# Modeling and Simulation of Complex Power Systems

Simulation is a critical activity in engineering design, becoming more and more critical as power systems grow in complexity. Objectives of this class are: review and critical evaluation of the most typical modeling and simulation methods for electrical power systems; understanding of the role and the problems connected with multi-physics simulation; understanding of the impact of complexity in simulation; understanding of the uncertainty in modeling and simulation.

To improve the student’s learning experience, access to the interactive development platform Jupyter will be provided, which enables to test lecture examples and implement own simulations. Notes, lecture slides, recent scientific papers to support the most advanced topics and simulation examples demonstrated during the lectures complete the whole course offer.

Automatic network analysis, to solve a generic electrical network in an automatized way. Difference between “signal flow” and “natural coupling”. Review of nodal analysis. Modified Nodal Analysis and “matrix stamp” concept, to build an object-oriented approach to modeling. Problem of matrix inversion and matrix inversion algorithms.

Resistive Companion simulation method, used by most of the network solvers in commercial tools. Concept of equivalent DC-Circuit. Different integration methods (Euler Forward, Euler Backward, Trapezoidal rule). Object-oriented approach for the implementation of dynamic simulation solvers. Non-linear automatic network analysis.

State equation and system simulation, as alternative philosophy with respect to the Resistive Companion method for solving electrical networks. Concept of state of a system and state equations. Object-oriented approach to state space modeling. Composing models in terms of state equation formulation. Predictor-corrector integration method.

Multi-physics simulation, with particular focus on the Modelica language (grammar, syntax, application examples). Difference between simulation languages and simulation solvers.

Decoupled electromagnetic/electromechanical transient simulation, to decouple complexity and enable large-scale power system simulation. Focus on Dynamic Phasors.

Methods for system partitioning. Complex systems and the curse of dimensionality. Methods of Diakoptics: theory, partitioning and limits. Latency Insertion Method: leap-frog algorithm, application and stability considerations.

Real Time Simulation and Hardware in the Loop, to test a component in interaction with the system. Motivations and challenges for Real-Time simulation. Difference between Hardware in the Loop and Power Hardware in the Loop. Interface design and stability issues.

System simulation and uncertainty, with analysis of methods to study uncertain processes. Traditional approach of Monte Carlo simulation (definition, advantages and disadvantages). Polynomial Chaos Theory: definition, approach to circuit simulation, limits and possible extensions.