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.

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.

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.

The electric power system is undergoing changes including large-scale introduction of renewable energy sources together with HVDC/FACTS, changes in the network such as increased amount of high voltage cables, industrial electrification, and changes in the load composition. These changes will impact the system in different ways and lead to challenges that must be addressed to facilitate planning, dimensioning, and operation of the system in a secure and economical way. 

The aforementioned changes introduce uncertainties in terms of operational state and modelling of both system and components. One example is the modelling of downstream networks and loads in harmonic propagation studies; the customer impedance may have a significant impact on both the resonance frequency and the damping, but its inclusion remains a challenge due to a lack of knowledge about its behaviour at harmonic frequencies. Another example is the calculation of overvoltages caused by line switching or transformer saturation in different operational states and for varying amounts of underground cable in the network. Methods for calculating overvoltages or harmonic propagation are often based on an assumed complete knowledge of the system under study; uncertainties in the system or components are typically addressed by performing Monte Carlo simulations. However, the use of Monte Carlo methods may be impractical or even unsuitable due to the number of calculations required. Deterministic methods, on the other hand, may provide overly pessimistic results leading to large design margins and high costs. 

This work investigates the application of different methods for managing uncertainties related to the calculation of overvoltages and harmonic propagation. The methods are described, and their advantages and limitations are discussed and illustrated through case studies considering typical uncertainties. Regarding harmonic propagation, two methods are considered: the first method uses copulas to aggregate the harmonic impedance of the downstream network and its loads while retaining its stochastic properties. The method is applied to several medium-voltage and low-voltage networks, and the results show that it is feasible to accurately represent the stochastic behaviour without modelling the downstream network in detail. The second method utilizes the unscented transform together with Cornish-Fisher expansion to calculate the harmonic distortion at the point of connection of a wind farm under different uncertainties. The method is able to estimate the 95% value of individual harmonics accurately when considering variations in emission and impedance, while using a limited number of calculations. 

Regarding overvoltages, three methods are considered: the first method can be used to determine representative fast front overvoltage levels for HVDC cable systems connected to HVDC overhead lines, from a limited number of calculations. The method, applicable to backflashover and shielding failure, accounts for the statistical distribution of lightning current magnitudes, as well as attenuation due to corona discharges on the line. To illustrate the proposed method, it is applied to a case study for a ±525 kV DC system. The second method considers the use of the unscented transform together with Cornish-Fisher expansion to estimate the 2%- value of switching overvoltages from a limited number of calculations. The method is evaluated by considering three-phase energization or reclosing of a line taking into account several aspects such as line length, type of feeding network, impact of trapped charge on the line, and attenuation of the overvoltage level by corona discharges. The method is shown to provide a good approximation of the 2%-value using only about one fifth to one tenth of the number of simulations typically used in traditional methods. The third method makes it possible to estimate a minimum VI-characteristic of surge arresters. This allows for accurate calculation of the absorbed energy when arresters are subjected to resonant overvoltages. 

While many uncertainties may be managed by carrying out a sufficient number of calculations, this may not always be the case. To this end, a method has been proposed to manage uncertainties during system operation, specifically considering the risk of resonant overvoltages due to transformer saturation following the clearing of a nearby line fault. The method utilizes partial disconnection of parallel cables according to a predetermined scheme to shift the system resonance frequency. The method is shown to reduce the duration of the temporary overvoltage and the stress on surge arresters and other equipment.

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.

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.

The electric power system is facing a number of changes as part of the transition to a more sustainable energy system, including a large-scale integration of renewable energy sources, changes in the grid such as the introduction of more cables at higher voltage levels, and changes in the load composition, e.g. due to a transition to energy-efficient appliances. These changes will lead to new technical challenges in transmission, subtransmission and distribution networks that need to be addressed in order to facilitate planning, dimensioning and operation of the power system in an economical and secure way.

Resonances affect both overvoltages and harmonic propagation and there are a number of trends that affect resonances, where the general trend is towards resonances at lower frequencies and with less damping. Another aspect that should be considered is an increased uncertainty in both resonances and harmonic sources, caused by the introduction of renewable energy sources, energy efficiency measures and an increase in flexibility. Calculation methods used for calculating overvoltages or harmonic propagation are often based on an assumed complete knowledge of the system under study. Uncertainties, e.g. in the operational conditions of the system or in the modeling of components, are addressed e.g. by performing Monte Carlo simulations. However, depending on the scale of the problem, this may not be practical or even possible. At the other end of the spectrum are deterministic methods, but in case of large uncertainties such methods may give overly pessimistic results. As a consequence, large design margins may be used which can result in barriers for the integration of renewable energy sources. To overcome these issues, there is a need for stochastic methods which can be used to estimate statistical values while reducing the required number of simulations.

Downstream networks and loads are important to consider in studies on harmonic propagation or resonant overvoltages since they can have a significant impact on both the frequency and damping of resonances. However, their inclusion remains a challenge for several reasons, e.g. due to a lack of knowledge about the customer impedance at harmonic frequencies. For the purpose of studying the impact of existing and future loads on the spread of harmonics and resonant overvoltages, there is a need for stochastic models, both at the individual customer level and aggregated. A method was developed which makes it possible to aggregate a given downstream network into equivalent impedances, whilst preserving its stochastic behavior. The aggregated model can then be used to represent the impact of the downstream network accurately in studies whilst significantly reducing the computational burden compared to modeling the downstream network in detail. The method has been illustrated by applying it to three Swedish LV networks.

More and more HVDC systems take the form of mixed cable/overhead line systems. In such a configuration, the cable system will be subject to overvoltages originating from lightning strikes to the line. Representative fast front overvoltage levels for HVDC cable systems connected to overhead lines are typically determined in a deterministic fashion without considering the statistical characteristics of the associated lightning overvoltages. As a consequence, this may lead to unnecessarily conservative dimensioning of the cable insulation. A statistical method for determining representative fast front overvoltage levels for the cable system has been developed previously based on the statistical concept for overvoltage protection of substations. The method focuses on backflashovers and accounts for the statistical distribution of the lightning current magnitude as well as attenuation of the overvoltage due to corona discharges. An improved statistical method has been developed which improves upon the original method by considering surge attenuation due to resistive effects as well as the influence of soil ionization. The improved method is also applicable to shielding failures. The goal of the method is to minimize the number of calculations required to determine overvoltage levels in the cable system related to the acceptable mean time between failure. The method was demonstrated by applying it to a case study for a ±525 kV dc cable system.

This article presents a publicly available power system model suitable for studying switching transients considering the effect of resonances, as well as the spread of harmonics. The model covers voltage levels from 400 kV to 400 V, with all relevant parameters included. The system is characterized by a large share of cables at transmission level, with a first resonance frequency between 100 and 150 Hz. This article describes the overall layout of the model as well as the modelling of different components. Application examples are given, including the study of transfer impedances and transformer energization transients. Limitations of the model and further developments of the model are provided.

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. In this article, a distinction is made between discrete and continuous stochastic uncertainties. This article further investigates uncertainties affecting resonant overvoltages. Several study cases investigating the impact of different uncertainties on resonances and temporary overvoltages, performed in PSCAD, are presented. The results show that some uncertainties may have a significant impact on the resulting impedance characteristics and potentially on the resulting overvoltage levels.