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A novel method for energy efficient warmup of lithium-ion batteries from sub-zero temperatures using predictive control

by Paul N. Blumberg, PhD

Many of the machines and appliances that are in common use today require that their power be available immediately, regardless of adverse ambient conditions such as sub-zero temperatures. For example, on a 0 °F day, we expect to be able to start our cars or trucks, which may have cooled down to near ambient conditions, and proceed to use them in the same manner as if we were in more moderate climates. To accomplish this, engineers and scientists have worked hard to ensure that in extremely cold temperature environments, the engine oil does not become too viscous and that there are sufficient high volatility components in the fuel so that vaporization and ignition within the engine are possible on an almost instantaneous basis.

The same requirement holds true for battery-powered devices or vehicles. The Lithium-ion battery has emerged as the current “battery of choice” for automotive hybrid and electric vehicle applications. Over the last decade, significant improvements in its energy and power density have been made through research in all aspects of its fundamental electrochemistry and materials. Nevertheless, due to fundamental electrochemical factors, the availability of “instantaneous” power at temperatures below approximately 15 ˚F remains a challenge.

Prior methods to achieve warmup to approximately 40 °F (~5 °C) have involved the use of electrical heating jackets or the convective circulation of a higher temperature fluid within the battery. This implies the need for intensive external hardware and control systems. In the absence of external power and hardware, internal current flow is the most effective means of heating the battery despite the fact that it reduces the battery’s State-of-Charge (SOC).

The traditional method for internal heating is based upon simple voltage-controlled battery discharge—the Constant Voltage Method (CVM). In recently published work[1], researchers at the University of Michigan (U of M) have focused on an internal heating technique in which an ultra-capacitor is paired with a Lithium-ion battery.

Employing a control-optimized asymmetric bidirectional current flow technique, referred to as the Pulsed Current Method (PCM), their results indicate that it is possible to reduce the energy loss from the battery’s State-of-Charge (SOC) and, also, the size of the ultra-capacitor by as much as 20% when compared to the use of the more traditional CVM.

The fastest way to warm up a battery is to draw the maximum current possible at a voltage corresponding its low voltage limit, i.e., the CVM method. However, this approach is the most “expensive” in terms of depleting the battery’s SOC compared to any other type of current waveform that can be used for the internal current flow warmup process.

This observation leads naturally to the need for identifying the magnitude and shape characteristic of a more optimal waveform that could be used to draw current from the battery. The optimal waveform would be subject to the requirements that the warmup be accomplished within a specified time and that the highest SOC possible be maintained after the warmup is complete.

In a practical scenario this might appear as follows—an individual heads to the parking lot and, in advance, signals the vehicle battery to warm-up in the most energy-conscious manner so that by the time they reach the vehicle they are able to drive away immediately.

In the past, it has been suggested to pair a battery with another battery to achieve the bi-directional currents for the necessary internal self-heating. However, low battery charging currents are needed to avoid lithium plating at low temperatures. These current charging limits constrain the magnitude of the bi-directional current in the paired-battery method. Due to internal resistance (I2R) heating losses, the low current approach could result in a slightly warmer but completely drained battery.

The ultra-capacitor, on the other hand, does not have the same stringent low current charging limits. Therefore, it provides the best “mate” for the battery in bouncing the electrons back and forth so that both power sources get warm fast and efficiently. Enabled by this degree of freedom, researchers at U of M’s Automotive Research Center developed an algorithm to define the asymmetric amplitudes of the bidirectional current.

The model-based method, described below briefly, minimizes the energy requirement to heat the battery while also indicating the point in time at which the battery is sufficiently warm to allow its use for providing output power for its particular application. The researchers focused on “pulse power” or the “State of Power”, rather than temperature, as the primary indicator of the operational capability of the battery. The power capability of the battery is defined as the maximum continuous current that can be drawn over a fixed time interval at a voltage that is commensurate with current and voltage constraints.

To design this warm-up technique, a two-step analytical approach was adopted. In the first step the behavior of the battery at low temperatures was modeled, and, in the second step, the best current trajectory for the battery was determined. The internal processes of Lithium-ion batteries at low temperature are complex and difficult to model. Therefore, in the first step, the researchers at U of M developed a reduced-order (i.e., less complex) representative model of the electrical and thermal behavior of cylindrical Lithium-ion batteries. This model of the battery was validated via measuring the battery core temperature during the warmup time under pulsed conditions from a temperature of negative 20 °C to negative 10 °C over a period of 180 seconds.

In the second step, the task of determining the best current trajectory was posed as an optimal control problem. Based on electrochemical considerations, the profile of input current was stipulated to be a sequence of bi-directional pulses recurring at a certain frequency, i.e., the Pulsed Current Method (PCM).

The current trajectory was partitioned into blocks consisting of a repeating pulse period. The magnitude of the pulses and current during every period in each block were determined by solving a constrained quadratic problem. The first block of optimal currents was applied.

Subsequently, the power capability of the battery was assessed; if the required power could not be provided, the pulsing was repeated until the requirement for the necessary power level could be met.

As noted previously, the results of the PCM were compared to the traditional CVM method, the latter, drawing the maximum allowable current continuously.

The results indicated that by employing PCM it is possible to reduce both the energy dissipated as excess heat and the size of the ultra-capacitor by as much as 20% when compared to the CVM method of constant voltage discharge. Furthermore, in analyzing the results of simulations, it was observed that PCM can reduce the growth of damaging over-potentials inside the battery and, hence, perform better than CVM.

However, it was also found that there is a trade-off between the reduction in the size of the external storage device, i.e., the ultra-capacitor, and the SOC lost versus the time required to warm up the battery.

It should be noted that previously reported results in which pulsed currents were applied at room temperatures have indicated a tendency for an increased rate of battery degradation. The researchers at U of M’s ARC are aware of this fact and of the requirement that the PCM method not exacerbate deleterious effects related to the health of batteries in the context of the low temperature warmup operation.

In order to fully gage the practicality of the proposed energy-efficient strategy, experiments using the proposed PCM technique are set to be undertaken at the University of Michigan ARC in the upcoming months.

Dr. Blumberg is currently a Visiting Research Scientist, Mechanical Engineering, College of Engineering at the University of Michigan, Ann Arbor.


  • [1] Shankar Mohan, Youngki Kim and Anna. G. Stefanopoulou (2016) “Energy-Conscious Warm-Up of Li-ion Cells from Sub-Zero Temperatures”, IEEE Transactions on Industrial Electronics Volume: 63, Issue: 5, Pages: 2954 – 2964. doi: 10.1109/TIE.2016.2523440


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