System-wide Temperature Estimation for IMS based Power Electronics

PEDS2009

System-wide Temperature Estimation for IMS based Power Electronics Circuits J. D. Holmes, M. P. Foster and D. A. Stone Electrical Machines and Drives Group Dept. of Electrical and Electronic Engineering, The University of Sheffield Mappin Street, Sheffield, S1 3JD, UK and initial conditions. The latter approach has three key advantages over a discrete measurements: i) it can estimate temperatures inaccessible to practical measurement (i.e. internal component temperatures), ii) future temperatures can be estimated and extrapolated for the current operating conditions allowing for dynamic evasion of predicted undesirable operating conditions and iii) it is proposed that only a single temperature measurement is required to update a model estimating many temperatures in the system, cutting costs & physical complexity over a multisensor approach. These concepts are applicable to most high power density electronic systems viz. motor drives, inverters, AC-DC converters etc.

Abstract—An observer-based thermal modelling technique suitable for computation on embedded microprocessors to provide system wide prediction and projection of thermal state of function for a minimum increase in part count is proposed. High accuracy 3D finite element simulation is employed to calibrate a low complexity lumped parameter model from which a Luenberger observer is derived. Only a single temperature measurement from the system is required to close the Luenberger loop providing system temperature at critical locations. Whilst this approach is applicable to many power electronic systems, to give the paper focus, a practical AC-DC converter is considered and used to experimentally demonstrate the accuracy of the technique. Keywords-thermal management;

modelling;

IMS;

observer;

thermal

II. I.

PROTOTYPE CONVERTER HARDWARE

To demonstrate the temperature prediction principles, a practical system has been developed. This system comprises the active devices of a typical modern universal input AC-DC converter with PFC and synchronous rectification. IMS is employed to aid heatsinking of the devices. The wide range of input voltages such converters are designed to operate from and the variations in load present a wide range of operating conditions each resulting in different loss distributions about the converter. The basic schematic of the converter is shown in Figure 1 and the physical implementation of the active devices shown in Figure 2.

INTRODUCTION

It is predicted that by 2010 power densities in DC-DC converters will reach 20kVA/dm3 [1]. Since the volume of certain key passive components such as the DC-link capacitor or EMC filter components will remain largely unchanged due to physical limitations in their manufacture, efforts to reduce system volume have recently focused on minimising the volume occupied by active components and their associated heatsinking [2]. This is most readily achieved through the migration to device packages such as the D2PAK mounted on high performance circuit materials such as Insulated Metal Substrates (IMS). The prices of such IMS technologies have been steadily falling in recent years making them suitable for a much wider range of commercial applications [3]. Such technologies afford the system designer a potentially greater thermal budget; however the increase in thermal proximity of all of the loss generating components in a system presents new thermal challenges. If all power devices are mounted to a single IMS board, the operating temperature of each device is dependent on that of its neighbours, often forcing the system designer to play safe when determining the amount of energy each device may dissipate in order to avoid one device causing neighbours to overheat and suffer damage [4], an approach which prevents achieving maximum power density.

BRIDGE RECTIFIER

ACTIVE PFC

HALF BRIDGE

RESONANT CIRCUIT

SYNCHRONOUS RECTIFICATION

Figure 1. Basic Schematic of Example SMPS System

The work described in this paper aims to model the thermal cross-coupling and operating temperatures of two particular devices, Q3 and Q4, although the principles discussed here could be extended to all devices. Included on the IMS board is a central monitor node which reports a reference temperature to the thermal monitoring system via serial peripheral interface (SPI) bus. This node is intended to be used as a single point

One solution to this problem is to introduce a thermal controller and appropriate sensors to measure all device temperatures and determine suitable operating limits at runtime. An alternative is to employ a model of the system, run by a controller, to estimate device temperatures based on losses

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PEDS2009 feedback for the model and facilitate the prediction of all other nodes in the system.

IV.

Lumped parameter models derived as above can yield reasonably accurate temperature estimates for thermal modelling assuming good knowledge of the systems initial states and instantaneous power dissipations. In real thermal monitoring applications however, it is impractical to know all initial states. Also, knowledge of instantaneous power dissipations around the system can only practically be approximated. These effects when coupled with the approximate nature of the model itself severely limit the open loop accuracy of temperature estimation using lumped parameter modelling. To remedy this, a closed loop approach based on a Luenberger observer is proposed.

Figure 2. Prototype Hardware for Active Devices Based Mounted on IMS.

III.

OBSERVER SYSTEM

SYSTEM MODELLING

To facilitate implementation on a microcontroller a thermal model of the system with low computational complexity is required. The approach taken here is to employ a simplified equivalent circuit lumped parameter model which features thermal cross-coupling between the active devices. Since high accuracy is desirable, a 3D model of the demonstrator is first simulated using the Ansys finite element analysis (FEA) package. A low-complexity lumped-parameter is then derived from the FEA model. The use of FEA yields an accurate model and also has the benefit that it can be completed in the system design phase before any hardware has been manufactured and makes use of geometries direct from circuit layout CAD software, Figure 3.

The observer uses a single temperature measurement reported from the board's monitor node, which is contrasted against an equivalent temperature estimated by the model from Section 3. The difference between the two temperatures is used to compensate for the approximations and inaccuracies in the model. Since erroneous initial temperatures for each part of the system are generally in error by a similar amount, correcting the model as a whole based on a single point measurement is effective at mitigating inaccuracies introduced in this way. In order to implement the equivalent circuit in Figure 4 in a computationally efficient way, state variable modelling is employed [6]; this also simplifies the implementation of an observer. The model is expressed in standard state-variable form (1), where x is the state vector, u the input vector, A and B are the system and input matrices respectively. For the equivalent circuit model shown in Figure 4, the matrices and vectors are formed as in (2) and (3) respectively. •

x = Ax + Bu 1 1 ⎡ −1 ⎢ R 2C1 − R 4C1 − R1C1 ⎢ 1 A= ⎢ ⎢ R1C 2 ⎢ −1 ⎢ R 2C 3 ⎣

Figure 3. FEA Thermal Model of Prototype IMS

A low complexity approximation of this model is represented using equivalent circuit lumped parameter thermal modelling, which is computationally simple enough for execution on an embedded microcontroller. Lumped parameter thermal modelling has been extensively used for many years to provide first order approximations of temperature distributions within thermal systems, as in [5]. The derived model is in the form of the Cauer network shown in Figure 4 where the drain temperatures of Q3 & Q4 and the monitor temperature are analogous to the capacitor voltages VC2, VC3 and VC1 respectively.

1 R1C1

−1 1 − R1C 2 R5C 2 0

(1) ⎤ ⎥ ⎥ ⎥ 0 ⎥ −1 1 ⎥ − ⎥ R 2C 3 R3C 3 ⎦ 1 R 2C1

(2)

⎡VC1 ⎤ ⎢ ⎥ x = ⎢VC 2 ⎥ (3) ⎢ ⎥ ⎢⎣VC 3 ⎥⎦ The input vector and matrix define the influence of power dissipation in the model and are adjusted to represent dissipation in either devices as in (4) and (5).

Figure 4. Lumped Parameter Model of Critical System Nodes

616

⎡ 0 ⎤ ⎡ 0 ⎤ ⎢ ⎥ ⎢ 1 ⎥ ⎢ ⎥ B1 = ⎢ ⎥, OR B2 = ⎢ 0 ⎥ ⎢C2⎥ ⎢ 1 ⎥ ⎢⎣ 0 ⎥⎦ ⎢⎣ C 3 ⎥⎦

(4)

u1 = PQ3 , OR u2 = PQ 4

(5)

PEDS2009 A prototype of the proposed observer is implemented using Simulink as shown in Figure 5. The output matrix C is chosen to select only the monitor node temperature (VC1 in the equivalent circuit representation) for inclusion in the observer. This is subtracted from the measured monitor temperature and multiplied by gain L before being fed back into the model. A second output matrix C_ is applied in parallel to retrieve all state variables, representing the corrected component temperatures. This feedback mechanism reduces the impact of model anamalies.

Drain Temp (oC)

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CORRECTED ESTIMATED TEMPERATURES

D

Figure 5. Luenberger Observer Implemented using Simulink

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EXPERIMENTAL RESULTS

The test set up shown in Figure 6 is used to assess system performance. A constant power source is used to apply a test waveform to the reverse diode of either Q3 or Q4. The level of power dissipated is measured by a watt-meter and reported to the observer system. The monitor temperature is reported via SPI bus and interpreted for processing in Simulink via National Instruments DAQmx interface. Actual temperatures are measured by means of thermocouples and data logged for comparison. The observer is operated with a fixed time-step of 1 second.

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INTEGRATOR

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Power Dissipation (W)

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LUENBERGER GAIN

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Figure 7. Comparison of Open Loop Temperature Estimation and Observer System. Q3 Excited by Test Signal, Initial Conditions offset by 10 °C Q4 Drain Temperature Predicted and Experimental Drain Temp (oC)

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CONSTANT POWER SOURCE

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CORRECTED TEMPERATURE ESTIMATES

Power Dissipation (W)

WATT METER

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SPI BUS

Q3 TEMP

Figure 6. Diagram of Test Setup, Measure Heating Effect of Q3

Figures 7 & 8 show the resulting observer predicted temperatures of devices Q3 and Q4 when one of the devices is excited with a test power profile. The results are compared with measured temperatures and the equivalent open-loop estimate. The initial conditions for both model and observer are offset by 10°C from the experimental starting temperature to evaluate their performance under a real world operating scenario.

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Figure 8. Comparison of Open Loop Temperature Estimation and Observer System. Q4 Excited by Test Signal, Initial Conditions offset by 10 °C

The open loop model presents an approximation of the system, with temperatures following a similar profile to

617

PEDS2009 operating “open loop” are reliant on unacceptably comprehensive knowledge of system initial states, input stimuli and system behaviour.

measured results. However, the inaccurately assumed initial conditions and model imperfections prevent it from achieving good correlation with measured results, with accuracy only decreasing during periods of non-steady state operation. Typical open loop estimation errors were up to 10%. When the observer is introduced, the erroneous initial conditions are corrected within 20 seconds and the estimated temperatures continue to track the measured results fairly well throughout the course of the experiment, with all estimates staying within 2.5% of the measured result and typically within 1%.

The Luenberger observer technique presented in this work coupled with a single point of feedback presents an excellent means of mitigating common errors inherent in open loop estimation. These improvements are made at a minimal cost in additional hardware and computational complexity making them a viable option for implementation on embedded hardware.

Figures 9 & 10 show the above experiment repeated, but instead to investigate the effects of poorly assumed device power dissipations. In this case, the initial conditions assumed by the model are consistent with the experimental results, but the power dissipations are assumed to be 10% above their measured value.

Q4 Drain Temperature Predicted and Experimental

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Figure 10. Comparison of Open Loop Temperature Estimation and Observer System. Q4 Excited by Test Signal offset from Experimental by 10%

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REFERENCES

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Figure 9. Comparison of Open Loop Temperature Estimation and Observer System. Q3 Excited by Test Signal offset from Experimental by 10%

[1]

The accuracy of open loop estimates are affected more severely by incorrectly assumed power dissipation than wrongly assumed initial conditions leading to consistently poor results. The observer corrected results however again show good error compensation compared to the open loop response.

[2]

VI.

[3] [4]

CONCLUSIONS

[5]

Lumped Parameter thermal modelling expressed in state variable form presents a viable computationally efficient means of predicting system temperatures on embedded hardware, providing system thermal information without the need for multiple hardware sensors. However, accurate results when

[6]

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