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**Advanced modeling of electromechanical system - 100 hours**

__PART 1 - ENHANCED BACKGROUND (25 HOURS)__

1. Lagrange and Hamilton equations of electromechanical systems. (2 hours)

Description of elements, Lagrange and Hamilton functions, constrains equations, general coordinates, degrees of freedom.

2. Modeling of Electro-Mechanical Converters (EMCs) by using Lagrange and Hamilton formalism (4 hours).

Possibility and limitation, energy and co-energy functions, equations of converters, algorithms for generation of converter equations at arbitrary winding connection,

3. Parameters of EMCs (4 hours)

Representation of windings and magnetic circuit geometry, simplified method of calculations of inductances,

4. Structures of EMC equations, ( 4 hours)

Structural and parametric nonlinearity, symmetry and asymmetry of windings and magnetic circuit, transformation of variables, role of symmetrical components, equivalent schemes,

5. Mode of operations of EMCs (2 hours)

Dynamic and steady states, electromagnetic transients at constant rotary speed,

6. Methods of solving of EMC equations (6 hours)

Reducibility of equations, analytical solutions for transient and steady-states, numerical techniques

7. Introducing saturation into mathematical models of EMCs (3 hours)

Energy base modeling, equivalent magnetizing current, properties of the co-energy function

__PART 2 - ADVANCED EXAMPLES (25 HOURS)__

1. Advanced models of asynchronous machines (5 hours)

Modeling internal asymmetry of windings, rotor eccentricities and cage asymmetry.

2. Advanced models of synchronous machines (5 hours)

Modeling internal asymmetry of windings and rotor eccentricities.

3. Modeling mechanical part of a drive with EMCs (2 hours)

Interactions of electromagnetic and mechanic phenomena.

4. Design and analysis of PM machines (10 hours)

Introduction to electromechanical devices with permanent magnet: materials, analysis, and applications, mathematical models of PM machines, field analysis of PM machines, brushless motors, PM generators for wind and water application.

5. Parameter calculations of circuital models of electrical machines by field methods (3 hours)

Calculations of magnetic co-energy and linkage fluxes by FEM, separation of leakage fields, determination of winding inductances based on the co-energy, fluxes or magnetic field distribution in air gap, approximating relationships between linked fluxes and currents of windings in nonlinear magnetic core.

__PART 3 - ADVANCED EXAMPLES (25 HOURS)__

1. Advanced models of asynchronous machines (5 hours)

Modeling internal asymmetry of windings, rotor eccentricities and cage asymmetry.

2. Advanced models of synchronous machines (5 hours)

Modeling internal asymmetry of windings and rotor eccentricities.

3. Design and analysis of PM machines (10 hours)

Introduction to electromechanical devices with permanent magnet: materials, analysis, and applications, mathematical models of PM machines, field analysis of PM machines, brushless motors, PM generators for wind and water application.

4. Parameter calculations of circuital models of electrical machines by field methods (5 hours)

Calculations of magnetic co-energy and linkage fluxes by FEM, separation of leakage fields, determination of winding inductances based on the co-energy, fluxes or magnetic field distribution in air gap, approximating relationships between linked fluxes and currents of windings in nonlinear magnetic core.

__PART 4 - MODELLING OF POWER ELECTRONICS FOR ELECTRO-MECHANICAL SYSTEMS (25 HOURS)__

1. Structures of power electronics converters applied for electrical drives (7 hours)

Choppers, rectifiers, inverters, power converters, principles of control, control signals, filtering, automatic control structures for drives.

2. Methods of computer modelling (7 hours)

Models of power switches, modelling of real structures, modelling of converters as controlled voltage and current sources.

3. Practical modelling of selected converters (7 hours)

Formulation of control signals, creation of a converter model using both the methods simulation.

4. Modelling power electronics in frequency domain (4 hours)

Parametric model of switching devices, formulation of voltage-current equation, harmonic balance methodology on example of matrix converter.

The course is conducted by employees of Cracow University of Technology.

Price:** 3300 Euros **

Date: **February - June 2012**

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