# Dynamic Impedance Estimation: Challenges and Considerations
## 1 Introduction  
Estimating the magnitude and phase of harmonics in electrical power systems (EPS) still presents significant challenges, mainly when we focus on medium voltage (MV) and high voltage (HV) systems and in dynamic scenarios. There are still limitations for these systems, given the complexity and costs of developing measurement equipment that meets the voltage levels and frequency range determined by standards [1, 2]. As a consequence, the harmonic measurements performed in the secondary of the transformers do not faithfully represent the distortions present in the primary, thus limiting the analysis of harmonic propagation in MV and HV and their applications, such as: the identification and quantification of the harmonic sources responsibilities, the estimation of the electrical system parameters, the correlation of errors in the protection system with the power quality (PQ), among others. Methods for correcting the frequency response for voltage and current transducers (VT and CT, respectively) are discussed in the literature. Most of them are based on frequency domain correction [2, 3] and require laboratory tests to obtain the frequency response and correction. This procedure makes it impossible to equalize the VT and CT already installed. Additionally, as reported in [1], the transducer's frequency responsedepends on temperature and load impedance, among other factors, which often makes the calibration process in the laboratory unsatisfactory. In addition to the errors caused by VT and CT, errors are arising from the harmonic component estimation algorithms. The estimation of harmonics is generally performed using the discrete Fourier transform (DFT), specifically through its fast algorithm, the fast Fourier transform (FFT). It is known that the estimation of the harmonic phasor by FFT is strongly affected if there is variation in the nominal frequency of the system and the noise level present in the signal is high. Although the systems are designed for operating at 60 Hz (50 Hz), the imbalance between the generated power and the consumed power causes small variations in the frequency. However, even if less than 1%, these small variations can produce very inaccurate results in high-order harmonics estimations [4]. To reduce the error due to frequency deviation, the most usual solution is the use of interpolators or resamplers that guarantee synchronous sampling, reducing errors due to spectral spreading [4]. Resampling (interpolation) methods work very well when the signal's noise is low to the level of harmonics. However, when this does not occur, significant errors are introduced. A signal-to-noise ratio (SNR) of 40 dB (typical values in EPS range from 40-60 dB) degrades the interpolation efficiency producing total vector error (TVE) higher than 12% for high order harmonics. It is important to note that resampling methods are extensively used to estimate the magnitude of harmonics. However, more recently, the harmonic phase's estimation has aroused great interest from the scientific community and companies, having seen the new applications made possible thanks to GPS synchronization [5; 6]. The synchronized estimation of the harmonics' magnitude and phase can be named harmonic synchrophasor estimation (HSpE), as a direct extension of the concept of synchrophasor estimation. Consequently, the need for improving conventional algorithms to reduce the error in the phase estimation has been identified. Methods to improve the estimation of harmonic components in noise are also available in the literature. Among them, the ESPRIT method stands out [7; 8]. The ESPRIT is a parametric method and, therefore, needs to have a predetermined model order. Although it is a robust method, it has a high computational cost in relation to noise and does not need synchronous sampling, not being suitable for real-time implementation, especially in low-cost electronic systems.