# A Review of Harmonic Detection, Suppression, Aggregation, and Estimation Techniques
## 5 Harmonic Estimation Models
The researchers also introduce a novel harmonic reduction theorem that can calculate equivalent virtual FCMs for unobservable portions of a network [85]. The study [86] examines how grid impedance affects the FCM approach to model the harmonic generated by a three-phase variable frequency drive. It suggests a method to identify FCM elements when grid impedance is present. In FCM, with the increase in voltage harmonics orders increased admittance coefficients in the admittance matrix are increased in multiples. The FCM-based model uses a form of  
Figure 12:1  
where \(x\) is the current harmonic order, \(y\) is the voltage harmonic order, and \(I_{x,Base}\) is the response of fundamental harmonic in supply voltage; the total load current is the cumulative-sum of all harmonic currents, i.e., same-order and cross-order. Figure 19 shows the basic diagram of the based Harmonic load reaction model. Ref. [87] presents an experimental non-linear load assessment of the sensitivity of current harmonics to supply voltage harmonics. The proposed waveform variation definition model (WVDM) provides an in-depth coordination of actual load physical operation when the inter-order coupling between the supply voltage and the variations in the current harmonics occurs. The proposed model, shown in Figure 20, specifies how to implement the non-impedance relationship and the separate phase and size response components in the empirical results of the voltage-to-current harmonic variation relationship. Furthermore, the proposed model can provide a precise estimate of the cumulative influence of different power supply harmonics, including the most likely power supply harmonics in  
Figure 12:2 Harmonic load reaction FCM model. Figure 12:3 Simplified circuit of adjustable speed derive DC link when (**a**) conventional type (**b**) Slim DC-link capacitor (SDLC) type filter is employed. the residential network and the low-order strange harmonics. This model provides an excellent correlation of the harmonic voltage influence estimates on the harmonic levels of the measured load current, including phase and magnitude values. Recent research in harmonic estimation has focused on developing efficient and robust algorithms that can accurately estimate the harmonic content of a signal in the presence of noise and other distortions. Some popular harmonic estimation algorithms that have been widely used in recent research include the harmonic product spectrum (HPS) [88], the harmonic sum spectrum (HSS), and the iterative adaptive harmonic estimation (IAHE) algorithm [89; 90]. The harmonic product spectrum (HPS) algorithm is a non-parametric method that estimates the harmonic content of a signal by multiplying the magnitude of the Fourier transform of the signal at different harmonic frequencies. The HPS method is relatively simple to implement and computationally efficient, but it can be sensitive to noise and other distortions. The harmonic sum spectrum (HSS) algorithm is another non-parametric method that estimates the harmonic content of a signal by adding the magnitude of the Fourier transform of the signal at different harmonic frequencies. The HSS method is also relatively simple to implement and computationally efficient, but it can also be sensitive to noise and other distortions. The iterative adaptive harmonic estimation (IAHE) algorithm is a parametric method that estimates the harmonic content of a signal by fitting a harmonic model to the signal using an iterative optimization process. The IAHE algorithm is more computationally intensive than the HPS and HSS methods, but it can provide more accurate estimates of the harmonic content of a signal in the presence of noise and other distortions. The comparison of harmonic estimation methods is given in Figure 12:4