Part 1: Electrical Networks---Biot-Savart's Law, Ampere's law, Circuit models of passive elements, AC and DC circuit theory & analysis with passive elements, network theorems, mesh/loop analysis, phasor analysis, transient analysis, real-, reactive-, and apparent-power flow, power factor, electromagnetic induction, flux & flux linkages, self & mutual inductances, magnetically coupled circuits, LC resonance.

Part 2: Electrical Machines---Transformers, windings architectures, ideal & non-ideal analysis, magnetization current vs load current, leakage & magnetizing inductance, Equivalent Circuit Development---steady-state & dynamic, voltage regulation, Generators/Alternators---architecture & construction of stator & rotor, air-gap flux & variation, full-pitched & short-pitched windings, induced EMF expressions, armature, rotating magnetic field creation via rotor or stator, induction motor architecture, synchronous motor architecture, torque-speed characteristics, efficiency characteristics, ideal vs non-ideal behavior, performance metrics.

Image credit: Gemini

Part 1: System Dynamics & Analysis---Introduction to Systems and Dynamic Systems, Properties of Dynamic Systems, Differential Equations as System Models, Time-Domain Analysis of Linear Systems, The Concept of System Response, Time-Domain Behavior of First-Order & Second-order Systems, Step and Impulse Responses, Natural Frequency, Damping Ratio, and Time-Response Characteristics, Bandwidth, Time-constant, Transient & Steady State Behavior, Steady-State Errors, Matrix formulation of Dynamic Systems, Matrix Exponentials for State-Space Systems, State-Matrix & Eigenvalues, Introduction to Frequency-Domain Analysis, Fourier Series, Fourier Transforms, Laplace Transforms, Concept of Transfer-Functions, Poles & Zeros, Graphical Analysis Tools—Bode Plots, Nyquist Diagrams.

Part 2: System Models & Modeling---Modeling of Electrical Systems—RLC Circuits, Electromechanical Analogies, Modeling of Mechanical Systems—Translational and Rotational Systems, Modeling of Electromechanical Systems—DC & AC Motor fundamentals, Sensors, and Actuators, Modeling of Thermal Systems, Introduction to Lumped vs. Distributed Parameter Models, Long-transmission line model, wave-propagation and reflection phenomena.

Part 3: System Controls---Analysis & Synthesis Introduction to Control Systems. Open-loop vs. Closed-loop Systems, Concept of System disturbance and noise, Block Diagrams and Transfer Functions, Concept of Interconnected Systems, Introduction to Feedback, Need for Feedback Control, Advantages & Trade-offs, Proportional (P) Control, Proportional-Integral (PI) and Proportional-Derivative (PD) Control. Introduction to PID Control, Introduction to Stability Analysis in the s-Plane, Stability Metrics, Gain Margin, Phase Margin, Routh-Hurwitz Criterion, Nyquist Criterion, Performance Metrics—Transient Response, Steady-state Errors, Stability & Robustness Guarantees, Design-oriented Analysis.

Image credit: Gemini

Part 1: Review of Fundamentals---Essentials in Power Electronics, Power Systems, and Control Systems.

Part 2: Models & Modeling Approaches---Electrical dynamic modeling and Design-oriented Analysis of solar PV, batteries & supercapacitors; Inverter/converter modeling approaches--- frame transformations, dynamic phasors, State-Space and Frequency-Domain modeling for control; Large-signal nonlinear dynamical models, Linearization---large-signal feedback vs small-signal Taylor series methods, Jacobian & Eigenvalues, feedback vs feedforward controls, Internal model principle, second-order generalized integrator (SOGI) & Resonant Controllers,  Grid synchronization & PLLs; Common-mode modeling of inverter circuits, electromagnetic noise, EMI/EMC considerations & filters.

Part 3: Systems-level Architectures & Control---Battery-energy storage systems (BESS), PV inverters, Hybrid dual-mode inverters, Battery Chargers, Front-end converters, PFC controls, MPPT controls for PV systems---modeling & control analysis, Grid-following (GFL) control of inverters, anti-islanding schemes, next-generation control paradigms---Grid-Forming (GFM) of inverters---droop, VSM, VOC flavors; Stability analysis, fault ride through capabilities; Grid codes and standards 1547 & 2800.

Image credit: Gemini