Thermal impact analysis of circulating current in high power modular online uninterruptible power supplies application

In a modular uninterruptible power supplies (UPS), each DC/AC module was designed to work in a circular way considering the reliability and power stress issues of the whole system. Thus unsynchronized PWMs will occur if any of the DC/AC modules is plugged in or out of the system at any time. On the other hand, modular difference is another issue that will bring such kind of circulating current. In order to reduce system size and cost, each module shares the same DC and AC bus without any isolation or passive elements in the system. Consequently, potential zero-sequence current is possible to occur and should be paid specific attention. In this paper, a four-module online UPS system is designed. And thermal and loss distribution condition are investigated under different circulating current condition with conventional three phase H-bridge topology.


Introduction
Recently, more and more advanced technologies are entering human beings everyday life.A large number of modern electrical facilities, such as communication equipment, IT facilities, medical equipment, and so on, are widely used in both the industrial field and daily life [1].As a result, the utility suffers great challenges in order to provide a clean, continuous, and reliable electrical energy.On the other hand, with the prosperity of the renewable energy sources, more and more factories and offices tend to use a local smart utility system [2].However, renewable energy sources are unpredictable.This will have negative impacts on the power quality that they provide.Consequently, uninterruptible power supply (UPS) system is receiving more and more attention from both researchers and industrial application engineers [3].
Based on IEC 62040-3, UPS system is able to be divided into three categories, namely offline UPS system, line interactive UPS system, and online UPS system.Compared with the other two, online UPS system, also known as double conversion UPS system, mainly aims at high power application scenarios due to its outstanding capability in output voltage control and decoupling of the utility and the load [4,5].In order to improve UPS performance, a series of enhanced different online UPS structure is proposed in [6][7][8].Among them, the modular concept is drawing more and more attention due to its attractive flexibility and expansibility.Consequently, when the system is required to be maintained or has module failure, a modular online UPS system is still able to operate normally by replacing to stop the damaged module.
Normally a number of DC/AC modules operates in parallel and shares the same DC bus and AC bus (as shown in Figure 1a) in a typical modular online UPS system.Thus, possible paths for potential zero sequence circulating current exist (which is marked by red in Figure 1b).It still has negative impacts on losses and thermal distribution of the power semiconductor devices.The unbalanced losses and thermal distribution performances, especially in high power modular scenarios, are required to be investigated further, which can be a guidance concerning heat problems in designing the modular online UPS systems.In order to avoid such kinds of circulating current, a number of approaches are proposed, namely isolation [9][10][11], high impedance [12,13], synchronized issues [14][15][16][17], and active issues [18][19][20].Isolation and high impedance issues will add extra devices into the system, such as extra DC sources, transformers, or inter-phase reactors and these will increase the UPS system cost.As such, it is not a cost effective and volume effective issue.As a result, synchronization and active issues are considered hereby.
Energies 2017, 10, 50 2 of 11 required to be investigated further, which can be a guidance concerning heat problems in designing the modular online UPS systems.In order to avoid such kinds of circulating current, a number of approaches are proposed, namely isolation [9][10][11], high impedance [12,13], synchronized issues [14][15][16][17], and active issues [18][19][20].Isolation and high impedance issues will add extra devices into the system, such as extra DC sources, transformers, or inter-phase reactors and these will increase the UPS system cost.As such, it is not a cost effective and volume effective issue.As a result, synchronization and active issues are considered hereby.On the other hand, active power and reactive power of each of the DC/AC modules should be equally shared in order to minimize the active power circulating current.A number of parallel technologies have been proposed in [21][22][23][24][25][26], which can be categorized into two main types, namely communication based and communication-less.Since the mature digital signal processor (DSP) technology provides a smaller data transmit time delay, a communication based parallel technology is used here.By using virtual resistor and phase regulating methods, both active and reactive power are shared among all the modules.
In this paper, unsynchronized pulse width modulation (PWM) condition and physical parameters mismatch is considered since these two are more common in real applications.With the power devices thermal model proposed in [27], the thermal impedance of devices is edited in the simulation software PLECS.Thus, the temperature and losses of devices are able to be monitored to investigate the zero circulating current impacts on the losses and temperature of different power semiconductor devices.
This paper is organized as follows: Section 2 depicts the system control mechanism; Section 3 presents experimental results while the thermal analysis results are presented in Section 4; and Section 5 gives the final conclusion.

System Control Mechanism
As shown in Figure 1a, one three-phase AC/DC creates the DC bus for the DC/AC modules.Its control is considered in the conventional dq frame, which is descripted in [28] in detail.Several DC/AC modules are working in parallel and the detailed information for the modules is listed in Table 1.On the other hand, active power and reactive power of each of the DC/AC modules should be equally shared in order to minimize the active power circulating current.A number of parallel technologies have been proposed in [21][22][23][24][25][26], which can be categorized into two main types, namely communication based and communication-less.Since the mature digital signal processor (DSP) technology provides a smaller data transmit time delay, a communication based parallel technology is used here.By using virtual resistor and phase regulating methods, both active and reactive power are shared among all the modules.
In this paper, unsynchronized pulse width modulation (PWM) condition and physical parameters mismatch is considered since these two are more common in real applications.With the power devices thermal model proposed in [27], the thermal impedance of devices is edited in the simulation software PLECS.Thus, the temperature and losses of devices are able to be monitored to investigate the zero circulating current impacts on the losses and temperature of different power semiconductor devices.
This paper is organized as follows: Section 2 depicts the system control mechanism; Section 3 presents experimental results while the thermal analysis results are presented in Section 4; and Section 5 gives the final conclusion.

System Control Mechanism
As shown in Figure 1a, one three-phase AC/DC creates the DC bus for the DC/AC modules.Its control is considered in the conventional dq frame, which is descripted in [28] in detail.Several DC/AC modules are working in parallel and the detailed information for the modules is listed in Table 1.
with k pv , k rv , ω o , k hrv , h, k pc , k rc , and k hrc being the voltage proportional term, fundamental frequency voltage resonant term, fundamental frequency, the hth harmonic voltage compensation term, harmonic order, current proportional term, fundamental frequency current resonant term, and the hth harmonic current compensation term, respectively.Two typical PRs are used due to its harmonic compensation capability.

Power Balance among Modules
As mentioned in [24], if the output impedance of the DC/AC modules is designated to be mainly resistive, the active power and reactive power that each DC/AC module injects into the AC bus are able to be regulated by voltage amplitude and phase, respectively, thus a virtual resistor and phase regulating loop are inserted into the control loop: Here n is the number of DC/AC module (1, 2, 3, . . ., N), k is the phase order (a, b, c), V nkref is the nominal voltage reference, Z vir is the virtual resistor, δ nkref is the nominal phase reference, k ph is the phase regulating coefficients, and Q nk is the reactive power of each phase of each DC/AC module.

Voltage Amplitude and Phase Synchronized
By measuring AC critical bus voltage, two typical Proportional Integrator (PI) controllers are used to keep online UPS output voltage tightly synchronized with the utility: with k pv_rec , k iv_rec , k pδ_rec , and k iδ_rec being voltage amplitude recovery proportional term, voltage amplitude recovery integral term, phase recover proportional term, and phase recover integral term, respectively.The overall control diagram is shown in Figure 2a.

Cycle and Plug'n'Play Control
The modular online UPS system is designed to be flexible, which means that any of the DC/AC modules can be plugged into or out of the system randomly due to module failure or maintenance reasons.Thus, some voltage overshoot or sag will occur in the AC critical bus, and this requires a control that can suppress the voltage overshoot or sag in a short transient time.In the standard IEC 62040-3, detailed requirements are included for the transient performance for an online UPS system, which is shown in Table 2.
Energies 2017, 10, 50 4 of 11 62040-3, detailed requirements are included for the transient performance for an online UPS system, which is shown in Table 2.

Load Type Voltage Variation (%) Dynamic Time Requirement (ms)
Linear Load It can be seen that with a smaller voltage overshoot or sag, the transient time for the system can be a little longer.While designing the system, the overshoot or sag should be guaranteed that its amplitude should be controlled small as 10% compared with the nominal critical bus voltage amplitude.Thus, less stress will be put on the transient performance of the controller.
On the other hand, another reason for using modular UPS structure is that modules can operate in turns in order to allow all modules to be maintained or repaired equally, as shown in Figure 2b.When one of the modules disconnects with the AC critical bus, another module that has already finished the maintenance will start to connect with the AC critical bus at the same time in a fixed sequence, called Normal Cycle (NC).As a result, there is voltage transient during this process, which should be paid specific attention.Normally, such a cycle duration time is quite long in real applications, for instance, routinely numbering in the hours.However, in case of an emergency condition, such as module failures, the fixed sequence is interrupted and it will have a much shorter cycle duration time, which is called Emergency Cycle (EC).
Such kinds of plug'n'play modules will result in PWM unsynchronized problems, which will cause strong potential zero sequence circulating current.In addition, although each module is designated to be the same, they still have many differences, such as filter inductors, capacitance, control parameters, and so on.These things will also provide the possibility for the zero sequence circulating current to occur.

Experimental Results
An experimental setup was built in the MicroGrid Intelligent Lab

Load Type Voltage Variation (%) Dynamic Time Requirement (ms)
Linear Load It can be seen that with a smaller voltage overshoot or sag, the transient time for the system can be a little longer.While designing the system, the overshoot or sag should be guaranteed that its amplitude should be controlled small as 10% compared with the nominal critical bus voltage amplitude.Thus, less stress will be put on the transient performance of the controller.
On the other hand, another reason for using modular UPS structure is that modules can operate in turns in order to allow all modules to be maintained or repaired equally, as shown in Figure 2b.When one of the modules disconnects with the AC critical bus, another module that has already finished the maintenance will start to connect with the AC critical bus at the same time in a fixed sequence, called Normal Cycle (NC).As a result, there is voltage transient during this process, which should be paid specific attention.Normally, such a cycle duration time is quite long in real applications, for instance, routinely numbering in the hours.However, in case of an emergency condition, such as module failures, the fixed sequence is interrupted and it will have a much shorter cycle duration time, which is called Emergency Cycle (EC).
Such kinds of plug'n'play modules will result in PWM unsynchronized problems, which will cause strong potential zero sequence circulating current.In addition, although each module is designated to be the same, they still have many differences, such as filter inductors, capacitance, control parameters, and so on.These things will also provide the possibility for the zero sequence circulating current to occur.

Experimental Results
An experimental setup was built in the MicroGrid Intelligent Lab [28].Four Danfoss converters were used.One of them works as AC/DC while the other three are working as the DC/AC modules.A control system was established in Matlab/Simulink and complied into the dSpace 1006 to achieve the real time control for the experimental setup.

Modules Plug'n'Play Performance
Hereby, one of the modules connected and disconnected with the AC critical bus in order to test the proposed control transient performance.Active and reactive power performance was monitored on the control desk in PC while the voltage real time performance was observed in scope.
At t 1 , one module was plugging out of the system and both reactive and active power was well shared among the other two modules.At t 2 , it plugged into the system again and the power was equally shared among the three modules, as shown in Figure 3a,b.
Energies 2017, 10, 50 5 of 11 A control system was established in Matlab/Simulink and complied into the dSpace 1006 to achieve the real time control for the experimental setup.

Modules Plug'n'Play Performance
Hereby, one of the modules connected and disconnected with the AC critical bus in order to test the proposed control transient performance.Active and reactive power performance was monitored on the control desk in PC while the voltage real time performance was observed in scope.
At t1, one module was plugging out of the system and both reactive and active power was well shared among the other two modules.At t2, it plugged into the system again and the power was equally shared among the three modules, as shown in Figure 3a,b.

Cycle Control Transient Performance
The transient performance, when two DC/AC modules were switched, is presented in Figure 3c.In real applications, supervisory control monitors the operating condition of each of the DC/AC modules to decide operating rules.At t3, module #3 was ordered to disconnect and rest for maintenance and module #2 was required to start working again in order to avoid overloading of the other modules, and at t4, module #2 and #3 were switched for the second time.It can be observed that both active power and reactive power were well shared among the remaining modules.
The voltage detail at t3 and t4 is shown in Figure 4a,b.The voltage overshoot can be calculated through the scope, which is Δv = (620 − 570) V/570 V = 8.77% or (610 − 560) V/560 V = 8.92%.This value is below 10%, and the transient time is about three and a half utility periods (i.e., 70 ms), which is faster than 100 ms.

Cycle Control Transient Performance
The transient performance, when two DC/AC modules were switched, is presented in Figure 3c.In real applications, supervisory control monitors the operating condition of each of the DC/AC modules to decide operating rules.At t 3 , module #3 was ordered to disconnect and rest for maintenance and module #2 was required to start working again in order to avoid overloading of the other modules, and at t 4 , module #2 and #3 were switched for the second time.It can be observed that both active power and reactive power were well shared among the remaining modules.
The voltage detail at t 3 and t 4 is shown in Figure 4a,b.The voltage overshoot can be calculated through the scope, which is ∆v = (620 − 570) V/570 V = 8.77% or (610 − 560) V/560 V = 8.92%.This value is below 10%, and the transient time is about three and a half utility periods (i.e., 70 ms), which is faster than 100 ms.

Thermal Analysis Results
The thermal condition of power devices is an important issue that should be taken into consideration.It is tightly related with the cooling system of each DC/AC module, especially in high power application scenarios.Based on the thermal model shown in Figure 5, the thermal impedance from junction to case Z(j-c) is able to be treated as a four layer resistor-cpacitor (RC) network.For a specific power device, the information can be found in the manufacture datasheet.Since the thermal capacitance is mainly related with the dynamic process before steady state [29], big thermal capacitance of ZT/D(c-h) and Z(h-a) can be neglected in order to achieve a faster simulation.Based on the module information shown in Table 1, the IGBT pack 5SND-0800M170100 from ABB was chosen for the power semiconductor devices, whose thermal information is shown in Table 3 [30].With PLECS, the thermal impedance model of IGBT pack 5SND-0800M170100 can be edited in simulation.Thus, thermal information, including losses and temperature can be monitored.In [31], it mentions that normally DC/AC modules are designed to work in the load condition from 50% to

Thermal Analysis Results
The thermal condition of power devices is an important issue that should be taken into consideration.It is tightly related with the cooling system of each DC/AC module, especially in high power application scenarios.Based on the thermal model shown in Figure 5, the thermal impedance from junction to case Z (j-c) is able to be treated as a four layer resistor-cpacitor (RC) network.For a specific power device, the information can be found in the manufacture datasheet.Since the thermal capacitance is mainly related with the dynamic process before steady state [29], big thermal capacitance of Z T/D(c-h) and Z (h-a) can be neglected in order to achieve a faster simulation.

Thermal Analysis Results
The thermal condition of power devices is an important issue that should be taken into consideration.It is tightly related with the cooling system of each DC/AC module, especially in high power application scenarios.Based on the thermal model shown in Figure 5, the thermal impedance from junction to case Z(j-c) is able to be treated as a four layer resistor-cpacitor (RC) network.For a specific power device, the information can be found in the manufacture datasheet.Since the thermal capacitance is mainly related with the dynamic process before steady state [29], big thermal capacitance of ZT/D(c-h) and Z(h-a) can be neglected in order to achieve a faster simulation.Based on the module information shown in Table 1, the IGBT pack 5SND-0800M170100 from ABB was chosen for the power semiconductor devices, whose thermal information is shown in Table 3 [30].With PLECS, the thermal impedance model of IGBT pack 5SND-0800M170100 can be edited in simulation.Thus, thermal information, including losses and temperature can be monitored.In [31], it mentions that normally DC/AC modules are designed to work in the load condition from 50% to Based on the module information shown in Table 1, the IGBT pack 5SND-0800M170100 from ABB was chosen for the power semiconductor devices, whose thermal information is shown in Table 3 [30].With PLECS, the thermal impedance model of IGBT pack 5SND-0800M170100 can be edited in simulation.Thus, thermal information, including losses and temperature can be monitored.In [31], it mentions that normally DC/AC modules are designed to work in the load condition from 50% to 75%.As such, in the analysis, the load condition is considered from 50% to 100%, and losses and temperature information of T 1 , T 2 , D 1 , and D 2 are discussed.

Single DC/AC Module
In order to compare with the modular UPS system, a single DC/AC module was simulated.Figure 6a,b presents the devices temperature and losses.It can be seen that the losses and temperature are distributed nearly balanced between T 1 and T 2 , and D 1 and D 2 .
Another critical parameter, namely the temperature fluctuation amplitude of the devices, is also important for power semiconductor devices.In Figure 6c,d, it can be observed that T 1 and T 2 share nearly the same temperature fluctuation amplitude, and a similar result can be seen for D 1 and D 2 .Figure 6e shows the steady state temperature information in 100% load condition.

Single DC/AC Module
In order to compare with the modular UPS system, a single DC/AC module was simulated.Figure 6a,b presents the devices temperature and losses.It can be seen that the losses and temperature are distributed nearly balanced between T1 and T2, and D1 and D2.
Another critical parameter, namely the temperature fluctuation amplitude of the devices, is also important for power semiconductor devices.In Figure 6c,d, it can be observed that T1 and T2 share nearly the same temperature fluctuation amplitude, and a similar result can be seen for D1 and D2. Figure 6e shows the steady state temperature information in 100% load condition.

DC/AC Modules with Zero Sequence Circulating Current
In this condition, an unsynchronized PWM was given to the three DC/AC modules.Moreover, each module filter inductor was given a 30% difference to emulate the manufacturer difference.The control parameters were also different among different modules.Thus, an obvious circulating current can be observed, as shown in Figure 7a.It can be seen that there is some DC component; this is because both physical and control parameters differences will result in a small amount of active power circulating current.

DC/AC Modules with Zero Sequence Circulating Current
In this condition, an unsynchronized PWM was given to the three DC/AC modules.Moreover, each module filter inductor was given a 30% difference to emulate the manufacturer difference.The control parameters were also different among different modules.Thus, an obvious circulating current can be observed, as shown in Figure 7a.It can be seen that there is some DC component; this is because both physical and control parameters differences will result in a small amount of active power circulating current.

Single DC/AC Module
In order to compare with the modular UPS system, a single DC/AC module was simulated.Figure 6a,b presents the devices temperature and losses.It can be seen that the losses and temperature are distributed nearly balanced between T1 and T2, and D1 and D2.
Another critical parameter, namely the temperature fluctuation amplitude of the devices, is also important for power semiconductor devices.In Figure 6c,d, it can be observed that T1 and T2 share nearly the same temperature fluctuation amplitude, and a similar result can be seen for D1 and D2. Figure 6e shows the steady state temperature information in 100% load condition.

DC/AC Modules with Zero Sequence Circulating Current
In this condition, an unsynchronized PWM was given to the three DC/AC modules.Moreover, each module filter inductor was given a 30% difference to emulate the manufacturer difference.The control parameters were also different among different modules.Thus, an obvious circulating current can be observed, as shown in Figure 7a.It can be seen that there is some DC component; this is because both physical and control parameters differences will result in a small amount of active power circulating current.Figure 8a,b shows the losses and temperature information of each module.It can be seen that they are distributed unbalanced.In all the three modules, T 1 has a higher loss and temperature than T 2 , and D 2 has a higher loss and temperature than D 1 .A similar trend is also observed for the temperature fluctuation amplitude and fluctuation amplitude difference of the devices, as shown in Figure 8c.In Figure 7b, the steady state temperature for devices in 100% load condition is presented.It can be seen that the temperature is distributed in an unbalanced way.Since the thermal impedance of the heat sink is smaller in scale, the difference is not too obvious.
Figure 8a,b shows the losses and temperature information of each module.It can be seen that they are distributed unbalanced.In all the three modules, T1 has a higher loss and temperature than T2, and D2 has a higher loss and temperature than D1.A similar trend is also observed for the temperature fluctuation amplitude and fluctuation amplitude difference of the devices, as shown in Figure 8c.In Figure 7b, the steady state temperature for devices in 100% load condition is presented.It can be seen that the temperature is distributed in an unbalanced way.Since the thermal impedance of the heat sink is smaller in scale, the difference is not too obvious.

DC/AC Modules with Suppressed Zero Sequence Circulating Current
Hereby, the zero sequence circulating current was suppressed.All the PWM for the three modules were synchronized, and zero vector operating time in the space vector modulation was tuned based on the active suppression method proposed in [18].The zero sequence circulating current is presented in Figure 9a.It can be seen that the zero sequence circulating current was suppressed to a small amount of value.Figure 10a shows the losses of each module.All three modules shared the same loss distribution condition that T2 has a higher loss and temperature than T1, and D1 had a higher loss and temperature than D2.Consequently, they had the same temperature results, as shown in Figure 10b.

DC/AC Modules with Suppressed Zero Sequence Circulating Current
Hereby, the zero sequence circulating current was suppressed.All the PWM for the three modules were synchronized, and zero vector operating time in the space vector modulation was tuned based on the active suppression method proposed in [18].The zero sequence circulating current is presented in Figure 9a.It can be seen that the zero sequence circulating current was suppressed to a small amount of value.Figure 10a shows the losses of each module.All three modules shared the same loss distribution condition that T 2 has a higher loss and temperature than T 1 , and D 1 had a higher loss and temperature than D 2 .Consequently, they had the same temperature results, as shown in Figure 10b.As for the temperature fluctuation amplitude, three modules shared the same changing pattern.ΔT2 first had a sudden increase at 90% load and then decreased.It was higher than ΔT1.ΔD1 decreased smoothly and was higher than ΔD2.The fluctuation difference also presented a similar trend, as shown in Figure 10c.
The detailed temperature information of the three modules at 100% load condition is shown in Figure 9b.It can be seen that the T2 had a higher loss and temperature than T1, and D1 had a higher loss and temperature than D2.

Conclusions
In this paper, the plug'n'play capability for a modular online UPS system was proposed and tested.Experimental results were provided to validate the proposed control steady and transient performance, which were able to meet the standard IEC 62040-3.Moreover, zero sequence circulating current impact on thermal and losses distribution of the power semiconductor devices was discussed.Through simulation results, it can be concluded that while operating in different kinds of conditions associated with circulating current, T1 had a higher temperature than T2 while D2 had a higher temperature than D1.In order to suppress zero sequence circulating current, synchronization issues As for the temperature fluctuation amplitude, three modules shared the same changing pattern.∆T 2 first had a sudden increase at 90% load and then decreased.It was higher than ∆T 1 .∆D 1 decreased smoothly and was higher than ∆D 2 .The fluctuation difference also presented a similar trend, as shown in Figure 10c.
The detailed temperature information of the three modules at 100% load condition is shown in Figure 9b.It can be seen that the T 2 had a higher loss and temperature than T 1 , and D 1 had a higher loss and temperature than D 2 .As for the temperature fluctuation amplitude, three modules shared the same changing pattern.ΔT2 first had a sudden increase at 90% load and then decreased.It was higher than ΔT1.ΔD1 decreased smoothly and was higher than ΔD2.The fluctuation difference also presented a similar trend, as shown in Figure 10c.
The detailed temperature information of the three modules at 100% load condition is shown in Figure 9b.It can be seen that the T2 had a higher loss and temperature than T1, and D1 had a higher loss and temperature than D2.

Conclusions
In this paper, the plug'n'play capability for a modular online UPS system was proposed and tested.Experimental results were provided to validate the proposed control steady and transient performance, which were able to meet the standard IEC 62040-3.Moreover, zero sequence circulating current impact on thermal and losses distribution of the power semiconductor devices was discussed.Through simulation results, it can be concluded that while operating in different kinds of conditions associated with circulating current, T1 had a higher temperature than T2 while D2 had a higher temperature than D1.In order to suppress zero sequence circulating current, synchronization issues

Conclusions
In this paper, the plug'n'play capability for a modular online UPS system was proposed and tested.Experimental results were provided to validate the proposed control steady and transient performance, which were able to meet the standard IEC 62040-3.Moreover, zero sequence circulating current impact on thermal and losses distribution of the power semiconductor devices was discussed.

Figure 1 .
Figure 1.Modular uninterruptible power supplies (UPSs) system architecture and circulating current path: (a) modular UPS system structure; and (b) circulating current flowing path.

Figure 1 .
Figure 1.Modular uninterruptible power supplies (UPSs) system architecture and circulating current path: (a) modular UPS system structure; and (b) circulating current flowing path.

Figure 2 .
Figure 2. Control mechanism for modular UPS system: (a) overall control; and (b) plug'n'play control mechanism.PWM: pulse width modulation.

Figure 2 .
Figure 2. Control mechanism for modular UPS system: (a) overall control; and (b) plug'n'play control mechanism.PWM: pulse width modulation.

Figure 3 .
Figure 3. Power performance: (a) one module plug out; (b) module plug in; and (c) cycle control.

Figure 3 .
Figure 3. Power performance: (a) one module plug out; (b) module plug in; and (c) cycle control.
temperature T A : Ambient temperature Z (j-c) : Thermal impedance form junction to case Z (c-h) : Thermal impedance from case to heat sink Z (h-a) : Thermal impedance from heat sink to ambient

Figure 4 .
Figure 4. Real time voltage waveform: (a) details at t 3 ; and (b) details at t 4 .

Figure 7 .
Figure 7. Circulating current and detailed temperature result with obvious circulating current: (a) three modules circulating current; and (b) detailed temperature in 100% load.

Figure 7 .
Figure 7. Circulating current and detailed temperature result with obvious circulating current: (a) three modules circulating current; and (b) detailed temperature in 100% load.

Figure 7 .
Figure 7. Circulating current and detailed temperature result with obvious circulating current: (a) three modules circulating current; and (b) detailed temperature in 100% load.

Figure 8 .
Figure 8. Thermal results of the modules with obvious circulating current flowing: (a) three module junction temperature; (b) devices losses; and (c) junction temperature differences.

Figure 8 .
Figure 8. Thermal results of the modules with obvious circulating current flowing: (a) three module junction temperature; (b) devices losses; and (c) junction temperature differences.

Figure 9 .
Figure 9. Circulating current and detailed temperature result without circulating current: (a) three modules circulating current; and (b) detailed temperature in 100% load.

Figure 10 .
Figure 10.Thermal results of the modules without obvious circulating current flowing: (a) three module device losses; (b) junction temperature; and (c) junction temperature differences.

Figure 9 .
Figure 9. Circulating current and detailed temperature result without circulating current: (a) three modules circulating current; and (b) detailed temperature in 100% load.

Figure 9 .
Figure 9. Circulating current and detailed temperature result without circulating current: (a) three modules circulating current; and (b) detailed temperature in 100% load.

Figure 10 .
Figure 10.Thermal results of the modules without obvious circulating current flowing: (a) three module device losses; (b) junction temperature; and (c) junction temperature differences.

Figure 10 .
Figure 10.Thermal results of the modules without obvious circulating current flowing: (a) three module device losses; (b) junction temperature; and (c) junction temperature differences.