Monte Carlo, Sensitivity, and Fault Analysis of Resonant LLC Converters
Overview
The advantages of resonant converters include zero-voltage switching (ZVS) at turn-on and zero-current switching (ZCS) at turn-off, high-efficiency and high-energy density, electrical isolation and magnetic integration, wide output operation range and stable no-load operation, low EMI footprint, low capacitor current ripple, and low voltage stress for power devices. They are used in a wide variety of applications such as wireless heating, battery chargers, LED light controllers, LCD TVs, electric vehicle charging stations, renewable energy systems, welding machines, etc. It is important to perform different reliability analyses on these converters to ensure their high design reliability.
PSIM provides several useful analysis tools such as Monte Carlo, Sensitivity, and Fault Analysis as shown in Fig. 1. One can apply these analysis tools after a resonant converter is designed using PSIM’s Power Supply Design Suite.
Fig. 1: Summary of different analysis tools in PSIM
Although this application note provides guidelines on how to apply Monte Carlo, sensitivity, and fault analysis to a half-bridge resonant LLC converter, the procedures are general and can be extended to all other power converters.
Monte Carlo Analysis is a statistical analysis that calculates the response of a circuit when the parameters of its components vary randomly between specified tolerance limits according to a given statistical distribution.
Sensitivity Analysis allows users to evaluate how the characteristic of a circuit varies when one or several of its components changes.
Fault Analysis helps users determine the performance of a circuit under extreme conditions such as a short circuit or open circuit of a component.
In this application note, each analysis option will be demonstrated step by step for a half-bridge resonant LLC converter.
In comparison to other elements of the converter, the resonant network component (LLC) is more sensitive in causing deviations in the normal operating point of the design. Therefore the capacitor (Cs) and inductor (Ls) of the LLC network are selected for Sensitivity Analysis to determine which one is more sensitive to affect the converter output voltage and current; the capacitor (Cs) is selected to evaluate the output voltage variation impact with Monte Carlo Analysis.
With the diode rectifier topology in the converter output stage, the diodes are often subjected to short-circuit and open-circuit conditions. Although it is obvious that the short-circuit failure of one of the diodes can cause the output voltage to collapse, it is important to analyze what will happen to other key components in the converter such as the other diode, power switches on the primary side, and the transformer, with the increase of the currents on both primary and secondary side. In order to investigate the failure mode impact due to the short-circuit condition, it is necessary to perform a Failure Analysis of the converter circuit.
On the other hand, the operation of the resonant converter may not be interrupted when one of the diodes has an open-circuit failure. In this case, Fault Analysis is applied to assist Design Failure Mode and Effect Analysis (DFMEA) of the converter design to determine its effect on the performance of the converter.
The results of these analyses are also validated with the simulation of the converter under the aforementioned conditions.
This application note covers the following topics:
- Design of the half-bridge resonant LCC converter with the Power Supply Design Suite.
- Description of setting up the values of the parameters of interest that are used in the different analysis tools.
- Procedure to modify the design of the resonant converter to open-loop operation according to normal operation specifications. Simulation of the modified converter to verify the operation at the nominal output voltage.
- Application of Monte Carlo Analysis considering deviations of the capacitor (Cs) in the resonant network. Comparison of analysis tool results with simulations.
- Application of Sensitivity Analysis on the capacitor (Cs) and inductor (Ls).
- Application of Fault Analysis considering one of the diodes in the converter output stage is short-circuited/open-circuited. Comparison of analysis tool results with simulations.
Design of the Half-Bridge Resonant LLC Converter
To start designing a half-bridge resonant LLC converter, in PSIM, go to Design Suite >> Power Supply Design Suite, and select Half-bridge resonant LLC. A schematic will appear in PSIM as shown below.
Figure 1: Schematic of a half-bridge resonant LLC converter
The design specifications of the half-bridge resonant LLC converter for this applicate note are:
The operating conditions are:
Resonant frequency (f_res): 200 kHz
Rated Q factor (Q_rated): 0.5
Inductance factor (K_ind): 5
Relative frequency factor (K_rel_freq): 0.822
The inductance factor K_ind is defined as Lm/Ls, and the relative frequency factor K_rel_freq is defined as fsw/f_res where fsw is the operating switching frequency.
One can enter the above information into the Power Supply Design Suite, and obtain the resonant LLC converter design with a feedforward controller that meets the design requirements.
For this application note, the feedforward controller is not used. After the schematic is simplified, and with the parameters entered, the schematic is shown as below. Note the value of K_rel_freq is set as 0.822 to achieve the desired output voltage.
Fig. 2: Half-bridge resonant LLC converter for analysis
The converter is designed based on the procedure described in the document “Tutorial – Resonant LLC Converter Design Using Power Supply Design Suite.pdf”. The schematic with the final design is given in the file “Half-bridge resonant LLC.psimsch” in the “simu (AN009)” folder.
The converter parameters can be obtained from the parameter file “parameters-main.txt” by selecting Edit >> Show Values:
Ro = 80Ω
Lm = 22.2μH
Ls = 4.4μH
Cs = 142nF
a_sp = 2.68
Electrical parameters and switching waveforms of the key components of the converter are shown in Fig. 3.
Fig. 3: Electrical parameters and switching waveforms of the key components of the converter
Under the normal condition, it can be verified that the peak current values are Ipk(Q1) = Ipk(Q2) = 28A, and Ipk(Cs) = 28A. This information facilitates the selection of the converter components based on the operating current.
Monte Carlo Analysis on Degradation of Capacitor Cs
Capacitors can lose their rated capacitance over time which could cause variations in the resonant frequency and output voltage of the converter. Monte Carlo Analysis is applied to evaluate the effect of the capacitance Cs variation on the output voltage.
To perform the Monte Carlo Analysis, Cs is selected as the input parameter while other circuit parameters are set as constants as shown in Fig. 4.
Fig. 4: Converter schematics used for Monte Carlo Analysis
The Cs value in the parameter file must be disabled when performing the analysis. Since the rated capacitance of Cs is 142nF, the Cs variation range is selected as:
90nF≤C_s≤142nF
In this Monte Carlo Analysis, we want to study how the degradation Cs affects the output voltage Vo and the maximum output current I_sec at the steady-state. In order to eliminate the influence of the start-up transient, make sure the time-domain simulation of the open-loop resonant converter reaches the steady-state at the Print Time as shown in Fig. 5 below. To help reach the steady-state condition faster, a level-2 inductor Ls with 1mΩ ESR is used.
Fig. 5: Steady-state region of the simulation used for Monte Carlo Analysis
With the schematic file “Half-bridge resonant LLC – Monte Carlo.psimsch” loaded, select Analysis >> Monte Carlo Analysis. The dialog window of the Monte Carlo Analysis tool is displayed as shown in Fig. 6.
Fig. 6: Monte Carlo Analysis configurations
Set up the Monte Carlo Analysis as below:
- In the Parameters section, select Cs as name, Uniform as Distribution, Min=90nF, and Max=142nF. Then click Add button to add Cs to the Parameters window.
- In the Outputs section, select out1 as Output, Vo as Scope, and Steady-State as Type. Then click Add button to add Vo to the Outputs window. Select out2 as Output, I_sec as Scope, and Max as Type. Then click Add button to add I_sec to the outputs window.
- Set the number of simulations as 10. Select out1 and out2 in Output window, Cs in the Parameter window.
Click Run Analysis to perform Monte Carlo Analysis. Select File >> Save to save the Monte Carlo Analysis setting to a file with the extension mc.xml. This file can be loaded back later.
A file is already prepared for this application note. In the Monte Carlo Analysis dialog, go to File >> Open, and open the file “Half-bridge resonant LLC – Monte Carlo.mc.xml” in the “simu (AN009)” folder. Then run the analysis.
The results of the Monte Carlo Analysis for output voltage Vo and secondary current I_sec is shown in Fig. 7.
Fig. 7: Results of Monte Carlo analysis.
It is clearly seen that as Cs is decreased from its rated value of 142nF to 90nF, the output voltage increases from 420V to 510V, and the maximum secondary current I_sec increases from 17A to 27A.
The button Update Diagram is used to update the diagram of the output signal out1 or out2.
The function Save results provides the following options to save the results: None; Save statistical results; Save simulation results files; or save all.
Once the analysis is finished, a detailed summary of the Monte Carlo analysis with mean, standard deviation, normalized slope, and variance proportion of Cs is generated as shown in Table I below.
Table I: Summary of Monte Carlo Analysis results
Sensitivity Analysis of Cs and Ls
To understand which resonant network component has a bigger impact on the output voltage Vo and secondary current I_sec, Sensitivity Analysis is applied to the resonant components Cs and Ls.
To perform Sensitivity Analysis on Cs and Ls, Cs and Ls are selected as the input parameter while other circuit parameters are set as constants in the converter circuit shown in Fig. 4. The Cs and Ls values in the parameter file must be disabled when performing the analysis. A -10% variance is selected for both Cs and Ls when Sensitivity Analysis is performed.
With the schematic file “Half-bridge resonant LLC – Sensitivity.psimsch” loaded, select Analysis >> Sensitivity Analysis. The dialog window of the Sensitivity Analysis tool is displayed as shown in Fig. 8.
Set up the Sensitivity Analysis as below:
- In the Parameters section, select Ls as name, 4.4u as Nominal value, -10 as Variation (%), then click Add button to add Ls to the Parameters window.
- Similarly select Cs as name, 142n as Nominal value, -10 as Variation (%), then click Add button to add Cs to the Parameters window.
- In the Outputs section, select out1 as Output, Vo as Scope, and Steady-State as Type, then click Add button to add Vo to the outputs window.
Click Run Analysis to perform the Sensitivity Analysis.
Fig. 8: Sensitivity Analysis configurations
A file is already prepared for this application note. In the Sensitivity Analysis dialog, go to File >> Open, and open the file “Half-bridge resonant LLC – Sensitivity.sens.xml” in the “simu (AN009)” folder. Then run the analysis.
Once the analysis is finished, a detailed summary of the Sensitivity Analysis with Absolute and Relative Sensitivities of Cs and Ls is generated as show in Table II below. It shows that Cs (Rel Sensitivity=3.2159e-01, ranking=++) is more sensitive to the output voltage Vo than Ls (Rel Sensitivity=4.9170-01, ranking=+) when -10% variation is used.
Table II: Summary of Sensitivity Analysis
Fault Analysis on Diode Rectifier
Two possible failure cases of the diode rectifier are considered in this application note.
- Diode D1 is open-circuited (Fault F1)
- Diode D1 is short-circuited (Fault F2)
To simulate the open-circuit fault, we set the diode resistance to 20MOhm.
Fault F1 is a less critical failure condition due to diode device opening. The fault can cause a reduction of the output voltage with greater ripples. Though the converter can still operate with the correction of the K_rel_freq factor, other abnormities such as un-balanced primary current, transformer saturation, may cause problems in the operation.
On the other hand, Fault F2 represents a critical failure condition since it would cause an output voltage interruption, and lead to a big increase in the currents in the transformer, un-faulted diode, resonant components as well as primary power devices.
In order to investigate the impact of such faults on various components in the resonant converter, we need to obtain the nominal values of current and voltage for the inspected components under the normal operating condition as shown in Fig. 9. The mean value of current in Lm is 0A, the maximum current of D2 is 10A, the maximum currents of both Q1 and Q2 are around 30A, and the mean value of Vo is 420V.
Fig. 9: Normal Voltages and currents of inspected components
Based on the nominal electrical values of inspected components above, the failure criteria values can be assigned as below:
With the schematic file “Half-bridge resonant LLC – Fault.psimsch” loaded, select Analysis >> Fault Analysis. The dialog window of the Fault Analysis tool is displayed as shown in Fig. 10. Set up the Fault Analysis as below:
- In the Fault section, select F1 as Name, Parameter fault as Type, D1 (DIODE) as Element, Rd as Parameter, 20M as fault value, then click Add button to add F1 to the Faults window.
- Similarly select F2 as Name, Short-circuit as Type, D1 (DIODE) as Element, and then click Add button to add F2 to the Faults window.
- In the Tests section, select Test1 as Name, I(Lm) as Scope, Mean as Type, Greater than as Criteria Type, 5.0 as Value, then click Add button to add Test1 to the Tests window.
- Similarly, configure other tests based on previous procedures and the table above.
Click Run Analysis to perform the Fault Analysis as shown in Fig. 10.
Fig. 10: Fault Analysis configurations
A file is already prepared for this application note. In the Fault Analysis dialog, go to File >> Open, and open the file “Half-bridge resonant LLC.fa.xml” in the “simu (AN009)” folder. Then run the analysis.
Once the analysis is finished, a detailed summary of the Fault Analysis is generated as shown in Table III below. Under fault condition F1, the mean value of current in Lm is 13.7A, which exceeds the 5A limit and drives the transformer into deeper saturation. The maximum current of D2 is 16.5A. The maximum current of Q1 is 23A. The maximum current of Q2 is 33.6A, and the mean value of Vo is 413.3V.
Under fault condition F2, the mean value of current in Lm is 833.9A, which far exceeds the 5A limit and can cause the transformer burn-out. The maximum current of D2 is 171.3A that can destroy the diode D2. The maximum currents of Q1 and Q2 are 77A which can also destroy the MOSFET Q1 and Q2, and the mean value of Vo is around 0V as expected for a short-circuit fault.
Table III: Summary of Fault Analysis
After the Fault Analysis report is generated, simulations for each failure case are performed to validate the analysis results. The Fault F1 condition in the simulation schematic is created by setting the resistance of diode D1 as 20MΩ as shown in Fig. 12. The Fault F2 condition in the simulation schematic is created by shorting diode D1 as shown in Fig. 13. The voltage and current waveforms of inspected components shown in Fig. 12 and Fig. 13 agree with the results from the analysis.
Fig. 11: Voltages and currents of inspected components under open-circuit fault F1
Fig. 12: Voltages and currents of inspected components under short-circuit fault F2
Conclusions
The process of applying Monte Carlo, sensitivity, and fault analysis to a half-bridge resonant LLC converter is presented in this application note. These analyses can be easily set up in PSIM. They provide powerful tools to perform Design Failure Mode and Effect Analysis (DFMEA) to ensure the robustness and reliability of the design.