Wide-Band Harmonic Interaction and Characteristic Analysis of Flexible Cooperative Traction Power Supply System ^†

Abstract

Integrating renewable energy systems (RES) and hybrid energy storage systems (HESS) into railway traction power supply systems represents a critical pathway toward low-carbon and sustainable railway transportation as it enables the utilization of clean energy and enhances energy efficiency. However, this integration introduces new harmonic resonance challenges that require systematic analysis. To quantitatively analyze these harmonic resonance issues, this paper studies a flexible cooperative traction power supply system (FCTPSS) integrated with RES and HESS. Based on harmonic transmission theory, mathematical models of harmonic transmission for both the traction power supply system (TPSS) and the FCTPSS are established. Simulation models of the TPSS and FCTPSS are developed in MATLAB2021b/Simulink. Using these simulation models, the harmonic transmission characteristics of the TPSS and FCTPSS are compared and analyzed. The results indicate that the position of the locomotive and the access position of RES and HESS influence the harmonic transmission characteristics. Importantly, integrating RES and HESS shifts the resonant frequency to higher orders and effectively alleviates resonance issues, thereby improving power quality and supporting the reliable operation of sustainable railway systems. These findings offer valuable design guidance for incorporating RES and HESS into traction power supply systems to facilitate the transition toward greener and more sustainable rail transportation.

1. Introduction

Currently, numerous studies have explored the integration of renewable energy systems (RES) and energy storage systems (ESS) into the grid [1,2,3,4,5]. RES can generate electricity in a green and clean manner, thereby reducing carbon emissions. ESS can mitigate the output volatility of renewable energy and improve power quality. Similarly, several studies have investigated the integration of RES and ESS into traction power systems (TPSS), which represents a crucial step toward decarbonizing railway transportation. For example, East Japan Railway Company has connected photovoltaic systems and energy storage to the traction power supply system [6,7,8,9,10]. Integrating RES and hybrid energy storage systems (HESS) into railways not only supports the green and sustainable development of the railway sector but also promotes the consumption of renewable energy, contributing to the low-carbon transformation of rail transit.

The integration of RES and HESS into TPSS is a new research direction, and most of the research is at present just starting. Reference [11] proposed a photovoltaic (PV) DC microgrid topology with HESS, which connected to TPSS through a railway power conditioner (RPC). This paper proposed the control strategy of the system and simulated the operation scheduling and energy flow of the system. Wu put forward a back-to-back PV power generation system for an electrified railway, designed its control strategy, established a simulation model and verified the feasibility of the system in [12]. In [13], Deng proposed a hybrid traction power supply system integrated with photovoltaic sources (HTPSS-PVSs), which can realize on-site access and consumption of PV power along the line without affecting the original structure of TPSS. In [14,15], the scheme of integrating RES and HESS into the TPSS was put forward, and by considering the uncertainty of RES output, the optimal solution of the power flow between RES, HESS, the power grid and the traction load was obtained, which reduced carbon emissions and the demand for power grid energy. In [16], Ying proposed a flexible intelligent traction power supply system that consisted of an AC–DC–AC traction substation and a microgrid along the railway, which can effectively alleviate the problem of negative sequence current and improve the utilization rate of regenerative braking energy and RES. These efforts collectively highlight the growing consensus that integrating distributed energy resources into railway systems is a promising pathway toward achieving sustainable and energy-efficient rail transportation.

Although the above references have done a lot of research on the topology and energy control strategy of the TPSS system accessed by RES and HESS, the research on the harmonic transmission characteristics of the new system is insufficient. Currently, AC–DC–AC an electric locomotive used in an electrified railway has the characteristics of a high power factor and low harmonic content, but its harmonic spectrum is relatively wide. Coupled with the spatiotemporal nature of locomotive movement mode, the introduced harmonics may appear as harmonic resonance and amplification in the propagation process of a traction network with a complex structure [17,18]. In addition, the access of RES and HESS will change the topology of TPSS, and new changes may appear in the harmonic interaction characteristics. Reference [19] has studied the distribution characteristics of harmonics in the power supply system running the super-capacitor tram and has proposed a new harmonic processing measure based on a notch high-pass filter. However, the topology of the TPSS remained unchanged in [19]. Therefore, to support the reliable and sustainable operation of future green railway systems, the objectives of this paper are to: (1) establish mathematical models for harmonic transmission in TPSS and FCTPSS; (2) develop a simulation model to validate the theoretical analysis; and (3) quantitatively compare locomotive current harmonic transmission and THD characteristics in traditional TPSS and CTPSS, providing a reference for future RES and HESS integration, thereby providing a technical foundation for the safe integration of RES and HESS in alignment with sustainable railway development goals.

This paper is organized as follows: Section 2 introduces the topology of FCTPSS and the mathematical models of harmonic transmission for TPSS and FCTPSS. Section 3 presents the simulation models of TPSS and FCTPSS developed in MATLAB2021b/Simulink. In Section 4, the harmonic transmission characteristics are simulated and verified, and the results are presented. Finally, Section 5 provides the conclusion and discussion for future work.

2. Topological Structure and Theoretical Analysis of Harmonic Characteristics of FCTPSS

2.1. Topology of FCTPSS

Co-phase power supply provides an idea to solve the power quality problem and the power phase separation problem of high-speed railway systems [20,21,22] and also provides a good integration method for the access of RES and HESS [16,23]. Co-phase power supply is the development direction of high-speed railway power supply systems in the future. Based on the scheme of co-phase power supply, this paper constructs a FCTPSS including wind power generation, photovoltaic power generation and HESS. The scheme proposed in this paper is to integrate wind power generation, photovoltaic power generation and HESS by connecting the converter to the DC bus, and then connect to TPSS through the DC/AC inverter connected to the step-down transformer, so as to supply power together with the power grid, as shown in Figure 1. The wind power generation is connected to the DC bus through the 3AC/DC converter, the photovoltaic power generation is connected to the DC bus through the DC/DC boost converter and the HESS is connected to the DC bus through the bidirectional DC/DC converter.

The advantages of the topological structure shown in Figure 1 are as follows: (1) the common DC bus provides a flexible interface for aggregating different RESs and HESS with different voltage and current characteristics; (2) it decouples the control of RES/HESS from the AC power grid, simplifying power management; (3) it is consistent with the architecture of the same phase traction power supply system, which is considered the future development direction of high-speed railway traction power supply systems.

2.2. Theoretical Modle of Harmonic Transmission in FCTPSS

The traction network includes two parts: the power supply network and the return network. The power supply network consists of a catenary (T), including contact wire, messenger wire, reinforcing wire, etc.; the return network consists of steel rail (R), negative feeder (NF), positive feeder (PF), protective wire (PW), etc. At present, there are two main power supply modes:a direct power supply with negative feeders and an autotransformer (AT) power supply, as shown in (a) and (b) of Figure 2 (single-wire traction network shown in the Figure 2). As a whole, the traction network is a parallel multi-conductor system. A power supply arm of a traction network is a chain network composed of series impedance elements and parallel admittance elements from the view of topology.

Both RES and the locomotive generate harmonics during operation. When the harmonic frequency matches the system parameters, a harmonic resonance phenomenon will occur [24,25,26,27]. In this section, the mathematical models of the harmonic characteristics of TPSS and FCTPSS are established, respectively, to analyze their harmonic transmission characteristics.

(1) The circuit network of the traction power supply system is equivalent to a π equivalent circuit model, as shown in Figure 3. Z_ss is the system impedance of traction substation, including power grid reactance and traction transformer reactance; I₁ is locomotive current flowing to the traction substation; I₂ is the locomotive current flowing to the section post; I_load is the locomotive current; l₁ is the distance from locomotive to substation in kilometers; l₂ is the distance from the locomotive to the section post, in kilometers. Z_L and Y_L are the equivalent impedance between train and substation; Z_R and Y_R are the equivalent impedance between the train and the section post.

The equivalent impedance of the traction network is:

$$\left\{\begin{array}{l}{Z}_L=Z_{0}sh(\gamma l_1),Y_L={\displaystyle \frac{(ch(\gamma l_1)-1)}{Z_{0}sh(\gamma l_1)}}\\ Z_R=Z_{0}sh(\gamma l_2),Y_R={\displaystyle \frac{(ch(\gamma l_2)-1)}{Z_{0}sh(\gamma l_2)}}\end{array}\right.,$$

(1)

where, $Z_0=\sqrt{Z/Y}$ is the characteristic impedance of traction network line, Z is the equivalent impedance per unit length of traction network line and Y is the equivalent admittance per unit length. $\gamma =\sqrt{ZY}$ is the propagation coefficient of the traction network line. Assuming the contact network is a uniform transmission line, the actual line parameters Y = 17.96 × jω, Z = 0.106 + 0.0017 × jω (ω = 2πf) are used. The theoretical analysis in this section adopts this set of parameters.

From this point of the train, the equivalent input impedance Z_q of the traction network is:

$$Z_q={\displaystyle \frac{Z_{0}ch\gamma l_2(Z_{ss}ch\gamma l_1+Z_{0}sh\gamma l_1)}{Z_{ss}sh\gamma l+Z_{0}ch\gamma l}},$$

(2)

According to Formula (1), the image of the change of the equivalent input impedance Z_q of the traction network with the locomotive position and harmonic frequency can be drawn as shown in Figure 4. It can be seen that Z_q changes with the locomotive access location and harmonic frequency. The equivalent impedance Z_q has a peak value around the 25th and 81st harmonic frequencies, which are resonant frequencies. And, at the 25th harmonic, the farther away from the substation, the greater the value of Z_q.

The locomotive harmonic current will change through the transmission of the traction network. Assume that the train current at x₁ from the substation is I_x1, as shown in Figure 5.

Then I₁ and I_x1 are, respectively:

$$\left\{\begin{array}{l}{I}_1={\displaystyle \frac{ch\gamma l_2(Z_{ss}sh\gamma l_1+Z_{0}ch\gamma l_1)}{Z_{ss}sh\gamma l+Z_{0}ch\gamma l}}{I}_{load}\\ I_{x1}={\displaystyle \frac{(Z_{ss}sh\gamma x_1+Z_{0}ch\gamma x_1)}{Z_{ss}sh\gamma l_1+Z_{0}ch\gamma l_1}}{I}_1={\displaystyle \frac{ch\gamma l_2(Z_{ss}sh\gamma x_1+Z_{0}ch\gamma x_1)}{Z_{ss}sh\gamma l+Z_{0}ch\gamma l}}{I}_{load}\end{array}\right.,$$

(3)

Q_am is defined as the amplification factor of locomotive current amplified by the traction network, and the Q_am of current I_x1 at distance x₁ from substation is:

$$Q_{am}={\displaystyle \frac{I_{x1}}{I_{load}}}={\displaystyle \frac{ch\gamma l_2(Z_{ss}sh\gamma x_1+Z_{0}ch\gamma x_1)}{Z_{ss}sh\gamma l+Z_{0}ch\gamma l}},$$

(4)

According to Formula (4), when the denominator in the equation is 0 or close to 0, Q_am reaches the maximum, that is, harmonic resonance occurs. The resonant condition is: $Z_{ss}sh\gamma l+Z_{0}ch\gamma l=0$, because γl << l, thγl ≈ γl, $Z_{ss}=-Z_0/\left(\gamma l\right)$. $Z_{ss}$ is expressed by traction transformer inductance $L_{ss}$ as $Z_{ss}=\omega L_{ss}$, and the resonant frequency $f_0=1/2\pi \sqrt{L_{ss}C}$.

When $x_1=0$, the current $I_{ss}$ flowing into the traction substation can be obtained, and the Q_am of the current I_ss at the substation is:

$$Q_{am}={\displaystyle \frac{I_{ss}}{I_{load}}}={\displaystyle \frac{Z_{0}ch\gamma l_2}{Z_{ss}sh\gamma l+Z_{0}ch\gamma l}},$$

(5)

According to Formula (5), the Q_am of I_ss is shown in Figure 6. It is known that the peak value of Q_am appears around the 25th and 81st harmonics like Z_q. The variation of Q_am is the same as Z_q.

(2) Assume RES and HESS are connected to the traction power supply system of the traction substation. In order to decouple the influence of RES/HESS impedance from its harmonic emission, the DC side is represented by a constant voltage source, where RES and HESS can be equivalent to equivalent impedance. This enables us to isolate and study the impact of parallel converters as passive impedances on locomotive harmonic propagation. Therefore, the conclusion on power quality only specifically involves locomotive harmonics; the additional harmonic contribution of RES inverters is a separate issue that requires future research using detailed converter models. The equivalent circuit of FCTPSS can be simplified to the circuit structure shown in Figure 7.

Make ${1/Z}_{SR}{=1/Z}_{SS}+1/Z_{RH}$, from this point of the train, the equivalent impedance Z_q’ of the traction network connected to RES and HESS is as follows.

$$Z_q^{\prime }={\displaystyle \frac{Z_{0}ch\gamma l_2(Z_{SR}ch\gamma l_1+Z_{0}sh\gamma l_1)}{Z_{SR}sh\gamma l+Z_{0}ch\gamma l}},$$

(6)

According to Formula (6), the image of Z_q’ changing with locomotive location and harmonic frequency is shown in Figure 8. It can be seen from the image that when resonance occurs, the peak value of Z_q’ is significantly lower than Z_q of TPSS, and the resonance frequency shifts to the right and appears near the 27th and 87th harmonics. In addition, there is also a slight resonance at the 5th harmonic frequency.

At this point, Formula (7) can be derived.

$$\left\{\begin{array}{l}{I}_1={\displaystyle \frac{ch\gamma l_2(Z_{SR}sh\gamma l_1+Z_{0}ch\gamma l_1)}{Z_{SR}sh\gamma l+Z_{0}ch\gamma l}}{I}_{load}\\ I_{SR}={\displaystyle \frac{Z_0}{Z_{SR}sh\gamma l_1+Z_{0}ch\gamma l_1}}{I}_1={\displaystyle \frac{Z_{0}ch\gamma l_2}{Z_{SR}sh\gamma l+Z_{0}ch\gamma l}}{I}_{load}\\ I_{SS}={\displaystyle \frac{Z_{RES}}{Z_{RES}+Z_{SS}}}{I}_{SR}=({\displaystyle \frac{Z_{RES}}{Z_{RES}+Z_{SS}}})({\displaystyle \frac{Z_{0}ch\gamma l_2}{Z_{SR}sh\gamma l+Z_{0}ch\gamma l}})I_{load}\end{array}\right.,$$

(7)

In this case, the harmonic Q_am’ is,

$${Q_{am}}^{\prime }={\displaystyle \frac{I_{ss}}{I_{load}}}=({\displaystyle \frac{Z_{RES}}{Z_{RES}+Z_{SS}}})({\displaystyle \frac{Z_{0}ch\gamma l_2}{Z_{SR}sh\gamma l+Z_{0}ch\gamma l}}),$$

(8)

According to Formula (8), the image of Q_am’ changing with locomotive location and frequency is drawn, as shown in Figure 9. It can be seen from the image that when resonance occurs, the peak value of Q_am’ decreases obviously, the resonant frequency shifts to the right and resonance occurs near the 27th and 87th harmonics. In addition, a slight harmonic current amplification occurs near the 5th harmonic.

In order to verify the theoretical analysis in Section 2.2, a simulation model is established in Section 3.

3. Simulation Model of FCTPSS

3.1. Simulation Model of Traction Network

The traction network is a parallel multi-conductor system. In terms of topology, one power supply arm of the traction network forms a chain network. The chain network is composed of longitudinal series of impedance elements and transverse parallel admittance elements, as shown in Figure 10. The parallel multi conductor system is cut into different segments by the admittance elements in transverse parallel.

In Figure 10, the series impedance element Z_k is the branch impedance between two adjacent sections; the parallel admittance element Y_k is the admittance between the wires on section k; I_k is the injection current source of the wires on section k, which is used to simulate the harmonic current injected into the traction network by the train load at the position of the supply arm; V_k is the voltage of the wires on section k. From the chain network in the Figure 10, the node voltage equation can be listed as shown in Formula (9). According to Formula (9), the voltage and current at each node and the corresponding impedance at a specific frequency can be obtained.

$$\begin{array}{l}\left[\begin{array}{ccccccc}{Y}_1+Z_1^{-1}& -Z_1^{-1}& & & & & \\ -Z_1^{-1}& Z_1^{-1}+Y_2+Z_2^{-1}& -Z_2^{-1}& \cdots & & & \\ & & ⋮& \ddots & & & \\ & & -Z_{k-1}^{-1}& Z_{k-1}^{-1}+Y_k+Z_k^{-1}& -Z_k^{-1}& \cdots & \\ & & & & ⋮& \ddots & \\ & & & & -Z_{n-2}^{-1}& Z_{n-2}^{-1}+Y_{n-1}+Z_{n-1}^{-1}& -Z_{n-1}^{-1}\\ & & & & & -Z_{n-1}^{-1}& -Z_{n-1}^{-1}+Y_n\end{array}\right]•\\ {\left[\begin{array}{ccccccc}{V}_1& V_2& \cdots & V_k& \cdots & V_{n-1}& V_n\end{array}\right]}^T={\left[\begin{array}{ccccccc}{I}_1& I_2& \cdots & I_k& \cdots & I_{n-1}& I_n\end{array}\right]}^T\end{array}$$

(9)

No matter what power supply mode is adopted for the traction network or whether the line is single line or double line, the essence of the traction network is a chain network composed of multi conductor transmission lines. In order to make the simulation model of the traction network more realistic, this chapter adopts a more accurate multi conductor transmission line structure to establish a simulation circuit, which can better simulate the real situation of the traction network. As shown in Figure 11, the structure diagram of the double line traction network with direct supply and return line power supply mode (T–R + NF) is presented. When modeling, the traction network is generally divided evenly according to the natural cutting of the transverse parallel elements. In order to simplify the modeling process, the wires are merged according to the parallel connection. The contact wire and catenary of the same traction network are equivalent to one conductor (T), and the rails of the same line are combined into one (R). When calculating the self-impedance, mutual impedance, self-admittance and mutual admittance coefficient matrix, the influence of other merged wires is also taken into account, so the accuracy of the model will not be reduced by merging wires for modeling. The number of conductors in Figure 11 is 6, which are the up and down contact wires T₁ and T₂, the up and down negative feeder lines F₁ and F₂ and the up and down rails R₁ and R₂. According to the distributed parameter method of traction networks proposed in reference [28], the simulation model of the T–R + NF power supply mode for double line traction network is established in Matlab2021b/Simulink software with a unit of 1 km, as shown in Figure A1 in Appendix A. Main system parameters of the traction network, external power supply and traction transformer are shown in Appendix A.

3.2. Simulation Model of RES and HESS

RES and HESS converters for FCTPSS are similar to converters commonly used in power systems. The core part is the single-phase DC/AC converter, which can convert the DC bus voltage to 27.5 kV AC voltage for the locomotive load. The converter used in this simulation system is a voltage-type bidirectional DC/AC converter, and its topology is shown in Figure 12.

The DC/AC converter adopts a double closed loop control strategy, and its control block diagram is shown in Figure 13. The main control parameters are shown in

Table 1. Main control parameters of DC/AC converter.

Parameters	Value
Carrier frequency	2000 Hz
DC-side capacitor	20,000 μF
AC side filter inductor	0.1 mH
Proportional coefficient of PI	10
Integral coefficient of PI	250

. The outer voltage loop is used to stabilize the DC bus voltage, and the inner current loop is used to control the converter output grid connected current. The voltage outer loop compares the measured DC bus voltage with the reference voltage, and the error obtained is output as a DC flow I_cp^* through the PI regulator. The reference current I_c^* is obtained by multiplying I_cp^* by the AC network voltage U_L through the phase locked loop processing. In order to quickly track the current command value, the DC/AC converter is controlled by current hysteresis comparison tracking, so that the converter has a fast response speed. The hysteresis width will affect the response speed. When the hysteresis width is large, the switching frequency is low, the response speed is slow and the current tracking error is large; when the ring width is small, the switching frequency is high, the response speed is fast and the current tracking error is small. However, a smaller ring width will increase the switching loss, and when the ring width exceeds a certain range, the circuit will not work properly, so the selection of hysteresis width needs to be considered comprehensively. The inner current loop compares the measured current I_c with the reference current I_c^* to obtain the error signal. The obtained error generates the control signal of DC/AC converter through the hysteresis comparator to ensure the converter can respond quickly, so as to achieve grid connected current tracking control.

This paper only explores the influence of the introduction of RES and HESS on the harmonic current transmission characteristics of the locomotive. In order to avoid the influence of the harmonic generated by RES, the DC side of the inverter (renewable energy system and hybrid energy storage system) is replaced by a constant DC source.

3.3. Simulation Model of Locomotive Load

The locomotive is the main harmonic source of the traction power supply system. The simulation model of CRH3 EMU is established in this paper. The electric drive system of CRH3 EMU mainly includes a pantograph, on-board transformer, four quadrant converter, intermediate DC link, pulse width modulation (PWM) inverter, traction motor, etc. The intermediate DC link can effectively suppress the influence of the inverter side on the grid side system, that is, the high order harmonics on the locomotive grid side are mainly generated by the four quadrant converter modulation. During modeling, the PWM inverter and traction motor can be simplified and equivalent resistance can be used to simulate motor side load. The simplified model is shown in Figure 14, where e is the grid side power supply, R_t and L_t are the leakage impedances of the on-board transformer, C_dc is the DC support capacitor, C₂ and L₂ are the secondary filtering branches, U_dc is the DC side voltage and R_L is the equivalent load.

CRH3 EMU traction rectifier adopts transient current control strategy (TCCS), and the control block diagram is shown in Figure 15. The principle of transient current control is shown in Formula (10).

$$\left\{\begin{array}{l}{I}_{s1}=K_p(U_{dc}^{*}-U_{dc})+1/K_i{\displaystyle \int (U_{dc}^{*}-U_{dc})\mathrm{dt}}\\ I_{s2}=I_{dc}{U}_{dc}/U_s\\ I_s^{*}=I_{s1}+I_{s2}\\ u_{ab}(t)=U_s(t)-\omega L{I}_s^{*}\cos (\omega t)-R_t{I}_s^{*}\sin (\omega t)-K\left(I_s^{*}\sin (\omega t)-i_s(t)\right)\end{array}\right.,$$

(10)

where,$U_{dc}$^* is the given value of DC side voltage, and $U_{dc}$ is the actual value of DC side voltage. I_s^* is the command value of network side current; i_s(t) is the actual current value of the network side; K_p, K and K_i are proportional integral coefficients; I_dc indicates the DC load current. $U_s$, I_s and $U_{dc}$ are input signals of the control system.

According to the control principle, the locomotive model is established in Matlab2021b/Simulink, as shown in Figure 16, and the main parameters are shown in

Table 2. Main parameters of locomotive CRH3.

Parameters	Value
Carrier frequency	350 Hz
DC capacitor	1000 μF
Secondary filtering inductor	1.9 mH
Secondary filtering capacitor	1330 μF
Proportional coefficient of voltage loop	0.5
Integral coefficient of voltage loop	7
Proportional coefficient of current loop	5
Integral coefficient of current loop	0

. In order to verify the accuracy of CRH3 EMU load model, the harmonic output characteristics are simulated and analyzed in Appendix B.

4. Simulation Results and Analysis

4.1. Results and Analysis of Harmonic Current Transmission Characteristics

In the traction power supply system, the power and position of the locomotive change at any time, which leads to the constant change of impedance frequency characteristics and harmonic current amplification characteristics in the traction network under different space–time states. According to Section 2.2, when the length of traction network and other parameters are fixed, the harmonic transmission characteristics of traction power supply system are related to the access position of RES and HESS and the operating position of locomotive. Therefore, this part verifies the influence law of related factors of TPSS and FCTPSS harmonic transmission characteristics by simulation. The verification process and results are as follows.

4.1.1. Results and Analysis of Harmonic Transmission Characteristics of TPSS

The change of locomotive location will cause the change of voltage and current distribution of traction network. A 25 km long traction network simulation model is established with a 1 km traction network as the basic unit. By changing the location where the locomotive is connected to the traction network, the harmonic current amplification characteristics of the traction power supply system at different locations are obtained as shown in Figure 17.

It can be seen from Figure 17 that when the traction network is 25 km long, Q_am will have a peak value near the 15th and 87th harmonics, that is, harmonic resonance occurs; When the locomotive runs at 5 km, the Q_am (near the 15th harmonic) is 25.78; when the locomotive runs at 25 km, the Q_am (near the 15th harmonic) is 28.42; the further the locomotive is from the substation, the larger the Q_am becomes. As the locomotive is far away from the substation, the longer the transmission distance of current on the traction network is, the more likely the resonance will occur. It can be seen that the simulation results are consistent with the theoretical model analysis results in Section 2.2.

4.1.2. Results and Analysis of Harmonic Transmission Characteristics of FCTPSS

According to the theoretical analysis in Section 2.2, when RES and HESS are connected, the resonant frequency of the system will shift to the right, and the amplification of harmonic current will decrease. In this section, RES and HESS will be accessed at 0, 5, 10, 15, 20 and 25 km respectively, and the locomotive will be placed at a distance of 10 km from the substation. Figure 18 shows the harmonic current amplification characteristics of the FCTPSS.

As can be seen from Figure 18, the harmonic resonance phenomenon has been significantly weakened, and the harmonic resonance frequency has shifted to the right, transferring to the vicinity of the 23rd harmonic frequency, avoiding the harmonic characteristic range of the locomotive. In FCTPSS, the maximum Q_am’ is only 7.88 times, which is about 3.6 times lower. In addition, it can be seen from the Figure 18 that under the FCTPSS, a slight resonance will be generated near the 5th harmonic, and the maximum Q_am’ is 4.94 times, which is also consistent with the theoretical analysis in Section 2.2.

4.2. Power Quality Simulation Results

Harmonic current will increase the copper loss and stray loss of the traction transformer, cause the transformer temperature to rise and shorten the service life. The total harmonic current distortion (THD) is an index to measure the overall situation of harmonic current. IEEE 519 recommends a typical THD limit of 5% for general distribution systems [29]. This part analyzes the THD of I_CRH3 generated by the locomotive and I_ss under TPSS and FCTPSS. (1) In TPSS, the locomotives are, respectively, connected at 5, 10, 15, 20 and 25 km from the substation. The THD changes of I_CRH3 and I_SS are shown in Figure 19a. The THD of I_SS has the same rule as that of I_CRH3, but its amplitude is more than twice that of I_CRH3. This is because the harmonic current is amplified by the traction network. (2) In FCTPSS (RES and HESS are connected to 5 km), locomotives are also connected 5 km, 10 km, 15 km, 20 km and 25 km away from the substation, respectively. The THD changes of I_CRH3 and I_SS are shown in Figure 19b. The THD of I_CRH3 increases slightly, but the THD of I_SS decreases significantly, which will improve the operation of the traction transformer, reduce copper loss and stray loss of the transformer, prolong its service life and reduce costs.

5. Conclusions and Discussion

5.1. Conclusions

In this paper, the harmonic transmission characteristics of TPSS and FCTPSS are analyzed theoretically, the simulation models of TPSS and FCTPSS are established in Matlab2021b/Simulink and the accuracy of the models is verified. The change of harmonic current amplification and THD with the locomotive access position under TPSS are simulated and analyzed. In addition, the variation of harmonic current amplification and THD are simulated and analyzed when RES and HESS are connected at different locations in FCTPSS. This work contributes to the reliable and sustainable development of green railway systems by providing a technical foundation for the safe integration of renewable energy and energy storage. The conclusions are as follows.

(1) The frequency spectrum characteristics (main frequency component) of locomotive harmonic current do not vary with the power and operating state of the locomotive, but, under traction conditions, the harmonic content decreases with the increase of the power of the locomotive.

(2) When the parameters and length of the traction network are fixed, the system resonance frequency is fixed, independently of the location of the locomotive. But the further the locomotive is from the substation, the stronger the resonance phenomenon will be.

(3) Compared to traditional TPSS, in FCTPSS, the resonant frequency of the system will shift to the right, and the overall amplification amplitude of harmonic currents will be reduced.

(4) In FCTPSS, THD of I_SS will be significantly reduced, and the operation of traction transformer will be improved.

5.2. Discussion

The results of the simulation model established in this paper can be consistent with the theoretical analysis, and can be used to study the harmonic transmission characteristics of RES and HESS connected to TPSS. By elucidating the harmonic transmission characteristics of FCTPSS integrated with RES and HESS, this study provides valuable insights for the design of future sustainable railway power supply systems that aim to incorporate renewable energy while maintaining high power quality. However, the limitation of idealizing RES/HESS as a constant DC power source in simulation studies excludes their harmonic coupling effects. Future work should incorporate detailed RES/HESS models and validate the results through hardware in the loop or on-site testing.