# Real-Time Simulator for Dynamic Systems on FPGA
## 2 Related Work
The acceleration is based on FPGA technology using Runge-Kutta methods to solve the Ordinary Differential Equation (ODE), and the results are compared with GPP (2.83 GHz Intel Core 2 Quad CPU). In the work of [4], a simulation was made of a photo-voltaic system using the ML605 kit to develop a simulation environment that enabled a step of approximately 1 \(\mu\)s. The use of the FPGA was determined by the maximum step size that the system supported, approximately 5 \(\mu\)s, which was not viable for studies using platforms such as \(\times\)86 CPUs or digital signal processors (DSPs). This system was also implemented in Matlab/Simulink, generating off-line (non-real-time) simulation data for comparison and validation purposes. Auxiliary hardware items including a PC and DSP were used for data acquisition and conditioning of the final data. For communication, connection of the FPGA with the PC employed a Peripheral Component Interconnect Express (PCIe) bus, enabling a communication rate of up to 5 Gbps. Successful implementation was achieved with a time step of 1 \(\mu\)s.  
An example of FPGA for real-time simulations on dynamic systems is shown in [32]. This version works with a time step between 150 us and 200 us. The main target of this product is the simulation of power systems and High-Voltage Direct Current (HVDC). An overview of a real-time simulations approach to a smart-grid is presented in [33]. This work shows the current context of real-time simulators and the new demands from smart-grid and similar systems, such as machine-to-machine (M2M) systems, the Internet of Things (IoT), and others. The work presented in [18] presents a methodology for assessing the credibility of simulations in electronic control systems using an FPGA-based HIL platform. The work addresses the need for efficient testing methods for complex control systems by proposing a HIL platform replicating the actual operating conditions of these systems. The evaluation methodology considers performance, time-domain response, and frequency-domain response, enabling the quantification of simulation credibility. The results show that the platform achieves credibility indices above 60%, offering a quantitative approach for validating simulations in electronic control systems. Similarly, ref. [19] developed and implemented a real-time simulator based on ADC, focusing on the optimal selection of switch model parameters. The work deals with modeling power converters using the Associated Discrete Circuit (ADC) method and Modified Nodal Analysis (MNA). The authors employed the Particle Swarm Optimization (PSO) algorithm to optimize the simulator's behavior to adjust conductance and damping resistance values, minimizing numerical errors and improving simulation accuracy. The results demonstrate that the proposed simulator accurately reproduces the voltage and current waveforms of the modeled converters, validating the method's effectiveness in real-time simulation. The manuscript presented in [20] proposes the implementation of a real-time simulator for electrical systems using floating-point arithmetic on an FPGA. The study aims to develop a low-cost simulation platform that offers performance comparable to high-cost commercial simulators. The authors use Hardware Description Language (HDL) to ensure flexibility in FPGA architecture selection and avoid dependence on commercial packages. The results demonstrate that the developed simulator can operate in real time, allowing for precise analysis of interactions between the simulated electrical system and its control, with efficiency similar to commercial solutions. Similarly, ref. [22] explores the application of HIL techniques and digital control in single-phase PFC converters. The study presents an approach that allows for testing digital controllers under realistic conditions without the need for physical prototypes, using FPGAs to implement the mathematical models of the converters in real time.