Abstract: To ensure the safety of urban rail transit, the detection and protection against stray currents in steel reinforcement bars near corroded rails has become essential. The complex environment makes direct detection of stray currents difficult. Therefore, this paper delves into the mechanism of stray current corrosion, derives theoretical formulas for stray current distribution using circuit theory, and establishes a discrete power supply theoretical model. Based on the distribution law of stray currents, the various parameters affecting stray currents are analyzed, and an effective distributed stray current monitoring model for rail transit based on power supply sections is designed. Keywords: Stray Current; Distribution; Mass Transit; Monitor System Abstract: In order to protect the Urban Mass Transit, it was necessary to check and defend the stray current which rusted the reinforcing steel bar of the building near the railway. It was difficult to monitor the stray current directly on complicated environment, so the paper researched deeply on the principle of the stray current corrosion, the theory formula of stray current distribution was deduced by applying circuit net theory, and the discrete supply theory model was established. According to the distribution rule of the stray current, analyzing the different parameters of the stray current, a distributed and effective stray current monitoring model of urban mass transit based on a power supply zone was designed. Keywords: Stray Current; Distribution; Mass Transit; Monitor System 1 Introduction At present, the traction mode of urban rail transit in China is electric traction, and most of them are DC power supply. The traction substation supplies power to the train through the contact network (overhead line or contact rail) [1], and the power flows back to the substation through the running track. It is difficult to completely insulate the rails of underground tunnels or roads from the ground, so that some of the traction current leaks from the rails into the ground and then flows back to the traction substation. The larger the traction current in the running rails or the worse the insulation of the rails from the ground, the larger the current leaked into the ground. The current is stray current [2], also known as stray current. The stray current corrodes the steel bars in the rails and nearby buildings, causing safety hazards. Moreover, due to the complex environment of stray current, it cannot be directly detected. Therefore, this paper studies the stray current mechanism, uses circuit theory to derive a stray current monitoring model, and designs a monitoring system to protect the safety of rail transit. 2 Discrete power supply system model Although the stray current flows back through the ground and cannot be directly measured, the similarity of the current rail transit driving mode can help find certain patterns. The train has to go through acceleration, constant speed, deceleration and braking between each station. The length of each section is different, which makes the load change. At the same time, the geological conditions of each section are different, so it is impossible to derive a more accurate theoretical formula for stray current leakage. Most of the empirical formulas currently used are derived from current theory and use approximate estimates, resulting in relatively low monitoring accuracy. If cross-regional power supply is not allowed in each power supply section, and stray currents are restricted to a single section, the mutual influence between them is very small, or even non-existent. This reduces the difficulty of studying stray currents. Based on this, deriving a stray current model requires two assumptions to simplify the problem: 1) The resistance between the track and the drainage network is only caused by the insulating rubber mat and is completely insulated at other locations; 2) The track and the drainage network have no electrical connection with the outside world. These two assumptions also provide a theoretical basis for the monitoring and protection of stray current corrosion in subways. These assumptions simplify the complex continuous spatial field into a discrete planar circuit. According to the dual-sided DC power supply in the power supply section, a discrete model of stray current can be established, and its equivalent circuit is shown in Figure 1. [align=center] Figure 1 Discrete model of subway traction power supply system[/align] According to the circuit diagram, mesh equations can be established. Taking U0=0, a matrix of voltage equations for each node can be formed, and the voltage at each point can be easily solved, as shown in Figure 2. To facilitate the solution of various currents, it is uniformly stipulated that the track current and the drainage network current are positive from left to right in the circuit diagram. Among them, the leakage current (stray current) is positive from the track to the drainage network. Thus, the current in each section, the current on the drainage network, and the leakage current can be solved by Ohm's law. At this time, the discretized model only considers the first-level drainage network. However, the design of most rail transit systems requires the drainage network to be divided into a main drainage network and an auxiliary drainage network in order to further control the flow of stray current through other metal objects. In this case, the equivalent circuit of the dual-side power supply is shown in Figure 3. The matrix form of the solution equation of the discrete model can be simplified to the formula: (1) The matrix G is a strictly diagonally dominated square matrix, r(G)=n. The equation has a solution and can be solved by LU decomposition. The solution process is: (2) Where L and M are the upper triangular matrix and the lower triangular matrix, respectively. [align=center] Figure 2 Matrix representation of the equation set for solving the node voltage Figure 3 Discrete model of the main and auxiliary drainage subway traction power supply system[/align] Compared with the discrete power supply system model, the circuit model in Matlab simulation [3] is shown in Figure 4. The current and voltage at any point can be observed. In the simulation experiment, the general law of stray current distribution can be derived: 1) When the train is running in the middle of the section, the track voltage is at its maximum positive value, which also corresponds to the maximum value of stray current. At the return point, the track voltage is at its maximum negative value. The drainage network here is in the anode area, which is the area with the most severe stray current corrosion. 2) The track voltage increases with the increase of the train traction current, and the increase is large. The track voltage at the train is at its maximum value. Although the stray current also increases with the increase of the train traction current, the increase is not large. 3) With the increase of the longitudinal resistance of the track, the track voltage increases significantly. The stray current does not increase significantly when the initial longitudinal resistance value of the track is small, but with the increase of the longitudinal resistance value of the track, the increase rate of stray current is faster and faster. 4) The transition resistance has the greatest impact on the distribution of stray current. The smaller the transition resistance, the larger the stray current. When the transition resistance is less than 3 (Ω•km), the stray current leakage is relatively serious, while when the transition resistance is 15 (Ω•km), the stray current leakage is very small; when the transition resistance is greater than 15 Ω•km, the stray current can be ignored; when the transition resistance is greater than 3 Ω•km, the stray current changes very little; when the transition resistance is <3 Ω, the stray current changes drastically; when the transition resistance is <0.5 Ω, the stray current leakage is serious, and effective measures must be taken to deal with it. [align=center] Figure 4 Matlab simulation model of subway traction power supply system[/align] 5) The drainage network resistance has little impact on track voltage and stray current. When calculating the cross-section of the steel reinforcement in the concrete structure in engineering design, the main consideration is the requirements of the civil engineering profession for the concrete strength. 6) As the distance between power supply sections increases, both track voltage and stray current increase, and the increase is also relatively large. Shortening the distance between power supply sections as much as possible is of great significance for reducing stray current. These stray current patterns show that the stray current effects between different sections are independent, thus allowing for inter-section monitoring of stray currents in rail transit. To reduce stray currents, the above patterns indicate the rules that should be followed in rail transit design. The most important application of these patterns is that, based on Kirchhoff's first and second laws, a formula can be given to calculate the transition resistance of the entire power supply section when a train is at any point L during operation. (3) Where: R[sub]W[/sub]—the transition resistance value of the entire power supply section; ΔV—the potential difference between the rail and the structural steel under the locomotive wheel at point L; and the potential differences V[sub]1[/sub] and V[sub]2[/sub] between the two endpoints of the power supply section and the structural steel are measured simultaneously. 3 Distributed monitoring model for stray currents Stray currents in subways are difficult to measure directly, and indirect methods are generally used to reflect the corrosion situation of stray currents. The determination is made by measuring the potential polarization shift. The main parameters monitored for stray current corrosion in subways include track potential, polarization potential of buried metal structures, transition resistance, and longitudinal resistance of the track, as specified in the rail transit industry standard "Technical Specification for Stray Current Corrosion Protection of Subways". This indicates the danger of stray current corrosion to the metal bodies and equipment through which it flows. [align=center] Figure 5 Schematic diagram of distributed stray current monitoring[/align] In domestic rail transit design, stray current is designed as an independent monitoring system, requiring the laying of independent transmission channels along the entire line to transmit the collected signals. This is costly, and the monitoring accuracy and real-time performance are relatively low. Based on the discretized model of the main and auxiliary drainage subway traction power supply system, the sensor was redesigned, and only two parameters were collected at each point: ① the potential of the structural steel bars in the building to the reference electrode; ② the potential of the track to the structural steel bars. The monitoring device enters the section through the fieldbus, forming an independent section monitoring, which also meets the needs of the discretized model calculation and improves the safety of the monitoring system. In the monitoring system, the most important thing is to calculate the transition resistance of a power supply section through formula (3). With a fieldbus, any sensor distributed throughout the section can trigger the measurement of three electrical signals when a stray current is passing through, calculating the transition resistance of the section. The minimum value of all measurements for the entire section throughout the day is then selected as the transition resistance for that day. Different monitoring subsystems converge at the command center via the existing SCADA communication channels of the rail transit system, completing the monitoring of stray currents along the entire line and forming a distributed stray current monitoring system, as shown in Figure 5. SCADA significantly reduces system construction costs, and communication distance is unlimited. Data is also transmitted to the substation integrated automation system, achieving resource sharing. The actual distributed stray current monitoring system uses sensors and monitoring devices forming a low-level network via a CAN bus; through SCADA, each monitoring device and the monitoring center form a high-level network. This two-level network not only simplifies communication but also makes the system more flexible. 4. Innovation of the author In view of the shortcomings of the current stray current monitoring scheme, this paper proposes a distributed stray current monitoring scheme based on the power supply section. The two-layer network structure system can flexibly and conveniently realize real-time monitoring of stray current distribution, provide effective means for safety protection, and improve the safety and stability of the stray current monitoring system. References [1] Fang Ming. Power supply system and feeding method of urban rail transit [J]. China Railway, 2003, 4: 49-53. [2] Lin Jiang et al. Subway stray corrosion and its protection technology [J]. Journal of Building Materials, 2002, 3: 72-76. [3] Liang Feihua, Huang Yuxin et al. Simulation of robot kinematics under AutoCAD.VBA and MATLAB environment [J]. Microcomputer Information, 2006, 8: 206-208.