Extending the Herman-Beta transform for probabilistic load flow analysis of radial feeders

Chihota, Munyaradzi Justice

Extending the Herman-Beta transform for probabilistic load flow analysis of radial feeders

Doctoral Thesis

2019

Abstract

The increased penetration of distributed generation (DG) mostly derived from renewable energy sources (RES) such as wind and photovoltaic (PV) systems presents two main forms of technical issues. The system is more susceptible to voltage-rise and equipment overload conditions, while the levels of uncertainty associated with the power system’s parameters increase significantly. The resulting networks characterised by the bi-directional flow of power, uncertainty from stochastic customer load variations and the intermittent generation from DGs, require appropriate load flow assessment tools. Classic deterministic load flow (DLF) approaches which assume the input parameters are fixed, or address the associated variability using empirical factors, have been shown to be inadequate. As a result, probabilistic load flow (PLF) approaches based on statistical foundations were proposed to account for the impacts of the uncertainty. For the PLF methods, the efficiency of a specific approach is influenced by two major constraints; the accuracy of the method and the associated computational effort that affects speed. For instance, numerical methods such as the renowned Monte-Carlo simulation (MCS), offer the most accuracy (within the limits of randomness) but are very computationally demanding and undesirable for practical applications. Usually, speed is coupled with loss of accuracy. Most approaches based on analytical and approximation approaches, which offer higher computational speeds, have limited accuracy due to excessive simplifications. Consequently, a trade-off between accuracy and speed is key to a robust PLF approach. Furthermore, the model solutions must be applicable to both small and large systems, consider the dependency between random variables, and avoid complex formulations which limit the practical usefulness. This research proposes a non-iterative analytical approach referred to as the Herman-Beta extended (HBE) transform to meet the performance and scope requirements of a model PLF solution. The method is based on the beta probability density function (PDF) as a universal descriptor of inputs, and the method of moments for the computation of the output PDFs. The novel formulation of the transform with consideration of complex-type input parameters redresses the network model simplifications of unity power factor loads and resistive feeders in the original HB algorithm (HBA) and the limitation of the representation using absolute values. Further, the effects of dependence between loads and generators are incorporated directly using covariances. The proposed approach opens many possibilities for new applications, including the accurate analysis of the PLF for feeders at any voltage (LV, MV and HV), compensated feeders (shunt reactors and shunt capacitors), and systems with voltagedependent load or DG. The performance of the proposed technique is demonstrated using representative test feeders, modified IEEE 33, 34 and 69-bus test systems, as well as practical distribution networks. The results from several test cases demonstrate a good correlation between the LF outcomes from the proposed method and those from the MCS method and with significant computational advantage. The performance of the method compared with its predecessor shows advanced accuracy while maintaining high computational speed.

Keywords

Electrical Engineering

Reference:

Collections

PhD / Doctoral

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