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Flux www.cedrat.com Example Creation date Three-phase cable: Computation of the dielectric losses 2009 Author : Pascal Ferran - Université Claude Bernard Lyon Ref. FLU2_EH_REL_01 Program Dimension Version Physics Application Work area Flux 2D 10.3 Electric Steady AC Electric networks FRAMEWORK Presentation General remarks Study of the dielectric losses in a three-phase insulating cable according to the loss factor and the insulator permittivity. This example explains how to evaluate the sensitivity of the losses results according to the properties of the electric cable material. Objective Computation of the dielectric losses value in the insulator according to different parameters. The parameters the user can change are : Global insulator’s relative permittivity (RP) Global insulator’s loss factor (LF) Theoretical reminders There is no theoretical formula to easily calculate the dielectric losses in our device but we can rely on theoretical notions related to dielectric losses to obtain approximate results. Properties - Rated conductor diameter D = 10 mm - PVC insulating sheath with thickness ID = 4 mm - Rated properties of the insulating sheath are : r = 8 and tg ()= 0.1 - Global insulating cable : r = 8 and tg ()= 0.1 - Ext. Radius of the cable REXT = 50 mm - Rated radius of the circle where the conductors circles are located : R = 15 mm - Voltage applied to each of the conductors : Efficient value V = 15000 V and frequency f = 50 Hz. Illustration Main characteristics CEDRAT S.A. 15, Chemin de Malacher Inovallée – 38246 MEYLAN Cedex (France) – Tél : +33 (0)4 76 90 50 45 – Email : [email protected] FRAMEWORK Flux Some results … Power density distribution at a rated working point Equipotential lines distribution at the initial moment for the specified characteristics PAGE 2 Three-phase cable: Computation of the dielectric losses Flux FRAMEWORK Dielectric losses = f (loss factor of the global insulator) (other parameters are rated) Dielectric losses = f (permittivity of the global insulator) (other parameters are rated) To go further … - Coupling between the conductors (Computation of corresponding impedance matrix) … Three-phase cable: Computation of the dielectric losses PAGE 3 MODEL IN FLUX Flux MODEL IN FLUX Domain Dimension 2D Depth 10000 Infinite Box Length unit. mm Angle unit. degrees Size Periodicity In. radius : Symmetry Characteristics Out. Radius : none Repetition number : Offset angle : Even/odd periodicity Application Steady AC electric Properties Electric potential stiff at 0V in periphery Geometry / Mesh Full model in the FLUX environment Mesh 2nd order type Mesh Number of nodes 3369 Input Parameters Name Type RP Physical LF Physical V Physical PAGE 4 Description Relative permittivity of the global insulator Loss factor of the global insulator Voltage source Rated value 8 0.1 15000 V Three-phase cable: Computation of the dielectric losses Flux MODEL IN FLUX Material Base NAME B(H) model Magnetic property J(H) model Electrical property D(E) model Dielectric property PVC Linear isotropic with losses GIP Linear isotropic with losses r = 8 tg ( r = RP tg (LF K(T) model K(T) characteristics RCP(T) model RCP(T) characteristics - - NAME Nature CONDUCTORS Surface region Type Inactive region Material Mechanical Set Corresponding circuit component - CI Surface region Dielectric and conductive region PVC - GI Surface region Dielectric and conductive region GIP - - - - Electrical characteristics - - - Current source - - - Thermal characteristics - - - Possible thermal source - - - NAME Nature Type Material Mechanical Set Corresponding circuit component L1 Line region Stiff electric potential - L2 Line region Stiff electric potential - L3 Line region Stiff electric potential - - - - Electrical characteristics V volts = 0° Current source - V volts = - 120° - V volts = - 240° - Thermal characteristics - - - Possible thermal source - - - Regions Three-phase cable: Computation of the dielectric losses PAGE 5 MODEL IN FLUX Flux Mechanical Set Fixed part : Compressible part : Type Characteristics Miscellaneous Mobile part : Type of kinematics Internal characteristics: External characteristics : Mechanical stops Electrical circuit Component Type Characteristics Associated Region Electric scheme Solving process options Type of linear system solver Type of non-linear system solver Automatically chosen Parameters Precision Newton Raphson Automatically defined 0.0001 Method for computing the relaxation factor Nb iterations 100 Automatically defined Thermal coupling Advanced characteristics Solving Scenario Name of parameter Controllable parameter Variation method Interval definition Step selection SCENARIO_1 SCENARIO_2 RP LF Physical Physical Step value Steps list 1 to 10 0.001 to 1000 Step of 1 Factor 10 between each step Duration of the solving PAGE 6 SCENARIO_1 : 8 seconds SCENARIO_2 : 6 seconds Operating System Windows XP 32 bits Three-phase cable: Computation of the dielectric losses Flux ANNEX ANNEX Theoretical reminders Dielectric properties of a few materials Typical values The below table reviews the typical values of the relative permittivity and loss factor for high voltage cables insulators. Insulating material Fluid oil low pressure Fluid oil high pressure Relative permittivity:r 3.3 3.5 PVC 8 PE Impregnated paper Loss factor: tan () 0.004 0.0045 0.1 2.3 0.001 4 0.1 The below table reviews the voltage value (between phases) from which the dielectric losses have to be taken into account. Insulating material Fluid oil PVC PE Impregnated paper Voltage (kV) 110 10 225 66 Three-phase cable: Computation of the dielectric losses PAGE 7