## AC/DC Module Updates

For users of the AC/DC Module, COMSOL Multiphysics^{®} version 5.6 offers a new *Magnetic Fields, Currents Only* interface, empirical loss models, and various improvements to the existing *Electrical Circuit* interface. Learn about these and other AC/DC Module updates in more detail below.

### New Physics Interface for Inductance Matrix Computations

The new *Magnetic Fields, Currents Only* interface is designed to efficiently compute the lumped inductance matrix of complex circuits in 3D, such as those commonly found on printed circuit boards (PCBs). It can be used to calculate the partial contributions from magnetic fields generated by open conductors, also known as nonsolenoidal conductors. The ability to handle open conductors significantly reduces modeling complexity for users needing to solve for mutual inductance matrices.

The interface uses the magnetic vector potential as the dependent variable, and computes the magnetic fields generated by currents under the assumption that all regions are nonmagnetic (in other words; that they have a uniform relative magnetic permeability of "one"). This new formulation does not require the conductor currents to be divergence-free. In free space, it returns the value of the *Biot–Savart* integral. The interface supports the *Stationary* and the *Stationary Source Sweep* study steps. The latter is an efficient way of sweeping over many terminals. You can see this interface in use in the new Inductance Matrix Calculation of PCB Coils tutorial model and in the updated Magnetic Field of a Helmholtz Coil model.

*An inductively coupled array of PCB coils, subjected to a coil sweep using the*Magnetic Fields, Currents Only

*interface. The resulting L-matrix can be used to construct a lumped circuit representation of the PCB.*

### Loss Models for Laminated Cores and Yokes in Motors and Transformers

The new *Loss Calculation* feature uses empirical models (*Steinmetz*, *Bertotti*, or *User defined*) to calculate iron loss caused by magnetic hysteresis, eddy currents, and other effects in (laminated) cores or yokes in, for example, electric motors and transformers. As a fallback option for materials like copper, it is able to provide the cycle average resistive losses.

In the Model Builder, *Loss Calculation* is available as a subnode to the *Ampère's Law* node, domain *Coil* node, *Faraday’s Law* node, and *Magnetic Flux Conservation* node. It is available for both *Time Dependent* and *Frequency Domain* studies. For *Time Dependent* studies, the *Loss Calculation* feature is designed to be used in combination with the dedicated *Time to Frequency Losses* study step. This study step determines the different harmonics present in the time-dependent solution, and inserts them into one of the frequency-dependent empirical loss models. You can see this new feature in these updated models:

- permanent_magnet_motor_in_3d
- modeling_of_an_electric_generator_in_3d
- generator_in_2d
- e_-_core_transformer

*The empirical loss model*Steinmetz,

*used to determine the cycle-average (frequency-dependent) losses in the laminated iron of a stator yoke. The different harmonics can be analyzed individually.*

### Wide Support for Eigenfrequency Analysis

The *Eigenfrequency* study is now supported for most of the AC/DC Module interfaces: *Electric Currents*, *Electric Currents in Shells*, *Electric Currents in Layered Shells*, *Electrical Circuit*, *Electrostatics*, and *Magnetic Fields*. In addition to supporting full-wave cavity mode analysis in the *Magnetic Fields* interface, it is possible to run eigenfrequency analyses with models involving electrical circuits. The eigenfrequency support is primarily developed for the AC/DC Module, but other modules that provide one of the affected physics interfaces will benefit from it too.

*The resonance peak of a simple RLC circuit. The eigenfrequency and Q-factor are analyzed and compared to analytically determined values.*

### New and Enhanced Functionality for the Electrical Circuit Interface

For *Time Dependent* studies, the *Electrical Circuit* interface has been equipped with an "event-based" *Switch* feature. This allows you to model the "instantaneous" on-off switching of certain connections in the circuit. The switch can be current controlled, voltage controlled, or controlled by user-defined Boolean expressions.

Furthermore, *Parameterized Subcircuit Definitions* are added. Together with the *Subcircuit Instance*, these allow you to create your own building blocks containing smaller circuits, and use multiple parameterized variants of those in your larger circuit. Finally, the state, event, and solver machinery has been improved, especially the transient modeling of nonlinear (semiconductor) devices, which has become more robust.

The circuit improvements are primarily developed for the AC/DC Module, but other modules that provide access to the *Electrical Circuit* interface will benefit too. You can view the new functionality in these updated models:

- operational_amplifier_with_capacitive_load
- battery_over_-_discharge_protection_using_shunt_resistances
- p_-_n_diode_circuit
- reverse_recovery_of_a_pin_diode

### New Default Plots for the Magnetic Physics Interfaces

New default plots have been developed specifically for physics interfaces that support magnetic fields: *Magnetic Fields*, *Magnetic Fields, No Currents*, and the *Rotating Machinery, Magnetic* multiphysics interface. The magnetic flux density norm is plotted as a multislice or a surface plot, together with streamlines or contours to indicate the field direction. In 2D and 2D axisymmetric models, the streamlines show a divergence-free magnetic field. Whenever possible, a contour plot of the out-of-plane magnetic vector potential is included, which is more exact than the streamlines, in the sense that the contours are closed, and the contour density is directly proportional to the local magnetic flux density. In 3D, the streamlines follow the magnetic field after it has been projected onto the slice planes. The resulting pattern is not necessarily divergence free, but still provides a clear, intuitive indication of what the 3D field will look like. You can view this new plot functionality in the following models:

- inductance_matrix_calculation_of_pcb_coils (new model)
- generator_in_2d
- voltage_induced_in_a_coil_by_a_moving_magnet
- modeling_of_a_3d_inductor
- magnetic_damping_of_vibrating_conducting_solids
- vector_hysteresis_modeling

*The new default plots, as seen for loudspeakers in the Topology Optimization of a Magnetic Circuit model.*

### Ferroelectric Material Model in Electrostatics

For the *Charge Conservation* feature in the *Electrostatics* interface, the list of dielectric material models has been extended with a *Ferroelectric* material option. The ferroelectric material model is the dielectric equivalent of the *Jiles Atherton* magnetic hysteresis model; instead of a time-varying magnetization, it models a time-varying polarization. You can view this feature in the new Hysteresis in Ferroelectric Material tutorial model.

This material model is the electrostatic part of a new *Ferroelectroelasticity* multiphysics interface, intended for analysis of ferroelectric materials, which exhibit nonlinear piezoelectric properties. The *Ferroelectric* material option is included in the AC/DC Module. However, the *Ferroelectroelasticity* multiphysics interface additionally requires either the MEMS Module or the Structural Mechanics Module.

*A screenshot of the Hysteresis in Ferroelectric Material tutorial model, showing both the used material model and the resulting hysteresis curve.*

### Magnetic Materials from Bomatec

The *AC/DC* material library has been extended with magnetic materials from Bomatec. This includes all the NdFeB standard grades ("normal", M, H, SH, UH, EH, AH, BH, /S, M/S, H/S, SH/S, UH/S, EH/S, AH/S, BH/S, H/ST, SH/ST, UH/ST, EH/ST, AH/ST, and BH/ST); NdFeB (bonded, injection molded, and extruded); ferrite (isotropic, anisotropic, and injection molded); SmCo (injection molded); SmFeN (injection molded); SmCo5 grades; Sm2Co17 grades; and AlNiCo (cast and sintered).

The materials include electromagnetic properties — relative permittivity , recoil permeability , and remanent magnetic flux density norm — as well as several properties related to thermal modeling: thermal conductivity, ; density, ; and heat capacity at constant pressure .

### Enhanced Feature: Coil with Slanted Cut

The *Coil* domain feature (both for the *Single Conductor* model and the *Homogenized Multiturn* case) has been equipped with support for a *Slanted Cut*. The *Slanted Cut* setting allows you to relax the constraints used for determining the coil geometry (it applies the input/output boundary constraint "on average" rather than locally). Relaxing the constraint is needed for cases where the natural direction of the current (or the wires) is at an angle with respect to the input or output normal. A typical example is a helical coil, where the input/output boundaries represent a periodicity plane — as is the case for twisted three-phase cables, or fully resolved Litz wires or Milliken conductors. You can see this new feature in the updated Cable Tutorial Series tutorial model.

*The effect of the slanted cut setting on the current direction is illustrated in the wire to the right.*

### Faster Cable Analysis: New Tutorial Model

The Cable Tutorial series has been updated to demonstrate short-twisted periodicity, a kind of periodicity that allows you to reduce the computational effort required for fully resolved 3D twisted cable models, from hours on large cluster systems to about a minute on a laptop. The logic behind the used periodicity is explained in detail, including cases that involve more than two lay lengths, cables with fully resolved Milliken conductors, stranded screens, or a double armor, for example.

The theory for twisted strands and the use of appropriate meshing follows the latest developments in numerical research, and applies to both large-scale insulated submarine cables and umbilical cables, EV charging cables, fully-resolved Litz wires, and the bare cables used in overhead power lines. Additionally, the series discusses the resistive, capacitive, inductive, and thermal properties of cable systems, as well as different bonding schemes: single-point bonding, solid bonding, and cross bonding. You can see this new feature in the updated Cable Tutorial Series tutorial model.

- For a more in-depth look: Modeling Busbars and Cables in COMSOL Multiphysics
^{®} - For 2D modeling in particular: Modeling Cable Systems in COMSOL

*A demonstration model showing a double armor, based directly on the design and theory discussed in the Cable Tutorial Series. (Note: The double armor model is not included in the series explicitly, rather, it is directly derived from it.)*

### New Tutorial Models

COMSOL Multiphysics^{®} version 5.6 brings several new tutorial models to the AC/DC Module.

#### Hysteresis in Ferroelectric Material

*A new model demonstrates how to analyze the nonlinear polarization behavior of ferroelectric materials. The image shows the hysteresis loops fully established after three cycles for different values of the maximum applied voltage.*

Application Library Title:

*ferroelectric_hysteresis*

#### High-Voltage Insulator

*The image shows the distribution of the electric potential of a typical high-voltage insulator. The insulator is widely used in high-voltage power transmission lines to support the weight of suspended conductors without allowing the current to flow through the tower to the ground.*

Application Library Title:

*high_voltage_insulator*

#### Position Optimization of Grading Rings

*A new model that extends the High-Voltage Insulator model and shows how to find the optimum position of grading rings using the*Optimization

*interface. The figure compares the z-component of the tangential electric field along the surface of the first six sheds from the line end in different cases.*

Application Library Title:

*grading_ring_optimization*

#### Inductance Matrix Calculation of PCB Coils

*A new model shows how to compute the inductance matrix of a series of conductors with the new*Magnetic Fields, Currents Only

*interface. The image shows the computed inductance matrix of a PCB composed of 12 independent conductors.*

Application Library Title:

*inductance_matrix_pcb_coils*