Exploring the Limitations of Electric Field Energy Harvesting

Abstract

Energy harvesting systems are key elements for the widespread deployment of wireless sensor nodes. Although many energy harvesting systems exist, electric field energy harvesting is a promising choice because it can provide uninterrupted power regardless of external conditions and depends only on the presence of AC voltage in the grid, regardless of the magnitude of the line current, even under no-load conditions. However, it also has some disadvantages, such as low power availability, the need for storage, or reliance on capacitive coupling, which is a complex phenomenon that depends on parasitic capacitances. This paper aims to provide useful and practical information on the possibilities of electric field energy harvesting for both high- and low-voltage applications. Since the objective of this paper is to quantify the physical limit of the harvested energy, it considers only the physical harvester itself and not the electronic circuitry required to transfer the harvested energy to the load. Theoretical, simulation, and experimental results show the feasibility of this energy source for low-power applications such as wireless sensor nodes.

1. Introduction

Today, wireless sensors are being used to monitor low- and high-voltage utility assets and power lines. Because these sensors operate autonomously without a grid connection, most are powered by electrochemical batteries, which are costly and often difficult and impractical to replace. Therefore, there is a need for self-powered, wireless sensor nodes that are more environmentally friendly and minimize the costs associated with periodic maintenance. Energy harvesting (EH) offers a potential solution to this problem, as this technology enables the conversion of ambient energy into electrical energy [1]. This harvested energy can be stored in electrochemical batteries or capacitors for later consumption or used directly [2]. It has been shown that electronic systems requiring average power levels between 200 μW and 10 mW can be powered by energy harvesting systems from ambient sources [3]. There are many ways to harvest energy from ambient sources, such as thermal energy harvesting [4,5], solar [6], vibration [7], radio frequency [2], piezoelectric [8], magnetic field [9], or electric field [1], among others.

Electric field energy harvesting (EFEH) is a promising technology because it can provide reliable and continuous power with the only condition that the line is energized, regardless of the magnitude of the line current, even under no-load conditions. Since the line frequency and voltage are tightly controlled, the expected power production can be accurately predicted, and it is easy to install and implement [2,10], so the use of batteries is not mandatory. Although most energy harvesting systems today use auxiliary batteries, they require periodic replacement due to their finite lifetime and generate waste, so batteryless systems are needed. Due to the characteristics of batteryless energy harvesting systems, they allow electronic sensors to be deployed in remote or inaccessible regions while contributing to the reduction of the carbon footprint [2]. However, EFEH also has some drawbacks, such as low power availability, so there is a need for storage. EFEH relies on capacitive coupling, which is a complex phenomenon, so the parasitic capacitances can affect the power output. Finally, size constraints could also limit the power output [10], especially for low-voltage applications.

It is well known that any energized conductor generates a radial electric field, which is a potential source of energy. In AC systems, there is a capacitive displacement current between the energized conductor and the ground through the surrounding air that can charge a nearby capacitor, so that the energy stored in that capacitor, E_C, can be expressed as half the product of its capacitance and the square of its voltage. An electric field harvester is designed to capture some of this energy [1]. The electric field generated by a transmission line is independent of the amount of current, as it depends only on the voltage applied. Therefore, EFEH is the only method that can provide effective EH at any time the line is energized, even when it is not carrying current. This makes electric field EH the most viable option for powering sensors in terms of predictability, availability, and controllability [10]. The idea of harvesting energy from the electric fields is not new [11]. Unlike many conventional harvesting methods, EFEH is almost independent of environmental variables [12], making it more durable and reliable. It can operate on any conductive material to which a voltage is applied, making it ideal for applications that require a certain quality of service. Because the frequency and voltage of transmission lines are tightly regulated, the electric field they generate is stable, allowing predictable amounts of energy to be harvested due to the constant rate of power harvesting [10]. Electric field EH is well suited for high-voltage transmission lines due to the strong electric fields associated with them, although various works have shown that it is also feasible in low-voltage applications [13,14] using low-power electronics and switches.

In most cases, due to the scarce energy scavenged by the EH unit, EH-based systems typically operate in an intermittent on-off pattern [15,16]. Since the device communicates cyclically with a gateway, communication protocols typically present different communication phases (advertising parameter initialization, advertising start, transmission, delay, and sleep) that exhibit a cyclic load profile [16]. Due to these constraints, the EH unit typically requires an electronic circuit that includes diodes to rectify the generated voltage and prevent the harvested energy from being fed back, storage capacitors or supercapacitors, and a controlled switch to regulate the energy usage. The switch allows the capacitor to be automatically charged when the voltage is below a certain level and connects the capacitor to the load when the stored energy is high enough for transfer. To save energy, EH-based systems are typically programmed to operate in low power mode during the sleep phase, when the capacitor is charging. When the capacitor is sufficiently charged, it transfers the energy to the rest of the circuit, which is activated. Therefore, it is essential to use high-efficiency rectifiers, microcontrollers, and regulators to optimize the overall efficiency of the energy harvester [10]. The efficiency of the circuit that controls the charging and discharging of the capacitor is a key point, as it can range from about 3% to >90% [17].

Several EFEH approaches can be found in the technical bibliography. In [18], a wire wound around an insulated single-phase 3-wire 220 V cable was used to harvest energy from the stray electric field, generating an average of 680 nW. In [10,19], an EFEH system is proposed using a dielectric layer and a conductive sheath wound around the conductor, generating a stray capacitance that is used to harvest energy from the electric field generated by the conductor. A multilayer structure is also possible. A similar approach was applied in [14], using a 220 V power line as a reference, showing an average extracted power of about 47 μW. In [1], using a copper sheet wrapped around a 230 V power line, the authors harvested 367.5 μW. In [20], a similar EFEH method was applied using a power line insulator, and the authors state that up to 17 mW of continuous power can be extracted from a 12.7 kV medium-voltage power line. Similar circuits can be applied using metal plates instead of wrapping a conductive sheath around the conductor [18,21]. In [22], it is shown that 2.5 µW can be extracted from a 120 V power line using a metal plate. A similar approach is proposed in [23], which shows that a displacement current of fractions of mA can be induced.

Most of the papers found in the technical literature focus on a specific application in the low or high voltage range or analyze specific impedance matching circuits to optimize the extraction of energy from the physical harvester element. This paper, however, aims to generalize and provide useful information to practitioners about the physical limits of EFEH for both low- and high-voltage applications. Since the objective of this paper is to determine the physical limit of the harvested energy, it considers only the physical harvester itself and not the circuitry required to transfer the harvested energy to the load. Therefore, this paper does not analyze the different possibilities of switching circuits since there are different possible strategies that will be studied and evaluated in a paper. This paper also develops a theoretical analysis and presents simulation and experimental results, showing the feasibility of this technology to supply low-power wireless sensor nodes.

2. EFEH for Low-Voltage Multicore Insulated Wires

This section discusses how to harvest energy from the electric field around low-voltage insulated wires.

Figure 1 shows the basic configuration of the low-voltage insulated wire energy harvester. To harvest energy from the surrounding electric field, the multi-conductor insulated wire is covered with a thin copper foil. While the conductor of the hot wire acts as the inner electrode, the copper foil acts as the outer electrode. While C_c is the capacitance between two wires, C_g is the capacitance between one wire and the copper foil. Due to the symmetry of the layout shown in Figure 1, all C_c capacitances are identical, as well are all C_g capacitances.

In TN and TT grounding systems, the ground and neutral wires are almost at the same potential, so the layout presented in Figure 1b is equivalent to that shown in Figure 1a. Note that since the capacitance 2C_c is connected in parallel with the AC supply, it does not change the voltage seen by the series connection of C₁ = C_g and C₂ ≈ 2C₁. Capacitances C₁ and C₂ are in the order of 100–200 pF, so for resistive loads below 1 MΩ, the capacitance C₂ has very little effect on the voltage in the load resistance; only the top capacitance C₁ in Figure 1b affects the voltage across the load terminals. The values of capacitances C₁ and C₂ can be determined from experimental measurements, as shown in Section 4.

Due to the presence of the parasitic capacitances C₁ and C₂, the surrounding copper foil behaves as a voltage source due to the displacement current generated by this configuration, so it can be used for energy harvesting purposes [13]. This cylindrical harvester configuration is equivalent to a capacitive voltage divider.

The voltage generated by the energy harvester can be rectified using a two-diode rectifier or a four-diode full-wave rectifier, the former being the simplest and most effective solution. In this way, it is possible to charge a storage capacitor while preventing it from discharging through the rest of the circuit. Due to the reduced power generated by the harvester, IoT devices can typically use an intermittent strategy. Energy is generated and stored in the storage capacitor, and when there is enough energy, the sensor and communication systems are activated.

According to Figure 1, when a purely resistive load is connected directly in parallel with C₂, the AC output voltage V_out across the load resistor R_L is determined as follows:

$$\begin{array}{cc}\overline{I}=\frac{{\overline{V}}_s}{\frac{1}{j\omega C_1}+\frac{R_L\frac{1}{j\omega C_2}}{R_L+\frac{1}{j\omega C_2}}}& [\mathrm{A}]\end{array}$$

(1)

When a purely resistive load R_L is directly connected in parallel with C₂, the voltage V_out between the terminals of the load can be obtained as follows:

$${\overline{V}}_{out}={\overline{V}}_s·\frac{C_1}{C_1+C_2+1/j\omega R_L}\hspace{1em}[\mathrm{V}]$$

(2)

where V_s is the supply voltage, as shown in Figure 1.

Therefore, when R_L is infinite, V_out results in the expression of a capacitive voltage divider:

$${\overline{V}}_{out}={\overline{V}}_s·\frac{C_1}{C_1+C_2}\hspace{1em}\hspace{1em}[\mathrm{V}]$$

(3)

In Section 4, it is shown that for the geometry analyzed in Figure 1 C₁ ≈ 0.5C₂. From (3), it follows that V_out ≈ V_s/3.

Assuming a purely resistive load R_L, the output power can be calculated as

$$P_{out}=\frac{V_{out}^2}{R_L}=\frac{V_s^2{C}_1^2/R_L}{{(C_1+C_2)}^2+1/{(\omega R_L^{})}^2}=\frac{{\omega }^2{R}_L{V}_s^2{C}_1^2}{{\omega }^2{R}_L^2{(C_1+C_2)}^2+1}\hspace{1em}[\mathrm{W}]$$

(4)

The optimum value of the load resistance to obtain the maximum output power can be obtained by deriving the output power in (4) with respect to R_L, which gives:

$$R_{L,\max \_power}=\frac{1}{\omega (C_1+C_2)}\hspace{1em}[\mathsf{\Omega }]$$

(5)

Finally, by combining (4) and (5), the maximum power transferred to the load becomes:

$$P_{out,\max }=\frac{\omega V_s^2{C}_1^2}{2(C_1+C_2)}\hspace{1em}[\mathrm{W}]$$

(6)

According to [11], the effective power that can be transferred to the load can be calculated as

$$P_{effective}=f\frac{1}{2}{C}_1{V}_{C_1,RMS}^2=f\frac{1}{2}{C}_1{V}_{out,RMS}^2\hspace{1em}[\mathrm{W}]$$

(7)

As shown in Figure 1e, a capacitor C_storage can be added to store energy for later use by the electronic circuit. However, a diode rectifier is required to charge the capacitor, which reduces the power given by (4) [1]. To increase the output power and shorten the discharge time, the EFEH system requires a switching circuit, as shown in Figure 1b,c [1]. When the voltage across the terminals of C_storage is below a threshold value (charge stage). Otherwise, when the voltage across the terminals of C_storage is sufficient, the switching circuit disconnects C_storage from the harvester and connects it to the load (discharge stage). The energy released by C_storage is used to power the sensors, electronics, and communication module, gradually discharging it until the voltage threshold is reached. The switching circuit then disconnects C_storage from the load and reconnects it to the harvester in a cyclic mode.

The amount of energy stored E_stored in the capacitor and extracted from the harvester can be calculated as follows:

$$E_{stored}=\frac{1}{2}{C}_{storage}{V}_{}^2\hspace{1em}[\mathrm{J}]$$

(8)

where V is the voltage in the storage capacitor. Assuming that during the transmission phase of the communication circuit, the capacitor discharges from V₁ to V₂, where V₂ < V₁, the energy released from the capacitor is as follows:

$$E_{released}=\frac{1}{2}{C}_{storage}{V}_2^2-\frac{1}{2}{C}_{storage}{V}_1^2\hspace{1em}[\mathrm{J}]$$

(9)

Therefore, the corresponding power dissipated by the storage capacitor between two times t₁ and t₂ can be calculated as [19]

$$P=\frac{1}{2}{C}_{storage}\frac{V_2^2-V_1^2}{t_2-t_1}\hspace{1em}[\mathrm{W}]$$

(10)

From (8)–(10), it can be deduced that the size of the storage capacitor and its maximum voltage greatly influence the energy it can store, but at the expense of longer charging times, which limits the communication rate of the entire electric field EH system.

3. EFEH for High-Voltage Overhead Power Lines and Substation Bus Bars

Figure 2 shows the basic configuration of the energy harvester for high-voltage overhead power lines and substation bus bars. This cylindrical harvester also acts as a capacitive voltage divider. While C₁ is the capacitance of the cylindrical shell, C₂ is the leakage capacitance to ground. The conductor acts as the inner electrode, which is wrapped by a thin layer of an insulating or dielectric material covered by a thin copper foil, which acts as the outer electrode.

It should be noted that although a full-wave diode rectifier can be used, experimental results show that the voltage at the load resistor is almost the same as that obtained with a half-wave diode rectifier. Therefore, the latter rectifier will be used in the remainder of this document. It is known that the capacitance of a cylindrical capacitor with inner and outer radius r₁ and r₂, respectively, can be calculated as [17,24]

$$C_1=\frac{2\pi {\epsilon }_o{\epsilon }_{r}L}{\ln (r_2/r_1)}\hspace{1em}[\mathrm{F}]$$

(11)

where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free air, ε_r [-] is the relative permittivity of the insulating material, L [m] is the axial length of the harvester, and r₁ and r₂ are the radii of the inner and outer electrodes, respectively.

The capacitance to ground of a cylindrical conductor of infinite length is determined as [25]

$$C_2=\frac{2\pi {\epsilon }_{o}L}{\ln \left[\frac{h+{(h^2+r_1^2)}^{1/2}}{r_1}\right]}\hspace{1em}[\mathrm{F}]$$

(12)

According to Figure 2, when a purely resistive load is connected directly in parallel with C₁, the AC output voltage V_out across the load resistor R_L is determined as follows:

$$\overline{I}=\frac{{\overline{V}}_s}{\frac{1}{j\omega C_2}+\frac{R_L\frac{1}{j\omega C_1}}{R_L+\frac{1}{j\omega C_1}}}\hspace{1em}[\mathrm{A}]$$

(13)

where V_s is the voltage of the source and ω = 2πf is the angular frequency of the line.

The voltage V_out at the terminals of the load R_L is given by

$${\overline{V}}_{out}=\overline{I}\frac{R_L\frac{1}{j\omega C_1}}{R_L+\frac{1}{j\omega C_1}}={\overline{V}}_s\frac{C_2}{C_1+C_2+1/j\omega R_L}\hspace{1em}[\mathrm{V}]$$

(14)

When R_L is infinite, V_out gives the expression of a capacitive voltage divider so that the voltage induced across the terminals of C₁ is given by

$${\overline{V}}_{out}={\overline{V}}_s\frac{C_2}{C_1+C_2}\hspace{1em}[\mathrm{V}]$$

(15)

Section 4 shows that for overhead power lines, C₁ >> C₂, 1/(ωC₁) << 1/(ωC₂) so that the current flowing through the leakage capacitors C₁ and C₂ is largely determined by C₂; C₁ has little influence, and the value of V_out is a small fraction of the value of V_s.

The module of V_out can be obtained as

$$V_{out}=V_s\frac{C_2}{\sqrt{{(C_1+C_2)}^2+{(1/\omega R_L)}^2}}\hspace{1em}[\mathrm{V}]$$

(16)

The output power at the load R_L can be determined as

$$P_{out}=\frac{V_{out}^2}{R_L}=\frac{V_s^2{C}_2^2/R_L}{{(C_1+C_2)}^2+1/{(\omega R_L^{})}^2}=\frac{{\omega }^2{R}_L{V}_s^2{C}_2^2}{{\omega }^2{R}_L^2{(C_1+C_2)}^2+1}\hspace{1em}\hspace{1em}[\mathrm{W}]$$

(17)

According to (17), to maximize the power at the load impedance, its value must be increased as much as possible [19]. Therefore, special care must be taken to select a specific transmission system with very low energy consumption (high impedance), especially during sleep mode when the storage capacitor must store the energy for the different communication phases. Smart devices often communicate cyclically with a nearby gateway, so the energy consumption has a cyclic profile consisting of five modes (advertisement parameter initialization, advertisement start, transmission, delay, and sleep) [26].

The optimal value of the load resistance to obtain the maximum output power is [1] and can be obtained by deriving the output power in (17) with respect to R_L, which results in

$$R_{L,\max \_power}=\frac{1}{\omega (C_1+C_2)}\hspace{1em}[\mathsf{\Omega }]$$

(18)

Finally, by combining (17) and (18), the maximum power transferred to the load is given by

$$P_{out,\max }=\frac{\omega V_s^2{C}_2^2}{2(C_1+C_2)}\hspace{1em}[\mathrm{W}]$$

(19)

It is worth noting that the maximum power that can be extracted from the harvester increases linearly with the supply frequency and quadratically with the voltage of the source and with the value of C₂, since C₁ >> C₂.

4. Experimental Results

4.1. Experimental and Simulation Results with the Low-Voltage Multicore Insulated Wire

The tested low-voltage multicore insulated wire (3 × 2.5 mm², PVC insulation, TOPFLEX VV-F H05VV-F, TopCable, Rubí, Barcelona, Spain) has an external diameter of 9.80 mm and is composed of 3 wires of 2.5 mm² each (diameter = 2.4 mm each). Figure 3 shows the low-voltage multicore insulated wire.

Figure 4 shows the low-voltage multicore insulated wire and the copper foil required to build the harvester.

The following procedure is used to experimentally determine the capacitances C₁ and C₂. Various resistors are connected directly in parallel with C₂ as shown in Figure 1c, without the rectifier and C_storage. The experimental values of the load resistances and the AC output power of the load are shown in Figure 5. The experimental optimum value of the load resistance is about 8.1 MΩ, which gives a maximum output power in the load of 346.5 μW at 230 V. This means that this energy harvester can only supply ultra-low-power devices. Next, the maximum of the R_L–P_out graph is located, so that the values of C₁ and C₂ are determined from (17) and (18) as follows:

$$\left\{\begin{array}{l}{R}_{L,\max }=8.1\times {10}^6\mathsf{\Omega }=\frac{1}{100\pi (C_1+C_2)}\\ P_{out,\max }=346.5\times {10}^{-6}\mathrm{W}=\frac{100\pi {230}^2{C}_2^2}{2(C_1+C_2)}\end{array}\right.\hspace{1em}\hspace{1em}{C}_1=128 \mathrm{pF}, C_2=265 \mathrm{pF}\approx 2C_1$$

Figure 5 shows experimental measurements of the power generated by the low-voltage energy harvester when various purely resistive loads are connected directly to the harvester’s terminals. It also shows the simulation performed in LTspice version 17.1.8 with the layout shown in Figure 1e without the rectifier and C_storage using the calculated values C₁ = 128 pF and C₂ = 265 pF.

Table 1. Experimental and simulated results at V_s = 115 V-RMS and V_s = 230 V-RMS. The length of the copper foil is 100 cm.

	Vs [V-RMS]	RL [MΩ]	Vout [V-RMS] Exp./Sim. 1	Pout [μW] Experimental	Vout,max [V-DC] Exp./Sim. 2
Common ground	115 V	0.10	0.46/0.45	2.12	0.20/0.20
		0.20	0.93/0.90	4.32	0.43/0.41
		0.39	1.79/1.76	8.22	0.84/0.80
		0.50	2.27/2.25	10.31	1.10/1.02
		1.00	4.54/4.48	20.61	2.19/2.03
		5.00	19.59/19.69	76.75	-/9.40
	230 V	0.10	0.91/0.92	8.28	0.40/0.41
		0.20	1.87/1.85	17.48	0.82/0.83
		0.39	3.70/3.60	35.10	1.68/1.61
		0.50	4.64/4.61	43.06	2.06/2.05
		1.00	9.22/9.17	85.01	4.17/4.06
		5.00	38.48/38.75	296.14	-/18.80
Independent ground 3	115 V	0.10	0.19	0.36	-
		0.20	0.41	0.84	-
		0.39	0.85	1.85	-
		0.50	1.09	2.38	-
		1.00	2.26	5.11	-
		5.00	10.18	20.73	-
	230 V	0.10	0.37	1.37	-
		0.20	0.79	3.12	-
		0.39	1.65	6.98	-
		0.50	2.13	9.07	-
		1.00	4.46	19.89	-
		5.00	19.67	77.38	-

¹ The load resistor is connected directly to the harvester. ² The load resistor is connected to the harvester through the two-diode rectifier and C_storage. ³ The independent ground was made with a piece of copper (247 mm × 122 mm × 12 mm) placed directly on the ground.

shows the experimental results obtained with a 100 cm long harvester by connecting various load resistances directly in parallel with C₁ (without the diode rectifier and storage capacitor). The simulations assume C₁ = C_g = 128 pF and C₂ ≈ 2C_g = 265 pF. Note that two harvesters of 30 cm and 100 cm have been tested and proportional results have been obtained, i.e., the voltage at the load follows the pattern V_L,30cm = 30V_L,100cm /100.

The values shown in Table 1 were corrected to compensate for the effect of the internal impedance of the multimeter (Fluke 289, input impedance 10 MΩ < 100 pF, Fluke, Everett, Washington, DC, USA). These results show that the harvested voltage increases almost linearly with the value of the load resistance. The results in Table 1 also confirm the dependence of the harvested voltage on the supply voltage, as the amplitudes of the harvested voltages at 230 V-RMS are approximately twice those at 115 V-RMS. It should be noted that when the harvester is connected to an independent ground, the output voltage is reduced to approximately half of that obtained with a common ground.

Next, the load resistance was fed through the two-diode rectifier and a 0.1 mF tantalum storage capacitor, as shown in Figure 1b. The experimental and simulated results obtained with V_s = 230 V-RMS are shown in Figure 6. The simulations were performed in LTspice version 17.1.8 with the layout shown in Figure 1e.

The results shown in Figure 6 show the great similarity between the experimental and simulated results, thus validating the simple model presented in Figure 1.

The experimental and simulation results presented in this section show that the voltage across the load terminals is directly proportional to the source voltage. When a rectifier and a storage capacitor are added, the load voltage is also almost independent of the value of C_storage. However, for a given resistive load, the time required to charge the capacitor increases with the product τ = R_L·C_storage, where τ [s] is the time constant.

4.2. Experimental and Simulation Results with High-Voltage Power Lines and Substation Bus Bars

4.2.1. Calculation of the Capacitances C₁ and C₂

Figure 7 shows the tubular aluminum bus bar and the physical harvester made of silicone rubber and a copper foil, the harvester placed in the high-voltage laboratory, and the Comsol Multiphysics FEM simulations performed to determine the stray capacitance to ground C₂ (see Figure 2).

A thin layer of insulating material (ε_r = 3.2, length = 170 mm, thickness = 3.5 mm) was wrapped around the tubular bus bar (inner electrode). The insulating material (silicone rubber) was covered with a thin copper foil acting as the outer electrode, as shown in Figure 7a. Equation (11) was used to calculate the value of C₁, with ε_r = 3.2, L = 0.17 m, r₁ = 0.025 m, and r₂ = 0.0285 m, resulting in C₁ = 230.97 pF. The capacitance was then measured with the LCR precision bridge, which gave C₁ = 228.29 pF, so a value of C₁ = 230 pF is used for calculation purposes, which at a line frequency of 50 Hz gives a reactance of 13.84 MΩ.

The tubular busbar was placed horizontally at a height h = 1.5 m above the ground plane. Due to the geometry shown in Figure 2, there are no analytical equations to determine C₂, so FEM simulations are required for this purpose. These simulations yield a value of C₂ = 8.5 pF, which corresponds to a reactance of 370.1 MΩ at 50 Hz.

According to (18) and (19), the theoretically optimal value of the load resistance for the configuration considered in this paper is 13.35 MΩ, which gives 19.0 mW at 20 kV and 119.0 mW at 50 kV, although a load resistance of this value is impractical. In a previous study [26], it was shown that a smart device for high-voltage power lines based on Bluetooth Low Energy (BLE) communication consumes about 5 uA at 2.55 V in sleep mode, thus resulting in a load resistance R_Load ≈ 0.5 MΩ. Therefore, in this section, this value is considered the reference load resistance during the storage capacitor charging phase. For values of R_Load below 0.5 MΩ, the result of paralleling C₁ and R_Load is almost R_Load, so the influence of C₁ in the results is very small, but according to (16) and (17), the influence of C₂ is very important.

4.2.2. Experimental and Simulation Results with the High-Voltage Cylindrical Bus Bar

This section describes the results obtained in the high-voltage laboratory, whose dimensions are length = 7.1 m, width = 4.4 m and height = 3.1 m. The aluminum tubular bus bar shown in Figure 7a was used in the experiments and simulations. The tubular bus bar was placed horizontally at a height of 1.5 m above the ground plane.

Table 2. Experimental and simulated results at V_s = 20 kV-RMS and V_s = 20 kV-RMS. The bus bar is placed parallel to the ground plane at a height of 1.5 m. R_L is connected directly in parallel to C₁.

	RL [MΩ]	Vout [V-RMS] Measured	Vout/Vout,0.1MΩ	Vout [V-RMS] Simulated	Pout [mW] Experimental
	0.10	5.3	1.00	5.3	0.3
	0.20	10.6	2.00	10.6	0.6
20 kV	0.39	20.7	3.91	20.8	1.1
	0.50	26.1	4.92	26.7	1.4
	1.00	52.3	9.87	53.3	2.7
	0.10	13.3	1.00	13.4	1.8
	0.20	26.9	2.02	26.7	3.6
50 kV	0.39	52.0	3.91	52.0	6.9
	0.50	66.4	4.99	66.7	8.8
	1.00	132.7	9.97	133.2	17.7

shows the experimental results obtained in the high-voltage laboratory when different load resistances are connected directly in parallel with C₁ (without the diode rectifier and the storage capacitor). Note that the values shown in Table 2 have been corrected to compensate for the effect of the internal impedance of the multimeter (Fluke 289, input impedance 10 MΩ, <100 pF, Fluke, Everett, Washington, DC, USA).

The results in Table 2 show the high values of the voltage in the load resistor, the linear behavior of the harvester, and the great similarity between the experimental and simulation results. The results in Table 1 also show that the voltage in the load resistor is linearly correlated with the voltage of the power supply and that the power in the load resistor is proportional to the load resistor.

It should be noted that large values of the load resistance produce large values of the voltage in the load, which becomes impractical in real applications due to the voltage that the storage capacitor must withstand. Therefore, a control circuit is required to turn off the capacitor when the voltage is close to its maximum allowed value.

Next, the two-diode rectifier and a 1 mF storage capacitor were added to the circuit to supply the load resistor, as shown in Figure 2. Note that a tantalum capacitor was selected for its low leakage current, high capacitance, and long-term stability. The experimental results obtained with a 20 kV RMS power supply are shown in Figure 8. The simulations were performed in LTspice version 17.1.8 with the layout shown in Figure 2.

Figure 8 shows the great similarity between the experimental and simulated results, confirming the usefulness of the equivalent circuit shown in Figure 2.

The experimental and simulation results presented in this section show that the voltage across the load terminals is directly proportional to the source voltage and is almost independent of the values of C₁ and C_storage. However, for a given resistive load, the time required to charge the capacitor increases with the product τ = R_L·C_storage, where τ is the time constant.

4.3. Concluding Remarks

This section develops the concluding remarks, which can be summarized as follows:

▪

The results presented in this paper clearly show that when applying EFEH strategies, a limited amount of energy and power can be harvested, so low-power or ultra-low-power (ULP) wireless sensor nodes are required.

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The results presented in Section 4.1 and Section 4.2 clearly show that the supply voltage V_s largely determines the energy harvesting potential, so that EFEH for high-voltage applications results in higher harvested energies.

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The output voltage V_out also increases linearly with the supply voltage in both low- and high-voltage systems.

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In general, high-voltage systems are preferred for EFEH because the high voltage supply tends to produce higher capacitive currents. However, high-voltage systems require greater insulation distances, i.e., the distances between live parts and ground, which reduces capacitive coupling and therefore the value of C₂. It has been shown that it is possible to harvest power from typical residential voltages of 230 V due to the higher capacitive coupling. Although the energy harvested in low-voltage applications is lower than in high-voltage applications, the increased capacitive coupling partially compensates for the voltage limitations of EFEH in low-voltage systems. Therefore, there is a trade-off between voltage level and capacitive coupling, the latter depending on the insulation distance, since as this distance increases, the value of C₂ and the potential for energy harvesting decrease.

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For low-voltage systems, the harvester capacitance C₁ in the layout shown in Figure 1 has a large effect on the output voltage V_out because C₁ and V_out are proportional. Therefore, longer harvesters increase the energy scavenged.

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For high-voltage systems (see Figure 2), the value of C₁ has almost no effect on the output voltage or the energy harvested. This means that the dimensions of the harvester have little effect on the energy harvested.

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Since the performance of EFEH systems depends on the values of the stray capacitances, the results are not always fully repeatable because the parasitic capacitance can be affected by external factors such as the effects of nearby grounded objects or environmental variables such as humidity or temperature [27].

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It has also been observed in both low- and high-voltage applications that the output voltage V_out increases almost linearly with the value of the load resistance R_L. However, the load resistance depends on the power of the electronic circuit associated with the harvester, which is usually less than a few MΩ.

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By adding a diode rectifier and a storage capacitor C_storage, the DC output voltage is almost independent of the value of C_storage.

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The use of a two-diode rectifier is advantageous over a four-diode rectifier due to the reduced number of components and the results obtained, which are almost the same.

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By increasing the value of C_storage, more energy can be stored and used by the electronic circuit. However, for a given resistive load, the time required to charge the capacitor increases with the product τ = R_L·C_storage, where τ is the time constant, thus reducing the frequency of the communications. Therefore, the size of C_storage must be accurately calculated to store enough energy for all sensing and communication cycles while maximizing the number of communication cycles per day.

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The effective value of the load resistance R_L depends on the power required by the rest of the circuit (sensor module, DC/DC converter, microprocessor, and communication module). In a real circuit, it changes cyclically with the load level of C_storage and the phase of the communication cycle (advertising parameter initialization, advertising start, transmission, delay, and sleep), exhibiting a cyclic load profile.

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The final power available to the load depends strongly on the efficiency of the control circuit, which is a key point for the commercialization of EFEH-based sensors.

5. Conclusions

This paper has quantified the physical limit of electric field energy harvesting intended for low and high voltage power lines from theoretical, simulation, and experimental points of view. It has considered the physical harvester itself, but not the electronic circuitry required to transfer the harvested energy to the load. Energy harvesting systems are key elements for the widespread use of wireless sensor nodes. It has been shown that although high-voltage systems make it easier to harvest energy from the electric field, the increased capacitive coupling partially compensates for the voltage limitations of low-voltage EFEH. It has also been shown that increased load resistance results in higher output voltages and increased harvested power. EFEH-based sensors must typically operate in an intermittent on-off pattern due to the low energy harvested, requiring a storage capacitor. Therefore, the size of the capacitor must be carefully selected in order to store enough energy for all the sensing and communication cycles while optimizing the communication rate. In addition, stray capacitance affects EFEH performance, so this effect must be taken into account in the design phase of EFEH-based systems. The results presented in this work are valuable for batteryless and wireless sensor nodes for low voltage and high voltage, ranging from a few hundred V to a few hundred kV.