Harmonic Impedance Scanning

Harmonic impedance scanning is a powerful analytical technique used in electrical power systems to evaluate system behavior across a range of frequencies. This method is particularly useful for identifying resonance conditions and assessing the impact of harmonics on the quality of supply (Power Quality (PQ)).

Key Aspects of Harmonic Impedance Scanning

Purpose and Function

Harmonic impedance scanning calculates and plots the magnitudes and phase angles of bus driving point impedance over a specified frequency range¹. This analysis allows engineers to:

1. Identify parallel resonance conditions and their corresponding frequencies
2. Tune harmonic filter parameters
3. Evaluate the system’s response to harmonic distortions

Frequency Range

The frequency range for scanning typically starts from the fundamental frequency (e.g., 50 Hz or 60 Hz) and can extend as high as needed for the specific analysis¹. The upper limit is determined by the user based on the harmonics of interest in the system.

Impedance Representation

The scan generates a system impedance matrix for the electric network in the phase domain. This matrix is then collapsed into an equivalent matrix as seen from the interface point, and this process is repeated for each frequency specified in the analysis parameters².

Implementation and Tools

Several software packages and tools are available for performing harmonic impedance scans:

1. ETAP Harmonic Frequency Scan module
2. PSCAD Interface to Harmonic Impedance Solution
3. Custom-developed software for specific applications

These tools often provide graphical outputs and reports that include:

• Tabulated listings of bus driving point impedances
• Plots of impedance magnitude and phase versus frequency
• One-line diagrams with impedance information¹

Considerations and Assumptions

When performing harmonic impedance scans, certain assumptions are typically made:

1. Transformer saturation and arresters are assumed to be in their unsaturated region
2. Power electronic devices are considered to be in their OFF state
3. Synchronous and induction machines are represented as grounded inductors
4. The minimum frequency for calculation is usually around 1 mHz, meaning DC resistance is not computed²

Applications

Harmonic impedance scanning is used in various scenarios, including:

1. Power system planning and design
2. Harmonic filter design and tuning
3. Resonance identification and mitigation
4. Power quality assessment and improvement
5. Integration of renewable energy sources and power electronic devices

Experimental Validation

Researchers have developed experimental setups to validate harmonic impedance measurement methods in real high-voltage (HV) systems⁴. These setups help verify the accuracy of theoretical models and simulation results, providing valuable insights for practical applications.

Advanced Techniques

Recent advancements in harmonic impedance scanning include:

1. Improved estimation methods based on similarity measures to enhance accuracy³
2. Integration with stability analysis techniques, such as the LTP Nyquist criterion for power converter networks⁵
3. Development of frequency-scanning harmonic generators for inter-harmonic impedance tests in specific applications, such as railway systems⁶

By utilising harmonic impedance scanning, power system engineers can gain valuable insights into system behaviour, identify potential issues related to harmonics and resonance, and develop effective mitigation strategies to ensure reliable and high-quality power delivery.

Reference

What is the Linear Time-Periodic (LTP) Nyquist criterion?

The term “LTP Nyquist criterion” refers to a specific application of the Nyquist stability criterion in the context of Linear Time-Periodic (LTP) systems. The Nyquist criterion is a fundamental principle in control theory and signal processing that helps determine the stability of a system based on its frequency response.

1. Nyquist Stability Criterion:
   • The Nyquist criterion is used to assess the stability of a feedback control system by analysing the open-loop frequency response. It involves plotting the Nyquist plot, which represents the complex frequency response of the system as a function of frequency.
   • The criterion states that a system is stable if the Nyquist plot does not encircle the critical point (-1, 0) in the complex plane, considering the number of poles of the open-loop transfer function in the right half-plane.
2. Linear Time-Periodic (LTP) Systems:
   • LTP systems are characterised by their parameters changing periodically over time, which can complicate the analysis of stability. In such systems, the Nyquist criterion must be adapted to account for the periodic nature of the system’s dynamics.
   • The LTP Nyquist criterion extends the traditional Nyquist analysis to these systems, allowing engineers to evaluate stability while considering the time-varying characteristics.
3. Application in Harmonic Impedance Scanning:
   • In the context of harmonic impedance scanning, the LTP Nyquist criterion can be particularly relevant. Since harmonic analysis often involves evaluating system behaviour across a range of frequencies, understanding how the system responds to periodic inputs (harmonics) is crucial.
   • By applying the LTP Nyquist criterion, engineers can identify potential stability issues that may arise due to resonance conditions or harmonic distortions, which are critical for maintaining power quality in electrical systems.

In summary, the “LTP Nyquist criterion” is an important concept in control theory that helps analyse the stability of linear time-periodic systems, particularly in the context of harmonic impedance scanning. It allows engineers to ensure that systems remain stable when subjected to periodic disturbances, which is essential for the reliable operation of electrical power systems.