Degree Name

Doctor of Philosophy


School of Electrical, Computer and Telecommunications Engineering


The presence of excessive levels of voltage unbalance (VU) stands as a problem of power quality that has far reaching consequences for both customers and electric utilities. Thus, the development of well researched engineering practices is required to maintain acceptable voltage unbalance levels while utilising the total voltage unbalance absorption capacity of the power system.

Although the connection of an unbalanced installation changes the existing un- balance level at the point of evaluation (POE), the installation is not solely responsible for the total VU emission level that results at the POE. A provision should be given to the contribution made by network inherent asymmetries as well. Thus, location of VU emission contributors, allocation of individual emission limits, compliance assessment and implementation of any corrective measures have been found to be key aspects of the total VU management process.

The International Electrotechnical Commission (IEC) Technical Report IEC/TR 61000-3-13:2008 prescribes guiding principles for coordinating negative sequence VU between various voltage levels of a power system through the allocation of emission limits to installations. Although the IEC report is based on widely accepted basic concepts and principles, it requires refinements and original developments in relation to some of the key aspects, especially compliance assessment at the post-connection stage. Compliance assessment is a less developed area and is essential to ensure that the emission limits set by the IEC VU emission allocation methodology in the pre- connection stage are complied by an installation. This thesis primarily focuses on the development of VU emission assessment techniques, thus making contributions for further improvements to the IEC report.

The core hypotheses of the work brings a generalised approach for classifying different sources of unbalance at the POE (covering both radial networks and inter- connected networks) giving emphasis to the discrimination between customer and network responsibility on VU emission. In the case of interconnected networks, concurrently existing sources of VU, while taking their multiple interactions at the POE into account, are analysed in a generalised manner. Accordingly, major emission contributors are identified as (a) contribution made by local load asymmetry, (b) contribution made by local line asymmetries and (c) contribution made by back- ground voltage unbalance asymmetries (taking into account the effect of VU propagation from upstream or surrounding busbars to the busbar under observation (i.e. POE)). Mathematical models which are based on the use of complex voltage unbalance factors (VUFs) are developed to decompose the total VU emission at the POE into its constituent components. Further, the proposed deterministic methodologies utilise pre-connection and post-connection voltage/current measurements at busbars along with known system parameters, ensuring that such data can be relatively easily established. Theoretical bases are verified using three-phase unbalanced load flow studies in relation to several hypothetical and practical networks. The proposed methodologies are used to examine the VU behaviour of a practical, interconnected sub-transmission network giving emphasis to the identification of the most dominant emission contributors and hence a ranking of emission sources is established.

Some of the key aspects used in the IEC VU emission allocation methodology are reviewed using rigorous outcomes of proposed VU emission assessment techniques. Similar to the counterpart IEC guidelines for harmonics (IEC 61000-3-6) and flicker (IEC 61000-3-7) allocation, IEC/TR 61000-3-13 also apportions the global emission allowance to an installation in proportion to the ratio between the agreed apparent power and the total available apparent power of the system seen at the busbar where it is connected. An additional factor, kuE is introduced to apportion the total VU emission allowance between load and line asymmetries, of which a rudimentary approach is provided for its evaluation. In this thesis, while giving a systematic methodology to determine the kuE factor, a sensitivity analysis is carried out to investigate its dependency on various power system parameters.

VU propagation is an important aspect in determining individual emission limits to unbalanced installations. Although the IEC technical report IEC/TR 61000-3- 13:2008 quantifies VU propagation from higher voltage to lower voltage levels in terms of transfer coefficients, and from one busbar to other neighbouring busbars of a sub-system in terms of influence coefficients, the IEC method is proven to have anomalies. The proposed VU emission assessment techniques can separate the influence made by background unbalance on the total VU emission at the POE based on which a systematic approach is presented to evaluate VU propagation coefficients in a generalised manner considering different load types.

Although the resultant VU emission is theoretically defined as the vector sum- mation of unbalanced voltage components caused by individual sources at the POE, VU emission allocation methodology utilises the application of a general summation law for accumulating numerous sources of unbalance to take into account the contributions made by random variations of unbalance. Outcomes of deterministic studies are used to develop a statistical approach in order to assess the post-connection VU levels by revising the existing general summation law which provides path ways to initiate an economic analysis in relation to VU, adopting uncertainties involved in the power system.

As an essential tool for carrying out the studies presented in this thesis, an unbalanced load flow program based on the phase coordinate reference frame incorporating the component level load flow constraints and the three-phase modelling of system components is developed in MATLAB in addition to the simulations carried out in PSCAD/EMTDC and DIgSILENT PowerFactory platforms.