Hereby I present a PhD thesis by publications. Altogether, the thesis includes: a) two journal papers, b) three IEEE conference papers. The journals include IEEE Transactions on Industrial Informatics while the second has been submitted. The conference list includes World Renewable Energy Congress (WREC), Asian conference on energy, power and transportation electrification (ACEPT) and IEEE Conference on Probabilistic Methods Applied in Power Systems (PMAPS). The PMAPS conference is the only event that exclusively discusses probability and statistic methods applied to power system analysis. The thesis presents several novel methods. The first novelty is the development of a new probabilistic model for estimating the solar radiation incident to residential roofs which is compatible with the Australian meteorological conditions. The second is the development of new probabilistic approach called “probabilistic hosting capacity” to estimate the hosting capacity of distribution networks. The third one is the utilization of sparse grid numerical approximation techniques in handling the uncertainty computations. The last contribution is the new assessment method for quantifying the risk of connecting a large number of correlated distributed generators (DGs) into the distribution networks. In glance, these contributions are highlighted in the following paragraphs. The development of the probabilistic method to estimate the solar irradiation is aimed to represent the uncertainty of produced power from residential solar panels. By utilizing the relation between clearness index and diffuse fraction, a probability density function (PDF) of produced power is derived from the total radiance quantity incident of a tilted area to the horizontal plane. Given the characteristics of the day time and the place, the uncertainty associated with power production by solar panels can be probabilistically estimated from the total solar irradiation of a tilted area. Two mathematical models are proposed: the first utilizes the HDKR (Hay, Davies, Klucher, Reindl) mathematical representation for total irradiance, while the second one involves the use of Hay-Davies mathematical representation. Without losing the scope of the work, only the first model is compared with real data obtain from a site in Adelaide. The second model is used for conducting the power flow calculations due to the low computational time is required to deliver results. The interest in the development of probabilistic hosting capacity comes as DGs in the distribution networks rely mainly on the renewable energy. Probabilistic hosting capacity is aimed to deliver a probabilistic estimate of the maximum amount of DGs that can be connected into the existing distribution network without jeopardizing the utility’s system operation and/or customers’ connected appliances. The approach is built up after defining the main uncertainties, resulted from the stochastic behaviours of the small-scale of wind turbines and solar panels as well as domestic loads. The impacts of these uncertainties on the operation of a distribution network are assessed by establishing a set of operational performance indices and the use of the probability of occurrence notion. Three types of hazardous impacts are defined (tolerable, critical and serious). The approach is time-dependent and includes network bi-directionality feature which complies with the fundamentals of automation approaches for active distribution networks. The third contribution is the use of sparse grid numerical techniques (SGTs) as an efficient tool to handle the uncertainty computation which is multi-dimensional problem. It replaces the use of classical numerical techniques based on tensor product grids which suffers from the curse of dimensionality. Additionally, the SGT in comparison with Monte Carlo Technique (MCT) is able to achieve improved efficiency in computation with acceptable accuracy. The last contribution is the development of a new risk analysis approach to quantify the effect of increasing levels of DG penetration on distribution networks. The proposed novel analysis utilises the following techniques and concepts: the Nataf transformation to represent spatial correlation of the DGs connected in the same distribution network; the consideration of likelihood (relative frequency of event occurrence) as well as severity (accumulative depth of event occurrence) of the performance indices in assessing the operation of distribution networks with the increase of DG connections. The Nataf transformation was used to ensure the rank correlation modelling among the non-Gaussian uncertainty representations in which the inter-dependences are modelled. The risk components, likelihood and severity, are visualized along with the increase of correlated DG connections. The purpose of this analysis is to provide an estimate of degree of risk in assessing the operational performance of a distribution network as whole, instead of the traditional methods that assess the network by parts, such as assessing individually a line or bus. The effectiveness of developed methods in this thesis is demonstrated by performing tests on two actual distribution networks: small and large. The small network consists of 11 buses with one substation transformer; while the existing large distribution network, situated in South Australia, consists of 59 (11/0.4 kV) feeder-transformers serving commercial, residential and industrial loads. The large network is segmented into different zones according to their likelihood of having DGs. The results are visualized, analysed and discussed for each proposed methods or approaches. All system modelling and algorithms are performed using MATLAB software and implemented on the distribution networks modelled in the industry accepted software OpenDSS, introduced by Electrical Power Research Institute (EPRI).Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 201
