# Loss Calculation in a Three-Phase 3-Level Inverter

This example shows how to compute switching losses in a three-phase 3-level inverter, combining Specialized Power Systems and Simscape blocks.

### General

From a +/- 1800 volts DC source, a 400-kW, three-phase 3-level inverter delivers variable power to a distribution power system. The inverter output is connected to the 25-kV, 40 MVA, 50-Hz system through a 2200 V / 25 kV transformer. The inverter topology is based on the model described in [1]. Each 3-level leg of the inverter comprises three commercial half-bridge IGBT modules. The IGBT pulsing of module 3 is not required since only the anti-parallel diodes are operating as neutral clamping diodes. The control system contains two PI controllers (one PQ regulator and one current regulator) to generate the required inverter pulses to achieve the reference output power.

The Phase-A leg is implemented using three Half-bridge IGBT with Loss Calculation blocks. Both switching and conduction losses are calculated and injected into a thermal network. The simulation illustrates the achievable output power versus switching frequency for the three-phase, 3-level inverter.

### The Half-bridge IGBT With Loss Calculation Block

The half-bridge is modeled by two IGBT/Diode blocks. The upper and lower IGBT/Diode blocks are pulsed from an external pulse generator. The loss calculations are based on the specifications found on the manufacturer's data sheets.

The IGBTs losses are computed as follows:

Turn-on loss: Pre-switching value of the voltage across the device, post-switching value of the current flowing into the device, and the junction temperature are used to determine the energy losses with the help of a 3-D lookup table. This energy is converted into a power pulse which is injected into the thermal network.

Turn-off loss: Pre-switching value of the current flowing into the device, post-switching value of the voltage across the device, and the junction temperature are used to determine the energy losses with the help of a 3-D lookup table. This energy is converted into a power pulse which is injected into the thermal network.

Conduction loss: Value of the current (Ic) flowing in the device and its junction temperature determine what would be the saturation voltage (Vce) across the IGBT using a 2-D look-up table. This Vce is then multiplied by Ic to obtain the losses which are injected into the thermal network.

The diode's losses are computed as follows:

Reverse recovery loss: Pre-switching value of the current flowing into the device, post switching value of the voltage across the device, and the junction temperature are used to determine the energy losses with the help of a 3-D lookup table. This energy is converted into a power pulse which is injected into the thermal network.

Conduction loss: Value of the current (If) flowing in the device and its junction temperature determine what would be the on-state voltage (Vf) across the diode using a 2-D look-up table. This Vf is then multiplied by If to obtain the losses which are injected into the thermal network.

The thermal capacitance of the device junction as well as its junction-to-case thermal resistance are represented by a one-cell Cauer network modeled with a Simulink® State-space block.

### The Thermal Network

Simscape blocks from the thermal foundation library are used to build a two-cell Cauer network based on the thermal capacitances (case and heat sink) and resistances (case-to-sink and sink-to-ambient). For the sake of simplicity, the two-cell Cauer network uses arbitrary values for the thermal capacitances in order to reduce the time required to simulate the thermal phenomena.

### Demonstration

Run the simulation and observe the following operating points:

From t=0 sec to t=5 sec: the inverter outputs 372 kW (power factor = 0.85) using a switching frequency of 850 Hz. The converter total losses are 2.7 kW and the highest junction temperature (125 C) is observed on IGBT1 of Module 1 (or IGBT2 of Module 2). See Tj(Celsius) Scope block inside the Additional Scopes & Measurements block.

From t=5 sec to t=12 sec, the inverter outputs 210 kW (power factor = 0.85) using a switching frequency of 1850 Hz. The converter total losses are 2.7 kW and the highest junction temperature (125 C) is still observed on IGBT1 of Module 1.

### Reference

[1] Raffael Schnell, Manager Application, ABB Switzerland, "High-Voltage Phase-Leg Modules for Medium Voltage Drives and Inverters".