Chapter 1. LITERATURE REVIEW1.1 Simulation of power electronic circuitsTo simulate a power electronic circuit or any electrical circuit, there are a few procedures that are required to be followed. At first a mathematical model of the circuit under test is formed, then the circuit is represented by some mathematical or network equations and finally some techniques are chosen to solve those equations. After a proper model is chosen the mathematical equations for the model can be developed by using Maxwell’s cyclic current, widely known as Kirchhoff’s Voltage Law (KVL), nodal analysis or Kirchhoff’s Current Law (KCL) and the relatively newer approach called Modified Nodal Analysis (MNA). Nodal analysis had some advantages over mesh analysis, one being reduced number of equations compared to mesh analysis. But there were difficulties in the use of the classical nodal analysis particularly in computer simulation; certain elements such as voltage sources, dependent sources, transformers etc. could not be included in the analysis unless some conversion was done to some extent but on conversion there was always loss of information about the model 1. MNA was proposed by Chung-Wen Ho, in 1975 2, 3 to resolve the limitations of the classical nodal analysis. MNA can considerably reduce computation time for solving the network matrices and is easier to implement on a computer thus making it more suitable for simulation of electrical circuits. Real Time Simulation (RTS) of power electronic circuits demands even faster computation times and MNA was further upgraded to a Fixed Admittance Modified Nodal Analysis Method (FAMNM) 4, 5. This method allowed the system equations to be solved in very small time steps as required by RTS of fast switching power electronic converters. 1.2 Real Time SimulationWhenever a computer simulation of a computer model of any physical process or a system is done in parallel to its physical counterpart can be referred to as the Real Time Simulation (RTS). The virtual representation of physical system i.e. a virtual model runs simultaneously and also for the same time as the physical system. They may share common input variables and come out with comparable output. One good example for a RTS can be operation of the Fuel Injection System of a modern day computer controlled car engine, the onboard computer (Engine Control Unit) calculates the duration of operation and the interval between each operation based upon the throttle input, camshaft position, inputs from Oxygen Sensors, inputs from NOx sensors etc. all of which are measured in real time. A computer does all the computations using an operating system which eventually does all of its calculations in the form of 0’s and 1’s. All the differential equations, state equations or any mathematical functions representing a physical system will converted to a discrete system of 0’s and 1’s, these will be solved by the computer simulation software using their own solvers. The solvers use different numerical methods to do the computations and each may take different amount of time and produce results with different accuracy. To work with RTS the simulation associated would be for discrete time with a constant step size. Variable time-steps simulation is not suitable for RTS and hence the time is incremented in equal step sizes called Simulation Time Steps and the simulation itself is often called Fixed Time Simulation.As mentioned earlier the differential equations and the mathematical functions representing the model are solved to perform the I/O operations and to obtain the output of the model. However during a ‘discrete non real time simulation’ the actual time required to solve the aforementioned equations and functions may be more or less than the simulation time step. But in case of real time simulation it is necessary that (apart from the precise modeling of the physical system) all the computations are done within the simulation time step so that the model under test can accurately represent the functioning and perform all the I/O operations of its equivalent real or physical system. If the computations are not complete within the simulation time step the real time simulation results are not accurate, which is also referred to as an ‘overrun’. Moreover, if the computations are done before the simulation time step is complete then the remaining time, called the ‘idle-time’ 7 is simply lost, which is in contrast to the accelerated simulations where the remaining time would be utilized to perform the computations of the subsequent time step. Fig. 1.1. to Fig. 1.3. distinguishes between the characteristics of a real time and non-real time simulations. Fig. 1. 1. Timing diagram when Computation Time is less than Simulation Time Step (non-real time) Fig. 1. 2. Timing diagram when Computation Time is greater than Simulation Time Step (non-real time) Fig. 1. 3. Timing diagram during Real Time Simulation1.3 Selection of the real time simulatorAs suggested in 7-12 selection of real time simulators can be done based upon the applications to which they are intended for and can be categorized as:Rapid Control Prototyping (RCP):In a Rapid Control Prototyping a physical setup is always used and the controller is implemented in a real time simulator. The presence of a virtual controller enables it to be configured with more flexibility and be debugged easily. Since the modelling and testing of the controller becomes easy and fast, the prototype model of the controller can be developed sooner to a final robust product. Hardware in the Loop (HIL):In Hardware in the Loop a virtual model of the physical system is run on a real time simulator this virtual model emulates and behaves like a physical test bench; this virtual model is then controlled by a physical controller. In a variation of HIL, another real time simulator can function as a physical controller and feed the virtual model in a separate simulator. This configuration is very beneficial because the physical controller can be tested even without a physical setup, the tests are very repeatable and can be done without any fear of damage as in case of a real hardware based setup. The work in this literature uses Hardware in the Loop (HIL) Software in the Loop (SIL):Software in the Loop is possible as the simulators grow more and more powerful. This allows the controller and the virtual plant model to be implemented in the same real time simulator. Here no physical input/outputs (I/O) are used and that ensures that the fidelity of the signals are maintained. Moreover the simulations can now run only in the virtual mode and there are no constraints in following the time clock of the real world. Simulation can now take their own time and if resources are available simulations can run faster than the real world time while maintaining the integrity of the results.1.4 CPU and FPGA Based SimulationThe computer architecture has changed a lot in the last two decades, the advent of multiple cores, increase in parallel processing capabilities, decrease in the I/O latencies, faster working memories and improved hardware interfaces 13 have made the modern computer quite suitable for real time simulations. Fig. 1.4. shows an Intel chipset architecture widely used until 2011, Fig. 1.5. shows an architecture used currently in most modern computers. Fig. 1. 4. Computer chipset architecture prevalent before Sandy Bridge microarchitecture introduced in 2011 Fig. 1. 5. Modern computer chipset using Nehalem microarchitectureHowever, even though the CPU of a modern computer has a very high clock frequency the sequential nature of the operating system and the latencies still present at the i/o communications buses/ports allows it to have a minimal sampling time of about 5-10 ?s. This sampling time is often enough for the real time simulation of systems with slower dynamics such as a motor but for fast systems like the high frequency switches in the power electronic systems, this sampling rate is inadequate. So a methodology was developed wherein the models requiring very low sampling times are simulated in Field Programmable Logic Gate Arrays (FPGAs) 14 – 16, the highly parallel structure of the FPGA allowed very high sampling rates with simulation time steps as low as 250ns. Fig. 1.6. shows a CPU based simulation and Fig. 1.7. shows a FPGA based simulation. Fig. 1. 6. CPU Based Simulation Fig. 1. 7. FPGA Based Simulation1.5 Discrete Time Switch Model in Real Time SimulationThere are a number of models for representing a switch in order to make it suitable for computer simulations. Some simulators model the switch as a small resistance when it is ON and a large resistance when it is OFF 5, the value of the ON and OFF resistances are updated at every step of the iteration in the numerical method used for the simulation 5. The trouble with this approach is that for a large network with a number of switches huge amount of computational resources may be consumed for the updating of the resistance parameters at every step of the simulation. 17 proposes a model with a RC circuit for an open circuit and an inductor for a short circuit, this representation removes the need of a system matrix inversion when the switch state changes from ON to OFF or OFF to ON. Another model proposed in 18 represents the switch as a resistance across a capacitance, when the switch turns ON this resistance goes low and goes high when it is turned OFF. In the switch model mentioned in 5 an ideal switch is modelled as a conductance in parallel with a current source. This conductance will not change with the iteration steps and the current source shall provide details of the state of the switch. The work in this thesis shall consider this model for real time simulation.1.6 Validation of Power Electronic CircuitsValidation of power electronic systems is necessary to ensure that a virtual model behaves like a real physical system to the extent possible. Real time simulation of fast switching power electronic converters using a FPGA based ‘Electric Hardware Solver (eHS) 8 is discussed in 16. The design flow for the solver as well as validation results of the RTS of a number of power electronic converters are also covered. The results were validated by comparing the output of the eHS with those from the solver of SimPowerSystems (SPS). Some of the shortcomings of this method of simulating fast switching devices has also been discussed. Notwithstanding the shortcomings the technique of performing real time simulation of power electronic systems in FPGAs has a lot of potential.1.7 Multilevel InvertersAn introduction to the different topologies and working principles of multilevel converters are covered in 20. A more detailed overview about NPC inverters along with the modulation techniques is provided in 21. Different modulation schemes for a three level inverter are introduced in 22. A comprehensive working of the three level NPC inverter is discussed in 23, 24, this will also be covered in detail in the Chapter 3 along with a step by step procedure in the hardware validation of the same. The results obtained from the simulation of a three phase three level inverter in SimScape Power Systems (SPS), a FPGA based electrical Hardware Solver (eHS) and the physical converter shall be compared. Furthermore few techniques for optimizing the switch conductance for the Pejovic discrete time switch model shall be discussed in more details in Chapter 4.1.8 ConclusionA brief introduction to circuit simulation and real time simulation of power electronic converters is provided in this chapter. The chapter introduces some of the current trends in real time simulation and also familiarizes the reader with the basics of RTS. The chapter also introduces some switch models which are often used in the RTS of electrical systems. Certain constraints in the RTS of power electronic systems are also discussed, this chapter also reckons with related work done by other researchers and gives a glimpse of the work that shall be done to complete this thesis. ?