An alternative to the difference equation using the trapezoidal integration developed in Chapter 4 for the solution of the differential equations has been described in this chapter. It involves the exponential form of the difference equation and has been developed using the root-matching technique. The exponential form offers the following advantages: 1) Eliminates truncation errors, and hence numerical oscillations, regardless of the step length used. 2) Can be applied to both electrical networks and control blocks. 3) Can be viewed as a Norton equivalent in exactly the same way as the difference equation developed by the numerical integration substitution (NIS) method. 4) It is perfectly compatible with NIS and the matrix solution technique remains unchanged. 5) Provides highly efficient and accurate time domain simulation. The exponential form can be implemented for all series and parallel RL, RC, LC and RLC combinations, but not arbitrary components and hence is not a replacement for NIS but a supplement.
{"title":"The root-matching method","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_CH5","DOIUrl":"https://doi.org/10.1049/PBPO039E_CH5","url":null,"abstract":"An alternative to the difference equation using the trapezoidal integration developed in Chapter 4 for the solution of the differential equations has been described in this chapter. It involves the exponential form of the difference equation and has been developed using the root-matching technique. The exponential form offers the following advantages: 1) Eliminates truncation errors, and hence numerical oscillations, regardless of the step length used. 2) Can be applied to both electrical networks and control blocks. 3) Can be viewed as a Norton equivalent in exactly the same way as the difference equation developed by the numerical integration substitution (NIS) method. 4) It is perfectly compatible with NIS and the matrix solution technique remains unchanged. 5) Provides highly efficient and accurate time domain simulation. The exponential form can be implemented for all series and parallel RL, RC, LC and RLC combinations, but not arbitrary components and hence is not a replacement for NIS but a supplement.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129653788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the exceptions of a few auxiliary components, the electrical power system is a continuous system, which can be represented mathematically by a system of differential and algebraic equations. A convenient form of these equations is the state variable formulation, in which a system of n first-order linear differential equations results from an n order system. The state variable formulation is not unique and depends on the choice of state variables. The following state variable realisations have been described in this chapter: successive differentiation, controller canonical, observer canonical and diagonal canonical. Digital simulation is by nature a discrete time process and can only provide solutions for the differential and algebraic equations at discrete points in time, hence this requires the formulation of discrete systems. The discrete representation can always be expressed as a difference equation, where the output at a new time point is calculated from the output at previous time points and the inputs at the present and previous time points.
{"title":"Analysis of continuous and discrete systems","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_ch2","DOIUrl":"https://doi.org/10.1049/PBPO039E_ch2","url":null,"abstract":"With the exceptions of a few auxiliary components, the electrical power system is a continuous system, which can be represented mathematically by a system of differential and algebraic equations. A convenient form of these equations is the state variable formulation, in which a system of n first-order linear differential equations results from an n order system. The state variable formulation is not unique and depends on the choice of state variables. The following state variable realisations have been described in this chapter: successive differentiation, controller canonical, observer canonical and diagonal canonical. Digital simulation is by nature a discrete time process and can only provide solutions for the differential and algebraic equations at discrete points in time, hence this requires the formulation of discrete systems. The discrete representation can always be expressed as a difference equation, where the output at a new time point is calculated from the output at previous time points and the inputs at the present and previous time points.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129072451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The basic theory of the single-phase transformer has been described, including the derivation of parameters, the modelling of magnetisation non-linearities and its numerical implementation in a form acceptable for electromagnetic transients programs. The need for advanced models has been justified, and a detailed description made of UMEC (the Unified Magnetic Equivalent Circuit), a general transformer model developed for the accurate representation of multiphase, multiwinding arrangements. UMEC is a standard transformer model in the latest version of PSCAD/EMTDC. Rotating machine modelling based on Park's transformation is reasonably stan dard, the different implementations relating to the way of interfacing the machine to the system. A state variable formulation of the equations is used but the solution, in line with EMTP philosophy, is carried out by numerical integrator substitution.
{"title":"Transformers and rotating plant","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_ch7","DOIUrl":"https://doi.org/10.1049/PBPO039E_ch7","url":null,"abstract":"The basic theory of the single-phase transformer has been described, including the derivation of parameters, the modelling of magnetisation non-linearities and its numerical implementation in a form acceptable for electromagnetic transients programs. The need for advanced models has been justified, and a detailed description made of UMEC (the Unified Magnetic Equivalent Circuit), a general transformer model developed for the accurate representation of multiphase, multiwinding arrangements. UMEC is a standard transformer model in the latest version of PSCAD/EMTDC. Rotating machine modelling based on Park's transformation is reasonably stan dard, the different implementations relating to the way of interfacing the machine to the system. A state variable formulation of the equations is used but the solution, in line with EMTP philosophy, is carried out by numerical integrator substitution.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"01 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130204767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Definitions objectives and background","authors":"","doi":"10.1049/pbpo123e_ch1","DOIUrl":"https://doi.org/10.1049/pbpo123e_ch1","url":null,"abstract":"","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130600760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-05DOI: 10.1049/PBPO123E_APPENDIXB
N. Watson, J. Arrillaga
This appendix chapter from the book Power Systems Electromagnetic Transients Simulation covers: Review of classical methods; Truncation error of integration formulae and Stability of integration methods.
{"title":"Appendix B: Numerical integration","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO123E_APPENDIXB","DOIUrl":"https://doi.org/10.1049/PBPO123E_APPENDIXB","url":null,"abstract":"This appendix chapter from the book Power Systems Electromagnetic Transients Simulation covers: Review of classical methods; Truncation error of integration formulae and Stability of integration methods.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116956153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-10-26DOI: 10.1002/9780470749012.APP1
S. Bilbao
In this appendix, various simple code fragments are provided. All can be viewed as prototypes for physical modeling sound synthesis. The coding style reflects something of a compromise between efficiency, on the one hand, and brevity and intelligibility, on the other. The choice of Matlab as a programming environment definitely reflects the latter sensibility, though the use of Matlab as an actual synthesis engine is not recommended. Some of these examples make use of constructs and features which need not appear in a code fragment intended for synthesis, including various calls to plotting functions, as well as the demonstration of energy conservation in some cases. It should be clear, in all cases, which elements of these examples may be neglected in an actual implementation. For the sake of brevity, these examples are too crude for actual synthesis purposes, but many features, discussed at various points in the texts and exercises, may be added.
{"title":"Appendix E: MATLAB® code examples","authors":"S. Bilbao","doi":"10.1002/9780470749012.APP1","DOIUrl":"https://doi.org/10.1002/9780470749012.APP1","url":null,"abstract":"In this appendix, various simple code fragments are provided. All can be viewed as prototypes for physical modeling sound synthesis. The coding style reflects something of a compromise between efficiency, on the one hand, and brevity and intelligibility, on the other. The choice of Matlab as a programming environment definitely reflects the latter sensibility, though the use of Matlab as an actual synthesis engine is not recommended. Some of these examples make use of constructs and features which need not appear in a code fragment intended for synthesis, including various calls to plotting functions, as well as the demonstration of energy conservation in some cases. It should be clear, in all cases, which elements of these examples may be neglected in an actual implementation. For the sake of brevity, these examples are too crude for actual synthesis purposes, but many features, discussed at various points in the texts and exercises, may be added.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"87 21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126302238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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