MODELING SIMULATION AND HARMONIC ANALYSIS OF A SERIES RESONANT INVERTER FEEDING RL LOAD: CONSIDERING TRANSFORMER PARAMETERS

Series Resonant Inverter (SRI) is a source of very high frequency energy and is used for high frequency applications, such as Induction heating, Metal and thin film plastic surface treatment, communication and AC power flow areas (HVDC and HVAC) etc. SRIs are linked with the load through high frequency transformers to improve the current gain. Inclusion of transformers and RL load leads to higher frequency harmonic components in the load voltage. The present papers includes the harmonic analysis of a basic SRIs (Class – A), feeding RL load with the consideration of transformer parameters. System is modeled first in continuous time domain and then harmonic analysis is carried out using MATLAB/SIMULINK which is extended to the filtering out the higher frequency harmonic components using Butterworth IIR filter. Abstract inverter and finally the results were compared with the real data. In the present work we have concentrated ourselves onto analyzing the effect on the load voltage if transformer parameters are considered. System is first modeled and transfer function is obtained. System is represented in terms of block diagram and simulated using MATLAB/SIMULINK. Further using the tools available in MATLAB harmonic analysis and filtering of higher order frequency component has been carried out. temperature plasma


Problem Formulation
System considered for analysis is 2 -MHz, 2 -kW high frequency high power series resonant inverter: for low temperature plasma generator [8]. Circuit is shown in Fig. 1.
As our aim is to analyze the effect on the load voltage, when transformer parameters are considered. This can be done by considering a basic SRI (Class -A) in place of Class -D [5], [9] or Class -E Series resonant inverter [8].
Later on the analysis can be extended to Class -D or Class -E inverters without the loss of generality as here for our analysis we are concerned with output of the resonant inverter being fed to transformer connected in parallel with the capacitor for current gain as shown in Figure 2a For the present work we have considered that the R-L load is connected to inverter through high frequency transformer and the turn ratio of the transformer is 1:1. All the parameters of the transformer are considered in per unit system. The system to be analyzed with the consideration and equivalent diagram of the transformer is shown in Fig. 4.
Referring to the circuit shown in Fig. 4, with the consideration that the turn ratio is 1:1 voltage balance equation of primary and secondary windings of the transformer in time domain can be written as: By taking Laplace transform and solving the above equation and with the consideration that system is initially relaxed, transfer functions relating input voltage to transformer, primary current, secondary current and load voltage is obtained and given below   Table 1.

A. Harmonic analysis of the load voltage
Harmonic analysis on the load voltage can be carried out using FFT tool available in Matlab. Results obtained are shown in Figure 8. Filtering out the high frequency components from the load voltage using Butterworth IIR filter Higher frequency components in the load voltage due to the consideration of transformer parameters and RL nd load are filtered out using 2 order Butterworth IIR filter. Filtered load voltage is shown in figure 9. Figure 9a shows the load voltage with and without filter including the transients and Figure 9b shows the load voltage during steady state without and with filter.

Conclusion
Effects of considering transformer parameters on the load voltage of a series resonant inverter have been analyzed using obtained transfer function model. From the harmonic analysis using FFT it is clear that significant amount of harmonic contents are injected in the load voltage due to transformer and RL load. From the tables II and III it is clear that by using Butterworth IIR filter unwanted harmonic contents are reduced up to much extent. The analysis carried out can be extended to Class -D and Class -E series resonant inverters and the consideration of transformer parameters may reduce the error between experimental results and that obtained from the models used for the analysis and filter design.