A System for Harvesting Energy from Stray Magnetic

Sens Imaging (2015)16:18 DOI 10.1007/s11220-015-0121-4 ORIGINAL PAPER

A System for Harvesting Energy from Stray Magnetic Fields L. A. Feler1 • M. Rigoni1 • H. F. Santos1 • R. A. Elias1 • N. Sadowski1 • P. Kuo-Peng1 N. J. Batistela1 • J. P. A. Bastos1

•

Received: 11 May 2015 Ó Springer Science+Business Media New York 2015

Abstract In this paper we propose an original system for replacing batteries or feeding cables used to feed monitoring equipments exposed to stray magnetic fields. The main elements of this system are a coil intended to capture the energy from magnetic field and an electronic circuit for voltage controlling. Two voltage control systems are presented: a DC–DC converter yielding a regulated voltage and a voltage tripler circuit carrying a load capacitor. This system furnishes approximately 10 mW depending on the field magnitude and the coil core material. It is shown that the low consumption feeding circuit is effective and the use of core material may increase the furnished power to up to 25 %. Keywords harvesting

Stray magnetic field Energy conversion Energy sources Energy

1 Introduction Remote sensing systems have been employed in several areas of electrical engineering. Generally, they are used in systems where the power supply depends only on batteries or via power cables. Sometimes, cable cannot be used then batteries are employed. Batteries have, as main drawback, a limited lifetime (considering their load itself or their limitation on maximum number of recharge cycles). The improvement of semiconductors, enabling the construction of dedicated low consumption circuits allowing extending the batteries life is still in This article is part of the Topical Collection on Green Solutions for Body Area Networks. & J. P. A. Bastos [email protected] 1

GRUCAD/EEL/Universidade Federal de Santa Catarina, UFSC, P. O. Box 476, Floriano´polis, SC 88040-900, Brazil

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Sens Imaging (2015)16:18

development in the electronics industry. Concomitantly, new alternative feeding technologies have been developed. These new technologies can both expand batteries lifetime as well as eliminate their use. In this case, they harvest energy from non conventional sources (Energy Harvesting) [1]. The most common sources are related to solar irradiation [2], vibration [3] or electric/magnetic fields [1] whose power varies from microwatts to few dozen of milliwatts. For many remote sensing systems this power range is sufficient for their operation. This paper addresses the problem of harvesting the power related to low frequency magnetic fields power spread in the environment, particularly on electric power substations. These plants use monitoring systems for maintaining the reliability and longevity of the power system equipment. In some situations, the way to supply fixed monitoring systems installations can be facilitated by feeding techniques using the environment magnetic field energy. Application examples are the leakage current monitoring high voltage lightning rod or acoustic signals and partial discharges in power transformers. In the majority of cases the magnitude of the magnetic fields near substation equipments varies between 1 and 50 A/m [4–6]. The system studied in this work consists of three functional subsystems, as shown in the block diagram of Fig. 1. A coil is associated to an electronic rectifier and a DC–DC converter. A Helmholtz coil is used for generating a controlled magnetic field. Finally, the system is tested in order to verify its energy supply capacity according to the variation of the magnetic field.

2 Experimental Apparatus As shown in Fig. 1, electronic DC–DC conversion circuits and a coil for converting magnetic energy into electrical energy are employed and they will be presented in this section. The magnetic field shown in the same figure is generated by means of a Helmholtz coil. 2.1 Coil (Harvester) The coil design is crucial for the efficiency of the system. Particularly, the coil core should have a high magnetic permeability. Industrial frequencies and the relatively low magnitude of magnetic fields hardly bring the core to a saturated state. The core material must have an adequate permeability to be employed under typical field intensities (from 10 to 100 A/m), found in substation areas not close to high current intensities. A non-oriented grain electrical steel is chosen on this investigation. Its

Fig. 1 Block diagram of the experimental apparatus

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relative permeability at the system operation point [initial part of the B(H) induction-field curve] is 77 for magnetic inductions under 50 mT (Rayleigh region) [7]. Moreover, for allowing maximum power transfer, the coil output and electronic circuit input impedances must have the same value. 2.1.1 Coil Designing The main input parameters for designing the coil are the number of turns Nturns , the wire diameter Dwire in cm, the magnetic field amplitude Hmax in A/m, the material (constant) relative permeability at the considered magnetic field levels lr and the geometric dimensions of the reel and the core. With this data set, some output quantities listed after can be analytically calculated: the open circuit r.m.s. voltage Vorms in V, the maximum output power Porms in W, the wire electrical resistance Rwire in X and the active materials (copper and iron) total mass Mtotal in g. Other necessary physical quantities are presented in Table 1. Considering time harmonic magnetic field, the coil open circuit voltage is calculated according to Faraday’s law: Vorms ¼

Nturns Siron Bmax x pffiffiffi 2

ð1Þ

where Siron is the coil magnetic core effective surface, Bmax the magnetic induction amplitude calculated from lr and Hmax and x the waveform angular frequency. On the other hand, the maximum output power Pomax is calculated considering the maximal power transfer between the coil and the electronic circuit. This is achieved by matching the impedances of the coil and the electronic device: Pomax ¼

2 Vorms 4Rwire

ð2Þ

In the impedance matching process, the inductive effect can be compensated with a series capacitor Cs (see Fig. 2). Thus, the impedance matching for maximum power transfer is simplified to a resistive circuit. The coil resistance Rwire must be equal to the load. Thus, the load voltage becomes half the value of the source voltage. However, because the induced voltages are relatively low, this compensation method does not provide appropriate voltage magnitudes for feeding electronic circuits. To improve the voltage magnitude, a DC–DC regulation circuit is employed (it will be shown in Sect. 2.1).

Table 1 Physical constants

Constant

Value

Description

Unit

qcopper

8.8

Copper volume density

g/cm3

qiron

7.874

Iron volume density

g/cm3

rcopper

581,000

Copper electrical conductivity

S/cm

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Fig. 2 Equivalent electric circuit including the coil and series compensation capacitor

Another possibility would be to use the RLC circuit consisting of the coil in parallel with the capacitor. The output of the circuit are the voltage over the coil and the capacitor. This circuit is further detailed in Sect. 2.4. 2.1.2 Results of the Model A coil prototype was constructed as shown in Fig. 3. Non oriented silicon steel sheets were chosen for the magnetic core. The main characteristics of the coil prototype are given in Table 2. To check the system’s response and the representation of the model, an open circuit voltage curve versus magnetic field imposed by a Helmholtz coil (in Sect. 2.5) was obtained experimentally and compared to results provided by the model. Theoretical and experimental results are shown in Fig. 4 and Table 3. One can observe an accurate representation of the model, where the maximum relative difference between the voltage values is less than 2 %. For the quantities Miron , Mcopper and Rwire the differences do not exceed 5 % between simulation and experimentation. 2.2 Rectifier As available magnetic field is alternate, an AC–DC conversion is necessary because monitoring systems are generally fed with continuous voltages. Therefore, a full wave rectifier is included in the device. Such a rectifier circuit is assembled with four diodes and an output filter capacitor as illustrated in Fig. 5. Diodes D1 , D2 , D3 and D4 are fast signal diodes 1N4148 [8] and C is an electrolytic condenser.

Fig. 3 Coil prototype

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Sens Imaging (2015)16:18 Table 2 Coil prototype data

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Symbol

Value

Description

Unit

Liron

3.0

Steel sheet width

cm

niron

0.05

Steel sheet thickness

cm

Nlam

32

Number of steel sheets

Nturns

11,700

Number of turns

Lbob

3.2

Coil internal widht

Hbob

2.6

Coil internal height

cm

Dwire

0.018

Copper wire diameter

cm

Lstk

28

Steel sheet length

cm

Lstkbob

10

Coil length

cm

lr

77.5

Adopted steel relative permeability

cm

Fig. 4 Experimental and measured coil voltage output values with differences percentage values

Table 3 Comparison between simulated and practical data

Parameter

Practical

Modeling

Difference

Unit

Miron

1113.4

1058.2

4.95 %

g

Mcopper Rwire

350.0

334.3

4.48 %

g

1060.0

1010.0

4.71 %

X

2.3 DC–DC Converter As energy source, the available magnetic field has very low magnitude. Therefore, the voltage levels directly obtained from these fields are too low to charge a battery

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Fig. 5 Full wave rectifier

directly from the rectifier output. To solve it, a DC–DC converter is used for increasing the voltage level. In recent years, some semiconductor manufacturers are investing in DC–DC converter lines for low power applications with various energy sources such as solar [9], vibration [10] and temperature [11]. In this study the LTC3105 converter [9], from Linear Semiconductors manufacturer, is chosen. It is a DC–DC converter with input voltage limits ranging from 250 mV to 5 V, and regulated output voltage at 5 V. In addition this converter has a fully independent secondary output that guarantees 3.3 V and 6 mA if the converter input voltage is within its operating range. It is an interesting solution to feed a hibernating microcontroller. Another key feature to choose this converter is its maximum power control mode, which enables the user to extract the maximum power of the source even if the load on converter output is not fixed. The integrated circuit uses an internal control for varying the average current in the inductor of the converter, so that the input impedance seen by the source is modified and adjusted to the optimum value for maximum power transfer [5]. This function, even though redundant with the inductance compensation procedure by adding a series capacitance, makes a fine adjustment at the point of maximum power transfer in spite of the nonlinearities of the system. Originally, this converter was designed for use in applications with solar energy. The characteristics of this component meet the voltage requirements of this application whose source energy are stray magnetic fields, since the coil output voltage originally sinusoidal, is rectified and acquires properties similar to the

Fig. 6 Voltage tripler and load capacitor scheme

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output voltage of photovoltaic cells. However, when a load of a few milliwatts is driven, the total consumption of the load and the regulation circuit exceeds the maximal generation capacity of the harvesting system. An alternative is to use an RLC circuit as already commented in Sect. 2.1.1. This circuit is used with a voltage tripler as described in the next section. 2.4 Voltage Tripler Circuit and Load Capacitor The alternative circuit for obtaining higher voltage levels operates as shown in Fig. 6. Capacitor CResonant serves to amplify the voltage level, the tripler circuit multiply this voltage three times. Thus, the circuit is able to charge the capacitor up to 30 V at a given time interval, more than enough for the electronic circuits operation. 2.5 Helmholtz Coil For testing the system at different magnetic field levels, one needs a source with a well controlled field. For doing so, a Helmholtz coil, shown in Fig. 7, was employed. This apparatus consists of two circular coils of radius r spaced apart by a distance L. For a uniform magnetic field in the central region of the device, the distance between coils must be equal to their radius, i.e., r ¼ L [12]. When this relationship is satisfied, the magnetic field is given by H0 ¼ nIr 2 ðr 2 þ 0:25r 2 Þ3=2

ð3Þ

3 Experimental Results The coil prototype and the electronic apparatus described in Sects. 2.1, 2.2 and 2.3 were tested under fields produced by the Helmholtz coil. Three sets of tests were performed to characterize the system:

Fig. 7 Helmholtz coil

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(a) (b) (c)


in a first study, only the coil was subjected to various field values; in a second investigation, the entire system was tested; finally, different materials were used for the coil core and the results are compared.

3.1 Harvester Subjected to Different Field Levels In this test, several field values generated by the Helmholtz coil were applied to the harvester. Four curves of power delivered by the coil as function of magnetic field level were obtained for distinct load values (110 kX, 10 kX, 1 kX, 100 X) as shown in Fig. 8. In Fig. 8 one observes that the 1 kX load curve has the highest transferred power since the wire resistance Rwire is 1060 X and the coupling is very effective. Also relevant is the fact that, for a field larger than 50 A/m, the resulting power is over 7 mW, sufficient for feeding several circuits as the amplifier INA118 [13] (maximum power consumption 6 mW), often used for conditioning small signals. 3.2 Entire System Testing After the preliminary tests with the coil, the complete system (coil, series 270 nF capacitor, rectifier and DC–DC converter) was exposed to the magnetic field generated by the Helmholtz coil. Figure 9 presents the curve of the power delivered by the system as function of the imposed magnetic field. In this second test considering the complete system, smaller power values (compared with the first essay) were obtained. It is due to amount of losses verified in cascade. In spite of having a high performance DC–DC converter, its efficiency may decrease as function of the input voltage. Moreover, the rectifier circuit also adds losses. As a matter of fact each diode 1N4148 reduces the voltage by 0.7 V [8].

Obtained power versus magnec field strength 80 70

Power [mW]

60 50

110k

40

10k 1k

30

100

20 10 0

0

20

40

60

80

100

120

Magnec field strength [A/m]

Fig. 8 Power delivered by the coil as function of magnetic field

123

140

160


Page 9 of 13 18 Obtained power versus magnec field strength

40 35

Power [mW]

30 25 20 15 10 5 0

0

50

100

150

200

250

Magnec Field [A/m]

Fig. 9 Power delivered by the system as function of the magnetic field

Nevertheless, even considering that the device can be improved, it was possible to obtain 10 mW for magnetic fields of 80 A/m as shown in Fig. 9. 3.2.1 Use of Different Core Materials and Alternative Circuit In this study, the maximum power supplied by the system during the charging cycle of a capacitor was analyzed. To fill the core, three different silicon steels were used, in addition to the air. These materials are classified according to their relative permeability as function of the magnetic field as shown in Fig. 10. As can be seen, material A has the best relative permeability for magnetic fields of up to 100 A/m, whereas for larger fields, material C has the highest relative permeability. In the context of Fig. 10, material B can be regarded as the one with Relave permeability curves

12000

Material A

10000

Material B

Relave permeability μr

Material C

8000

6000

4000

2000

0

0

50

100

150

200

250


Fig. 10 Relative permeability of different core materials as function of magnetic field

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the worst quality. The results presented in this figure were obtained with a MPG 100 Brockhaus tester shown in Fig. 11. With the circuit proposed in Sect. 2.4 new practical results were obtained using three different core materials. With the change of the core, the electrical characteristics of the coil changed as shown in Table 4. Three 60 Hz magnetic field amplitude values were applied and the capacitor charge and discharge curves were observed and collected via an oscilloscope. For instance, a charge and discharge curve is shown in Fig. 12. As seen in this figure, the charging time of the capacitor is much larger than the discharge time (time that the capacitor serves as a power source to the circuit). This is due to the fact that the harvesting system provides a smaller power than the power required by the circuit fed by it. This feature of the system is not critical, since the system can be used in applications that require the circuit only briefly. The power supply capacity and the equivalent power can be calculated on the load capacitor. The voltage on the capacitor is directly related to the stored energy. The average power of the charging/discharging cycle of the capacitor placed after the tripler circuit is given by Eq. 4, which shows that energy variation in a given time interval is equal to the obtained average power. Paver ¼

DU 12 CðVf2 Vi2 Þ ¼ Dt Dt

ð4Þ

where Dt ¼ Tf Ti and for other variables see Fig. 12. The average power values obtained as a function of the magnetic field and the core material are given in Table 5. Analyzing Table 5, one observes that the coil core with material A is able to provide greater power to the capacitor. In order to compare these three materials, Fig. 13 shows the percentage difference between the power values obtained for the different cores with respect to the worst core (material B). For all the magnetic field amplitudes, material A provided the highest power. For a 50 A/m value the coil with material A furnished 12 % more power than material B and material C provided 4.5 % more power. The biggest difference is noted in the

Fig. 11 Device used for obtaining the relative permeability of the core materials

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Table 4 Coil characteristics for different core materials

Core A

Core B

Core C

Air core

Inductance (H)

24.22

18.58

22.34

1.5

Resistance (kX)

1.06

1.06

1.06

1.06

Resonant capacitor (nF)

290

378

315

4700

Load capacitor (mF)

6.6

6.6

6.6

6.6

Fig. 12 A capacitor charge and discharge curve

Table 5 Average power (mW)

Field (A/m)

Material A

Material B

Material C

Air core

50

1.183

1.055

1.104

1.650E-06

100

5.326

4.409

4.797

1.940E-05

150

11.682

9.438

10.789

2.606E-04

Relave difference between cores

25

% Diff A-B

Percentage difference [%]

% Diff C-B

20

15

10

5

0

50 A/m

100 m/A

105 A/m


Fig. 13 Percentage relative difference between the power provided by the different cores

case of a 100 A/m field, where material A provided a 21 % higher power than material B and material C gave a 9 % higher power than the same reference (material B). From these analyses one observes a 12 % difference between the

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power obtained by the system with materials A and C, both with respect to material B. One also observes that for a 150 A/m field, the use of material A increases the furnished power by nearly 25 % compared to results obtained for material B.

4 Conclusions The proposed harvesting systems are able for powering instrumentation circuits used on monitoring electrical installations of substations or even high power electrical machines as, for instance, large generators. The complete system is able to furnish reasonable power values for fields above 80 A/m (10 mW), noticing that one could improve it, particularly, on aspects concerning the coil and the core material. The use of other magnetic core materials having higher relative permeability value is promising for a significant improvement in the system. The circuit proposed in Sect. 2.4 is appropriate to directly load a supercapacitor. Another possibility consists on using the supercapacitor operating as source and feeding the DC–DC converter circuit.

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11. Linear semiconductors, auto-polarity, ultralow voltage step-up converter and power manager, 2010. 12. Tumanski, S. (2011). Handbook of magnetic measurements. Boca Raton, FL: CRC Press. 13. Texas instruments, precision, low power instrumentation amplifier, 1998.

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