This article presents a stochastic aggregate harmonic load model that can be used to accurately replicate the stochastic behavior of the network impedance downstream of a point of aggregation. The method has been applied to three low voltage networks and the results show that it is able to accurately represent their stochastic behavior while significantly reducing the computational burden compared to modelling the downstream network in detail.

HVDC cable systems connected to HVDC overhead lines are subject to fast front overvoltages emanating from the line when lightning strikes a shield wire (backflashover) or a pole conductor (shielding failure). Representative fast front overvoltage levels for HVDC cable systems are usually established without considering their statistical characteristics. A statistical method to determine overvoltages related to the acceptable mean time between failure (MTBF) for the cable system was developed previously. The method accounts for the statistical distribution of lightning current magnitudes as well as the attenuation of the overvoltage wave due to corona discharges on the line, since this effect dominates for system voltages up to about ±320 kV. To make the method suitable for higher system voltages as well, this article introduces an improved statistical method which also accounts for surge attenuation through resistive effects, soil ionization, and statistical treatment of overvoltages due to shielding failures. To illustrate the improved method, it is applied to a case study for a ±525 kV DC line. 

A number of changes in the power system have increased the risk for more serious resonances in the harmonic frequency range. The changes also result in an increased uncertainty with regard to the frequency and damping of those resonances. Uncertainties could be related to variations with time, uncertain future developments in the grid, and the modelling of individual components. This article investigates uncertainties affecting resonant overvoltages caused by transformer energization. Several study cases investigating the impact of different uncertainties on resonances and resonant overvoltages, performed in PSCAD, are presented. The results show that some uncertainties may have a significant impact on the resulting impedance characteristics and on the resulting overvoltage levels.

Changes in the power system such as an increased use of cables in transmission systems lead to lower resonance frequencies, a possible consequence being an increased risk for resonant overvoltages. This paper presents a method for protecting the power system from resonant overvoltages caused by transformer energization or fault clearing in the vicinity of large transformers. The method utilizes disconnection of cables according to a predetermined scheme that shifts the system resonance in case the harmonic voltage exceeds a threshold. Compared to other available mitigation measures, the proposed method is inexpensive, robust, and acts only when needed, thereby minimizing any impact during normal operation. The method is exemplified using a realistic network model in PSCAD, showing that by employing the method it is possible to reduce the duration of the overvoltages, and thereby the stress on surge arresters and other equipment.

Uncertainties in power system studies are typically managed by Monte Carlo methods or by applying some worst case assumptions. As the number of uncertainties increases, there is a need for methods that can estimate statistical parameters from a limited number of calculations. This paper utilizes a method called the Unscented Transform together with Cornish-Fisher expansion to estimate the 2%-value of switching overvoltages using only about one tenth the number of calculations as a Monte Carlo method, with similar accuracy. The uncertainties considered are the energizing instants of the three phases. The method is illustrated through EMT simulations in PSCAD and it is shown to provide a good approximation of the 2%-value in most of the studied cases.

This paper utilizes the Unscented Transform together with Cornish-Fisher expansion to estimate the 2%-value of switching overvoltages when considering the impact of trapped charge and corona attenuation. Simulations were performed using a piecewise linear corona model for twin- and triple-conductor lines. The proposed method was compared to Monte Carlo methods through simulations in PSCAD. The method is shown to be able to estimate the 2%-value with comparable accuracy to methods used in industry today, but with only one fifth of the number of calculations.

This paper has applied a method for aggregating downstream networks while retaining their stochastic properties, for use in harmonic propagation studies in distribution networks. The method has been applied to two Swedish medium-voltage networks where the connected low-voltage networks, including customer loads, are represented by stochastic aggregated harmonic load models. The results show that the studied medium-voltage networks exhibit a relatively low resonance frequency for their first resonance point. In the frequency range around the first resonance, the uncertainty in the impedance was found to be high, whereas for higher frequencies the uncertainty in the impedance characteristic was much smaller.

Uncertainties in power system studies are often considered using Monte Carlo methods, or by the use of deterministic methods, often based on some worst-case assumptions. With an increasing number of uncertainties, there is a need for methods that can estimate statistical parameters from a limited number of calculations. This paper utilizes a method called the Unscented Transform together with Cornish-Fisher expansion to calculate harmonic distortion at the point of connection of a wind farm under different uncertainties. The method is shown to be able to estimate the 95% value of individual harmonics accurately when considering variations in emission and impedance, using only a limited number of calculations.