Simulink^{®} software provides a variety of solvers. Most of the variablestep solvers work well with linear circuits. However circuits containing nonlinear models, especially circuits with circuit breakers and power electronics, require stiff solvers.
Best accuracy and fastest simulation speed is usually achieved
with ode23tb
.
Solver 

Relative tolerance 

Absolute tolerance 

Maximum step size 

Initial step size 

Solver reset method 

Normally, you can choose auto
for the absolute
tolerance and the maximum step size. In some instances you might have
to limit the maximum step size and the absolute tolerance. Selecting
too small a tolerance can slow down the simulation considerably. The
choice of the absolute tolerance depends on the maximum expected magnitudes
of the state variables (inductor currents, capacitor voltages, and
control variables).
For example, if you work with highpower circuit where expected voltage and currents are thousands of volts and amperes, an absolute tolerance of 0.1 or even 1.0 is sufficient for the electric states. However, if your electrical circuit is associated with a control system using normalized control signals (varying around 1), the absolute tolerance is imposed by the control states. In this case, choosing an absolute tolerance of 1e3 (1% of control signal) would be appropriate. If you are working with a very low power circuit with expected currents of milliamperes, set the absolute tolerance to 1e6.
Note
Usually, keeping the Solver reset method parameter
of the ode23tb solver to its default value ( 
Three methods are available for continuous simulation of switches and power electronic devices:
Purely resistive switch — The switch and the linear elements are simulated as a variable topology circuit. The statespace model of the circuit is recalculated at each switch opening or closing. When the switch is in series with an inductive element, a snubber is required.
Ideal switch — The switch is modeled using the Ideal Switching Device method. The statespace model of the circuit is recalculated at each switch opening or closing. Snubbers are not required.
Inductive switch — The switch contains a series inductance (Diode and Thyristor with Lon > 0, IGBT, MOSFET, or GTO). The switch is simulated as a current source driven by voltage across its terminals. The nonlinear element (with a voltage input and a current output) is then connected in feedback on the linear circuit, as shown in the Interconnection of Linear Circuit and Nonlinear Models.
Note You have the choice to simulate diodes and thyristors with or without Lon internal inductance. In most applications, it is not necessary to specify an inductance Lon. However, for certain circuit topologies, you might have to specify a switch inductance Lon to help commutation. 
Modeling switches, such as circuit breakers or power electronic
devices, as current sources implies that the onstate switch resistance
Ron cannot be zero. Also, as switches are modeled by a current source,
they cannot be connected in series with an inductive circuit or with
another switch or current source. In such a case, you must add a circuit
(R or RC snubber) in parallel with the switches so that their offstate
impedance has a finite value. If the real circuit does not use snubbers,
or if you want to simulate ideal switches with no snubber, you must
at least use resistive snubbers with a high resistance value to introduce
a negligible leakage current. The drawback of introducing such highimpedance
snubbers is that the large difference between the onstate and the
offstate switch impedance produces a stiff statespace model. For
example, if a 1 H inductance is connected to a voltage source by a
switch having a onstate resistance Ron= 0.001 ohms and a snubber
resistance Rs= 1e6 ohms, the time constant L/R of this first order
circuit varies from 1000 s when the switch is closed to 1 µs
when the switch is open. If you simulate this circuit with a continuous
solver, such a wide range of time constants requires a variablestep
stiff solver such as ode23tb
. The model stiffness
affects the simulation speed. If the snubber resistances are too large,
the solver might become extremely slow or even fail to find a solution.
If you are using a discretized model, you might observe numerical
oscillations if your sample time is too large.
When you model switches using the Ideal Switching Device method, snubbers are not required. To enable this method:
Open the Powergui dialog box and select Configure parameters. The Powergui block parameters dialog box opens.
In the Solver tab of this dialog
box, set the Simulation type parameter to Continuous
and select Enable use
of ideal switching devices.
Additional options are displayed, allowing you to disable switch snubbers, as well as their Ron resistance (Ron=0) and their forward voltage (Vf=0), when applicable.
You can select Disable snubbers in switching devices, which disables snubbers of all switches. Otherwise, you may individually disable snubbers of selected switches by specifying Rs=inf in their block menus. You can also simulate perfectly ideal switches by disabling the resistances (Ron) and the forward voltages (Vf).
Eliminating the snubbers reduces the circuit stiffness and lets
you use a nonstiff solver, for example, ode45
instead
of ode23tb
, to achieve correct results and good
simulation speed.
Assuming a circuit containing nx states, ns switches, and ny voltage or current outputs, the software determines:
nx
state derivatives to be computed
from the A and B matrices of
$$\dot{x}=A\xb7x+B\xb7u$$
ns
switch variables (either voltages
across open switches or currents through closed switches)
ny
output variables to be computed
from the C and D matrices of
$$y=C\xb7x+D\xb7u$$
A total of nx + ns + ny equations is obtained.
Unknown variables are state derivatives dx/dt, outputs y, and switch variables (switch voltages or switch currents). Known variables are state variables x and inputs u (voltage sources or current sources).
As the switch status (open or closed) is undetermined, circuit equations are expressed using both switch voltages (v_{D1}, v_{D2}) and switch currents (i_{D1}, i_{D2}).
These equations express Kirchhoff current laws (KCL) at circuit nodes and Kirchhoff voltage laws (KVL) for the independent loops. These equations are completed by the output equations.
Computation of the statespace model is incorporated in an Sfunction and performed each time a switch status is changing.
To get a list of the circuit equations in the Command Window, select the Display circuit differential equations check box in the Solver tab of the Powergui block parameters dialog box.
Continuous Solver Required. The Ideal Switching Device method is not supported with discretized models.
Specifications of Snubber Values. This method was developed to avoid use of snubbers across switches. However, the method still works when you use snubbers. For example, models of the Power Electronic Models examples will work when you keep snubbers, Ron and Vf, in service.
For discretized models, in the Powergui block, change the Simulation
type from Discrete to Continuous and
select Enable use of ideal switching devices.
Then specify a continuous solver (recommended solver: ode23tb
with
relative tolerance 1e4
).
If you specify resistive snubber values that are too large, the circuit model might become badly conditioned and cause the simulation to stop. In such a case, reduce snubber resistances so that the resulting leakage current remains acceptable (for example 0.01% to 0.1% of switch nominal current).
Specification of Ron When Vf is Greater Than Zero. In some circuits, using switches with a forward voltage Vf greater than zero and Ron=0 might cause simulation to stop and display an error message due to a StateSource dependency. To avoid this problem, specify a small Ron value.
Consider the fullwave rectifier shown in the following figure.
FullWave Rectifier
When you simulate this circuit without using the ideal switching method, you must use snubbers across diodes D1 and D2 because these elements are connected in series with inductances (transformer leakage inductances of the two secondary windings and filter inductance L). Otherwise, when you start the simulation SimPowerSystems™ prompts an error message.
Open the power_FullWaveRectifier
example.
The parameters are typical for a 60W, 120 Vac / 24 Vdc rectifier.
Resistive snubbers (Rs = 1e6 Ω) are used across diodes.
Open the Configure parameters section of the Powergui block. Clear the Enable use of ideal switching devices parameter.
Set the Simulation type parameter
of the Powergui block to Continuous
, and
define the following solver:
Type 

Solver 

Relative tolerance 

Solver reset method 

Stop time 

Other parameters 

Start the simulation. You see the following waveforms.
Increase the snubber resistance by specifying Rs =
1e8 Ω in the two diode blocks and simulate again. When using
such high snubber resistances, simulation results become incorrect.
To get correct results, you must increase the solver accuracy by either
limiting the Max step size to 1e7
,
or setting the Solver Reset Method to Robust
.
When you try to get rid of snubbers in large circuits containing many power electronic devices, reduction of maximum step size or solver tolerances might result in an unacceptable simulation time. In some circumstances, the solver might even fail to find a solution..
Open the block parameters of the Powergui block and select Enable use of ideal switching devices parameter. Select Disable snubbers in switching devices parameter. To simulate perfectly ideal switches, you can also disable the diode resistances (Ron) and the forward voltages (Vf).
Make sure that your solver parameters are as shown in 3. Simulate and observe that waveforms are correct.
Eliminating the snubbers has reduced the circuit stiffness.
You can now use ode45
solver instead of ode23tb
.