Detailed Power Loss Analysis of T-Type Neutral Point Clamped Converter for Reactive Power Compensation

Abstract

The paper presents an analysis of power losses in a three-phase T-type neutral point clamped converter with insulated gate bipolar transistors. The paper’s main aim is to perform a detailed analysis of power losses in the converter operating as an active power filter. The study is based on the use of characteristics of semiconductor devices provided by the manufacturer in the module datasheet. Thanks to the analysis, it is possible to recognise the value of power losses, which facilitates the design of the converter cooling system. Identifying how power losses are distributed between the module switching devices is also possible. Power losses are shown as functions of the output current and module temperature. The analysis results were successfully verified by measuring power losses using a laboratory model of the converter with rated currents of 10 and 20 A. The obtained results indicate relatively low power losses and a relatively even distribution of power losses between the semiconductor devices. This is a superior feature of the three-level T-type neutral point clamped converter topology.

1. Introduction

1.1. Motivations

Power losses in power electronic converters play a crucial role in the design of their cooling system. Better recognition of power losses allows the converter designers to choose the appropriate cooling system in terms of its performance and size. This paper presents a detailed analysis of the power losses of the T-type Neutral Point Clamped (TNPC) converter, which is applied to the active power filter. The selection of this converter topology is dictated by the relatively low power losses and the fact that in this topology, as in other three-level topologies, the middle point of the dc circuit is available. In the case of an active filter, the neutral wire is connected to this middle point so that a fourth converter leg is not required. An additional advantage of the selected converter, in relation to the classical two-level topology, is the possibility of reducing the dimensions and the cost of the grid-side passive filter.

1.2. Literature Review

The topologies of multilevel converters were developed more than twenty years ago [1,2]. Multilevel converters were introduced mainly because of their possible use in converting medium voltage energy. Thanks to these converters, it was possible to efficiently convert electrical energy without using expensive and large transformers [3,4]. Over the years, it has become clear that many multilevel converter topologies often have better performance parameters than the classic two-level converter, even at low voltage levels [5,6,7,8,9]. One of the most important features of these converters is high efficiency, which was not always an obvious fact with the greater number of semiconductor devices used in converters with a very high number of voltage levels [10,11,12]. The high efficiency of the converter is an essential parameter because due to low power losses, the converter’s lifetime is longer, and the total cost of its operation is lower [13].

Because power loss evaluation of converters is a complex and multivariable issue [14,15,16,17,18,19], it is crucial to identify power losses in converters operating under various conditions accurately. The knowledge about converter power losses is vital for designers of converter cooling systems and manufacturers of semiconductor modules. Nowadays, semiconductor modules can be optimised for one converter operating mode but will not be suitable for other operating conditions. For example, the module optimised for grid-tied PWM rectifiers has diodes with higher current ratings than the module optimised for the PWM inverter. Typically, power loss analysis is performed individually for each converter topology.

This paper analyses the three-phase T-type neutral point clamped (TNPC) converter. The converter belongs to the group of three-level converters [20] in which there are also classical neutral point clamped (NPC) converter [21], active neutral point clamped (ANPC) converter [22], and advanced neutral point clamped converter [23].

The NPC converter, apart from lower power losses and better output voltage waveform, is characterised by an uneven distribution of power losses among semiconductor devices [24]. The solution to this issue is the development of the ANPC converter, which, using transistors instead of clamping diodes, makes it possible to distribute power losses between the semiconductor devices better. A further improvement of the three-level converter is the TNPC converter [25]. The power losses of this converter are analysed in this article. A very advantageous feature of this converter is the lower number of semiconductor switches compared to the ANPC or NPC topologies and lower power losses [26].

The selection of the T-type neutral point clamped converter for the active power filter is made mainly based on the requirements for reducing the size of the grid filter and the dimensions of the cooling system. The second aspect, which directly relates to the power loss analysis, is a topic of this paper. The other reason for the selection of the 3-level topology is the access to the medium point of the dc-link circuit. By the connection of the neutral wire to the medium point, it is possible to reduce the number of necessary converter legs, which additionally reduces the converter losses.

The proposed method of calculating power losses in the TNPC converter is similar to the method proposed in [26]. The difference is that in [26,27,28], the semiconductor switch output characteristics have been approximated by linear functions. Still, in this paper, the approximation is made with more precise power functions that also recognise the influence of temperature on these characteristics. Further, the functions of energy losses are more accurately presented than in [26,27,28]. The results of power loss analysis are shown in this paper mainly as a function of the output current and temperature with the switching frequency and phase-shift angle set to constant values.

Currently, intensive works are ongoing worldwide on converters with SiC MOSFETs, such as the TNPC converter [29] or the ANPC hybrid converter combining the IGBTs with the SiC-MOSFETs in a single topology [30]. This topology is characterised by even lower power losses than the TNPC topology. Despite the increasing share of converters with SiC-MOSFET transistors, the topology of the TNPC converter using IGBT transistors still has good properties. Such properties include low power losses, favourable output voltage, and a low level of generated disturbances. It is believed that accurate recognition of the power loss is needed.

1.3. Contribution

The analysis presented in this paper is performed for the TNPC converter operating as an active filter. The details on the laboratory model of the TNPC converter are given in [31]. This converter practically generates reactive current with only a small share of power losses constituting the active power. Connecting the converter to the electrical grid causes the modulation index and the phase-shift angle to be almost constant. This, in turn, means that the analysis presented in the article can be performed with a limited number of changing parameters affecting power losses.

Power losses generated in the TNPC converter should be small due to the long operation time of the converter and the need for its long lifetime. In many cases, the lifetime of power electronic converters is approx. 20 years, during which even minor losses contribute to high costs for the end-user of the converter.

Many works on power losses in the TNPC converters are devoted to inverters with a phase-shift angle close to zero. For this mode of operation, the natural parameter is the converter efficiency, which, in the case of the converter operating as an active filter, cannot be used. The converter efficiency parameter is replaced in this paper by a per kVA power loss ratio. Such a parameter can be useful when comparing different converter topologies or different active filter solutions.

The main contributions of this paper are listed below.

• The development of a detailed analysis of power losses for the TNPC converter. This analysis allows the user to quickly determine the power losses when one or more operating parameters of the converter or its design parameters are changed. The developed power loss model of the TNPC converter is an analytical model that has an advantage over the simulation model because obtaining results in the form of characteristics is much faster. However, this is done at the expense of the use of a number of mathematical equations, which in the case of simulation models do not need to be used.
• The model uses an accurate approximation of characteristics of semiconductor devices for currents changed between 0 and the rated current value. This approximation guarantees that power losses are better mapped than in the case of using a model with a piecewise-linear approximation.
• The analysis proposed in the paper is based on characteristics obtained from the semiconductor datasheet. The development of such an analysis is faster when compared to analyses requiring the prior measurements in specific test circuits as is typically used in the literature, e.g., [27,28]. Using the datasheet characteristics can be done, however, when the parameters of the converter gate circuit and the dc-link circuit are comparable to the parameters used in the datasheet.
• The analysis proposed in the paper has regard to eight different parameters influencing the power losses they are (1) output current amplitude of the fundamental component, (2) dc-link voltage, (3) switching frequency, (4) phase-shift angle of the fundamental components of output current and voltage, (5) semiconductor temperature, (6) modulation index, (7) PWM modulation technique, and (8) gate resistances in a transistor driver circuit. Such analysis is comprehensive and can be applied to converters operating under different conditions. In this paper, the operational conditions are restricted to the operation of the active power filter.

It is believed that a detailed power loss analysis for the TNPC converter is needed and is an original contribution. In many papers, power losses are presented only for a specific case of converter operation, and this is mainly for the inverter operation. In this paper, power losses are shown more broadly.

1.4. Paper Organisation

This paper is organised as follows. Section 2 shows the complete power loss analysis in the TNPC converter. Section 3 presents the experimental validation of power loss analysis on the example of two test setups with TNPC converters. Section 4 presents the conclusions. After the conclusions, the nomenclature is presented in which all parameters used in this paper are listed. After that, Appendix A lists all values of the design parameters of the TNPC converter in the study.

2. Power Loss Analysis

Most converter power losses in power electronic converters are generated due to the conduction and switching of semiconductor devices. This paper only considers these two sources of losses generated in a T-type NPC converter without considering the dead-time effect and dc-link voltage ripple. Both conduction and switching losses are calculated analytically based on approximated IGBT module characteristics provided by the manufacturer [32]. Although a single leg of the TNPC converter consists of four transistors and two diodes, as seen in Figure 1, power losses in only three semiconductor devices are considered. They are transistors T₁ and T₂ and diode D₄. This approach is adopted because transistors T₁ and T₄ have the same parameters and are exposed to the same currents and voltages phase-shifted by half of the fundamental period. A similar situation exists for transistors T₂ and T₃ and diodes D₁ and D₄. Other losses generated in the converter are also considered, among which are the dc-link capacitor losses and losses generated in pcb tracks due to resistance.

2.1. Conduction Power Losses

The conduction losses (Equation (1)) are calculated separately for each switching device by calculating the average value of the power obtained from the integral of instantaneous power p_X (t) = i_X (t) v_X (t), where i_X (t) is the device X current and v_X (t) is the voltage across this device. The integration of instantaneous power is performed in the ωt domain from angle α₁ to α₂. Because the device current i_X (ωt) is a modulated phase current i_O (ωt), it must be multiplied by the modulation function S_X (t), i_X (ωt) = i_O (ωt) S_X (ωt). The modulation function is closely related to the modulating signal S_M (ωt) used in the converter PWM modulator.

$$P_{\mathrm{conX}}\left(T_{\mathrm{X}}\right)=\frac{1}{2\mathsf{\pi }}{\displaystyle \underset{\mathsf{\alpha }1}{\overset{\mathsf{\alpha }2}{\int }}\left\{i_{\mathrm{X}}\left(\mathsf{\omega }t\right)·v_{\mathrm{X}}\left(\mathsf{\omega }t, T_{\mathrm{X}}\right)\right\}}d\mathsf{\omega }t=\frac{1}{2\mathsf{\pi }}{\displaystyle \underset{\mathsf{\alpha }1}{\overset{\mathsf{\alpha }2}{\int }}\left\{i_{\mathrm{O}}\left(\mathsf{\omega }t\right)·S_{\mathrm{X}}\left(\mathsf{\omega }t\right)·v_{\mathrm{X}}\left(\mathsf{\omega }t,T_{\mathrm{X}}\right)\right\}}d\mathsf{\omega }t,$$

(1)

2.1.1. Output Characteristic Approximation

In the presented power loss analysis, the output current is assumed as sinusoidal, i_O = I_m sin (ωt − φ), and the device voltage v_X (t, T_X) is a function of the current and device junction temperature T_X as in Equation (2).

$$v_{\mathrm{X}}\left(\mathsf{\omega }t,T_{\mathrm{X}}\right)=v_{\mathrm{X}}\left(i_{\mathrm{X}}\left(\mathsf{\omega }t\right),T_{\mathrm{X}}\right)=V_{\mathrm{X}0}\left(T_{\mathrm{X}}\right)+\left(V_{\mathrm{Xn}}\left(T_{\mathrm{X}}\right)-V_{\mathrm{X}0}\left(T_X\right)\right){\left(\frac{i_{\mathrm{X}}\left(\mathsf{\omega }t\right)}{I_{\mathrm{n}}}\right)}^{\frac{1}{n_{\mathrm{X}}\left(T_{\mathrm{X}}\right)}},$$

(2)

where V_X0 (T_X) is a temperature-varying threshold voltage, V_Xn (T_X) is a temperature-varying device voltage at nominal current I_n, and 1/n_X (T_X) is a temperature-varying exponent of the power function representation of the device on-state characteristic. The threshold voltage V_X0 (T_X) and nominal voltage V_Xn (T_X) are linear functions obtained from on-state characteristics at temperatures T_X = 25 and T_X = 125 °C (Equations (3) and (4)).

$$V_{\mathrm{X}0}\left(T_{\mathrm{X}}\right)=a_{\mathrm{X}0}{T}_{\mathrm{X}}+b_{\mathrm{X}0}=\frac{V_{\mathrm{X}\mathrm{0,125}}-V_{\mathrm{X}\mathrm{0,25}}}{125 °\mathrm{C}-25 °\mathrm{C}}{T}_{\mathrm{X}}+V_{\mathrm{X}\mathrm{0,25}}-\frac{V_{\mathrm{X}\mathrm{0,125}}-V_{\mathrm{X}\mathrm{0,25}}}{125 °\mathrm{C}-25 °\mathrm{C}}25 °\mathrm{C},$$

(3)

$$V_{\mathrm{Xn}}\left(T_{\mathrm{X}}\right)=a_{\mathrm{Xn}}{T}_{\mathrm{X}}+b_{\mathrm{Xn}}=\frac{V_{\mathrm{Xn},125}-V_{\mathrm{Xn},25}}{125 °\mathrm{C}-25 °\mathrm{C}}{T}_{\mathrm{X}}+V_{\mathrm{Xn},25}-\frac{V_{\mathrm{Xn},125}-V_{\mathrm{Xn},25}}{125 °\mathrm{C}-25 °\mathrm{C}}25 °\mathrm{C},$$

(4)

The values of function parameters given in Equations (3) and (4) for the analysed IGBT TNPC module are listed in

Table 1. Parameters of temperature-varying functions V_X0 (T_X) and nominal voltage V_Xn (T_X) of transistors T₁ and T₂ and diode D₄.

Device X	VX0,25, V	VX0,125, V	VXn,25, V	VXn,125, V	aX0, V/°C	bX0, V	aXn, V/°C	bXn, V
T1	0.70	0.50	1.72	1.94	−0.002	0.750	0.0022	1.665
T2	0.70	0.50	2.35	2.46	−0.002	0.750	0.0011	2.323
D4	0.75	0.55	1.69	1.85	−0.002	0.800	0.0016	1.650

and shown in Figure 2.

Finding exponent n_X(T_X) of the power function is performed by applying the curve fitting method to a normalised function (Equation (5)), which is obtained from Equation (2)

$$\frac{i_{\mathrm{X}}}{I_{\mathrm{n}}}=f(T_{\mathrm{X}})={\left(\frac{v_{\mathrm{X}}\left(i_{\mathrm{X}},T_{\mathrm{X}}\right)-V_{\mathrm{X}0}\left(T_{\mathrm{X}}\right)}{\left(V_{\mathrm{Xn}}\left(T_{\mathrm{X}}\right)-V_{\mathrm{X}0}\left(T_X\right)\right)}\right)}^{n_{\mathrm{X}}\left(T_{\mathrm{X}}\right)},$$

(5)

where v_X (i_X, T_X) is the output characteristic voltage taken from the IGBT module datasheet. For transistor T_1, the normalised function (Equation (5)) for T_T1 = 125 °C is depicted in Figure 3. The normalised function (Equation (5)) always crosses points (0, 0) and (1, 1) even though the temperature T_X varies.

In Figure 3, one can see that the normalised function i_T1/I_n for T_T1 = 125 °C with n_T1 (125 °C) = 1.65 matches the data for a normalised voltage in the range between 0 and 1. Still, for voltages between 1 and 2, some discrepancy is observed. This discrepancy is not problematic because it occurs for currents higher than the rated value I_n in the range, which is out of the scope of the analysis presented in this paper. The best-fitting exponents for normalised functions of all converter devices are collected in

Table 2. Exponents of power functions for output characteristics of all TNPC converter devices T₁ and T₂ and D₄ for two temperatures T_X = 25 and T_X = 125 °C.

Device X	nX (25 °C)	nX (125 °C)
T1	1.51	1.65
T2	1.71	1.66
D4	1.89	1.81

; these parameters are given for temperatures T_X = 25 and T_X = 125 °C.

The exponent n_X (T_X) given in Equation (5) is a function of temperature T_X and is approximated by a linear function obtained from two points, n_X (25 °C) and n_X (125 °C), which are calculated from Equation (6).

$$n_{\mathrm{X}}\left(T_{\mathrm{X}}\right)=a{n}_{\mathrm{X}}{T}_{\mathrm{X}}+b{n}_{\mathrm{X}}=\frac{n_{\mathrm{X}}\left(125 °\mathrm{C}\right)-n_{\mathrm{X}}\left(25 °\mathrm{C}\right)}{125 °\mathrm{C}-25 °\mathrm{C}}{T}_{\mathrm{X}}+n_{\mathrm{X}}\left(25 °\mathrm{C}\right)-\frac{n_{\mathrm{X}}\left(125 °\mathrm{C}\right)-n_{\mathrm{X}}\left(25 °\mathrm{C}\right)}{125 °\mathrm{C}-25 °\mathrm{C}}25 °\mathrm{C},$$

(6)

After substituting Equations (2)–(6) into Equation (1), each device’s conduction losses are given as Equation (7).

$$P_{\mathrm{conX}}\left(T_{\mathrm{X}}\right)=\frac{1}{2\mathsf{\pi }}{\displaystyle \underset{\mathsf{\alpha }1}{\overset{\mathsf{\alpha }2}{\int }}\left\{I_m\sin \left(\mathsf{\omega }t-\mathsf{\phi }\right)·S_{\mathrm{X}}\left(t\right)·\left[V_{\mathrm{X}0}\left(T_{\mathrm{X}}\right)+\left(V_{\mathrm{Xn}}\left(T_{\mathrm{X}}\right)-V_{\mathrm{X}0}\left(T_{\mathrm{X}}\right)\right){\left(\frac{I_m\sin \left(\mathsf{\omega }t-\mathsf{\phi }\right)}{I_{\mathrm{n}}}\right)}^{\frac{1}{n_{\mathrm{x}}\left(T_{\mathrm{X}}\right)}}\right]\right\}}d\mathsf{\omega }t,$$

(7)

2.1.2. Conduction Angles and Modulation Function

Power loss analysis is performed in the ωt domain. Therefore, it is essential to identify the corresponding conduction angles for each semiconductor device in the TNPC converter (Figure 1). All devices’ currents for exemplary output current and modulation index m_a are shown in Figure 4.

Each TNPC converter device conducts switched currents for different angles. The angle at which a device starts conducting is referred to as α_1, and the angle when a device stops conducting the current is α₂. Both angles are different for each converter device, as is seen in Figure 4 and

Table 3. Conduction angles α₁ and α₂ and modulated functions S_X (ωt) of devices T₁, T₂ and D₁.

Device X	α1	α2	SX (ωt)
T1	φ	π	SM (ωt)
T2	φ	π + φ	1−|SM (ωt)|
D4	π	π + φ	−SM (ωt)

. In Figure 4, device currents are modulated according to modulation functions S_X (ωt). For example, transistor T₁’s current, i_T1, is modulated by function S_T1 (ωt) = S_M (ωt), but transistor T₂’s current is modulated by the complementary function S_T2 (ωt) = 1−S_M (ωt) for ωt = (0, π) and S_T2 (ωt) = 1 + S_M (ωt) for ωt = (π, 2π). Modulation functions of all device currents are given in Table 3.

2.1.3. Results of Conduction Power Losses

After substituting all parameters related to device output characteristics, conduction angles and modulation function into Equation (7), the total conduction power losses can be calculated. It is assumed that the output current is sinusoidal with the phase-shift-angle equal to φ = π/2 and the modulation index m_a = 0.86. The phase-shift angle φ = π/2 corresponds to the converter operation as a reactive power compensator. In practice, the converter operates with a small share of power losses, which reduces the phase-shift angle to nearly φ = 89°. Since such a difference in the angles does not significantly impact the value of the power losses, the value of φ = π/2 is assumed. The analysis also assumes that power losses are calculated for the same junction temperature of all switching devices. The conduction losses of the three-phase TNPC converter given as a function of temperature T_j are depicted in Figure 5a. These losses are calculated as the sum of losses in all devices multiplied by the number of phases and duplicated due to the number of devices in each converter leg, P_con = 6P_conT1 + 6P_conT2 + 6P_conD4.

From the characteristics shown in Figure 5b, conduction power losses for the current of I_Orms = 20 A decrease with temperature increase. Such behaviour of power losses can be explained by the negative thermal coefficient occurring in output device characteristics present for currents below 15 A for transistors T₁ and T₄ (as in Figure 2), below 35 A for transistors T₂ and T₃, and below 30 A for diodes D₁ and D₄.

Conduction power losses for the device temperature of 25 °C and the output currents of I_Orms = 20 and 50 A equal 73.6 and 250.1 W, respectively. The distribution of conduction power losses among converter devices is not even, as presented in Figure 6.

From Figure 6, one can see that the distribution of conduction power losses for a constant phase-shift angle φ and modulation index m_a is slightly different with the change of the output current rms value. The RB-IGBT transistors T₂ and T₃ have the largest share of conduction losses. This is because these transistors conduct modulated currents for half of the fundamental period (α₂ − α₁ = π) compared to transistors T₁ and T_4, which conduct modulated currents for α₂ − α₁ = π − φ = π/2 (for φ = π/2) and diodes D₁ and D₄, which conduct such currents for α₂ − α₁ = π + φ − π = π/2.

2.2. Switching Power Losses

The TNPC converter has smaller switching power losses compared to other converters. This is because switching losses in transistors T₁ and T₄ occur at blocking voltages V_dc/2 even these transistors must withstand the entire V_dc similarly as in a two-level converter. In a two-level converter, power losses occur at voltages V_dc; thus, switching losses, which are proportional to the blocking voltage, in the TNPC converter is reduced to half of such losses of a two-level converter. This is true when a TNPC converter uses identical transistors as a two-level converter. However, RB-IGBTs (T₂ and T₃) have better switching performance because they are designed for withstanding the voltage of V_dc/2.

Switching power losses are generated in IGBTs during transistor turn-on and turn-off processes. They can be calculated as an average value of a sum of energies during turn-on E_on and during turn-off E_off over the fundamental period multiplied by the switching frequency f_S. These energies are functions of the device current i_X (ωt), device temperature T_X, blocking voltage V_b and the resistances of the gate circuit R_G. In the presented analysis, resistances R_G are chosen to the same values selected by the manufacturer in the module datasheet [32]. However, due to the resistance of driver output, the resistances are equal R_G1 = 3.2 Ω, R_G2 = 5.7 Ω. The switching power losses are an integral of energies in the interval restricted by switching angles α₃ and α₄ (Equation (8)).

$$P_{\mathrm{swX}}\left(T_{\mathrm{X}}\right)=f_{\mathrm{S}}\frac{1}{2\mathsf{\pi }}{\displaystyle \underset{\mathsf{\alpha }3}{\overset{\mathsf{\alpha }4}{\int }}\left\{E_{\mathrm{onX}}\left(i_{\mathrm{X}}\left(\mathsf{\omega }t\right),T_{\mathrm{X}},V_{\mathrm{b}}\right)+E_{\mathrm{offX}}\left(i_{\mathrm{X}}\left(\mathsf{\omega }t\right),T_{\mathrm{X}},V_{\mathrm{b}}\right)+E_{\mathrm{rrX}}\left(i_{\mathrm{X}}\left(\mathsf{\omega }t\right),T_{\mathrm{X}},V_{\mathrm{b}}\right)\right\}}d\mathsf{\omega }t,$$

(8)

where E_rr is the switching energy generated in the diode due to reverse recovery. For diodes, energies E_on and E_off are equal to zero; similarly, for transistors, E_rr is equal to zero.

2.2.1. Switching Angles

The switching angles α₃ and α₄, which are not the same as conduction angles, can be shown by device current and voltage waveforms in Figure 7 and are listed in

Table 4. Switching angles α₃ and α₄ of devices T₁, T₂, D₂ and D₄ with indicated switching mode.

Device X	α3	α4	Mode
T1	φ	π	A
T2	π	π + φ	B
D2	φ	π	A
D4	π	π + φ	B

.

Contrary to conduction losses, the switching losses in transistor T₂ and diode D₂ are calculated separately. The RB-IGBT conduction losses are taken together for transistor T₂ and diode D₂, which are connected in series and are represented by a single output characteristic. The switching losses in RB-IGBT are separated for transistor T₂ and diode D₂. For $0<\mathsf{\omega }t\le \mathsf{\pi }$, transistor T₂ is still turned on; thus, for positive device currents, which is for $\mathsf{\phi }<\mathsf{\omega }t\le \mathsf{\pi }$, the switching power losses occur on diode D₂ due to its reverse recovery E_rr. This phenomenon can be explained by the fact that in this angle range, the voltage v_T2 is switched between negative voltage −V_dc/2 and 0. For i_T2 > 0 and $\mathsf{\pi }<\mathsf{\omega }t\le \mathsf{\pi }+\mathsf{\phi }$, switching losses are generated in transistor T₂. In Table 4, one can see the modes of commutation (Mode A and Mode B), which correspond to modes distinguished by the manufacturer of the IGBT module. For Mode A, losses are generated in transistors T₁ and T₄, but because the switching losses in T₄ are the same as in T₁, only losses in T₁ are calculated. In mode A, switching energies E_rr are generated in diodes D₂ and D₃. In mode B, switching energies are generated in transistors T₂ (and T₃) and diodes D₄ and D₁.

2.2.2. Characteristics of Switching Energies

All characteristics of switching energies E_on, E_off and E_rr are presented in Figure 8 as functions of the device current for both switching modes. These functions are given for two temperatures T_X = 25 and T_X = 125 °C, the blocking voltage V_dcref = 300 V, the gate resistors R_G1 = R_G4 = 2.2 Ω and R_G2 = R_G3 = 4.7 Ω and for the gate voltages ranging from −15 to +15 V.

Switching energy characteristics for transistors given in Figure 8 can be approximated by quadratic functions as in Equation (9) and multiplied by a factor k_RGXY representing the effect of the gate resistance on switching losses. The approximating function coefficients for device current from 0 to 75 A are listed in

Table 5. Coefficients of approximating quadratic functions of transistor switching energies as in Equation (9).

Device X	Switching Y	kRGXY	TX	${\mathit{a}}_{\mathbf{YX}}\times {\mathbf{10}}^{-\mathbf{9}}, {\mathbf{J}/\mathbf{A}}^{\mathbf{2}}$	${\mathit{b}}_{\mathbf{YX}}\times {\mathbf{10}}^{-\mathbf{6}}, \mathbf{J}/\mathbf{A}$	${\mathit{c}}_{\mathbf{YX}}\times {\mathbf{10}}^{-\mathbf{6}}, \mathbf{J}$
T1	on	1.083	25 °C	75.0	14.3	10.0
	on		125 °C	150.6	19.1	32.9
	off	1.010	25 °C	−107.1	39.2	44.2
	off		125 °C	−244.0	55.5	18.3
T2	on	1.055	25 °C	47.6	20.4	18.3
	on		125 °C	95.2	22.5	38.3
	off	1.020	25 °C	45.8	17.6	21.3
	off		125 °C	−25.6	23.2	42.1

.

$$E_{\mathrm{YX},\mathrm{TX}}\left(i_{\mathrm{X}}\right)=k_{\mathrm{RGYX}}\left(a_{\mathrm{YX},\mathrm{TX}}{i}_{\mathrm{X}}^2+b_{\mathrm{YX},\mathrm{TX}}{i}_{\mathrm{X}}+c_{\mathrm{YX},\mathrm{TX}}\right)\hspace{1em}\hspace{1em}for \mathrm{Y}=\left\{\mathrm{on},\hspace{0.17em}\mathrm{off}\right\},$$

(9)

The approximation of diode reverse recovery energy characteristics by quadratic functions does not provide satisfactory results; therefore, the cubic function (Equation (10)) is chosen for these characteristics. The coefficients a_YX, b_YX, c_YX and d_YX are obtained using a fitting algorithm for device currents from 0 to 75 A.

$$E_{\mathrm{rrX},\mathrm{TX}}\left(i_{\mathrm{X}}\right)=k_{\mathrm{RGYX}}\left(a_{\mathrm{rrX},\mathrm{TX}}{i}_{\mathrm{X}}^3+b_{\mathrm{rrX},\mathrm{TX}}{i}_{\mathrm{X}}^2+c_{\mathrm{rrX},\mathrm{TX}}{i}_{\mathrm{X}}+d_{\mathrm{rrX},\mathrm{TX}}\right),$$

(10)

The approximating cubic function coefficients for reverse recovery energy losses in diodes are listed in

Table 6. Coefficients of approximating cubic functions of diode reverse recovery energies.

Device X	TX	kRGX	${\mathit{a}}_{\mathbf{rrX}}\times {\mathbf{10}}^{-\mathbf{9}}, {\mathbf{J}/\mathbf{A}}^{\mathbf{3}}$	${\mathit{b}}_{\mathbf{rrX}}\times {\mathbf{10}}^{-\mathbf{6}}, {\mathbf{J}/\mathbf{A}}^{\mathbf{2}}$	${\mathit{c}}_{\mathbf{rrX}}\times {\mathbf{10}}^{-\mathbf{6}}, \mathbf{J}/\mathbf{A}$	${\mathit{d}}_{\mathbf{rrX}}\times {\mathbf{10}}^{-\mathbf{6}}, \mathbf{J}$
D2	25 °C	0.96	5.38	−0.88	54.1	−9.39
	125 °C		6.31	−1.25	85.3	−22.12
D4	25 °C	1.00	8.84	−1.34	64.3	−10.30
	125 °C		9.32	−1.39	68.5	−0.76

.

The temperature influence on switching energies in each device is considered by approximation of each polynomial coefficient z = a, b, c and d by linear function obtained from two points z_YX,25 (for T_X = 25 °C) and z_YX,125 (for T_X = 125 °C), which is given in Equation (11).

$$z_{\mathrm{YX}}\left(T_{\mathrm{X}}\right)=\frac{z_{\mathrm{YX},125}-z_{\mathrm{YX},25}}{125 °\mathrm{C}-25 °\mathrm{C}}{T}_{\mathrm{X}}+z_{\mathrm{YX},25}-\frac{z_{\mathrm{YX},125}-z_{\mathrm{YX},25}}{125 °\mathrm{C}-25 °\mathrm{C}}25 °\mathrm{C}$$

(11)

2.2.3. Results of Switching Power Losses

The calculation of switching power losses in all four semiconductor devices is performed using Equations (12)–(15). In the analysis, it is assumed that the junction temperature of all switching devices is the same, the switching frequency is f_S = 20 kHz, and the blocking voltage V_b is equal to V_dc/2 = 370 V (while the blocking voltage for which datasheet data is obtained is equal to V_dcref = 300 V). Total switching power losses in the three-phase TNPC converter is the sum of switching losses of all devices multiplied by six as in Equation (16).

$$P_{\mathrm{swT}1}\left(T_{\mathrm{T}1}\right)=f_{\mathrm{S}}\frac{1}{2\mathsf{\pi }}\frac{V_{\mathrm{dc}}/2}{V_{\mathrm{dcref}}}{\displaystyle \underset{\mathsf{\phi }}{\overset{\mathsf{\pi }}{\int }}\left\{E_{\mathrm{onT}1}\left(i_{\mathrm{T}1}\left(\mathsf{\omega }t\right),T_{\mathrm{T}1}\right)+E_{\mathrm{offT}1}\left(i_{\mathrm{T}1}\left(\mathsf{\omega }t\right),T_{\mathrm{T}1}\right)\right\}}d\mathsf{\omega }t,$$

(12)

$$P_{\mathrm{swT}2}\left(T_{\mathrm{T}2}\right)=f_{\mathrm{S}}\frac{1}{2\mathsf{\pi }}\frac{V_{\mathrm{dc}}/2}{V_{\mathrm{dcref}}}{\displaystyle \underset{\mathsf{\pi }}{\overset{\mathsf{\pi }+\mathsf{\phi }}{\int }}\left\{E_{\mathrm{onT}2}\left(i_{\mathrm{T}2}\left(\mathsf{\omega }t\right),T_{\mathrm{T}2}\right)+E_{\mathrm{offT}2}\left(i_{\mathrm{T}2}\left(\mathsf{\omega }t\right),T_{\mathrm{T}2}\right)\right\}}d\mathsf{\omega }t,$$

(13)

$$P_{\mathrm{swD}2}\left(T_{\mathrm{D}2}\right)=f_{\mathrm{S}}\frac{1}{2\mathsf{\pi }}\frac{V_{\mathrm{dc}}/2}{V_{\mathrm{dcref}}}{\displaystyle \underset{\mathsf{\phi }}{\overset{\mathsf{\pi }}{\int }}\left\{E_{\mathrm{rrD}2}\left(i_{\mathrm{D}2}\left(\mathsf{\omega }t\right),T_{\mathrm{D}2}\right)\right\}}d\mathsf{\omega }t,$$

(14)

$$P_{\mathrm{swD}4}\left(T_{\mathrm{D}4}\right)=f_{\mathrm{S}}\frac{1}{2\mathsf{\pi }}\frac{V_{\mathrm{dc}}/2}{V_{\mathrm{dcref}}}{\displaystyle \underset{\mathsf{\pi }}{\overset{\mathsf{\pi }+\mathsf{\phi }}{\int }}\left\{E_{\mathrm{rrD}4}\left(i_{\mathrm{D}4}\left(\mathsf{\omega }t\right),T_{\mathrm{D}4}\right)\right\}}d\mathsf{\omega }t,$$

(15)

$$P_{\mathrm{sw}}\left(T\right)=6\left(P_{\mathrm{swT}1}\left(T\right)+P_{\mathrm{swT}2}\left(T\right)+P_{\mathrm{swD}2}\left(T\right)+P_{\mathrm{swD}4}\left(T\right)\right),$$

(16)

The characteristic of switching power losses Equation (16), as a function of device temperature (with the assumption that all devices are exposed to the same temperature), is shown in Figure 9a. As presented, the switching losses increase with the temperature increase and are between 1.6 and 2.3 times higher than the conduction losses for I_Orms = 20 A and constitute 0.9 to 1.2 of conduction losses for I_Orms = 50 A. Unlike conduction power losses, switching losses (Equation (16)) always have a positive thermal coefficient, as shown in Figure 9b. The switching power losses are nearly linear functions of current compared to quadratic functions for conduction losses.

It is interesting that for small currents, switching losses converge to zero. This is because the output current is assumed as sinusoidal in the presented analysis. In the real converter, current ripples are present in the output current, increasing the switching losses particularly close to zero current fundamental components. This phenomenon is presented in the next section.

The distribution of switching losses among devices (Equations (12)–(15)) is presented in Figure 10 for the rms value of the output current I_Orms = 20 and I_Orms = 50 A. This distribution shows that the highest power losses occur in transistors T₁ and T₄, opposite to the conduction losses where the highest losses occur in transistors T₂ and T₃.

2.3. DC-Link Capacitor Losses

In addition to power losses in semiconductor devices, this paper also attempts to estimate the losses in both dc-link circuit capacitors C_dc1 and C_dc2, as in Figure 1. Capacitor power losses P_Cdc are generated in two capacitors due to non-zero values of equivalent series resistance R_ESR and are calculated from Equation (17).

$$P_{\mathrm{Cdc}}=2{\left(I_{\mathrm{dcrms}}\right)}^2{R}_{\mathrm{ESR}}=2{\left(k_{\mathrm{ICdc}}{I}_{\mathrm{Orms}}\right)}^2{R}_{\mathrm{ESR}}$$

(17)

where I_dcrms is the rms value of the capacitor current i_dc. The waveform of the capacitor current i_dc1 is shown in Figure 11.

The rms value of the capacitor current depends on phase-shift angle φ, modulation index m_a, the switching frequency f, and output current rms value I_Orms. Because the first three listed parameters are set as constant in the paper, it is possible to present the capacitor current rms value only as a function of the output current rms value. The simulation model performed in GeckoCIRCUITS shows that the capacitor current rms value equals 9.75 A when the output current is I_Orms = 20 A. Because the rms value of the capacitor current depends linearly on the output current, the ratio of these currents is always constant and equals k_ICdc = 9.75 A/20 A = 0.488.

In the analysed converter, the equivalent series resistance of capacitor batteries, measured for a frequency of 20 kHz, is equal to R_ESR = 35 mΩ; thus, total capacitor power losses can be calculated from Equation (17) and given as a function of the output current, as is shown in Figure 12.

It is evident from Figure 12 that the power losses in capacitors account for less than 10% of the conduction losses or switching losses generated in semiconductor devices, and these losses should not be ignored in the power loss analysis of the TNPC converter.

2.4. Total Power Losses

The sum of conduction and switching power losses together with capacitor losses are referred to as total power losses. Because the analysed converter operates as a grid-side converter, the modulation index m_a is nearly constant and equal to m_a = 0.86, and its influence on power losses is out of the scope of this paper. The switching frequency, a major parameter significantly impacting switching losses, is also set to f_S = 20 kHz. Dc-link voltage is V_dc = 740 V, satisfying the requirement for m_aV_dc/2 = U_m, where U_m is the magnitude of the phase voltage. The capacitor power losses are present for a set temperature of 25 °C because it is assumed that capacitors are located at a relatively large distance from the IGBT module, which is a significant heat source inside the converter. Total power losses as a function of temperature and current are shown in Figure 13.

The distribution of the sum of power losses (P_con + P_sw + P_Cdc) generated in converter components is presented in Figure 14.

2.5. Per kVA Power Loss Ratio

For a converter operating with a large share of reactive power, such as the active power filter, the classical definition of converter efficiency cannot be applied. This is because the converter is connected to one power port, and there are no input and output powers as other converters transfer active power between power ports. In this paper, power losses are referenced to the apparent power as Equation (18), where S₁ is the apparent power for fundamental frequency f_m, and V_ll is the line-to-line voltage rms value.

$$R_{\mathrm{loss}}=\frac{P_{\mathrm{tot}}}{S_1}=\frac{P_{\mathrm{tot}}\left(I_{\mathrm{Orms}}\right)}{\sqrt{3}{V}_{\mathrm{ll}}{I}_{\mathrm{Orms}}},$$

(18)

The definition of the power loss ratio is similar to the one used for capacitors used for reactive power compensation. These losses are a function of the output current rms value and are shown in Figure 15. The value of the current equal to 75 A corresponds to the apparent power of 52 kVA.

3. Experimental Validation of Power Loss Analysis

The laboratory model of a three-phase TNPC converter has been tested to validate the presented power loss analysis. This laboratory model is a part of a four-wire active power filter with the neutral wire connected to the medium point of the dc-link capacitors [31]. The converter is based on a three-phase TNPC IGBT module 12MBI75VN120-50, the parameters of which are used in the analysis shown in Section 2. For the validation of the power loss analysis, the following two experimental tests have been carried out:

• Test of the TNPC converter supplied from dc power supply operating with a three-phase inductor at the converter output;
• Test of the grid-connected TNPC converter;

Both tests are performed with a nearly constant modulation index m_a = 0.86 with a significant reactive component of the output current.

3.1. Power Losses of TNPC Converter Supplied from the DC Power Supply

The converter is supplied from two dc power supplies, each supplying variable voltage V_dc/2. A three-phase inductor with a nominal inductance of L_AC = 33 mH is chosen as a load. The sum of the inductor resistance and the resistance of wires equals R_LAC = 0.49 Ω leading to the phase-shift angle φ = 87.6°. Such a load has been chosen to carry out experimental tests at V_dc/2 = 370 V with modulation index m_a = 0.86, at which the output current rms value equals a rated value I_Orms = I_On = 20 A. The selected value of V_dc/2 equals the rated value of the tested active power filter. The switching frequency is 20 kHz. The tests have been carried out with a WT5000 power analyser connected to the converter, as shown in Figure 16. The photograph of the experimental setup is presented in Figure 17.

The results of power loss measurements are collected in

Table 7. Results of power loss measurement of TNPC converter operating with 33 mH inductors.

vdc1, V	vdc2, V	idc1, A	idc2, A	Pin, W	IOrms, A	PO, W	Ptot, W
202.90	201.09	0.580	0.638	241.83	11.056	156.69	85.15
254.04	251.52	0.703	0.774	366.96	13.852	245.68	121.28
305.07	302.10	0.827	0.913	518.79	16.649	354.74	164.07
356.04	352.55	0.956	1.056	700.15	19.451	485.50	214.65
370.24	370.59	1.003	1.109	768.90	20.338	534.20	234.70

. During the test, five input elements were used, two for the dc-side of the converter and three for the ac-side. Power is measured at the input as P_in and the output as P_out, together with calculating the power losses as their difference. Figure 18 shows the exemplary screen images from the power analyser for the rms output current I_Orms = 20 A.

In Table 7, the measurement data for the dc-side are represented by two voltages, v_dc1 and v_dc2, and currents i_dc1 and i_dc2. For the ac-side, due to the space limitation, only one current I_Orms is given, which is the average value of the three-phase currents. The difference between these currents (Figure 18) results from using a three-phase three-limb coupled inductor in which the lowest current occurs in the phase where the winding is wound around the centre limb.

The measured power losses and theoretical total power losses, given for conditions during the test, are shown in Figure 19 as a function of the output current.

The theoretical losses are presented for an assumed temperature T = 45 °C, the varying blocking voltage, constant phase-shift angle φ = 87.6°, and modulation index m_a = 0.86. The phase-shift angle is adopted from each phase active power measurement according to Equation (19). The reason for the temperature T selection was that a forced cooling system set this temperature as a steady-state thermal value.

$$\mathsf{\phi }=\arctan \left(\frac{\mathsf{\omega }{L}_{\mathrm{AC}}}{R_{\mathrm{AC}}}\right)=\arctan \left(\frac{\mathsf{\omega }{L}_{\mathrm{AC}}}{\frac{1}{3}\left(\frac{P_{\mathrm{A}}}{I_{\mathrm{OArms}}^2}+\frac{P_{\mathrm{B}}}{I_{\mathrm{OBrms}}^2}+\frac{P_{\mathrm{C}}}{I_{\mathrm{OCrms}}^2}\right)}\right),$$

(19)

where P_A, P_B and P_C are phase A, B and C output powers and I_OArms, I_OBrms and I_OCrms are corresponding rms values of phase currents. In Equation (19), it was assumed that in each phase, the inductance of the inductor is the same and equal to L_AC = 33 mH.

From Figure 19, it is evident that the measured losses are higher than the theoretical ones. This is because, in the converter, additional power losses are generated in pcb wires and connectors. The resistance of all wires and connections has been measured and is estimated to be 4.5 mΩ for each converter phase. The characteristic of the theoretical total power losses with additional losses is also shown in Figure 19. The correlation between theoretical and measured losses is high. The presented measurements have been performed for varying dc-link voltage, which did not correspond to the normal operation of the converter. However, they reveal the correct dependence of losses on dc-link voltage.

3.2. Power Losses of Grid-Connected TNPC Converter

In this test, the TNPC converter has been connected to the three-phase 3 × 400 V grid and operated as the active power filter. The dc-link voltage was kept constant at V_dc/2 = 370 V. The converter was connected to the grid through the LCL filter with the sum of inductances L_f = L_f1 + L_f2 = 750 + 150 μH = 900 μH and filter capacitance C_f = 4.4 μF. During the measurement of power losses, the converter has been generating capacitive and inductive reactive power. These power losses are compared with theoretical power losses obtained by applying the method proposed in Section 2. For theoretical power losses, it is assumed that the phase-shift angle φ = 90.0° and the modulation index m_a = 0.86 for all output current rms values I_Orms ranging from =0 to 10 A. This assumption also neglects the small capacitive current of the filter capacitor. In the analysis, the switching frequency is considered equal to 20 kHz. The tests have been carried out with a power analyser connected to the converter, as shown in Figure 20.

The results of the power loss measurements are listed in

Table 8. Results of power loss measurement of the TNPC converter operating as the active power filter.

IOrms, A (Inductive)	Ptot, W
11.00	120.2
9.90	110.7
8.80	100.4
7.71	90.3
6.61	80.3
5.53	70.2
4.45	60.4
3.40	49.7
2.40	38.7

, where power losses for inductive output currents are given. The output voltage and current waveforms for inductive reactive power generation at I_Orms = 11.0 A are shown in Figure 21. The measurement power losses of the three-phase TNPC converter are compared with the theoretical power losses as given in Section 2 and are shown in Figure 22. Apart from generating reactive power, the analysed converter also consumes active power in the form of power losses. Nevertheless, the analysis assumes that the phase-shift angle φ = 90°. The analysis does not consider the slight change in modulation index m_a with the output current change. Thus, the modulation index is constant and equal to m_a = 0.86. Due to a stable thermal condition guaranteed by the cooling system, the temperature during the test was constant and equal to T = 45 °C. This temperature was measured by an NTC resistor from the IGBT module.

As seen in Figure 22, the measured power losses are always higher than the theoretical losses. This is particularly true for low rms values of the output current. The main reason for such a difference in power losses is the switching frequency output current ripples. It should be noted that during the first tests, when the converter was supplied from the dc power supply, such output current ripples did not occur due to relatively large inductances of the three-phase inductor, which were equal to L_AC = 33 mH. Another reason for the discrepancy between measurement data and theoretical results is the assumption that the device temperature is the same as the temperature of the module base. In a real module, the device temperature is higher by several degrees Celsius.

It should be noted that similar power loss characteristics can be obtained for the generation of capacitive reactive power. In the case of using different design parameters of the active power filter, i.e., with the different switching frequency, dc-link voltage, and temperature, the proposed power loss analysis can also be applied.

4. Conclusions

This paper presents a detailed analysis of power losses of a three-level T-type NPC converter. The study is performed thoroughly; however, the focus is on the converter operation as an active power filter. The accurate recognition of power losses allows the converter designer to carry out the proper steps during the converter designing stages, which, among others, are: setting the switching frequency, designing the cooling system, and designing the gate drivers.

In the paper, the detailed power loss analysis is based on characteristics provided by the IGBT module manufacturer. Obtained power losses are given as functions of the rms value of the output current and temperature. However, they can be extended to other parameters influencing them. Power losses are divided into conduction and switching losses with a given distribution among all semiconductor devices of the T-NPC converter. This division of power losses is essential for designers of IGBT modules and converters because it is possible to find the semiconductor device with the highest power losses for different operating conditions. In the analysed converter operating as the active power filter, the most significant share of losses occurs in transistors T₂ and T₃. Together with losses in diodes D₂, they constitute nearly half of the total power losses. These even shares of power losses are a very advantageous feature of the converter.

The measured power losses agree with the losses obtained from the analysis. In the first test, the converter output current has been changed from 10 to 20 A. The difference between the analytical results and measured power losses ranged from 5% to 9%. It is believed that such a good correlation between the measured and analysed results is due to the very small output current ripples in the test, which are neglected in the analysis.

In the second test of the TNPC converter operating as an active power filter, the power losses from the analysis were consistent with the measurements, but better results were obtained for operation at higher currents, close to 11 A. For lower currents, the compliance is lower. This is believed to be due to the presence of current ripples for lower currents power losses that are not the same as for sinusoidal currents.

The TNPC converter has been tested with the rms values of the current ranging from 0 to 20 A when it was supplied from the dc power supply and from 0 to 10 A when it was connected to the grid. For higher currents, the discrepancy between power losses observed during the experiments and theoretical ones can be explained by the existence of higher component junction temperatures than the single temperature measured on the module and the existence of output current ripples.

The future works on presented detailed power loss analysis can be extended with the thermal model of the IGBT module. In such an extended model, the temperatures of individual semiconductor devices are not the same and are higher than the temperature of the module base plate.

It should be noted that the detailed power loss analysis can also be applied to other converter topologies. In such a case, the modification of some parameters is required that relate to different conduction angles, switching angles and modulation functions.