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FPGAbased realtime simulation for EV station with multiple highfrequency chargers based on CEMTP algorithm
Protection and Control of Modern Power Systems volume 5, Article number: 27 (2020)
Abstract
The electric vehicle (EV) charging station is a critical part of the infrastructure for the wide adoption of EVs. Realtime simulation of an EV station plays an essential role in testing its operation under different operating modes. However, the large numbers of highfrequency power electronic switches contained in EV chargers pose great challenges for realtime simulation. This paper proposes a compact electromagnetic transient program (CEMTP) algorithm for FPGAbased realtime simulation of an EV station with multiple highfrequency chargers. The CEMTP algorithm transforms the traditional EMTP algorithm into two parallel subtasks only consisting of simple matrix operations, to fully utilize the high parallelism of FPGA. The simulation time step can be greatly reduced compared with that of the traditional EMTP algorithm, and so the simulation accuracy for highfrequency power electronics is improved. The EV chargers can be decoupled with each other and simulated in parallel. A CPUFPGAbased realtime simulation platform is developed and the proposed simulation of the EV station is implemented. The control strategy is simulated in a CPU with 100 μs timestep, while the EV station circuit topology is simulated in a single FPGA with a 250 ns timestep. In the case studies, the EV station consists of a twolevel rectifier and five dualactive bridge (DAB) EV chargers. It is tested under different scenarios, and the realtime simulation results are validated using PSCAD/EMTDC.
Introduction
The electric vehicle (EV) is an effective way to tackle environmental challenges such as carbon emission [1, 2]. Due to limited battery capacity, increasing utilization of EVs requires widely installed charging stations [3]. Realtime simulation plays an essential role in the study of the electromagnetic transient characteristics of EV charging stations. These can accelerate the design of control and protection systems. In addition, realtime simulation with hardwareintheloop (HIL) simulation can realize joint simulations of an EV charging station model and an actual control prototype. This can reduce test costs and shorten the development cycle compared with offline simulation [4, 5]. However, simulating multiple highfrequency EV chargers realtime in small steps is a significant challenge due to the need for detailed devicelevel modeling of power electronic converters (PECs) and accurate interactions [6, 7]. Therefore, it is valuable to develop an efficient realtime simulation algorithm and implementation method for the system.
The typical time step of traditional realtime simulators is in the range of 20 μs ~ 100 μs, and interpolation algorithms are required to accurately reflect the switching events [8, 9]. However, the interpolation algorithms incur a great computing burden in realtime simulation. Therefore, in recent years, the field programmable gate array (FPGA) is used for small time step realtime simulation of detailed models because of its numerous logic resources [10,11,12,13], which can achieve high parallel computing. Thus, fastswitching circuit topology can be simulated in the FPGA while the control strategy is still performed in the CPU [14]. In this work, a lightweight CPUFPGA architecture realtime simulation platform is established for simulating an EV station with multiple highfrequency EV chargers in a single FPGA.
There are currently two main categories of EMTP algorithm: statespace method [15, 16] and nodal analysis method [17], while both methods have been applied in realtime simulation. To achieve high accuracy and efficiency in devicelevel realtime simulation, a compact EMTP (CEMTP) algorithm is proposed for the EV station simulated on FPGA. The CEMTP algorithm compresses the serial computing process of a traditional EMTP into two parallel subtasks consisting of simple matrix calculation, to make full use of the high parallelism of FPGA. In addition, the CEMTP algorithm avoids the calculation of intermediate variables such as injection current, and thus the computational complexity in each step is greatly reduced. The simulation time step is thus reduced and hardware resources are saved by optimizing the simulation process. In addition to optimizing the simulation algorithm, there have been some studies on the decoupling of the simulation circuit [18, 19]. A system decoupling method is proposed for the EV station in this paper. This decouples the EV station into multiple EV chargers to be simulated in parallel. Different from the traditional EMTP algorithm, using this method in CEMTP can divide large matrix operations into small matrix operations, so as to further reduce the computing burden of FPGA. In addition to the CEMTP algorithm, the associated discrete circuit (ADC) switch model [20, 21] is adopted to accurately reflect the switching moments to further improve the performance of the realtime simulation.
Using highlevel synthesis tools for FPGA implementation can improve the efficiency of the simulation [22]. In addition to the lightweight hardware platform and the CEMTP algorithm mentioned above, implementation methodologies are proposed to optimize the EV station simulation. Given the fastswitching characteristic of the EV chargers and computing complexity of the control strategy, the circuit is simulated at 250 ns timesteps while the control signals are updated every 100 μs. The simulation loop operation of each subsystem can be pipelined to reduce resource consumption and latency. The idle time is eliminated to further reduce the time step of the simulation, while the use of fixed point matrix operation method saves hardware resources.
This paper is organized as fellows. The structure of the realtime simulation system for the EV station is discussed in Section II. The CEMTP algorithm and system decoupling method are proposed in Section III, while Section IV gives the details of the implementation. The simulation study and resource consumption are discussed in Section V. These are verified by PSCAD/EMTDC simulations. Finally, the conclusion is drawn in Section VI.
The structure of the simulation system
The EV station, which is integrated with five EV chargers and one central rectifier, is chosen as the study case to perform on the realtime simulation platform. Each EV charger uses the dual active bridge (DAB) topology, while the central rectifier is a twolevel converter. The main parameters are shown in Table 1. In this paper, the central rectifier maintains the DC bus voltage and each EV charger controls its battery charging power, as shown in Fig. 1.
The main architecture of the lightweight CPUFPGAbased platform is shown in Fig. 2. It integrates the CPU and FPGA resources. The PXIe8135 is the master board, which contains a quadcore Intel i73610QE processor, dual channel DDR3, 1600 MHz memory controller, all the standard I/O, and an integrated hard drive, and is connected with the Kintex7 XC7K410T FPGA board and the hostPC. The control strategies are performed in the CPU, which receives the instantaneous circuit parameters from the FPGA and sends the modulated wave signals to the FPGA through the PXIe bus. The cores of the CPU run at 2.3GHz. The FPGA board is a slave board, which performs the realtime simulation of the EV station circuit and the generation of PWM switch signals under the instruction of the master board. The clock frequency of the FPGA board is set to 160 MHz. There are 254,200 lookup tables (LUTs) and 508,400 flipflops (FFs) which constitute the configurable logic blocks (CLBs) to realize both the combinational logic and sequential logic. The FPGA contains 1540 digital signal processing (DSP) slices and 28,620 block RAMs, which provide 25 × 18 multipliers and memory resources mainly used in the matrix operation for the history current update and circuit parameter calculation. In addition, the FPGA I/O interfaces can be connected to oscilloscopes to observe the simulation results.
Communication between the CPU controller and the FPGA plays a vital role in realtime simulation. PXI Express increases the available bandwidth to 8GB/s, enabling lowlatency data exchange and improving the realtime simulation system performance, particularly when a submicrosecond level time step is required. The hostPC provides a humanmachine interface (HMI), receiving sampling data from the CPU and displaying the control and simulation waveforms.
The simulation algorithm of EV Station
The CEMTP algorithm
The traditional EMTP proposed by Professor Dommel is mainly based on a nodal analysis method, which involves complex serial calculations. The traditional EMTP algorithm also contains the calculation of intermediate variables such as injection current. However, only the node voltage and branch current in the simulation are required. In order to improve simulation efficiency, the CEMTP algorithm is proposed so that the circuit parameters can be obtained directly by redesigning the simulation process. At the same time, the serial calculations are transferred into two parallel subtasks, which only contain simple matrix calculations.
Similar to the traditional EMTP, all the branches in the network are transformed into Norton equivalent circuits. The following steps show the process of the simulation adopting the CEMTP algorithm.
Step 1: The incidence matrix M_{NAM} is formed in such a way that its matrix elements correspond to the nodes and branches in the circuit, as:
where N_{n} is the number of nodes and N_{b} is the number of branches in the circuit. When node i is connected to branch j and the current of branch j flows away from node i, the entry of M_{NAM} (m_{ij}) is 1. On the other hand, when the current of branch j flows away from node i, the entry of M_{NAM} (m_{ij}) is − 1. When node i and branch j have no connection in the network, M_{NAM} (m_{ij}) is 0.
Step 2: Voltage source or current source branches are represented by equivalent admittance and parallel current sources, while other branches are represented by equivalent admittance and a parallel history current source. The history current of each branch can be expressed by the branch voltage and current as:
where Y_{b} is the equivalent admittance of the branch, α is the voltage coefficient and β is the current coefficient.
If the backward Euler method is applied for numerical integration, the equivalent admittance of all branches can be obtained. For the inductance branch L, there are:
For the capacitance branch C, there are:
For the switch branch, α and β vary with the switch state. The switch is equivalent to a small inductance L_{s} when it is on, and to a small capacitance C_{s} when it is off. Thus, according to (3) and (4), there are:
In order to improve the efficiency of simulation, an appropriate inductance L_{s} and capacitance C_{s} are chosen to keep Y_{b} constant, as:
In this step, only α and β need to be updated during the simulation (Fig. 3).
Rewriting (2) to matrix form yields:
where I_{h}, V_{b}, and I_{b} are the N_{b} × 1 vectors consisting of I_{h}, V_{b}, and I_{b} of each branch, respectively. Y_{b} is the N_{b} × N_{b} diagonal matrix composed of Y_{b}, whereas α and β are the N_{b} × N_{b} diagonal matrices consisting of α and β, respectively.
Step 3: According to the history current I_{h} and equivalent current I_{s} of voltage/current source, there is
where I_{inj} is the N_{b} × 1 vector composed of the injection current. Then, the nodal voltage vector V_{n}, the branch voltage vector V_{b}, and the branch current vector I_{b} can be expressed as:
where Y_{n} is the N_{n} × N_{n} nodal admittance matrix. By analyzing the relationship between branch voltage and current, the following equation can be obtained:
Equations (7)–(11) reveal that the simulation requires many serial steps. When implemented on hardware, the intermediate variables of the traditional EMTP algorithm consume large resources and reduce efficiency. Therefore, a compact simulation loop is derived as:
where K and J are coefficient matrices, which can be precalculated and prestored. Thus, the CEMTP algorithm saves the resources occupied by intermediate variables during the simulation loop. This is beneficial for the simulation speed while at the same time may also reduce the error diffusion.
In the simulation loop, the node voltage and branch current are decided purely by the last time step history current and source equivalent current. Recording the index of node number and branch number such that the first N_{n} nodes are node voltage and the latter N_{b} branches are branch current, the following matrix equation can be obtained:
The simulation loop is more compact and the number of penalties required in a single step is reduced compared to the traditional EMTP method.
System decoupling method
The EV station with multiple highfrequency EV chargers consists of detailed converter models, especially the switching frequency of EV chargers is 50 kHz. Thus, in order to guarantee that the simulation loop can be completed in a time step, a system decoupling method is adopted to further improve the realtime simulation performance. This method decouples the system into multiple EV chargers, which can interact through the interface. This method realizes the parallel simulation of each EV charger and makes full use of the parallelism of FPGA. In comparison, the nondecoupled system involves largescale nondiagonal matrix operations, which limit the minimum simulation time step and consume more hardware resources to execute. Dividing a system into multiple subsystems can effectively reduce the complexity of matrix operations.
The capacitor C is selected as the interface between multiple subsystems as shown in Fig. 4. It is equivalent to two same voltage sources in branch p and branch q. Then, the interface voltage can be written as:
The error analysis of the decoupling method is given in the Appendix. The thirdorder local truncation error caused by the decoupling method is relatively small compared to the nondecoupling method and the influence on the results is negligible.
Based on the CEMTP algorithm, the realtime simulation procedure is shown in Fig. 5. The green part shows the initialization of the electrical circuit, in which each subsystem performs its own initialization and the coefficient matrices and variables are loaded to the corresponding simulation steps. The subsystems are updated according to (15) in the blue part, while the blue part and yellow part indicate a closed loop between the circuit and control. The node voltage V_{n} and brand current I_{b} are sent to the CPU and the control signals are transferred to α and β to control the circuit. The purple part shows the interface calculation between the subsystems.
The whole EV station circuit is modeled in one single FPGA board for maximum resource utilization. This method avoids the amount of data to be exchanged between boards and reduces simulation latency. Normally, the subsystems are decoupled at the capacitor, and thus each EV charger composes a subsystem and the central rectifier is also defined as a subsystem. With this decoupling method, the scalability of the electric vehicle charging station simulation is improved, and the number of simulated EV chargers can be adjusted at any time according to actual needs.
Platform implementation
Simulation loop
To improve the efficiency of simulating a larger EV station in one FPGA board, a CPUFPGAbased realtime simulation platform is constructed in the National Instruments (NI) PXI chassis, in which the control strategy and circuit topology are simulated at different time steps. Figure 6 shows the system simulation loop between the electrical and control systems. This indicates the cooperation between the FPGA and CPU.
For the EV station, all the calculations of the circuit and control subsystems start simultaneously. The control signal calculation on the CPU usually takes more time than the circuit update on the FPGA depending on the actual execution times of the CPU and FPGA. As a result, the FPGA must wait for the CPU until the next time step is reached. In order to improve realtime simulation performance, the control signal calculation in the CPU has a 100 μs timestep and the circuit simulation is calculated in the FPGA with a 250 ns timestep. In this way, the FPGA and CPU operations are relatively independent while the data exchange is performed every 100 μs. When the control signals are not updated, the FPGA runs the next simulation cycle with the control signals of the previous calculation.
When a simulation loop starts, the FPGA reads the control signal and the CPU reads the electrical variables of the last step. Then, all the modules of the electrical calculation begin simultaneously. At the same time, the CPU begins to update the control signal. During each time step in the FPGA, the node voltages, branch currents, history current sources and switch status are updated. By adopting the pipeline method, not only can each subsystem be calculated in parallel, but the calculation within the subsystem can also be performed in parallel, which further reduces the simulation time step in the FPGA.
FPGA implementation
The whole simulation implementation in the FPGA is shown in Fig. 7. As shown, data exchanges between the CPU and FPGA are through FIFO. The FPGA receives the modulation wave signal and voltage or current source signal of the circuit from the CPU, while transmitting calculation results of the node voltage and branch current to the CPU. Since the control signal calculation on the CPU and circuit simulation on the FPGA are simulated with different time steps, the FIFO performs data exchange to realize asynchronous communication to ensure accurate interaction between the FPGA and CPU (Fig. 7).
In the FPGA, the CEMTP algorithm simulates the electrical system, which mainly contains the update of the switch states, the history current and the calculation of the node voltage and the branch current. The system can be solved by floatingpoint operation in offline simulation to obtain high accuracy results. However, it is more suitable to adopt fixedpoint operation to satisfy the clock requirement and limit FPGA multiplier resources. The fixedpoint format of the variables is set to <±,25,12>, which is confirmed by the DSP multiplier. A DSP slice is used for the 25bits × 18bits multiplication, and the <±,25,12 > fixedpoint multiplication uses two DSP slices that are fewer than in the singleprecision floatingpoint format.
While the switch states are being updated to regenerate α and β, the multiplier reads the matrix K and J prestored in block RAM for the next calculation. In calculating the node voltage and branch current, mainly 25bits × 18bits matrixvector multiplications using DSP multipliers are performed. Matrix multiplications occupy the most resources and time in FPGAbased realtime simulation, while the multiplier consumption of nondiagonal matrix multiplications is linearly proportional to the matrix order. According to the proposed system decoupling method, largescale matrices existing in the nondecoupled EV station simulation are divided into smallscale matrices to avoid complex serial multiplications. For example, the EV station contains 48 nodes and 73 buses, which will generate a 73 × 73 matrix to be solved. Using the system decoupling method, the 73 × 73 matrix can be divided into one 13 × 13 matrix and five 12 × 12 matrices, which can be solved in parallel. The multiplications involving nondiagonal matrices are achieved by a multiplyaccumulate module, which is executed in serial and spends the most clock cycles in each time step. The pipeline method is also adapted to execute the multiplication and accumulation. This saves nearly half of the execution time in each step.
To update the history current, mainly logic blocks are used for operations. Since α and β representing the switch states are both 1, 0 or − 1, logic resources are used for calculations to replace multipliers. This improves the history current update speed and saves multiplier resources.
Simulation results and discussion
The tested EV station consists of a twolevel rectifier and five highfrequency DAB EV chargers. This section applies the CEMTP algorithm to the CPUFPGAbased realtime simulation platform to simulate the EV station. The results of the realtime simulation and corresponding PSCAD simulation are displayed in Fig. 8.
Resource consumption
According to the FPGA implementation details, the execution time, as well as the hardware resource utilization of each subsystem, are presented in Table 2. Lookup tables (LUTs), flipflops (FF), digital signal processing (DSP) slices and block RAMs are recorded as the mainly consumed resources.
As discussed in Sections 3 and 4, the latencies of the additional steps in each subsystem are the same, and only the inconsistency of matrix dimensions leads to different latency and resource consumption. The number of rows of the matrix determines the DSP slice needed for calculation, and the number of matrix columns determines the time required for matrix multiplication. For example, the central rectifier subsystem that contains 8 nodes and 13 branches consumes the most simulation time and hardware resource because the matrices P and Q have a larger size (21 × 13) than other subsystems (20 × 12).
In the EV station realtime simulation, the execution time is constant which is consistent with the central rectifier subsystem. It demonstrates that the latency is determined by the central rectifier subsystem, which has the largest maximum latency of 38 clock cycles. When new EV chargers are integrated, the execution time will not increase as long as the scale of the new subsystem is not larger than the previous ones. If the traditional EMTP method is used, the realtime simulation can only be realized with a simulation step of 1 μs. However, when the electric vehicle charging station is working at a switching frequency of 50 kHz, the simulation step must be 250 ns or less to achieve the required simulation accuracy. Therefore, the CEMTP algorithm must be used. In addition, to attain a smaller time step, the scales of the subsystems are similar in case of an increase of the system latency. The parallel structure ensures that more EV chargers can be integrated to take full advantage of the FPGA resources without time constraints.
For comparison, the central rectifier is simulated using the CEMTP algorithm and the traditional algorithm, and the latencies of the simulations are shown in Table 3. It can be seen that the latency of the CEMTP algorithm is much smaller than the traditional EMTP algorithm, proving that the CEMTP algorithm greatly improves simulation efficiency. When trying to simulate the EV station with the traditional EMTP algorithm, the execution time exceeds 2 μs, which is too large for the DAB switched at 50 kHz. However, when the EV station is simulated with the CEMTP algorithm, the 250 ns timestep realtime simulation is realized. Since the system clock is 160 MHz, it means that the circuit simulation of the EV station in one time step is accomplished within 40 clock cycles.
Plugandplay scenarios
The EV charger is designed to achieve plugandplay capability and can adjust the output power according to different vehicles. This greatly improves the convenience of charging. Figure 8 shows the transient waveforms of the plug and play scenarios. EV chargers 4 and 5 start charging the EVs at the power of 4 kW and 5 kW at 2 s and the charging power of EV charger 1 changes from 8 kW to 3 kW at 3 s. At 4 s, EV chargers 3 and 5 are cut off from the charging station. When there is an abrupt power change, both the AC and DC buses experience disturbances. The charging current of the EV station and input DC bus voltage of the EV chargers observed from the oscilloscope are shown in Fig. 8 (a1) and (a2), respectively. Since the central rectifier is responsible for maintaining the DC bus voltage, the DC voltage returns to the rated voltage quickly after each disturbance. Figure 8 (a3) shows the power tracing performance of the EV chargers observed from the host PC, and all follow the control signals well. From Fig. 8 (a1)(a3) it can be seen that the output power of the EV chargers track the power commands instantly after the plug and disconnection of the EVs. When the charging power changes, the input current changes accordingly. The offline simulation results in PSCAD/EMTDC are conducted for validation as shown in Fig. 8 (b1)(b3).
Fault operation scenarios
A singlephase to ground fault is applied to the AC bus at 2.0 s of the simulation with the steadystate initial condition and is cleared after 0.1 s. The transient waveforms of the AC bus voltage and current and DC bus voltage are presented in Fig. 8(c1)(c3). The AC side operates under an asymmetric operating condition and the DC bus voltage fluctuates significantly during the fault. As the charging voltage is isolated by the DAB from the fault location, the voltage is only slightly affected so the impact of faults on EVs is effectively reduced. When the fault is cleared, the DC bus voltage is restored to the rated voltage and the EV chargers go back to normal operation mode. It indicates that the EV station has the ability to ride through the fault. The fault transient results in PSCAD/EMTDC are shown in Fig. 8 (d1)(d3). Through the realtime simulation with the CEMTP algorithm, the fault transient waveform can be obtained and the control strategies for the EV station can be verified.
Conclusion
In this paper, a CEMTP algorithm has been proposed to achieve realtime simulation of an EV station in a lightweight CPUFPGAbased platform. The simulation results of the CEMTP algorithm for an EV station with multiple highfrequency EV chargers prove to have a good consistency with the simulation results in PSCAD with a switching frequency of 50 kHz. The time latency study shows that compared with the traditional EMTP algorithm, the CEMTP algorithm for the EV station reduces the simulation execution time by more than 65%, which means that a small time step of 250 ns can be used. The system decoupling method ensures that the time step remains constant when the scale of the simulation increases. The proposed CEMTP algorithm and platform implementation in high switchingfrequency simulation has great potential for highprecision simulation of power systems with high converter penetration.
Availability of data and materials
Not Applicable.
Abbreviations
 EV:

Electric Vehicle
 CEMTP:

Compact Electromagnetic Transient Program
 FPGA:

Fieldprogrammable Gate Arrays
 PEC:

Power Electrical Converters
 LUT:

Lookup Table
 FF:

Flipflop
 CLB:

Configurable Logic Block
 DSP:

Digital Signal Processing
 HMI:

Humanmachine Interface
 NI:

National Instruments
 DAB:

Dualactive Bridge
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Acknowledgements
This work is supported by China Postdoctoral Science Foundation (BX20200221, 2020 M671122), National Key Research and Development Program of China (2019YFE0122600), National Natural Science Foundation of China (51877133).
About the authors
Z. R. Li(1996), male, PHD student, Major in modeling and realtime simulation of power system integrated with renewable energy.
Email: lzr9602@sjtu.edu.cn.
J. Xu(1991), male, PHD and Postdoctor, Major in power system stability analysis, power electronic modeling, and realtime simulation.
Email: xujin20506@sjtu.edu.cn.
K. Y. Wang(1979), male, PHD and Professor, Major in power system dynamic and stability, renewable energy integration, and converter dominated power systems.
Email: wangkeyou@sjtu.edu.cn.
P. Wu(1995), male, PHD student, Major in control, modeling and realtime simulation of renewable energy.
Email: panghuwu@sjtu.edu.cn.
G. J. Li(1965), male, PHD and Professor, Major in power system analysis and control, wind and PV power control and integration, and microgrid.
Email: liguojie@sjtu.edu.cn.
Funding
This work is supported by China Postdoctoral Science Foundation (BX20200221, 2020 M671122), National Key Research and Development Program of China (2019YFE012784), National Natural Science Foundation of China (51877133).
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Zirun Li performed the study of the algorithm, verified the simulation and draft the manuscript. Jin Xu, Keyou Wang and Guojie Li engaged in modifying the paper and submitted it to the PCMP. Pan Wu participated in the realtime simulation experiments. All authors read and approved the final manuscripts.
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Appendix
Appendix
The error of the decoupling method in Section 3.2 has negligible effect on the simulation results. According to the decoupling method in Fig. 4, the capacitor voltage is expressed as:
It can be seen from the above equation that the capacitor is discretized by the Euler method. At the same time, the rest of the circuit still uses the backward Euler method.
For the Euler method, the local truncation error is:
If the decoupling method is not used, the whole circuit adopts the backward Euler method and the capacitor voltage is expressed as:
For the backward Euler method, the local truncation error is:
The local truncation errors relative to the analytical solution under both methods are:
It can be seen from the above analysis that the use of the decoupling method has little effect on the system simulation error, while both methods have firstorder accuracy.
The local truncation error of the decoupling method relative to the nondecoupling method is:
In the same way, the error caused by the decoupling method is negligibly small compared to the nondecoupling method.
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Li, Z., Xu, J., Wang, K. et al. FPGAbased realtime simulation for EV station with multiple highfrequency chargers based on CEMTP algorithm. Prot Control Mod Power Syst 5, 27 (2020). https://doi.org/10.1186/s4160102000171x
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Keywords
 Dualactive bridge (DAB)
 Electromagnetic transient program (EMTP)
 Fieldprogrammable gate arrays (FPGA)
 EV charger
 Realtime simulation