Existing low-voltage networks may not accommodate high penetrations of low-carbon technologies. The topic of this thesis is unbalance, which if minimised can delay or avoid the constraining of these technologies or the replacing of still-useful network assets. Most of the discussion on unbalance, as seen in the standards and the literature, centres on the effects of voltage unbalance on consumer equipment. Its effects on the network are not equally reported. This thesis recognises fundamental differences between the consumer and network perspectives. It can inform distribution network operators on the interpretation of measurements taken on low-voltage networks and guide research on unbalance due to high penetrations of low-carbon technologies. Much of the work involved simulations of LV networks. Initially, existing 3 x 3 or 5 x 5 approaches to the forward-backward sweep method were thought suitable. After a review of these approaches however, there were doubts as to how accurately they accounted for the shared neutral-earth return path on which the out-of-balance current flows. This led to the derivation of a new 5 x 5 approach using only Kirchhoff s voltage (KVL) and current laws (KCL). Its results are validated thoroughly in the thesis. In addition to satisfying KVL and KCL, they match Matlab SimPowerSystems exactly and are in close agreement with measurements taken on a very unbalanced rural feeder. This thesis also investigates the mitigation of unbalance using the static balancer. This is a transformer with a single interconnected-star winding. It was used in 1930-1950s to correct unbalance. Contributions are made for its possible re-introduction as a retrofit option. They include a model for use in the forward-backward sweep method, validated by laboratory and field measurements, and the quantification of the static balancer s strengths and weaknesses as this can help identify when it should be used.

In recent years, photovoltaic (PV) power production have seen an increase and the PV power systems are often located in the distribution grids close to the consumers. Since the distributions grids rarely are designed for power production, investigation of its effects is needed. It is seen in this thesis that PV power production will cause voltages to rise, potentially to levels exceeding the limits that grid owners have to abide by. A model of a distribution grid is developed in MathWorks MATLAB. The model contains a transformer, cables, households, energy storage systems (ESS:s) and photovoltaic power systems. The system is simulated by implementing a numerical Forward Backward Sweep Method, solving for powers, currents and voltages in the grid. PV power systems are added in different configurations along with different configurations of ESS:s. The results are analysed, primarily concerning voltages and voltage limits. It is concluded that addition of PV power production in the distribution grid affects voltages, more or less depending on where in the grid the systems are placed and what peak power they have. It is also concluded that having energy storage systems in the grid, changing the power factor of the inverter for the PV systems or lowering the transformer secondary-side voltage can bring the voltages down. / På senare tid har det skett en ökning i antalet solcellsanläggningar som installeras i elnätet och dessa är ofta placerade i distributionsnäten nära hushållen. Eftersom distributionsnäten sällan är dimensionerade för produktion så behöver man utreda effekten av det. I det här arbetet visas det att solcellsproduktion kommer att öka spänningen i elnätet, potentiellt så mycket att de gränser elnätsägarna måste hålla nätet inom överstigs. En modell över lågspänningsnätet skapas i MathWorks MATLAB. Modellen innehåller transformator, kablar, hushåll, energilager och solcellsanläggningar. Systemet simuleras med hjälp av en numerisk Forward Backward Sweep-lösare som beräknar effekter, strömmar och spänningar i elnätet. Solcellanläggningarna placeras ut i elnätet i olika konfigurationer tillsammans med olika konfigurationer av energilager. Resultaten från simuleringarna analyseras främst med avseende på spänningen i elnätet utifrån dess gränser. De slutsatser som dras i arbetet är att solcellsproduktion kommer att påverka spänningen, mycket beroende på var i elnätet anläggningarna placeras och storleken hos dem. Det visas också att energilager, justering av effektfaktor hos solcellsanläggningarna eller en spänningssänkning på transformatorns lågspänningssida kan få ner spänningen i elnätet. / <p>LiTH-ISY-EX--19/5194--SE</p>