Model-Based Energy Budget Estimation Algorithms

The first type of EBE algorithms is said to be “model-based”. This type of algorithm relies on a model of the energy source it is associated with. Using the characteristics of the energy source, the algorithm is able to predict the future harvested energy and to adapt the calculated energy budget EB to past, present and future energy

harvesting conditions. Such algorithms heavily rely on predictors to estimate the future harvested energy. Therefore, model-based algorithms combine two problems: how to accurately predict future amount of harvested energy and how to decide the best EB using this parameter. As they use a model of an energy source to predict

the future harvested energy, prediction algorithms are specific to the energy source they were designed for. Due to the progresses of energy harvesting technologies and use-cases, the design of energy harvesting prediction algorithms has been an active area of research during the past years, as detailed in the next paragraphs.

Although RF energy harvesting is not the most efficient energy source, it is easier to predict, as multiple works try to predict the future power of RF signal, in order to increase the quality of radio links. These work can be adapted to estimate the future power harvested with RF energy harvesting. For example in [173], De Araujo

et al. model the link as a Markov chain and discover its parameters on the fly. This

solution makes use of genetic machine learning algorithms to adapt itself to new radio conditions. This work is extended in [174] with the introduction of the notion of orientation in order to represent the tendency of the signal strength to increase or decrease. Machine learning is also used in [175] to predict the future link quality. In this work, link quality data is used to train a prediction model based on logistic regression, which enables a lower computational cost than alternatives such as Bayes classifiers and artificial neural networks.

The first energy predictor for solar sources for WSN has been proposed by Kansal

et al. in [168], which introduced the concept of power management for energy harvest-

ing WSN nodes. In this work, the predictor is based on an Exponentially Weighted Moving Average (EWMA) algorithm [176], with a window size of 24 hours divided in time slots of 30 minutes. The energy harvested during a slot is expected to be simi- lar to the the energy harvested in the same slot of previous days. This assumption makes the algorithm sub-optimal for environments where the weather varies a lot.

Piorno et al. [170] mitigate this issue with the Weather-Conditioned Moving Aver-

age (WCMA) algorithm, which is able to predict the output of a solar panel with a 10 % accuracy by taking into account both present and past weather measure- ments. [177] uses a phase displacement regulator to extend the WCMA algorithm and reduces its average error. A comparison of these different algorithms is given in [178], which shows the higher efficiency of the WCMA algorithm over EWMA and a neural network solution. However, WCMA requires more memory and com- putational power than the alternative solutions. [179] presents SunCast, an indoor solar energy harvesting predictor which learns predictable losses of luminosity due the the environment (e.g. trees, nearby buildings...). [180] proposes to estimate the harvested energy with EWMA when there are no clouds, and use meteorological models to scale this value when there are clouds. Finally, [181] uses Q-Learning, a reinforcement learning approach, to efficiently predict future harvested power based on past and present measurements.

Procarelli et al., in [34], proposes an energy predictor dedicated to forecast the

availability of a wind energy source. The predictor uses a linear regression over a 30 s sliding window, using the last power measurement to predict the next one, and adapts the power converter settings to the harvested power. The Adaptive Response Rate Single Exponential Smoothing (ARRSES) is presented in [182]. This predictor is based on EWMA, but varies the smoothing factor proportionally with the fluctuations of input power, increasing its response time to weather variations. This approach is extended in [183] which considers longer forecasting periods.

Although most approaches are specific to a single energy source, some solutions can be adapted to fit multiple sources. [184] presents Pro-Energy, which predicts the future harvested energy by, once per time slot, comparing the energy harvested in the current day and saved energy harvesting profiles of past days. Pro-Energy is able to make short-term and medium-term predictions, and dynamically adapts its set of saved energy profiles, based on their age and similarities, to adapt itself to

82 Energy Budget Estimation Algorithms and Methods

new conditions. [185] extends this work with the introduction of Pro-Energy VLT, which also dynamically adapts the lengths of time slots. [186] presents a study of both indoor light and thermoelectric energy harvesting in the context of Body area Networks (BAN), taking in account the impact of human activity. The system uses measurement to know the current state of the energy source and a Kalman filter to predict the next state of the source and how much energy it will provide. Finally, [187] proposes the use of Markovian models to simulate the behavior of piezoelectric and solar energy harvesting sources. The authors conclude that although both sources can be modeled by the same principles, the piezoelectric source is better modeled by a generalized Markovian model while the solar source is better modeled by a stationary Markovian model.

The prediction algorithm delivers the estimated future harvested energy to the model-based EBE, which then estimates the energy budget EB. Multiple EBE algo-

rithms have been designed to rely on energy prediction.

The first EBE is proposed in [168]. This EBE directly controls the duty cycle of the WSN node based on the difference between the estimated future harvested energy and the actual measurement energy input. Due to this, the EBE is directly impacted by the lack of precision of the EWMA predictor when the environment varies quickly. Moreover, the duty cycle is not balanced over the observation period, and thus is highly variable between periods of plentiful energy and periods where no energy can be harvested. It can be noted that this EBE does not take into account the residual energy ER, which leads to power failures.

In [188], Casgnetti et al. present two EBE, named OL PM (Open Loop Power Manager) and CL PM (Closed Loop Power Manager) which both aim to reach ENO. The harvested energy EH is used to estimate the recharge rate of the energy storage.

OL PM calculates a duty cycle based on this recharge rate, while CL PM predicts the periods where the recharge rate is below a threshold, meaning not enough energy is harvested. In these so-called Zero Energy Intervals (ZEI), CL PM tries to save as much energy as possible. When enough energy is harvested, it uses the same policy as OL PM. A similar approach is taken in [6], where the power manager uses the EWMA predictor to decide the duty cycle during non ZEI periods and uses a specific NE PM (Negative Energy Power Manager) during ZEI, which focuses on avoiding power failures.