A fast and accurate energy source emulator for wireless sensor networks

2.1 Modeling

While the fastest and most accurate way to model an energy source is to sample (with the sampling rate determining the accuracy of the model) the I−V curve and store these samples on main memory, this approach cannot be implemented in embedded systems for most energy sources due to the high number of parameters which do not fit the main memory. In fact, the memory footprint of the model increases as O(n ^m+1), where n is the number of samples and m is the number of independent parameters.

A second approach, which has both memory footprint and execution time bounded by O(1), can be represented by analytically modeling the I-V curve. This approach is well suited for an embedded device providing a good trade-off between fast execution time, model accuracy, and memory footprint.

Moreover, there are mainly two methods used to create an analytic model of an energy source behavior: (i) curve fitting and (ii) modeling the equivalent circuit of the energy source.

Curve fitting is the process of interpolating a set of experimental data taken from the energy source’s I-V characteristic in a curve which approximates it. When this curve can be described analytically, evaluating it is significantly faster than interpolating at run-time a set of points.

An equivalent circuit model (ECM) is an ideal circuit which describes the energy source in terms of an ideal voltage (by applying Thevenin’s theorem) or current (using Norton’s theorem) generator and passive components. Solving the equivalent circuit by using Kirchhoff’s laws gives the energy source’s behavior in terms of tension and current (v(t) and i(t)). The I-V curve can be obtained by manipulating these two functions. Since solving the equivalent circuit requires to solve a system of differential equations, it might not be possible to obtain exact solutions.

Analytical models are often parameterized (e.g., a battery output voltage depends also on its internal resistance) and determining these parameters might take more effort than determining the I-V characteristic itself. In fact, while the I-V curve and parameters depending on the energy source itself can be determined once, before the emulation starts, parameters depending on environmental factors (e.g., temperature, incident light, and load resistance) require a new evaluation every time the parameter changes.

Some authors describe a direct relation between measured variables and I-V curve’s parameters (e.g., the I-V curve of a thermoelectric cell can be described as a function of heat absorbed by the cold side, temperature of the cold side and the slope of the experimental V(I) curve at Δ T=0), while others suggest an iterative approach (e.g., many models of solar panels try to fit the manufacturer I-V curve by varying iteratively a set of parameters of the ECM). The first approach can still be computed in O(1) while the second one depends on the approximation algorithm used and on the desired degree of accuracy.

2.2 Emulation

Despite its enormous potential, the energy source emulation for wireless sensor networks is a relatively unexplored field of research. Currently, there are several projects on designing emulation hardware for batteries and solar cells but only few contributions address the problem in a general way or are portable and intended for a massive distribution in a wide testbed.

For instance, B# [13] is a battery emulator based on an adjustable linear regulator which emulates the output battery voltages. It works in the range of 1.0–4.5 V and it can source a maximum current of 800 mA. The emulation board is controlled by means of a desktop computer running the Dualfoil electrochemical simulator for lithium-ion battery cells [14]. The main computer takes in input the current draw by the powered system and finds the corresponding voltage using a look-up table. S# [15] extends the B# architecture by adding a new front-end which allows the user to emulate a solar panel. In particular, S# can run either in the simulation mode or the emulation mode. In the simulation mode, it takes a current profile and a sunlight trace as inputs and generates a simulated power profile on the host computer. In the emulation mode, a real load is connected to the output of the emulation circuit and the solar model is written to the memory of the microcontroller which generates at run-time an appropriate voltage to drive the load. A similar approach is also presented by other authors which introduce solar panel emulation circuits controlled by means of a LabView PC [16–18].

The SunaPlayer photovoltaic emulator should be mentioned for its distinctive feature of using a Darlington transistor as the last circuit stage to build a non-linear model of a solar panel [19]. SunaPlayer is based on a microcontroller and can be battery powered. It supports a wide operating range, spanning output currents from 430 μA to 1.89 A and output voltages from 0.02 to 9.8 V with a measured accuracy of about 99 %. At run-time, the microcontroller needs to choose between several stored I-V curves in order to determine the appropriate tension value to be applied to the Darlington transistor gate. This task is very time expensive so that the major drawback highlighted by the authors is the extremely high latency which, in the worst case, has been measured in about 10 s.

Finally, in the photovoltaic domain, there are a plethora of emulators for high power (up to 3000 W) solar panels such as [20, 21] which are basically designed for industrial applications.

More close to a generic energy source emulator targeted for wireless sensor networks, we can report the Ekho project which is a generic energy harvesting emulator designed for small currents [22, 23]. In particular, Ekho uses a simple design where first of all each energy harvester needs to be characterized by recording its distinguishing I-V curves using a high-precision acquisition instrument. Then, the appropriate I-V curve is replayed at run-time by means of a dedicate board. The Ekho replaying board uses a capacitor to power the load and a sensing resistor (10 Ω) to estimate the supplied current. At run-time, the corresponding operating point on the I-V curve is calculated and the appropriate output tension is set. The system uses a FPGA to speed up the I-V calculation in the first release while the more recent implementation is based on a 32 Mhz ATMEL microcontroller. While the system shows a satisfactory emulation accuracy of about 77.4 μ A during a solar panel emulation its latency, measured in 7.4 ms, can negatively impair the ability to emulate a generic energy source for wireless sensor networks.

Another generic approach can be represented by the simulation/emulation framework described by De Mil et al. [24] where a generic energy harvester is simulated/emulated as a complex energy source which is composed by a harvester always connected to a energy storage such as an ultracapacitor. The energy harvester and the storage element are virtual, and implemented in software. The voltage drop across this virtual capacitor is calculated using a static model and a feedback is applied by means of a DAQ plus a voltage follower. Authors do not report accuracy or time latency but the entity of the microcontroller (a Texas Instrument MSP430 running up to 20 Mhz) reveals a high response time.

For reasons of completeness, a generic energy source emulator can also be represented by programmable power supplies such as those produced by National Instruments which are capable of simulating different energy sources with a wide range of operations [25]. These power supplies offer fine-grained measurement and a high degree of programmability but they are not portable and they can not be used in a massive installation because of their cost that exceeds $4000.

3.1 A battery model

Battery modeling is an active research area due to the widespread diffusion of battery-powered devices in several application fields. As a consequence, many possible methodologies and models are available [26]. Again, the exploration of this design space implies the evaluation of the trade-off between accuracy and computational complexity of the model. To evaluate the performance of the proposed emulator platform we implemented an analytical model suitable for rechargeable batteries of different types [27]. The methodology is based on curve fitting of the V(Q) discharge curve (at constant load) taken from the manufacturer’s datasheet.

The model discriminates between charge and discharge curves and describes them separately to take into account the fact that the I-V curve of a battery presents an hysteresis phenomenon. The discharge curve is described by a single equation valid for lead-acid, Li-ion and NiCd/NiMH batteries, while the charge curve is slightly different for each kind of battery. These curves are parameterized by maximum voltage, state of charge, internal resistance, polarization voltage, polarization resistance, instantaneous drawn current, and low-pass filtered current (which models the slow response of the battery to a change in load).

Every parameter but state of charge and current (both unfiltered and filtered¹) can be obtained from a typical manufacturer’s datasheet by applying a set of equations on three points of the experimental discharge curve. The state of charge is computed as the drawn current integrated with respect to time. In order to reduce model complexity the authors make several assumptions, namely: battery capacity does not change at different discharge rate (no Peukert effect), no effect of temperature on the model, no memory effect, same parameters for both charge and discharge, constant internal resistance, and negligible self discharge.

This approach results into a model with the following features: (i) parameters can be easily derived (only three points are required) from the battery discharge curve or even from its datasheet; (ii) the computational complexity to evaluate the model is O(1), the most expensive operation being a single floating point exponentiation for the discharge I-V curve; (iii) maximum relative error on the I-V curve has been estimated to be 10 % in the worst case (state of charge of 0−20 % with highly dynamic load).

3.2 Energy harvesters

A generic energy harvester is typically composed of the following elements: (i) a transducer that transforms some form of energy available from the environment into electrical power; (ii) an energy buffer, used to provide energy storage capabilities to the system; (iii) an input regulator, which provides any signal conditioning (i.e., DC-AC, DC-DC conversion) required to adjust any mismatch between the operating range of the transducer and that if the buffer; (iv) an output regulator in charge of adapting the signal provided by the energy buffer to the operating range required by the load. Some components can be optionally included/excluded in the scheme described so far, in some cases. For instance, the scavenger could be directly coupled to the load without any buffering or output regulator, depending on the features of the target application.

To provide a more comprehensive view of the wide range of possible sources that can be implemented within the proposed architecture, we introduce in the following two models representative of a wide number of possible energy scavenging sources, namely photovoltaic and thermoelectric cells.

Solar cells exploit the photovoltaic effect (PV) to transform solar energy into electrical energy. The electrical power delivered by a PV panel (an array of interconnected solar cells) depends on several parameters, namely, solar radiance, incidence angle, working temperature, and load impedance. Different production technologies (monocrystalline, polycristalline, and amorphous silicon) result into different I-V curves, whose accurate modeling represents an issue to be addressed in order to gain insight about the amount of energy flow produced under different working conditions [28].

A common modeling approach entails the description of a PV module through an equivalent circuit with lumped components, the most commonly adopted being a circuit containing a current generator (accounting for the light generated current), a diode (used to shape the knee of a typical I-V characteristic), a series, and a shunt resistor (to account for connection losses). To fully characterize the working points of a cell, the extraction of parameters from these circuit representations is carried on by means of numerical nonlinear methods [28–30]. The computational requirements posed by these numerical models are critical for their implementation on embedded real-time systems. The inherent trade-off between convergence speed and accuracy of the emulated model is therefore an issue to be explored for the emulation of this type of energy source.

Thermoelectric cells (also known as thermoelectric generators, TEG for short) are devices capable of converting heat (given a thermal gradient across the plates) into electrical energy, exploiting the Seebeck effect. In particular, the voltage generated by a given cell is proportional to the temperature difference Δ T through a proportionality coefficient S (the Seebeck coefficient). The converse physical process may also be observed, namely, the heat transfer between the two sides of a TEG (Peltier effect). In order to design accurate models for analyzing both transient and steady conditions and encompassing non-linear electrical and thermal coupled effects, several methods have been proposed, leading to SPICE [31, 32] or Matlab/Simulink models [33, 34]. Other models, describing the interaction of a TEG with heat generated by CPUs (e.g., in a server farm monitoring application), have been derived by regression on the empirical relationship between temperature gradients and TEG output power (when the TEG is coupled to a DC-DC boost converter) [35]. Again, the complexity of computing the model output needs to be carefully evaluated, since it may severely affect its applicability in real-time environments and its implementation on embedded platforms. Moreover, circuit models need to take into account a model of the load to be powered, which might be particularly difficult to obtain in certain cases.

3.3 Compositional models

The proposed modeling framework allows to smoothly integrate and compose different building blocks representative of a cascade of devices. Indeed, in some applications, the energy flow provided by a given harvester needs to be properly shaped for compatibility with the load to be powered. For example, voltage limiters or output stage regulators (DC-DC converters) could be used to couple a photovoltaic scavenger to an embedded device equipped with integrated circuits requiring to be powered with stable voltage [28]. Another example could be represented by chips used to drive battery recharging according to optimized policies [36]. The composition of the I-V curves of each single block into a suitable I-V characteristic representative of the whole cascade allows us to emulate modular scavenging systems, providing a twofold benefit: on the one side we extend the emulation process to a wider spectrum of possible power source behaviors, on the other side we decouple and isolate the contribution of each single block (e.g. the photovoltaic cell and the recharge chip are separately characterized and composed) thus enabling to perform significant fine-grain emulations.

4.1 Hardware

Figure 2 shows an actual picture of the emulator prototype which highlights its relative small size (73 ×57 mm) while Fig. 3 shows the main architectural characteristics. The emulator core consists of the ATSAM4E16E microcontroller provided by Atmel corporation which is based on a high-performance 32-bit ARM®;Cortex®;-M4 RISC processor running at a maximum speed of 120 MHz and features up to 1024 kB of Flash and 128 kB of RAM [37].

This microcontroller family offers a rich set of advanced connectivity peripherals including an Ethernet port, a full-speed USB, and an high-speed MCI for SD and MMC memories. From the analog point of view, the microcontroller is equipped with two 16-bit ADC, one 12-bit DAC (2-channels), and an analog comparator which allow us to build the emulation interface described later in Section 4.2. The power supply unit consists of two low-dropout (LDO) voltage regulators designed to provide up to 1.5-A output current which receive the power through the ethernet connector using the Power over Ethernet (PoE) standard technology [38, 39]. Moreover, a precise analog reference has been provided to the microcontroller by means of an LM4132 precision voltage references chip in order to provide stable and accurate analog measures [40].

4.2 The emulation interface

The emulation interface refers to the particular schema and components used to build a complete feedback system starting from the microcontroller. In particular, Fig. 4 shows the adopted emulation interface which powers a generic sensor node represented into the right by a dashed rectangle. The DAC of the microcontroller can output a voltage signal with 12-bits of resolution mapped into an analog range starting from \(\frac {1}{6}\)ADVREF up to \(\frac {5}{6} \text {ADVREF}]\). Because of the standard power supply voltage of several consumer devices is 3.3 V which corresponds to our ADVREF, the A ₁ operational amplifier (MAX4239) is provided to boost the DAC output (DACC_out) to 3.3-V level [41]. Moreover, the boosted DAC output is used to drive the A ₂ (AD8397) operational amplifier which is working as a voltage buffer and decouples the supplied current from the DAC output signal [42].

In order to measure the current supplied to the generic load, a resistor (R _sense) has been placed between the load and the ground and the resulting voltage drop (V _sense) is amplified by A ₃ (MAX4239) and then measured by an ADC channel. R _sense has been opportunely dimensioned to obtain a good compromise between the current measurement resolution and the voltage drop which unavoidably affects the voltage perceived by the generic load. In particular, in our tests we use a sensing resistor of 6.22 Ω and a precision differential amplifiers with a gain of 10 [43]. Thus, for a value of 3.3 V (the max readable value for the ADC), we obtain a measurable current in the range from about 0.05 up to about 53 mA (considering a resolution of the ADC set to 16 bits).

Due to the voltage drop across the sensing resistor, a generic load is supplied by a voltage difference (V _load) which is reduced with respect to the boosted DAC output imposed by the emulator. In order to compensate this reduction, a nominal voltage restoring mechanism has been implemented which consists on overloading the output of the DAC by the same voltage drop measured on the R _sense as soon as the voltage drop has been read. This hardware-software loop guarantees a V _load compliant to the nominal expected conditions with a delay equal at least to the hardware-software latency.

Finally, a second ADC channel (ADC _V ) has been used to constantly monitor the real output value of the voltage buffer (A ₂) for debugging purpose.

4.3 Software

The software architecture has been designed to achieve high performance and at the same time to allow the execution of different source models. Moreover, the emulator firmware has been developed to simplify the simulation parameter initialization and management in real conditions of utilization.

The software architecture has been designed in a modular way to guarantee the easy maintenance and the reuse of the source code. In particular, the overall architecture can be represented by the following six elements: (i) processor; (ii) communication; (iii) measuring; (iv) model; (v) output; (vi) data storage.

The processor element consists of the main loop function which manages the remaining elements. The main function loop iterates at the maximum achievable speed while executing the main instruction chain. In particular, at each iteration, a communication element, which is designed to manage the emulator via Telnet, is polled to handle potential incoming ethernet packets. If no commands have been issued by the Telnet channel a start measuring command is triggered to the measuring element. When the measure has been completed, the control is passed to the model element which executes the current model and produces output values. The calculated output values are then passed to the output element which properly configures the DAC output also including the nominal voltage restoring mechanism described in the previous section. Finally, a data storage element is also provided to optionally log system events and emulation data to an external SD memory card.

The main loop contained in the processor element is the major contributor to the emulator performance.

In fact, each stage of the loop is executed sequentially because of the single execution unit provided by the microcontroller so that the delay of each element is added to the others. For this reason, minimizing the execution time of each element is a crucial task which directly impacts the emulator performance. The optimization of the execution time of the element containing the energy source models should be treated separately since there is a trade-off between computational complexity and accuracy of each model which can impacts the emulator performance in different ways. This treatment is out of the scope of this paper and it will be discussed in a future work.

Basically, the period of time that elapses between two consecutive measurements is a phase in which the emulator is insensible to the variations of the supplied current and it can not react by setting a proper output value. This period of time can be named emulator latency and it should be minimized and properly characterized. In order to reduce the emulator latency, several expedients have been played out, such as disabling configuration Telnet commands when the emulation is running, or selecting among different level of the logger verbosity in order to reduce the time spent to save data to the SD card.

5.1 Experimental setup

The current consumption of the device powered by the emulator was measured and sampled by means of a National Instruments PXI-4071 digital multimeter with a sensitivity down to 1 pA [44] while digital waveforms were sampled by means of a National Instruments NI-DAQmx PCI-6251 16-channel data acquisition board connected to a BNC-2120 shielded connector block [45, 46]. Square waves were produced using a TG2000 Aim-TTi analogue and digital function generators [47]. During the experiments, the emulator prototype was powered at 12 V by a NGMO2 Rohde & Schwarz dual-channel power supply [48]. The emulator was tested with constant load by connecting it to simple static resistors while an ad-hoc designed DC electronic load was used in constant current experiments. Finally, more realistic operating conditions have been experimented by using the emulator as a power source for a real VirtualSense sensor node [49].

5.2 Supplied current measurement error

The first set of experiments was carried out to deeply characterize the capability of the emulator to measure the current supplied to the powered device. For this purpose the emulator was programmed to generate a constant output in terms of voltage and, at the same time, to measure the supplied current. Understanding the capability to measure the supplied current is crucial because an error on its determination will introduce an obvious approximation on the model computation which results on a gap between emulation and reality regardless of the approximation of the implemented model.

The measurement error of the supplied current essentially derives from two different factors: (i) the characteristics of the ADC integrated into the microcontroller unit and (ii) the noise, introduced by the analog circuit which amplifies the signal collected from the sensing resistor (R _sense in Fig. 4). While the ADC channel performance is well known and documented by the microcontroller manufacturer, the amplifier circuit should be properly characterized together with the ADC coupling.

Figure 5 shows the measurement error obtained while measuring the current supplied by the emulator to constant loads powered at different voltages. In particular, a set of resistors, with different values of resistance, were connected to the emulator output and the corresponding current flowing into the circuit has been measured, at the same time, with the high sensitivity digital multimeter and with the emulator sensing circuit. The difference between the real current (the current measured with the high sensitivity multimeter) and the current measured by the emulator prototype is reported on the figure for different current level obtained, both changing the resistor load, that changing the voltage supply level. As expected, the error increases while the supplied current increases, and it shows an absolute error ranging from about 0.05 to about 1.3 mA which can be considered satisfactory for an embedded device. However, the particular distribution of the measured errors suggests a strong predictability and repeatability, also confirmed by the high coefficient of determination (about 0.993) obtained while fitting this error distribution using a linear model (the black solid line in Fig. 5).

Thanks to the high confidence of the linear fitting described above an error compensation based on the regression curve has been introduced in order to increase the current measurement accuracy. In particular, Fig. 6 shows the percentage of error in current estimation, obtained while varying a resistive load supplied at 3 V, with the error compensation mechanism both enabled and disabled. Notice that for each resistive load the compensation mechanism decreases the measurement error which, in the worst case, does not exceed 7 %, for a measured current of about 300 μA, against about 24 % without the error compensation.

The last set of experiments has been carried out to investigate the capability of the emulator to measure the supplied current to a highly variable load. A VirtualSense sensor node, which was sensing the radio channel for incoming packets and blinking a led, has been powered at a constant voltage of 3.3 V by means of the emulator prototype [49]. Figure 7 contains the waveforms of the supplied current collected by the emulator, with and without the error compensation mechanism, compared with that collected by the National Instruments PXI-4071 digital multimeter. As expected the uncompensated curve (the blue line) underestimates the real supplied current (the black line) while the compensated ones (the red line) is almost coinciding. The emulator collected curves also denote that rapid state transitions, such as a channel clear assessment (CCA), which determine a rapid increase in the current consumption, have been appropriately sampled end measured (see the zoomed curve plotted in the rectangle of Fig. 7).

5.3 Latency estimation

The emulator latency has been accurately characterized by means of a set of dedicated experiments. In particular the goal of these experiments was the measurement of the minimum latency without considering the contribution of any particular model. The minimum latency can be measured by taking into account the time that elapses between a variation of the load, which determines a variation of V _load due to a different current flowing through the R _sense (see Fig. 4), and the restoring of the nominal condition by means of the emulator nominal voltage restore mechanism.

To accurately measure this time, the emulator was connected to a static resistive load which was instantly changed by means of an electromechanical relay which switches between two different resistor. The relay was driven by a square wave generated through the TG2000 Aim-TTi digital function generators [47]. Figure 8 shows four different plots illustrating the results of the latency measurements. In particular, the black line represents the current drawn through the load which instantly decreases from 28 to 15 mA as the result of the relay activation, while the value of the V _load, the blue line in the figure, grows accordingly until the emulator restores the nominal condition. The figure also shows a square wave (the red line) which represents the start and the end of the reading of V _sense by means of the ADC channel. In particular, the rising edge corresponds to the start of the reading procedure while the falling edge is the end of it. As soon as the emulator finishes reading the V _sense value it applies the new DACC_out value to neutralize the effect of the voltage drop on R _sense. Therefore, starting from the plot of Fig. 8, the latency can be measured by taking into account the two points of variation of the V _load. The four plots of the figure show four different conditions which lead to different latency values. In particular, the subplot (a) represents the worst case in which the ADC reading starts just few microseconds before the relay activation, so that we need to wait the succeeding ADC reading to realize the variation in the V _sense. In this case, the measured latency is about 210 μs while it decreases in plots (b), (c), and (d) due to the different relative positions between the relay activation and the ADC reading. For instance, the (d) plot represents the best case, which is due to the perfect synchronization between the relay activation and the ADC reading, with a latency of only about 145 μs. In conclusion, given the peculiarity of the described mechanism, the emulator latency can be estimated as an average value between the four represented conditions which lead to an average latency of about 172 μs.

5.4 Emulating a battery discharge

As a case study to support the suitability of the proposed platform in emulating an energy source for wireless sensor networks, the battery model proposed by Tremblay and Dessaint has been implemented and tested on the emulator [27].

In particular, in a first set of experiments a real 550-mAh lithium battery has been discharged through an electronic load at a constant rate of 24 mA and the so obtained discharge curve has been used to obtain the model parameters. The emulator running the battery model has been initialized using the measured parameters and then connected to the same electronic load to emulate the battery discharge. Figure 9 shows the comparison between the real discharge curve and the corresponding curves obtained by the emulator with and without the error compensation mechanism. In particular, the real discharge curve (the black line in the figure) shows a typical lithium battery discharge behavior with a discharge time of about 24 h and 28 min, while the emulated battery (the red line in the figure) exhausts its charge in about 24 h and 5 min. The uncompensated experiment, as expected, suffers of the underestimation of the supplied current so that the emulated battery needs about 25 h and 12 min to discharge itself.

In order to increase realism to the testing conditions, the emulated battery has been used to power a VirtualSense node which has been programmed to continuously send broadcast packets to the wireless channel. During the execution, VirtualSense passes from a current consumption of about 24 mA, which corresponds to a packet transmission, to about 10 μA in the standby state, in few milliseconds. Figure 10 shows the real discharge curve (the black line) obtained by powering VirtualSense by means of a 550-mAh lithium battery compared with the emulated discharge curve. The real battery took about 31 h and 15 min to completely discharge while the emulated battery sustained the VirtualSense activity only for about 29 h and 43 min resulting in a gap of about 1 h and 32 min. Despite the sizable gap between the real and the emulated battery, the obtained results are completely in line with the performance of the battery model which declares an average error of about 10 %.