Managing uncertainties through efficient calculation of transients and harmonic propagation in power systems

Abstract: 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, 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 behavior 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 often addressed by performing Monte Carlo simulations. However, the use of Monte Carlo simulations 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.The thesis investigates the application of different methods for managing uncertainties related to 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 behavior 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, two 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 back flashover 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 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 tenth of the number of simulations typically used in traditional methods. 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 stress on the surge arresters and other equipment. 

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