Thermal Concepts
Heat Sink Concept
The core component of the thermal library is an idealized Heat Sink depicted as a semitransparent box as in Fig. 54. A heat sink absorbs the thermal losses dissipated by the components within its boundaries. At the same time, a heat sink defines an isotherm environment and propagates its temperature to the components which it encloses.
Fig. 54 Heat Sinks as Semitransparent Boxes
Heat conduction from one heat sink to another or to an ambient temperature is modeled with lumped thermal resistances and capacitances that are connected to the heat sinks. This approach allows you to control the level of detail of the thermal model.
Implementation
Each heat sink has an intrinsic thermal capacitance versus the thermal reference node. All thermal losses absorbed by the heat sink flow into this capacitance and therefore raise the heat sink temperature. Heat exchange with the environment occurs via the external connectors.
Fig. 55 Schematic Representation of a Heat Sink
You may set the intrinsic capacitance to zero, but then you must connect the heat sink either to an external thermal capacitance or to a fixed temperature, i.e. the Constant Temperature block or the Controlled Temperature block.
Thermal Loss Dissipation
There are two classes of intrinsic components that dissipate thermal losses: semiconductor switches and ohmic resistors.
Semiconductor Losses
Power semiconductors dissipate losses due to their non-ideal nature. These losses can be classified as conduction losses and switching losses. For completeness the blocking losses due to leakage currents need to be mentioned, but they can usually be neglected.
Semiconductor losses are specified by referencing a thermal data sheet in the component parameter Thermal description. See Thermal Description Parameter and Thermal Library for more details.
Conduction Losses
The conduction losses can be computed in a straightforward manner as the product of the device current and the device voltage. By default the on-state voltage is calculated from the electrical device parameters as \(v = V_\mathrm{f} + R_\mathrm{on}\cdot i\).
However, PLECS also allows you to specify the on-state voltage used for the loss calculation as an arbitrary function of the device current and the device temperature: \(v = v_\mathrm{on}(i, T)\). You may also specify additional custom function arguments. This function is defined in the Conduction Loss tab of the thermal description as a 2D lookup table or a functional expression (see Thermal Editor).
Fig. 56 Example on-state voltage characteristic of a semiconductor device
A setting of \(0\,\mathrm{V}\) for a single temperature and current value means no conduction losses. If you do not specify a thermal description in the device parameters, the default will be used, i.e. the losses are calculated from the electrical device parameters.
Note
If you specify the Thermal description parameter, the dissipated thermal power does not correspond to the electrical power that is consumed by the device. This must be taken into account when you use the thermal losses for estimating the efficiency of a circuit.
Switching Losses
Switching losses occur because the transitions from on-state to off-state and vice versa do not occur instantaneously. During the transition interval both the current through and the voltage across the device are substantially larger than zero which leads to large instantaneous power losses. This is illustrated in Fig. 57. The curves show the simplified current and voltage waveforms and the dissipated power during one switching cycle of an IGBT in an inverter leg.
Fig. 57 Turn-on and turn-off behavior of a IGBT device during one switching cycle
In other simulation programs the computation of switching losses is usually challenging because it requires very detailed and accurate semiconductor models. Furthermore, very small simulation time-steps are needed since the duration of an individual switching transition is in the order of a few hundred nanoseconds.
In PLECS this problem is bypassed by using the fact that for a given circuit the current and voltage waveforms during the transition and therefore the total loss energy are principally a function of the pre- and post-switching conditions and the device temperature: \(E = E_\mathrm{on}(v_\mathrm{block}, i_\mathrm{on}, T)\), \(E = E_\mathrm{off}(v_\mathrm{block}, i_\mathrm{on}, T)\). You may also specify additional custom function arguments. These functions are defined in the tabs Turn-on Loss and Turn-off Loss of the thermal editor as 3D lookup tables or functional expressions (see Thermal Editor).
Fig. 58 Example switching energy characteristic of a semiconductor device
A setting of \(0\,\mathrm{J}\) for a single voltage, current and temperature value means no switching losses.
Note
Due to the instantaneous nature of the switching transitions, the dissipated thermal energy cannot be consumed electrically by the device. This must be taken into account when you use the thermal losses for estimating the efficiency of a circuit.
Loss Calculation
As described above, the conduction and switching losses are defined by means of lookup tables. From these tables the actual losses are calculated during a simulation using linear interpolation if the input values (on-state current, pre- and post-switching current or voltage, junction temperature) lie within the specified index range. If an input value lies out of range, PLECS will extrapolate using the first or last pair of index values.
If the calculated loss value is negative, PLECS will issue a diagnostic message and/or crop the value to zero. You can select the diagnostic action to be taken with the diagnostic parameter Negative switch loss in the simulation parameters dialog (see PLECS Standalone Parameters and PLECS Blockset Parameters).
Supported Devices
The following semiconductor components implement this loss model:
In addition, the Set/Reset Switch is also included in this group to enable you to build your own semiconductor models.
Ohmic Losses
Ohmic losses are calculated as \(i^2 \cdot R\) resp. \(u^2 / R\). They are dissipated by the following components:
Heat Sinks and Subsystems
By default, if you place a subsystem on a heat sink, the heat sink temperature is propagated recursively into all subschematics of the subsystem. All thermal losses dissipated in all subschematics flow into the heat sink. In some cases this is not desirable.
The implicit propagation mechanism is disabled if a subschematic contains one or more heat sinks or the Ambient Temperature block. This latter block provides a thermal connection to the heat sink enclosing the parent subsystem block.
Fig. 59 Heat Sink to Ambient
As an example the figure Fig. 59 shows the subschematic of the Diode with Reverse Recovery. By default, this diode model would only dissipate the ohmic losses from the three resistors and the conduction losses of the internal ideal diode. However, the losses from the reverse recovery current injected by the current source would be neglected because current sources (and also voltage sources) do not dissipate thermal losses.
The Diode with Reverse Recovery therefore uses a Controlled Heat Flow block to inject the electrical power loss into the thermal model via the Ambient Temperature block. The power loss is calculated by multiplying the device voltage and the device current.
Temperature Initialization
The state variables of a thermal model are the temperatures of thermal capacitances, and like other state variables they need to be initialized with a starting value. For this purpose the Thermal Capacitor and other components that implicitly contain thermal capacitances have a parameter Initial temperature that allows you to specify this starting value.
However, you can also let PLECS calculate the initial value for you based on other temperatures in the thermal system. To do so, simply leave the parameter blank or enter nan (a floating point constant standing for “Not A Number”). At the beginning of a simulation, PLECS will perform a “DC analysis”, treating thermal capacitances with known initial values like constant temperature sources and calculating the unknown initial values such that the system would be in steady state.
As an example, consider the following thermal system consisting of a constant temperature source and three thermal R/C pairs (Fig. 60). If you leave the Initial temperature parameter of the three capacitances blank, all three will “inherit” the starting temperature from the source. On the other hand, if you leave only the parameters of the first two capacitances blank and specify an initial value of 125 for the third one, PLECS will initialize the first capacitance with \(T_0=25+(125-25)\cdot\frac{2}{2+3+5}=45\) and the second one with \(T_0=25+(125-25)\cdot\frac{2+3}{2+3+5}=75\). Of course, as soon as the simulation starts, the temperatures in all three capacitances will eventually drop to the temperature of the source.
Fig. 60 Example thermal system
Fig. 61 Thermal behavior of the example thermal system shown in Fig. 60
Thermal Description Parameter
Most semiconductor components in PLECS have a parameter Thermal description. Also, masked subsystems can have mask parameter of type Thermal (see Mask Dialog). Thermal parameters can be used in two ways:
to select a data sheet from the thermal library or
to assign the value of a reference variable that is defined e.g. as a thermal mask parameter or in the base workspace.
Selecting Thermal Data Sheets
To select a data sheet from the thermal library, choose the menu entry From library…. This will open a submenu Selecting a data sheet from a thermal library that shows all data sheets that match the device type; e.g. in the dialog box of a diode only those data sheets appear that have their Type field set to Diode.
Fig. 62 Selecting a data sheet from a thermal library
If no data sheet is available, the menu entry is disabled. See section Thermal Library for more information on how to create new data sheets.
Using Reference Variables
To use a reference variable in the Thermal description parameter, select the menu entry By reference from the parameter menu. Afterwards, the reference variable can be entered in the text field.
The reference variable can be the variable name of a Thermal mask parameter in the mask definition of a parent Subsystem (see Mask Dialog).
The reference variable can also be a string specifying a thermal description file. The string must begin with file: followed by the file path of the data sheet. It is possible to use an absolute file path to a thermal description file including the .xml extension, for example:
thLosses = 'file:C:\Thermal\Vendor\mydiode.xml'
Alternatively, the name of a data sheet from the thermal library can be specified. In this case the data sheet must be on the thermal search path. Its name must be provided as a relative path without the .xml extension, for example:
thLosses = 'file:Vendor/mydiode'
Thermal Modeling with Parallel Devices
In power electronic systems, semiconductor devices are often connected in parallel to share power dissipation and reduce the thermal stress on individual components. PLECS supports several approaches for modeling parallel semiconductor devices:
Multiple discrete components: Multiple semiconductor components can be placed in parallel, each with its own electrical and thermal connection. This approach provides full electrical and thermal detail, but becomes increasingly complex as the number of parallel devices grows. Increased schematic block density, additional gate signal routing, and the need to maintain consistent parameterization across all paralleled devices increase the likelihood of configuration errors. This approach is therefore not recommended.
Custom masked subsystem: You can create a masked subsystem (see Masking Subsystems) in which paralleling equations are applied in the initialization commands to scale device currents, losses, and thermal impedance used by the thermal model. This approach offers flexibility and can be useful for custom modeling workflows, but requires manual setup and maintenance.
Built-in parallel device support: As of PLECS 5.0, the following semiconductor components include a Number of parallel devices parameter that automatically scales thermal losses while maintaining a single electrical device model. This approach is recommended for most applications as it provides accurate thermal scaling with minimal modeling effort.
Example Model
See the example model “Thermal Modelling with Parallel Devices”.
Find it in PLECS under Help > PLECS Documentation > List of Example Models.
Note
The paralleling approaches above assume ideal current sharing between the parallel devices.