Marco Landini | Università di Bologna (original) (raw)
Papers by Marco Landini
Convegno Nazionale AEIT 2009, 2009
In questo lavoro vengono dapprima esaminate le metodologie analitiche consolidate per il calcolo ... more In questo lavoro vengono dapprima esaminate le metodologie analitiche consolidate per il calcolo del campo di induzione magnetica generato da una terna di conduttori avvolti ad elica, assai complesse in quanto fanno uso delle funzioni di Bessel modificate del primo e secondo tipo, e delle loro derivate in un sistema di riferimento con coordinate cilindriche. Successivamente, con una procedura di tipo euristico, vengono ricavate formule innovative assai pi\uf9 semplici di quelle analitiche esatte, che risultano comunque una buona approssimazione delle espressioni esatte, come dimostrato da un caso applicativo di riferimento per cavi elicordati per la distribuzione dell\u2019energia elettrica
La valutazione dell\u2019esposizione ai campi magnetici generati da elettrodotti MT in doppia ter... more La valutazione dell\u2019esposizione ai campi magnetici generati da elettrodotti MT in doppia terna a partire da misure di campo effettuate in loco viene qui condotta estrapolando i valori misurati ai valori di corrente di riferimento secondo una metodologia di calcolo innovativa, semplice e pratica. La metodologia \ue8 di validit\ue0 generale per linee a doppia terna non ottimizzate, e potenzialmente applicabile anche a linee di questo tipo in AT e AAT
Associazione Italiana Gestione Energia (AIGE), 2011
I cavi trifase avvolti ad elica, frequentemente utilizzati per la distribuzione di energia elettr... more I cavi trifase avvolti ad elica, frequentemente utilizzati per la distribuzione di energia elettrica in media e bassa tensione, sono la pi\uf9 comune tipologia di cavo per la connessione in rete di impianti di produzione dell\u2019energia elettrica da fonti rinnovabili. La progressiva diffusione di impianti di generazione da fonti rinnovabili da connettere alla rete di distribuzione rende indispensabile la valutazione dell\u2019impatto ambientale di tali sistemi energetici, incluso il calcolo del campo magnetico nelle immediate vicinanze dei cavi elicordati di connessione. La formulazione esatta per tale calcolo risulta estremamente complessa e la formula approssimata gi\ue0 esistente nella letteratura porta ad errori sempre maggiori all\u2019avvicinarsi del punto-campo ai conduttori. Con una procedura euristica, gli autori hanno derivato una formula innovativa assai pi\uf9 semplice di quella analitica rigorosa, che inoltre fornisce risultati migliori della formula approssimata di letteratura, specie in prossimit\ue0 dei conduttori. In questo lavoro la formula innovativa semplificata \ue8 dapprima applicata alle terne elicordate singole e successivamente viene estesa alle terne elicordate doppie, mediante diverse simulazioni sviluppate in MatlabTM per vari casi di interesse pratico
AEIT, 2011
In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 se... more In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 semplici di quelle analitiche rigorose per il calcolo del campo magnetico generato sia da terna singola che doppia di conduttori avvolti ad elica. Tali formule forniscono risultati in buon accordo con le espressioni analitiche rigorose, come dimostrato da diversi casi applicativi per la distribuzione dell\u2019energia elettrica
AEIT, 2011
In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 se... more In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 semplici di quelle analitiche rigorose per il calcolo del campo magnetico generato sia da terna singola che doppia di conduttori avvolti ad elica. Tali formule forniscono risultati in buon accordo con le espressioni analitiche rigorose, come dimostrato da diversi casi applicativi per la distribuzione dell\u2019energia elettrica
2014 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2014
ABSTRACT This paper presents the development of an innovative measurement system of magnetic fiel... more ABSTRACT This paper presents the development of an innovative measurement system of magnetic fields. The instrument is smart as it is able to measure and postprocess the data to obtain the prediction of the maximum magnetic field. The description of the system and the data postprocessing theory are provided. Some results of the correlation obtained with the instrument are shown.
Progress In Electromagnetics Research, 2014
This work aims to provide a physical interpretation of the "Maxwell's displacement current" and g... more This work aims to provide a physical interpretation of the "Maxwell's displacement current" and generalize the use of the derivative function of the electrical flux "dΨ/dt" in the magnetic field calculation. The innovative contribution of this study is a mathematical model to describe the origin of magnetic field as a variation of electric flux. By this approach, it follows that only the function "dΨ/dt" can generate a "magnetic tension": this leads to an interesting unification of electrical phenomena. Displacement current and conduction current are interpreted as complementary aspects of the same phenomena. It is shown how the use of the "dΨ/dt" allows the recovery of a formal symmetry in Maxwell's relations of electromagnetic induction law and circuit magnetic law. Included also is a generalized expression of the function "dΨ/dt".
La valutazione dell'esposizione ai campi magnetici generati da elettrodotti MT in doppia tern... more La valutazione dell'esposizione ai campi magnetici generati da elettrodotti MT in doppia terna a partire da misure di campo effettuate in loco viene qui condotta estrapolando i valori misurati ai valori di corrente di riferimento secondo una metodologia di calcolo innovativa semplice e pratica. La metodologia è di validità generale per linee a doppia terna non ottimizzate, e potenzialmente applicabile anche a linee di questo tipo in AT e AAT. Premessa Questo lavoro tratta la valutazione del livello di esposizione della popolazione ai campi magnetici generati da elettrodotti MT in doppia terna a partire da misure di campo effettuate in loco. In base alla conoscenza delle correnti istantanee durante il periodo di misura, i valori misurati sono estrapolati ai valori di corrente di riferimento-secondo quanto prescritto dalla normativa vigente-seguendo una metodologia di calcolo innovativa, sviluppata specificamente per questo tipo di elettrodotti, che si vale della tecnica della reg...
2017 IEEE Radio and Antenna Days of the Indian Ocean (RADIO)
This paper proposes a very simple analytical formula for the magnetic field arising from single-c... more This paper proposes a very simple analytical formula for the magnetic field arising from single-circuit twisted three-phase cables as a tool to diagnose faults. Indeed, in the presence of cable faults the magnetic field around these cables increases dramatically. Then, by calculating the field with the formula using the current measured on one phase and by comparing the calculated and the measured field, one gets a direct indication of failure if the latter field is much greater than the former.
2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe)
This paper presents a novel algorithm for the 3D calculation of the magnetic field generated by c... more This paper presents a novel algorithm for the 3D calculation of the magnetic field generated by complex configurations of overhead power lines. The algorithm implements the Laplace formula and allows the catenary to be discretised in differential elements in order to obtain the three components Bx, By and Bz of the magnetic flux density. The calculation may be carried out at a point, on a plane or in a region of space.
Electricity
The verification of the limits of the population’s exposure to the magnetic field generated by do... more The verification of the limits of the population’s exposure to the magnetic field generated by double-circuit power lines from field measurements carried out on site is not trivial. It requires knowledge of the power line current instant values during the measurement period, the determination of the relationship between current and field at the measurement points (made more complex by the double-circuit overhead line configuration) and the use of that relationship to extrapolate the field values. Nevertheless, the verification of exposure limits for double-circuit power lines from on-site measurements is often conducted with rough, or not particularly stringent, procedures. A practical and straightforward procedure of general validity for non-optimized double-circuit lines is proposed here. No specific measurement position or conductors disposition knowledge is required as well as no complex three-dimensional finite element method code is necessary. The procedure, potentially also a...
2014 International Symposium on Electromagnetic Compatibility, Sep 1, 2014
In this paper an approach to predict the electromagnetic interference generated by a switched-mod... more In this paper an approach to predict the electromagnetic interference generated by a switched-mode power supply (SMPS) on a victim circuit is presented. The electromagnetic field coupling between the main sources of electromagnetic interference of the SMPS and the victim is represented by mutual impedances which are calculated using the induced EMF method. The noise voltage on a circular loop representing a magnetic field probe used for electromagnetic interference troubleshooting is then predicted. Measurements on two switched-mode power supply converters with different layouts are carried out to assess the prediction capability of the approach.
2011 IEEE International Conference on Smart Measurements of Future Grids (SMFG) Proceedings, 2011
ABSTRACT This work deals with the experimentally-based evaluation of the total magnetic induction... more ABSTRACT This work deals with the experimentally-based evaluation of the total magnetic induction field B generated by multiple sources in complex three-dimensional arrangements, carried out on the basis of the measurement of the field components in a Cartesian coordinate system, Bx, By and Bz. Such a goal is achieved by means of an innovative measurement and evaluation system, that is proposed, described and validated in the paper. The ultimate goal is verifying that magnetic induction intensity is within the prescribed limits.
2012 IEEE Power and Energy Society General Meeting, 2012
ABSTRACT An innovative measurement and evaluation system is proposed, described and validated in ... more ABSTRACT An innovative measurement and evaluation system is proposed, described and validated in this paper for verifying that the magnetic induction intensity is within the prescribed limits. The total magnetic induction field B generated by multiple sources in complex three-dimensional arrangements is experimentally evaluated on the basis of the measurement of the field components in a three-dimensional Cartesian coordinate system.
8th IEEE Symposium on Diagnostics for Electrical Machines, Power Electronics & Drives, 2011
This paper proposes a simple innovative formula for the calculation of the magnetic field generat... more This paper proposes a simple innovative formula for the calculation of the magnetic field generated by a single and a double circuit twisted three-phase power cable line. The formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level. The effectiveness of this simple innova- tive formula is examined in the case of a double-circuit twisted three-phase power cable line following the 'worst case' approach and we propose an approximate expression for the total magnetic field generated by both twisted three-phase power cables that can be used as a diagnostic tool in fault detection algorithms, as the magnetic field can provide useful information on the phasors of the currents flowing through the conductors. WISTING of phase conductors is frequently used in me- dium voltage (MV) and low voltage (LV) power cables. For example, twisted cables are often employed for connecting wind-generators and photovoltaic systems with the distribu- tion grid. Computing the magnetic field close to a three-phase twisted cable is essential for the evaluation of its impact on the adjacent sensitive receptors, as well as for the determination of the distance at which a maximum limit value of the rms mag- netic induction is reached (1). The calculation of the magnetic field can also be used for the diagnostics of electrical equip- ment. In fact, from the measurement of the magnetic field at a point near the conductors, information on the phasors of the currents flowing in the conductors can be obtained, allowing fault conditions to be detected. Thus, simple and fast calcula- tion procedures can then be advantageous for rapid fault detec- tion. The exact (analytical) expressions of the radial and binor- mal components - in helical coordinates - of the rms magnetic induction field generated by twisted three-phase cables, along with the resulting total magnetic field, are based on infinite- term series of modified Bessel functions of the first and second kind and their derivatives (2)-(5). An approximate formula for the total magnetic field exists in the literature that provides acceptable results for distances higher than the pitch of the helix, but gives sharply increasing errors as the field- points approach the twisted three-phase cable. The authors of this paper obtained an innovative formula for the total magnetic field, derived via an heuristic procedure, that is much simpler than the rigorous analytical one. Al-
Central European Journal of Engineering, 2011
This paper proposes a simple innovative formula for the calculation of the magnetic field generat... more This paper proposes a simple innovative formula for the calculation of the magnetic field generated by a single and a double circuit twisted three-phase power cable line. The formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by some cases of a twisted three-phase power cable used for power distribution at the medium voltage level. The effectiveness of this simple innovative formula is also examined in the case of a double-circuit twisted three-phase power cable line following the’ worst case’ approach and concluding at proposing an approximate expression for the total magnetic field generated by both twisted three-phase power cables.
IEEE Transactions on Power Delivery, 2000
This paper firstly examines the consolidated analytical methodologies available in literature for... more This paper firstly examines the consolidated analytical methodologies available in literature for the calculation of the magnetic field generated by a twisted three-phase conductor arrangement carrying balanced three-phase currents. Such literature methodologies consist of an exact analytical expression of the RMS magnetic induction given in the form of complicated Bessel-function series and of an approximation of such exact expression where only the first term of the series is considered. Subsequently, a simple innovative approximated formula for the RMS magnetic induction generated by twisted three-phase power cables is obtained by means of an heuristic procedure. This formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level.
IEEE Transactions on Industrial Electronics, 2000
Convegno Nazionale AEIT 2009, 2009
In questo lavoro vengono dapprima esaminate le metodologie analitiche consolidate per il calcolo ... more In questo lavoro vengono dapprima esaminate le metodologie analitiche consolidate per il calcolo del campo di induzione magnetica generato da una terna di conduttori avvolti ad elica, assai complesse in quanto fanno uso delle funzioni di Bessel modificate del primo e secondo tipo, e delle loro derivate in un sistema di riferimento con coordinate cilindriche. Successivamente, con una procedura di tipo euristico, vengono ricavate formule innovative assai pi\uf9 semplici di quelle analitiche esatte, che risultano comunque una buona approssimazione delle espressioni esatte, come dimostrato da un caso applicativo di riferimento per cavi elicordati per la distribuzione dell\u2019energia elettrica
La valutazione dell\u2019esposizione ai campi magnetici generati da elettrodotti MT in doppia ter... more La valutazione dell\u2019esposizione ai campi magnetici generati da elettrodotti MT in doppia terna a partire da misure di campo effettuate in loco viene qui condotta estrapolando i valori misurati ai valori di corrente di riferimento secondo una metodologia di calcolo innovativa, semplice e pratica. La metodologia \ue8 di validit\ue0 generale per linee a doppia terna non ottimizzate, e potenzialmente applicabile anche a linee di questo tipo in AT e AAT
Associazione Italiana Gestione Energia (AIGE), 2011
I cavi trifase avvolti ad elica, frequentemente utilizzati per la distribuzione di energia elettr... more I cavi trifase avvolti ad elica, frequentemente utilizzati per la distribuzione di energia elettrica in media e bassa tensione, sono la pi\uf9 comune tipologia di cavo per la connessione in rete di impianti di produzione dell\u2019energia elettrica da fonti rinnovabili. La progressiva diffusione di impianti di generazione da fonti rinnovabili da connettere alla rete di distribuzione rende indispensabile la valutazione dell\u2019impatto ambientale di tali sistemi energetici, incluso il calcolo del campo magnetico nelle immediate vicinanze dei cavi elicordati di connessione. La formulazione esatta per tale calcolo risulta estremamente complessa e la formula approssimata gi\ue0 esistente nella letteratura porta ad errori sempre maggiori all\u2019avvicinarsi del punto-campo ai conduttori. Con una procedura euristica, gli autori hanno derivato una formula innovativa assai pi\uf9 semplice di quella analitica rigorosa, che inoltre fornisce risultati migliori della formula approssimata di letteratura, specie in prossimit\ue0 dei conduttori. In questo lavoro la formula innovativa semplificata \ue8 dapprima applicata alle terne elicordate singole e successivamente viene estesa alle terne elicordate doppie, mediante diverse simulazioni sviluppate in MatlabTM per vari casi di interesse pratico
AEIT, 2011
In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 se... more In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 semplici di quelle analitiche rigorose per il calcolo del campo magnetico generato sia da terna singola che doppia di conduttori avvolti ad elica. Tali formule forniscono risultati in buon accordo con le espressioni analitiche rigorose, come dimostrato da diversi casi applicativi per la distribuzione dell\u2019energia elettrica
AEIT, 2011
In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 se... more In questo lavoro, con una procedura euristica vengono ricavate formule innovative assai pi\uf9 semplici di quelle analitiche rigorose per il calcolo del campo magnetico generato sia da terna singola che doppia di conduttori avvolti ad elica. Tali formule forniscono risultati in buon accordo con le espressioni analitiche rigorose, come dimostrato da diversi casi applicativi per la distribuzione dell\u2019energia elettrica
2014 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2014
ABSTRACT This paper presents the development of an innovative measurement system of magnetic fiel... more ABSTRACT This paper presents the development of an innovative measurement system of magnetic fields. The instrument is smart as it is able to measure and postprocess the data to obtain the prediction of the maximum magnetic field. The description of the system and the data postprocessing theory are provided. Some results of the correlation obtained with the instrument are shown.
Progress In Electromagnetics Research, 2014
This work aims to provide a physical interpretation of the "Maxwell's displacement current" and g... more This work aims to provide a physical interpretation of the "Maxwell's displacement current" and generalize the use of the derivative function of the electrical flux "dΨ/dt" in the magnetic field calculation. The innovative contribution of this study is a mathematical model to describe the origin of magnetic field as a variation of electric flux. By this approach, it follows that only the function "dΨ/dt" can generate a "magnetic tension": this leads to an interesting unification of electrical phenomena. Displacement current and conduction current are interpreted as complementary aspects of the same phenomena. It is shown how the use of the "dΨ/dt" allows the recovery of a formal symmetry in Maxwell's relations of electromagnetic induction law and circuit magnetic law. Included also is a generalized expression of the function "dΨ/dt".
La valutazione dell'esposizione ai campi magnetici generati da elettrodotti MT in doppia tern... more La valutazione dell'esposizione ai campi magnetici generati da elettrodotti MT in doppia terna a partire da misure di campo effettuate in loco viene qui condotta estrapolando i valori misurati ai valori di corrente di riferimento secondo una metodologia di calcolo innovativa semplice e pratica. La metodologia è di validità generale per linee a doppia terna non ottimizzate, e potenzialmente applicabile anche a linee di questo tipo in AT e AAT. Premessa Questo lavoro tratta la valutazione del livello di esposizione della popolazione ai campi magnetici generati da elettrodotti MT in doppia terna a partire da misure di campo effettuate in loco. In base alla conoscenza delle correnti istantanee durante il periodo di misura, i valori misurati sono estrapolati ai valori di corrente di riferimento-secondo quanto prescritto dalla normativa vigente-seguendo una metodologia di calcolo innovativa, sviluppata specificamente per questo tipo di elettrodotti, che si vale della tecnica della reg...
2017 IEEE Radio and Antenna Days of the Indian Ocean (RADIO)
This paper proposes a very simple analytical formula for the magnetic field arising from single-c... more This paper proposes a very simple analytical formula for the magnetic field arising from single-circuit twisted three-phase cables as a tool to diagnose faults. Indeed, in the presence of cable faults the magnetic field around these cables increases dramatically. Then, by calculating the field with the formula using the current measured on one phase and by comparing the calculated and the measured field, one gets a direct indication of failure if the latter field is much greater than the former.
2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe)
This paper presents a novel algorithm for the 3D calculation of the magnetic field generated by c... more This paper presents a novel algorithm for the 3D calculation of the magnetic field generated by complex configurations of overhead power lines. The algorithm implements the Laplace formula and allows the catenary to be discretised in differential elements in order to obtain the three components Bx, By and Bz of the magnetic flux density. The calculation may be carried out at a point, on a plane or in a region of space.
Electricity
The verification of the limits of the population’s exposure to the magnetic field generated by do... more The verification of the limits of the population’s exposure to the magnetic field generated by double-circuit power lines from field measurements carried out on site is not trivial. It requires knowledge of the power line current instant values during the measurement period, the determination of the relationship between current and field at the measurement points (made more complex by the double-circuit overhead line configuration) and the use of that relationship to extrapolate the field values. Nevertheless, the verification of exposure limits for double-circuit power lines from on-site measurements is often conducted with rough, or not particularly stringent, procedures. A practical and straightforward procedure of general validity for non-optimized double-circuit lines is proposed here. No specific measurement position or conductors disposition knowledge is required as well as no complex three-dimensional finite element method code is necessary. The procedure, potentially also a...
2014 International Symposium on Electromagnetic Compatibility, Sep 1, 2014
In this paper an approach to predict the electromagnetic interference generated by a switched-mod... more In this paper an approach to predict the electromagnetic interference generated by a switched-mode power supply (SMPS) on a victim circuit is presented. The electromagnetic field coupling between the main sources of electromagnetic interference of the SMPS and the victim is represented by mutual impedances which are calculated using the induced EMF method. The noise voltage on a circular loop representing a magnetic field probe used for electromagnetic interference troubleshooting is then predicted. Measurements on two switched-mode power supply converters with different layouts are carried out to assess the prediction capability of the approach.
2011 IEEE International Conference on Smart Measurements of Future Grids (SMFG) Proceedings, 2011
ABSTRACT This work deals with the experimentally-based evaluation of the total magnetic induction... more ABSTRACT This work deals with the experimentally-based evaluation of the total magnetic induction field B generated by multiple sources in complex three-dimensional arrangements, carried out on the basis of the measurement of the field components in a Cartesian coordinate system, Bx, By and Bz. Such a goal is achieved by means of an innovative measurement and evaluation system, that is proposed, described and validated in the paper. The ultimate goal is verifying that magnetic induction intensity is within the prescribed limits.
2012 IEEE Power and Energy Society General Meeting, 2012
ABSTRACT An innovative measurement and evaluation system is proposed, described and validated in ... more ABSTRACT An innovative measurement and evaluation system is proposed, described and validated in this paper for verifying that the magnetic induction intensity is within the prescribed limits. The total magnetic induction field B generated by multiple sources in complex three-dimensional arrangements is experimentally evaluated on the basis of the measurement of the field components in a three-dimensional Cartesian coordinate system.
8th IEEE Symposium on Diagnostics for Electrical Machines, Power Electronics & Drives, 2011
This paper proposes a simple innovative formula for the calculation of the magnetic field generat... more This paper proposes a simple innovative formula for the calculation of the magnetic field generated by a single and a double circuit twisted three-phase power cable line. The formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level. The effectiveness of this simple innova- tive formula is examined in the case of a double-circuit twisted three-phase power cable line following the 'worst case' approach and we propose an approximate expression for the total magnetic field generated by both twisted three-phase power cables that can be used as a diagnostic tool in fault detection algorithms, as the magnetic field can provide useful information on the phasors of the currents flowing through the conductors. WISTING of phase conductors is frequently used in me- dium voltage (MV) and low voltage (LV) power cables. For example, twisted cables are often employed for connecting wind-generators and photovoltaic systems with the distribu- tion grid. Computing the magnetic field close to a three-phase twisted cable is essential for the evaluation of its impact on the adjacent sensitive receptors, as well as for the determination of the distance at which a maximum limit value of the rms mag- netic induction is reached (1). The calculation of the magnetic field can also be used for the diagnostics of electrical equip- ment. In fact, from the measurement of the magnetic field at a point near the conductors, information on the phasors of the currents flowing in the conductors can be obtained, allowing fault conditions to be detected. Thus, simple and fast calcula- tion procedures can then be advantageous for rapid fault detec- tion. The exact (analytical) expressions of the radial and binor- mal components - in helical coordinates - of the rms magnetic induction field generated by twisted three-phase cables, along with the resulting total magnetic field, are based on infinite- term series of modified Bessel functions of the first and second kind and their derivatives (2)-(5). An approximate formula for the total magnetic field exists in the literature that provides acceptable results for distances higher than the pitch of the helix, but gives sharply increasing errors as the field- points approach the twisted three-phase cable. The authors of this paper obtained an innovative formula for the total magnetic field, derived via an heuristic procedure, that is much simpler than the rigorous analytical one. Al-
Central European Journal of Engineering, 2011
This paper proposes a simple innovative formula for the calculation of the magnetic field generat... more This paper proposes a simple innovative formula for the calculation of the magnetic field generated by a single and a double circuit twisted three-phase power cable line. The formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by some cases of a twisted three-phase power cable used for power distribution at the medium voltage level. The effectiveness of this simple innovative formula is also examined in the case of a double-circuit twisted three-phase power cable line following the’ worst case’ approach and concluding at proposing an approximate expression for the total magnetic field generated by both twisted three-phase power cables.
IEEE Transactions on Power Delivery, 2000
This paper firstly examines the consolidated analytical methodologies available in literature for... more This paper firstly examines the consolidated analytical methodologies available in literature for the calculation of the magnetic field generated by a twisted three-phase conductor arrangement carrying balanced three-phase currents. Such literature methodologies consist of an exact analytical expression of the RMS magnetic induction given in the form of complicated Bessel-function series and of an approximation of such exact expression where only the first term of the series is considered. Subsequently, a simple innovative approximated formula for the RMS magnetic induction generated by twisted three-phase power cables is obtained by means of an heuristic procedure. This formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level.
IEEE Transactions on Industrial Electronics, 2000