# Optimal Routing for Time-Driven EH-WSN under Regular Energy Sources
## 3 Solar Energy-Harvesting Models  
The literature on solar-based energy harvesting models is extensive. A good classification is provided in [23]. Here, a first distinction is established between models for the solar irradiance (environmental models), and models for the solar energy-harvesting devices (harvester models). Harvester models are typically used for design or energy management optimization purposes. In turn, they can be classified into high-level and low-level. High-level models ignore the details about the actual hardware implementation of the harvester; rather, the harvester is viewed as a black-box that performs an energy transfer function between the actual solar radiation and the energy that feeds the sensor node. Accordingly, efficiency is the magnitude that best characterizes the performance of this energy transfer process. Since high-level models are relatively simple, their analytical formulation is feasible [24; 25] and can be easily integrated into general-purpose simulation software environments. In contrast, low-level models are highly implementation-dependent and hence tightly associated with specific architectures. Low-level modeling relies on equivalent circuits of the integrated components,which are then combined into a system model to accurately describe the behavior of a given hardware architecture [26; 27; 28]. These low-level models can be implemented via specialized simulation software environments, like SPICE [29] or Simulink (a visual programming tool for model-based design that supports automatic code generation in Matlab), or directly executed by using EH-WSN-oriented simulation tools, like GreenCastalia [30], SolarCastalia [31], SensEH [32] and others, which already include an energy module that integrates the energy-harvesting, rechargeable battery and energy consumption models.  
Environmental models focus on the estimation of solar irradiance. As stated in [23], they can be further classified into statistical models and astronomical models. Statistical models make use of historic measurements of solar irradiance to predict future values of this magnitude at locations close or similar to the measurement points [33; 34; 35; 36; 37]. Optimized versions of the predictive algorithms used for these purposes can also be incorporated into node operation in order to obtain real-time estimates of future solar irradiance and correspondingly adjust the node duty cycle [38]. Irradiance measurements are typically stored in large databases, like Meteoromr [39] or the NASA POWER Project database [40]. Since these databases are publicly available, the collected data can also be used to conduct simulations based on real radiation levels [41]. In contrast to statistical models, astronomical models calculate solar irradiance on the basis of geometric calculations that include the solar panel inclination, the panel orientation, the latitude, the day of the year and the time of the day. So, in essence, these are deterministic models that do not take into account weather conditions or local obstacles. Some examples can be found in [42; 43]. These models are relatively simple and thus they can be easily included in analytical methods. Since the focus of the present paper is not on the characterization of solar irradiance, but on the determination of the optimal routing strategy for EH-WSN and the comparison of this strategy with other alternatives, any model can be used as long as all alternatives are compared under the same conditions. Consequently, a simple analytically-tractable model is preferable. In particular, the model proposed in [44] has been used for numerical evaluation (Section 6). This model, in addition to formulating solar irradiance as a simple quadratic function of the time of the day (for given parameters about location and month of the year), is consistent with the accurate model proposed in [43].