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## Power systems modelling

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An introduction to the topic of power systems modelling has been given. There are many aspects of power systems that make their modelling different from other analogue systems; however, constructing a small -signal model provides fast analysis of the behaviour, subject to certain limitations as having been discussed. The efficiency of a power system is determined by many parasitic components not just in the core converter but many times also in the external components. An insight into the nonideal behaviours and lossy mechanisms of capacitors and inductors has been given. Battery modelling is an area of active research driven by the plethora of low power wireless applications and electric vehicle adoption, and the reader is referred to the references for further reading on this topic.

Chapter Contents:

• 10.1 Introduction
• 10.2 Small-signal models of DC– DC converters
• 10.2.1 Motivation
• 10.2.2 Assumptions
• 10.2.3 Test vehicle
• 10.2.4 Partitioning of the circuit
• 10.2.5 Model types
• 10.2.5.1 Switching model
• 10.2.5.2 Averaged model – continuous-time model
• 10.2.5.3 Small-signal model – AC model
• 10.2.5.4 Used models
• 10.2.6 Basic theory for averaged – continuous-time model
• 10.2.6.1 Small-ripple approximation
• 10.2.6.2 Averaging
• 10.2.6.3 Example of an averaged signal
• 10.2.7 Duty-cycle signal model
• 10.2.8 Pulse width modulator model
• 10.2.9 Model of the power stage
• 10.2.10 Complete switching, linear and small-signal model
• 10.2.11 The small-signal open-loop transfer function
• 10.2.12 Comparison of various models
• 10.2.12.1 Used parameters
• 10.2.12.2 Small-signal models
• 10.2.12.3 Linear and switching model
• 10.2.13 Other outputs of the small-signal model
• 10.2.14 Switching frequency effect
• 10.2.14.1 Switching small-signal analysis
• 10.2.14.2 The additional phase shift due to the sampling
• 10.2.14.3 The gain of the PWM
• 10.2.15 Comparison of the averaged and switching models
• 10.2.16 Limitations of the averaged model
• 10.3 Efficiency modelling
• 10.4 Battery models
• 10.5 Capacitance modelling
• 10.6 Modelling the inductors
• 10.6.1 Spice modelling
• 10.6.3 Saturation current effects and modelling
• 10.7 Conclusion
• References

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