The electric power system is among the biggest and most complex man-made physical network worldwide. The increase of electricity demand, the integration of ICT technologies for the modernization of the electric grid and the introduction of intermittent renewable generation has resulted in further increasing the complexity of operating and planning the grid optimally. For this reason the analysis of large-scale power systems considering all state variables is a very complicated procedure. Thus, it is necessary to explore methods that represent the original network with smaller equivalent networks in order to simplify power system studies. The equivalent network should provide an accurate and efficient estimation of the behavior of the original power system network without considering the full analytical modelling of the grid infrastructure.   This thesis investigates partitioning methods and reduction methodologies in order to develop a proper reduction model. The K-means and K-medoids clustering algorithms are employed to partition the network into numerous clusters of buses. In this thesis the Radial, Equivalent, and Independent (REI) method is further developed, implemented, and evaluated for obtaining a reduced, equivalent circuit of each cluster of the original power system. The basic idea of REI method is to aggregate the power injections of the eliminated buses to two fictitious buses through the zero power balance network.   The method is implemented using Julia language and the PowerModels.jl package. The reduction methodology is evaluated using the IEEE 5-bus, 30-bus, and 118-bus systems, by comparing a series of accuracy and performance indices. Factors examined in the comparison include the chosen number of clusters, different assumptions for the slack bus as well as the effect of the imposed voltage limits on the fictitious REI buses. / Elsystemet är ett av de största och mest komplexa människotillverkade fysiskanätverken i världen. Ökad elförbrukning, integration av informationsteknik föratt modernisera elnäten samt införandet av varierande förnybar elproduktion harresulterat i ytterligare ökad komplexitet för att driva nätet optimalt. Därför ärdet mycket komplicerat att analysera storskaliga elsystem samtidigt som man tarhänsyn till alla tillståndsvariabler. Det är således nödvändigt att utforska metoderför att modellera det ursprungliga nätverket med ett mindre ekvivalent nätverk föratt underlätta studier av elsystem. Det ekvivalenta nätverket ska ge en noggrann ocheffektiv uppskattning av det ursprungliga systemets egenskaper utan att inkludera enkompletta analytisk modell av nätverkets stuktur.Den här rapporten undersöker metoder för att dela upp och reducera ett nätverkför att få fram en lämplig ekvivalent modell. Klusteranalysalgotmerna K-meansoch K-medoids används för att dela in nätverket i ett antal kluster av noder. Irapporten vidareutvecklas, implementeras och utvärderas REI-metoden för att ta framreducerade ekvivalenta nätverk för varje kluster i det ursprungliga systemet. Dengrundläggande idén med REI-metoden är att den aggregerar elproduktionen i deelminerade noderna i två fiktiva noder genom ett nolleffektbalansnätverk.Metoden är implementerad i programspråket Julia och programpaketetPowerModels.jl. Reduceringsmetoderna utvärderas på IEEE:s system med 5 noder,30 noder respektive 118 noder, genom att jämföra ett antal index för noggrannhetoch prestanda. De faktorer som undersäks i jämförelsen inkluderar det valda antaletkluster, olika antagande om slacknoden samt följderna av spänningsgränserna för defiktiva REI-noderna.v

For planning issues, it is useful to know the upper limit for photovoltaics (PV) in the electrical grid with current design and operation (defined as hosting capacity) and how this limit can be increased. Future costs for grid reinforcement can be avoided if measures are taken to implement smart grid technology in the distribution grid. The aim of this project is to identify challenges in Swedish electricity distribution grids with a high penetration of local generation of electricity from PV. The aim is also to help Swedish Distribution System Operators (DSOs) to better understand hosting capacity issues, and to see which room for PV integration there is before there is need for actions to maintain power quality. Three distribution grids are modelled and simulated in Matlab: Rural area, Residential area and City (Stockholm Royal Seaport). Since the project is a cooperation between Uppsala University and Fortum, three different representative grids from Fortum’s grid software ”Power Grid” have been used as input to a flexible simulation program developed at Uppsala University. The simulation includes Newton-Raphson power-flow computing but has also been improved with a model of the temperature dependency of the resistance. The results show that there is room for a lot of PV systems in the Swedish grids. When using voltage rise above 1.1 p.u. voltage as limitation, the hosting capacity 60% PV electricity generation as a fraction of the yearly load were determined for the rural grid and the suburban grid. For the city grid, which is very robust, the hosting capacity 325% was determined. When using overload as limitation, the hosting capacities 70%, 20% and 25%, were determined for the same grids.