Subject : Power Electronics
Unit : DC to AC Converters
Frequency Domain Analysis
Frequency Domain Analysis:
Fig: Normalized load voltage and load current for L/R = 2T & Superimposed normalized load current waveforms for L/R = 2T
- The load current may similarly be taken as superposition of harmonic currents produced by the different harmonic voltages. The load current may be expressed in terms of these harmonic currents.
- The expressions for different harmonic components of load current are calculated in terms of load parameters: R and L/R (or τ) and inverter parameters: dc link voltage (E_{dc}) and time period of square wave (T).
- For the fundamental harmonic frequency the load impedance (Z_{1}) and load power factor angle (φ_{1}) can be calculated to be
- The load impedance and load power factor angle for the n^{th }harmonic component (Z_{n }and φ_{n }respectively) will similarly be given by,
- The fundamental and n^{th }harmonic component of load current, (I_{load})_{1 }and (I_{load})_{n }respectively, can be found to be
- The algebraic summation of the individual harmonic components of current will result in the following expression for load current.
- The contribution to load current from very higher order harmonics become negligible and hence the infinite series based expression for load current may be terminated beyond certain values of harmonic order ‘n’.
- For L/R ratio = 2T, the individual harmonic components of load current normalized against a base current of has been calculated below:
- For L/R = 2T, the contribution to load current from 13^{th }and higher order harmonics are less than 1% of the fundamental component and hence they may be neglected without any significant loss of accuracy.
- The load voltage and algebraic summation of the first five dominant harmonics (fundamental, 3^{rd}, 5^{th}, 7^{th }and 11^{th}) in the load current, the expressions for which have been given above. It may be seen that the load current waveform calculated using truncated series of the frequency domain analysis very nearly matches with the exact waveform calculated using time domain analysis.