# Dynamic Impedance Estimation: Challenges and Considerations
## 2 Transducers Online Equalization  
### A. Transducer Equalization Review  
With the increasing number of PQ monitors installed in the transmission networks, traditional instrument transformers are also being used for measuring the harmonic components [1; 2; 19; 20]. However, it is well known that traditional measurement transformers, whether in distribution or transmission systems, present distortions in their frequency response, both in magnitude and in phase, which introduces measurement errors in the harmonic components.  
The process of correcting the frequency response of measuring instruments, in this paper, will be called instrument equalization, using the terminology equivalent to the equalization of communication channels, whose purpose is exactly to correct the frequency distortions introduced by the communication channels.  
Taking this into account, several methods for correcting these errors are further investigated. In [1], the authors investigate two possible approaches: the invasive and the non-invasive methods. The invasive method provides a more accurate correction; however,  
Figure 1: The three subjects addressed in this work and their interdependence.  
it requires disconnecting the instrument from the power grid and injecting test signals to obtain the frequency response, which is not always feasible. On the other hand, the non-invasive method is limited to harmonics already present in the investigated network that the instrument is connected to. Additionally, in the non-invasive method, it is necessary to temporarily connect a reference meter (typically a resistive divider) to equalize the already installed meters.  
In [2], the authors present a laboratory calibration for three instrument transformers, one of which is used as a reference for measuring the frequency response. The work is based on a two-step procedure that uses isolated high voltage gas capacitors and a digital bridge, a digital current comparator. This procedure is adopted to explore the harmonics' amplification due to the differentiation circuit to obtain accurate measurements of high order and low magnitude harmonics.  
The CTs are covered in more detail in [19]. The authors use the frequency coupling matrix technique, widely used in studies of harmonic penetration in power systems. The experimental results use the compensation technique in commercial CTs up to 10 kHz. The CTs are then characterized, modeled, and tested in the laboratory. Thus, it is possible to analyze their non-linearity, the phase dependence between harmonics, and propose compensation that allows the CT to maintain its accuracy class for a wide frequency range.  
A problem scarcely addressed in the literature is CT's and VT's online and adaptive equalization. Many works, such as those mentioned above, work with offline techniques. In [3], the authors present an online compensation method, although it is not adaptive. The compensation is performed in real-time, but it is based on the transducer model's laboratory identification. Once the infinite impulse response (IIR) equalization filter has been identified, the reverse filter's coefficients are incorporated into the measurement system and are not updated anymore. Thus, if any characteristic of the transducer changes, the equalization will not be significant.