Loss Calculation Methods of Half-Bridge Square-Wave Inverters

The insulated gate bipolar transistors (IGBTs) are widely used in many modern fields of power electronics that are related to power conversion, transmission and distribution. Today IGBTs with blocking voltages up to 6.5 kV are commercially available, allowing simple and robust two-level topologies to be used in applications with nominal DC voltages up to 3.6 kV without the need of series connection of several IGBTs. The other advantages of IGBTs are easy driving and snubberless operation. On the other hand, the high-voltage IGBTs have limited current capability and high power losses, resulting in limited switching performance due to thermal issues. Therefore, thermal management became one of the most important aspects in the development of high-voltage IGBT converters. The accurate estimation of power losses is an important step in thermal management system design [1–3]. A number of calculation methods have been proposed. One of the approaches is based on the switching functions or coefficients obtained through measurements to guide the simulation during switching transients [4, 5]. However, this method requires a number of parameters to be extracted from the test waveforms. Another approach is based on the use of simple functions derived for losses based on typical switching waveforms [6, 7]. This method was extended in [1, 8] by deriving a set of formulae for switching losses based on the predicted current and voltage waveforms of the device. In this method the predicted waveforms conform to the physics of the switching process and take into account the dependency of the switching losses on various factors such as the switching voltage, switching current, stray inductance and the reverse recovery process of the freewheeling diode [8]. Another advantage is that it requires a smaller number of parameters from the test waveforms. If a power electronic system prototype is unavailable, the losses can be estimated by the help of the datasheet parameters of the devices using linear interpolation of characteristic curves [9, 10]. This approach is generally limited in accuracy, however could be considered as a first approximation. This paper will focus on the improvement of the calculation methods using manufacturers’ datasheet parameters of semiconductors for inverters with the square-wave output [11]. The second part presents an analytical method of estimating losses, including the losses caused by parasitic components of the circuit.


Introduction
The insulated gate bipolar transistors (IGBTs) are widely used in many modern fields of power electronics that are related to power conversion, transmission and distribution.Today IGBTs with blocking voltages up to 6.5 kV are commercially available, allowing simple and robust two-level topologies to be used in applications with nominal DC voltages up to 3.6 kV without the need of series connection of several IGBTs.The other advantages of IGBTs are easy driving and snubberless operation.On the other hand, the high-voltage IGBTs have limited current capability and high power losses, resulting in limited switching performance due to thermal issues.Therefore, thermal management became one of the most important aspects in the development of high-voltage IGBT converters.The accurate estimation of power losses is an important step in thermal management system design [1][2][3].A number of calculation methods have been proposed.One of the approaches is based on the switching functions or coefficients obtained through measurements to guide the simulation during switching transients [4,5].However, this method requires a number of parameters to be extracted from the test waveforms.Another approach is based on the use of simple functions derived for losses based on typical switching waveforms [6,7].This method was extended in [1,8] by deriving a set of formulae for switching losses based on the predicted current and voltage waveforms of the device.In this method the predicted waveforms conform to the physics of the switching process and take into account the dependency of the switching losses on various factors such as the switching voltage, switching current, stray inductance and the reverse recovery process of the freewheeling diode [8].Another advantage is that it requires a smaller number of parameters from the test waveforms.
If a power electronic system prototype is unavailable, the losses can be estimated by the help of the datasheet parameters of the devices using linear interpolation of characteristic curves [9,10].This approach is generally limited in accuracy, however could be considered as a first approximation.This paper will focus on the improvement of the calculation methods using manufacturers' datasheet parameters of semiconductors for inverters with the square-wave output [11].The second part presents an analytical method of estimating losses, including the losses caused by parasitic components of the circuit.

Definitions
The power loss of each switching operation for the given current and voltage waveforms of the IGBT is divided into three sections as illustrated in Fig. 1 [12].The leakage loss is only a small part of the total loss so that neglecting it the error is usually insignificant.Therefore, the total energy losses during each operating cycle of the IGBT are the sum of the turn-on and turn-off loss, saturated conduction loss as well as the reverse-recovery loss of the integrated freewheeling diode (FWD) [8] where I(t) and U(t) are transistor current and voltage, respectively.
Fig.  The datasheets of IGBTs contain typical information about switching transients, on-state behaviour and energy losses during a single operation pulse.These characteristics refer to a specific test circuit which simulates a clamped inductive load operating with a specific diode [6].Typical datasheet values of Infineon 200 A 6.5 kV IGBT module are presented in Table 1.For high-voltage IGBT modules, the turn-on energy loss E on is generally defined as the integral of the product of the collector current and the collector-emitter voltage over the interval from when the collector current rises above 10% of the test current to when the voltage falls below 10% of the test voltage (Fig. 2).The turn-off energy loss E off is the integral of the product of the collector current and the collector-emitter voltage over the interval starting from when the collector-emitter voltage rises above 10% of the test voltage to when the collector current reaches 10% of the test current (Fig. 3).The diode reverserecovery energy E rec is the integral of the product of the diode current and voltage over the interval starting from when the voltage across the diode rises above 10% of the test voltage to when the diode reverse current drops to 10% of its peak value (Fig. 4).

Loss calculation method using datasheet parameters
General equations.The on-state voltage drop of the non-punch-through (NPT) IGBT device generally increases with a higher collector current and the junction temperature.Moreover, it could vary from one device to another.The datasheets typically indicate the typical and the maximum values.The maximum values generally refer to the worst case device that the manufacturers consider as qualitative.For example, the 200A 6.5 kV IGBT collectoremitter saturation voltage varies from 5.3 V (typical) to 5.9 V (maximal) for the 200 A collector current at the junction temperature of 125°C.Generally, use of typical values at the maximum junction temperature could be considered reasonably accurate.The conduction losses are estimated by where T sw is the switching period, t on is the on-state time, I is the IGBT current, T j is the switch junction temperature, k (sat) is the scale factor based on the properties of the device considered.
The switching energy loss of a device is variable due to the device's current, voltage, gate resistance and junction temperature.Generally, the latter dependency is not indicated in the datasheets, while the energy loss versus current and gate resistance are indicated at the maximum junction temperature.Since the losses increase with increased temperature, it is assumed in the following that the junction temperature will be 125°C as a worst case [9].In general, the turn-on and turn-off energies are obtained by: Calculation equations, linear approximation.To achieve fast analytical calculations, the on-state voltage drop can be characterized by a dynamical resistance r T and a constant voltage drop U T0 .The voltage drop across the IGBT with rms collector current is then determined by where U T0 is the device's threshold voltage, r T is the device's slope resistance and rms C I is the transistor RMS collector current.
For inverters with the square-wave output voltage the on-state energy dissipation for typical output current waveforms (Fig. 5) could be obtained by simple equations.
Conduction energy losses for the given pulse length Conduction energy losses for the given pulse length Conduction energy losses for the given pulse length The conduction power losses can then be calculated by No simple expression can be found for the voltage and current during a switching transient.The datasheet parameters concerning the switching losses can be used in this case.To simplify the analysis for different current levels, the datasheet energy loss curves could be replaced by their linear interpolations using simple equations: where I C(1) , I C( 2) are currents and E on( 1) , E on(2) corresponding energy loss values taken from the datasheet graphs.The turn-off coefficients A off and B off are calculated in the similar way.
Since the actual operation parameters of semiconductors are in most cases different from the reference circuit, datasheet values should be scaled accordingly.If the gate resistor of a user's gate drive does not have the same value as the gate resistor in the test circuit specified in the datasheet some corrections may be necessary.This can be done with the help of the datasheet using graphs E on =f(R G ) and E off =f(R G ).The scale factor is obtained by the relation between the switching losses with the used-specific gate resistance US on G R  and the one The turn-off resistor scale factor Generally, the switching losses scale almost linearly with U CE , hence the following approximation of the scale factor for the actual commutation voltage could be considered reasonably accurate where where US off CE U  is DC voltage at IGBT after the end of the turn-off transition.The switching energy losses for typical current waveforms (Fig. 5) can be approximated by the following expressions.
Diode reverse-recovery losses.The data available to calculate the diodes' reverse recovery losses differs from one manufacturer to another.Furthermore, these losses depend on the current slope during the transition which in standard VSIs is basically determined by the inductance of the circuit, IGBT dI/dt during turn-on and operation temperature [12].If the reverse-recovery energy in the datasheet is provided only for one operating point, then the scale factor k rr can be calculated according to [13] , where  Calculation equations, least square approximation.The drawback of the above presented equations is generally related to the limited accuracy of the linearly interpolated characteristics of U CE =f(I C ), E on =f(I C ) and E off =f(I C ).A better result, especially at lower currents, can be achieved by approximating these curves with the following function .) ( The coefficients A, B, C and F of the proposed function can be estimated from the datasheet curves using the least square method with the help of software, such as SOLVER in EXCEL.The comparison of results obtained with different interpolation methods is shown in Fig. 6.
The conduction losses can then be expressed as where I(t) could be expressed according to Eqs. 6, 8 and 10.

Analytical loss estimation method of two-level VSI
The turn-on energy losses indicated in the datasheet of the IGBT typically include the losses caused by the reverse-recovery current of turning-off freewheeling diode (Fig. 7).
No simple expression can be provided for these additional losses, as they depend on a number of factors: turn-on di/dt, citruit inductance and diode characteristics.The following equation assumes that the voltage across the diode stays close to zero volts during the interval t 0 -t 5 , rising to the supply voltage during t 5 -t 6 (Fig. 4) where I rr is the peak reverse-recovery current.
However, in the square-wave two-level half-bridge converters, the reverse-recovery process of freewheeling diodes is finished during the freewheeling state.Hence, there is no additional current during the turn-on of the IGBT, resulting in lower losses.Due to the leakage induction of the transformer and the parasitic capacitances of HV-IGBT modules there are oscillations after the IGBT turn-off (Fig. 8).The energy stored in the circuit is lost during this process, moreover the IGBT modules seem to sustain additional reverse-recovery losses.This process was studied in [11] and the energy lost during the oscillation period is where L E is the total parasitic inductance of the circuit, I osc is the peak value of the oscillating current.
The proposed improved approximation of the transistor switching process is shown in Fig. 9.The turn-on energy is calculated by integrating multiplied turn-on voltage and current ramp.As the current changes slower than the voltage at the turn-on, the power loss equation is divided into two parts.In the first part both the voltage and current are changing, in the second part only the current changes.This energy is multiplied by the switching frequency f sw .The result of this equation is the IGBT turn-on power loss Transistor turn-off losses could be calculated assuming the current through the IGBT stays close to I C (2) during the interval t off1 -t off2 and the voltage across the IGBT is close to U CE (2) during the interval t off2 -t off3 .The turn-off energy loss can then be approximated by 2 Using the analytical approach (Eqs.25-34) and the measured waveforms of the converter prototype the switching losses of the IGBT module are estimated (Table 2).Using the proposed analytical loss estimation method it is possible to estimate the contribution of the turn-on or turn-off losses in the total switching losses, which could be beneficial in estimating the feasibility of implementation of different loss reduction methods in semiconductors, such as passive or active snubbers.As known, the IGBT turn-on energy loss decreases while turnoff energy loss increases with the stray inductance.Both effects almost compensate each other [13].In the studied converter due to the high stray inductance of the isolation transformer this effect is clearly observed.

Conclusions
As a result of increased heat dissipation from electronic devices, thermal management appears to be one of the most important issues of power converter design.The estimation of power dissipation of semiconductor devices is essential to determine operation parameters and cooling system requirements of a power converter.This paper presented an overview of different methods for loss calculation in inverters with the square-wave output, using IGBT module parameters extracted from the manufacturer's datasheets and test waveforms.A better method of approximating datasheet curves for fast analysis (29) (32) at different current levels is proposed.Further, an improved analytical loss calculation method using test results of the half-bridge converter prototype is introduced.

Fig. 4 .
Fig. 4. FWD switching times and energy definitions during reverse-recovery

Fig. 5 .
Fig. 5. Typical transistor current waveforms operating in inverters with the square-wave voltage output US on CE U  is DC voltage across the IGBT during the off-state before the beginning of the turn-on transition, DS CE U is the collector-emitter voltage cpecified in the datasheet graphs E on =f(I C ), E off =f(I C ).The scale factor for the actual commutation voltage ) ( is obtained in the similar way

Table 1 .
Characteristic values of 200 A 6500 V IGBT (FZ200R65KF2) 1. Three sections of losses http://dx.doi.org/10.5755/j01.eee.113.7.604 where t on1 to t on3 is the total IGBT turn-on time; t on1 to t on2 is the IGBT collector-emitter voltage fall time from operation to saturation level, and t on1 to t on3 is the IGBT collector current rise time.U CE(on) (t) is the IGBT collectoremitter voltage at turn-on and I C(on) (t) is the collector current function during the turn-on of the IGBT.To simplify the calculations, voltage and current waveforms can be replaced by the linear functions:

Table 2 .
Results of the analytical loss calculation