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## Numerical integrator substitution

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Numerical Integration Substitution (NIS) constitutes the basis of Dommel's EMTP, which is now the most generally accepted method for the solution of electromagnetic transients. This book chapter describes the basic formulation and solution of the numerical integrator substitution method as implemented in the electromagnetic transient programmes.

Chapter Contents:

• 4.1 Introduction
• 4.1 Introduction
• 4.2 Discretisation of R,L,C elements
• 4.2 Discretisation of R,L,C elements
• 4.2.1 Resistance
• 4.2.1 Resistance
• 4.2.2 Inductance
• 4.2.2 Inductance
• 4.2.3 Capacitance
• 4.2.3 Capacitance
• 4.2.4 Components reduction
• 4.2.4 Components reduction
• 4.3 Dual Norton model of the transmission line
• 4.3 Dual Norton model of the transmission line
• 4.4 Network solution
• 4.4 Network solution
• 4.4.1 Example: conversion of voltage sources to current sources
• 4.4.1 Example: conversion of voltage sources to current sources
• 4.4.2 Network solution with switches
• 4.4.2 Network solution with switches
• 4.4.3 Example: voltage step applied to RL load
• 4.4.3 Example: voltage step applied to RL load
• 4.5 Non-linear or time varying parameters
• 4.5 Non-linear or time varying parameters
• 4.5.1 Current-source representation
• 4.5.1 Current-source representation
• 4.5.2 Compensation method
• 4.5.2 Compensation method
• 4.5.3 Piecewise linear method
• 4.5.3 Piecewise linear method
• 4.6 Subsystems
• 4.6 Subsystems
• 4.7 Sparsity and optimal ordering
• 4.7 Sparsity and optimal ordering
• 4.8 Numerical errors and instabilities
• 4.8 Numerical errors and instabilities
• 4.9 Summary
• 4.9 Summary
• References
• References

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