Multi-objective cooperative control of a junction-temperature-orientated three-level traction converter

Abstract

The Insulated-Gate Bipolar Transistor (IGBT) module is the core of the three-level (3L) traction converter. In order to improve the lifetime of the traction converter, a model predictive torque control (MPTC) based on the junction temperature constraint is proposed. Firstly, the optimization range is reduced by judging the sector where the reference voltage vector locates, as the traditional MPTC needs to be optimized 27 times in each sampling period, which requires a large amount of calculation. Secondly, by simplifying the calculation of IGBT power loss and dynamically constraining it in the cost function, the performance of optimal voltage vector balancing control can be balanced with power loss. Simulation results show that the proposed method reduces the junction temperature of the power semiconductor and prolongs the converter lifetime compared with the traditional strategy.

1. Introduction

The traction converter is regarded as the ‘heart’ of the rail transit train, providing strong power for train operation. However, as the key executive part of the converter to realize electric energy conversion, the Insulated-Gate Bipolar Transistor (IGBT) module is affected by variable working conditions and is relatively fragile, which brings great challenges to the safe operation of trains [1]. The lifetime of the IGBT module is largely determined by the amplitude of junction temperature variation and the average junction temperature [2]. Therefore, reducing the average junction temperature and junction temperature fluctuation of the IGBT is of great significance for improving the lifetime of the IGBT module and thus the lifetime of the traction converter.

In order to improve the lifetime of the power semiconductor, Wolfle et al. [3] reduced the junction temperature by limiting the load current amplitude or by dynamically adjusting the switching frequency. In Ref. [4], the difference between IGBT loss under a given voltage and under the temperature limit was calculated, and the DC voltage was adjusted by feedback to reduce IGBT loss and junction temperature under the whole working condition. Du et al. [5] carried out hybrid modulation of continuous pulse width modulation (CPWM) and discontinuous pulse width modulation (DPWM) to reduce the switching loss, reduce junction temperature and finally optimize the lifetime of power devices. Ma et al. [6] aimed at stabilizing the junction temperature fluctuation of power devices during gusts by controlling the reactive power circulating between parallel converter systems in wind farms. In terms of balancing the junction temperature of power semiconductors, Ma et al. [7] used improved space vector modulation to balance the junction temperature between various power devices. Wu et al. [8] reduced the overlap area of voltage and current of power devices during switching operation, and reduced switching loss. The above literature is based on reducing the switching loss and thus reducing the junction temperature, optimizing the control method or improving the power electronic hardware to improve the IGBT lifetime, and less consideration is given to the conduction loss of the IGBT and diode of the converter, without direct control.

For the traction transmission system of subways, it is very important to achieve high performance control in the full speed domain [9]. MPTC is a kind of on-line optimization control algorithm for motors. It stands out among the existing motor control methods because it is an intuitive concept, is easy to model and to add constraints [10]. Since the traditional MPTC only outputs one voltage vector in one sampling period, the control performance is limited, so the three-vector MPTC method is used [11] to improve the steady-state accuracy of the system. Due to the different dimensions of MPTC torque and flux, it is necessary to assign a weight coefficient to the flux. In order to avoid complicated weight coefficient tests, the method of torque and flux change rate was adopted [12] to eliminate the weight coefficient. In addition, the three-level (3L) traction converter also needs to consider the balance control of the neutral point voltage (NPV). In Ref. [13], a factor k of the NPV imbalance was introduced, and a small vector conducive to the NPV balance was selected based on the factor k and the phase current direction, so as to realize the precise control and balance of the NPV. Jiang et al. [14] proposed a virtual space voltage vector modulation strategy, which first selects a vector with a lower common-mode voltage (CMV) and then generates a new virtual voltage vector, so as to realize the cooperative control of NPV and CMV. In Ref. [15], a virtual vector is constructed to meet the requirements according to the voltage difference between the upper and lower capacitors on the DC side, so that the NPV is close to equilibrium. Zhang et al. [16] proposed an MPTC strategy which uses the objective function to nonlinear constrain the capacitor voltage of a 3L NPC fault-tolerant inverter, and finally control the NPV. The methods of controlling the NPV mentioned in the above literature are all complicated in theoretical calculation, and the implementation efficiency is not high, which can not meet the multi-objective cooperative control.

In order to improve the lifetime of the 3L traction inverter and reduce the average junction temperature and junction temperature fluctuation of the IGBT, a junction temperature-orientated 3L model predictive torque control strategy is proposed in this paper.

2. Asynchronous motor mathematical model

The mathematical model of an asynchronous motor in a two-phase stationary coordinate system can be expressed as:

$$\begin{eqnarray} \left\{ \begin{array}{l} \frac{\text{d}{{i}_{\text{s}}}}{\text{d}t}=-\left( \frac{{{R}_{\text{s}}}+{{\left( {{L}_{\text{m}}}\text{/}{{L}_{\text{r}}} \right)}^{2}}{{R}_{\text{r}}}}{\sigma {{L}_{\text{s}}}}+\text{j}{{\omega }_{\text{k}}} \right){{i}_{\text{s}}}+\frac{{{L}_{\text{m}}}}{\sigma {{L}_{\text{s}}}{{L}_{\text{r}}}}\left( \frac{1}{{{\tau }_{\text{r}}}}-\text{j}{{\omega }_{\text{r}}} \right){{\psi }_{\text{r}}}+\frac{1}{\sigma {{L}_{\text{s}}}}{{u}_{\text{s}}} \\ \frac{\text{d}{{\psi }_{\text{r}}}}{\text{d}t}=\frac{{{L}_{\text{m}}}}{{{\tau }_{\text{r}}}}{{i}_{\text{s}}}-\left[ \frac{1}{{{\tau }_{\text{r}}}}+\text{j}\left( {{\omega }_{\text{k}}}-{{\omega }_{\text{r}}} \right) \right]{{\psi }_{\text{r}}} \\ \end{array} \right. \end{eqnarray}$$

(1)

$$\begin{eqnarray} {{\psi }_{\text{r}}}=\frac{{{L}_{\text{r}}}}{{{L}_{\text{m}}}}{{\psi }_{\text{s}}}+\left( {{L}_{\text{m}}}-\frac{{{L}_{\text{s}}}{{L}_{\text{r}}}}{{{L}_{\text{m}}}} \right){{i}_{\text{s}}} \end{eqnarray}$$

(2)

$$\begin{eqnarray} \left\{ \begin{array}{l} \sigma =1-\frac{L_{\text{m}}^{2}}{{{L}_{\text{s}}}{{L}_{\text{r}}}} \\ {{\tau }_{\text{r}}}=\frac{{{L}_{\text{r}}}}{{{R}_{\text{r}}}} \\ \end{array} \right. \end{eqnarray}$$

(3)

where ψ_s represents the stator flux; ψ_r represents the rotor flux; u_s represents the voltage vector acting on the stator; i_s indicates the stator current; R_s indicates the stator resistance; R_r indicates the rotor resistance; L_s indicates the stator inductance; L_m indicates the mutual inductance; ω_r indicates the motor rotor speed; ω_k represents the rotation speed of the coordinate system; τ_r represents the rotor time constant.

3. The traditional MPTC strategy

The stator flux and stator current at k+1 can be estimated, as shown in Eqs. (4)−(6).

$$\begin{eqnarray} {\psi _{\rm{s}}}\left( {k + 1} \right) = {\psi _{\rm{s}}}\left( k \right) + {T_{\rm{s}}}\left[ {{u_{\rm{s}}}\left( k \right) - {R_{\rm{s}}}{i_{\rm{s}}}\left( k \right)} \right] \end{eqnarray}$$

(4)

$$\begin{eqnarray} {{i}_{\text{s}}}\left( k+1 \right)&=&\left[ 1+\frac{{{T}_{\text{s}}}}{{{\tau }_{\sigma }}} \right]{{i}_{\text{s}}}\left( k \right)+\frac{{{T}_{\text{s}}}}{{{\tau }_{\sigma }}+{{T}_{\text{s}}}}\left\{ \frac{1}{{{R}_{\sigma }}}\left[ \left( \frac{{{k}_{\text{r}}}}{{{\tau }_{\text{r}}}}-{{k}_{\text{r}}}\text{j}\omega \right){{\psi }_{\text{r}}}\left( k \right)\right.\right.\\ && \left.+{{u}_{\text{s}}}\left( k \right) \bigg] \right\} \end{eqnarray}$$

(5)

$$\begin{eqnarray} \left\{ \begin{array}{l} {{\tau }_{\sigma }}=\frac{\sigma {{L}_{\text{s}}}}{{{R}_{\sigma }}} \\ {{R}_{\sigma }}={{R}_{\text{s}}}+{{R}_{\text{r}}}k_{\text{r}}^{2} \\ {{k}_{\text{r}}}=\frac{{{L}_{\text{m}}}}{{{L}_{\text{r}}}} \\ \end{array} \right. \end{eqnarray}$$

(6)

Therefore, the motor torque at k+1 time can be obtained from the predicted stator flux and stator current.

$$\begin{eqnarray} {T_{\rm{e}}}\left( {k + 1} \right) = \frac{3}{2}p \cdot {\rm{Im}}\left\{ {{{\bar \psi }_{\rm{s}}}\left( {k + 1} \right){i_{\rm{s}}}\left( {k + 1} \right)} \right\} \end{eqnarray}$$

(7)

The MPTC selects the optimal voltage vector that minimizes the cost function, and then applies the voltage vector to the next time. The main objective is to track the stator reference flux and the reference torque, and its cost function is shown as follows:

$$\begin{eqnarray} g = \left| {T_{\rm{e}}^* - {T_{\rm{e}}}\left( {k + 1} \right)} \right| + {\lambda _{\rm{f}}}\left| {\psi _{\rm{s}}^* - {\psi _{\rm{s}}}\left( {k + 1} \right)} \right| \end{eqnarray}$$

(8)

where |$T_e^*$| and |$\psi _s^*$| represent the reference torque and the reference flux, respectively; and λ_f represents the weight coefficient of the stator flux.

4. Multi-objective optimization MPTC strategy

Considering that the traditional MPTC needs to be substituted into 27 voltage vector cycles in each sampling period, which is a large amount of calculation, the 3L basic voltage vector is divided into six sectors with an interval of 60°. By calculating the phase angle of the voltage vector in the two-phase static coordinate, the sector in which the reference voltage vector is located is determined, and the number of alternative vectors is reduced from 27 to 10. At the same time, the weight of flux in the cost function (8) can be cancelled, which simplifies the adjustment of the weight coefficient. Since Eq. (7) can be further expressed as:

$$\begin{eqnarray} {T_{\rm{e}}}\left( {k + 1} \right) = \frac{3}{2}p\frac{{{L_{\rm{m}}}}}{{\sigma {L_{\rm{s}}}{L_{\rm{r}}}}}\left| {{\psi _{\rm{s}}}} \right|\left| {{\psi _{\rm{r}}}} \right|{\rm{sin}}\left( {\angle {\psi _{\rm{s}}} - \angle {\psi _{\rm{r}}}} \right) \end{eqnarray}$$

(9)

From Eq. (9), the angle relationship between the stator flux and the rotor flux can be deduced as follows:

$$\begin{eqnarray} \angle {\psi _{\rm{s}}} = \angle {\psi _{\rm{r}}} + {\rm{si}}{{\rm{n}}^{ - 1}}\left( {\frac{{2\sigma {T_{\rm{e}}}{L_{\rm{s}}}{L_{\rm{r}}}}}{{3p{L_{\rm{m}}}\left| {{\psi _{\rm{r}}}} \right|\left| {{\psi _{\rm{s}}}} \right|}}} \right) \end{eqnarray}$$

(10)

By substituting the torque reference value and the stator flux reference value into Eq. (10), it is obtained:

$$\begin{eqnarray} \angle \psi _{\rm{s}}^* = \angle {\psi _{\rm{r}}} + {\rm{si}}{{\rm{n}}^{ - 1}}\left( {\frac{{2\sigma T_{\rm{e}}^*{L_{\rm{s}}}{L_{\rm{r}}}}}{{3p{L_{\rm{m}}}\left| {{\psi _{\rm{r}}}} \right|\left| {{\psi _{\rm{s}}}} \right|}}} \right) \end{eqnarray}$$

(11)

The component of the given value of the flux in the two-phase rest coordinate system is:

$$\begin{eqnarray} \left\{ \begin{array}{@{}l@{}} \psi _{{\rm{s}}\alpha }^* = \left| {\psi _{\rm{s}}^*} \right|{\rm{cos}}\angle \psi _{\rm{s}}^*\\ \psi _{{\rm{s}}\beta }^* = \left| {\psi _{\rm{s}}^*} \right|{\rm{sin}}\angle \psi _{\rm{s}}^* \end{array} \right. \end{eqnarray}$$

(12)

Combine Eqs. (4) and (12), the following can be obtained:

$$\begin{eqnarray} \left\{ \begin{array}{@{}l@{}} u_{{\rm{s}}\alpha }^* = \frac{1}{{{T_{\rm{s}}}}}\left( {\psi _{{\rm{s}}\alpha }^* - {\psi _{{\rm{s}}\alpha }}\left( k \right)} \right) + {R_{\rm{s}}}{i_{{\rm{s}}\alpha }}\left( k \right)\\ u_{{\rm{s}}\beta }^* = \frac{1}{{{T_{\rm{s}}}}}\left( {\psi _{{\rm{s}}\beta }^* - {\psi _{{\rm{s}}\beta }}\left( k \right)} \right) + {R_{\rm{s}}}{i_{{\rm{s}}\beta }}\left( k \right) \end{array} \right. \end{eqnarray}$$

(13)

The reference values |$u_{{\rm{s}}\alpha }^*$| and |$u_{{\rm{s}}\beta }^*$| of the inverter function at k+1 are derived from Eq. (13). By calculating the angle of the reference voltage in the two-phase stationary coordinate system, the sector in which the reference voltage is located can be judged, as shown in Fig. 1(a), and a simplified set of alternative vectors can be obtained. Then only the basic voltage vector in the sector is substituted into the iterative calculation of the cost function. The set of alternative vectors is shown in Table 1.

Fig. 1.

Sector division diagram: (a) 3L space voltage vector; (b) 3L traction inverter.

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Table 1.

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Sector and corresponding alternative voltage vector.

Sector	Corresponding alternative voltage vector
I	POO ONN PPO OON PNN PON PPN PPP OOO NNN
II	PPO OON OPO NON PPN OPN NPN PPP OOO NNN
III	OPO NON OPP NOO NPN NPO NPP PPP OOO NNN
IV	OPP NOO OOP NNO NPP NOP NNP PPP OOO NNN
V	OOP NNO POP ONO NNP ONP PNP PPP OOO NNN
VI	POP ONO POO ONN PNP PNO PNN PPP OOO NNN

Sector	Corresponding alternative voltage vector
I	POO ONN PPO OON PNN PON PPN PPP OOO NNN
II	PPO OON OPO NON PPN OPN NPN PPP OOO NNN
III	OPO NON OPP NOO NPN NPO NPP PPP OOO NNN
IV	OPP NOO OOP NNO NPP NOP NNP PPP OOO NNN
V	OOP NNO POP ONO NNP ONP PNP PPP OOO NNN
VI	POP ONO POO ONN PNP PNO PNN PPP OOO NNN

Table 1.

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Sector and corresponding alternative voltage vector.

Sector	Corresponding alternative voltage vector
I	POO ONN PPO OON PNN PON PPN PPP OOO NNN
II	PPO OON OPO NON PPN OPN NPN PPP OOO NNN
III	OPO NON OPP NOO NPN NPO NPP PPP OOO NNN
IV	OPP NOO OOP NNO NPP NOP NNP PPP OOO NNN
V	OOP NNO POP ONO NNP ONP PNP PPP OOO NNN
VI	POP ONO POO ONN PNP PNO PNN PPP OOO NNN

Sector	Corresponding alternative voltage vector
I	POO ONN PPO OON PNN PON PPN PPP OOO NNN
II	PPO OON OPO NON PPN OPN NPN PPP OOO NNN
III	OPO NON OPP NOO NPN NPO NPP PPP OOO NNN
IV	OPP NOO OOP NNO NPP NOP NNP PPP OOO NNN
V	OOP NNO POP ONO NNP ONP PNP PPP OOO NNN
VI	POP ONO POO ONN PNP PNO PNN PPP OOO NNN

Comparing the alternative voltage vector in the sector where the inverter is located with the reference voltage, a new cost function is established with the error as follows:

$$\begin{eqnarray} g = \left| {u_{{\rm{s}}\alpha }^* - {u_{i\alpha }}} \right| + \left| {u_{{\rm{s}}\beta }^* - {u_{i\beta }}} \right| \end{eqnarray}$$

(14)

where u_iα and u_iβ represent the two voltage components of the i-th vector in a two-phase stationary coordinate system, i = 1 to 10.

Due to the non-zero neutral point current i_o on the DC side of the 3L inverter, there are charging and discharging situations between the two DC capacitors. Therefore, the cost function also needs to consider the control of the NPV.

The relationship between the neutral point current of the 3L NPC inverter and the three-phase switching state is:

$$\begin{eqnarray} {i_{\rm{o}}} = \sum\limits_{x = A{\rm{,}}B{\rm{,}}C} {\left( {1 - \left| {{S_x}} \right|} \right){i_x}} \end{eqnarray}$$

(15)

Eq. (15) shows that when the three phases are in the O state, the neutral point current is related to the load current. The relationship between capacitance voltage and capacitance current can be expressed as

$$\begin{eqnarray} \left\{ \begin{array}{@{}l@{}} {C_1}\displaystyle\frac{{{\rm{d}}{U_{C1}}}}{{{\rm{d}}t}} = C \displaystyle\frac{{{\rm{d}}{U_{C1}}}}{{{\rm{d}}t}} = {i_{C1}}\\ {C_2}\displaystyle\frac{{{\rm{d}}{U_{C2}}}}{{{\rm{d}}t}} = C \displaystyle\frac{{{\rm{d}}{U_{C2}}}}{{{\rm{d}}t}} = {i_{C2}} \end{array} \right. \end{eqnarray}$$

(16)

It can be obtained from Eq. (16)

$$\begin{eqnarray} C\frac{{{\rm{d}}\left( {{U_{C1}} - {U_{C2}}} \right)}}{{{\rm{d}}t}} = {i_{C1}} - {i_{C2}} = {i_{\rm{o}}} \end{eqnarray}$$

(17)

Then:

$$\begin{eqnarray} {U_{C1}}\left( t \right) - {U_{C2}}\left( t \right) = \frac{1}{C}\int {{i_{\rm{o}}}{\rm{d}}t} + {U_{C1}}\left( 0 \right) - {U_{C2}}\left( 0 \right) \end{eqnarray}$$

(18)

where U_C₁(0) and U_C₂(0) represent the initial values of the two capacitor voltages. After rewriting Eq. (18), Eq. (19) can be obtained, representing the relationship between the two capacitor voltages on the DC side at the previous time and the next time.

$$\begin{eqnarray} \Delta {U_C}\left( {k + 1} \right) = \frac{1}{C}\int {{i_{\rm{o}}}{\rm{d}}t} + {U_{C1}}\left( k \right) - {U_{C2}}\left( k \right) \end{eqnarray}$$

(19)

The above integral can be discretized:

$$\begin{eqnarray} \Delta {U_C}\left( {k + 1} \right) = {U_{C1}}\left( k \right) - {U_{C2}}\left( k \right) + \frac{{{T_{\rm{s}}}}}{C}{i_{\rm{o}}}\left( k \right) \end{eqnarray}$$

(20)

Due to the fact that traditional MPTC is directly applied to the auxiliary inverter of high-speed trains, the junction temperature of the IGBT module will be higher, the aging speed will be accelerated and unpredictable damage will be caused to the safe and stable operation of the inverter. Therefore, the switching loss and conduction loss of the IGBT module are approximately equivalent, and the power loss factor related to the collector voltage and collector current is obtained. By predicting the direction of each phase current, furthermore, it predicts the switching and conduction conditions of the IGBT module, dynamically adds a power loss factor and constrains the power loss of each phase of the IGBT and its freewheeling diode in the cost function so that the optimal voltage vector reduces power loss while ensuring certain control performance.

The power loss factor is represented as follows:

$$\begin{eqnarray} \left\{ \begin{array}{@{}l@{}} {p_{{\rm{sw\_g}}}} = {{{U_{{\rm{dc}}}}{i_{a,b,c}}}/ 2}\\ {p_{{\rm{con\_g}}}} = {r_{\rm{g}}}i_{a,b,c}^2 \end{array} \right. \end{eqnarray}$$

(21)

where i_a_,_b_,_c represents the three-phase current, and r_g represents the on-state resistance of the IGBT. Since the cost function includes current control items and NPV control items, when the above loss factors are directly added to the cost function, the current control and NPV control effects will be reduced, and the results will be omitted. Therefore, it is necessary to dynamically predict the state of the IGBT at (k+1) time relative to k time (switching state/conducting state). Then add a factor to reduce the corresponding power loss in the corresponding state to achieve the purpose of multi-objective optimization control. The following uses phase A as an example.

In Fig. 1(b), it is specified that the current flowing out of the inverter and running into the resistive load is in the positive direction. When i_a > 0, S_a(k) = 0 and S_a(k + 1) = 1, it indicates that D_A5 and I_A2 are in the conducting state at the previous time, and other power devices are in the off state. At the next moment, I_A1 and I_A2 are in the conducting state, while the other power devices are in the off state. During the switching process, D_A5 switches from the conducting state to the turn-off state, which will generate switching loss. The conduction state of I_A2 is unchanged before and after switching, resulting in switching loss; I_A1 switches from the turn-off state to the turn-on state, resulting in switching loss and conduction loss. To sum up, three power semiconductors are involved in this switching process, and the loss cost function of phase A is as follows:

$$\begin{eqnarray} {g_A} &=& {\lambda _{{\rm{sw}}}}{p_{{\rm{sw\_g}}}} + {\lambda _{{\rm{con}}}}{p_{{\rm{con\_g}}}} + {\lambda _{{\rm{con}}}}{p_{{\rm{con\_g}}}} + {\lambda _{{\rm{sw}}}}{p_{{\rm{sw\_g}}}}\\ &=& 2{\lambda _{{\rm{sw}}}}{p_{{\rm{sw\_g}}}} + 2{\lambda _{{\rm{con}}}}{p_{{\rm{con\_g}}}} \end{eqnarray}$$

(22)

when i_a < 0, if S_a(k) = 0 and S_a(k + 1) = 1, as shown in Fig. 1(b), it indicates that I_A3 and D_A6 were in the conducting state and other power devices were in the off state at the previous time; at the next moment, D_A1 and D_A2 are in the conducting state, while the other power devices are in the off state. D_A6 and I_A3 switch from conducting state to off state during the switching process, resulting in turn-off loss. When D_A1 and D_A2 switch from the off state to the conducting state, conduction loss will be generated. To sum up, four power semiconductors are involved in this switching process, and the loss cost function of phase A is as follows:

$$\begin{eqnarray} {g_A} = 2{\lambda _{{\rm{sw}}}}{p_{{\rm{sw\_g}}}} + 2{\lambda _{{\rm{con}}}}{p_{{\rm{con\_g}}}} \end{eqnarray}$$

(23)

When the direction of the A-phase current is different, the relationship between the switching state and the A-phase loss cost function is shown in Table 2. Combining current control, NPV control and reducing power loss, the final cost function obtained is as follows:

$$\begin{eqnarray} g = {\left| {u_{{\rm{s}}\alpha }^* - {u_{i\alpha }}} \right|^2} + {\left| {u_{{\rm{s}}\beta }^* - {u_{i\beta }}} \right|^2} + {\lambda _C}\Delta {U_C}\left( {k + 1} \right) + {g_A} + {g_B} + {g_C} \end{eqnarray}$$

(24)

where λ_C represents the weight coefficient of the NPV; and g_B and g_C represent the loss function of phase B and phase C. Since the improved MPTC considers more control variables than the traditional MPTC, in order to avoid the torque and flux control effect being greatly affected, the voltage error term is replaced by the square of the voltage error term.

Table 2.

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The relationship between phase A current direction, switching state and loss cost function.

\|${\boldsymbol{i_a}}$\|	\|${\boldsymbol{S_a(k)}}$\|	\|${\boldsymbol{S_a(k+1)}}$\|	\|${\boldsymbol{g_A}}$\|
i_a > 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	3λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con
i_a < 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	3λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con

\|${\boldsymbol{i_a}}$\|	\|${\boldsymbol{S_a(k)}}$\|	\|${\boldsymbol{S_a(k+1)}}$\|	\|${\boldsymbol{g_A}}$\|
i_a > 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	3λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con
i_a < 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	3λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con

Table 2.

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The relationship between phase A current direction, switching state and loss cost function.

\|${\boldsymbol{i_a}}$\|	\|${\boldsymbol{S_a(k)}}$\|	\|${\boldsymbol{S_a(k+1)}}$\|	\|${\boldsymbol{g_A}}$\|
i_a > 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	3λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con
i_a < 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	3λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con

\|${\boldsymbol{i_a}}$\|	\|${\boldsymbol{S_a(k)}}$\|	\|${\boldsymbol{S_a(k+1)}}$\|	\|${\boldsymbol{g_A}}$\|
i_a > 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	3λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con
i_a < 0	0	1	2λ_swP_sw+2λ_conP_con
	1	0	3λ_swP_sw+2λ_conP_con
	0	−1	2λ_swP_sw+2λ_conP_con
	−1	0	λ_swP_sw+2λ_conP_con
	1(0/−1)	1(0/−1)	2λ_conP_con

5. Simulation verification part

In the SIMULINK environment, based on the actual task curve of a subway, the parameters of a 190-kW asynchronous traction motor are used to verify the cooperative control theory of a 3L inverter, as shown in Table 3. The DC voltage U_dc is 2000 V. MPTC-I is used to represent the traditional MPTC. MPTC-II was used to represent the multi-objective cooperative control strategy. SVMDTC represents direct torque control of the traditional SVPWM.

Table 3.

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Simulation values.

Parameter	Value
DC voltage U_dc/V	2000
Rated power P_e/kW	190
Rated voltage U/V	2000
Rated frequency f_N/Hz	66
Pole-pair count p	2
Rated stator leakage inductance L_ls/mH	0.951
Rated rotor leakage inductance L_lr/mH	1.115
Rated mutual inductance L_m/mH	24.898
Stator resistance R_s/Ω	0.05 685
Rotor resistance R_r/Ω	0.04 315

Parameter	Value
DC voltage U_dc/V	2000
Rated power P_e/kW	190
Rated voltage U/V	2000
Rated frequency f_N/Hz	66
Pole-pair count p	2
Rated stator leakage inductance L_ls/mH	0.951
Rated rotor leakage inductance L_lr/mH	1.115
Rated mutual inductance L_m/mH	24.898
Stator resistance R_s/Ω	0.05 685
Rotor resistance R_r/Ω	0.04 315

Table 3.

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Simulation values.

Parameter	Value
DC voltage U_dc/V	2000
Rated power P_e/kW	190
Rated voltage U/V	2000
Rated frequency f_N/Hz	66
Pole-pair count p	2
Rated stator leakage inductance L_ls/mH	0.951
Rated rotor leakage inductance L_lr/mH	1.115
Rated mutual inductance L_m/mH	24.898
Stator resistance R_s/Ω	0.05 685
Rotor resistance R_r/Ω	0.04 315

Parameter	Value
DC voltage U_dc/V	2000
Rated power P_e/kW	190
Rated voltage U/V	2000
Rated frequency f_N/Hz	66
Pole-pair count p	2
Rated stator leakage inductance L_ls/mH	0.951
Rated rotor leakage inductance L_lr/mH	1.115
Rated mutual inductance L_m/mH	24.898
Stator resistance R_s/Ω	0.05 685
Rotor resistance R_r/Ω	0.04 315

According to the results in Fig. 2 , MPTC-II can track the reference speed and the reference torque faster. In Fig. 3, before the time of 2 s, the reference torque is 500 N·m, and at 2 s the torque is suddenly increased to 800 N·m. It can be observed that the speed of SVMDTC fluctuates significantly before and after the torque mutation, and its torque tracking response speed is slightly slower in following the reference torque. In contrast, MPTC-II and MPTC-I exhibit nearly identical dynamic response capabilities in terms of speed and torque, both being faster than SVMDTC. As shown in Figs. 4(a) and (b), the steady-state stator current Total Harmonic Distortion (THD) and steady-state torque ripple of MPTC-II are smaller than those of MPTC-I and SVMDTC. As shown in Fig. 4(c), the steady-state NPV fluctuation value of MPTC-II is slightly larger than that of MPTC-I, about 2 V, which is similar to the NPV fluctuation value of 2000 V DC voltage.

Fig. 2.

Simulation results of speed, three-phase current, torque and neutral point capacitance voltage: (a) MPTC-II; (b) MPTC-I; (c) SVMDTC.

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Fig. 3.

Simulation results of speed, three-phase current, torque and neutral point capacitance voltage when torque changes abrupt: (a) MPTC-II; (b) (b) MPTC-I; (c) SVMDTC.

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Fig. 4.

Comparison of steady-state control performance: (a) steady-state stator current THD comparison; (b) steady-state torque ripple comparison; (c) steady-state neutral point voltage deviation comparison.

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The outer tubes refer to I_A1/I_A4, while the inner tubes refer to I_A2/I_A3. Figs. 5–7 show the IGBT junction temperature comparison results of three strategies within a task interval. As shown in Fig. 7, the outer tube T_jm1 of MPTC-II is reduced by 9.73 °C compared to MPTC-I, and by 18.53 °C compared to SVMDTC. The outer tube ΔT_j1 of MPTC-II is reduced by 3.61 °C compared to MPTC-I, and by 4.13 °C compared to SVMDTC. The inner tube T_jm2 of MPTC-II is reduced by 0.22 °C compared to MPTC-I, and by 7.91 °C compared to SVMDTC. The outer tube ΔT_j2 of MPTC-II is reduced by 0.34 °C compared to MPTC-I, and by 2 °C compared to SVMDTC. Therefore, compared to the other two strategies, MPTC-II exhibits lower average junction temperature and junction temperature fluctuations.

Fig. 5.

Temperature comparison of outer IGBT junction: (a) MPTC-II; (b) MPTC-I; (c) SVMDTC.

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Fig. 6.

Comparison of the temperature of the inner IGBT junction: (a) MPTC-II; (b) MPTC-I; (c) SVMDTC.

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Fig. 7

Comparison of the average junction temperature and junction temperature fluctuation of the inner and outer IGBTs in steady state.

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In order to accurately evaluate the inverter lifetime after the three strategies are applied to a task curve, the lifetime of IGBT is calculated using the standard IGBT module lifetime model proposed by the LESIT research project team in Switzerland.

$$\begin{eqnarray} \left\{ \begin{array}{@{}l@{}} {N_{\rm{f}}} = m{\left( {\Delta {T_{\rm{j}}}} \right)^{ - n}} \cdot {e^{\frac{{{E_{\rm{a}}}}}{{k{T_{{\rm{jm}}}}}}}}\\ R = \sum\limits_{n = 1}^b {\frac{1}{{{N_{{\rm{f}}n}}\left( {\Delta {T_{{\rm{j}}n}}} \right)}}} \end{array} \right. \end{eqnarray}$$

(25)

where, N_f represents the number of cycles; and ΔT_j represents the IGBT junction temperature fluctuation, which is the difference between the maximum and minimum junction temperatures. T_jm represents the average junction temperature of IGBT, that is, the average of maximum junction temperature and minimum junction temperature. m/n is a constant; E_a represents the internal material activation energy of IGBT; k represents the air constant, which is 8.314 J/(mol·K); b represents the number of junction temperature cycles; R indicates the proportion of life consumption; and 1/R indicates the maximum working cycle of the IGBT cycle, that is, the lifetime. Taking the minimum lifetime of all IGBTs as the inverter life, the calculated 1/R of MPTC-II is 2.5×10⁷⁰, the 1/R of MPTC-I is 2.5×10⁵⁰ and the 1/R of SVMDTC is 2.05×10⁴⁴. The inverter lifetime of MPTC-II is obviously longer than that of MPTC-I and SVMDTC.

6. Conclusions

In summary, the proposed 3L cooperative multi-objective MPTC can restrain the IGBT power loss and reduce the junction temperature of the traction inverter on the premise of good output performance, and finally improve the lifetime of the inverter.

Funding

This paper is supported by the following funding: Hunan Provincial Department of Education Outstanding Youth Project (Grant No. 24B0025); Regional Joint Fund Project of Hunan Province (Grant No. 2025JJ70036), and National Natural Science Foundation of China (Grant No. 52002409).

Conflict of interest statement. None declared.

References

Zhang

Yang

Overview of lifetime evaluation on key components in vehicular traction converter

Journal of Power Supply

2021

;

140

–

Google Scholar

OpenURL Placeholder Text

WorldCat

Lai

Chen

Ran

et al.

IGBT lifetime model based on aging experiment

Transactions of China Electrotechnical Society

2016

;

173

–

Google Scholar

OpenURL Placeholder Text

WorldCat

Wolfle

Nitzsche

Troster

et al.

Combination of two variables in a junction temperature control system to elongate the expected lifetime of IGBT-power-modules

IEEE International Conference on Power Electronics and Drive Systems, Honolulu

2017

–

Lemmens

Vanassche

Driesen

Dynamic DC-link voltage adaptation for thermal management of traction drives

IEEE Energy Conversion Congress and Exposition, Denver

2013

180

–

et al.

A hybrid modulation method for improving the lifetime of power modules in the wind power converter

Proceedings of the CSEE

2015

;

5003

–

Google Scholar

OpenURL Placeholder Text

WorldCat

Liserre

Blaabjerg

Reactive power influence on the thermal cycling of multi-MW wind power inverter

IEEE Trans Ind Appl

2013

;

922

–

Google Scholar

Crossref

WorldCat

Blaabjerg

Modulation methods for neutral-point-clamped wind power converter achieving loss and thermal redistribution under low-voltage ride-through

IEEE Trans Ind Electron

2013

;

835

–

Google Scholar

Crossref

WorldCat

Zhou

Wang

et al.

Internal thermal management of power converter based on switching trace adjustment

Journal of Power Supply

2016

;

–

Google Scholar

OpenURL Placeholder Text

WorldCat

Lin

Yang

et al.

A single-loop field-weakening control strategy for high-speed train traction motor with lncreased torque output capability under six-step mode

Journal of the China Railway Society

2019

;

–

Google Scholar

OpenURL Placeholder Text

WorldCat

10.

Wang

Simplified model predictive torque control algorithm of induction motor using multiscalar model

Proceedings of the CSEE

2022

;

9053

–

Google Scholar

OpenURL Placeholder Text

WorldCat

11.

Zhang

et al.

Three-vector based model predictive torque control of eliminating weighting factor

Transactions of China Electrotechnical Society

2018

;

3925

–

Google Scholar

OpenURL Placeholder Text

WorldCat

12.

Xiong

Shi

et al.

lmproved model predictive torque control of permanent magnet synchronous motor

Journal of Hunan University of Technology

2022

;

–

Google Scholar

OpenURL Placeholder Text

WorldCat

13.

Xiang

Cheng

Han

et al.

Improved virtual space vector modulation for three-level neutral-point-clamped converter with feedback of neutral-point voltage

IEEE Trans Power Electron

2018

;

5452

–

Google Scholar

Crossref

WorldCat

14.

Jiang

Wang

et al.

A novel virtual space vector modulation with reduced common-mode voltage and eliminated neutral point voltage oscillation for neutral point clamped three-level inverter

IEEE Trans Ind Electron

2020

;

884

–

Google Scholar

Crossref

WorldCat

15.

Tao

Wan

et al.

Common mode voltage and neutral point voltage balance control based on virtual vector diode clamped inverter

Energy Storage Science and Technology

2020

;

927

–

Google Scholar

OpenURL Placeholder Text

WorldCat

16.

Zhang

Wang

Liang

YH.

Finite control set model predictive torque control for IM systems driven by three-phase eight-switch fault-tolerant inverter

Journal of Railway Science and Engineering

2020

;

207

–

Google Scholar

OpenURL Placeholder Text

WorldCat

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Article Contents

Multi-objective cooperative control of a junction-temperature-orientated three-level traction converter

Abstract

1. Introduction

2. Asynchronous motor mathematical model

3. The traditional MPTC strategy

4. Multi-objective optimization MPTC strategy

5. Simulation verification part

6. Conclusions

Funding

References

Citations

Views

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Article Contents

Multi-objective cooperative control of a junction-temperature-orientated three-level traction converter

Abstract

1. Introduction

2. Asynchronous motor mathematical model

3. The traditional MPTC strategy

4. Multi-objective optimization MPTC strategy

5. Simulation verification part

6. Conclusions

Funding

References

Citations

Views

Altmetric

Email alerts

Citing articles via

Most Read

Latest

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