**1. Introduction**

The "2022 Climate Services Status" report released by the World Meteorological Organization (WMO), a specialized agency of the United Nations, states that the clean energy power supply must be doubled by 2030 to limit the global temperature rise. Railway transportation is a significant contributor to energy consumption and carbon emissions in the transportation sector due to its massive electricity usage. With the depletion of fossil fuels and the consequences of global warming, there is mounting pressure on the railway industry to take action and reduce its carbon emissions. To achieve the green transformation of railways, progress has been made internationally in the adoption of new energy sources for railways: JR-East has installed 453 kW solar panels at Tokyo Station, serving locomotives on the Tokaido line 3 [1]; the subway operator in Santiago, Chile, built two solar photovoltaic power stations in 2017, supplying 60% of the subway's electricity and achieving a renewable energy utilization rate of 76% [2]; 100% of the primary energy used by the Dutch railway is provided by wind [3]; a 2.2 MW rooftop photovoltaic system has been built at Wuhan Railway Station in China; a 10 MW solar power generation device has been installed on the roof of Hangzhou East Station [4]; the total installed capacity of

**Citation:** Wang, Y.; Xin, Y.; Xie, Z.; Mu, X.; Chen, X. Research on Low-Frequency Stability under Emergency Power Supply Scheme of Photovoltaic and Battery Access Railway Traction Power Supply System. *Energies* **2023**, *16*, 4814. https://doi.org/10.3390/en16124814

Academic Editors: Luis Hernández-Callejo, Jesús Armando Aguilar Jiménez and Carlos Meza Benavides

Received: 16 May 2023 Revised: 18 June 2023 Accepted: 19 June 2023 Published: 20 June 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the photovoltaic system of the Xiong'an high-speed railway in China is 6 MW [5]. The photovoltaic (PV) resources along China's AC-electrified railways are abundant, and their high proportion of utilization can promote China's achievement of the "dual carbon" goal and increase the national independent contribution under the global energy conservation and emission reduction goal [6].

Currently, access methods of PV and battery devices are roughly divided into two categories: one is to access the battery device from the side of the locomotive to recover braking energy and control the voltage fluctuation of the traction network [7], and the other is to access the traction network side. For example, China's electrified railway mainly considers access to PV and battery devices from the high-voltage side (110 kV) and the traction side (27.5 kV). There are two types of PV and battery inverters: one is a threephase inverter combined with a three-phase/two-phase transformer, and the other is a back-to-back single-phase inverter [8]. The high-voltage side access method is suitable for small-capacity PV and battery devices, and the large capacity required for three-phase inverters leads to higher costs. At present, the railway power conditioners (RPCs) that utilize single-phase inverters to connect multiple source devices from the traction side have received frequent attention due to their excellent comprehensive performance [9]. The authors of [10–14] studied the unbalanced power compensation and harmonic control of the traction power supply systems with different RPC topologies. In [15], the train braking energy was recycled and reused through a RPC in conjunction with battery devices. In [16], a coordinated control scheme based on a RPC for PV and battery access to a traction power supply system was proposed, utilizing new energy to provide additional active power. Most of the above studies considered using PV or battery compensation power to reduce the consumption of fossil fuels but electricity is still mainly provided by thermal power generation. In [17], an overview of an emergency traction scheme for locomotive and substation coordination based on battery devices was presented and this paper aims to solve the problem of sudden accidents such as substation failures leading to locomotive power loss. In this state, the locomotive is completely powered by the battery. However, the research on the combined application of PV and battery for emergency traction in locomotives is not yet widely explored, and more research is needed to explore its potential and feasibility, if the PV power is connected to the battery for charging and collaborates with the battery to traction the locomotive, almost all of the electrical energy comes from renewable energy. However, to design the emergency power supply scheme for PV and battery systems and identify whether the collaborative integration of PV and battery systems can further change the railway energy supply system to achieve the longterm stable full-power traction of locomotives, the above-mentioned problems are worth deep research and solving. Due to the wide coverage of Chinese railways and superior energy storage conditions, as well as the long routes and abundant solar resources along such lines, solar power for AC-electrified railways has broad application prospects and extensive benefits. Therefore, this article takes the AC power supply system of Chinese railways with a rated voltage of 27.5 kV as an example and proposes the use of RPC access to PV and battery devices to achieve the emergency or long-term traction of locomotives, thus, expanding the function of RPCs and promoting the consumption of PV resources. In addition, due to differences in operational modes and design parameters between DC railways and AC railways, this article does not explore issues related to DC railways.

However, it is also important to determine whether the system remains stable when using the PV and battery locomotive traction and to reveal the main factors and laws that affect the stable operation of the system; all of these issues need to be addressed prior to the implementation of PV and battery traction locomotives in practice. At present, there are multiple frequency-scale instability issues in the traction power supply system of railways, such as low-frequency oscillation (LFO), harmonic resonance, and harmonic instability. Among them, LFO has been commonly reported in the electric railway domain around the world, thus, attracting widespread research attention [18,19]. The first reported occurrence of the LFO phenomenon dates back to 1996 in Norway when a rotating converter was

adopted in a traction substation [20]. Since then, in Germany, Sweden, and Norway, rotating converters have been used to interface the traction network, transforming three-phase utility power into a single phase for the catenary network [21]. The main cause of LFO has been attributed to the electromechanical characteristics of rotating converters [22]. However, for other electric railway systems [23,24], the mechanism of LFO remains unclear. Recently, from 2008 to 2016, there has been an increasing frequency of LFOs observed in Chinese railways [25,26]. Many studies have revealed that the occurrence of LFO in China is caused by the introduction of more converters and impedance mismatch [27–29]. Concurrently, locomotives have a LC resonant onboard filter that may oscillate, in addition, such a filter combined with the line can be triggered in oscillation by electric arcs, which is quite a commonplace phenomenon caused by the sliding contact mechanism [30]. In PV and battery locomotive traction, more converters may be introduced, which may further induce LFO. Research on the low-frequency stability of multi-source connected traction power supply systems is not yet complete. In [31], the integration of PV power into the traction network through a RPC was considered and an impedance model of a "PV-locomotivetraction network" was established. It was found that unreasonable parameter settings during the integration of the PV systems did indeed induce LFO; at the same time, the parallel connection of the PV modules led to multiple increases in the converters, which can also lead to LFO in the system. However, the instability mechanism of the system and methods to improve the system stability were not specifically revealed. The variation in the source impedance caused by the parallel connection of the subsystem modules and the parameter adjustment of the converter controller may lead to artificial active enhancement or the weakening of the low-frequency stability of the system. Therefore, to further improve the system stability, it is necessary to specifically reveal the sensitivity and law of the influence of controller parameters on the system's stability.

Regarding the above issues, this article proposes an emergency power supply scheme based on RPC access to PV and battery devices in Section 2.1. Through coordinated control strategies, PV and batteries can be used independently for the day and night emergency traction of locomotives. They may achieve "low-carbon" locomotive operation and also serve as a backup power source for the long-term traction of locomotives. On this basis, an impedance model of the "PV–battery locomotive network" coupling system under this scheme is established on the RPC DC bus side in Section 2.2. Then, the critical amplitude margin is defined for the first time based on the impedance ratio criterion; the influence of parameters on the low-frequency stability of the system is quantitatively evaluated and passive evidence is introduced to reveal the mechanism of the influence of the parallel number of PV and battery modules on the stability. Furthermore, parameter adjustment criteria and main circuit impedance reshaping governance are proposed to prevent LFO in Section 2.3. Finally, the feasibility of the emergency power supply scheme and the correctness of the stability study are verified through testing on the Starsim platform in Section 3.

#### **2. Materials and Methods**

#### *2.1. Proposal of Emergency Power Supply Scheme*

#### 2.1.1. System Topology

The topology of the "PV–battery locomotive network" system is shown in Figure 1, which includes a traction network, a high-speed locomotive, a railway power conditioner, and a new energy power supply system composed of PV and a battery.

**Figure 1.** System topology and control block diagram.

The three-phase electricity from the grid is converted from the traction substation to a 27.5 kV single-phase AC current, which is sent to the α and β power supply arms. The PV and battery are integrated into a 2 kV DC bus via their respective DC/DC converters, and the RPC-side single-phase inverter and LC-type filtering circuit are used to convert the power into 1.5 kV single-phase AC power through step-up transformers *T*α and Tβ, which is then sent to the α and β power supply arms. The *U*dc is the DC voltage on the input side of the RPC; *U*<sup>0</sup> is the single-phase AC voltage on the output side of the filtering circuit; *U*<sup>i</sup> is the unfiltered voltage of the RPC; *C*bus is the capacitor on the DC side of the RPC; VSC<sup>α</sup> and VSC<sup>β</sup> are single-phase inverters in RPC; *i*α, *u*α, and *u*<sup>β</sup> are the corresponding voltage and current of the supply arm; RMS means root-mean-square extraction; *P*PV and *P*Bat, respectively, represent the output power of the PV and battery; PLL stands for phaselocked loop; *U*0RMS is the root-mean-square value of *U*0; *i*<sup>L</sup> is the output current of the RPC inverter; *i*<sup>0</sup> is the output current after filtering; and sin*ωt* is the reference sine wave and *Z*load is the equivalent load in Section 2.2.2. DC converters in PV systems mainly include voltage regulation control and maximum power point tracking control (MPPT), while in battery systems they mainly include charging and voltage regulation control. Under the emergency power supply scheme, the PV and battery systems provide the locomotive's traction but it is still necessary to consider the overall plan for the connection of the PV and battery systems to the traction power supply system to formulate the control strategy.

The RPC converter is a dual-mode single-phase inverter. Its control strategy is shown in Figure 1. When it is applied to power compensation, the voltage *U*<sup>0</sup> is controlled to track the phase frequency of the traction network voltages *u*<sup>α</sup> and *u*β, and the output signal is compared with the harmonic and negative sequence reference signal, followed by the PWM input signal from the PI controller. At this time, the PV and battery are used as auxiliary power supplies, and the traction net is used as the main power source to control the single-phase inverter to support the voltage amplitude and frequency of both the DC and AC sides of the RPC. In the emergency power supply scheme, the PV and battery provide the DC-side voltage, the *U*dc amplitude, and the AC-side *U*<sup>0</sup> frequency support through a DC converter, and the inverter independently outputs the sinusoidal AC power. At this time, the PV and battery serve as the main power supply. The DC converter coordinates with the RPC inverter according to the actual working conditions to achieve traction network voltage management and locomotive traction under different power supply schemes.

#### 2.1.2. Division of Multiple Working Modes

The sum of the power inputs and outputs of the PV, battery, and RPC ports will affect the DC bus voltage *U*dc, as shown in Figure 1. It is necessary to balance the power of each port through the division of the working modes. The flowchart for the system's power control is shown in Figure 2.

**Figure 2.** Flowchart for the traction power supply system's power control.

In the above figure, *P*PV is the output power of the PV system, *P*Bat is the output power of the battery system, *P*Load is the maximum operating power of locomotives, and *P* is the power of the power supply arm calculated by measuring the voltage and current of the power supply arm. Based on the positive, negative, and zero values of *P*, the locomotive's operating conditions can be distinguished, which are namely, traction, braking, and no-load. In cases where *P* ≤ 0, if there is remaining capacity in the battery, it can be used to absorb the energy generated by the braking of the locomotive, as well as the energy provided by the PV system; In cases where *P* > 0 but the total power generated from the PV and battery systems is still lower than *P*load, the RPC system will operate under the power compensation scheme. However, if the traction substation experiences a fault or the output power generated from the PV and battery systems goes beyond *P*load, the RPC system will automatically switch to the emergency power supply scheme in order to utilize the PV and battery systems for the locomotive traction. Furthermore, the state-of-charge (SOC)

threshold value is considered to prevent over-charging and over-discharging from affecting the battery life.

This article focuses on the study of using PV and battery systems for emergency locomotive traction. For different working conditions, such as different levels of irradiance and state-of-charge (SOC), the proposed emergency power supply scheme includes different working modes as follows:

**Mode One:** When the PV power generation is much greater than the sum of the maximum operating power of the load and the lithium battery charging power, i.e., *P*PV  *P*Load + *P*Bat, and the SOC is less than 90%, the PV system can be used to provide the locomotive's traction and simultaneously charge the battery. When *P*PV  *P*Load + *P*Bat but the SOC is above 95%, in order to prevent the battery from over-charging, the PV system will be responsible for the locomotive's traction while the battery will be on standby.

**Mode Two:** When the PV power generation is slightly greater than the maximum operating power of the load but there is no additional power to charge the battery, that is, *P*Load < *P*PV ≤ *P*Load + *P*Bat, and the SOC is less than 90%, the PV system will only supply power to the locomotive, and the battery will be on standby.

**Mode Three:** When the PV power generation is less than the maximum operating power of the load, that is, *P*PV < *P*Load < *P*PV + *P*Bat, and the battery's SOC is higher than 5%, the PV and battery will work in voltage control mode to jointly provide the locomotive's traction.

**Mode Four:** When the PV power generation approaches zero, that is, *P*PV < *P*Load < *P*PV + *P*Bat, and the battery's SOC is higher than 5%, the PV system will be on standby, and the battery will provide the locomotive's traction.

The system topologies under the above four modes are different, meaning that it will be time-consuming and complex to analyze the system stability from the RPC AC side by using the impedance method. However, the operating conditions of the PV and battery combined locomotive traction under mode three are relatively common. Meanwhile, when carrying out RPC DC bus segmentation modeling, since the control method of each mode's DC converter is similar to mode three, the parallel connection or split of the DC converter output impedance is equivalent to the switching of modes, and the impedance resolution of the other modes becomes a high-proportion intersection or a subset of mode three, which is convenient to quickly reveal the factors and regularity affecting the stability under multiple working modes. The next section builds a mathematical model for the "PV–battery locomotive network" coupling system using the specific control method of mode three.
