executing an analytical battery model known as T-KiBaM in low-power MCUs. The model validation took into account experimental data. As shown in Section 4, the T-KiBaM model can accurately estimate the lifetime of Ni-MH batteries and is also able to estimate the voltage behavior over time at different temperatures, which is an important issue when considering devices (nodes) that require a minimum voltage value to maintain their operation.

The analytical models were implemented upon different micro-controllers. As a result, although running T-KiBaM on low-power MCUs requires long computing times, such computing times do not represent a significant slice of the estimated battery lifetime. Therefore, the time required to estimate the battery behavior (which includes tracking both its SoC and voltage level over time) is feasible. As future work, we are interested in finding a way to integrate the knowledge about both the discharge current and voltage level of the battery to feed the T-KiBaM in real time, similar to the use of a fuel gauge IC in a smart battery pack.

In this sense, it would become possible to implement a closed-loop approach, allowing the correction of predictions over time. Other issues will also be addressed in future work, such as a full research on the use of duty cycle discharge profiles at different temperatures. The validation of the estimates can also be made through the implementation of the proposed battery model in sensor nodes of a physical WSN. In this case, an application with a basic set of tasks should be used to allow the construction of a well-known fixed discharge profile.

Source: University of Santa Catarina
Authors: Leonardo M. Rodrigues | Carlos Montez | Gerson Budke | Francisco Vasques | Paulo Portugal

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