- Email: [email protected]
Thermal stress reduction of quasi-Z source inverter drive by model predictive control
Microelectronics Reliability 88–90 (2018) 1247–1250
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Thermal stress reduction of quasi-Z source inverter drive by model predictive control
T
⁎
Ping Liua,b, , Huai Wangb, Yi Liub,c, Frede Blaabjergb a
Hunan University, Changsha, China Aalborg University, Aalborg 9220, Denmark c Wuhan University, Wuhan, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Thermal stress Model predictive control Inverter
The quasi-Z source inverter (qZSI) is one of the most promising power electronics converter topologies suitable for traction applications. The thermal stress in power modules is one of the most important causes of their failure, which is not considered during the control of qZSI drive. Thus, this paper proposes a thermal stress reduction scheme for qZSI drive, which utilizes finite control set model predictive control. The cost function is designed by including terms of switching counts, number of cycles to failure and inverter constraints in addition to the currents and capacitor voltage. This allows one to achieve the minimum thermal stress for the best possible overall performance of qZSI drive. The approach is proved using simulation and experimental results.
1. Introduction The ever-increasing peak torque and power density requirements of electric drives push the limits of inverter, while demands on reliability are getting increasingly stringent as well [1]. Power devices are considered to be the most fragile components in a drive system [2]. Further, an important cause of aging and failures of these devices is the thermal cycles [3]. New developments such as system and control strategy are necessary to improve reliability. Only limited research has been carried out to reduce the thermal cycling with junction temperature control of the semiconductors, also called active thermal control (ATC). Different control variables such as the switching frequency, modulation method, output current and the DC-link voltage are chosen to regulate the losses and junction temperatures [4, 5]. However, these approaches are performed with the reliability-system performance or efficiency trade-off [6, 7]. In [6], the amplitude of the thermal cycles is reduced by lowering the motor/inverter current amplitude limit. However, ATC by means of regulating the current control limit benefits lifetime on the one hand, but implies a restriction of system performance. The lifetime extension of the converter by means of ATC may lead to a problem of increased loss and reduced efficiency. In a study case [7], the lifetime of a power converter is increased by 39% at the expense of 9.7% higher losses. Model predictive control (MPC) has found successful in industry control process applications for more than 30 years. Nowadays, the
⁎
Corresponding author at: Hunan University, Changsha, China. E-mail address: [email protected] (P. Liu).
https://doi.org/10.1016/j.microrel.2018.06.068 Received 31 May 2018; Accepted 25 June 2018
0026-2714/ © 2018 Elsevier Ltd. All rights reserved.
finite control-set model predictive control (FCS-MPC) is becoming more and more widely applied in power converters and electrical drives [8–10]. It presents several advantages. For instance, it allows for nonlinearities and multiple control objectives to be incorporated into the control law in a straightforward manner. The quasi-z-source inverter (qZSI) has attracted much attention for motor drives and renewable energy applications due to its numerous advantages, such as capability to boost or buck in a single converter stage, and improved inverter reliability [11, 12]. Recently, FCS-MPC becomes to integrate in quasi-Z-source inverters for controlling of both DC side by the capacitor voltage and inductor current control and AC side control [13–16]. Research efforts have been made in the topics of prediction model, cost function that considers the qZSI inductor current, the dc capacitor voltage, and the three-phase output currents. The existing research work is performed to improve the performance in terms of fast dynamics and high accuracy in steady state, whereas the thermal stress and lifetime of the module of qZSI are still open issues to be investigated. This paper presents a modified FCS-MPC to reduce the thermal stress of qZSI. It can reduce thermal stress in a power module meanwhile fulfilling the applications demand. It allows an optimal control of every switching event and including of qZSI model and thermal model into the control law.
Microelectronics Reliability 88–90 (2018) 1247–1250
P. Liu et al.
Gate control
Gate driver
Load current
MPC control law Cost function minimization 1. Compute costs 2. Minimize costs 3. Apply switch action
S
Physical system (e.g. inverter, load)
=
≈
System control
Switching frequency
Constraints
Power converters
Modulation control
Modulation scheme
References
Predictive model (e.g. electrical, heat)
Load
DC-link voltage Fig. 2. Block diagram of the MPC scheme. Fig. 1. Active thermal control possibilities.
2. Basics of ATC and MPC 2.1. ATC Power electronic system reliability is typically constrained by the thermal stress so by the overall losses. It is well known that the power losses in any semiconductor can be mainly expressed as the sum of the switching losses and conduction losses. The switching losses are the product of switching energies of the device and the switching frequency. And the conduction losses can be expressed as function of conducting current. Thus the power losses can be changed via the control of the amplitude of the current, the switching frequency and switching energies. ATC is used to actively regulate the power losses [4]. There are several possibilities to apply ATC approaches [4–7], which is summarized in Fig. 1. Active gate control can directly influence the conduction and switching losses of the semiconductors. Another way to control loss can be the modulation control. The thermal stress of the devices can be reduced by applying the optimized modulation scheme or lowing the switching frequency. System control can also be applied to control the power loss and thermal loading of power devices. It can be realized by changing the DC-link voltage or the maximum current limit. The potential of the various ATC approaches is highly dependent on the applications [5]. For the application in electric drives, the gate driver and the switching frequency control are promising since they can have an immediate effect. The modulation is limited in this application. The control of the dc-link is only feasible if it can be adjusted. The control of the load current in this application implies a limitation of performance of the drive system.
Fig. 3. Control structure of a qZSI-fed drive system. TH is the heatsink temperature which is used to estimates the junction temperature.
possible to obtain the desired electrical and thermal behavior of the system by including the electrical and thermal information in the system model, and defining the cost function. 3. Thermal stress based MPC for qZSI The overall control scheme of the qZSI drive system is shown in Fig. 3. The proposed FCS-MPC is applied to achieve output current, qZSI capacitor voltage and ATC. The motor speed is controlled in a field oriented control scheme using a PI controller. Compared to present ATC, this algorithm offers the possibility to apply an optimal space vector directly to the qZSI system as no modulator is used in this nonlinear control structure of MPC. Then the fatigue of power module can be lowered by reducing the thermal stress.
2.2. MPC The working principle of MPC is based on the prediction of the system behavior using a linear/nonlinear model of it and the optimization of the cost function to fulfill the control objectives. Since the MPC is easy to include non-linearities in the model and meet with multiple control goals, this algorithm is an attractive, and competitive alternative for the control of power electronics and electrical drives [9]. The algorithm starts with the variable measurements at the beginning of the sampling time. Then it calculates the predicted variables using the system model. The controller outputs are computed by evaluation of a cost function based on this prediction. Fig. 2 shows the general structure of MPC. MPC offers high flexibility to control different converter topologies and to manage several control objectives, without adding significant complexity. For example: if the load or converter changes, only the model or switching states must be modified, and if the control objective changes, only the cost function must be adapted accordingly. Thus, it is
3.1. Electrical predictive model 3.1.1. Predictive model for qZSI The predicted capacitor voltage and inductor current of the impedance network [15] has been applied in this work. The variables of capacitor voltage and inductor current are then predicted with the measured present variables. Then, the optimization during which the optimal switching state is chosen is performed to minimize the cost function. 3.1.2. Predictive model for electrical machine Permanent magnet synchronous motors (PMSMs) present several characteristics that make them very attractive for drive applications. In this study, the machine control is implemented as a current control scheme, where the current references are generated by the external 1248
Microelectronics Reliability 88–90 (2018) 1247–1250
P. Liu et al.
Fig. 6. Experimental setup.
Fig. 4. Online junction temperature estimation model for MPC. Table 1 System parameters. qZSI parameter
Value
PMSM parameter
Value
Vin L1, L2 RL1, RL2 C1, C2
310 V 500 μH 0.01 Ω 400 μF
Rated power Rated speed Rated torque Pole pairs
11 kW 1500 rpm 70 Nm 2
speed PI controller. The machine equations in [9] is adopted for predicting the stator currents components for different voltage vectors generated by the inverter. 3.2. Junction temperature and lifetime estimation The junction temperature estimation is based on power loss calculations and thermal model of the power module. Due to variable switching frequency in FCS-MPC, the existing electro-thermal model described in PWM based control systems is not applicable. Fig. 4 presents a modified junction temperature estimation model. The IGBT conduction loss can be calculated using the collector current ic and the collector-emitter voltage vce which can be described by ic and junction temperature Tj using the characteristic curves shown in the datasheet of IGBT power module—Infineon FS50R12KT3. Thus the conduction loss as a function of ic can easily be approximated with Eq. (1). Note that the conduction current can be derived from the switching signals and the measured output currents iabc.
Pc,IGBT (ic , Tj ) = 1.65 × 10−2⋅ic2 + 0.7⋅ic + 5 × 10−5⋅ic⋅Tj
Fig. 7. Experimental results of average switching frequency and speed, (a) without thermal control, (b) with proposed control.
IGBT switching energy losses Eon and Eoff are provided in datasheet graphs as a function of current at reference vce with 600 V.
(1)
Eon (ic ) = 4 × 10−7⋅ic2 + 7 × 10−5⋅ic + 5.3 × 10−4
Fig. 5. Simulation of a qZSI drive. (a) without thermal control, (b) with proposed control. 1249
(2)
Microelectronics Reliability 88–90 (2018) 1247–1250
P. Liu et al.
is implemented on a control board with a Texas Instruments TMS320F28335 DSP. Fig. 6 presents the experimental setup. The thermal optimized FCS-MPC is applied to reduce the thermal stress in a power module during acceleration of a qZSI drive. The experimental results obtained from the conventional FCS-MPC and the proposed control scheme are shown in Figs. 7–8. The speed and average switching frequency measured by an oscilloscope are obtained from D/ A of DSP board. The negative thermal coefficient (NTC) thermistor built-in FS50R12KT3 is used for the module temperature measurement. It is used to validate the proposed thermal optimization by FCS-MPC. From Figs. 7–8, the proposed control results in significant decrease of the average switching frequency during acceleration. This reduces the power losses, and therefore a lower temperature.
Fig. 8. Measurement of NTC's temperatures during acceleration of a 4.5 kW PMSM motor under light mechanical load.
Eoff (ic ) = (−1.948 × 10−7)⋅ic2 + 1.212 × 10−4⋅ic − 1.938 × 10−5
(3)
5. Conclusions
Note that these equations are only valid if switching occurred. If not, switching loss falls to zero. The well-known Coffin–Manson–Arrhenius model [17] is selected in this paper to estimate the module's lifetime. The number of cycles to failure Nf is described in dependency of the amplitude of thermal cycles ΔTj and the mean temperature Tj, mean.
α = −5.039, where, coefficients A = 3.025 × 10 , Ea = 9.891 × 10−20 J, and kB is the Boltzmann constant.
This paper has proposed a thermal stress reduction method of a qZSI drive by FCS-MPC. The information of switching counts, number of cycles to failure and inverter constraints are considered in the MPC cost function optimization. Thanks to the proposed approach, a reduction of thermal stress in the power module of qZSI has been achieved to improve the lifetime and the reliability of the qZSI drive. The simulation and experiments are performed to validate the thermal stress reduction method. The results show that, the junction temperature could be reduced by 10 K with the proposed method.
3.3. Cost function design
Acknowledgements
The cost function for the proposed MPC with reduced thermal stress is designed in the following. It includes terms for the current reference error, capacitor voltage reference error, switching counts, number of cycles to failure and inverter constraints.
This research has received funding from the Provincial Strategic Emerging Industries Scientific and Technological Researches and Major Scientific and Technological Achievement Transformation Project (2017GK4020), and from the National Natural Science Foundation of China (51507055).
Nf = A⋅(ΔTj )α ⋅exp(Ea/(kB⋅Tj, mean ))
(4) 5
g(x) = λi (|id∗ − id (k + 1)| + |iq∗ − iq (k + 1)|) + λ vc ⋅|vc∗ − vc1 (k + 1)| 6
+ λn ∑
l=1
References
|Sl (k ) − Sl (k − 1)|2 + λNf ⋅Nf −1 (k + 1) + g i max + g Tj max (5)
[1] E. Ali, Y.J. Lee, K. Rajashekara, Power electronics and motor drives in electric, hybrid electric, and plug-in hybrid electric vehicles, IEEE Trans. Ind. Electron. 55 (6) (2008) 2237–2245. [2] Y.T. Song, B.S. Wang, Survey on reliability of power electronic systems, IEEE Trans. Power Electron. 28 (1) (2013) 591–604. [3] H. Wang, M. Liserre, F. Blaabjerg, Toward reliable power electronics: challenges, design tools, and opportunities, IEEE Ind. Electron. Mag. 7 (2) (2013) 17–26. [4] J. Torres Murdock, J. Connors, R. Lorenz, Active thermal control of power electronic modules, IEEE Ind. Appl. 42 (2) (March 2006) 552–558. [5] M. Andresen, K. Ma, G. Buticchi, J. Falck, F. Blaabjerg, M. Liserre, Junction temperature control for more reliable power electronics, IEEE Trans. Power Electron. 33 (1) (2018) 765–776 (D). [6] J. Lemmens, P. Vanassche, J. Driesen, Optimal control of traction motor drives under electrothermal constraints, IEEE J Emerg. Sel. Top Power Electron. 2 (2) (2014) 249–263. [7] M. Andresen, B. Giampaolo, M. Liserre, Study of reliability-efficiency tradeoff of active thermal control for power electronic systems, Microelectron. Reliab. 58 (2016) 119–125. [8] J. Falck, Markus M. Andresen, M. Liserre, Thermal-based finite control set model predictive control for IGBT power electronic converters, Proc. ECCE 2016 IEEE, 2016, pp. 1–7. [9] J. Rodriguez, C. Patricio, Predictive Control of Power Converters and Electrical Drives, John Wiley & Sons, 2012. [10] S. Kouro, M. Perez, J. Rodriguez, A. Llor, H. Young, Model predictive control: Mpc's role in the evolution of power electronics, IEEE Ind. Electron. Mag. 9 (4) (Dec 2015) 8–21. [11] Y. Liu, H. Abu-Rub, B. Ge, F. Blaabjerg, O. Ellabban, P.C. Loh, Impedance Source Power Electronic Converters, John Wiley & Sons, 2016. [12] O. Ellabban, H. Abu-Rub, An overview for the Z-source converter in motor drive applications, Renew. Sust. Energ. Rev. 61 (2016) 537–555. [13] A. Ayad, P. Karamanakos, R. Kennel, Direct model predictive current control strategy of quasi-Z-source inverters, IEEE Trans. Power Electron. 32 (7) (July 2017) 5786–5801. [14] Y. Liu, H.A. Abu-Rub, Y. Xue, F. Tao, A discrete-time average model based predictive control for quasi-Z-source inverter, IEEE Trans. Ind. Electron. 99 (2017) (1-1). [15] M. Mosa, R.S. Balog, H. Abu-Rub, High-performance predictive control of quasi-impedance source inverter, IEEE Trans. Power Electron. 32 (4) (April 2017) 3251–3262. [16] A. Bakeer, M.A. Ismeil, M. Orabi, A powerful finite control set-model predictive control algorithm for quasi Z-source inverter, IEEE Trans. Ind. Inform. 12 (4) (Aug. 2016) 1371–1379. [17] F. Blaabjerg, K. Ma, D. Zhou, Power electronics and reliability in renewable energy systems, Proc. ISIE, 2012, pp. 19–30. [18] P. Liu, H.P. Liu, Permanent-magnet synchronous motor drive system for electric vehicles using bidirectional z-source inverter, IET Electron. Syst. Transport. (2012) 178–185.
where, id∗ is the reference d-axis current, which is set to 0, as in [18], iq∗ is the reference q-axis current, vc∗ is the capacitor voltage reference, which is equal to twice the motor phase peak voltage value, Sl is the switching state of IGBT l in the module, and λi, λvc, λn, λNf are weighting factors. The last two terms of the cost function are constraints to safeguard inverter from excessive current and temperature amplitudes. If a constraint occurs, the value of the cost function is set to infinity, then all switches of the inverter must be turned off.
∞ |iabc | > i max g i max = ⎧ ⎨ else ⎩0
(6)
∞ Tj, l > Tj max g Tj max = ⎧ ⎨ else ⎩0
(7)
4. Simulation and experimental verification Simulation and experimental verification are implemented in this section. The control scheme is shown in Fig. 3. The system parameters applied in both simulation and experiments are given in Table 1. An FS50R12KT3 power module is employed. Fig. 5 shows the simulation results for qZSI drive with and without thermal stress based MPC control. It can be seen that, in the proposed control, the number of counts of switching and average switching frequency are significantly reduced, and the thermal cycle amplitude shows a 10 K reduction. To validate the reduction of the thermal stress by using the proposed algorithm, it has been applied on a three-phase qZSI drive. The control 1250
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Thermal stress reduction of quasi-Z source inverter drive by model predictive control
T
⁎
Ping Liua,b, , Huai Wangb, Yi Liub,c, Frede Blaabjergb a
Hunan University, Changsha, China Aalborg University, Aalborg 9220, Denmark c Wuhan University, Wuhan, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Thermal stress Model predictive control Inverter
The quasi-Z source inverter (qZSI) is one of the most promising power electronics converter topologies suitable for traction applications. The thermal stress in power modules is one of the most important causes of their failure, which is not considered during the control of qZSI drive. Thus, this paper proposes a thermal stress reduction scheme for qZSI drive, which utilizes finite control set model predictive control. The cost function is designed by including terms of switching counts, number of cycles to failure and inverter constraints in addition to the currents and capacitor voltage. This allows one to achieve the minimum thermal stress for the best possible overall performance of qZSI drive. The approach is proved using simulation and experimental results.
1. Introduction The ever-increasing peak torque and power density requirements of electric drives push the limits of inverter, while demands on reliability are getting increasingly stringent as well [1]. Power devices are considered to be the most fragile components in a drive system [2]. Further, an important cause of aging and failures of these devices is the thermal cycles [3]. New developments such as system and control strategy are necessary to improve reliability. Only limited research has been carried out to reduce the thermal cycling with junction temperature control of the semiconductors, also called active thermal control (ATC). Different control variables such as the switching frequency, modulation method, output current and the DC-link voltage are chosen to regulate the losses and junction temperatures [4, 5]. However, these approaches are performed with the reliability-system performance or efficiency trade-off [6, 7]. In [6], the amplitude of the thermal cycles is reduced by lowering the motor/inverter current amplitude limit. However, ATC by means of regulating the current control limit benefits lifetime on the one hand, but implies a restriction of system performance. The lifetime extension of the converter by means of ATC may lead to a problem of increased loss and reduced efficiency. In a study case [7], the lifetime of a power converter is increased by 39% at the expense of 9.7% higher losses. Model predictive control (MPC) has found successful in industry control process applications for more than 30 years. Nowadays, the
⁎
Corresponding author at: Hunan University, Changsha, China. E-mail address: [email protected] (P. Liu).
https://doi.org/10.1016/j.microrel.2018.06.068 Received 31 May 2018; Accepted 25 June 2018
0026-2714/ © 2018 Elsevier Ltd. All rights reserved.
finite control-set model predictive control (FCS-MPC) is becoming more and more widely applied in power converters and electrical drives [8–10]. It presents several advantages. For instance, it allows for nonlinearities and multiple control objectives to be incorporated into the control law in a straightforward manner. The quasi-z-source inverter (qZSI) has attracted much attention for motor drives and renewable energy applications due to its numerous advantages, such as capability to boost or buck in a single converter stage, and improved inverter reliability [11, 12]. Recently, FCS-MPC becomes to integrate in quasi-Z-source inverters for controlling of both DC side by the capacitor voltage and inductor current control and AC side control [13–16]. Research efforts have been made in the topics of prediction model, cost function that considers the qZSI inductor current, the dc capacitor voltage, and the three-phase output currents. The existing research work is performed to improve the performance in terms of fast dynamics and high accuracy in steady state, whereas the thermal stress and lifetime of the module of qZSI are still open issues to be investigated. This paper presents a modified FCS-MPC to reduce the thermal stress of qZSI. It can reduce thermal stress in a power module meanwhile fulfilling the applications demand. It allows an optimal control of every switching event and including of qZSI model and thermal model into the control law.
Microelectronics Reliability 88–90 (2018) 1247–1250
P. Liu et al.
Gate control
Gate driver
Load current
MPC control law Cost function minimization 1. Compute costs 2. Minimize costs 3. Apply switch action
S
Physical system (e.g. inverter, load)
=
≈
System control
Switching frequency
Constraints
Power converters
Modulation control
Modulation scheme
References
Predictive model (e.g. electrical, heat)
Load
DC-link voltage Fig. 2. Block diagram of the MPC scheme. Fig. 1. Active thermal control possibilities.
2. Basics of ATC and MPC 2.1. ATC Power electronic system reliability is typically constrained by the thermal stress so by the overall losses. It is well known that the power losses in any semiconductor can be mainly expressed as the sum of the switching losses and conduction losses. The switching losses are the product of switching energies of the device and the switching frequency. And the conduction losses can be expressed as function of conducting current. Thus the power losses can be changed via the control of the amplitude of the current, the switching frequency and switching energies. ATC is used to actively regulate the power losses [4]. There are several possibilities to apply ATC approaches [4–7], which is summarized in Fig. 1. Active gate control can directly influence the conduction and switching losses of the semiconductors. Another way to control loss can be the modulation control. The thermal stress of the devices can be reduced by applying the optimized modulation scheme or lowing the switching frequency. System control can also be applied to control the power loss and thermal loading of power devices. It can be realized by changing the DC-link voltage or the maximum current limit. The potential of the various ATC approaches is highly dependent on the applications [5]. For the application in electric drives, the gate driver and the switching frequency control are promising since they can have an immediate effect. The modulation is limited in this application. The control of the dc-link is only feasible if it can be adjusted. The control of the load current in this application implies a limitation of performance of the drive system.
Fig. 3. Control structure of a qZSI-fed drive system. TH is the heatsink temperature which is used to estimates the junction temperature.
possible to obtain the desired electrical and thermal behavior of the system by including the electrical and thermal information in the system model, and defining the cost function. 3. Thermal stress based MPC for qZSI The overall control scheme of the qZSI drive system is shown in Fig. 3. The proposed FCS-MPC is applied to achieve output current, qZSI capacitor voltage and ATC. The motor speed is controlled in a field oriented control scheme using a PI controller. Compared to present ATC, this algorithm offers the possibility to apply an optimal space vector directly to the qZSI system as no modulator is used in this nonlinear control structure of MPC. Then the fatigue of power module can be lowered by reducing the thermal stress.
2.2. MPC The working principle of MPC is based on the prediction of the system behavior using a linear/nonlinear model of it and the optimization of the cost function to fulfill the control objectives. Since the MPC is easy to include non-linearities in the model and meet with multiple control goals, this algorithm is an attractive, and competitive alternative for the control of power electronics and electrical drives [9]. The algorithm starts with the variable measurements at the beginning of the sampling time. Then it calculates the predicted variables using the system model. The controller outputs are computed by evaluation of a cost function based on this prediction. Fig. 2 shows the general structure of MPC. MPC offers high flexibility to control different converter topologies and to manage several control objectives, without adding significant complexity. For example: if the load or converter changes, only the model or switching states must be modified, and if the control objective changes, only the cost function must be adapted accordingly. Thus, it is
3.1. Electrical predictive model 3.1.1. Predictive model for qZSI The predicted capacitor voltage and inductor current of the impedance network [15] has been applied in this work. The variables of capacitor voltage and inductor current are then predicted with the measured present variables. Then, the optimization during which the optimal switching state is chosen is performed to minimize the cost function. 3.1.2. Predictive model for electrical machine Permanent magnet synchronous motors (PMSMs) present several characteristics that make them very attractive for drive applications. In this study, the machine control is implemented as a current control scheme, where the current references are generated by the external 1248
Microelectronics Reliability 88–90 (2018) 1247–1250
P. Liu et al.
Fig. 6. Experimental setup.
Fig. 4. Online junction temperature estimation model for MPC. Table 1 System parameters. qZSI parameter
Value
PMSM parameter
Value
Vin L1, L2 RL1, RL2 C1, C2
310 V 500 μH 0.01 Ω 400 μF
Rated power Rated speed Rated torque Pole pairs
11 kW 1500 rpm 70 Nm 2
speed PI controller. The machine equations in [9] is adopted for predicting the stator currents components for different voltage vectors generated by the inverter. 3.2. Junction temperature and lifetime estimation The junction temperature estimation is based on power loss calculations and thermal model of the power module. Due to variable switching frequency in FCS-MPC, the existing electro-thermal model described in PWM based control systems is not applicable. Fig. 4 presents a modified junction temperature estimation model. The IGBT conduction loss can be calculated using the collector current ic and the collector-emitter voltage vce which can be described by ic and junction temperature Tj using the characteristic curves shown in the datasheet of IGBT power module—Infineon FS50R12KT3. Thus the conduction loss as a function of ic can easily be approximated with Eq. (1). Note that the conduction current can be derived from the switching signals and the measured output currents iabc.
Pc,IGBT (ic , Tj ) = 1.65 × 10−2⋅ic2 + 0.7⋅ic + 5 × 10−5⋅ic⋅Tj
Fig. 7. Experimental results of average switching frequency and speed, (a) without thermal control, (b) with proposed control.
IGBT switching energy losses Eon and Eoff are provided in datasheet graphs as a function of current at reference vce with 600 V.
(1)
Eon (ic ) = 4 × 10−7⋅ic2 + 7 × 10−5⋅ic + 5.3 × 10−4
Fig. 5. Simulation of a qZSI drive. (a) without thermal control, (b) with proposed control. 1249
(2)
Microelectronics Reliability 88–90 (2018) 1247–1250
P. Liu et al.
is implemented on a control board with a Texas Instruments TMS320F28335 DSP. Fig. 6 presents the experimental setup. The thermal optimized FCS-MPC is applied to reduce the thermal stress in a power module during acceleration of a qZSI drive. The experimental results obtained from the conventional FCS-MPC and the proposed control scheme are shown in Figs. 7–8. The speed and average switching frequency measured by an oscilloscope are obtained from D/ A of DSP board. The negative thermal coefficient (NTC) thermistor built-in FS50R12KT3 is used for the module temperature measurement. It is used to validate the proposed thermal optimization by FCS-MPC. From Figs. 7–8, the proposed control results in significant decrease of the average switching frequency during acceleration. This reduces the power losses, and therefore a lower temperature.
Fig. 8. Measurement of NTC's temperatures during acceleration of a 4.5 kW PMSM motor under light mechanical load.
Eoff (ic ) = (−1.948 × 10−7)⋅ic2 + 1.212 × 10−4⋅ic − 1.938 × 10−5
(3)
5. Conclusions
Note that these equations are only valid if switching occurred. If not, switching loss falls to zero. The well-known Coffin–Manson–Arrhenius model [17] is selected in this paper to estimate the module's lifetime. The number of cycles to failure Nf is described in dependency of the amplitude of thermal cycles ΔTj and the mean temperature Tj, mean.
α = −5.039, where, coefficients A = 3.025 × 10 , Ea = 9.891 × 10−20 J, and kB is the Boltzmann constant.
This paper has proposed a thermal stress reduction method of a qZSI drive by FCS-MPC. The information of switching counts, number of cycles to failure and inverter constraints are considered in the MPC cost function optimization. Thanks to the proposed approach, a reduction of thermal stress in the power module of qZSI has been achieved to improve the lifetime and the reliability of the qZSI drive. The simulation and experiments are performed to validate the thermal stress reduction method. The results show that, the junction temperature could be reduced by 10 K with the proposed method.
3.3. Cost function design
Acknowledgements
The cost function for the proposed MPC with reduced thermal stress is designed in the following. It includes terms for the current reference error, capacitor voltage reference error, switching counts, number of cycles to failure and inverter constraints.
This research has received funding from the Provincial Strategic Emerging Industries Scientific and Technological Researches and Major Scientific and Technological Achievement Transformation Project (2017GK4020), and from the National Natural Science Foundation of China (51507055).
Nf = A⋅(ΔTj )α ⋅exp(Ea/(kB⋅Tj, mean ))
(4) 5
g(x) = λi (|id∗ − id (k + 1)| + |iq∗ − iq (k + 1)|) + λ vc ⋅|vc∗ − vc1 (k + 1)| 6
+ λn ∑
l=1
References
|Sl (k ) − Sl (k − 1)|2 + λNf ⋅Nf −1 (k + 1) + g i max + g Tj max (5)
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where, id∗ is the reference d-axis current, which is set to 0, as in [18], iq∗ is the reference q-axis current, vc∗ is the capacitor voltage reference, which is equal to twice the motor phase peak voltage value, Sl is the switching state of IGBT l in the module, and λi, λvc, λn, λNf are weighting factors. The last two terms of the cost function are constraints to safeguard inverter from excessive current and temperature amplitudes. If a constraint occurs, the value of the cost function is set to infinity, then all switches of the inverter must be turned off.
∞ |iabc | > i max g i max = ⎧ ⎨ else ⎩0
(6)
∞ Tj, l > Tj max g Tj max = ⎧ ⎨ else ⎩0
(7)
4. Simulation and experimental verification Simulation and experimental verification are implemented in this section. The control scheme is shown in Fig. 3. The system parameters applied in both simulation and experiments are given in Table 1. An FS50R12KT3 power module is employed. Fig. 5 shows the simulation results for qZSI drive with and without thermal stress based MPC control. It can be seen that, in the proposed control, the number of counts of switching and average switching frequency are significantly reduced, and the thermal cycle amplitude shows a 10 K reduction. To validate the reduction of the thermal stress by using the proposed algorithm, it has been applied on a three-phase qZSI drive. The control 1250