Integration of distributed generation (DG) and energy storage systems (ESS) into the grid introduces 
various power quality challenges like reverse power flow and voltage fluctuations. Extensive research 
has investigated the application of solid-state transformer (SST) in smart grids within power systems to 
take advantage of benefits such as reactive power compensation, bidirectional power flow control, and 
significant size and weight reduction compared to traditional line-frequency transformers[1]. Due to 
limitations from semiconductor switches and magnetic components, high-voltage and high-power SST 
applications, such as light rail transit (LRT) trains, require series and/or parallel connections as shown 
in Fig 1. In this regard, SST circuit poses serious challenges in voltage balancing and power control 
considering integration of various energy sources[2].
This paper presents a multiport-active-bridge (MAB) based SST for dc charging system of LRT 
trains. As shown in Fig 2, the MAB converter is operated in symmetric or asymmetric manner with a 
single magnetic core to integrate various power sources for the purpose of high power density. In this 
digest, the operation principle of the MAB-based SST and its power control considering various LRT
operating scenarios will be studied and verified by preliminary simulations. The final paper will 
further include circuit design of the MAB-based SST and hardware-in-the-loop (HIL) verification.
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(a) (b)
Fig 1: Modularized connection (a) Input in series (b) 
Input in parallel.
Fig 2: Generalized MAB circuit. Fig 3: The proposed MAB-based SST.
II. OPERATION PRINCIPLE
Fig 3 depicts the proposed MAB-based SST. The CHB converter with m individual H-bridges in 
cascaded connection to synthesize a 2m+1 level waveform for single-phase ac/dc conversion. The 
H-bridge converter generates dc voltage, followed by the MAB-SST to integrate power from the grid, 
solar photovoltaic, energy storage system, and the charging system. 𝐿𝑠 and 𝐶𝑖
(i = 1,…,m) are
smoothing inductor and dc capacitors. 
A. CHB Converter
CHB is used for AC-DC rectification, where m H-bridges are in cascaded connection to 
synthesize a 2m+1 level waveform. Its control system includes two layers: an upper control system 
that adjusts the power factor and total DC voltage, and a lower control system that maintains the 
balance of capacitor voltages in each module. Fig 4 (a) shows the control diagram of the CHB in 
single-phase dq coordinates. A detailed description of this controller's modeling can be found in [3]. 
The basic concept relies on constructing a hypothetical lagging phase signal by 90° for dq 
transformation. Fig 4(b) shows the upper controller, which generates the active power component 
with duty cycle 𝑑𝑑 and the reactive power component with duty cycle 𝑑𝑞 for modulation.
To balance the voltage between the module capacitors, the lower controller introduces a duty 
cycle modification Δ𝑑𝑖
to the common duty cycle 𝑑𝑑 for each H-bridge, as illustrated in Fig 5.
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Fig. 4 (a) dq transformation, (b) Upper controller for CHB Fig. 5 Voltage balancing controller for CHB converter
B. MAB Converter
The MAB converter employed in the DC/DC stage allows power transfer among various power 
sources and loads by adjusting the phase shift between ports i and j. This relationship is described 
by (1).
𝑃𝑖𝑗 =
𝑉𝑖𝑉𝑗
2𝑓𝑠𝐿𝑖𝑗
𝑑𝑖𝑗(1 − 𝑑𝑖𝑗), 𝑑𝑖𝑗 = 𝑑𝑖 − 𝑑𝑗 (1)
where 𝑉𝑖 and 𝑉𝑗 are the input and output voltages referenced to port 1 by turn ration of the 
transformer, 𝑓𝑠
is the switching frequency of the converter, 𝐿𝑖𝑗 is the equivalent inductance seen from 
port 1 between port i and port j, and 𝑑𝑖𝑗 is the phase shift of the PWM signals normalized between 
the ith and jth ports[4].
In a multi-port system, it's essential to decouple the 
currents flowing through the interconnected ports to 
achieve individual control of each port. This paper
presents a method for achieving this based on a multi￾port nonlinear power decoupling technique. As shown 
in Fig 6, a PI controller is used to adjust the current of each power source to a reference value, the 
power reference value divided by the voltage generates a reference current, which is subtracted from 
the actual current, the resulting error value is then processed by the PI controller. Equations (2) and 
(3) show how the decoupling matrix is used to calculate the required phase shift, which enables 
independent control of each port. Here, 𝑑1 is the phase shift angle of the first winding, which is set 
to 0.
𝑑𝑖𝑗
𝑘+1 = 𝑑𝑖𝑗
𝑘 − [𝑓
′
(𝑑𝑖𝑗
𝑘
)]
−1
∙ 𝑓(𝑑𝑖𝑗
𝑘
) (2)
Figure 6: Power controller for MAB converter.
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𝑓
′
(𝑑𝑖𝑗
𝑘
) =
[
 
 
 
 
 
 
𝜕𝐼2
𝜕𝑑2
𝜕𝐼2
𝜕𝑑3
𝜕𝐼2
𝜕𝑑4
𝜕𝐼3
𝜕𝑑2
𝜕𝐼3
𝜕𝑑3
𝜕𝐼3
𝜕𝑑4
𝜕𝐼4
𝜕𝑑2
𝜕𝐼4
𝜕𝑑3
𝜕𝐼4
𝜕𝑑4]
 
 
 
 
 
 
(3)
III. SIMULATION RESULTS
In this section, simulations were conducted with circuit parameters given in TABLE I.
TABLE I - CIRCUIT PARAMETERS
Parameters Value
Number of H-bridge modules (m) 37
AC grid voltage 𝑉𝑠
22.8 kV
AC grid frequency 60 Hz
Transformer turns ratio 1:1:1:1
𝑉𝑑𝑐, 𝑉𝑜
750 V
𝑃𝑝𝑣,𝑚𝑎𝑥 11.19 kW
Nominal Capacity (LRT / ESS) 9 kWh / 45 kWh
Power rate (LRT) 1800 kW each station (Total 66.6 MW)
A. AC Grid Charging LRT only
In case A, the light rail charging is entirely supplied by the AC grid. Figure 7(a) shows AC grid
voltage and current, while Figure 7(b) displays power transmission characteristics.
(a) (b)
Fig. 7 (a) Case A Grid voltage and current, (b) Output power from grid to LRT
B. AC Grid and ESS Charging LRT
In case B, considering no solar power generation, the battery supplies half of the energy for light 
rail charging. The AC grid power decreases, as shown in Figure 8(a), while the power transmission 
in the DC microgrid is illustrated in Figure 8(b).
(a) (b)
Fig. 8 (a) Case B Grid voltage and current, (b) Power transmission in the DC microgrid
𝑷𝑴𝑽𝑫𝑪
𝑷𝒑𝒗
𝑷𝑬𝑺𝑺
𝑷𝑳𝑹𝑻
𝑷𝑴𝑽𝑫𝑪
𝑷𝑳𝑹𝑻
1800 kW
-1799 kW
901.418 kW
0kW
900 kW
-1800 kW
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C. AC Grid and PV Charging ESS
In the presence of solar power generation, charging the battery when there are no trains at the 
station to maintain battery capacity. AC grid power is depicted in Figure 9(a), and DC microgrid 
power transmission is illustrated in Figure 9(b).
(a) (b)
Fig. 9 (a) Case C Grid voltage and current, (b) Power transmission in the DC microgrid
IV. CONCLUSIONS AND FUTURE WORKS
This paper proposes a MAB-based SST for dc charging system of light rail transit (LRT) trains. 
Operation principle and simulations were conducted. Considering various scenarios of LRT 
operations. The results show that with the proposed MAB-based SST, peak power in the grid is
reduced by half. The reactive power between stations and the DC input voltage are balanced by CHB 
converter. The final paper will include design of the MAB-based SST and verification based on the 
hardware-in-the-loop (HIL) simulation写一下审稿意见