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In dual traction power supply systems, the overhead catenary system operates in different power supply modes. It passes across the AC section, DC section, and a neutral part, which influences the features and properties of the feedback current and aggregates its effects on stray current and rail potential. This research paper presents an integrated model of an AC and DC traction power system (TPS), along with a unified chain equivalent circuit model, the ground wire through the AC section, and the insulation joints fixed in the AC–DC neutral section under different operating positions. To make a unified impedance and admittance matrix for traction network, a virtual conductor wire has been added in the DC section to make the balance order of the TPS. The influence of reflex system configuration on rail potential, stray current, and distribution of rail potential at AC and DC stations has also been calculated. The simulation results demonstrate that establishing the insulation joints in the AC–DC section and using ground wires in the AC part can significantly decrease the stray current and rail potential. [ABSTRACT FROM AUTHOR]

Objective In the DC (direct current) traction power supply system of urban rail transit, excessive rail potential and stray current issues are persistent problems and common ailments for operational routes. Therefore, it is necessary to summarize and generalize the rail potential suppression technology in urban rail transit running rail circuit return system. Method Based on the situation and prominent issues of rail potential and stray current in operational lines in China, starting from the mechanism of DC traction power supply system return flow, the main factors affecting rail potential in the system are sorted. A rail potential suppression technology is introduced, some methods for suppressing overvoltage generation are compared and analyzed, such as parallel resistors, parallel capacitors, and incorporating locking current logic protection set values. Technical solutions for the novel rail potential limitation device with linked shielding doors, the intelligent stray current suppression type rail potential limitation device using IGBT (insulated gate bipolar transistor), and the flexible topology rail potential limitation device are presented. Result & Conclusion By implementing power electronic full-power converter topological units, the dynamic and flexible control of rail-to-ground voltage and current demonstrates a highly promising remedial measure for future comprehensive control of rail potential and stray current in running rail circuit return system. During the line design phase requirements of different systems, rail potential reduction can be met by increasing traction voltage, optimizing traction spacing, reducing longitudinal track resistance, and eliminating direct grounding of running rails in depot garages. Additionally, complete isolation of electrical systems between mainlines and depots and between different lines is also an important measure to suppress rail potential.

[Objective] In the DC (direct current) traction power supply system of urban rail transit, excessive rail potential and stray current issues are persistent problems and common ailments for operational routes. Therefore, it is necessary to summarize and generalize the rail potential suppression technology in urban rail transit running rail circuit return system. [Method] Based on the situation and prominent issues of rail potential and stray current in operational lines in China, starting from the mechanism of DC traction power supply system return flow, the main factors affecting rail potential in the system are sorted. A rail potential suppression technology is introduced, some methods for suppressing overvoltage generation are compared and analyzed, such as parallel resistors, parallel capacitors, and incorporating locking current logic protection set values. Technical solutions for the novel rail potential limitation device with linked shielding doors, the intelligent stray current suppression type rail potential limitation device using IGBT (insulated gate bipolar transistor), and the flexible topology rail potential limitation device are presented. [Result & Conclusion] By implementing power electronic full-power converter topological units, the dynamic and flexible control of rail-to-ground voltage and current demonstrates a highly promising remedial measure for future comprehensive control of rail potential and stray current in running rail circuit return system. During the line design phase requirements of different systems, rail potential reduction can be met by increasing traction voltage, optimizing traction spacing, reducing longitudinal track resistance, and eliminating direct grounding of running rails in depot garages. Additionally, complete isolation of electrical systems between mainlines and depots and between different lines is also an important measure to suppress rail potential. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Railway Science & Engineering is the property of Journal of Railway Science & Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Objective The data of various monitoring points regarding rail potential as monitoring object is correlated in time and space, and the direct manifestation of changes in rail-to-rebar structural resistance is reflected in rail potential variation. It is aimed to explore a method for monitoring the rail-to-ground insulation state and diagnosing defects based on rail potential spatiotemporal correlation. Method The stray current monitoring system with rail potential as the monitoring object is elaborated. The characteristics of rail potential data under insulation defects are analyzed and a feature matrix for the data is established. Based on the anomaly detection principle of Minkowski distance, the detection steps for abnormal sections of rail-to-ground insulation and for insulation defect locationing are explained. A project in Qingdao Rail Transit is taken as study case for modeling and simulation to evaluate the effectiveness and accuracy of the proposed method. Result & Conclusion The proposed method can effectively monitor the rail insulation state and accurately locate insulation defects.

Abstract In dual traction power supply systems, the overhead catenary system operates in different power supply modes. It passes across the AC section, DC section, and a neutral part, which influences the features and properties of the feedback current and aggregates its effects on stray current and rail potential. This research paper presents an integrated model of an AC and DC traction power system (TPS), along with a unified chain equivalent circuit model, the ground wire through the AC section, and the insulation joints fixed in the AC–DC neutral section under different operating positions. To make a unified impedance and admittance matrix for traction network, a virtual conductor wire has been added in the DC section to make the balance order of the TPS. The influence of reflex system configuration on rail potential, stray current, and distribution of rail potential at AC and DC stations has also been calculated. The simulation results demonstrate that establishing the insulation joints in the AC–DC section and using ground wires in the AC part can significantly decrease the stray current and rail potential.

[Objective] The data of various monitoring points regarding rail potential as monitoring object is correlated in time and space, and the direct manifestation of changes in rail-to-rebar structural resistance is reflected in rail potential variation. It is aimed to explore a method for monitoring the rail-to-ground insulation state and diagnosing defects based on rail potential spatiotemporal correlation. [Method] The stray current monitoring system with rail potential as the monitoring object is elaborated. The characteristics of rail potential data under insulation defects are analyzed and a feature matrix for the data is established. Based on the anomaly detection principle of Minkowski distance, the detection steps for abnormal sections of rail-to-ground insulation and for insulation defect locationing are explained. A project in Qingdao Rail Transit is taken as study case for modeling and simulation to evaluate the effectiveness and accuracy of the proposed method. [Result & Conclusion] The proposed method can effectively monitor the rail insulation state and accurately locate insulation defects. [ABSTRACT FROM AUTHOR]

As the quick advancement of urban rail transit, the power supply safety is gradually receiving attention. In the direct-current traction power supply system, the abnormal increase in rail potential is very significant, seriously affecting the regular working of the system. Therefore, to address the above issues, the mechanism of abnormal increase in rail potential is explored, and genetic algorithms are applied to optimize the power distribution of the system. The simulation results show that when the starting threshold is 1600 V, the highest value of the rail potential is only about 40 V, which is reduced by about 70 V compared to the other thresholds of 1800 V. When two trains are running in the system, as the travel time of Train 2 increases, the cross-zone transmission current gradually increases to around 1100 A. And the rail potential first decreases and then increases to over 90 V. It can be seen that the power distribution situation has a significant impact on the rail potential. After genetic algorithm optimization, the peak potential of the rail is only 66.2 V, with a decrease of 40.3%. The regenerative braking power allocated by the upstream regenerative braking train Cs1 to the accelerating train Cs2 decreases to 2703.5 kW, with a decrease of 35.6%. In addition, the regenerative braking power allocated by the Cx 1 regenerative train to the accelerated train Cx 2 is 2738.7 kW, which is at least 35.6% lower than before optimization. The above results indicate that the power distribution situation has a significant impact on the abnormal increase of rail potential. And optimizing the power distribution situation through genetic algorithm can effectively avoid the abnormal increase of rail potential.

In areas where urban tracks are used as public transportation, dynamic stray currents cause high maintenance costs for the tracks and metal structures near the tracks. S tray currents caused by rail vehicles depend on many factors (traffic density, vehicle speed, acceleration and deceleration, soil and track moisture), so it is very difficult to get a clear picture of the harmfulness of the stray current based on the results of a single field measurement. However, there are several measurement methods that can be used to determine the presence of stray currents and predict appropriate track maintenance actions. Some of these methods are described in this article, namely the use of stray current mapper, measurement of rail potential and rail current, measurement at the stray current collection system, and the use of non-destructive sensors. In track construction, measuring the electrical potential between rail and ground is one of the most common methods of detecting the damaging influence of stray current.

Featured Application: This work belongs to the field of railway electrification engineering. The results have certain reference value for reducing the rail potential to ensure the safe operation of electrified railways. For high-speed railways, the rail potential, i.e., the electrical potential difference between the rail and the ground, can be considerably higher than that of conventional speed electric railways and become a safety risk to the signaling devices along the line, because of the large train currents and the high rail–ground leakage resistance. Proper countermeasures must be taken to decrease the rail potential to a safe level. This paper first provides a brief theoretical discussion of the principles of how the rail potential arises and how to suppress it. Then, a program, TRANAS, that was developed for traction network analysis is used to calculate the effects of various suppression countermeasures for an AT feeding system, which include cross-bonding of tracks, inserting CPWs, grounding using catenary masts, laying bare buried ground wires and connecting to dedicated grounding grids, which are evaluated based on the calculation results. The use of buried ground wires shows good prospects for solving electric safety problems in an integrated way, which is investigated in detail. The fact that GWs can suppress the rail potential is attributed to the decrease in the leakage resistance of the return circuit, meaning a relatively small cross-section will be enough for them. [ABSTRACT FROM AUTHOR]

The NEG-ETP system that providing zero resistance closed circuit reducing the reverse path of current on the running rail is presented in this article. The NEG-ETP system is created by installing additional electronics in conventional electrical systems. Without modifying trains, tracks, or tunnels. Using MATLAB program through models for MRT purple line (North), rail potential and stray current are assessed in accordance with EN 50122 standards of all three systems, including CON-ETP, REC-ETP, and NEG-ETP. According to the simulation, the percentage reduction of the rail potential was 9.14% when the REC-ETP versus the CON-ETP system was 32.99% when the NEG-ETP system compared to the CON-ETP system and 26.25% when the NEG-ETP system versus the REC-ETP system could be seen in this negative resistance converter system, which can reduce the cost of rails and leakage currents in the DC system. It can also be applied to new rail transport.

In areas where urban tracks are used as public transportation, dynamic stray currents cause high maintenance costs for the tracks and metal structures near the tracks. Stray currents caused by rail vehicles depend on many factors (traffic density, vehicle speed, acceleration and deceleration, soil and track moisture), so it is very difficult to get a clear picture of the harmfulness of the stray current based on the results of a single field measurement. However, there are several measurement methods that can be used to determine the presence of stray currents and predict appropriate track maintenance actions. Some of these methods are described in this article, namely the use of stray current mapper, measurement of rail potential and rail current, measurement at the stray current collection system, and the use of nondestructive sensors. In track construction, measuring the electrical potential between rail and ground is one of the most common methods of detecting the damaging influence of stray current. [ABSTRACT FROM AUTHOR]

Copyright of Railway Signalling & Communication Engineering is the property of Railway Signalling & Communication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

For high-speed railways, the rail potential, i.e., the electrical potential difference between the rail and the ground, can be considerably higher than that of conventional speed electric railways and become a safety risk to the signaling devices along the line, because of the large train currents and the high rail–ground leakage resistance. Proper countermeasures must be taken to decrease the rail potential to a safe level. This paper first provides a brief theoretical discussion of the principles of how the rail potential arises and how to suppress it. Then, a program, TRANAS, that was developed for traction network analysis is used to calculate the effects of various suppression countermeasures for an AT feeding system, which include cross-bonding of tracks, inserting CPWs, grounding using catenary masts, laying bare buried ground wires and connecting to dedicated grounding grids, which are evaluated based on the calculation results. The use of buried ground wires shows good prospects for solving electric safety problems in an integrated way, which is investigated in detail. The fact that GWs can suppress the rail potential is attributed to the decrease in the leakage resistance of the return circuit, meaning a relatively small cross-section will be enough for them.

Copyright of Railway Standard Design is the property of Railway Standard Design Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

By the field investigation of the metro system, it is found that there is relatively serious corrosion in the terminal of the metro line, and overvoltage protection device (OVPD) often operates when the metro system is in the valley level. In order to analyze the causes of these conditions and alleviate the related problems caused by high rail potential. In this paper, establish a simulation model of metro system by CDEGS software, and consider the influence of the track-to-track cross bond on rail potential. It is analyzed that the causes of high rail potential in the terminal of the metro line and high rail potential operating small number of trains in the metro line. And it is analyzed that the influence on the rail potential of metro line, the influence on OVPD outside the power supply section, the influence on the station grounding gird where the OVPD is, caused by OVPD operation. The results show that the rail potential can be reduced to some extent by setting the track-to-track cross bond. No traction power substation (TPS) in the terminal of the metro line increases the rail potential. When the braking train supplies power to the accelerating train outside the power supply section in the metro line, the rail potential of some part of the line increases. The OVPD operation increases the ground potential around the station grounding gird, and may lead to the continuous operation of other OVPD in the metro line.

Rails are a part of track structure where corrosion process inevitably occurs, except if they are fully insulated and devoid of contact with any other part of the structure (sleepers, fastening accessories) or electrolyte like moist soil or water in track structure. Corrosion occurs much faster in the presence of stray currents, which very soon results in the loss of material at the rail foot. The paper presents an overview and description of parameters influencing stray current levels, such as electrical potential in rail and longitudinal rail conductivity, rail-to-earth electrical resistance, electrical conductivity of load-bearing concrete layers of truck structure, and electrical conductivity of soil.

The calculation of rail potential and stray current in the DC traction power system can guide the protection against the rail overvoltage problem and mitigate the electrolytic corrosion due to stray current. To obtain the accurate stray current distribution, the infinitesimal method based calculation of metro stray current in multiple power supply sections (PPSs) is studied in this paper. The through-type structure characteristics of power supply system and that of return current system which is constituted of rails - stray current collection mats - tunnel reinforcements - ground (RSTG) are considered in the proposed calculation method. In the traction power supply system, the currents injected into the rail by train, and absorbed by traction power substation (TPS) or regeneratively braking train, are solved by the power flow calculation which considers stray current. In the return current system, these currents are used as the boundary conditions for stray current calculation. Then the rail potential and stray current in multiple PPSs are solved by the infinitesimal method. The verification result shows that the proposed calculation method can effectively calculate the rail potential and stray current in multiple metro PPSs. At last, the novel calculation method is used to gain the dynamic stray current along the metro line and evaluate the influence factors of stray current.

The paper presents a new, unconventional energy harvesting (EH) method for supplying low-power devices on electrified railway lines that utilises stray currents and the non-zero potential of the rails to the ground. The EH device gathers the energy and stores it in batteries. It could even work in extremely unfavourable weather conditions and could be easily placed in almost any location. The presented real-life data show that the average available power is less than 250 mW and the average useful power is about 100 mW. This is enough to supply ultra-low power microcontrollers, which only occasionally use energy-consuming modules to perform measurements or communicate. The disadvantage of the EH method is the introduction of resistance between the rail and the earth, which increases stray currents and could increase the electrochemical corrosion of the rail. To reduce the impact of this resistance, a method for balancing the flowing charge is proposed. After balancing, the average of the flowing current is zero and electrochemical corrosion should be reduced. The proposed charge balancing algorithms could reduce the unbalanced charge to nearly zero at the expense of energy gathering efficiency, which decreases by 20–40%.

The paper presents results of a stray current assessment study performed for MRT Purple Line in Bangkok, Thailand. Factors of interest in the study are a rail-to-earth conductance per unit length and rail potential. A grounding system model is developed in MATLAB/Simulink using electrical resistances of track composite materials. From the simulation results, both conductance per unit length and rail potential comply with the European Standard EN 50122 for all viaduct structures and track configurations even in absence of stray current collector system. [ABSTRACT FROM AUTHOR]

• Measurements are performed on P60 rail over an extended frequency range (50 Hz to nearly 3 kHz) at 20A currents, so that skin effect phenomena are clearly visible. The parameters of the P60 rail equaled to a tubular conductor model are determined. • A foster equivalent circuit of the rail considering the skin effect is constructed. Measure P60 rail in the extended current amplitude range (100A to nearly 600A 50 Hz), the correctness of the model is verified by finite element method and measured results. The DTS's structure is decoupled in the reflux system model. • The simulation models of the reflux system are built. Compared with the equivalent DC resistance and the 1st-order RL circuit of rail, the simulated rail potential by the foster equivalent circuit is closer to reality. The model can also more accurately predict the actual operation of OVPD. Compared with the equivalent the 1st-order RL circuit and DC resistance, the rail potential results of the modified equivalent circuit of the reflux system are significantly improved. • The dynamic simulation model included the cases of multi-trains, multi-stations, and OVPD actions is applied. The current injected into the rail contains is rich in 1 ∼ 50 Hz components and some sextuple harmonic components. Due to the skin effect of the rail and rail impedance frequency characteristics, the sextuple harmonic current component has a hazardous impact on rail potential. The simulation results of the DTS can accurately predicate the rail potential. The existing simulation of rail potential only considers the equivalent DC resistance and 1st-order RL circuit of a rail. However, the rail current contains a large number of harmonic components, which greatly affects the calculation of rail potential. To accurately calculate the rail potential, the rail is equivalent to a tubular conductor considering the skin effect. The improved equivalent circuit of reflux system is established by vector fitting method (VF), and the 8th-order foster equivalent circuit of rail is built. The dynamic simulation model considering multi-trains, multi-stations, and over voltage protection device (OVPD) actions is established. By measuring the actual internal impedance of the rail, the parameters of the equivalent tubular conductor model of the rail are fitted with the least square method. The maximum error between VF method and finite element simulation, field test results is 6.531%, and 7.271%, respectively. Compared with the equivalent of the 1st-order RL circuit and DC resistance, the rail potential results of the modified model are significantly improved, the rail potential is evaluated more accurately. [ABSTRACT FROM AUTHOR]

Running rails used as a return conductor and ungrounded scheme have been widely adopted in DC traction power systems. Due to the longitudinal resistance of running rails and insulation resistance of rail-to-ground, there will be a potential rise between running rails and the ground when return current flows through the running rails, which is known as rail potential. At present, abnormal rise of rail potential exists widely in DC traction power systems. The present rail potential model still cannot simulate and explain the abnormal rail potential in the system. Based on the analysis of power distribution with multiple trains running in multiple sections, a dynamic simulation model of rail potential in the whole line is proposed. The dynamic distribution of rail potential and stray current in DC traction power systems when multiple trains run in multiple sections is analyzed, and the impact of traction current distribution on rail potential is evaluated. Simulation results show that the abnormal rise of rail potential during the dynamic operation of the system can be evaluated effectively. [ABSTRACT FROM AUTHOR]

Direct current (DC) traction power systems are widely used in metro transport systems, with running rails usually being used as return conductors. When traction current flows through the running rails, a potential voltage known as “rail potential” is generated between the rails and ground. Currently, abnormal rises of rail potential exist in many railway lines during the operation of railway systems. Excessively high rail potentials pose a threat to human life and to devices connected to the rails. In this paper, the effect of regenerative power distribution on rail potential is analyzed. Maximum safety regenerative power tracking is proposed for the control of maximum absolute rail potential and energy consumption during the operation of DC traction power systems. The dwell time of multiple trains at each station and the trigger voltage of the regenerative energy absorbing device (READ) are optimized based on an improved particle swarm optimization (PSO) algorithm to manage the distribution of regenerative power. In this way, the maximum absolute rail potential and energy consumption of DC traction power systems can be reduced. The operation data of Guangzhou Metro Line 2 are used in the simulations, and the results show that the scheme can reduce the maximum absolute rail potential and energy consumption effectively and guarantee the safety in energy saving of DC traction power systems.

Summary as part of the correct operation of any electrical system it is necessary to guarantee the safety of the persons and the equipment or elements that constitute the system; therefore, the electrical traction systems must be furnished with a grounding system that takes into account their particularities and differences with regard to other electrical systems. This paper proposes a generalized multi-train model to simulate the behavior of the rail voltage and the stray currents in the grounding system, based on equivalent circuit models, processing the instantaneous power obtained from a multi-train DC transport systems electrical demand simulator. [ABSTRACT FROM PUBLISHER]

The ungrounded scheme with overvoltage protection device (OVPD) has been adopted in the construction of Nanjing Metro Line 1. During the operation of Line 1, a high rail potential was observed, which caused the OVPDs installed at some traction supply substations (TSSs) to keep turning on at any moment, and the stray-current leakage increased obviously. Since the magnitude of rail potential and stray current depends on the modes of a running vehicle, including accelerating, coasting, constant speed, or braking, Line 1 suspected that the vehicle running modes were the cause of a potential rise in the rail. This paper presents the results of field tests and numerical simulations to study whether different vehicle running modes have an impact on rail potential and stray current in Line 1. The results show that the rail potential in the acceleration and brake modes is significantly higher than that in the other modes, which are in the opposite direction. Moreover, within the stray-current interference, the maximum shifts of buried-conductor potential may exceed the limit in these two modes. In addition, the high rail potential and buried-conductor potential occur when the running mode changes from acceleration to coasting or the maximum brake power is reached. As a vehicle is running between two different TSSs, the rail potential is highest in its position. [ABSTRACT FROM PUBLISHER]

The diode-grounded scheme for stray-current collection in some systems, such as the Taipei rapid transit systems (TRTS), has been constructed to gather the stray current leaking from the running rails and avoid corrosion damage to the system as well as the surrounding metallic objects. During operation of the TRTS, a high potential between the negative return bus and system earth bus at traction substations, referred to as rail potential, has been observed on the Blue line between BL13 and BL16. Since the Blue and Red-Green lines have their running rails and stray-current collector mats in junction at the G11 station, the TRTS suspects that the impedance bond at G11 is the cause of rail potential rise. This paper presents the results of field tests for studying whether the impedance bond at G11 of the tie line has an impact on rail potential and stray currents in TRTS. The results show the rail potential can be reduced by disconnecting the impedance bond at G11 of the tie line so that the negative return current of the Blue line cannot flow to the rails of the Red-Green Line, and vice-versa. In addition, rail potential and stray currents occurring at a station of the Blue line are numerically simulated by using a distributed two-layer ladder circuit model. The simulation results are compared with the field-test results and they are consistent with each other. [ABSTRACT FROM AUTHOR]

This article presents the effects of different grounding strategies (ungrounded, direct grounded, and diode grounded), bonding, and insulation on rail potential and stray currents in the Taipei rapid transit systems (TRTSs). The TRTS is a direct current transit railway and its running rails are used as the return conductor for traction currents. The advantage is that no dedicated return conductor is required, whereas the disadvantages are rail potential and stray-current problems. Thus, the analysis of grounding strategies is important and necessary. Moreover, the effects of cross-bonding of the running rails and stray-current collector cables (traction earth conductors) are investigated since bonding is usually used to balance traction negative return currents, to reduce resistances of the negative return circuit, aswell as to decrease rail potential. Meanwhile, the effects of insulation on stray currents are also described. Simulation results for the Blue line are presented in TRTS. [ABSTRACT FROM AUTHOR]

This paper studies the effects of different grounding strategies, including ungrounded, solidly grounded, and diode grounded on rail potential and stray currents in the Taipei Rail Transit Systems (TRTS). The TRTS is a dc transit railway and the running rails are used as the return conductor for traction currents. The advantage is that no dedicated return conductor is required while the disadvantages are rail potential and stray current problems. Thus, the analysis of grounding strategies is important and necessary. Sample simulation results for the red line between Tamshui (R33) and Chuwei (R31) stations are presented. [ABSTRACT FROM AUTHOR]

The paper presents a new, unconventional energy harvesting (EH) method for supplying low-power devices on electrified railway lines that utilises stray currents and the non-zero potential of the rails to the ground. The EH device gathers the energy and stores it in batteries. It could even work in extremely unfavourable weather conditions and could be easily placed in almost any location. The presented real-life data show that the average available power is less than 250 mW and the average useful power is about 100 mW. This is enough to supply ultra-low power microcontrollers, which only occasionally use energy-consuming modules to perform measurements or communicate. The disadvantage of the EH method is the introduction of resistance between the rail and the earth, which increases stray currents and could increase the electrochemical corrosion of the rail. To reduce the impact of this resistance, a method for balancing the flowing charge is proposed. After balancing, the average of the flowing current is zero and electrochemical corrosion should be reduced. The proposed charge balancing algorithms could reduce the unbalanced charge to nearly zero at the expense of energy gathering efficiency, which decreases by 20–40%. [ABSTRACT FROM AUTHOR]