The Mathcad^{®} program accounts for the motor parameters and operating condition because they affect the module losses.

It's important to make assumptions that will reduce computing time without compromising accuracy.

The design specification for a 3-phase power converter to drive an ac induction motor included a dual output power rating of 100 hp with a 60-sec 150% overload capability and 125 hp with 110% overload capability. Nominal input voltage was 480Vac and operating ambient was 45°C.

As with most new products, this was not a clean-sheet approach. The new product's converter topology had to match an existing range of drives and ensure reliable operation in multi-drive systems that use common dc bus connections. Use of an existing plastic cover reduced tooling charges on this lower volume product. This defined the product footprint and set strict constraints on the thermal package. Verification that we could meet the design's thermal limits involved the generation of a three-step, 3-D model:

- Calculate the power losses of all main components.
- Calculate the airflow through the product by constructing a computer space model.
- Calculate the temperature distribution throughout the unit using the computer model.

Obtaining the desired results required an iterative process because the losses in most electronic components are temperature related. Plus, any mechanical changes affect fan back pressure, airflow, and hence air temperature.

We modeled heat-generating components to varying degrees of detail depending on their overall importance and margin of safety to their thermal limits. In this design the most critical components are the power silicon and dc link capacitors. For brevity, only these component losses, temperatures, and thermal models are shown, although we modeled all heat-generating components.

### Loss Calculations

The drive topology was standard for an ac motor drive power converter. We used a 3-phase inductor on the 3-phase input to help protect the drive against line transients and reduce the input harmonic and peak currents. A thyristor full-wave rectifier bridge rectified the ac mains and pre-charged a dc link capacitor bank. The motor drive output is a full 3-phase IGBT bridge module that generates a sinusoidal current into the motor windings using a PWM switching pattern.

*Table 1* lists the calculated loss estimates in the input bridge, bus capacitors and IGBT module, as well as the target operating temperature. The two operating modes were: 125 hp steady-state output and 100 hp output with 150% overload for 1 min.

For the input rectifier devices, PSPICE simulation provided the rms and average current, which — combined with the data sheet on-state voltage and resistance slope — gave the loss in each dual module. The maximum rated junction temperature for the thyristors selected was 125°C. A target steady-state temperature of 110°C allows overloads and other factors, such as input voltage phase imbalance.

To determine the losses for the dc link capacitors, a PSPICE simulation provided the harmonic currents at multiples of 360 Hz and 3 kHz, assuming a fixed PWM carrier. The manufacturer's data of ESR vs. frequency vs. temperature produced an estimate of the total losses in each capacitor. Assuming a target operating life of 30,000 hr, the manufacturer's data recommends a maximum core temperature of 90°C.

We calculated the IGBT module losses for both the IGBT and diode, with IGBT losses subdivided into on-state losses and switching losses. A Mathcad program calculates the on-state loss by simulating the actual IGBT current waveform. A random modulation pattern in the product minimized the audible noise in the motor, but a fixed frequency switching pattern estimated the losses, simplifying the calculations with minimal changes to the loss calculations. Polynomial approximations of the device's on-state voltage, and the IGBT turn-on and turn-off losses vs. current data provided the instantaneous power loss over each switching cycle. Integrating and summing the waveform for each switching cycle over time produced the total power loss.

The Mathcad^{®} program accounts for the motor parameters and operating condition because they affect the module losses. The IGBT and diode maximum operating junction temperature is 150°C; a target maximum steady state operating temperature of 125°C allows for transient conditions, spreads in device characteristics, and long-term silicon reliability.

### Mechanical Layout

We used the I-DEAS^{™} software, published by SDRC (Structural Dynamics Research Corp.), in the mechanical design. *Fig. 1* shows the mechanical layout; the final product is in the *Photo* on page 54. The drive has one bottom-mounted 190 mm high performance radial impeller, which draws ambient air in through grills from the bottom of the product, and through two vents in the topsides of the plastic covers. There are two heat sinks; the lower, a bonded fin with 5-in. fins, has the IGBT module, and the upper, an aluminum extrusion with 2-in. fins, has the input thyristors and brake module. Mounted behind the upper heat sink is the inductor. Four traverse-mounted bus capacitors are above the heat sinks and attached to a mounting and cooling plate on their right-hand side.

We selected this layout for several reasons. The main fan draws cool air over the internal electronics, eliminating the need for internal stirring fans and subsequent fan loss protection. The bus capacitor's electrical connections are physically close to the IGBT connections, reducing stray inductance in the bus and reducing the voltage overshoot across the IGBT module under output short-circuit conditions. The cool air from the top vents flows over the capacitors and capacitor mounting/cooling plate that extracts most of the thermal energy from the capacitor core. Inductor orientation ensures optimal winding cooling by forcing the air to flow longitudinally through the windings at high velocity. Also influencing the inductor location were the mounting requirements of this heavy component, the desire to maximize space efficiency, and the manufacturability of the bus bar system. Although it's in preheated air from the IGBT heat sink, it has a 200°C temperature rating.

We used iterating candidate designs with a 3-D solid model and evaluated them for thermal, cost, and manufacturability considerations to determine the final mechanical layout. For example, reversing the position of the thyristors and IGBT from top to bottom reduced the bus bar complexity but it increased the IGBT temperature by more than 5°C, so we rejected it.

### Fluid Model

To evaluate and optimize the mechanical layout for thermal considerations without resorting to prototypes, we used the combined 3-D computational fluid dynamics (CFD) and finite-difference-based thermal solver Electronic System Cooling (ESC) published by SDRC. The model involved gridding or dividing the 3-D geometric space into small polygons or elements. Next, these elements were converted into finite volumes for the CFD solver and finite difference equations for the thermal solver by the software. The differential equations that govern the properties of the fluid (in this case air) for each polygon are approximated by a polynomial and solved for the boundary or surface conditions. An iterative calculation process resulted in a converged solution. It's important to make assumptions that will reduce computing time without compromising accuracy. For example, we used larger elements where there are lower rates of change of pressure or temperature. For this design we assumed the air changes density with changing temperature but not with changing pressure (incompressible) and ignored natural convection and radiation effects. Included in the model is the fan performance curve that predicts its operating point on the pressure — flow rate curve.

To further reduce the required computational time, the complete coupled model includes three separate models: one complete system modeling-only flow and the two separate coupled thermal-flow models shown in *Fig. 2*, on page 64. This approach is possible because the internal fan provides a natural place to break the model and the average air temperature at the fan inlet is very close to ambient. The system model used coarser elements to determine the fan's operating point, i.e. flow rate, assumed constant for the other models. Solving the left-hand sub-model involved adding the inlet air to the dissipation of the right-hand model components in *Fig. 2* and the fan motor.

We modeled the p. c. boards as thin shells with a set of average-sized components distributed over the surface for drag and thermal calculations. We also modeled the capacitor cans as orthotropic thin shells with the thermal properties approximated from the actual construction using the volume fractions of the various materials, epoxy-coated aluminum overwrapped with a PVC sheath. *Fig. 3* shows this approach. The core of the capacitors used orthotropic solid elements with core and crush zone thermal properties taken from ^{[1]}. The core was thermally coupled to the case and terminals using thermal resistances calculated from measurements on a dissected capacitor. We added thermal resistances, based on the interface material and typical thickness to simulate interfaces between the capacitor base and heat sink.

Thin shell model elements represented the IGBT module, silicon dies, transistors and diodes, and device baseplate. They were thermally coupled to each other and the heat sink using the manufacturer's values for thermal conductance. We applied the thermal loads to the die elements.

### Thermal Results

*Fig. 2*, on page 64, shows a cross section of the predicted airflow through the centerline of the drive. Airflow over the capacitor cooling plate and internal electronics of the product was about 1 m/s, while airflow over and through the inductor windings was about 4 m/s. Airflow through the lower heat sink was about 5 m/s and approaching 10m/s through sections of the upper heat sink. We verified the predicted airflow by measuring the volumetric flow rate at the drive exhaust, often referred to as a “bag” test. The measured airflow was within 3% of the predicted airflow.

*Fig. 4* shows a cross section of the hottest capacitor. The model predicted a steady state core temperature rise of 26°C compared to measurements of 24.6°C. The cooler center cylinder in *Fig. 4*, on page 66, is the electrically-isolated mounting post, an aluminum rod that also acts as a cooling path for the heat generated in the core. The design of the capacitor heat sink and the local flow conditions over the heat sink strongly affects the capacitor core temperature.

*Fig. 5*, on page 66, indicates the temperature of the IGBT module baseplate at the end of a 150% current overload assuming a 0°C ambient temperature. The model shows a 30°C differential across the module baseplate even though it's made of 3 mm thick copper. This high gradient is difficult to measure accurately in the drive; however, you must take it into account when designing for worst case IGBT and diode junction temperatures. *Table 2* lists test results.

We analyzed two transient thermal conditions. The first condition is a 60-sec, 150% overload starting from a steady state operating point of 100 hp. *Tables 1*, on page 54, and *2* provide the losses and temperatures. *Fig. 6* shows the dynamic temperature change of the heat sink under the IGBT module over a 120-sec time period during and after the overload. Note that the initial rise and fall in temperature during the changes in load are higher with the model than with the measured values. The reason for this is that in the simulation, the change in load is applied instantaneously but in the motor stand used for the actual tests, the load took several seconds to be applied and removed.

The second transient condition simulates the drive starting a motor with a jammed shaft. The drive will generate 150% of rated current at a low output frequency equivalent to the slip frequency of the motor, typically 2 Hz or less. Under these conditions the transient thermal impedance of the silicon devices becomes more dominant. The Mathcad also helps to predict the die junction transient temperatures using the principle of superposition. Using the published data for the thermal impedance, the effect on the die temperature for each time slice is summed to generate the die temperature over the complete cycle as shown in *Fig. 7*. The results show a 27°C peak-to-peak temperature variation with a mean temperature rise of 11°C. The worst-case die temperature is obtained by combining the information shown in *Figs. 5*, on page 66, and *7*.

The described model illustrates how modern simulation tools can predict with acceptable accuracy the temperatures in a power electronic converter. Analysis results should always be verified through testing; however, once a given model has been shown to be accurate, many different operating modes such as fan failure, unusual overload conditions or different supply voltages, can be simulated quickly and at a fraction of the cost of testing.

### References

1. *Parler, Sam G. Jr., “Thermal Modeling of Aluminum Electrolytic Capacitors,” IEEE Industrial Applications Society Conference, October 1999*.