SIMSCAPE Electrical Modelling of the IGBT with Parameter Optimization Using Genetic Algorithm

Abstract

The concept introduced by MathWorks in the Simscape product is the link representation between the SIMSCAPE library components that correspond to physical connections transmitting power. In this paper, a power insulated-gate bipolar transistor (IGBT) model using MATLAB graphical software is reproduced. An electrical IGBT behavior model using the Simscape Electronics library components is developed and analyzed. This model is parameterized using the constructor datasheet to ensure a good representation of the dynamic and static IGBT behaviors. An extraction and optimization studies of the IGBT model parameters using a stochastic algorithm implemented in Matlab are presented. The proposed method is based on the Genetic Algorithm (GA) to perfectly extract and optimize the model parameters using the mathematical model circuit equations and the provided datasheet characteristics. A simulation in the Matlab/Simulink environment and a comparison with the experimental results for an IGBT device example are carried out to demonstrate the proposed model accuracy.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

For reducing design costs and increasing electronic power circuits’ reliability, the modeling of power semiconductor devices becomes indispensable. The model must capture the dynamic and static behavior of the power semiconductor devices to ensure the safe global circuit operating area. The IGBT is one of the most important power semiconductor devices widely used in different power electronic applications.

In the literature, several IGBT models were developed at different complexity levels and for various uses. At this level, an accurate physical device description has been required in [1, 2]. Hefner’s model and a model list based on the Hefner work are examples of suitable mathematical models for circuit simulator implementation, which have proved to have a good accuracy and high reliability [3–5]. In [6, 7], the authors have proposed a complete and complex mathematical model using a complex equation for each model part, including the wide-base PNP section, the MOSFET channel section, capacities, the JFET effect, and the thermal effect. The difference between the analytical models is in the simplifications made in order to reduce the simulation time. To have more accurate results, numerical methods were employed to solve the 2 D and 3 D ambipolar diffusion equations. However, the numerical models’ implementation requires special simulators. These model types are specially developed to optimize IGBT structure technologies [8].

For macromodels, they are used when high accuracy is not needed and the representation of some phenomena is ignored. Thus, the physical IGBT mechanisms are not considered in the models. Indeed, the fitted characteristics of the IGBT component are translated to an equivalent electrical circuit [9, 10].

The literature reported several works on the automatic extraction and optimization of IGBT model parameters. In [11], the authors developed the most suitable physical models and reference for the IGBT, and the IMPACT software has been elaborated to extract the IGBT model parameters. The IMPACT software has included five programs, which have extracted the 20 physical and structural parameters from the most recent version of the developed IGBT model. Each program has provided automatic algorithms to perform the extraction, using experimental measurements for each parameter set. The behavioral model of Oh and El Nokali implemented in Saber [12] has been reproduced by Kang et al. who have developed a new extraction algorithm to determine its parameters [13]. The algorithm is based on the availability of experimental switching loss data and the manufacturer-supplied characteristics, while the Matlab optimization toolbox is used to find model parameters automatically.

In [14], the IGBT model based on the finite-elements (FEM) physics has been implemented in the circuit simulator IsSPICE. The proposed extraction procedure is the numerical optimization algorithm called “Simulated Annealing” (SA). Its implementation is carried out in the Matlab programming environment, which allows a data exchange with IsSPICE.

This paper aims to model the IGBT device using the graphical Matlab software. The proposed electrical IGBT model is developed using Pspice [15, 16] and Saber simulators [17] in the previous contributions. The main contribution of this work is the automatic identification and optimization of the model parameters based on a stochastic algorithm. The nonlinear equations describing the IGBT model for each operating zone are rewritten as an optimization problem for their model parameters, which is solved using the Genetic Algorithm (GA) with the datasheet characteristics. The proposed technique is easily implemented in the Matlab environment, and the simulation results proved its high reliability. The rest of this paper is organized as follows: the electrical IGBT model is developed in Section 2, while Section 3 describes the model parameter optimization using GA. In Section 4, simulation results of the proposed model are discussed. Finally, conclusions are given in Section 5.

2. IGBT Design

2.1. Electrical IGBT Model

The insulated-gate bipolar transistor (IGBT) is a hybrid transistor, which includes the Metal Oxide Semiconductor Field Effect Transistor (MOSFET) at the input and the Bipolar Junction Transistor (TBJ) at the output. Consequently, the IGBT has low power control as an advantage of the MOSFET and presents the benefits of the TBJ which are low conduction losses and high-voltage handling [18]. The established model can predict the IGBT behavior for both dynamic and steady state. Besides, it can be easily parameterized using manufacturer data, and it represents an optimum compromise between accuracy and simulation complexity [17].

The static MOSFET model is constituted by

(i) D_G: a diode which allows the passage from the blocked state to the on state.

(ii) V_TH: DC voltage source. It represents the threshold voltage.

(iii) R_GE: leakage gate-emitter resistance.

(iv) J_mos: a controlled current source which represents the drain current (I_mos).

(v) R_DN: drain resistance which characterizes the resistive aspect of the MOSFET channel.

(vi) D_DC: an antiparallel body diode which allows the passage from the linear zone to the saturated zone. It is represented by a binary resistance R_ONDC/R_OFFDC.

The MOSFET current is controlled by V_GE voltage, according to three cases:

(i) V_GE < V_TH: the transistor is off, so the channel is not constructed

(ii) V_GE + V_CE0 − V_TH > V_CE:$$\begin{array}{}\text{(1)}& I_{mos}=K_p\frac{V_{\text{GE}}-V_{\text{TH}}\ast V_{\text{CE}}-V_{\text{CE0}}-{V_{\text{CE}}-V_{\text{CE0\hspace{0.17em}}}}^2/2}{1+\theta V_{\text{GE}}-V_{\text{TH}}}\end{array}$$

(iii) V_GE + V_CE0 − V_TH < V_CE:

$$\begin{array}{}\text{(2)}& I_{\text{mos}}=\frac{K_p}{2}\frac{{V_{\text{GE}}-V_{\text{TH}}}^2}{1+\theta V_{\text{GE}}-V_{\text{TH}}},\end{array}$$where K_p is the transconductance and θ is the correction factor, which takes into consideration the transverse field in the MOSFET channel

For the bipolar part, the static TBJ model is composed by

(i) D_E and D_P: the base-emitter and base-collector junctions

(ii) V_CE0: conduction threshold voltage of the base-emitter junction

(iii) J_PNP: a controlled current source which represents the current gain of the bipolar transistor

(iv) β: the bipolar gain

2.2. Dynamic IGBT Model

To model the dynamic IGBT behavior, other elements are added to the static model. These elements include nonlinear terminal capacitances and the voltage-controlled current source that models the load responsible of the tail current I_C at the turn off IGBT state.

Constructors provide the measurement capacitors between two terminals by eliminating one or two capacitors. The input capacitance (C_IE), reverse transfer capacitance (C_RE), and output capacitance (C_OE) allow us to determine the interelectrode capacitance values C_GE, C_CE, and C_GC using the following equations [19]:$$\begin{array}{}\text{(3)}& \begin{array}{c}{C}_{\text{IE}}=C_{\text{GE}}+C_{\text{GC}}\hfill \\ C_{\text{OE}}=C_{\text{CE}}+C_{\text{GC}}\hfill \\ C_{\text{RE}}=C_{\text{GC}}\hfill \end{array}⟹\begin{array}{c}{C}_{\text{GE}}=C_{\text{IE}}-C_{\text{RE}}\hfill \\ C_{\text{CE}}=C_{\text{OE}}-C_{\text{RE}}\hfill \\ C_{\text{GC}}=C_{\text{RE}}\hfill \end{array}.\end{array}$$

Figure 1 shows the evolution of C_GE, C_CE, and C_GC capacitances versus V_CE. We note that the C_GE capacity remains almost constant while the C_GC and C_CE capacities vary strongly nonlinear following the device operating area. These two capacities change values around the same threshold voltage V_CET0.

[figure omitted; refer to PDF]

C_GC capacity: this capacity can be constituted of two capacities in series: C_OXD oxide capacity that is fixed by the constructor and C_GCJ depletion capacity. In Figure 1, the C_GC capacity changes value from a certain V_CE threshold voltage V_CET. We can use the diode model [16] to represent the nonlinearity of the C_GC capacity between two values C_GCmin and C_GCmax (Figure 2).

[figure omitted; refer to PDF]

The C_GCmax capacity is represented by a voltage-controlled current source, with a gain given by the following expression:$$\begin{array}{}\text{(4)}& G_{\text{GC}}=\frac{R_{\text{onGC\hspace{0.17em}}}{C}_{\text{GCmax}}}{L_{\text{GC}}}.\end{array}$$

C_CE capacity: this capacity, as it seen in Figure 1, varies also as nonlinear. It is represented in the same manner as that for the C_GC capacity. The coupling coefficient G_CE is given by the following expression:$$\begin{array}{}\text{(5)}& G_{\text{CE}}=\frac{R_{\text{onGC\hspace{0.17em}}}{C}_{\text{CEmax}}}{L_{\text{GC}}}.\end{array}$$

The bipolar part presents the responsible charge of the tail current I_C, and these charges can be represented only by the PNP base-emitter junction storing charges. Thereafter, these charges are modelled by a controlled source (Figure 3), whose expression is as follows:$$\begin{array}{}\text{(6)}& G_t=\frac{R_{\text{onDE\hspace{0.17em}}}{C}_{\text{BE}}}{L_{\text{BE}}},\end{array}$$where C_BE represents the bipolar part storing charges, with C_BER_onDE = t_off, where t_off is deduced from the device datasheets.

[figure omitted; refer to PDF]

The studied IGBT model is shown in Figure 3.

2.3. The IGBT Model Parameter Extraction

This section aims to develop and show the extraction method of the IGBT model parameters. To identify the model parameters in the static case, the main idea is to take out the circuit equations according to the diode states (Figure 4). Indeed, the diodes states define the different IGBT operation zones.

[figure omitted; refer to PDF]

For the Ohmic zone, all diodes are turned on. The resolution of the equations system described the static model gives the expression of the V_CE voltage versus the I_C current:$$\begin{array}{}\text{(7)}& V_{\text{CE}}=V_{\text{CE0}}-\frac{R_{\text{ONDP}}\ast R_{\text{ONDC}}}{R_{\text{ONDP}}+R_{\text{ONDC}}+R_{\text{DN}}}\ast I_{\text{mos}}+R_{\text{ONDE}}+\frac{R_{\text{ONDP}}\ast R_{\text{ONDC}}+R_{\text{DN}}\ast 1-G_P\ast R_{\text{ONDE}}}{R_{\text{ONDP}}+R_{\text{ONDC}}+R_{\text{DN}}}\ast I_C.\end{array}$$

For the quasisaturation zone, all the diodes are turned on except the D_P diode. The expression of the V_CE voltage versus the I_C current becomes$$\begin{array}{}\text{(8)}& V_{\text{CE}}=V_{\text{CE0}}-\frac{R_{\text{ONDC}}\ast R_{\text{OFFDP}}}{R_{\text{ONDC}}+R_{\text{OFFDP}}+R_{\text{DN}}}\ast I_{\text{mos}}+R_{\text{ONDE}}+\frac{R_{\text{OFFDP}}\ast R_{\text{ONDC}}+R_{\text{DN}}\ast 1-G_P\ast R_{\text{ONDE}}}{R_{\text{OFFDP}}+R_{\text{ONDC}}+R_{\text{DN}}}\ast I_C.\end{array}$$

For the saturation zone, it is characterized by the blocking diode D_DC of the MOSFET part and the blocking diode D_P of the bipolar part. The expression of the V_CE voltage becomes$$\begin{array}{}\text{(9)}& V_{\text{CE}}=V_{\text{CE0}}-\frac{R_{\text{OFFDC}}\ast R_{\text{OFFDP}}}{R_{\text{OFFDC}}+R_{\text{OFFDP}}+R_{\text{DN}}}\ast I_{\text{mos}}+R_{\text{ONDE}}+\frac{R_{\text{OFFDP}}\ast R_{\text{OFFDC}}+R_{\text{DN}}\ast 1-G_P\ast R_{\text{ONDE}}}{R_{\text{OFFDP}}+R_{\text{OFFDC}}+R_{\text{DN}}}\ast I_C.\end{array}$$

The parameters of the studied model are deduced from the technical datasheet and the equations established in [15]. The IGBT parameters are recorded in Table 1 for the commercial IGBT (IRGBC20U).

Table 1

IGBT electrical parameters (IRGBC20U).

	Parameters	Values
Static parameters	VCE0	1.9 V
	RONDE	8.66 10−2 Ω
	RDN	2.3073 10−3 Ω
	RONDC	2.479 10−1 Ω
	ROFFDC	108 Ω
	RONDP	3.42 10−3 Ω
	ROFFDP	2.373 107 Ω
	GP	1.154 Ω−1
	VTH	5.3 V
	KP	1.766
	Θ	8.47 10−2
	RGE	2 108
	Β	10−1
Dynamic parameters	CGE	3 10–10 F
	CGCmin, RGC, LGC,RONGCVCET	6 10−12 F, 10−1 Ω, 10−10 H, 103 Ω, 20V
	GGC	2.44 10−3F
	CCE, GCE	5.9 10−13 F, 3.06 103 Ω−1
	Gt	910 Ω−1

3. Optimization of the IGBT Model Parameters Using Genetic Algorithm

3.1. Genetic Algorithm

In classical information treatment, the problems are solved in fixed ways before the introduction of heuristic methods using random processes. In fact, during the design phase of a system, it receives all the necessary data for its operating conditions as known at the time of its conception, which prevents its adaptation to unknown changing environmental conditions. Therefore, computer researchers are studying methods to allow systems to adapt spontaneously to new conditions. Hence, the heuristic and stochastic methods emerge such as evolutionary programming based on the Darwin theory. The theory of the species evolution is exposed under the external constraints influence, and the fixed systems’ existence is rejected.

Among the evolutionary algorithms, the Genetic Algorithm (GA) is developed for optimization purposes. The genetic process is based on the natural selection theory and the evolution genetics. John Holland introduced the first formal model of genetic algorithms in 1976, which added an intelligence to a computer program with the crossing notion (genetic material exchange) and the mutation notion (genetic diversity source) [20]. Based on John Holland’s work, several research studies have been developed.

Unlike the different optimization techniques, the GA is characterized by

(i) The use of an encoding describing the parameters

(ii) GA works on a population of points, instead of a single point

(iii) It uses only the function values under study

(iv) It uses probabilistic, not deterministic, transition rules

A genetic algorithm offers acceptable solutions for difficult problems in a reasonable calculation time. It tries to optimize the defined solution for a number of iterations and chooses the most optimized solution available for a problem at the program end. The initial creation of the population, the evaluation of the optimization condition (adaptation function or fitness function), selection, crossing, and mutation are the five fundamental functions of the algorithm.

Figure 5 shows the genetic algorithm diagram. The genetic algorithm process simulates the evolution of a population, which is subjected to a selection at each generation, and the recombination and mutation operators are applied. The selection based on the fitness function allows improving the population [20]. This algorithm does not require knowledge of the problem, which can be represented by a black box with inputs representing the variables and outputs representing the objective functions. Then, the algorithm manipulates the inputs in order to improve the outputs.

[figure omitted; refer to PDF]

In order to optimize the static parameters of the IGBT model, an approach is used to combine the manual extraction method that allows obtaining a first estimation of the set of parameters and then using the numerical optimization by the GA to extract the optimal set of parameters using the Toolbox “GA” in MATLAB [23].

The flowchart of the proposed optimization approach is presented in Figure 7.

[figure omitted; refer to PDF]

The fitness function measures the error between manufacturer and simulated data. The used fitness function, for parameter evaluation, is defined by the sum of the deviation between the equation representing the manufacturer’s curve (desired value) and the equation of the curve containing the model parameters (calculated values). The fitness function is given as follows:$$\begin{array}{}\text{(10)}& F_{\text{fitness}}={\displaystyle \sum {I_{\text{Cdata}}-I_{\text{CM}}}^2},\end{array}$$where $I_{\text{Cdata}}$ is the value of the desired current given by the manufacturer and I_CM is the current value calculated by the simulated model.

Following that mentioned above, two programs are developed on MATLAB; the first one will use the mathematical equation of the transfer characteristic with equations (1) and (2) to optimize the coefficients K_P, V_TH, θ, and the bipolar gain β. The second program will use equations (7)–(9) with the mathematical equation of the output characteristic to calculate the other parameters V_CE0, R_ONDE, R_DN, R_ONDC, R_OFFDC, R_ONDP, R_OFFDP, and G_P.

The parameter values obtained by optimization and GA numerical information (data points and steps) are summarized in Tables 2 and 3, respectively.

Table 2

IGBT electrical parameters (IRGBC20U).

Parameters	Values
VCE0	1.6119 V
RONDE	8.04 10−2 Ω
RDN	2.0 10−3 Ω
RONDC	3.893 10−1 Ω
ROFFDC	4.690106 Ω
RONDP	8.0 10−3 Ω
ROFFDP	9.361 105 Ω
GP	1.3.830 Ω−1
VTH	5.3 V
KP	1.6166
Θ	8.10 10−2
RGE	2 108
Β	1.34910−1

Table 3

GA numerical information.

	Data points	Steps (s)
Transfer characteristic	1451	2.283353
Output characteristic	851	0.748621 to 0.860017

Figure 8 shows the optimization results obtained for the two studied cases. A good convergence of the solution giving by the genetic algorithm in the treated cases can be seen.

[figures omitted; refer to PDF]

The comparison between the obtained results and the simulation results without optimization is illustrated in Figure 9. The improvement brought by the model in the reproduction of the output and transfer characteristics in the saturation regime is shown. The error between the curves obtained by optimization and the curves given by the manufacturer is low.

[figures omitted; refer to PDF]

4. Results and Discussion

Figure 10 illustrates the experimental circuit used to perform the dynamic and static characteristics of the studied IGBT. The electrical IGBT environment is modelled by a wiring inductance L_P and a wiring resistance R_P. A single parasitic inductance is sufficient to represent the total circuit inductances [24]. The IGBT driver causes the rise and fall times of the V_G impulsion. This interaction between the control section and the device is also included in the test circuit simulation.

[figures omitted; refer to PDF]

4.1. Validation of the Static Behavior of the IGBT Model

To obtain the output characteristic, the simulation is performed as given in the manufacturer specifications in the following terms: the voltage V_GE is maintained at 15 V, and the voltage V_CE changes linearly from 1 V to 10 V during 25 μs. Figure 11 shows experimental (manufacturer data) and simulated static characteristics of the commercial IGBT IRGBC20U, obtained for test conditions of the manufacturer: (a) transfer characteristic; (b) output characteristic.

[figures omitted; refer to PDF]

To perform the transfer characteristic I_C (V_GE), the V_CE is fixed at 100 V while the V_GE varies from 5 V to 20 V.

Figure 11 presents the manufacturer and simulation results of static characteristics. In the two curves, simulation results show good agreements compared to manufacturer data.

4.2. Validation of the Dynamic IGBT Model Behavior

The switching IGBT characteristics are affected by parasitic impedances, especially parasitic inductances. The I_C current decreases and V_CE voltage increases at the turnoff switching phase owing to these parasitic inductances. According to Figures 12–14, it can be shown that the tail current I_C and the V_CE voltage peak caused by these parasitic inductances increase the duration of the switching operation. Then, the switching losses at the turnoff phase are increased. The model predicts with a good accuracy all dynamic IGBT characteristics, namely, slowly decaying current at turn off (tailing phenomenon characteristic of IGBTs due to bipolar transistor part) and the Miller effect in the gate voltage waveforms.

[figure omitted; refer to PDF][figure omitted; refer to PDF][figure omitted; refer to PDF]

5. Conclusions

This study presents the electrical modeling of the IGBT using the graphical software of Matlab. Parameter optimization of the model based on a metaheuristic algorithm using GA was proposed. The established method used electrical equations of the model and measurement data provided by the manufacturer to perform the model parameter optimization. The method implementation was carried out using the Matlab/Simulink environment. Simulation of the electrical model showed a good precision and high reliability for the static and dynamic behavior of the used IGBT.

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