能量收集系统的自我可持续性：概念、分析与设计
Self-Sustainability of Energy Harvesting Systems: Concept, Analysis, and Design
摘要：
环境能量收集被吹捧为一种低成本的解决方案，可以延长低功耗设备的寿命，减少碳足迹，并使系统自我可持续。迄今为止，大多数研究都集中在能量转换过程的物理方面，或者在系统层面上收集的能量的最佳消耗策略。然而，尽管直觉上理解，据我们所知，自我可持续性的想法还有待精确，并作为一个性能指标进行研究。在本文中，我们提供了一个数学定义的概念，自我可持续性的能量收集系统，最终中断的补充思想的基础上。特别地，我们分析了具有无限电池容量、随机能量到达和固定能量消耗率的收获-存储-消耗系统。利用随机游走理论，我们确定的必要条件，系统是自我持续的。以积分方程的形式给出了自维持概率的一般公式。由于这些积分方程很难解析求解，最终中断概率的指数上界给出了使用鞅。这个界限保证了最终的中断概率可以任意小，简单地通过增加初始电池能量。我们还给出了最终停运的一个渐近公式。对于能量到达服从泊松过程的特殊情况，我们能够找到最终中断概率的精确公式。我们还表明，收获-存储-消费系统在数学上等价于一个$GI/G/1$消耗系统，这使我们能够很容易地找到中断概率，在自我可持续性的必要条件被违反的情况下。Monte-Carlo模拟验证了我们的分析。
英文摘要：
Ambient energy harvesting is touted as a low cost solution to prolong the life of low-powered devices, reduce the carbon footprint, and make the system self-sustainable. Most research to date have focused either on the physical aspects of energy conversion process or on optimal consumption policy of the harvested energy at the system level. However, although intuitively understood, to the best of our knowledge, the idea of self-sustainability is yet to be made precise and studied as a performance metric. In this paper, we provide a mathematical definition of the concept of self-sustainability of an energy harvesting system, based on the complementary idea of eventual outage. In particular, we analyze the harvest-store-consume system with infinite battery capacity, stochastic energy arrivals, and fixed energy consumption rate. Using the random walk theory, we identify the necessary condition for the system to be self-sustainable. General formulas are given for the self-sustainability probability in the form of integral equations. Since these integral equations are difficult to solve analytically, an exponential upper bound for eventual outage probability is given using martingales. This bound guarantees that the eventual outage probability can be made arbitrarily small simply by increasing the initial battery energy. We also give an asymptotic formula for eventual outage. For the special case when the energy arrival follows a Poisson process, we are able to find the exact formulas for the eventual outage probability. We also show that the harvest-store-consume system is mathematically equivalent to a $GI/G/1$ queueing system, which allows us to easily find the outage probability, in case the necessary condition for self-sustainability is violated. Monte-Carlo simulations verify our analysis.
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