Table 8 Summary of transformation techniques

Time domain

Parametric

 120

Decomposition of unbalanced systems

One cycle or more should be analyzed

[36, 47, 50, 65, 67, 74, 82, 91, 102, 106, 108, 109, 111, 114, 115]

15

[136, 138,139,140, 151,152,153, 155,156,157,158, 161, 163, 167, 172, 174, 186]

31

[195, 200, 201, 206, 209, 211]

24

 DQ0

Decomposition of time-varying signals

The main frequency varies over time

 TT

Provide transient characteristic of signal

High computational burden

 SPM

Instantaneous data from 3ph systems

Single-phase information not available

 PSR

Instantaneous data from 3ph systems

Repeated information after transformation

 MM

Low computational burden

Not suitable for high-frequency distortions

Non-parametric

 KF

Accurate for parameter estimation

Used for single PQD detection until now (very specific applications)

 AF

Suitable for parameters self-tuning

 PLL

Accurate for parameter tracking

Frequency domain

 FFT

A computationally efficient technique for steady-state signals

Inaccurate for non-periodic signals

[61, 66, 80, 89, 90, 97, 99, 102, 128, 130]

10

[160, 184]

4

[188, 189, 192, 196, 202, 211]

24

 DFT

Realization of FT in discrete time

Inaccurate for non-periodic signals

High computational burden

Time–frequency domain

 STFT

Successful time–frequency decomposition of stationary signals

Trade-off between time and frequency resolution

[33,34,35,36,37,38,39,40,41,42,43,44,45,46, 48, 49, 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65, 68,69,70,71,72,73, 75,76,77,78,79,80,81, 83,84,85, 88, 92, 94,95,96, 98, 101, 102, 104, 105, 107, 109, 110, 113, 114, 117, 118, 120, 122, 123, 125, 126, 129, 130]

72

[133, 137, 142, 143, 146, 147, 149, 150, 154, 160, 168, 169, 173, 176, 178, 181, 184, 186]

33

[187, 189,190,191,192,193,194, 196,197,198,199, 202, 204, 208]

56

 WT

Information on non-stationary signals

Highly affected by noise

 GT

Good time–frequency resolution

High computational burden

Spectral cross-interference can appear

 ST

Combine advantages of WT and STFT

High computational burden

Performance depends on the windowing function

 HT

Information on non-stationary signals

Focused only on narrowband conditions

 CT

Combine advantages of WT and STFT

Detection of linear and non-linear frequency variations over time

High computational burden

Miscellaneous

 MD

Low computational burden (iterative)

Exhaustive search technique

[86,87,88, 93, 99, 100, 103, 112, 124, 129, 130]

12

[134, 153, 166, 176, 179, 181]

11

-

0

 SSD

Several PQDs processed simultaneously

Computation time (optimization problem)

 SSA

Noise suppression and forecasting

High computational burden