IEEE Power Electronics Magazine - September 2020 - 38

for solving purely continuous systems, but can be inefficient for simulating power electronic systems since the
integration of system states and locating of discrete events
are not well combined into one engine [2]. Under the DSED
framework [3], however, the perspective of solving the system is changed from the time axis to the state axis, which
gives an event-driven simulation mechanism based on the
concept of state-discretization. In Figure 1, the comparison
between conventional and DSED simulation framework
shows that DSED only calculates the points when an event
happens and any conventional approach needs to calculate
much more points sequentially in time.
Figure 1(a) shows the conventional time discretization
approach. Multiple points, e.g. t 1, t 2, t 3, etc., need to be
solved. Figure 1(b) shows the state-discretization approach,
where solution is only performed when an event occurs, for
example, at t 1, t 2, t 3, etc., requiring far fewer points of calculation. The DSED approach incorporates two key elements:
1) a discrete-state (DS) algorithm for flexible integration of
state variables, and 2) an event-driven (ED) mechanism for
efficient location of switching events. The DS algorithm is
highly flexible in adaptive numerical integration, which is
realized based on the discretization of system states and
contributes to higher computation efficiency. Meanwhile,
the simulation of power electronic systems involves not
only the integration of state variables but also the location
of discrete switching events. In DSED, switching events will
automatically trigger calculations and start a new simulation
step. Through this ED mechanism, unnecessary iterative
calculations for event location can be largely avoided, thus
dramatically reducing the computational costs and accelerating the simulation process.
With the DS algorithm and the ED mechanism, the DSED
simulation exhibits variable time-step feature. Though it
usually takes more time for a variable-step solver to calculate each time point than a fixed-step solver, the latter has
to adopt a time step that is small enough to follow the fastest transient in the system, and can be inefficient and unacceptably time-consuming considering that the simulation
process of power electronics usually includes both periods
of slow change and transients of fast change. Instead, a
variable-step solver can change the time step adaptively,

decrease the number of unnecessary calculated points and
maximize the simulation efficiency.

B) The PAT Model
In a conventional modeling approach, a power semiconductor device is described by a high-order nonlinear equivalent
circuit. Different mechanisms, such as the nonlinear capacitance, the loop inductance, the gate charging circuit, the
reverse recovery of the diode and so on, are all mixed
together, resulting in heavy burden in terms of computation
speed and convergence robustness. Although such a modeling approach is straight-forward, it is not practical for largesystem simulation.
In fact, the dominant physical mechanism is different in different stages. The idea is to divide the switching
transient into different stages, and simplify the equivalent
circuit accordingly. The PAT model [4] simplifies the piecewise equivalent circuit by considering only the dominant
components and therefore reducing computational costs
and stiffness of the model, as illustrated in Figure 2 using
the turn-on delay of an IGBT as an example. The basic criterion is to ignore the state variables inside the circuit that
do not change largely during one certain period and regard
them as constant sources. Experimental results in [4] suggest a relative error ranging from 2% to 20% in terms of key
transient features including rise time, fall time, maximum
voltage/current and switching loss.
Using such a decoupling method, we can derive an analytical model. Salient features of the model include: 1) It
achieves significant speed enhancement due to effective
simplification in each stage, 2) It is free of convergence
problem due to highly-decreased order of the circuit in
each stage, and 3) All model parameters can be derived
from manufacturer datasheets. The PAT model provides
a practical solution for switching transient simulation in
large-scale power electronic systems. To be implemented in
the DSED approach, the transition condition of each stage
given by the PAT model is used as an event-condition in the
event-driven mechanism. When a certain event is detected,
it triggers the transition of the PAT model from the previous
stage to the following stage, and then the corresponding
calculation with the new mathematical form in this stage.

x
Switching
Events
Switching
Events

event5
event2
event3
event1
event4

Switching
Events
Switching
Events
0

t 1 t 2 t3

t4 t5 t6

t7 t 8

t9 t10 t11 t12 t13

Time-Discretization
(a)

t4 t 5

Event-Driven Simulation
Based on State-Discretization
(b)

FIG 1 Comparison between conventional and DSED simulation framework. (a) Conventional simulation framework.
(b) DSED simulation framework.

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IEEE Power Electronics Magazine - September 2020

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