Time-Multiplexed Self-Powered Wireless Current Sensor for Power Transmission Lines

energies

Article Time-Multiplexed Self-Powered Wireless Current Sensor for Power Transmission Lines

Hao Chen , Zhongnan Qian , Chengyin Liu , Jiande Wu * , Wuhua Li and Xiangning He

College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China; [email protected] (H.C.); [email protected] (Z.Q.); [email protected] (C.L.); [email protected] (W.L.); [email protected] (X.H.) * Correspondence: [email protected]; Tel.: +86-1360-051-1674

Abstract: Current measurement is a key part of the monitoring system for power transmission lines. Compared with the conventional current sensor, the distributed, self-powered and contactless current sensor has great advantages of safety and reliability. By integrating the current sensing function and the energy harvesting function of current transformer (CT), a time-multiplexed self-powered wireless sensor that can measure the power transmission line current is presented in this paper. Two operating modes of CT, including current sensing mode and energy harvesting mode, are analyzed in detail. Through the design of mode-switching circuit, harvesting circuit and measurement circuit are isolated using only one CT secondary coil, which eliminates the interference between energy harvesting and current measurement. Thus, the accurate measurement in the current sensing mode and the maximum energy collection in the energy harvesting mode are both realized, all of which simplify the online power transmission line monitoring. The designed time-multiplexed working mode allows the sensor to work at a lower transmission line current, at the expense of a lower working frequency. Finally, the proposed sensor is veriﬁed by experiments.

Citation: Chen, H.; Qian, Z.; Liu, C.; Keywords: time-multiplexed; self-powered; current transformer; current sensor Wu, J.; Li, W.; He, X. Time-Multiplexed Self-Powered Wireless Current Sensor for Power Transmission Lines. Energies 2021, 14, 1561. https:// 1. Introduction doi.org/10.3390/en14061561 Power transmission and distribution networks has high requirements for reliability and security, and a reliable online condition monitoring system (OCMS) can provide the Academic Editor: Salvatore Celozzi guarantees [1]. Meanwhile, OCMS is also a prerequisite for the development of smart grid [2,3]. New technologies of smart grid, such as dynamic line rating [4] and situation Received: 4 February 2021 awareness [5], require wide-area line operation data based on widely distributed OCMS. Accepted: 8 March 2021 Published: 11 March 2021 In the OCMS for power transmission lines, line current measurement can directly reﬂect the operation status of transmission lines and different line faults [6]. Therefore, line current

Publisher’s Note: MDPI stays neutral measurement is an intuitive way of OCMS for power transmission lines [7]. with regard to jurisdictional claims in Lots of distributed current sensors are required for online current measurements. published maps and institutional afﬁl- Due to the high voltage and high current of power transmission lines, direct electrical iations. contact between sensors and transmission lines is dangerous. Thus, non-contact current measurement methods for electric power systems have been developed, such as current transformer (CT), Rogowski coil [8], Hall current sensor [9], ﬂuxgate and optical current sensor [10], etc. Among them, the CT is widely adopted. The line-clamped CT transforms the large power transmission line current to a small current on the secondary side, which is Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. safe to measure. This article is an open access article Besides, the power supply technology for distributed current sensors on power trans- distributed under the terms and mission lines is also a challenge. To overcome the battery replacement issue, energy har- conditions of the Creative Commons vesting methods have been widely studied for this application, including electromagnetic Attribution (CC BY) license (https:// coupling, thermal [11], solar [12], and wind [13]. Solar and wind power are highly de- creativecommons.org/licenses/by/ pendent on weather conditions, so the energy storage element is bulky for continuous 4.0/). power supply, which is undesirable on transmission lines. Thermal harvesters are also

Energies 2021, 14, 1561. https://doi.org/10.3390/en14061561 https://www.mdpi.com/journal/energies Energies 2021, 14, 1561 2 of 15

unstable for transmission line applications due to the wide temperature swing between transmission lines and ambient environments. Compared to them, the CT-fed power supply, a kind of magnetic coupling method, is more suitable for transmission line applications [14]. Since energy is sourced from the transmission lines by CT, the power supply can be constantly maintained to ensure the uninterrupted operation of sensors. Therefore, the line-clamped CT can be used for both current sensing and energy harvesting, which depends on different post-stage circuit designs. To simplify the OCMS structure, self-powered current sensors that combine the functions of current sensing and energy harvesting are proposed in [15–18]. Amaro et al. [15] proposed a system that is capable of supplying power to a wireless sensor and at the same time estimating the line current. The energy sourced by CT is stored in a capacitor, and the current value is estimated by promoting capacitor discharge and estimating the slope of the recharging voltage. Ren et al. [16] presented a self-powered current measuring sensor realizing measurement and power supply synchronously. The current is calculated by the voltage and current before and after the rectifier connected to post-stage of CT. Neither of the aforementioned two methods isolates the measurement circuit from the harvesting circuit, which decreases the current measurement accuracy. Moghe et al. [17] proposed a smart stick-on sensor for monitoring a variety of grid assets. It is pointed out that the isolation between current measurement circuit and harvesting circuit can improve the measurement accuracy. However, the detailed isolated circuit design is not given. Lim et al. [18] proposed a CT structure with two secondary coils for self-powered current sensors, in which one coil is used for current sensing, and the other one is used for energy harvesting. Through this CT structure, the measurement circuit and the harvesting circuit are successfully isolated. However, as the cost of the integration of two secondary coils into one core, a voltage reduction in the energy storage capacitor is expected. Consequently, the sensor needs a higher line current to operate. In this paper, a time-multiplexed self-powered wireless current sensor for transmission lines is proposed. The mode-switching circuit is designed to isolate the harvesting circuit and the measurement circuit, making the sensor work in time-multiplexed mode, which eliminates the interference between energy harvesting and current measurement. The accurate current measurement and the maximum energy collection are realized through only one CT secondary coil instead of two coils. Meanwhile, the time-multiplexed working mode allows the sensor to work at a lower transmission line current, at the expense of lower working frequency. The proposed sensor makes full use of the transducer and simplifies OCMS for power transmission lines. This paper is organized as follows. In Section2, the ideal and non-ideal models of CT are presented and analyzed. Based on the non-ideal model, the impedance matching of the post-stage circuit in both current sensing mode and energy harvesting mode is analyzed. In Section3, the design of time-multiplexed self-powered wireless current sensor is proposed, and its workflow is analyzed in detail. In Section4, experimental results are presented to verify the proposed sensor. In Section5, the conclusions are given.

2. Analysis of CT Operating Modes 2.1. Circuit Model of CT As shown in Figure1, the CT is clamped on a single-phase AC transmission line, and the secondary side is connected to the load. The turn ratio of the primary and the secondary is 1:N. Assuming magnetic core works in linear region and neglecting nonideal factors of CT, an ideal circuit model of CT can be derived. According to the principle of magnetic potential balance, when the transmission line carries current ip(t) (i.e., the primary side of CT), current is(t) will also be induced through the load (i.e., the secondary side of CT). The current relationship is:

iL(t) = is(t) = ip(t)/N (1) Energies 2021, 14, x FOR PEER REVIEW 3 of 15 Energies 2021, 14, x FOR PEER REVIEW 3 of 15

Energies 2021, 14, 1561 3 of 15 it  i t i t / N (1) LiLt s i s t p  i p t / N (1) (1)

TransmissionTransmission line line ip(t) ip(t)ip(t) is(t) is(t)is(t) AirAir gap gap Load N turnsN turns LoadLoad

MagneticMagnetic core core

Figure 1. CT setup. FigureFigureFigure 1. 1. CT 1.CT CT setup. setup. setup.

Thus,Thus,Thus, the the the ideal ideal ideal circuit circuit circuit model model model of of CTof CT CT is is built,is built, built, as as shownas shown shown in in Figurein Figure Figure 2.2. 2.

+ +

ip(t) / N ZL uo(t) p ip(t) / N ZL ZoL uo(t) - -

Figure 2. Ideal circuit model of CT. FigureFigureFigure 2. 2. Ideal 2.Ideal Ideal circuit circuit circuit model model model of of CT.of CT. CT.

ConsideringConsideringConsidering finite finite finite magnetizing magnetizingmagnetizing inductance, inductance, inductance, flux flux fluxleakage, leakage, leakage, core core loss core loss, an loss,, dan wired andwire loss, wireloss, a non a loss, non- - ideala non-ideal model of model CT can of be CT built, can beas built,shown as in shown Figure in 3a. Figure The magnetizing3a. The magnetizing inductance inductance Lm of CT idealideal model model of CTof CT can can be bebuilt, built, as shownas shown in Figurein Figure 3a. 3a. The The magnetizing magnetizing inductance inductance Lm Lofm CTof CT hasLm aof certain CT has shunting a certain effect shunting on the effect current on the source current ip(t) source/N. Especiallyip(t)/N. when Especially the air when gap theis hashas a certain a certain shunting shunting effect effect on onthe the current current source source ip(t) ip/(t)N./ NEspecially. Especially when when the the air airgap gap is is addedair gap in is the added core, in the the value core, theof L valuem will ofdropLm willdramatica drop dramatically,lly, and the shunting and theshunting effect will effect be addedadded in thein the core, core, the the value value of ofLm Lwillm will drop drop dramatica dramatically,lly, and and the the shunting shunting effect effect will will be be will be more noticeable, resulting in a much smaller current through the load than the moremore noticeable, noticeable, resulting resulting in ain much a much smaller smaller current current through through the the load load than than the the ideal ideal condi- condi- ideal condition. In addition, the core loss of CT also has a significant influence on the load tion.tion. In addition,In addition, the the core core loss loss of CTof CT also also has has a significant a significant influence influence on onthe the load load power, power, which which ispower, modeled which by the is modeled resistance by R them. The resistance leak inductanceRm. The leakLσ and inductance the wire lossLσ and resistance the wire Rw loss of is modeledis modeled by bythe the resistance resistance Rm .R Them. The leak leak inductance inductance Lσ Landσ and the the wire wire loss loss resistance resistance Rw Rofw of resistance R of the secondary winding are also non-ideal factors of practical CT. However, thethe secondary secondaryw winding winding are are also also non non-ideal-ideal factors factors of practicalof practical CT. CT. However, However, considering considering that that considering that the load impedance of the secondary side is typically much larger than thethe load load impedance impedance of theof the secondary secondary side side is typically is typically much much larger larger than than the the leak leak impedance, impedance, the leak impedance, the leak impedance of the secondary side can be ignored. Accordingly, thethe leak leak imped impedanceance of theof the secondary secondary side side can can be beignored. ignored. Accordingly, Accordingly, the the simplified simplified CT CT the simplified CT non-ideal circuit model can be derived, as shown in Figure3b. nonnon-ideal-ideal circuit circuit model model can can be bederived, derived, as shownas shown in Figurein Figure 3b. 3b.

Lσ Rw is(t) iL(t) is(t) iL(t) σ L w Rw is(t) iL(t) s is(t) L iL(t) σ is(t) iL(t) + + + + + +

Zm ip(t) / N jωLm Rm Zm ZL uo(t) ip(t) / N jωLm Rm Zm ZL uo(t) ip(t) / N jωLm Rm m Zm ZL uo(t) ip(t) / N jmωLm m Rm Zm L ZL uo(t) ip(t) / N jωLm Rm ZL uo(t) - - - - - (a) (a) (b)( b) Figure 3. Non-ideal circuit model of CT. (a) With leak impedance. (b) Ignore leak impedance. FigureFigureFigure 3. 3. Non 3.Non-ideal Non-ideal-ideal circuit circuit circuit model model model of of CT.of CT. CT. (a (a) )(Witha With) With leak leak leak impedance. impedance. impedance. (b (b) )(Ignoreb Ignore) Ignore leak leak leak impedance. impedance. impedance. 2.2. Current Sensing Mode of CT 2.2.2.2. Current Current Sensing Sensing Mode Mode of CTof CT When CT is utilized to sense the primary side current, assume that the CT is ideal, WhenWhen CT CT is utilizedis utilized to tosense sense the the primary primary side side current, current, assume assume that that the the CT CT is ideal,is ideal, thethe secondary secondary side side current current isi(t)s(t) completely completely through through the the load, load, as as shown shown in in Figure Figure 2.2. Thus, Thus, thethe secondary secondary side side current current is(t) is (t)completely completely through through the the load, load, as asshown shown in Figurein Figure 2. Thus,2. Thus, the primary side current ip(t) can be calculated by Equation (1) after the current is(t) the primary side current ip(t) can be calculated by Equation (1) after the current is(t) is isthe measured. primary side current ip(t) can be calculated by Equation (1) after the current is(t) is measured. measured.However, for the non-ideal CT model, as shown in Figure3b, due to the shunting However,However, for for the the non non-ideal-ideal CT CT model, model, as asshown shown in inFigure Figure 3b, 3b, due due to tothe the shunting shunting effect of Lm and Rm, the current through the load is smaller than the ideal condition. Thus, effect of Lm and Rm, the current through the load is smaller than the ideal condition. Thus, aeffect measurement of Lm and error Rm, the would current be produced through the if Equation load is smaller (1) is used than tothe calculate ideal condit the primaryion. Thus, a measurement error would be produced if Equation (1) is used to calculate the primary current.a measurement In the non-ideal error would model be shown produced in Figure if Equation3b, the current(1) is used through to calculate the load theZ primaryis: current. In the non-ideal model shown in Figure 3b, the current through the load ZLL is: current.current. In theIn the non non-ideal-ideal model model shown shown in Figurein Figure 3b, 3b, the the current current through through the the load load ZL ZisL: is: ip jωLm + Rm iL = · (2) N jωLm + Rm + ZL

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Energies 2021, 14, 1561 4 of 15

ip j Lmm R iL  (2) N j Lm R m Z L Thus,Thus, the the relative relative error error of of measuremen measurementt is is:: I Z IZLLL L δ = 1 −1= = (3(3)) Is jωLm + Rm + Z L Is j L m R m Z L

SinceSince LmL mandand RmR arem are determined, determined, for for minimizing minimizing the the relative relative error, error, ZZL Lis isexpected expected to to bebe much much less less than than (jωL (jωmL m+ R+mR),m which), which is the is the requirement requirement that that CT CT post post-stage-stage circuit circuit needs needs toto satisfy satisfy in in the the current current sensing sensing mode. mode. 2.3. Energy Harvesting Mode of CT 2.3. Energy Harvesting Mode of CT When CT is utilized for energy harvesting, the load ZL is expected to absorb power as When CT is utilized for energy harvesting, the load ZL is expected to absorb power as much as possible. According to the circuit model shown in Figure3b, the output power is: much as possible. According to the circuit model shown in Figure 3b, the output power is: 2 2 IIp jωLm + Rm P = p × j Lmm R × Z (4) ZLPZZ = L L (4) L N jωLm + Rm + ZL N j Lm R m Z L InIn this this mode, mode, when when the the parameters parameters of of CT CT and and the the primary primary current current are are fixed, ﬁxed, the the CT CT outputoutput power power is is related related to to the the impedance of thethe load.load. TheThe conventional conventional CT CT energy energy harvest- har- vestinging circuit circuit directly directly connects connects the the secondary secondary sideside to a resistive load, load, as as shown shown in in Figure Figure 4,4 , withoutwithout cons consideringidering the the compensation compensation for for CT CT magnetizing magnetizing inductance inductance LLm manandd impedance impedance matching.matching. The The maximum maximum output output power power of of the the harvest harvesterer without without compensation compensation and and with with compensationcompensation will will be be analyzed analyzed and and compared compared below below..

is(t) iL(t) +

Ip / N jωLm Rm Zm RL Uo

FigureFigure 4. 4.CTCT energy energy har harvestingvesting circuit circuit without without compensation. compensation.

InIn the the case case of of no no compensation, compensation, as as shown shown in in Figure Figure 4,4 ,the the parameters parameters of of CT CT and and the the primaryprimary current current are are fixed, ﬁxed, and and only only RRL isL isvariable. variable. When When RLR isL isset set as: as: 1 RL  1 RL = r 22 (5) 11 2   2 (5) 1  1 R + L  RLmmm   ω m  TheThe output output power power is ismaximized maximized to to:: 2 Ip2 1 Ip 1 PL1=· PL1 N "r 22# (6) N 1 2  1  2 1 (6) 221 + 1 + 1 Rm  ωLm  Rm RLRm   m  m  The harvester with compensation is shown in Figure5, a parallel capacitor C is The harvester with compensation is shown in Figure 5, a parallel capacitor Cr is utilizedr utilized to compensate the magnetizing inductance Lm. According to the principle of to compensate the magnetizing inductance Lm. According to the principle of impedance impedance matching, when Cr and RL satisfy Equation (7), the power absorbed by RL matching, when Cr and RL satisfy Equation (7), the power absorbed by RL is maximized. is maximized. ( 1 Cr = 2 ω Lm (7) RL = Rm

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Energies 2021, 14, 1561 5 of 15 Energies 2021, 14, x FOR PEER REVIEW is(t) iL(t) 5 of 15 +

Ip / N jωLm Rm Ym -1/jωCr RL YL Uo is(t) iL(t) +-

IFigurep / N 5. CTj ωenergyLm harvestingRm Y mcircuit with-1/ jcompensationωCr RL Ycapacitance.L Uo -  1 Cr  Figure 5. CT energy harvesting circuit with compensation 2 capacitance. Figure 5. CT energy harvesting circuit with compensation  Lm capacitance. (7)  RRLm In this case, the CT output power is: 1 C  In this case, the CT output power is: r 2 2 L  Ip 2mRm (7) PL2 = I p · R (8) RRLmN 4 m PL2  (8) N 4 InFor this the case, general the CT case output where power the C isr :matches Lm and the load RL is variable, the CT outputFor power the general is: case where the Cr matches L2 m and the load RL is variable, the CT out- I R put power is: 2 p 2m Ip PL2 R (8) P = · N m4 (9) L2 2 2 2 NIp RL + Rm/RRL + 2Rm P =  m For the general case where theL2 Cr matches Lm and2 the load RL is variable, the CT out-(9) Comparing Equations (6) and (9), theN maximumRRRRL m harvesting L2 m power of CT is improved putcompared power withis: that of without compensation, as shown in the following equation. Comparing Equations (6) and (9), the2 maximum harvesting power of CT is improved I 2 compared with that of without compensation, p s as shownRm  in the following equation. PL2= 2 (9) PL2 1 N RRRR2Rm 2 = 1 + 1 L+ m L2 > m 1 (10) PL1 PR2 1 ωLm L21  1  m  1 Comparing Equations (6) and (9), the maximum harvesting power of CT is improved(10 ) PLL12  m compared with that of without compensation, as shown in the following equation. Especially, when the air gap is added in the core, Lm is significantly decreased, yet Rm is almost unchanged (because there is no loss in the air2 gap),m so the ratio of R to ωL ism Especially, when the air gapPR is added1 in the core, L is significantly decreased,m yetm R L21  1  m  1 significantlyis almost unchanged increased. (because It can be there seen is from no loss Equation in the (10) air that,gap), atso this the time,ratio theof R CTm to output ωL(10m )is PLL12  m powersignificantly will be increased. significantly It can enhanced be seen byfrom paralleling Equation the(10) compensation that, at this time, capacitor the CT on output the secondarypower will side be ofsignificantly CT. enhanced by paralleling the compensation capacitor on the Especially, when the air gap is added in the core, Lm is significantly decreased, yet Rm secondaryWhen theside load of CT. of the harvester is a full-bridge rectifier with resistive load, as shown is almost unchanged (because there is no loss in the air gap), so the ratio of Rm to ωLm is in FigureWhen6, the the rectifier load of canthe beharvester approximated is a full to-bridge a resistive rectifier load with to the resistive harvester. load, as shown significantly increased. It can be seen from Equation (10) that, at this time, the CT output powerin Figure will 6, be the significantly rectifier can enhanced be approximated by paralleling to a resistive the compensation load to the harvester. capacitor on the RL(eq) ≈ Rrec/2 (11) secondary side of CT. RL(eq ) R rec /2 (11) When the load of the harvester is a full-bridge rectifier with resistive load, as shown in Figure 6, the rectifier can be approximated to a resistive load to the harvester. RL(eq) CT RL(eq ) R rec /2 (11)

is(t) i Lm D1 D2 + RL(eq) iR iL(t) CT Rrec C1 Vdc is(t) ip(t)/N Lm Rm Cr i Lm D1 D 2 + – iR iL(t) D3 D4 R C1 V rec dc ip(t)/N Lm Rm Cr FigureFigure 6. 6.Full-bridge Full-bridge rectiﬁer rectifier for for CT CT energy energy harvester. harvester.– D3 D4 3.3. Design Design of of Time-Multiplexed Time-Multiplexed Self-Powered Self-Powered Wireless Wireless Current Current Sensor Sensor 3.1. System Structure and Circuit Design Figure3.1. System 6. Full -Structurebridge rectifier and Circuit for CT energyDesign harvester. The system structure of the proposed time-multiplexed self-powered wireless current The system structure of the proposed time-multiplexed self-powered wireless cur- sensor is shown in Figure7. The CT of the sensor is clamped on the transmission line. 3.rent Design sensor of isTime shown-Multiplexed in Figure 7. Self The-Powered CT of the Wireless sensor is Currentclamped Sensor on the transmission line. The current sensing function and the energy harvesting function of CT are integrated into 3.1.the System sensor. Structure The system and hasCircuit two Design operating modes, energy harvesting mode, and current measurementThe system mode. structure The two of the modes proposed are converted time-multiplexed by mode switch. self-powered wireless current sensor is shown in Figure 7. The CT of the sensor is clamped on the transmission line.

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The current sensing function and the energy harvesting function of CT are integrated into Energies 2021, 14, 1561 6 of 15 the sensor. The system has two operating modes, energy harvesting mode, and current measurement mode. The two modes are converted by mode switch.

Air gap I CT p Transmission line

Energy N turns Energy harvesting storage Cr Is capacitor

Mode DC/DC Rectification switch module

Power supply Wireless Signal Current Signal conditioning communic MCU sampling and amplification ation module

Current measurement

Figure 7. System structure of the time-multiplexedtime-multiplexed self-poweredself-powered wirelesswireless currentcurrent sensor.sensor.

InIn the energy energy harvesting harvesting mode, mode, the the energy energy sourced sourced by byCT CT from from the thetransmission transmission line lineis stored is stored in an in an energy energy storage storage capacitor. capacitor. When When enough enough energy energy is is stored, stored, the system system switches to to the the current current measurement measurement mode mode,, and and the the measurement measurement circuit circuit is powered is powered.. The Themeasurement measurement circuit circuit senses senses the CT the secondary CT secondary side sidecurrent current value, value, calculates calculates the CT the pri- CT primarymary side side current current value, value, and and finally ﬁnally sends sends the the results results via via the wirelesswireless communication communication module to realize realize further further function. function. When the stored energy is is insufﬁcient, insufficient, the the system system switches the energyenergy harvestingharvesting mode,mode, andand thethe cyclecycle repeats.repeats. Thus,Thus, thethe harvestingharvesting circuitcircuit and the measurement measurement circuit circuit are are isolated isolated by by the the mode mode switch, switch, and and the sensor the sensor is time istime-mul- multiplexed,tiplexed, which which eliminates eliminates the interference the interference between between energy energy harvesting harvesting and current and current meas- measurement.urement. Compared Compared with the with method the method using usingtwo CT two secondary CT secondary coils, the coils, proposed the proposed sensor sensorrealizes realizes the isolation the isolation between between the harvesting the harvesting circuit circuitand the and measurement the measurement circuit circuit using usingonly one only CT one secondary CT secondary coil. coil. The current range of transmission lineslines needs toto be considered inin the implementation of thethe currentcurrent sensor. sensor. When When the the transmission transmission line line current current is low, is low, the traditionalthe traditional CT harvester CT har- may not be able to source enough energy to maintain a stable DC voltage to power the post- vester may not be able to source enough energy to maintain a stable DC voltage to power stage circuit. Due to the wide dynamic current range of the transmission line, an energy the post-stage circuit. Due to the wide dynamic current range of the transmission line, an storage device is necessary. On the other side, for the distributed wireless current sensor, energy storage device is necessary. On the other side, for the distributed wireless current one of the most critical challenges is to achieve optimum operational life. Compared to a sensor, one of the most critical challenges is to achieve optimum operational life. Com- lithium battery with a short life span [19], the electrolytic capacitor has extremely high cycle pared to a lithium battery with a short life span [19], the electrolytic capacitor has ex- life and operates with unexcelled reliability [20]. Accordingly, the high-capacity electrolytic tremely high cycle life and operates with unexcelled reliability [20]. Accordingly, the high- capacitor C1 is used as an energy storage device in the proposed sensor. The sensor works in capacity electrolytic capacitor C1 is used as an energy storage device in the proposed sen- time-multiplexed mode, the working frequency of the sensor varies with the transmission sor. The sensor works in time-multiplexed mode, the working frequency of the sensor line current. By extending the time operating in energy harvesting mode, it can adapt itself varies with the transmission line current. By extending the time operating in energy har- to a low current condition, at the expense of a lower operating frequency. The sensor can vesting mode, it can adapt itself to a low current condition, at the expense of a lower op- operate at a minimum transmission line current of 1 A. eratingAccurate frequency transmission. The sensor line can current operate measurement at a minimum needs transmission to ensure line the current effectiveness of 1 A. of EquationAccurate (1). transmission In other words, line current the primary measurement current ofneeds the to CT ensure has a linearthe effectiveness relationship of withEquation the secondary(1). In other current words, under the primary the utility-frequency current of the CT condition. has a linear To ensurerelationship the linear with relationship,the secondary the current magnetic under core the ofutility CT- needsfrequency to operate condition. in a To linear ensure region the tolinear prevent relation- the effectsship, the of magnetic loss and magneticcore of CT saturation, needs to operate because in saturation a linear region will cause to prevent secondary the effects current of distortionloss and magnetic [21]. Thus, saturation, an air gap because is added saturation in the core will to cause expand secondary the unsaturated current operatingdistortion range, as shown in Figure7, making the linear region of the core cover the maximum current range. The parameters and dimensions of CT need to consider the scale and power level of the transmission line. Considering the saturation of the magnetic core and the accuracy Energies 2021, 14, x FOR PEER REVIEW 7 of 15

[21]. Thus, an air gap is added in the core to expand the unsaturated operating range, as Energies 2021 14 , , 1561 shown in Figure 7, making the linear region of the core cover the maximum current range.7 of 15 The parameters and dimensions of CT need to consider the scale and power level of the transmission line. Considering the saturation of the magnetic core and the accuracy of ofcurrent current measurement, measurement, a asingle single CT CT cannot cannot satisfy satisfy the the needs needs of a widewide rangerange of of current current measurements.measurements. DifferentDifferent CTCT cancan bebe chosenchosen toto satisfysatisfy thethe needsneeds ofof thethe sensorsensor operatingoperating inin differentdifferent current current ranges ranges of of the the transmission transmission line. line. SinceSince thethe proposedproposed sensor sensor can can operate operate at at aa minimumminimum transmissiontransmission line c currenturrent of of 1 1 A, A, the the CT CT with with an an operating operating current current range range of of1– 1–100100 A A is is chosen. chosen. Thus, Thus, the the current current measurement measurement range range of of the the proposed proposed sensor is 1–1001–100 A.A. TheThe detaileddetailed circuitcircuit ofof thethe proposedproposed time-multiplexedtime-multiplexedself-powered self-powered wirelesswireless current current sensorsensor isis shownshown inin FigureFigure8 .8. The The circuit circuit consists consists of of three three parts, parts, energy energy harvesting harvesting part, part, currentcurrent measurementmeasurement part,part, andand modemode switchswitch part.part. TheThe energyenergy harvestingharvesting partpart includesincludes thethe CT,CT, the the compensation compensation capacitor capacitorC Cr,r, thethe full-bridgefull-bridge rectiﬁerrectifier (composed(composed ofof diodesdiodesD D11,, DD22,, andand bodybody diodesdiodes ofof QQ33 and Q4)),, and and the the energy energy storage storage capacitor capacitor C1.. The The current current meas- mea- surementurement part is composed of sample resister RR11 and R22,, differential differential ampliﬁcationamplification module,module, microprogrammedmicroprogrammed control control unit unit (MCU), (MCU), MOSFET MOSFET driver, driver, and and the the LoRa LoRa (Long (Long Range Range Radio) Ra- wirelessdio) wireless communication communication module, module, where where the R1 theand RR1 2andare R much2 are much smaller smaller than ( jthanωLm (+jωLRmm). + TheRm). mode The mode switch switch part consists part consists of a voltage-controlled of a voltage-controlled low dropout low dropout regulator regulator (LDO) module (LDO) andmodule MOSFET and MOSFETQ3 and Q Q4.3 and Q4.

iLm D1 D2 +

C1 Voltage- L R ip(t)/N m m Cr Vin controlled Q4 Q3 LDO Power vQ4 vQ3 supply

vg4 vg3 – - Sampling Differential R1 R2

amplification +

Power supply Data

vg3 Driver vg4 LoRa wireless module MCU

FigureFigure 8.8.Detailed Detailed circuitcircuitof of thethe time-multiplexedtime-multiplexedself-powered self-powered wireless wireless current current sensor. sensor.

3.2.3.2. ModeMode SwitchSwitch andand SystemSystem WorkﬂowWorkflow TheThe modemode switchswitch isis controlledcontrolled by by the the voltage-controlled voltage-controlled LDO LDO module. module. The The structure structure of of thethe voltage-controlledvoltage-controlled LDOLDO modulemodule isis shownshown inin FigureFigure9 .9. The The module module consists consists of of an an LDO LDO withwith aa turned-offturned-off statestate andand peripheryperiphery circuits.circuits. TheThe LDOLDO hashas anan enableenable pinpin EN,EN, whichwhich cancan control the operating state of the device. When the EN pin voltage is lower than a certain control the operating state of the device. When the EN pin voltage is lower than a certain threshold voltage (set as VEN_off), the LDO operates in the turned-off state, where the LDO threshold voltage (set as VEN_off), the LDO operates in the turned-off state, where the LDO output voltage is 0. When the EN pin voltage is higher than a certain threshold voltage output voltage is 0. When the EN pin voltage is higher than a certain threshold voltage (set (set as VEN_on), the LDO operates in a turned-on state, where the LDO outputs a constant as VEN_on), the LDO operates in a turned-on state, where the LDO outputs a constant voltage. voltage. The voltage of the EN pin when the LDO operates in the turned-off state is: The voltage of the EN pin when the LDO operates in the turned-off state is:

RRR4 45k R5 VEN VV=ENV=in · in  (12)(12) R1RRR+1R4 4k R 55 The voltage of the EN pin when the LDO operates in the turned-on state is:

Energies 2021, 14, x FOR PEER REVIEW 8 of 15

RRRR4 5 3 4 VVVEN=+ in out (13) RRRRRR1 4 5 5 3 4

Since the output voltage of LDO is constant in the turned-on state (set as Vout_std), thus, at turned-on critical point and turned-off critical point, the voltage of the EN pin is:

RR45 VVEN_on= in_on  (14) RRR1 4 5 Energies 2021, 14, 1561 8 of 15 RRRR4 5 3 4 VVVEN_off=+ in_off out_std (15) RRRRRR1 4 5 5 3 4

Vout R5 Vin Vout VIN OUT

EN GND

R4 LDO Vin_off Vin_on Vin

Figure 9. Voltage-controlled LDO module and its input/output characteristics. Figure 9. Voltage-controlled LDO module and its input/output characteristics.

TheThus, voltage through of the the EN peripheral pin when circuit the LDO design, operates the LDO in the can turned-on be turned state on when is: the input voltage is higher than Vin_on, and be turned off when the input voltage is lower than Vin_off, as shown in Figure 9. Vin_on andR4 kVin_offR5 are easy to beR calculated3 k R4 as: V = V · + V · (13) EN in R + R k R out R + R k R 1 4 5 RRR1 45 5 3 4 VVin_on= EN_on  (16) RR45 Since the output voltage of LDO is constant in the turned-on state (set as Vout_std), thus, at turned-on critical point and turned-off critical point, the voltage of the EN pin is: RRRRR VVV= - 3 4 1 4 5 in_off EN_off out_std k (17) RRRRR5R4 3R5 4 4 5 VEN_on = Vin_on · (14) R1 + R4 k R5 Based on the above analysis, the workflow of the system is presented, as shown in

Figure 10. In the beginning, the voltageR4 k R of5 C1 (Vin) is 0, theR voltage3 k R4 -controlled LDO is VEN_off = Vin_off · + Vout_std · (15) turned off and the MCU is poweredR1 + off,R4 hence,k R5 the Q3 andR Q5 4+ areR3 turnedk R4 off. The system operates in energy harvesting mode. The equivalent circuit is shown in Figure 11. The CT Thus, through the peripheral circuit design, the LDO can be turned on when the input with capacitance compensation sources energy from the transmission line. The full-bridge voltage is higher than Vin_on, and be turned off when the input voltage is lower than Vin_off, rectifier composed of diodes D1, D2, and body diodes of Q3 and Q4 converts the AC power as shown in Figure9. Vin_on and Vin_off are easy to be calculated as: on the secondary side of CT to DC power, and stores the energy in C1. When the voltage of C1 reaches Vin_on, the voltage-controlled LDOR is +turnedR k Ron and the MCU is powered. The V = V · 1 4 5 (16) MCU starts to operate and turnsin_on Q3 andEN_on Q4 on. At this point, the system is switched to the R4 k R5 current measurement mode. The equivalent circuit is shown in Figure 12. Since R1 and R2 are much smaller than (jωLm + Rm), the currentR3 throughk R4 R1 Rand1 + RR24 followsk R5 Equation (1). Vin_off = VEN_off− Vout_std · · (17) The voltage values of R1 and R2 are sensedR 5and+ R entered3 k R4 into Rthe4 k ADCR5 sampling pin of MCUBased after ondifferential the above amplification. analysis, the The workflow current of value the systemof R1 and is presented,R2 is calculated as shown by MCU, in and the transmission line current is further calculated according to Equation (1). Finally, Figure 10. In the beginning, the voltage of C1 (Vin) is 0, the voltage-controlled LDO is the results are sent via the wireless communication module to realize the further function. turned off and the MCU is powered off, hence, the Q3 and Q4 are turned off. The system operatesWith energy in energy consumption, harvesting the mode. Vin drops The equivalentuntil it reaches circuit Vin_off is shown, then the in Figurevoltage 11-control. The CTled withLDO capacitance is turned off. compensation The MCU is sources out of energypower fromand the the Q transmission3 and Q4 are line.turned The off. full-bridge Then the system re-enters the energy harvesting mode, and the cycle repeats. In a time-multiplexed rectifier composed of diodes D1, D2, and body diodes of Q3 and Q4 converts the AC power cycle, the energy consumed by the sensor is: on the secondary side of CT to DC power, and stores the energy in C1. When the voltage of C1 reaches Vin_on, the voltage-controlled1 LDO22 is turned on and the MCU is powered. WCVV1  in_on  in_off (18) The MCU starts to operate and turns Q23 and Q4 on. At this point, the system is switched to the current measurement mode. The equivalent circuit is shown in Figure 12. Since R1 and R2 are much smaller than (jωLm + Rm), the current through R1 and R2 follows Equation (1). The voltage values of R1 and R2 are sensed and entered into the ADC sampling pin of MCU after differential amplification. The current value of R1 and R2 is calculated by MCU, and the transmission line current is further calculated according to Equation (1). Finally, the results are sent via the wireless communication module to realize the further function.

With energy consumption, the Vin drops until it reaches Vin_off, then the voltage-controlled LDO is turned off. The MCU is out of power and the Q3 and Q4 are turned off. Then the system re-enters the energy harvesting mode, and the cycle repeats. In a time-multiplexed cycle, the energy consumed by the sensor is:

1 W = C · V2 − V2 (18) 2 1 in_on in_off Energies 2021, 14, 1561 9 of 15 Energies 2021, 14, x FOR PEER REVIEW 9 of 15 Energies 2021, 14, x FOR PEER REVIEW 9 of 15 Energies 2021, 14, x FOR PEER REVIEW 9 of 15

The voltage- Q3 and Q4 are Energy harvest controlledThe voltage LDO- is Q3 andTurned Q4 offare The voltage- Energy harvest Q3 and Q4 are controlledturned LDO off is Energy harvest Turned off controlled LDO is Turned off turned off No turnedYes off No Yes No No Yes Start Vin > Vin_on Standby No Vin < Vin_off No Start Vin > Vin_on Standby Vin < Vin_off Start Vin > Vin_on Standby Vin < Vin_off Yes Yes The voltageYes - Calculating the line controlledThe voltage LDO- is Calculatingcurrent and the setting line The voltage- Calculating the line controlledturned LDO on is currentout andthe resultsetting controlled LDO is current and setting turned on out the result turned on out the result

Q3 and Q4 are Sensing the voltage MCU is powered Sensing the voltage Q3 andTurned Q4 onare of R1 and R2 MCU is powered Q3 and Q4 are Sensing the voltage MCU is powered Turned on of R1 and R2 Turned on of R1 and R2 Figure 10. The workflow of the system. Figure 10. The workflow workﬂow of the system. Figure 10. The workflow of the system. CT CT CT

iLm D1 D2 iLm iLm D1 D2 D1 D2 + + C1 + L R ip(t)/N m m Cr C1 Vin L R Q4 Q3C1 ip(t)/N m m Cr Vin ip(t)/N Lm Rm Cr Q3 V vQ4 Q4 vQ3 in Q4 Q3 vQ3 – vQ4 v vQ4 Q3 – –

R1 R2 R1 R2 R1 R2

Figure 11. The equivalent circuit of the system operating in energy harvesting mode. Figure 11. The equivalent circuit of the system operating in energy harvesting mode. Figure 11. The equivalent circuit of the system operating in energy harvesting mode. CT CT CT iLm i iLm Lm + + C1 + Voltage- i (t)/N Lm Rm C p r C1 Vin Voltagecontrolled- L R Q4 Q3C1 Voltage- ip(t)/N m m Cr Vin controlledLDO Power i (t)/N Lm Rm C p r Q4 Q3 Vin controlledLDO Powersupply Q4 Q3 LDO Power v vg3 – supply g4 supply vg4 vg3 –

vg4 vg3 – - Sampling

Differential R1 R2 + - Sampling

amplification R1 R2

Differential - Sampling

Differential + R1 R2 amplification + Power amplification Powersupply Data supplyPower supply Data Data vg3 Driver vg3 vg4 LoRa wireless module MCU vg3 Driver vg4 LoRa wireless module MCU Driver vg4 LoRa wireless module MCU Figure 12. The equivalent circuit of the system operating in current measurement mode. Figure 12. The equivalent circuit of the system operating in current measurement mode. FigureFigure 12.12. TheThe equivalentequivalent circuitcircuit ofof thethe systemsystem operatingoperating inin currentcurrent measurementmeasurementmode. mode.

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Energies 2021, 14, 1561 10 of 15

To verify the operation of the proposed time-multiplexed self-powered current sensor, the circuit is simulated by the PSIM 9 circuit simulation tool. The system parameters in theTo simulation verify the are operation consistent of the with proposed those of time-multiplexed the prototype, as self-powered shown in Table current 1. The sensor, sim- theulation circuit results is simulated are shown by thein Figure PSIM 9 13. circuit The simulation time interval tool. between The system each parameters time the system in the simulationenters the measurement are consistent mode with those varies of with the prototype, the transmission as shown line in current. Table1. TheIn other simulation words, resultsthe operating are shown frequency in Figure of 13 the. The sensor time is interval limited between by the eachtransmission time the system line current. enters The the measurementlarger the transmission mode varies line withcurrent, the the transmission higher the lineoperating current. frequency In other of words, the sensor the oper-. ating frequency of the sensor is limited by the transmission line current. The larger the transmissionTable 1. Parameters line current, of the prototype. the higher the operating frequency of the sensor. Symbol Parameter Value Table 1. Parameters of the prototype. Lm CT’s excitation inductance 27.5 H Symbol- CT’s Parameterairgap 0.1 Value mm

N Lm TurnsCT’s of CT excitation secondary inductance side 27.54000 H Cr - CompensationCT’s airgapcapacitor 368 0.1 mmnF N Turns of CT secondary side 4000 C1 Energy storage capacitor 1 mF Cr Compensation capacitor 368 nF R1R2 Sampling resistance 2 Ω C1 Energy storage capacitor 1 mF Q3QR41 R2 SamplingMOSFET resistance FDS6990AS 2 Ω D1DQ23 Q4 SchottkyMOSFET diode SD1206S040S2R0 FDS6990AS LDOD1 D2 Schottky- diodeSP6201EM5 SD1206S040S2R0-L-3-3 LDO - SP6201EM5-L-3-3 Vin_on - 4.8 V Vin_on - 4.8 V Vin_off - 3.3 V Vin_off - 3.3 V

Transmission line current Ip Transmission line current Ip

Vin Vin

Vg3, Vg4 Vg3, Vg4

VR1 + R2 VR1 + R2

(a) (b)

FigureFigure 13.13. TheThe simulationsimulation results results of of the the proposed proposed sensor. sensor. (a )(a The) The transmission transmission line line current current is 10 is A.10 ( bA). The(b) The transmission transmission line line current is 5 A. current is 5 A.

3.3. Wireless Communication Module ConsideringConsidering the geographical geographical environment environment of of transmission transmission line lines,s, wireless wireless communi- commu- nicationcation is isthe the best best alternative alternative to exchange to exchange data data with with the thesensor. sensor. LoRa LoRa is a long is a- long-range,range, lowlow-power,power, lowlow-bitrate,bitrate, wireless wireless telecommunications telecommunications system, system, promoted promoted as an as infrastructure an infrastruc- turesolutio solutionn for the for theInternet Internet of Things of Things [22] [22. LoRa]. LoRa is isvery very suitable suitable for for the the application application of thethe proposed sensor,sensor, forfor thethe lowlow powerpower consumptionconsumption cancan improveimprove thethe operatingoperating frequencyfrequency ofof the sensor, andand thethe longlong communicationcommunication distancedistance cancan effectivelyeffectively minimizeminimize thethe numbernumber ofof sensors in unit space.space. The wireless communication module adopts an efﬁcientefficient ISMISM BandBand RF spread spectrum chip sx1278. The operating frequency of the module is 410–441410–441 MHzMHz,, receiving sensitivity is up to −136 dBm, transmitting distance is 3km, and minimum transmission power is less than 10 mW.

Energies 2021, 14, x FOR PEER REVIEW 11 of 15

receiving sensitivity is up to −136 dBm, transmitting distance is 3km, and minimum trans- Energies 2021, 14, 1561 11 of 15 mission power is less than 10 mW.

4. Experimental Verification 4. ExperimentalA test bench Veriﬁcationis built to demonstrate the proposed current sensor, as shown in Figure 14a. ItA includes test bench a prog is builtrammable to demonstrate AC source the proposed with a ma currentximum sensor, output as showncurrent in ofFigure 20 A (5014a . Hz),It includes a sliding a programmable rheostat as AC AC resistor source load with, and a maximum an oscilloscope. output currentThe output of 20 of A the (50 Hz),AC sourcea sliding is used rheostat to simulate as AC resistor the transmission load, and an line oscilloscope. on the primary The outputside of ofCT. the To AC achieve source an is equivalentused to simulate of 100 the A transmissionmaximum primary line on thecurrent, primary 5 turns side ofare CT. wound To achieve on the an equivalentCT primary of side.100 A The maximum prototype primary of the current, proposed 5 turns sensor are is wound shown on in the Figure CT primary 14b. A side.Cortex The-M4 prototype micro- controllerof the proposed STM32F407 sensor is is used shown for incontrolling Figure 14 b.and A sampling. Cortex-M4 The microcontroller prototype parameters STM32F407 are is listedused forin Table controlling 1. and sampling. The prototype parameters are listed in Table1.

Oscilloscope CT

Simulative transmission line Sensor

Programmable AC source

(a) (b)

FigureFigure 14. 14. (a(a) )Test Test bench bench for for proposed proposed sensor. sensor. ( (bb)) Prototype Prototype of of the the proposed proposed current current sensor. sensor.

TheThe functions functions of of the the proposed proposed sensor sensor and and the the accuracy accuracy of of measurement measurement are are verified veriﬁed byby experiment experiments.s. The The programmable programmable ACAC source source generates generates standard standard sinusoidal sinusoidal signals signals with differentwith different amplitudes amplitudes to simulate to simulate transmission transmission line current. line current. Through Through the oscilloscope, the oscilloscope, the operatingthe operating condition condition of each of each part partof the of circuit the circuit can be can observed, be observed, and andthe accuracy the accuracy of current of cur- measurementrent measurement can be can evaluated be evaluated by the by thedata data transmitted transmitted via via the the wireless wireless communication communication modulemodule and and received received by by an an upper upper computer. computer. TheThe experimental experimental waveform waveform of ofthe the prototype prototype is shown is shown in Figure in Figure 15, the 15 ,primary the primary side currentside current is set to is set5 A to (Channel 5 A (Channel 1). The 1). time The intervals time intervals of the two of the patterns two patterns in Figure in Figure15 repre- 15 sentrepresent two operating two operating modes. modes. It can be It canseen be that seen the that sensor the sensoris operating is operating alternatively alternatively in en- ergyin energy harvesting harvesting mode modeand current and current measurement measurement mode. mode.In the energy In the energyharvesting harvesting mode, themode, voltage the of voltage the energy of the storage energy capacitor storage C capacitor1 (ChannelC 2)1 (Channelkeeps risin 2)g until keeps it risingreaches until Vin_on it (4.8reaches V). ThenVin_on the(4.8 system V). Then enters the the system current enters measurement the current mode. measurement It can be mode. seen from It can the be enlargedseen from view the enlarged that in the view current that in measurement the current measurement mode, the output mode, thevoltage output of voltage the LDO of (Channelthe LDO 3) (Channel is 3.3 V, 3)which is 3.3 powers V, which other powers modules. other The modules. ADC samp The ADCling pin sampling signal pin(Channel signal 4)(Channel is a sine 4)wave is a sinewith wave DC offset, with DCthe offset,phase thelags phase the primary lags the current primary by current 90 degrees, by 90 and degrees, the amplitudeand the amplitude of the sine of wave the sine is directly wave is directlyproportional proportional to the CT to primary the CT primary side current side currentvalue. Aftervalue. sensing After sensing the amplitude the amplitude value of value the sine of the wav sinee, the wave, MCU the calculates MCU calculates the current the current value ofvalue the CT of the primary CT primary side and side sends and sendsout the out results. the results. In the In current the current measurement measurement mode, mode, en- energy is continuously consumed and the voltage of C drops until it reaches V (3.3 V), ergy is continuously consumed and the voltage of C1 1drops until it reaches Vin_offin_off (3.3 V), thenthen the the system system re re-enters-enters the the energy energy ha harvestingrvesting mode, mode, the the next next cycle cycle begins. begins. The The power power thethe measurement measurement module module requires requires while while it is it operating is operating is 50.4 is 50.4mW. mW.The period The period of the oftime the- multiplexedtime-multiplexed cycle is cycle about is about1.06 s, 1.06 and s, the and average the average power power consumption consumption of the of sensor the sensor esti- matedestimated by Equation by Equation (18) (18)is 5.7 is mW 5.7 mW.. The sensor works in time-multiplexed mode, the working frequency of the sensor varies with the transmission line current. The time interval between the measurements against the transmission line current is shown in Figure 16. It can be seen that the time interval reducing as the line current increases. By extending the time interval, the sensor can

Energies 2021, 14, 1561 12 of 15

adapt itself to a minimum line current of 1 A, at the expense of a low operating frequency. In this condition, the average power consumption of the sensor is 0.84 mW. Each time the sensor enters the current measurement mode, the upper computer can receive the data sent by the LoRa wireless communication module of the sensor. The data Energies 2021, 14, x FOR PEER REVIEW 12 of 15 is the measured primary current value, which is calculated by the MCU. The actual current values and the measured results are shown in Table2.

Energy Harvesting Current Measurement

t: 500 ms/div

Channel 1

ip: 10 A/div Channel 2

UC1: 5 V/div

Channel 3 ULDO_out: 5 V/div

Channel 4

UADC_pin: 2 V/div t: Enlarged t: 50 ms/div

Channel 1 ip: 5 A(RMS)

UC1: 4.8 V 3.3 V Channel 2

Channel 3 LDO output voltage: 3.3 V

Channel 4 ADC sampling pin voltage t:

FigureFigure 15. 15.Time-multiplexed Time-multiplexed waveform waveform of of the the prototype. prototype.

TheThe experimental sensor works current in time measurement-multiplexed mode, range ofthe the working sensor frequency is 1–100 A. of In the Table sensor2, thevaries actual with value the istransmission the constant line current current. output The oftime the interval AC source. between The the measured measurements value isagain the currentst the transmission value calculated line current by the is sensor. shown Toin Figure reduce 16. the It deviation can be seen caused that the by thetime toleranceinterval ofreducing components, as the linear line current ﬁtting ofincreases. data is carried By extending out by using the time OriginPro interval (OriginLab,, the sensor Northhampton MA, USA). The measured values and the actual values are used for the can adapt itself to a minimum line current of 1 A, at the expense of a low operating fre- linear ﬁtting. The empirical expression and the correlation factor are: quency. In this condition, the average power consumption of the sensor is 0.84 mW. y = 1.0121x − 0.076 (19) R2 = 0.99997

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The equation represents that the measured current value (i.e., the fitted value) obtained by the device is x when the actual current value is y. The error in Table2 is the difference between the fitted value and the actual value. And a total range (100 A) is the basis for estimating the errors. Therefore, the error in Table2 is the absolute error over the max current range. It can be seen that, within the designed current measurement range, the absolute error is within 0.5%, which demonstrates the current measurement accuracy of the proposed time-multiplexed self-powered wireless current sensor. For the parameters of the measurement circuit and the specification of CT are designed for the maximum current measurement range of 100 A, the relative error at low current is relatively high, which is the content that needs further optimization in the future. Table3 summarizes the performance of the self-powered current sensor in comparison with the previous literature. Compared Energies 2021, 14, x FOR PEER REVIEWto the previous CT-fed current sensor [15,16,18], the proposed sensor can work under lower13 of 15

line current and achieve smaller measurement error and shorter measurement interval.

FigureFigure 16. 16.The The time time interval interval between between the the measurements measurements against against the the transmission transmission line line current. current.

EachTable time 2. Calculated the sensor primary enters sidethe currentcurrent (unit: measurement A). mode, the upper computer can receive the data sent by the LoRa wireless communication module of the sensor. The data Time Interval per Actual Value Measuredis the Value measured primary Fitted Valuecurrent value, Error which (Error/Total is calculated Range) by the MCU. The actual cur- Measurement (s) rent values and the measured results are shown in Table 2. 1 0.92 0.85 0.15% 7.2 5Table 4.98 2. Calculated primary 4.96 side current (unit: A). 0.04% 1.06 10 9.87 9.91 0.09% 0.62 20 19.94 20.10 0.10%Error (Error/Total Time 0.37 Interval per Actual Value Measured Value Fitted Value 30 29.84 30.12 0.12%Range) Measurement 0.29 (s) 40 39.73 40.14 0.14% 0.25 50 49.631 0.92 50.16 0.85 0.16%0.15% 0.227.2 60 59.395 4.98 60.03 4.96 0.03%0.04% 0.211.06 80 78.7610 9.87 79.64 9.91 0.36%0.09% 0.190.62 100 98.9820 19.94 100.10 20.10 0.10%0.10% 0.180.37 30 29.84 30.12 0.12% 0.29 40 Table 3.39.73Performance comparison.40.14 0.14% 0.25 50 49.63 50.16 0.16% 0.22 Minimum Operating Number of CT Measurement Interval Literature Measuring Error Current60 59.39Secondary Coils60.03 0.03% (line Current:0.21 10 A) 80 78.76 79.64 0.36% 0.19 [16], Year 2019 20 A 1 <2.5% - [18], Year 2019 5 A100 98.98 2100.10 Not mentioned0.10% 8 s0.18 [15], Year 2015 0.8 A 1 <10% >60 s This work 1The A experimental current 1 measurement range <0.5% of the sensor is 1–100 A. 0.62 In sTable 2, the actual value is the constant current output of the AC source. The measured value is the current value calculated by the sensor. To reduce the deviation caused by the tolerance of components, linear fitting of data is carried out by using OriginPro (OriginLab, Northhampton MA, USA). The measured values and the actual values are used for the linear fitting. The empirical expression and the correlation factor are: yx1.0121 0.076  2 (19) R  0.99997 The equation represents that the measured current value (i.e., the fitted value) obtained by the device is x when the actual current value is y. The error in Table 2 is the difference between the fitted value and the actual value. And a total range (100 A) is the basis for estimating the errors. Therefore, the error in Table 2 is the absolute error over the max current range. It can be seen that, within the designed current measurement range, the absolute error is within 0.5%, which demonstrates the current measurement accuracy of the proposed time-multiplexed self-powered wireless current sensor. For the parameters of the measurement circuit and the specification of CT are designed for the maximum current measurement range of 100 A, the relative error at low current is relatively high, which is the content that needs further optimization in the future. Table 3 summarizes the

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5. Conclusions In this paper, a time-multiplexed self-powered wireless current sensor for power transmission lines is proposed and demonstrated. Two operating modes of CT, including the current sensing mode and the energy harvesting mode, are analyzed in detail. The current sensing function and the energy harvesting function of CT are integrated, the sensor can be self-powered while measuring line current. The mode-switching circuit is designed to isolate the harvesting circuit and the measurement circuit, which eliminates the interference between energy harvesting and current measurement. The accurate current measurement and the maximum energy collection are realized through only one CT secondary coil instead of two coils, which simpliﬁes the design of OCMS. The designed time-multiplexed working mode allows the sensor to work at a lower transmission line current, at the expense of a lower operating frequency. The functions of the proposed sensor are veriﬁed by the experiment. The experimental results demonstrate that the sensor can work at a minimum line current of 1 A with 0.84 mW power consumption. And when the transmission line current is within the range of 1 A–100 A, the proposed sensor can operate and measure line current stably. Compared to the previous CT-fed current sensor, the proposed sensor can work under a lower transmission line current and achieve smaller measurement error and shorter measurement interval.

Author Contributions: Conceptualization, H.C. and J.W.; data curation, H.C.; software, C.L.; vali- dation, H.C. and Z.Q.; formal analysis, H.C.; investigation, H.C. and Z.Q.; writing—original draft preparation, H.C.; writing—review and editing, H.C., Z.Q. and J.W.; visualization, C.L.; supervision, J.W., W.L. and X.H.; funding acquisition, X.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded in part by the National Key Research and Development Program of China under Grant 2017YFE0112400 and in part by the National Natural Science Foundation of China, under Grant U1834205. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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