A continuous function can be simulated by substituting a numerical integration formula into the differential equation and rearranging the function into an appropriate form. Among the factors to be taken into account in the selection of the numerical integrator are the error due to truncated terms, its properties as a differentiator, error propagation and frequency response. Numerical integration substitution (NIS) constitutes the basis of Dommel's EMTP , which, as explained in the introductory chapter, is now the most generally accepted method for the solution of electromagnetic transients.
{"title":"Numerical integrator substitution","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_CH4","DOIUrl":"https://doi.org/10.1049/PBPO039E_CH4","url":null,"abstract":"A continuous function can be simulated by substituting a numerical integration formula into the differential equation and rearranging the function into an appropriate form. Among the factors to be taken into account in the selection of the numerical integrator are the error due to truncated terms, its properties as a differentiator, error propagation and frequency response. Numerical integration substitution (NIS) constitutes the basis of Dommel's EMTP , which, as explained in the introductory chapter, is now the most generally accepted method for the solution of electromagnetic transients.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"70 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":"127081442","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 use of a single time frame throughout the simulation is inefficient for studies involving widely varying time constants. A typical example is multimachine transient stability assessment when the system contains HVDC converters. In such cases the stability levels are affected by both the long time constant of the electromechanical response of the generators and the short time constant of the converter's power electronic control. It is, of course, possible to include the equations of motion of the generators in the electromagnetic transient programs to represent the electromechanical behaviour of multimachine power systems. However, considering the different time constants influencing the electromechanical and electromagnetic behaviour, such approach would be extremely inefficient. Electromagnetic transient simulations use steps of (typically) 50 μs, whereas the stability programs use steps at least 200 times larger.
{"title":"Mixed time-frame simulation","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_ch12","DOIUrl":"https://doi.org/10.1049/PBPO039E_ch12","url":null,"abstract":"The use of a single time frame throughout the simulation is inefficient for studies involving widely varying time constants. A typical example is multimachine transient stability assessment when the system contains HVDC converters. In such cases the stability levels are affected by both the long time constant of the electromechanical response of the generators and the short time constant of the converter's power electronic control. It is, of course, possible to include the equations of motion of the generators in the electromagnetic transient programs to represent the electromechanical behaviour of multimachine power systems. However, considering the different time constants influencing the electromechanical and electromagnetic behaviour, such approach would be extremely inefficient. Electromagnetic transient simulations use steps of (typically) 50 μs, whereas the stability programs use steps at least 200 times larger.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"41 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":"132087608","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}
An important part of power quality is steady-state (and quasi-steady-state) waveform distortion. The resulting information is sometimes presented in the time-domain (e.g. notching) and more often in the frequency-domain (e.g. harmonics and interharmonics). Randomly varying non-linear loads, such as arc furnaces, as well as substantial and varying harmonic (and interharmonic) content, cause voltage fluctuations that often produce flicker. The random nature of the load impedance variation with time prevents an accurate prediction of the phenomena. However, the EMTP method can still help in the selection of compensating techniques, with arc models based on the experience of existing installations. Another application of the EMTP method for steady-state assessment is its use in developing accurate harmonically coupled models for other modelling frame-works, such as the harmonic domain. This is desirable as frequency-domain techniques are more amendable for simulating very large power systems.
{"title":"Steady-state assessment","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO123E_ch11","DOIUrl":"https://doi.org/10.1049/PBPO123E_ch11","url":null,"abstract":"An important part of power quality is steady-state (and quasi-steady-state) waveform distortion. The resulting information is sometimes presented in the time-domain (e.g. notching) and more often in the frequency-domain (e.g. harmonics and interharmonics). Randomly varying non-linear loads, such as arc furnaces, as well as substantial and varying harmonic (and interharmonic) content, cause voltage fluctuations that often produce flicker. The random nature of the load impedance variation with time prevents an accurate prediction of the phenomena. However, the EMTP method can still help in the selection of compensating techniques, with arc models based on the experience of existing installations. Another application of the EMTP method for steady-state assessment is its use in developing accurate harmonically coupled models for other modelling frame-works, such as the harmonic domain. This is desirable as frequency-domain techniques are more amendable for simulating very large power systems.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"18 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113938341","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_appendixc
{"title":"Appendix C: Test systems data","authors":"","doi":"10.1049/pbpo123e_appendixc","DOIUrl":"https://doi.org/10.1049/pbpo123e_appendixc","url":null,"abstract":"","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"234 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":"121852526","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 control equations are solved separately from the power system equations though still using the EMTP philosophy, thereby maintaining the symmetry of the conductance matrix. The main facilities developed to segment the control, as well as devices or phenomena which cannot be directly modelled by the basic network components, are TACS and MODELS (in the original EMTP package) and a CMSF library (in the PSCAD/EMTDC package). The separate solution of control and power system introduces a time-step delay, however with the sample and hold used in digital control this is becoming less of an issue. Modern digital controls, with multiple time steps, are more the norm and can be adequately represented in EMT programs. The use of a modular approach to build up a control system, although it gives greater flexibility, introduces time-step delays in data paths, which can have a detrimental effect on the simulation results. The use of the z-domain for analysing the difference equations either generated using NIS, with and without time-step delay, or the root-matching technique, has been demonstrated. Interpolation is important for modelling controls as well as for the non-linear surge arrester, if numerical errors and possible instabilities are to be avoided. A description of the present state of protective system implementation has been given, indicating the difficulty of modelling individual devices in detail. Instead, the emphasis is on the use of real-time digital simulators interfaced with the actual protection hardware via digital-to-analogue conversion.
{"title":"Control and protection","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_CH8","DOIUrl":"https://doi.org/10.1049/PBPO039E_CH8","url":null,"abstract":"The control equations are solved separately from the power system equations though still using the EMTP philosophy, thereby maintaining the symmetry of the conductance matrix. The main facilities developed to segment the control, as well as devices or phenomena which cannot be directly modelled by the basic network components, are TACS and MODELS (in the original EMTP package) and a CMSF library (in the PSCAD/EMTDC package). The separate solution of control and power system introduces a time-step delay, however with the sample and hold used in digital control this is becoming less of an issue. Modern digital controls, with multiple time steps, are more the norm and can be adequately represented in EMT programs. The use of a modular approach to build up a control system, although it gives greater flexibility, introduces time-step delays in data paths, which can have a detrimental effect on the simulation results. The use of the z-domain for analysing the difference equations either generated using NIS, with and without time-step delay, or the root-matching technique, has been demonstrated. Interpolation is important for modelling controls as well as for the non-linear surge arrester, if numerical errors and possible instabilities are to be avoided. A description of the present state of protective system implementation has been given, indicating the difficulty of modelling individual devices in detail. Instead, the emphasis is on the use of real-time digital simulators interfaced with the actual protection hardware via digital-to-analogue conversion.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"88 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":"114328388","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}
In the state variable solution it is the set of first order differential equations, rather than the system of individual elements, that is solved by numerical integration. The most popular numerical technique in current use is implicit trapezoidal integration, due to its simplicity, accuracy and stability. Solution accuracy is enhanced by the use of iterative methods to calculate the state variables. State variable is an ideal method for the solution of system components with time-varying non-linearities, and particularly for power electronic devices involv ing frequent switching. This has been demonstrated with reference to the static a.c.-d.c. converter by an algorithm referred to as TCS (Transient Converter Simu lation). Frequent switching, in the state variable approach, imposes no overhead on the solution. Moreover, the use of automatic step length adjustment permits optimising the integration step throughout the solution.
{"title":"State variable analysis","authors":"N. Watson, J. Arrillaga","doi":"10.1049/PBPO039E_CH3","DOIUrl":"https://doi.org/10.1049/PBPO039E_CH3","url":null,"abstract":"In the state variable solution it is the set of first order differential equations, rather than the system of individual elements, that is solved by numerical integration. The most popular numerical technique in current use is implicit trapezoidal integration, due to its simplicity, accuracy and stability. Solution accuracy is enhanced by the use of iterative methods to calculate the state variables. State variable is an ideal method for the solution of system components with time-varying non-linearities, and particularly for power electronic devices involv ing frequent switching. This has been demonstrated with reference to the static a.c.-d.c. converter by an algorithm referred to as TCS (Transient Converter Simu lation). Frequent switching, in the state variable approach, imposes no overhead on the solution. Moreover, the use of automatic step length adjustment permits optimising the integration step throughout the solution.","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"13 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":"116146518","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":"Transient simulation in real-time","authors":"","doi":"10.1049/pbpo123e_ch13","DOIUrl":"https://doi.org/10.1049/pbpo123e_ch13","url":null,"abstract":"","PeriodicalId":114635,"journal":{"name":"Power Systems Electromagnetic Transients Simulation","volume":"32 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":"121875126","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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