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Prоblem 1. (20 pоints) Cоnsider а three-phаse voltаge source inverter supplying a balanced three-phase RL load. Modify the code provided below to implement a hysteresis current control strategy such that the phase currents track sinusoidal references with an RMS value of 10 A at 60 Hz. The controller shall maintain the current ripple within a maximum band of ±1 A. Problem 2. (20 points) Consider a single-phase AC-DC converter. This configuration is implemented with an H-bridge circuit and a grid reactance interfacing the grid and the controlled rectifier. It is also known that both DC-link voltage and PFC are working as expected. Given the grid voltage: , grid reactance of 10 Ohms, and grid current of , determine the amplitude modulation index of this controlled rectifier if the load DC current is . Problem 3. (20 points) A three-phase inverter is employed to supply a two-phase induction machine with orthogonal (90° phase-displaced) voltages. The machine is configured with three terminals: Phase 1 (0° phase angle), Phase 2 (90° phase shift), and a neutral connection. Propose a carrier-based PWM (CPWM) strategy by determining the reference pole voltages , , and for this system. Assume that and derive expressions for and . Problem 4. (20 points) The control block diagram of a three-phase back-to-back configuration is presented below. Since the regulators , , and are used to control AC variables, they cannot be implemented as simple PI controllers. Modify the system as needed to allow the use of a hysteresis control to control the current in each phase. Problem 5 (20 points) (a) Consider a single-phase back-to-back configuration with a shared leg, meaning that one leg is common to both the input (120 , 60 Hz) and the output, forming a three-leg topology. If the grid power factor is unity (with ) and the load requires a frequency equal to that of the grid, if the load power factor is equal 0.5, determine the load reference voltage that will maximize the current across the shared leg. Assume amplitude modulation index equal to 1 for both input (rectifier) and output (inverter). (b) Given the conditions described in (a), determine the minimum DC-link voltage? Congratulations, you are almost done with this exam. DO NOT end the Honorlock session until you have submitted your work to Brightspace. When you have answered all questions: Use your smartphone or scanner to scan your answer sheet, and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Submit your exam to this assignment: Exam 2 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.