In many cases, the sensors are simply powered by rechargeable or non-rechargeable batteries. For example, Movesolutions society uses for a tiltmeter a 100 g Lithium battery type D of 19 Ah 3.6 V. This wireless sensor is waterproof IP67 and it operates in the range −40˚C, +85˚C. The device transmits in Lora the measured angle at regular time intervals. It is fully wireless; its battery offers eight years of autonomy [4] . Similarly, the BT510 Bluetooth 5 sensor platform of Laird is powered with a replaceable coin cell battery (CR2477, 3 V, 1000 mAh) and can operate for years in the field. The BT610 is a little bigger and powered with a primary Lithium battery type AA 3.6 V, 2400 mAh. For this product, Laird offers to use a tool to estimate battery life (typically 5 years) [5] .

For indoor Lorawan wireless sensors, the company Elsys also shares a similar tool [6] . On their ERS CO₂ device, the estimated battery life is up to 10 years, but this depends on the sample interval, transmit interval, data rate, and environmental factors. It is powered by two 3.6 V AA lithium batteries.

Similarly, Milesight-IoT Company has announced an autonomy of between 5 and 10 years for its indoor temperature and humidity sensors [7] and Wika has announced the same for its battery-powered wireless instruments for pressure, temperature, level, and force [8] .

Nevertheless, energy autonomy remains a key point in the sizing of a sensor node. Indeed, the lifetime of the battery that powers a sensor node remains a major bottleneck. In best cases, 5 or 10 years are expected. “But some batteries run out of power earlier than others, some of them are difficult to reach” [9] . Therefore, battery replacement has become a major drawback for industries that deploy many sensors. In this context, energy harvesting becomes an attractive option. In fact, routine maintenance and material costs are canceled as sensor nodes become maintenance-free with energy harvesting solutions.

Energy harvesting is based on a process by which energy is derived from external sources, such as solar power [10] , thermal energy, wind energy, salinity gradients, or kinetic energy (also known as ambient energy), and captured, and stored for small, wireless autonomous devices. The storage block is mandatory to provide the output power despite the intermittency and possible variations of the ambient energy.

Today, around a dozen of commercial integrated electronic circuits are sold as “energy harvesters” in the WSN power range, for example, SPV1050 from STMicroelectronics (chosen in our study and used in [11] [12] ), ADP5090, LTC3105, TLC3108 from Analog Devices, BQ25504, BQ25570 from Texas Instruments used in [11] , ECT310 from EnOcean, EM8502 from EM microelectronics, used in [12] , Energy Harvesting Boost Converter from Matrix Industries, EH4205 from Advanced Linear Devices and AEM10941 from e-peas, used in [11] .

Driving by the environment close to the node sensor, the harvested energy is extracted using an adapted transducer (photovoltaic cells, thermos-electro-generator, piezoelectric beam, rectenna antenna…).

Driving close to the node sensor, the harvested energy is extracted using an adapted transducer. In the following, this article will focus on indoor or outdoor light harvesting, although the ideas developed could be directly extended to systems powered by a thermoelectrogenerator using the same electronic circuits.

Sensors powered with energy harvesting have a long operating time, minimum 15 years. More, compared to a sensor node powered solely by a primary battery, the device which combines a rechargeable battery and an energy harvesting system [13] [14] may increase the measurement rate if the amount of harvested energy is favorable.

To minimize the size of the rechargeable battery, the association of battery and supercapacitor [15] [16] is a solution as short current peaks generated during radio transmissions are not available from any regular 3V Lithium battery type.

The next step consists of eliminating the battery and using a battery-free energy harvesting system. Indeed, a supercapacitor offers a very interesting lifetime (more than 300,000 cycles vs 500 for a rechargeable battery), often a larger range of temperature (typically [−40, 85]˚C for a PC10 supercapacitor vs [−20, 45]˚C for a LIR 2450-coin cell battery), and it can accept high peak currents. Unfortunately, the energy density of a supercapacitor is lower than that of a battery and the leakage current could be not negligible for a supercapacitor. These drawbacks are cleared when the daily average ambient power is sufficient to avoid long periods of complete autonomy of the node.

Despite these drawbacks, industrial sensors offer the user the option of a rechargeable battery or substituting it with a supercapacitor storage element [17] . Long term tests (more than 2 years) showed the maturity of free battery solution in IoT for smart agriculture [18] . For example, commercial battery-free products such as sealed (IP65) vibration sensors [19] [20] or indoor environment sensors are now available, but this is still a niche market. So, compared to a primary battery solution, and despite its initial higher cost, a battery-free, self-powered solution appears to be an ideal choice for remote monitoring sensors in hard-to-access locations and sites or in high-temperature environment. It is important to notice that like batteries, waste supercapacitors should be recycled according to EU directive 2002/96/EC on waste electric and electronic equipment.

A battery-free solution must overcome some obstacles.

A first important point is the sizing of the different components. It depends on the available ambient energy (light potential in the case of a photovoltaic solution), the consumption and must be carefully taken into account the different losses [21] [22] [23] . It must be realized without oversizing the elements for a massive deployment at a good price and volume.

The second point deals with the issue of the startup. Indeed, if the startup of a sensor node powered by a battery is immediate as soon as the battery is connected, this is not the case when the storage is performed with initially empty supercapacitors. Industrialists do not discuss the startup of battery-free sensor nodes, and this is generally the same in research papers [24] [25] [26] .

However, it is a real problem in complex industrial environments or in case of long-range transmission. Some articles present the restart after a phase without energy recovery [27] , and to avoid the cold start, a preload is sometimes used during laboratory tests [28] . But very few papers address the cold start issue [29] [30] .

With initially empty supercapacitors, thanks to the harvested power, the supercapacitors voltage increases but slowly (low efficiency phase). It is necessary to wait until the voltage at the terminals of the supercapacitors reaches a targeted level, before properly supplying the load.

This cold-start phase is often too long and does not allow an immediate signal from the sensor during its positioning on site. Of course, it is necessary to validate the radio communication of the sensor node. This means that the installer may have to wait for hours before the effective startup of the device, especially in indoors applications with low harvested power.

This article uses a classical solution using supercapacitors as storage stage and photovoltaics for energy harvesting. The objectives of the paper are firstly to propose a rigorous sizing methodology, and secondly to explain an interesting solution to avoid the drawback of a long startup and to facilitate the commissioning of the device.

The main new feature is the explanation of the method for preparing the initial startup. The original solution consists of both a preload with required conditions that minimizes leakages in supercapacitors, and after an external activation of the sensor node. Activation is carried out at the desired time without opening the enclosure, allowing the system to be completely sealed. In fact, once the solar cells’ dark protection has been removed, activation is instantaneous when the solar cells are exposed to even a brief burst of natural light or the flash of a smartphone.

This paper presents a 3.3 V 200 mA power supply dedicated to power a wireless sensor node without a battery, but as easily as with a battery. This system, modular for different light levels (indoor and outdoor) and easy to integrate in a sensor node, uses only commercial circuits.

The battery-free power supply is build using a small PV panel, a supercapacitor storage and an SPV1050 [31] circuit for energy harvesting and management. The node architecture and its sizing are exhibited in the Section 2 according to the light resource and the sensor consumption. The different parts of the SPV1050 are detailed and characterized.

The use of a photovoltaic harvester with supercapacitors storage is a classic one, well documented in term of its sizing. However, information on the initial start-up issue is very scarce. Section 3 is focused on the start-up issue. The cold start phase is analyzed. A solution to achieve a quick first startup is then detailed, using a specific feature of the SPV1050. The supercapacitors are preloaded without powering the output load and the initial start of all the electronic circuit remains blocked when the solar cells are in darkness. This minimizes the self-discharge of the supercapacitors.

As a result, the supercapacitors discharge very slowly, and the voltage remains favorable for future activation. The result is a potential delay between pre-charging and commissioning of over 3 weeks, which is sufficient for most applications.

Section 4 presents the on-site results of the whole system. Finally, a discussion concludes the article.

As far as light energy in indoor condition is characterized by the illumination E (Lux), irradiance G (W/m²) is used in outdoor condition. Randall [37] proposed a simplified conversion between illumination and irradiance:

1 lux = 1 / 120   W / m 2 (3)

The literature provides some information to estimate in a first approach the luminous potential according to the location of solar cells. Table 2 shows some typical values.

These values should be considered with caution, especially for indoor

locations [38] . In all cases, we suggest either to maximize the solid angle seen by the solar panel facing windows, or to position the solar panel towards an artificial light source.

For outdoor use, it is also important to assess the importance of masks that block both direct and diffuse radiations. Databases generally provide horizontal daily or hourly irradiations in kWh/m². These values should be supplemented by some in situ measurements. For a preliminary study Waltisperger [39] states “the following pessimistic hypothesis (currently used in the industry), […] the photovoltaic collector is positioned in the north and subjected to a rainy winter weather for 6 hours per day, which represents an available solar power density of 20 W/m²”. In fact, 20 W/m² corresponds to a typical value observed in December by rainy weather in Toulouse, France for a horizontal measurement.

1) Required Surface

Simple relations can be used to quickly size the available photovoltaic surface S. By the following, we assume that:

· η_PV is the efficiency of the solar cells,

· η_DC/DC is the efficiency of the SPV1050 Buck/Boost converter,

· η_LDO is the efficiency of its internal LDO,

· η_SC is the load/discharge efficiency of supercapacitors, assumed to be constant.

If we consider a system placed outdoors which receives an average irradiance G (W/m²) per day for a duration D (h), the recoverable energy in J/m²/day is:

E SUN_DAY = G ⋅ ( D ⋅ 3600 ) (4)

So, the surface S chosen must verify:

( E SUN_DAY ⋅ S ) ⋅ η PV ⋅ η DC / DC ⋅ η SC ⋅ η LDO ≥ E CONSO_DAY (5)

with:

E CONSO_DAY = ( 24 / T CYCLE ) ⋅ E CYCLE (6)

For a pre-sizing, we choose:

· η_PV = 5% (typical value with amorphous silicon or with crystalline cells at low irradiance),

· η_DC/DC = 75%, (slightly pessimistic value)

· η_LDO = 75%, (depending of the current and the dropout voltage)

· η_SC = 80%.

For a system placed outdoors with G = 20 W/m² during D = 6 h, Using a measuring rate T_CYCLE = 5 min, we find a minimum area S = 5 cm². With the same rate, indoor, with an illumination of 300 lux, 7 h per day (office lighting), S = 35 cm² is convenient.

2) Photovoltaic Panel Characteristics

Based on SPV1050 voltage range, we selected the Sanyo AM5706CAR amorphous PV module for outdoor and indoor use (Figure 4). Its characteristics for an illumination of 50 klux are:

· S: 5 cm × 7 cm = 35 cm²,

· V_OC = 6 V, I_SC = 22.6 mA,

V_MP - I_MP - P_MP: 4.6 V - 19 mA - 88 mW @ 50 klux and 4.6 V - 40 mA - 186 mW @ 100 mW/cm² = 1 Sun.

To validate this data, we decided to make our own measurements (Figure 4), which gave:

· V_OC = 5.3 V, I_SC = 3.1 mA,

· V_MP - I_MP - P_MP: 4.3 V - 2.6 mA - 11.2 mW @ 6000 lux.

In all cases, a photovoltaic efficiency between 5% and 6% for this panel has been found, and the ratio V_MP/V_OC remains constant. V_MP/V_OC = 80% ± 4%.

Simple relationships are generally used to estimate supercapacitors capacity. In a pre-sizing step, certain phenomena can be neglected, such as supercapacitors

self-discharge, balancing consumption, etc. some of them can be simplified, such as the constant value of the average efficiency, although it depends on the voltage of the supercapacitors and the current flow.

For supercapacitors:

· The equivalent capacity C_EQ (F) is calculated according to the desired autonomy -noted Aut (day).

· The supercapacitor voltage evolves over a useful range between V_{SC MAX} and V_{SC MIN}.

In the way to obtain the desired operating time, the energy available in the supercapacitors must be greater than the energy consumed during the phase without any refill. If we neglect losses induced by self-consumption, serial resistance, balancing system, and assuming a constant efficiency for the LDO, we obtain:

1 2 ⋅ C EQ ⋅ ( V SC_MAX 2 − V SC_MIN 2 ) ⋅ η LDO > Aut ⋅ ( N ⋅ E CYCLE ) (7)

Based on an industrial requirement for temperature measurement a sampling rate of T_CYCLE = 5 min has been selected and the intended system location leads to Aut = 15 days of operating time without recharging. We choose V_{SC_MAX} = 5.3 V and V_{SC_MIN} = 3.3 V; assuming η_LDO = 75%, we obtain C_EQ = 12.5 F. Two supercapacitors with a value of C = 25 F each should be suitable. We have therefore chosen these values for the supercapacitors used.

Following our specifications, we choose a Nesscap model ESHSR-0025C0-002R7 as their main characteristics are: 25 F, 2.7 V, ESR 21 mΩ, [−40˚C, 65˚C], 500,000 cycles, 1000 hours at 85˚C.

For this project, we choose to store the energy at a maximum voltage of 5.2 V. This requires two supercapacitors in series. The maximum load level remains below the acceptable level of 5.4 V for the supercapacitors and 5.3 V for the SPV1050. This gives a safe range for the whole system.

If C_EQ corresponds to the equivalent capacity of two serial supercapacitors, energy of the pack E_CAP is given by:

E CAP = 1 2 C EQ ⋅ V SC 2 (8)

Supercapacitors self-discharge is a critical issue for systems in both following cases:

· They must remain fully charged a long period of time before being used,

· They are used as power sources with a low potential recharge level.

Self-discharge has been assessed using a preload of the two supercapacitors pack, previously placed in a thermostatic enclosure at constant voltage for 12 hours. The open circuit voltage evolution has been monitored, using a dedicated device (Biologic BCS810) as a voltmeter. The results are given in Figure 5.

Based on these measurements, the relative energy losses can be evaluated after 5 days as 1% of the initial energy at 5˚C, 3% at 25˚C and 12% at 45˚C.

Losses increase with temperature but remains acceptable over a wide temperature range (3% @ 45˚C at the end of the first day).

The self-discharge current can be estimated from the slope of the curve using the following relationship:

I SELFDISCH = C EQ ⋅ Δ V SC Δ t (9)

For Δt = 1 day (from t = 0 to t = 1), a self-discharge current I_SELFDISCH = 3 µA @ 25˚C and 11 µA @ 45˚C has been measured. But some of this current is probably due to the charging of the slow branches of the supercapacitors.

For Δt = 2 days (from t = 3 to t = 5), we find I_SELFDISCH = 2 µA @ 25˚C and 6 µA @ 45˚C.

One problem associated with the use of two supercapacitors connected in series is that the voltage across each capacitor cell can be different if the C values are different.

Cells manufacturers regard over-voltage as a form of misuse, leading to loss of capacitance, an increase in equivalent series resistance (ESR,) bulging, possible venting, electrolyte decomposition, gas generation, and ultimately reduced life.

A simple way to balance a string of supercaps is with paralleled resistors. A rule of thumb is the same factor-of-ten that can be used to make an unloaded voltage divider. Whatever the leakage current of the supercap, a parallel resistor that has ten times the current at the nominal cell voltage can be used.

This approach has several problems:

· It doesn’t solve the tolerance imbalance problem,

· It adds resistor tolerances to the capacitor tolerance problem,

· The resistors will draw current that must be supply or it will discharge the capacitor string,

· They also won’t allow for variations in supercap leakage over time and temperature.

A much better solution is to use FET Transistors that will turn on slightly as the capacitor cell approaches the operating rated voltage. The FET manufacturer can control the threshold voltage with ion implantation of a floating gate, or by process, or by hand-selection: a more predictable and precise current at the cell voltage can be therefore considered.

Active balancing with FETs circuits is a more direct solution. The FETs will regulate the cell voltage and even considering for ageing and temperature changes.

In our application, we chose an ALD9100xx (xx denoting the nominal voltage), with xx = 24:2.4 V. This circuit (Figure 6) includes two MOSFETs, and the drain current increases with the voltage at the terminals of the MOSFET, which acts as a variable resistor. The variation is therefore, exponential, which allows a very small current to be consumed below the voltage used, 2.4 V. Above this, it favors the discharge of the supercapacitor.

Figure 7 describes the evolution of the current dissipated by the ALD910024 chip as a function of the voltage across the terminals of a supercapacitor. The total voltage in the study is limited to 5.2 V, i.e., 2.6 V per supercapacitor.

In normal operation, the leakage current due to balancing remains less than 1 µA. If there were a voltage imbalance between the two supercapacitors in series, one reaching its maximum voltage of 2.7 V, then it would result in a leakage current of 240 µA. On the contrary, the other supercapacitor, which remains below 2.5 V, has a leakage current below 10 µA. It tends to balance the two voltages.

Various commercial ICs recover the energy from solar cells and manage both the MPPT function and the charge of the storage element (rechargeable battery or supercapacitor). For our application, we choose an SVP1050 from STM

because it has the following features

· Maximum solar power extraction with MPPT control law with fraction of V_OC algorithm (the ratio is fixed using adjustable resistances),

· Charge management of the storage element (battery or supercapacitor) with adjustable end of charge and discharge voltage thresholds,

· Two independent LDO (1.8 V, 3.3 V, Imax 200 mA), each controllable via an Enable control pin.

Main features of this circuit are:

· Very wide solar voltage range: from 75 mV to 18 V, with a minimum voltage of 2.6 V and a minimum current of 5 µA for startup in Buck/Boost mode,

· For the storage stage, a load current £ 70 mA and a voltage between 2.2 V and 5.3 V,

· Consumption (datasheet):

o Shutdown current before first startup or discharged battery (V_SC < V_UV) ~1 nA;

o Standby current (inactive LDO_EN) ~1 µA;

o Normal current without charge ~2 µA with 1LDO on ~3 µA with both LDO ON.

The different phases of operation (ON/OFF position of the PASS Transistor, Activation/Deactivation of the buck/boost and of the output LDO) are depending on the V_STORE voltage. Different configurations explained below are summarized on Figure 8.

In the SPV1050, an internal transistor named PASS (Figure 9) acts as a static switch. It allows the V_STORE potential to be disconnected from the V_SC potential of the storage stage (supercapacitors or batteries) if the storage voltage is too low. In this case, the consumption of the storage stage is minimized but the load isn’t supplied.

PASS is open prior to the first power-up. It closes when the V_STORE voltage rises to the V_EOC threshold and remains closed unless V_STORE falls below the V_UVP threshold.

The V_UVP and V_EOC thresholds are adjustable by a resistance set (R₄, R₅, R₆), according to the relationships given by the manufacturer. For our application, V_UVP = 2.2 V and V_EOC = 5.2 V.

A DC/DC converter (Boost or Buck/Boost) is located between the solar panel and the storage stage. We chose the Buck/Boost configuration, due to PV Solar input voltage variations.

1) Starting Mode Operation

At the initial startup, the converter doesn’t switch. Instead, the positive pin of the photovoltaic source and the STORE pin are internally short-circuited. This phase lasts as long as V_STORE < 2.6 V.

When V_STORE = 2.6 V, the integrated Buck/Boost starts working properly. Once started, it will operate in MPPT Mode if V_UVP £ V_STORE < V_EOC.

To fully understand the different phases during the startup, it is important to note that C_STORE = 94 µF is very small compared to C_EQ = 12.5 F. This means that it is necessary to charge and discharge many times C_STORE to fill C_EQ.

We assume that the system is initially empty, meaning V_STORE = 0 and V_SC = 0. The DC/DC is OFF. PASS is open. Initial startup starts as soon as the PV panel receives some light. V_STORE connected internally to V_PV+ increases. The DC/DC starts switching as soon as V_STORE reaches 2.6 V. C_STORE fills and V_STORE reaches V_EOC. At this level, the PASS transistor closes, and in consequence, C_STORE discharges in C_EQ. Immediately, V_STORE falls under V_UVP, which means that PASS opens again, disconnecting C_EQ from C_STORE. As V_STORE < V_UVP, the converter also stops.

A new cycle begins but the circuit can’t extract the maximum available power from the PV panel during this sequence. Gradually, the V_SC increases. Once V_SC reached V_UVP, PASS keeps closed and assuming that the harvested power is greater than the consumed power, V_SC continues to increase. When V_SC reaches 2.2 V, the DC/DC works continuously and the amount of harvested power increases as the DC/DC remains in MPPT mode. Figure 9 summarizes the process.

2) Nominal Mode Operation

After the initial startup, the PASS transistor is ON meaning V_STORE = V_SC.

It remains closed as long as V_STORE > V_UVP = 2.2 V.

If V_UVP £ V_STORE < V_EOC, the converter works in maximum power point tracking (MPPT mode) with a « fraction of V_OC » algorithm. Due to circuit behavior, every 16 s, during 400 ms, the photovoltaic panel is placed in open circuit: the SPV1050 recovers the V_OC open circuit voltage. The DC/DC then works by regulating the PV panel voltage close to V_PV = k.V_OC. As exhibited in §3c, the V_MPP setpoint is located around 80% of the V_OC voltage. A set of two resistors fixes k = 0.8, which ensures that:

V PV ≈ V MPP ≈ k ⋅ V OC (10)

When the V_EOC threshold is reached (i.e., the storage stage is full), the DC-DC stops transferring power to avoid overloading. It starts again when V_STORE < V_EOC − ΔV, with ΔV = 50 mV.

3) Characterization

The DC/DC has been characterized (Figure 10) at different solar panel voltages and different V_STORE voltages. V_STORE is almost equal to V_SC, the difference being the voltage drop in the PASS transistor.

For currents below 1 mA, the efficiency of the buck/boost converter is close to 70%. It is higher than 78% for currents > 2 mA, which is quite correct.

The SPV1050 incorporates an LDO to supply the output with the required voltage level (3.3V). The enable pin of the LDO is driven by an external hysteresis comparator, powered by the V_STORE voltage (Figure 11). The voltage measured by the comparator is the V_SC voltage.

1) Setting of the Comparator

During initial start-up, the load can draw a significant amount of energy from the supercapacitors, particularly in the case of an initial connection to a network. This leads to a voltage drop of the storage stage. At the end of startup, the storage level must always be above the minimum level accepted by the LDO for proper operation. It sets the minimum V_H level. For a large margin of safety, specially to assure a sufficient autonomy after start-up phase, V_H = 4.3 V has been chosen. V_L is set just below the nominal LDO output voltage at 3.2 V.

Resistors of the comparator are chosen in the way to set the V_H and V_L switching thresholds. The comparator resistors are selected in accordance with [39] to set the V_H and V_L thresholds.

2) LDO + PASS + Comp + Balancing Efficiency

The following measurements (Figure 12) show η_LDO, the ratio between the output power of the LDO and the output power of the supercapacitors (replaced by a voltage source for these measurements). In this situation, the solar panel is in the darkness, so there is no power from the PV panel. PASS is switched ON. The efficiency in this test includes losses of the LDO, the PASS transistor serial

resistance (7 Ω), the comparator and the balancing circuit losses. Only self-discharge losses and Joule losses due to supercapacitor ESR are not included. Measurements were made to evaluate the performance of the system when the sensor node is in sleep mode and for the typical values during the active mode phase. Efficiency is independent of the current on the range 1 to 18 mA.

On the basis of the previous measurements, the autonomy is calculated iteratively

by performing the energy, noted E ′ CYCLE ( n ) , drawn during the nth cycle at the level of the supercapacitors. In this assessment, we must consider the active phase of the node, the standby phase, and the losses due to self-discharge, to supercapacitors ESR and to the internal resistance of the transistor PASS (R_DSON = 7 Ω).

E ′ CYCLE ( n ) = E ′ S L E E P + E ′ MEAS + E SELFDISCH + E ESR + E PASS (15)

with

E ′ SLEEP = E SLEEP / η LDO ( I SLEEP )

and

E ′ MEAS = E MEAS / η LDO ( I MEAS )

Figure 19 is used to modelise η_LDO as V_SC Î [3.3; 5.3] V, in the form of first orders:

η LDO ( I SLEEP = 11   μ A ) = − 0.237 ⋅ V SC + 1.672 (16)

η LDO ( I MEAS = 18   mA ) = − 0.198 ⋅ V SC + 1.629 (17)

Self-discharge losses are estimated with a constant self-discharge current I_SELFDISCH = 2 µA, so:

E SELFDISCH = I SELFDISCH ⋅ V SC ⋅ T CYCLE (18)

Losses due to serial resistors of supercapacitors and PASS are:

E ESR = 2 ⋅ ESR ⋅ ( I SLEEP 2 ⋅ ( T CYCLE − T SLEEP ) − I MEAS 2 ⋅ T MEAS ) (19)

E PASS = R DSON ⋅ ( I SLEEP 2 ⋅ ( T CYCLE − T SLEEP ) − I MEAS 2 ⋅ T MEAS ) (20)

These losses are negligible compared to other terms.

We calculate the energy lost E ′ CYCLE ( n ) for each cycle and we deduce the new voltage of the supercapacitors after a T_CYCLE time. At the end of n measurement cycles, we have:

E CAP ( n + 1 ) = E CAP ( n ) − E ′ CYCLE ( n ) (21)

And reversing the equation

E CAP ( n + 1 ) = 1 2 C EQ ⋅ V SC 2 ( n + 1 ) (22)

We obtain V_SC for the next iteration.

With I_SELFDISCH = 2 µA, we find 11.9 days of battery life respectively with a measurement rate of 5 minutes when the V_SC drops from 5.2 V to 3.4 V. This is in line with the 15 days required when sizing supercapacitors because when sizing supercapacitors, self-discharge was neglected and LDO efficiency was slightly overestimated.

To evaluate the real operating life without any harvesting, the sensor node is placed in a black box. The evolution of the V_SC voltage is shown in Figure 20. The last data transmission is obtained at a voltage equal to 3.4 V. An autonomy of 11.8 days is measured. This confirms that the model is correctly validated with a self-discharge current of 2 µA as measured during the initial tests.

From the simulation results, we deduce, that with I_SELFDISCH equal 2 µA, the energy repartition from supercapacitors is as follows:

· 61% powers the sensor node,

· 28% is lost for powering the electronic of the SPV1050, the LDO and the comparator,

· 9% is due to self-discharge of the supercapacitors and the PASS transistor is responsible of only 1% of the losses.

We notice that the global efficiency between the supercapacitors and the sensor node is close to 61%. The results show that the choice of supercapacitors with low leakage current is crucial to achieve a high level of autonomy.