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Impedance scanning of single-phase AC-DC converters is challenging due to frequency couplings, which map one injection frequency to a multiple of output frequencies. Single-tone injections are often preferred over wideband signals, as spectral overlap negates the benefits provided by quick-to-implement wideband scans. In this paper we take advantage of the time-frequency properties of chirp excitation signals, and develop a model so that a single chirp sweep can provide the impedance frequency response - formulated as a Harmonic Transfer Matrix, which takes into account the frequency couplings. Though we concentrate on single-phase AC-DC converters, the general HTM formulation extends application to any linear time-periodic and linear time-invariant system. Numerical impedance measurements are presented for a single-phase grid-connected converter, operating in grid-forming mode with dispatchable Virtual Oscillator Control.

With the increasing penetration of voltage-source-converter (VSC) -interfaced distributed generations (DGs) in power systems, oscillation issues have been widely concerned whereas the root cause and nature of the oscillation is sometimes not clear in real cases. This paper focuses on the instability mode recognition (IMR) based on a complete data-driven approach applied to the oscillation waves which can be obtained from the on-site recordings. To this end, we explore the Hilbert-Huang Transform (HHT) for diagnosing the root cause of instability, using only raw data such as the current and voltage waveforms which are accessible by operators. Special attention is paid to distinguish between the sub-synchronous oscillation (SSO) and the loss of synchronization (LOS) as they are two primary instability forms of grid-tied VSC which manifest with very similar waveforms. The pros and cons of the considered signal analysis tools in SSO and LOS recognition are discussed and new lines of investigations are proposed. The analysis and results presented in this paper could shed light on future data-driven analysis, e.g., serving as model-free or hybrid model database for artificial intelligence-based stability diagnosis and recognition.

This work investigates how the physical limitations and losses of an electric power takeoff (PTO) system affect the production of power for a wave energy converter (WEC) under suboptimal control strategies. The damping of the PTO system is either continuously tuned to the time-varying wave excitation force frequency, which is referred to as passive control (PC), or tuned to the mean centroid frequency of the spectrum, which is referred to as passive loading (PL). The time-varying frequency is estimated by the Hilbert-Huang transform (HHT) method. Numerical simulations with the wave-to-wire model of a WEC including a non-ideal PTO show that the limitations and losses of the system modify the output power for both control strategies, when compared to the ideal PTO case. Furthermore, the benefit of applying the time-varying damping obtained from HHT for certain types of wave spectra differs significantly from the cases when only the hydrodynamic model with an ideal PTO system is considered. While for an ideal PTO system, the greatest improvement of PC over PL is obtained for wideband spectra, this behaviour is not observed when the non-ideal PTO is considered.

For å opprettholde frekvensnivået i kraftsystemet er det nødvendig å kunne regulere produksjon på kort varsel. Reservemarkedet brukes til å utføre denne reguleringen, ved at systemoperatør kan justere produksjon ved kraftverk etter avtale med et kraftselskap. For vannkraftprodusenter kan det være lønnsomt å inngå en slik avtale med systemoperatør. Kostnader av en slik avtale vil være tapt inntekt fra spotmarkedet ved høye strømpriser, og uønsket forbruk av vann ved lavere priser. Ved inngått avtale om levering av volum til reservemarkedene er det interessant for kraftselskapet å finne den minst kostbare kombinasjonen av kraftverk å holde av effektvolumet ved. Fordi den tapte inntekten fra spotmarkedet er lik uavhengig av enheten volumet plasseres ved, vil optimal kombinasjon være mulig å finne ved å beregne hvilke kraftverk som gir laveste kostnad basert på vannforbruk og vannverdi ved enhetene. I denne avhandlingen ble dette gjort ved å beregne kostnader per MW som følge av vannforbruk. Aktivering av sekundærreserver (aFRR) på minuttoppløsning er beregnet som et gjennomsnitt av historiske data fra samarbeidsbedrift. Case som ble utført bestod av tre kraftverk, og totalt åtte enheter. Datoen 13.01.2019 ble benyttet og inputverdier ble basert på data fra samarbeidsbedriften, for produksjonsplan, vannverdier, vannstand og målinger av vannføring. Resultatet ble å beholde initiell kjøreplan, men å endre magasin ved ett av kraftverkene. Kostnaden som følge av vannforbruk ville ved initiell kjøreplan og ingen aktivering ha et gjennomsnitt på 48,9 EUR/MWh, høyeste kostnad lik 50,4 EUR/MWh og minste kostnad lik 46,8 EUR/MWh. Etter justert plan og medregnet aFRR aktiveringen ble kostnaden beregnet til å ha et gjennomsnitt på 48,1 EUR/MWh. Med høyeste kostnad lik 50,0 EUR/MWh og laveste kostnad lik 45,4 EUR/MWh. Resultatene viste seg å være sterkt avhengige av initiell spotplan, vannverdi og virkningsgrad. To maintain the frequency level in the power grid, it is necessary to be able to regulate the production level at short notice. The reserve market is used to do this regulation. The transmission system operator (TSO) adjust production at power plants given contract with a power company. For the hydropower company it can be profitable to enter into a contract like this with the TSO. Costs of such a contract will be loss of income from the spot market at high power prices, and unwanted use of water at low power prices. By signing an agreement on delivering reserves it is interesting to the power company to find the least costly combination of units to place the power volume at. Because the lost income from the spot market is the same, independent of which unit the volume is placed, the optimal combination will be possible to find by calculating which units gives the lowest cost based on water usage and water value at the units. In this thesis this was done by calculating costs in Euros per MW, as a consequence of the water consumption. Activation of secondary reserves (aFRR) is calculated as an average of historical data from the collaboration company. The case situation studied in this thesis contained three hydro power plants, and a total of eight units. The date 13.01.2019 was used and input was based on data from the collaboration company, on production plans, water values, water level and measurements on water flow. The result showed that the initial production plan should be kept, but that one of the reservoirs should be changed with another reservoir, due to a higher water level and better efficiency. The cost of the water consumption, when considering the initial plan and no activation of reserves, would have an average of 48,9 EUR/MWh. The highest cost was 50,4 EUR/MWh and the lowest cost was 46,8 EUR/MWh. After running the model, production plan was adjusted and activation was included, the average cost was 48,1 EUR/MWh. The maximum cost in this case was 50,0 EUR/MWh and the minimum cost was 45,4 EUR/MWh. The results were strongly dependent on initial production plan, water value and plant efficiency.

The paradigm shift towards a more sustainable energy supply with a less detrimental environmental impact successively changes the energy sector from a polycentric towards a more distributed energy system. The presence of distributed and renewable energy sources combined with the anticipated electrification of the transport sector results in changes along the entire value chain. This so-called transformation process is accompanied by energy market deregulation and restructuring of the power system. However, in order to increase energy efficiency and improve environmental protection, investigations are needed to establish reliable and secure infrastructures. This will be accompanied by the development of suitable computer aided software solutions for energy market participants and system operators. With further advances in information and communication technology and system automation, there are significant opportunities for realizing such a sustainable energy future. In this context, the thesis provides a comprehensive discussion of the potential application and deployment of Virtual Power Plants. Here, the aggregation concept serves as a vehicle for the implementation of coordinated and optimized control decisions by means of interconnected and interoperable solutions. The developed methodologies and functionalities are implemented through the service-oriented design and control scheme of the Virtual Power Plant for the determination of economic and technical feasible solutions in energy market and power system operations. Following the framework conditions of liberalized energy markets, an energy management algorithm for joint market operations is established which aims to integrate various distributed, renewable and mobile energy sources. A mixed integer linear programming formulation is proposed for solving the unit commitment and dispatch problem of the Virtual Power Plant operator in multi-period optimization processes. The presented methodology allows trading of various market products with variable time increments capable of solving real-time market transactions. By providing a uniform model architecture for scalable power plant portfolios, deterministic planning methods and comprehensive investigations are performed. In particular, electric vehicles are considered as additional sources of energy in joint market operations for the provision of service-oriented operations. Furthermore, multilateral transactions are reflected in the hierarchically structured optimization problem formulation for enhancing the allocation of power system services. The simulation results of the market-related interactions serve to identify the temporal and spatial effects in power system operations. Within this framework, a coordinated voltage control is proposed which combines both local droop controls with remote control algorithms. This allows the additional flexibilities provided by a comprehensive set of distributed, renewable and mobile energy sources to be exploited to mitigate time-varying voltage variations. In addition, the modeling of an active network management is carried out for the purpose of conducting control algorithms for electric vehicles charging in distribution systems. Appropriate evaluation functions and programming indicators are presented to determine the simulation results. Der Paradigmenwechsel hin zu einer nachhaltigeren Stromversorgung mit möglichst geringen Umweltauswirkungen verändert den Energiesektor sukzessive von einem polyzentrischen zu einem dezentralistischen Energiesystem. Die Anwesenheit einer Vielzahl dezentraler und erneuerbarer Energieanlagen in Verbindung mit einer antizipierten Elektrifizierung des Verkehrssektors führt zu Veränderungen entlang der gesamten Wertschöpfungskette. Dieser sogenannte Transformationsprozess ist gekennzeichnet durch eine Deregulierung des Energiemarktes und einer Umstrukturierung des Energieversorgungssystems. Um jedoch die Energieeffizienz zu steigern und Verbesserungen im Umweltschutz zu erreichen, sind Untersuchungen zum Aufbau zuverlässiger und sicherer Infrastrukturen erforderlich. Dies geht einher mit der Entwicklung geeigneter computergestützter Softwarelösungen für Energiemarktteilnehmer und Systembetreiber. Darüber hinaus ergeben sich mit weiteren Fortschritten in der Informations- und Kommunikationstechnologie und Systemautomatisierung erhebliche Chancen für eine nachhaltige Gestaltung einer solchen zukünftigen Energieversorgung. In diesem Zusammenhang erörtert die Arbeit in einer ausführlichen Diskussion Anwendungs- und Einsatzmöglichkeiten von virtuellen Kraftwerken. Hier dient das Aggregationskonzept als Instrument für die Umsetzung koordinierter und optimierter Kontrollentscheidungen durch die Bereitstellung interkonnektiver und interoperabler Lösungsansätze. Die entwickelten Methoden und Funktionalitäten werden in einem service-orientierten Design und Regelschema des virtuellen Kraftwerks eingebunden, um damit umsetzbare ökonomische und technische Lösungen für den Energiemarkt und das Energieversorgungssystem zu determinieren. Die Analysen zur Entwicklung ergänzender Implementierungsmethoden basieren auf numerischen Simulationen zur Ermittlung ökonomisch und technisch umsetzbarer Lösungen für die Teilnahme an den Energiemärkten sowie im operativen Netzbetrieb. Unter Einhaltung der Rahmenbedingungen liberalisierter Energiemärkte wird ein Energie-Management-Algorithmus für integrierte Marktoperationen vorgestellt, mit dem Ziel verschiedenartige verteilte, erneuerbare und mobile Energieanlagen berücksichtigen zu können. Hierfür wird eine gemischt-ganzzahlige lineare Programmierformulierung vorgestellt, um die Kraftwerkseinsatzplanung des Virtuellen Kraftwerksbetreibers in einem Mehrperiodenoptimierungsprozess lösen zu können. Die entwickelte Methodik erlaubt den Handel von verschiedenen Marktprodukten mit variabler zeitlicher Auflösung bis hin zur Ausführung von Echtzeit-Markttransaktionen. Durch die Bereitstellung einer einheitlichen Modellarchitektur für skalierbare Kraft-werks-Portfolios werden deterministische Planungsmethoden und umfassende Untersuchungen durchgeführt. Dabei werden besonders Elektrofahrzeuge als zusätzliche Energiequellen in gemeinsamen Marktoperationen für die Bereitstellung von serviceorientierten Operationen berücksichtigt. Darüber hinaus werden multilaterale Transaktionen für die Allokation von Systemdienstleistungen in eine hierarchisch strukturierte Formulierung des Optimierungsproblems einbezogen. Die Simulationsergebnisse der marktorientierten Interaktionen dienen zur Identifikation der zeitlichen als auch räumlichen Effekte im Netzbetrieb. In diesem Rahmen wird eine koordinierte Spannungsregelung vorgeschlagen, welche sowohl lokale als auch statische Proportionalregler mit Fernsteuerungsalgorithmen miteinander kombiniert. Dies ermöglicht die Nutzung zusätzlicher Flexibilitäten, die durch eine Vielzahl verteilter, erneuerbarer und mobiler Energieanlagen zur Verfügung gestellt werden, um zeitveränderliche Spannungsschwankungen abzuschwächen. Ergänzend wird ein aktives Netzmanagement modelliert, welches es unter anderem ermöglicht, Steuerungsalgorithmen für das Lademanagement von Elektrofahrzeugen in Verteilnetzen zu testen. Zur Bestimmung der Simulationsergebnisse werden entsprechende Auswertungsfunktionen und Programmierindikatoren vorgestellt.

Presently, phasor measurement units (PMUs) are the most accurate and advanced time-synchronized technology. PMUs are the main element of the Wide-Area Monitoring, Protection and Control System, the concept that provides an estimate of the actual condition of the system, allowing operators to run online simulations and determine the possibility of cascading events, the voltage values outside the limits, while the operator is still able to take proper actions, preventing the system blackout. However, for achieving complete observability of a power network, PMUs should be installed at about one-third of the total number of network buses. Due to the high expenses, TSOs and DSOs are not willing to integrate PMUs in the large scale. Consequently, by covering only small portions of the power grid, detailed snapshot of the power grid condition is not the possible and complete benefit of such advanced monitoring units cannot be gained. This was the source of the motivation for a presented master thesis. The contribution of the thesis is a development of the low-cost Phasor Measurement Unit, which performance complies with the IEEE C37.118.1 standard requirements. The prototype is based on Smart Discrete Fourier Transform technique for synchrophasor estimation. The algorithm is running on the embedded voltage sensor developed in Smart State Technology. During the research, the main question was how accurate performance of the prototype can be obtained by optimization of the algorithm to the processing power of the embedded sensor. The most optimal solution providing the accurate performance of the algorithm and sensor CPU load within processing limitations is found in ADC sampling rate of 1kHz, non-recursive DFT approach and mean filtering performed on SDFT frequency estimates.

This thesis represents a building block for future model predictive control of a battery connected to a complex energy system consisting of a photovoltaic (PV) system and a combined heat and power (CHP) plant. The complex energy system at Campus Evenstad in Norway is used a case study in this thesis. The aim of this thesis is bipartite: (1) the performance of the PV system is to be predicted, and (2) various control strategies of the battery will be investigated to see the flexibility that the battery may provide for the end-user. Two models have hence been developed: a PV model and an optimization model of the battery. Both models have been developed in Python with the help of the PVLIB and the Pyomo libraries. Two approaches to estimate the plane-of-array (POA) irradiance on the PV array were tested in the PV model: the dirindex and the erbs irradiance decomposition methods, which are both built-in functions in the PVLIB library. Results showed that the dirindex decomposition method gave the most accurate results. However, results for winter months are highly inaccurate, and hence the PV model should be improved to better predict the PV performance in such months. The model was also tested with various overall PV system efficiencies and surface types indicating how much reflected solar radiation that hits the receiver. An overall system efficiency of 74% and surface type asphalt resulted in the most accurate PV estimation. The optimization model was solved with three different objectives: (1) minimization of total import of electricity, (2) minimization of spot energy costs, and (3) peak shaving. In addition to analyzing the charge and discharge of the battery, the total cost of import was calculated for each control strategy. When using the battery to minimize the total import from the grid, the battery is not frequently used. The only recharging of the battery that takes place is a result of low demand in times of high PV production. The minimization of the spot energy cost control strategy reduces the energy cost of the imported electricity, but low spot prices lead to an increase in the import peak and hence an increase in the grid tariff cost. The total import cost of this control strategy comes out higher than the total cost of the other two control strategies. The variation in spot prices results in a rapid charge and discharge of the battery. Optimizing the utilization of the battery with the objective of performing peak shaving, the grid tariff, which is determined by the highest import peak in the last 12 months, is reduced. The grid tariff makes up the highest share of the total cost of import, and hence does this control strategy result in the lowest total cost.

Today, the world is facing a situation where only having an energy source is not the final priority, but, also having a clean energy source is the final concern. Where clean energy generation is concerned, only renewable energy resources come into the picture rather than conventional power generation sources. The tendency towards renewable energy sources has grown incredibly in recent years. It can be stated that wind and solar energy sources have the highest share of renewable energy sources. Nowadays, wind farms are usually located far away from load centers. Therefore, strong power transmission systems are required to transmit bulk power over long distances based on AC or DC solutions. Several detailed comparisons have been performed on High Voltage Alternating Current (HVAC) vs High Voltage Direct Current (HVDC) systems. It can be noted that the HVDC transmission system is the more feasible solution to transmit power in renewable energy power systems, especially collecting power from offshore power plants and distributing it among onshore consumers.\\ Line Commutated Converter (LCC) and Voltage Source Converter (VSC) are two available technologies in HVDC transmission systems. VSC (modern HVDC) technology with Pulse Width Modulation (PWM) has a number of advantages compared to the classical thyristor-based converters, such as the separate and fast-acting controls of active and reactive powers. Hence, VSC is the most suitable converter technology to make a multi-terminal DC (MTDC) power transmission system. It is desired that MTDC systems be capable of interfacing with all types of AC systems since the dynamic of MTDC systems is very fast. The main objectives to construct and use MTDC systems are the large-scale integration of renewable energy sources into the existing AC grids and the expansion of international energy markets through super grids.\\ This thesis presents ancillary services from HVDC systems and analysis power transmission systems based on VSC technology. The main focus of this thesis is to investigate the interactions of AC and DC grids and sharing power between them. A network based on MTDC power transmission system is designed in MATLAB/Simulink by developing a Matlab example to demonstrate interactions between the four AC grids and the MTDC system. In the test model, two AC systems, which are located at two different areas, are transmitting power via two VSCs (rectifiers) to two VSCs (inverters), and the inverters are finally connected to two other AC systems. Dynamic performance of the VSC MTDC system is examined by simulating different conditions to illustrate the energy balance in multi-area grids. Detailed simulations results are presented for normal operation and two case studies with different control strategies, such as active power control and DC voltage droop control to illustrate the behavior of the entire system under different conditions.

This thesis delves into the two fields of signal analysis and small-signal stability of power systems. Due to the extensive deployment of PMUs in today s Smart Grid, new possibilities arise to assess the small-signal stability by measurement based techniques. The benefits of this approach are many, the most compelling being that the power system has become too complex to be accurately modelled with a component-based approach. A whole range of methods are available for the purpose of signal analysis in power systems, all with various assumptions, strengths and weaknesses. Insight into the analysis methods and the measurement data in itself is important for choosing the appropriate techniques for a given signal. The methods described in this thesis are: Prony s method, Robust Recursive Least Squares (RRLS) and the FFT based Welch s method. Prony s method is known as a ringdown (post-disturbance transient) analyzer, while the two latter are known as ambient analyzers. To improve estimation robustness and accuracy, pre-filtering is implemented with the Empirical Mode Decomposition (EMD). This technique works as a non-linear and non-stationary band-pass filter, effectively extracting the desired frequency spectrum in the electro-mechanical range. This is validated using Welch s method, which reveals negligible change in the power spectral density of the investigated frequency range. Both Prony s method and RRLS assume an underlying parametric model, and require specifying a model order. This issue is transformed into a benefit, extracting the consistent information from multiple analyses with varying model order. Clustering is used as post-processing intelligence to identify the dominant modes of the estimation. The third technique, Welch s method, is used for validation purposes. The methods and data are contextualized; subsequently, the techniques are described with relevant theory, and thoroughly tested for both simulated and real-world data. The estimation from ringdown data is compared to the estimation from ambient data, which in real-time scenario often is the only option for evaluation. The three analyzers contribute to mutual validation of the modal content, improving the credibility of the estimates. For simulated data, the measurement based estimation is also evaluated against eigenvalue inspection of the linearized power system model. This thesis is based in part on a conference paper to be published at SPEEDAM 2018. This article describes theory of Prony s method, as well as the EMD and Clustering technique. Since then, the thesis has evolved in scope and depth. The results from detailed testing show that the investigated combination of methods performs well on real-world PMU-measurements. Prony s method identifies the modes of ringdown data and the RRLS method identifies the modal content in the ambient data. The damping ratio is in general slightly underestimated in the ambient data compared to ringdown data. However, both give a good indication of the modal content. A comprehensive toolbox of the methods mentioned above has been indigenously created (in Python) as a part of thesis work; the toolbox utilizes weaknesses of some methods, e.g. the model order selection problem in Prony s method and RRLS, as input to other methods, such as the clustering technique. The result is an autonomous algorithm, taking care of each submethod s deficiency.

PV-microgrids are becoming an affordable alternative to provide electricity access to remote or isolated regions, due to both a reduction in prices on solar panels and a strong focus on utilisation renewable energy resources. When designing microgrids, the use of optimization methods has traditionally been rather limited. Flexible systematic design tools that covers the full system path from data-acquisition to optimization and load-flow-analysis, are of limited availability. This thesis will seek to present a methodology for a cost-effective design of microgrids based on composable tools using optimization. Possible ways to overcome the lack of data will be discussed, along with the economic parameters used for the optimization process. A selection of already-existing tools will be presented, along with the advantages of the using novel sizing methodology presented in the thesis. The methodology presented will be applied to a case-study in Bhutan. Using measured data from the study, the accuracy of initial assumptions and data-acquisition can be evaluated. The findings were that initial assumptions can give a good idea on consumer behaviour, and thus system composition, however a more detailed study on local conditions will always be preferred. Finally stable operation of the optimized system will be validated through Matlab/Simulink-models.

The society depends on a reliable electrical power system. The socio-economic cost will be high if a wide-ranging disruption of the supply occurs over an extended period of time. Thus programs that help system operators to identify possible risk in electrical power systems are needed. The fast decoupled power flow, primal version, is found to have better convergence characteristic than the dual one, for power systems with a low X/R-ratio. Linear sensitivity factors have been utilized in several of the algorithms. These factors are based upon DC and can be used to find post-contingency flows very fast, hence useful for decision support. Contingency analysis is important in this report. The purpose of contingency analysis is to test systematically for outage of components like branches and generators. Most of the implemented code is contingency analysis algorithms. The efficient bounding method has been implemented. This method encircles the outage component and thus reduces the number of calculations needed. The number of expansion steps needed from the outage, are dependent on an angle spread criterion concerning the boundary nodes. EBM is found to be faster than normal DC power flow. The concentric relaxation method is a simpler variant of the EBM. It utilizes a pre-determined number of layers to enclose an outage. The EBM and the CRM are best used when only the largest flow violations are of interest. Both the EBM and CRM are DC algorithms. A post-compensation technique has been utilized for some of the algorithms, both AC and DC. This technique makes it possible to avoid time consuming factorization of matrices, thus allow for more calculations during a limited time frame. The post-compensation technique gives a more detailed output, and is faster than the EBM and the CRM. Even the AC-version used less time than the EBM when testing a large power system. Indirect ranking of contingencies using a performance index has been implemented in the DC contingency analysis algorithms. A modification is done to the method so that only overloaded branches contribute to the index; hence it prevents the phenomena known as "masking error". Efficient power flow algorithms are useful when time frame is limited. However, it is important to know the different algorithms' limitations. DC algorithms, for instance, should not be used for systems with a low X/R-ratio.

The simulation of large-scale power system models including transmission grid representations is limited by available computation power and time. Therefore, the reduction of transmission grid models is of paramount importance. This report proposes and tests a new method of reducing power grids. This method allows to reduce an existing transmission grid model to any desired size, however, at the cost of accepting increasing levels of inaccuracy. An algorithm is developed that reforms the total number of nodes in the full grid representation into a smaller number of clusters, which are then connected by equivalent power lines. The algorithm is designed in such way that those power lines remain in the transmission grid that are likely to form a bottleneck, thus restraining power flows. The accuracy of this method is measured by comparing the power flows in the reduced power grid to the flows from the original grid. The power flows of the full and reduced model are calculated by applying linear approaches based on PTDF matrices. PTDF matrices are commonly used in transmission grid analysis, linking node injections to power flows. The power flows are calculated based on a pre-defined set of injections, which represent cases of realistic power plant dispatches. The PTDF matrix for the reduced matrix is derived with the method proposed by Shi et al. The reduced matrix is operating point dependent, based on a set of reference injections. The results show that every country can be reduced up to 37.5% of its original size, when maintaining an allowable error of 20% of the available transfer capacity of a power line. Most countries can even be reduced further before they exceed the set accuracy benchmark. In addition to this, the report researches whether guidelines can be identified to which extend power grids can be reduced within preset limits of accuracy. Power grids in countries have different properties like topologies and grid characteristics, possibly leading to differing error behavior. The results show that no clear relation can be identified between the properties of a country s power grid and its error behavior, but is dependent on case specific situations in which node injections play a particularly decisive role. As the node capacity and node generation are random though, so are the occurring errors. Finally, the relation between accuracy and gained computation time in optimization simulations is identified. The relation between the number of variables in an optimization model and required computation time is exponential. This relation shows that without exceeding the preset boundaries of accuracy significant gains in computation time can be acquired. A grid reduced to 22.5% of its original sizes does not exceed the error limit in power lines, while the computation time reduces by a factor of 261.

The increased use of renewable energy sources in Continental Europe, in particular Germany, has led to a great variability in power production and prices. One proposed way to remedy the Continent s power balance which is also economically viable in a free power market is by the means of Norwegian pumped storage. However, the profitability in such an environment is highly dependent upon the extent of price variation in the market.In this paper, it has therefore been sought to find a stochastic price model in which the spot price is allowed to fluctuate around a sound forecast. With historical data from the German power market as the point of departure, a deterministic price curve with seasonal and daily patterns has been obtained through linear regression. This curve has been adjusted to the market expectations contained in power futures contracts. By contrasting the updated deterministic price curve with the actual spot price, it has been possible to obtain a time series model on the basis of deviations that are mainly stochastic.The time series model has been used to generate multiple spot price scenarios that serve as an input for a representative Norwegian pumped storage power station. Simulations show that both the power station s production planning and revenues are dependent on which scenario that is under consideration. Nonetheless, the production patterns under both the different scenarios and the real spot price are comparable, in particular with regards to the daily and weekly patterns. Similarly, the total profits depend upon the variance of the price scenarios, but all scenarios, including the actual spot price, has been shown to yield significant revenues.

The electrification of the transport sector is put on the agenda as an important means to reduce the greenhouse gas emissions in Norway, EU and other parts of the world. Chargeable vehicles have the potential to reduce the greenhouse gas emissions both because they are four to five times more energy effective than today s petrol-powered vehicles, and because the electricity they use can come from renewable production. Questions regarding sufficient access of conventional oil and increasing challenges with local emissions will also contribute in the electrification of the transport sector [1].The electrification of the transport sector brings with it some challenges. The charging of the electric vehicles leads to an increase in demand. If no sort of smart control of the charging is put in place, it could be safe to assume that many vehicle owners would plug-in their vehicles when they come home from their last journey of the day, leading to an increase in power demand at the time when there already might be a peak in demand. This charging regime is often referred to as dumb charging .This thesis focuses on smart strategies for charging of electric vehicles and presents two smart strategies for charging of the electric vehicles, the profit maximization scenario and the power factor control scenario. In these scenarios it is assumed that a control system is put in place so that specific chargers can be instructed to change the power factor and to begin and stop charging. The technical specifications of this control system has not been studied, it is simply assumed that such a control system is put in place. In the profit maximization scenario, it is assumed that technology facilitating the electric vehicles to discharge energy back to the grid is put in place. The electric vehicles are then instructed to charge when the electricity prices are low and discharge back to the grid when the electricity prices are high. Since the demand and electricity price pattern follows a similar pattern (high prices when the demand is high, and low prices when the demand is low), this procedure should have a smoothing effect on the demand pattern with the right choice of parameters.In the power factor control scenario, all electric vehicles are assumed to be plugged-in and start charging as soon as they return from the last journey of the day. When there are voltages in the grid below a certain value, electric vehicles charging at that time is instructed to reduce the charging power factor. By reducing the power factor, reactive power can be injected into the grid.To demonstrate the principles, algorithms have been developed and implemented in MATLAB for both the dumb charging scenario and the two smart charging scenarios. A model of the IEEE 13 node test feeder has been modelled in MATPOWER, and power flow simulations of the three charging scenarios have been run, assuming a vehicle adoption of 50%. The algorithms success has then been rated according to their capability to avoid low voltages on the demand nodes in this test case. For the purpose of this thesis it is assumed that the designed model is a distribution network in Norway. Therefore the base demand pattern used in the simulations follows the actual base demand pattern for a chosen 24-hour period in Norway.The results from the simulations showed that the when all vehicles were charged as soon as they return from their last journey of the day, it resulted in a major peak in demand, and thus a reduction of the voltage between 18:00 and 21:00.Both smart strategies presented in this thesis improved the voltage profile. While the lowest node voltage in the simulations of the dumb charging scenario was 0.915 pu, the lowest node voltage in the profit maximization scenario was 0.932, and the lowest voltage in the power factor control scenario was 0.934 pu.In the profit maximization scenario, the demand profile, and thus the voltage profile, did however not smooth out as much as expected. Since the electricity prices changes when there is a change in demand, the algorithm is designed to find the charging schedule for one vehicle at the time, changing the electricity prices in between. A further study on this scenario should focus on finding a better relationship between changes in demand and electricity prices.In the power factor control scenario, the minimum voltage allowed was not avoided at all nodes in the designed test case. The simulations showed that one of the nodes experienced a voltage violation. This scenario did however only assume that the vehicles were only available for grid services the first eight hours after the return of the last journey of the day. If the vehicles were available at other times too, this voltage violation could however been avoided.

With the introduction of an increasing number of regulation markets,hydropower producers face multiple opportunities regarding how toutilize their water optimally. Such regulation markets can increaseprofits drastically compared to a single day-ahead spot market, thus theuse and comprehension of multi-market optimization tools are valuablefor all hydropower producers with storage.This report contains the development of a stochastic multi-stageoptimization model where the effects of committing upon different levelsof regulation obligations in electricity markets are investigated seen froma hydropower producer s perspective. A mathematical formulation waswritten, and a corresponding optimization code implemented. Ananalysis was further conducted through a case study where a stochasticspot price was constructed and optimized upon by an implementedwatercourse with authentic properties.Comparison between different levels of regulation obligations, the effectconcerning the introduction of new information during the stochasticoptimization period and the benefits of multiple executions (MonteCarlo-simulations) are among the essential output data analyzed.The results indicate such comparisons of regulation obligations to beuseful when deciding whether or not to provide regulation capacity, andif so, at which level. Also, the value of good information should not beunderestimated when participating in markets with uncertaintyregarding the future.The market designs are affecting the choice and design of theoptimization strategy used in markets with more complex properties,analyzing multiple regulation obligations may prove hard to present andtime consuming to process. Thus, using a forecasted price of regulationmarkets is often preferred, but unfortunately such forecasts are hard toobtain. Nevertheless, decision-making tools regarding optimal levels ofregulation obligations can be utilized by considering factors such as theneeded regulation price to break even from a potential loss in the spotmarket, as well as the marginal cost of increasing a regulation obligation.

A reliable electric power supply is essential for modern society. Recently, severe blackouts worldwide have attracted attention to reliability studies in power system planning and operation. The relevance of the traditional N-1 criterion has been discussed, and much focus has been directed towards developing satisfactory probability based reliability tools. Goodtech Project & Services has developed a methodology for calculation of online power delivery reliability for use in power system operation and planning. The method, based on Markov models, analyzes the entire network for a large number of fault combinations, a useful approach for relatively small networks. However, the computation time increases polynomial with increasing system size. Because the impact of an outage has a limited geographical extent, it is desirable to reduce the system to be simulated, so that it only includes the affected area. The objective of this project is to develop methods for identifying the components that can be considered influenced by a fault. The focus of the pre-study was to evaluate which post-processing method best suited for developing a reduced network system. In the pre-study, power flow results from the standard DC load flow were used. The main focus of this thesis has been on developing and implementing fast methods for obtaining the necessary power flow data needed in order to use the post-processing methods. Three approaches have been investigated and tested, namely AC load flow based on the fast decoupled load flow with compensation techniques for obtaining the post- contingency power flows, DC load flow with compensation techniques and the efficient bounding method. The key principle of the compensation methods is that the effect of outages can be calculated by introducing simple compensation terms, thus avoiding the need to rebuild and factorize the system matrices for every contingency case. The bounding method is based on the principle of sensitivity factors and the fact that given knowledge about changes inside a boundary certain conclusions can be made regarding the changes outside it, thus eliminating the need for studying the entire system. The method based on the fast decoupled load flow is the only method that gives the possibility to provide an exact solution, and is also the only method that includes reactive power and voltage magnitudes. It is therefore recommended used in cases where a high degree of accuracy is important, or if reactive power and voltages are of interest. Tests show that the DC load flow is fastest. The accuracy is assumed sufficient for most intended purposes, and should therefore the preferred choice in most cases. Bounding methods are especially useful in highly meshed grids, and if only the largest changes are of interest.

Forventninger om høyere kraftpris og et generelt økende effektbehov, i tillegg til økte muligheter for politisk aksept og tilskudd, gir økt interesse for å etablere nye fornybare produksjonskilder i Norge. Et gradvis økende antall interessenter melder sin ankomst, og nye produksjonsetableringer dreier seg primært om små vannkraftverk eller vindparker. Slike etableringer vil kunne medføre problemstillinger som krever relativt omfattende undersøkelser og analyser for å finne påvirkninger i tilhørende nettområder. I Fusa kommune i Hordaland er det stor satsing på små vannkraftverk. Dette gir behov for konsekvensanalyser i nettområder som berøres av integrasjonen. Over 20 nye småkraftverk er planlagt etablert. Disse befinner seg på ulike stadier i etableringsfasen. Hovedtyngden av småkraftverkene er planlagt tilkoblet på distribusjonsnettnivå, og dette nettområde er derfor tillagt mest fokus i dette arbeidet.Integrasjonen medfører at enkelte tiltak blir nødvendig i distribusjonsnettet for å kunne handtere den nye mengden kraftproduksjon. Enkelte overføringer vil kreve oppgradering for å unngå overbelastning i forhold til merkeverdier. Én av fire sekundærstasjoner mellom regionalnett og distribusjonsnett må oppgraderes til en høyere ytelse. For å unngå for høye spenninger i distribusjonsnett burde enkelte småkraftverk ilegges ansvar for reaktiv effektregulering. Med gjeldende koblingsbilde må totalt syv av de 21 planlagte enhetene kunne importere en mengde reaktiv effekt tilsvarende en kapasitiv effektfaktor på 0.95 dersom spenninger skal kunne holdes innenfor den definerte spenningsgrensa brukt i denne oppgaven.Småkraftverk vil påvirke systemets dynamiske stabilitet. Særlig den transiente responsen for systemet vil bli påvirket. Tilgjengelig dokumentasjon for småkraftverkene i systemet viser at alle er utstyrt med synkrongenerator. Det bør stilles krav til parameterverdier for denne typen generatorer i distribusjonsnettet, og da særlig angående generatorens reaktansverdier. Reaktansverdier for små generatorer vil være helt avgjørende for dens respons under transiente forstyrrelser. Analyser utført i dette arbeidet viser at transient reaktans i synkrongeneratorens direkteakse må ha en tilstrekkelig lav verdi for at generatoren skal kunne være transient stabil.I arbeidet er det benytta samme type transiente forstyrrelse for de fleste av analysene rundt det transiente aspektet. Denne forstyrrelsen er foreslått av SINTEF Energi AS som en standard for transient hendelse til bruk i slike analyser. Analysene viser at den transiente direkteakse reaktansen primært ikke bør ha verdier over 0.3 pu for at synkrongeneratorene, uavhengig av merkeytelse og belastningsgrad, skal være transient stabile mot nevnte forstyrrelse. Transient stabil verdi for denne reaktansen varierer med andre korresponderende reaktanser, men verdier over 0.3 pu vil kreve til dels urealistiske verdier for andre parametre i småkraftverkene. Hvilke reaktansverdier som kan tillates vil være svært avhengig av generatorens belastning. En belastningsgrad i området 70 % - 80 % vil gi lavere krav til reaktansverdier enn tilfeller med høyere verdier for samme forhold.Av det totale antallet på 21 småkraftverk er fire av disse allerede installert i distribusjonsnettet. For at disse skal være transient stabile mot forannevnte forstyrrelse må de redusere sin nominelle produksjon i forhold til det tilgjengelig dokumentasjon beskriver. Mengden som må reduseres for de fire som er installert avhenger av synkrongeneratorens reaktansverdier. Resultatene viser at generatorer med høye reaktansverdier må redusere sin relative produksjon mer enn generatorer med lavere reaktansverdier.For å kunne finne anbefalte verdier for reaktanser til nye småkraftverk er det utvikla en alternativ metode til bruk av dynamiske analyseprogram. Denne metoden gir reaktansverdier som skaper forutsetninger for at synkrongenerator er transient stabil mot den benytta typen forstyrrelse. Metoden er relativt mye forenkla i forhold til beskrivelser i relevant litteratur på området, og krever med dette et minimum av inputverdier. Metoden er testet og funnet tilfredsstillende til å kunne gi veiledende verdier for reaktanser til nye småkraftverk med synkrongenerator.

The necessity of a revolution in the electrical system is obvious, and smart meters will be the solution. The development of smart grids will be built over the new electronic measuring devices, which imply a challenge for the next few years in the engineering field.In order to understand the basics of smart grids, we have carried a description and comparison of both the current and the next-gen electrical systems. Emphasizing the advantages and opportunities obtained by changing into the smart grids, it demonstrates the importance of moving towards a more modern measurement system.A very important issue is to decide which should be the minimum features in Smart Meters, therefore this thesis analyzes the different exiting models and also proposes several suggestions for the future. Finally, it was conducted a report of the current deployment situation of this new technology in various representative countries. Describing the settings and options chosen by each country, we can achieve a conclusion that unifies a standard solution by the choice of the best proposals.

This master thesis has investigated the possible application of voltage source converters (VSC) for the interconnection of offshore installations, i.e. wind farms and petroleum platforms, in a multiterminal DC (MTDC) grid. The master thesis is written at the Norwegian University of Science and Technology, Department of Electric Power Engineering and is a continuation of the project written during the autumn of 2009. The work has been carried out in cooperation with Statnett SF, the Norwegian TSO, as a contribution to an ongoing research and development program on offshore electrification. The motivation behind this thesis is the possibilities the VSC technology bring about for the realization of renewable wind energy far from shore and supplying petroleum installations from the main onshore grid, thus reducing emissions. A theoretical study has been conducted, describing the VSC technology from basic operation to topics related to the implementation of a high power rated offshore MTDC grid. A suggested model of a small power system was established in the simulation program PSS®E. The model consisted of a four converter MTDC connecting three separate AC systems. One of the AC systems was a simplified representation of a main onshore grid, and the other two were small offshore AC grids made up of a wind farm and a petroleum platform. The MTDC was modeled using ABB s HVDC Light Open model v 1.1.9-2, developed for use in PSS®E. A series of dynamic simulations have been performed using the model to demonstrate and analyze the principles of operation for a MTDC and the interaction between the AC systems and the MTDC. The dynamic simulations demonstrate the basic operation of a MTDC with a master-slave control scheme for the active power control, as implemented in the HVDC Light model. The simulation results confirm the functionality of a MTDC as described in the theoretical analysis of the technology.The analysis based on both the literature and simulations conclude that VSC technology is a realistic solution for an offshore grid with the objective of supporting passive network installations far from shore. Simulation results conclude that an advanced control system for the active power control operation (Poption) of all the converters in a MTDC may greatly improve the performance of the system following a disturbance. Both theoretically and through simulations it has been demonstrated that the VSC MTDC provides stability improvements to the connected AC grid, by actively controlling the injected active and reactive power to the grid. The possibility to use the MTDC as an alternative path for transferring large amounts of power has been investigated, and this was found to be beneficial for the system. The difficulties related to fault protection in a MTDC have been highlighted, and a theoretical analysis concluded that the protection scheme using IGBT circuit breakers is the preferred solution with present available technology.