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## Analysis of continuous and discrete systems

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Linear algebra and circuit theory concepts are used in this book chapter to describe the formulation of the state equations of linear dynamic systems. The Laplace transform, commonly used in the solution of simple circuits, is impractical in the context of a large power system. Some practical alternatives discussed here are Modal Analysis, Numerical Integration of the differential equations and the use of Difference Equations. An electrical power system is basically a continuous system, with the exceptions of a few auxiliary components, such as the digital controllers. Digital simulation, on the other hand, is by nature a discrete time process and can only provide solutions for the differential and algebraic equations at discrete points in time.

Chapter Contents:

• 2.1 Introduction
• 2.1 Introduction
• 2.2 Continuous systems
• 2.2 Continuous systems
• 2.2.1 State variable formulations
• 2.2.1 State variable formulations
• 2.2.1.1 Successive differentiation
• 2.2.1.1 Successive differentiation
• 2.2.1.2 Controller canonical form
• 2.2.1.2 Controller canonical form
• 2.2.1.3 Observer canonical form
• 2.2.1.3 Observer canonical form
• 2.2.1.4 Diagonal canonical form
• 2.2.1.4 Diagonal canonical form
• 2.2.1.5 Uniqueness of formulation
• 2.2.1.5 Uniqueness of formulation
• 2.2.1.6 Example
• 2.2.1.6 Example
• 2.2.2 Time-domain solution of state equations
• 2.2.2 Time-domain solution of state equations
• 2.2.3 Digital simulation of continuous systems
• 2.2.3 Digital simulation of continuous systems
• 2.2.3.1 Example
• 2.2.3.1 Example
• 2.3 Discrete systems
• 2.3 Discrete systems
• 2.4 Relationship of continuous and discrete domains
• 2.4 Relationship of continuous and discrete domains
• 2.5 Summary
• 2.5 Summary
• References
• References

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