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Renewable-integrated power conversion architecture for urban heavy rail systems using bidirectional VSC and MPPT-controlled PV arrays as an auxiliary power source

  • Jakkrit Pakdeeto , Tanatip Boontawee and Kongpan Areerak EMAIL logo
Published/Copyright: August 19, 2025
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Open Engineering
From the journal Open Engineering Volume 15 Issue 1

Abstract

This study proposes a modern architecture for heavy railway systems that integrates renewable energy from photovoltaic arrays. This study introduces a transformation of the existing 12-pulse diode rectifier circuit in traditional power distribution systems into a bidirectional voltage source converter that regulates the direct current (DC) bus voltage. When the DC bus is constant, it can connect with solar energy sources, including the maximum power point tracker, under varying irradiance conditions. The PI controller parameters were designed using basic control system theory based on a time-invariant mathematical model. The simulation results demonstrate the system’s capability to maintain DC bus voltage despite load variations while achieving maximum power from the photovoltaic (PV) arrays. Furthermore, this study presents an assessment highlighting the cost savings associated with renewable energy sources from PV arrays in the proposed system.

Keywords: heavy railway system; auxiliary power source; PV arrays; maximum power point tracking, PI controller design

1 Introduction

Global warming has emerged as one of humanity’s most critical challenges. Renewable energy technologies, such as solar and wind power, have emerged as sustainable solutions to reduce the dependence on finite fossil resources [1]. In Thailand, urban transit systems play a vital role in reducing road congestion and transportation-related emissions [2]. The Mass Rapid Transit (MRT) Purple Line, which connects Nonthaburi and Bangkok, exemplifies the country’s commitment to enhancing public transportation, which is the case study in this work [3]. From the literature review [4], 16 passenger stations cover 23 km from the Khlong Bang Phai Station located in Nonthaburi Province to the Tao Poon Station in Bangkok. The conventional MRT Purple Line system in Thailand obtains an alternating current (AC) power of 115 kV from the Metropolitan Electricity Authority (MEA), as illustrated in Figure 1 [4], which will be stepped down to 24 kV at the distributed substations. However, the traction system for train cars uses a direct current (DC) power distribution of 750 Vdc. For the traction system, the output voltage from the distributed transformer is converted to DC power using a 12-pulse rectifier. The conventional system with this rectifier technology poses limitations regarding efficiency and compatibility with renewable energy. The conventional rectifier, designed for unidirectional power conversion, cannot facilitate energy recovery or effectively integrate renewable energy sources. As a result, the conventional MRT system cannot be operated within Thailand’s broader renewable energy strategy designed to meet Thailand’s Power Development Plan [5]. From the literature reviews [6], current information and future architectural directions of intelligent hybrid AC to DC systems in railway microgrids have been proposed. The systems integrated renewable energies can support the railway electrification systems in Thailand following with the national Power Development Plan. To achieve this goal, it is necessary to replace the existing DC railway grids with hybrid AC-DC system. This transition includes converting conventional unidirectional rectifiers to bidirectional rectifiers. Such an upgrade would enhance the flexibility of incorporating renewable energy into the system and contribute to long-term sustainability. Additionally, various international applications of photovoltaic (PV) arrays in electric railway systems are summarized in Table 1 [6,7,8].

Figure 1 Conventional architecture of the MRT Purple Line. (a) Conventional MRT Purple Line power system. (b) Conventional MRT Purple Line schematic.
Figure 1

Conventional architecture of the MRT Purple Line. (a) Conventional MRT Purple Line power system. (b) Conventional MRT Purple Line schematic.

Table 1

Existing railway systems with PV arrays installation

Location Installation areas Rated power
Beijing South railway station, China Station/depot/tunnel rooftop 220 kWp
Hangzhou East railway station, China 10 MWp
Shaling depot, China 2.4 MWp
Xizhaotong depot, China 1 MWp
Yuzhu depot, China 5 MWp
Tokyo Station, Japan 453 kWp
Keiyo Rolling Stock Center, Japan 1.05 MWp
Belgium 3,300 MWh
Madhya Pradesh and Diwana in Haryana, India 2 MWp
Byron Bay Railway, Australia Train rooftop 6.5 kWp
DEMU, India 4.8 kWp
Bhilai, India Trackside 50 MWp
Pendolino Hall, Finland 800 kWp

Based on Table 1, many countries have already developed electric railway systems that utilize solar PV energy as a power source for train operations. However, the implementations of such systems in Thailand have not been applied. Therefore, this study investigates the potential benefits of replacing the conventional 12-pulse rectifier with a bidirectional voltage source converter (VSC) in the MRT Purple Line system. This conversion aims to enable the integration of PV arrays into the railway power system in which the proposed converter can regulate the DC bus voltage constant of 750 Vdc to work efficiently with the traction system.

Figure 1a shows an overview of the conventional MRT Purple Line power system, with its schematic circuit shown in Figure 1b. In the conventional system, the 12-pulse rectifier is used to convert the AC power to DC power; however, this rectifier supports only unidirectional power flow and lacks flexibility for integrating renewable energy sources. To overcome these limitations, the rectifier can be replaced by a bidirectional VSC, as illustrated in the grey area of Figure 1b. After the bidirectional VSC is applied, PV arrays can be installed on the rooftops of each station in which the new system architecture proposed in this work is illustrated in Figure 2.

Figure 2 Proposed architecture for heavy railway with PV integration.
Figure 2

Proposed architecture for heavy railway with PV integration.

As seen in Figure 2, modifications to the conventional system can be categorized into two categories. The first is the replacement of the AC power supplied by the MEA and the diode rectifiers with the bidirectional VSC to regulate the DC bus at a constant 750 Vdc using the PI controller. Moreover, this bidirectional VSC can obtain energy from the electric train under regenerative braking mode [9]. The second is the installation of PV arrays, which can be done on the passenger station rooftop to achieve renewable energy [10]. It can connect with the PV arrays controlled by the boost converter to track the maximum power point (MPP), which supplies power to the DC bus as the auxiliary source. Nevertheless, this study focuses on this modification at only one station, before extending it to other stations in the future. Therefore, two controllers must be designed to meet the voltage standard agreements [11]. The advantages of the new architecture proposed in this work are as follows:

  • Renewable energy from PV arrays connected to a boost converter controlled by the MPP tracking (MPPT) algorithm to achieve the MPP can be installed for the modern architecture of the heavy electrical railway system.

  • The ways to design the controllers for the bidirectional VSC and the boost converter are presented.

  • Simulation using hardware-in-loop (HIL) can ensure that both controllers can be implemented without errors from the C language programming code.

  • It is cost-effective.

The remainder of this study is structured as follows: Section 2 presents the proposed system, including the mathematical model. Section 3 presents the proposed system’s controllers. Section 4 discusses the simulation results using HIL and the cost-effectiveness evaluation of the proposed system. Finally, Section 5 provides the conclusion.

2 Considered system

Figure 3 shows the proposed architecture of the heavy electrical railway system. The structure consists of three main parts. The first part is the utility grid 115 kV from the MEA of Thailand, feeding the main power into the DC bus through the transformer, transmission line, and bidirectional VSC. For the second part, the PV arrays, as the auxiliary source, supply the maximum power tracked by the MPPT algorithm via the boost converter. This converter is used to step up the DC voltage from the PV arrays. The last part is the constant power loads (CPLs) represented for the two trains per passenger station.

Figure 3 The schematic of the proposed electric railway system.
Figure 3

The schematic of the proposed electric railway system.

In Figure 3, the gray area is modified from the conventional structure to be available for renewable energy. Two controllers for the converters in the proposed electrical railway system are concerned. PI controllers are used to regulate the DC bus voltage for a bidirectional converter. At the same time, the MPPT algorithm is applied to the boost converter to track the maximum power from the PV arrays. For the controller design process, the dynamic model is very important. However, the proposed system has many converters, resulting in a time-varying model that is complicated for controller design or stability prediction in the future. The literature reviews [12,13,14,15,16] show that the direct–quadrature (DQ) and generalized state space averaging (GSSA) approaches are suitable for analyzing a three-phase power system and a DC/DC converter, respectively. To obtain the time-invariant model, the DQ and GSSA methods are then applied, and basic circuit theories, such as Ohm’s and Kirchhoff’s laws, are also applied. The resulting mathematical model of the considered system is given in (1). The details of the model derivation can be found in the study by Pakdeeto et al. [14].

(1) I ̇ s , d = − R eq L eq I s , d + ω I s , q − 1 L eq V bus , d + 1 L eq V s , d I ̇ s , q = − ω I s , d − R eq L eq I s , q − 1 L eq V bus , q + 1 L eq V s , q V ̇ bus , d = 1 C eq I s , d + ω V bus , q − 1 C eq I in , d V ̇ bus , q = 1 C eq I s , q − ω V bus , d − 1 C eq I in , q I ̇ in , d = 1 L F V bus , d − R L F L F I in , d + ω I in , q − K pv K pi E dc ⁎ E dc A r L F + K pv K pi E dc E dc A r L F − K iv K pi E dc X v A r L F + K pi I in , d E dc A r L F − K ii E dc X id A r L F I ̇ in , q = 1 L F V bus , q − ω I in , d − R L F L F I in , q + K pi I in , q E dc A r L F − K ii E dc X iq A r L F E ̇ dc = K pv K pi E dc ⁎ I in , d A r C F − K pv K pi E dc I in , d A r C F + K iv K pi I in , d X v A r C F − K pi I in , d I in , d A r C F + K ii I in , d X id A r C F − K pi I in , q I in , q A r C F + K ii I in , q X i q A r C F + ( 1 − d ⁎ ) I Lboost , C F − P CPL1 , C F E dc − P CPL2 , C F E dc X ̇ id = K pv E dc ⁎ − K pv E dc + K iv X v − I in , d X ̇ iq = − I in , q X ̇ v = E dc ⁎ − E dc I ̇ Lboost , = V pv L boost − ( 1 − d ⁎ ) E dc L boost V ̇ pv = − I Lboost , C pv + N p C pv ( I s c . + K i ( T − T ref ) ) G G ref − I s c . e V o c . n C V t − 1 T T ref 3 e T T ref − 1 E g n C V t e V pv N s n C V t + I pv R s N p n C V − 1 .

The proposed mathematical model in (1) can be used to provide the system responses with a fast computational time compared with those of the exact topological model from the MATLAB program [14]. It can also be used for the controller design, which will be presented in the next section.

3 Controller design

For the considered system, two controllers will be designed for both the bidirectional VSC and boost converter. The PI controller regulates the DC bus voltage to be constant via the bidirectional VSC. Meanwhile, the MPPT algorithm was used to force the boost converter to track the maximum power from the PV arrays. The details of these controllers will be explained as follows:

3.1 PI controller for the bidirectional VSC

Figure 4 shows the PI controller diagram for the considered system. In this figure, there are four inputs, and the output is the control signal. This signal will be compared with the sinusoid carrier signal to provide the pulse width modulation called “SPWM” for the bidirectional VSC. Furthermore, in Figure 4, there are two loops, the voltage and current loops, forming a cascade control in the d-q axes. The output from the voltage loop in the d-axis is the reference current. The reference current in the q-axis is set to zero, resulting in the unity power factor. The output from the current loop in both the d and q axes is the modulation index in the d–q axes. These values will be changed into a three-phase signal using the inverse Park’s transformation [12].

Figure 4 PI controller structure for DC bus voltage regulation.
Figure 4

PI controller structure for DC bus voltage regulation.

As shown in Figure 4, the parameters following K pv , K iv , K pi , and K ii can affect the system’s performance. Therefore, the PI controller design is necessary to ensure that the system can be operated according to the EN 50163:2004 standard [11]. In this study, the PI controller parameters will be designed using the conventional method. The closed-loop transfer function of the voltage and current loops obtained from the accurate model will be compared with the transfer function of the general second order system shown in (2).

(2) T ( s ) = C ( s ) R ( s ) = ω n 2 s 2 + 2 ζ ω n s + ω n 2 ,

where ζ is the damping ratio and ω n is the natural frequency. The values of these two parameters influence the system performances [17], including rise time, settling time, and overshoot percentage. In addition, these values can be calculated from the basic control theory, while the system performances are desirably designed. In this study, the closed-loop transfer function for the current and voltage loop designs can be derived from the averaging model of (1). Then, the characteristic polynomials of these transfer functions are compared with those of (2). As a result, the equations to design the parameters K pv , K iv , K pi , and K ii are given in (3)–(6), respectively. The details of these equations and the PI controller design can be found in the study by Pakdeeto et al. [18].

(3) K pv = 2 ζ v ω nv E dc ⁎ 2 C F − 1 R Load M d P CPL ,

(4) K iv = ω nv 2 C F M d ,

(5) K pi = R L F − 2 ζ i ω ni L E dc ,

(6) K ii = − ω ni 2 L E dc .

These equations are used to design the PI controller parameters in which ζ v and ζ i are set to 0.8 for the underdamped response. In addition, ω nv is set to 50 rad/s, and the value of ω ni will be ten times more than that of ω nv . The results using the system parameters from Table A1 in the appendix are K pv = 44.9881 , K iv = 1443.98 , K pi = − 0.00001 , and K ii = − 0.04 . These PI controller parameters will be used for the simulation results in Section 4.

3.2 MPPT for the boost converter

Besides the PI controller, the perturbation and observation (P&O) algorithm [19] is used in this study to provide the maximum power from the PV arrays. This algorithm controls the boost converter while the irradiances are changed. The P&O algorithm is simple and can reliably track the MPP in both simulations and experiments [20]. The principle of the P&O algorithm operates in a time-stepped manner by adjusting the output voltage of the PV arrays. During the perturbation step, the voltage and current of the PV arrays were measured to calculate the power output. This power output is then compared between the current and previous time steps to determine whether to adjust the PV output voltage. This adjustment process is referred to as the observation process. The voltage adjustment of the PV cells is achieved by modifying the duty cycle of the boost converter. The principle of MPPT using the P&O algorithm can be explained using the characteristic curves in Figure 5, which represent different irradiances.

Figure 5 Characteristic curves demonstrating the P&O algorithm.
Figure 5

Characteristic curves demonstrating the P&O algorithm.

The P–V curve is also illustrated using the characteristic curves in Figure 5. The P 1 curve has an irradiance intensity greater than the P 2 curve. At point A on curve P 1 , the PV cell operates at its MPP. However, if the operating point shifts from B to A, the power difference ( Δ P ) between the current and previous time steps is positive, whereas the corresponding voltage difference ( Δ V ) is negative. This results in a negative ratio of ( Δ P / Δ V ) . To ensure that the PV arrays reach the MPP, the output voltage of the PV must be decreased. Alternatively, if the operating point moves from C to A, both Δ P and Δ V are positive. This results in a positive ratio of ( Δ P / Δ V ) > 0 . In this case, to reach the MPP, the output voltage of the PV must be increased. The ways to decrease or increase the PV output voltage can be controlled via the duty cycle of the boost converter, according to the relation in (7).

(7) V pv = ( 1 − d ⁎ ) E dc ,

where E dc is the DC bus voltage controlled as a constant with the bidirectional VSC, V pv is the output voltage of the PV arrays or the input voltage of the boost converter, and d * is the duty cycle of the converter.

The P&O algorithm presented in this study is straightforward, similar to the hill-climbing algorithm presented by Abdelsalam et al. [21]. It can be implemented in the experiment with the flowchart shown in Figure 6.

Figure 6 Flowchart of the P&O algorithm for MPPT.
Figure 6

Flowchart of the P&O algorithm for MPPT.

The flow chart of the P&O algorithm shown in Figure 6 can be implemented with the C-programing language in five steps, as follows:

Step I: Set the initial duty cycle.

Step II: Measure the voltage and current from the PV arrays.

Step III: Evaluate ∣ Δ P / Δ V ∣ ≤ ε s . If this condition is satisfied, the boost converter will be controlled with the same duty cycle as the previous one and will return to Step II. Otherwise, the algorithm will proceed to the next step.

Step IV: If the ratio Δ P / Δ V ≥ 0 is true, the duty cycle of the boost converter will be decreased by the step size ( Δ d ) . However, if the ratio Δ P / Δ V ≥ 0 is false, the duty cycle of the boost converter will be increased by Δ d .

Step V: Update the variable to the old values for the next iteration and return to Step II.

The P&O algorithm will be operated following the abovementioned steps until the MPPT is achieved. However, in this study, the maximum power of the proposed PV arrays is equal to 496 kW, which equals power generated by 1,240 PV panels with each generating 400 W [14]. The number of PV arrays is calculated from the width × length of one passenger station [10]. Figure 7 shows the P–V and I–V curves involving the proposed PV arrays. The P–V characteristic shows the MPP at any irradiance, and they will be used to confirm the MPPT using the P&O method in Section 4.

Figure 7 P–V and I–V characteristic of the proposed system.
Figure 7

P–V and I–V characteristic of the proposed system.

4 Simulation results

To confirm both controllers for the proposed system in this study, a simulation on the MATLAB program processed by a high-performance microcontroller board, sometimes called HIL, is presented. In addition, a cost-effectiveness assessment is also provided in this section.

4.1 HIL

HIL testing is a popular tool in modern engineering, ensuring that systems perform as intended under practical conditions [22]. In this study, the power converter models were used via the SimPowerSystem® block set, while the proposed controllers will be implemented in a physical microcontroller board TMDSDOCK28335 produced by Texas Instruments. This will result in enhanced safety and reduced costs. It can also ensure that the proposed architecture can be implemented without errors from the controller program. Figure 8 shows a signal flow diagram of the HIL simulation.

Figure 8 HIL signal flow diagram of a HIL simulation.
Figure 8

HIL signal flow diagram of a HIL simulation.

As seen in Figure 8, the input of the HIL microcontroller board, TMDSDOCK28335, comprises six signals. E dc ⁎ is the reference voltage, and E dc is the DC bus voltage response. V a , b , c and I a , b , c are the voltage and current at the transformer output in the three-phase power system, respectively. The mentioned variables will be used for the procedures of the PI controller programmed in C language in the TMDSDOCK28335 board. In addition, V pv and I pv are the voltage and current signals used to track the MPP of the PV arrays in which the P&O algorithm is also programmed in C language in the same TMDSDOCK28335 board. After the PI controller and MPPT are processed inside the microcontroller board, the output signals ( M a ⁎ , M b ⁎ , M c ⁎ ), which act as the control signal for the IGBT module of the bidirectional VSC, will be delivered into MATLAB. The parameter d ⁎ is the duty cycle of the boost converter. Figure 9 shows the physical connection between the MATLAB program and the microcontroller board.

Figure 9 Microcontroller board interface with MATLAB program.
Figure 9

Microcontroller board interface with MATLAB program.

In this study, two cases will be simulated by HIL while considering fixed irradiance and fixed CPL. The first case is load variations following the number of passengers per train, as shown in Table 2 [18], while the irradiance is a constant value of 1,000 W/m2, as shown in the system responses in Figure 10. The P CPL , 1 represents the power of a train in the passenger station, and the rated power per train is 1.055 MW following the load type W4, as shown in Table 2. However, the passenger station might be constructed with two trains per station. Therefore, the P CPL , 1 and P CPL , 2 will be used to represent the rated power of the trains per station.

Table 2

Load power depending on the passengers

Load type Passenger load TE (N) P train (MW)
W0 Tare load 19.1 0.642
W1 Seating 20.6 0.692
W2 Seating + Standee (5/m2) 26.9 0.904
W3 Seating + Standee (6/m2) 28.6 0.965
W4 Seating + Standee (8/m2) 31.4 1.055

TE is the tractive effort per motor. P train is the load power per train.

Figure 10 System responses when the irradiance is equal to 1,000 W/m2.
Figure 10

System responses when the irradiance is equal to 1,000 W/m2.

It can be seen from Figure 10 that E dc can be regulated at 750 Vdc with low oscillation following the voltage standard until the rated power is achieved. To ensure this case with other scenarios, the HIL results at irradiance values of 750 and 500 W/m2 are illustrated in Figures 11 and 12, respectively.

Figure 11 System responses when the irradiance is equal to 750 W/m2.
Figure 11

System responses when the irradiance is equal to 750 W/m2.

Figure 12 System responses when the irradiance is equal to 500 W/m2.
Figure 12

System responses when the irradiance is equal to 500 W/m2.

The responses in Figures 10–12 were used to confirm the PI controller that the system can be operated even when the system loads are changed. To confirm the MPPT, the HIL result when the irradiance is varied and with fixed P CPL , 1 and P CPL , 2 at W0 load type (0.642 MW) with a total equal to 1.284 MW is depicted in Figure 13.

Figure 13 PV power output under varying solar irradiance levels.
Figure 13

PV power output under varying solar irradiance levels.

The result in Figure 13 shows the system responses focusing on the output power ( P pv ) from PV arrays in which the MPP, according to the PV curve of Figure 7, as seen in the gray area, can be tracked using the P&O algorithm. When the irradiance equals 1,000 W/m2 after t = 2 s, P PV will be tracked at 486 kW. Although the irradiance changed from 1,000 W/m2 to 750 W/m2 to 500 W/m2 at 4 and 6 s, the P&O algorithm could still track the MPP at 355 and 228 kW, respectively. Moreover, Figure 13 shows that the system response can be controlled at 750 Vdc when the irradiance changes. This means that the proposed controllers programmed into the microcontroller board can be implemented without errors in the controller’s code.

4.2 Cost-effectiveness assessment

About 1,240 PV panels can be installed on the roof of a train station terminal, generating 496 kW of power under a solar irradiance of 1,000 W/m². To estimate the energy, the PV arrays can be produced around the 10 h daylight period (7 a.m. to 5 p.m.). The results are summarized in Table 3.

Table 3

Electrical energy generated by the 1,240 PV panels

Solar irradiance (W/m2) Maximum power (kW) Energy (kW h) Units in the 3-phase power system Electricity cost (THB/kWh) [23] Estimated daily savings (THB)
1,000 496 4,960 1653.33 2.3845 3942.37
750 358 3,580 1193.33 2845.50
500 233 2,330 776.67 1851.97

When considering the electricity generated from solar panels as an auxiliary energy source, it is revealed that these installed PV panels can significantly reduce the daily electricity costs of running the considered system. The approximate daily savings at one station are shown in Table 3, demonstrating the effectiveness of the solar panel installations in reducing electricity expenses.

5 Conclusion

This study proposes a modern architecture for the heavy railway system in Thailand. The proposed modern architecture uses a bidirectional VSC instead of the 12-pulse diode rectifier used in the conventional system. As a result, the energy from the regenerative braking and PV arrays and the constant DC bus voltage can be achieved. The PI controller controls the bidirectional VSC, resulting in a constant DC bus voltage, and the parameters of this controller are designed from the model to achieve the desirable performance. When the DC bus voltage is controlled, the P&O method tracking the MPP from the PV arrays is applied. In addition, the proposed mathematical model derived from the combination of the DQ and GSSA methods is presented. The simulation results via HIL are provided to ensure that the proposed system can be operated according to the voltage standard at the DC bus and that the MPP is tracked from PV arrays achieved at any irradiance. Moreover, a cost-effectiveness assessment is presented to clearly show the advantages of the proposed architecture for the heavy railway system.

Acknowledgments

This work was supported by Suranaree University of Technology.

  1. Funding information: This work was funded by (i) Thailand Science Research and Innovation (TSRI), and (ii) National Science, Research and Innovation Fund (NSRF) (NRIIS no. 195631).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript, consented to its submission to the journal, reviewed all results, and approved the final version. Jakkrit Pakdeeto contributed to the conceptualization, methodology, mathematical model derivation and validation, controller design and investigation, as well as writing and editing the original draft. Tanatip Boontawee was responsible for simulation, data curation, and manuscript formatting. Kongpan Areerak provided supervision, resources, visualization, funding acquisition, and project administration.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: All data generated or analyzed during this study are included in this published article.

Appendix

Table A1 shows the system parameters, including the descriptions used for the controller designs and the simulation results.

Table A1

System parameters

Parameters Values Descriptions
V s 115 kV MEA’s voltage source
ω 50 Hz System frequency
R eq 0.001 Ω Transmission line resistance
L e q 0.01 µH Transmission line inductance
C eq 12 nF Transmission line capacitance
R L F 0.5 µΩ Inductor’s inner resistance of the filter circuit
L F 1.2 µH Inductor value of the filter circuit
C F 500 mF Capacitor value of the filter circuit
K pv 44.9881 Proportional gain of the voltage loop
K iv 1443.98 Integral gain of the voltage loop
K pi −0.00001 Proportional gain of the current loop
K ii −0.04000 Integral gain of the current loop
N p 124 Amount of parallel PV stack
N s 10 Amount of PV per stack connected in series
I s .c . 10.17 A Short-circuit current of the PV module
V o .c . 47.8 V Open-circuit voltage of a PV module
G ref 1,000 W/m2 Standard irradiance value
T ref 25°C Standard temperature value
R sh 5 µΩ Shunt resistor value of the PV module
R s 5 MΩ Series resistor value of the PV module

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Received: 2025-03-11
Revised: 2025-06-05
Accepted: 2025-07-17
Published Online: 2025-08-19

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/eng-2025-0132
Keywords for this article
heavy railway system; auxiliary power source; PV arrays; maximum power point tracking, PI controller design
Creative Commons
BY 4.0

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