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Electric power systems continue to increase in complexity because of the deployment of market mechanisms, the integration of renewable generation and distributed energy resources (DER) (e.g., wind and solar), the penetration of electric vehicles and other price sensitive loads. These revolutionary changes and the consequent increase in uncertainty and dynamicity call for significant modifications to power system operation models including unit commitment (UC), economic load dispatch (ELD) and optimal power flow (OPF). Planning and operation of these ???smart??? electric grids are expected to be impacted significantly, because of the intermittent nature of various supply and demand resources that have penetrated into the system with the recent advances. The main focus of this thesis is on the application of the Affine Arithmetic (AA) method to power system operational problems. The AA method is a very efficient and accurate tool to incorporate uncertainties, as it takes into account all the information amongst dependent variables, by considering their correlations, and hence provides less conservative bounds compared to the Interval Arithmetic (IA) method. Moreover, the AA method does not require assumptions to approximate the probability distribution function (pdf) of random variables. In order to take advantage of the AA method in power flow analysis problems, first a novel formulation of the power flow problem within an optimization framework that includes complementarity constraints is proposed. The power flow problem is formulated as a mixed complementarity problem (MCP), which can take advantage of robust and efficient state-of-the-art nonlinear programming (NLP) and complementarity problems solvers. Based on the proposed MCP formulation, it is formally demonstrated that the Newton-Raphson (NR) solution of the power flow problem is essentially a step of the traditional General Reduced Gradient (GRG) algorithm. The solution of the proposed MCP model is compared with the commonly used NR method using a variety of small-, medium-, and large-sized systems in order to examine the flexibility and robustness of this approach. The MCP-based approach is then used in a power flow problem under uncertainties, in order to obtain the operational ranges for the variables based on the AA method considering active and reactive power demand uncertainties. The proposed approach does not rely on the pdf of the uncertain variables and is therefore shown to be more efficient than the traditional solution methodologies, such as Monte Carlo Simulation (MCS). Also, because of the characteristics of the MCP-based method, the resulting bounds take into consideration the limits of real and reactive power generation. The thesis furthermore proposes a novel AA-based method to solve the OPF problem with uncertain generation sources and hence determine the operating margins of the thermal generators in systems under these conditions. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a pdf. The AA-based approach is benchmarked against the MCS-based intervals, and is shown to obtain bounds close to the ones obtained using the MCS method, although they are slightly more conservative. Furthermore, the proposed algorithm to solve the AA-based OPF problem is shown to be efficient as it does not need the pdf approximations of the random variables and does not rely on iterations to converge to a solution. The applicability of the suggested approach is tested on a large real European power system.

In an electrical system there needs to be a constant balance between supply and demand ofelectricity and this is measured by the frequency in the grid. Due to the increasing awarenessof climate change, more renewable energy resources have been introduced in the Swedishelectricity system. This is, however, not solely positive since renewable energy sources areoften of intermittent character which entails more imbalances between supply and demand. Inaddition, statistics and data show that the deviation in the frequency in the Nordic system hasincreased during the latest years. Thus, in this thesis, the issues regarding the frequency havebeen addressed by examining the demand for frequency control in the Swedish electricitysystem and what balancing efforts that can be carried out on a local level to contribute to abetter balanced system. This thesis has been conducted at KTH Royal Institute of Technologywith collaboration with the commissioner Mälarenergi AB. A case study of the Swedish electricity system has been carried out to gather empiricalmaterial and this material has been analyzed using Geels theory on technical transitions, themulti-level perspective. The results indicates that it is likely the demand for frequency controlwill increase, and this is due to factors as more intermittent energy, current market design fortrading electricity, overseas transmission connections, decommissioning of nuclear powerand limited internal transmission capacity. Three other developments have been identified,which could have a large impact on the demand in the future, as an increasing use of electricvehicles, prosumers and the deployment of IoT in the energy sector. These developmentshave not been integrated to a large extent yet in the energy sector and thus have a moreuncertain impact. In terms of resources, the thesis has identified that it is likely that hydropower will continueto be the main resource for frequency regulation. Another source that could be used morefrequently than today and possibly compete with hydropower is combined heat and powerplants. Furthermore, the study has found that local actors can contribute by advertisingsmaller local resources on a market for trading regulating power called“reglerkraftmarknaden”, that balance providing companies collaborate, that the load iscontrolled in the local grids or that smaller local production facilities are operated in standalonemode during extreme situations. / För att uppnå ett välfungerande elektrisk system så måste det vara en konstant balans mellan produktion och konsumtion av el i systemet. Den här balansen mäts genom att mäta frekvensen i elnätet. Eftersom allt fler har blivit mer medvetna om de klimatförändringar vår planet står inför har det successivt införts mer och mer förnybara energikällor i det svenska elsystemet. Den här utvecklingen har inte enbart varit positivt, eftersom förnybara energikällor ofta är av intermittent karaktär, vilket har medfört att balansen mellan produktion och konsumtion av el har försämrats. Flertalet undersökningar har påvisat att det förekommer mer frekvensavvikelser i det nordiska elsystemet idag än tidigare. Denna rapport har således undersökt dessa problem genom att analysera efterfrågan på frekvensreglering i det svenska elsystemet och vilka initiativ som kan tas på lokal nivå för att förbättra balansen i elsystemet. Rapporten har genomförts på Kungliga Tekniska Högskolan i samarbete med uppdragsgivaren Mälarenergi AB. Rapporten har genomfört en fallstudie av det svenska elsystemet för att samla in empiriskt material, och detta material har i sin tur analyserats genom Geels flernivåsansats. De resultat som har framkommit i undersökningen visar på att det är troligt att efterfrågan av frekvensreglering kommer att öka. Denna ökning beror på faktorer som att mer intermittent energi integreras i elnätet, hur marknaden för att handla elektricitet är utformad, fler utländska överföringsförbindelser, nedrustning av kärnkraft och begränsad överföringskapacitet inom det nationella elnätet. Tre andra utvecklingar har identifierats som möjligen kan ha en stor påverkan på behovet av frekvensreglering. Dessa är ett ökat antal elektriska fordon, prosumenter och att energisektorn integreras av IoT och smarta objekt i större utsträckning än idag. Dessa faktorer har inte integrerats i det svenska elsystemet nämnvärt ännu och deras påverkan är därmed mer osäker. Denna studie har också kommit fram till att vattenkraft troligtvis kommer fortsätta att vara den resurs som används mest för frekvensreglering, men även att kraftvärmeverk har potential att användas mer för reglering än idag. Vidare har rapporten även identifierat att lokala aktörer kan bidra till en bättre balans i systemet genom att antingen annonsera mindre lokala resurser på reglerkraftmarknaden, öka samarbetet mellan balansansvariga företag, kontrollera lasten i lokala elnät eller att mindre lokala produktionsanläggningar drivs i ö-drift under extrema situationer.