Harmonic Analysis Functions
The harmonic analysis functionality is ideal for applications in transmission, distribution and industrial networks for filter design, ripple control signal simulation or for the determination of network resonance frequencies.
For analyzing the impact of harmonics in power systems, DIgSILENT PowerFactory provides two harmonic analysis functions.
Harmonic Load Flow
The DIgSILENT PowerFactory harmonic load flow features the calculation of harmonic voltage and current distributions based on defined harmonic sources and grid characteristics. It allows the modelling of any user-defined harmonic voltage or current source, both in magnitude and phase including inter-harmonics. The harmonic sources can be located at any busbar in the power system and may be implemented within any network topology.
Harmonic current sources can be associated with any load, SVC (TCR injection), rectifier or inverter. Harmonic voltage sources can be modelled using the AC voltage source model or the PWM AC/DC converter model. The built-in rectifier models inject the spectrum of ideal 6-pulse rectifiers if no other injection has been defined.
DIgSILENT PowerFactory supports any type of characteristic harmonic, un-characteristic harmonic (even harmonics etc.) and non-integer (inter-) harmonics. Unbalanced harmonic sources (e.g. single-phase rectifiers) are also fully-supported. The analysis of inter-harmonics or unbalanced harmonic sources is based on a complete abc-phase network model.
Because of the phase correct representation of harmonic sources and network elements, the superposition of harmonic currents injected by 6-pulse rectifiers (via Y-Y and Y-D transformers leading to a reduction in 5th, 7th, 17th, 19th etc. harmonic currents) is modelled correctly.
DIgSILENT PowerFactory calculates all symmetrical and asymmetrical harmonic indices for currents and voltages, as defined by relevant IEEE standards, including harmonic current indices and harmonic losses, such as:
- HD and THD
- IT product
- Harmonic losses
- Active and reactive power at any frequency
- Total active and reactive power, displacement and power factor
- RMS values
- Unbalance factors
Results can be represented:
- In the single line diagram (total harmonic indices)
- As histograms (frequency domain)
- As waveform (transformation into the time domain)
- As profile (e.g. THD versus busbars)
The frequency dependent representation of network elements such as lines, cables, two- and three-winding transformers, machines, loads, filter banks etc. for considering skin effects is fully-supported.
Frequency Sweep
The frequency sweep performs a continuous analysis in the frequency domain. The most common application is the calculation of self- and mutual network impedances for identifying the resonance points of the network and for supporting filter design.
- All impedances are calculated simultaneously in the same run. Since DIgSILENT PowerFactory uses a variable step-size algorithm, the calculation time of frequency sweeps is very low while the resolution around resonance points remains very high (typically 0.1 Hz).
- Frequency sweeps can either be performed with the positive-sequence network model (very fast) or the complete three-phase abc-network model.
- Calculation of self- and mutual network impedances
- Calculation of voltage amplification factors
- Impedance plots may be created in either Bode, Nyquist or magnitude/phase forms.
In addition to common applications relating to harmonic distortion, PowerFactory’s Frequency Sweep function can also be used for subsynchronous resonance studies. The calculation of damping and undamping torques is supported by special scripts.
Network Modelling
The skin effect is considered by associating frequency characteristics with line or transformer resistances and inductances. These characteristics can be specified by either setting the parameters of a polynomial expression or by entering the characteristic point by point using tables. DIgSILENT PowerFactory uses cubic splines or hermite polynoms for appropriate interpolation.
- Lines are modelled either by approximate PI sections or by the highly-accurate distributed parameter line model that should always be used for long lines or high frequency applications. The skin effect can be included in both line models.
- Filters can be specified by either ‘layout’ parameters or ‘design’ parameters. ‘Layout’ parameters are typically the rated reactive power, the resonance frequency and the quality factor. ‘Design’ parameters are the actual R, L, and C values.
In addition to the explicit specification of frequency dependent resistance or inductance via parameter characteristics, overhead lines can be modelled by defining the tower geometry and cables can be modelled by specifying the cable layout. In such cases, frequency dependent effects, such as the skin effect or frequency dependent earth return, are automatically calculated and considered by the model.
Ripple Control Signals
DIgSILENT PowerFactory provides full support for analyzing and dimensioning ripple control systems. Series and parallel coupling of ripple control systems can be modelled including all necessary filter elements.
- The level of the ripple control signal in the entire network is calculated and reported in the single line diagram, the output window or the browser.
Filter Rating
DIgSILENT PowerFactory features a special, easy-to-use function for calculating the rating of all components of a filter. All relevant voltages across all components are calculated and made available in the ‘Filter Sizing’ report.
