# A Review of Harmonic Detection, Suppression, Aggregation, and Estimation Techniques
## 5 Harmonic Estimation Models
Finite impulse response (FIR) harmonic estimators based on the Taylor signal model have gained attention for their ability to accurately estimate harmonic phasors in dynamic power systems [76]. However, these filters can introduce significant errors when the frequency deviates from the nominal value. A proposed solution in [77] involves the online calculation of Taylor weighted least squares (TWLS) to determine FIR filter bank coefficients and suggests a dynamic harmonic estimation algorithm by extending the symmetric TWLS algorithm to harmonic symmetric TWLS (HSTWLS). This algorithm aims to improve measurement accuracy at both nominal and off-nominal frequencies while reducing computational complexity. Based on the frequency-domain sampling theorem, a novel harmonic phasor estimator (HPE) is proposed in [77]. This HPE is compared with the Sinc interpolation function-based estimator (SIFE) [78] in terms of frequency response, model parameter selection scheme, and simulation tests. The proposed HPE has three advantages: a more manageable model parameter selection scheme, zero-error results under nominal frequency conditions, and higher accuracy under harmonic frequency deviations and modulation conditions. Harmonic distortion in residential distribution systems is a growing concern for utility companies, but understanding the extent of the distortion is challenging due to a lack of monitoring infrastructure. To address this, ref. [79] proposes a solution for estimating harmonic distortions in residential distribution systems by introducing a probabilistic harmonic load flow (HLF) algorithm. This algorithm uses the network model provided by the utility and incorporates available harmonic measurements to reduce estimation uncertainty. Measurements are taken at several representative service transformers, and a unified harmonic model is developed for the secondary residential system. The layout of the residential network is shown in Figure 16 and a flowchart for the proposed harmonic model is shown in Figure 17.  
The authors in [80] introduce an advanced frequency estimation algorithm that effectively compensates for the interference of harmonics using a new \"harmonics interference decomposition model\". In this model, the interference effect of harmonics is represented as the sum of two separate components: a deviation bias and an oscillatory disturbance. The deviation bias component includes only the uncoupled amplitude parameter terms, while the oscillatory disturbance component includes only the phase parameter coupled terms and represents the location of the power spectral peak. Adjustable speed drives (ASD), negatively impacting power quality in distribution networks by introducing harmonic distortions [81; 82]. Ref. [83] presents a new mathematical model for determining the current harmonics that flow through the DC-link in ASD; conventional and slim dc  
Figure 15: Harmonic estimation using extended harmonic domain algorithm. link filter equivalent circuits are shown in Figure 18. The model takes into account precise voltage ripple measurements across the DC-link to calculate current harmonics on the load side of the ASD, and uses mathematical calculations to determine the current harmonics passing through the DC-link based on the load side currents. Figure 16: Secondary Residential System layout. Figure 12:0 Proposed probabilistic harmonic flow using a single harmonic monitor. The electric power grid is experiencing a growing presence of power converters, which can generate harmonic currents and voltages that negatively impact power quality and protection devices. One of the effective techniques for modeling converter harmonics is the frequency coupling matrix (FCM) [84], which can be obtained through experimental characterization or direct calculation using a converter's internal parameters. This study presents a new method for estimating FCMs and harmonic line admittances from network measurements.