3.1.2. Coordinated Traction Test

The test setup of the operating power *P*load of the high-speed locomotive is set to 3.6 MW, and the light intensity will continue to rise, as shown in Figure 18 obtained from the upper computer. Among the modes, mode four to mode one correspond to battery traction, PV and battery co-traction, PV traction, and PV locomotive traction and battery charging. By switching operation modes under different working conditions, the locomotive traction power can be stabilized while charging the battery. Under this scheme, the renewable energy continuous closed-loop power supply allows the locomotive to remain "low-carbon" for a long time, and a substation can be used for backup power in case of accidents.

**Figure 18.** Energy self-sufficient traction power supply: (**a**) multi-mode power flow conditions; (**b**) voltage waveform on both sides of the RPC.

#### *3.2. Verification of Low-Frequency Stability Analysis*

The main purpose of this section is to verify the results of the low-frequency stability analysis in Section 2.3 to ensure the correctness of the analysis. The following subsections will present corresponding test results in the order of the analysis in Section 2.3.

#### 3.2.1. Verification of Parameter Adjustment Criterion

1. **Case 1:** Adjusting control parameters to address instability caused by deteriorating circuit parameters. Under the original parameters, the PV and battery stably provided co-traction for the locomotive, which is verified in Figure 18. However, at this time, the parameters of the energy storage inductor *L*bat deteriorated. The waveform of the traction-network-side voltage *U*ac and current *I*ac is shown in Figure 19b. The system experienced a low-frequency constant-amplitude oscillation of 5.7 Hz after 2 s, and after *k*Bup decreased after 2 s, the system was stabilized and restored. This case

demonstrates that numerically adjustable control parameters can govern LFO caused by the deterioration of topology circuit parameters.

**Figure 19.** Waveform for parameter adjustment after the deterioration of the main circuit parameters: (**a**) global diagram; (**b**) local diagram.

2. **Case 2:** Connecting a parameter-adjusted other-source subsystem to address singlesource traction instability. Due to the unreasonable setting of *k*PVup during the PV locomotive traction, the system became unstable. Finally, a parameter-adjusted battery system was connected to control the constant-amplitude oscillation. The experimental waveform is shown in Figure 20, where *u*dc and *u*<sup>0</sup> are the output voltages of the RPC DC and AC sides, respectively. By comparing and observing the oscilloscope, it was found that a lower value of *k*Bup made the bus voltage fluctuation smaller and smoother when the battery system was connected. The reason for the successful governance of the parameter adjustment, in this case, is reflected in the addition of the circuit topology of the battery subsystem and the parameter setting under the parameter adjustment criteria, which improved the impedance matching relationship. At the same time, the relatively lower electrical sensitivity under the combined traction of the PV and battery provided the control parameters with a wider range of choices in the stable domain.

**Figure 20.** When the PV locomotive traction is unstable, it can be corrected by connecting a parameteradjusted battery subsystem: (**a**) experimental waveform after the battery was connected when *k*Bup = 5; (**b**) experimental waveform after the battery was connected when *k*Bup = 15.

3. **Case 3:** Adjusting the control parameters to govern LFO caused by multi-locomotive operation (heavy load). The impedance ratio criterion mechanism shows that the smaller the load-side impedance, the more unstable the system will be. Therefore,

 

many studies on locomotive network systems have found that multi-locomotive operation or mixed operation is an important factor inducing LFO. The problem of heavy loads reducing the stability of traction power supply systems also exists in the study of PV and battery locomotive traction but the parameter-adjustable "artificially controllable traction network impedance" has a certain adaptability. The CRH3 high-speed locomotive was used as the research object, and the simulation waveform is shown in Figure 21, which includes the locomotive DC-side voltage *U*CRH3dc, locomotive-network-side voltage *U*CRH3ac, and locomotive-network-side current *I*CRH3ac. After 2.5 s, the addition of three high-speed locomotives caused a 4Hz low-frequency constant-amplitude oscillation among the high-speed locomotives. According to the parameter adjustment criteria, *k*PVup and *k*Bup were decreased after 2.5 s, and then the locomotives were stabilized.

**Figure 21.** Adjustment of the parameters to control system instability caused by multi-locomotive parallel connection: (**a**) global diagram; (**b**) local diagram.

3.2.2. The Impact of Parallel Connections of PV and Battery Modules


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**Figure 22.** (**a**) Overloading and worsening RPC parameters lead to system instability: (**b**) the ratio of PV and battery module parallel connections can multiply and increase to reshape the system impedance.

**Figure 23.** Deterioration of the system parameters leads to instability and multiple increases in the ratio of modules will aggravate the voltage oscillation.

#### **4. Discussion**

This paper mainly proposes an emergency power supply scheme to solve the problem of interruption in train power supply caused by unexpected faults in traction substations. The solution coordinates with the PV and battery systems to achieve emergency traction of locomotives, thereby expanding the functions of the railway power conditioner (RPC). Meanwhile, this paper proves through theoretical modeling and verification tests that the PV and battery traction locomotive additionally have the problem of low-frequency oscillation. To curb low-frequency oscillation occurring during the emergency power supply, this paper quantitatively analyzes the influence law of PI control parameters and topological structures on the low-frequency stability of the system, proposes a design method for the impedance real part greater than 0 of the PV and battery systems module, and provides parameter adjustment criteria to suppress or even prevent low-frequency oscillations.

Most studies on the integration of PV and battery into electrified railways focus on RPC grid compensation of traction power and harmonic governance. However, it is necessary to make RPC multifunctional, and few of the literature studies the coordinated control scheme of PV and battery for emergency train traction. If the majority of current RPC research's control strategies, such as the ones described in references [16,31], are used to independently traction the locomotive, the lack of phase information obtained by the phase-locked loop will cause the frequency and current of the traction network to be incorrect, forcing the locomotive to stop running. Therefore, this paper proposes the use of a dual-mode RPC with an independent power supply function, which can not only compensate for the power of the traction power supply system but also provide emergency traction for the locomotive.

Meanwhile, current research of the literature applies various criteria to analyze the low-frequency stability of a system. However, many research methods and processes in the literature are rather similar, in that they require graph redrawing every time a variable is modified to display the corresponding result [18,27,28]. This process is not intuitive enough and does not facilitate a thorough investigation of the impact of parameters on the stability and sensitivity of the system, simultaneously considering that there is little research on the low-frequency stability of the PV–battery locomotive network coupling system. Therefore, this paper defines CAM to quantify system stability and provides a method to calculate the sensitivity *ε* of parameters, which can weigh the importance of different parameters under different working conditions and explore the main influencing parameters and their influence laws. This paper also proposes the use of a passive criterion to reveal the influence mechanism of the number of PV and battery modules in parallel on system stability. Moreover, it finds that it has great potential for exploring parameter influence laws, it can intuitively give the law that a variable affects system stability within any value range through functions or three-dimensional drawings, however, the passive criterion still needs some improvement to achieve analysis accuracy similar to that of the Nyquist criterion.

Furthermore, PV and battery co-traction locomotives are environmentally friendly, because almost all of the electricity comes from renewable energy sources. Based on the research results of this article, further optimization and improvements in the power supply scheme of emergency traction locomotives, and exploring the impact of more variables on the low-frequency stability of the system, such as different types of locomotives running together under different working conditions, and conducting comprehensive research on the simultaneous impact of multiple parameters on the system, all have a profound significance and great value. Meanwhile, issues such as whether the emergency power supply scheme proposed in this article be used for long-term traction locomotives persist. How to configure the capacity of the PV and battery, whether the PV resources can be recycled by the power grid while the supply arm is idle and the locomotive is running, etc., are also the focus of future research. Compared to the traditional AC-electrified railway, the fact that the output of both PV and energy storage is DC suggests that there may be broader application prospects for PV and battery traction locomotives in DC railways and urban rail transit systems, and how to further explore its specific scheme and system stability are yet to be discussed.

### **5. Conclusions**

This work demonstrates that it is feasible to independently drive locomotives using PV and battery equipment under different working conditions during the day and night, and it established a one-dimensional impedance model for a PV–battery locomotive network system from the DC side. At the same time, this study suggests that low-frequency stability analysis of the system of the PV–battery locomotive network may be very important. On this basis, the stability of the system was studied using the generalized Nyquist criterion and a passive criterion. The critical amplitude margin (CAM) and the sensitivity of the controller parameters were proposed to quantitatively evaluate the influence law of the source-side DC converter control parameters and RPC control parameters on this system stability under different emergency traction modes, and corresponding parameter tuning criteria and design suggestions were provided to improve the stability of the system. Finally, the findings were verified through time-domain simulation models and semi-physical testing. The main research conclusions are as follows:


**Author Contributions:** Conceptualization, Y.W.; methodology, Y.X.; software, Z.X.; validation, Y.W. and Y.X.; formal analysis, X.M.; data curation, X.C.; writing—original draft preparation, Y.X.; writing review and editing, Y.W.; visualization, X.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (52067013); the Natural Science Key Foundation of Science and Technology Department of Gansu Province (22JR5RA318, 21JR7RA280, 22JR5RA353).

**Data Availability Statement:** Data are available on request from the authors. The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.
