With an increasing interest for renewable power, photovoltaics (PV) have becomemore and more common in the distribution network. If a customer wants to install aPV system, or another type of distributed generation (DG), the distribution systemoperators (DSO) needs a good way to determine if it the grid can handle it or not. InSweden, a guideline to aid the DSO was published in 2011. However, this guidelineonly considers one connection without considering other DG units. This project isabout developing new guidelines for DG connections in grids with a large number ofDG units. Based on a literature study it has been concluded that one of the mostcritical issue is over-voltage, which is the main focus of this project. Two new methods have been developed; the first proposed method is based onneglecting reactance and losses in the grid, a simple linear relationship between thevoltage level, the resistance in the lines, and the installed power is obtained. Thisrelationship is then used to calculate the voltage level at critical points in the grid. Thesecond method is to find the weakest bus, with a connected DG unit. By assumingthat all power is installed at that point we get a very simple guideline; it is veryconservative but can be used before the first method. A simulation tool has been developed in order to analyze the voltage level in grids forvarious cases with connected DG units. The simulated results have proven that theproposed guidelines are, when considering voltage issues, very reliable and can beuseful. However, further work needs to be done to ensure that other problems donot occur.

According to the EU Council in 2007, a target of 20% Renewable Energy Sources (RES) energy share was determined by the year 2020. Maximizing RES penetration, whilst simultaneously ensuring grid stability and security of electric supply, has become a major challenge for the grid operators. The aggregated effect of Distributed Generation (DG) units will affect increasingly the transmission grid operation and planning. More and more, the High Voltage (HV) grid has to export the excess of power produced at the Medium Voltage (MV) level, where DG units are connected. The energy flows become variable both in value and direction in substations at the interface with distribution networks, which is a complete change for the grid operator. Power flow congestions and voltage problems are particularly more likely to arise. Systematically reinforcing the network in order to absorb the last MWh produced by DG units located in unfavorable areas, while maintaining the traditional operation of the grid, is not efficient, i.e. neither economically viable for the community nor acceptable from the point of view of environmental impact. The intermittency of DG units makes it irrelevant to define the amount of connectable units on the basis of their installed power and the N-1 criterion. New paradigms to increase the grid capacity of accepting DG units before reinforcement are to be considered. And new methodologies for long-term and operational grid planning, giving allowance to this inherent variability in the generation, are therefore necessary.Active Network Management (ANM) allows to moving away from conventional grid operation towards a new approach, comprising (almost) real-time supervision and control of the DG units and network elements. Thanks to this new management of the system and accounting for the intermittent (i.e. weather-dependent) RES production, more DG units can be connected to an existing grid: the power produced by some DG units can be curtailed to eliminate possible congestions encountered for specific combinations of loads, generations and weather conditions. In others words, the use of an ANM scheme makes possible to maximize the grid utilization in enhancing the required flexibility of system operation to maintain power system security margins.A reasonable level of security in applying ANM is however required and it must be assessed before any possible application to the grid. This assessment can be performed based on a probabilistic approach: the uncertain parameters, i.e. each load and power produced by a DG unit, are modeled with probability density functions (pdf’s); the latter are then randomly sampled, to create so-called variants. These variants serve as input data for an Optimal Power Flow (OPF) module to find the possible redispatching or curtailment that could be necessary in each case. The state space is extremely vast, however, due to combinatorial explosion. Creating a sufficiently large sample of variants to cover all significant situations the grid can face appears intractable, and alternative approaches, combining a systematic search in the state space with an acceptable computation time, are to be developed.This research proposes a pragmatic methodology to handle the high dimensionality of the problem and estimate the impact of connecting a new DG unit, via the computation of several risk indices. A systematic approach guarantees searching all over the plausible congestion zones of the state space, while an on-target sampling drives the computational effort towards the direction of interest. This combined approach allows managing the computation time without falling into oversimplification or losing too much accuracy. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Distributed Generation (DG) is one of the technologies approved by the South African government for the country's generation expansion to meet future load demand and to support economic growth. DGs change the conventional power flow (generation, transmission to distribution) by injecting real and reactive power at distribution voltage levels. The change in the conventional power flow creates complexity in the power system grid planning due to the conversion of the power system from a passive network to an active network. Introduction of bi-directional power flow on the power system can, among other benefits reduce local power demand which opens opportunities for capital investment deferrals on the transmission and distribution sectors. Consequently, DG impact on the transmission and distribution grid planning has been studied by other researchers. However, previous studies evaluated DG integration on a regulated market and assumed a certain level of generation availability during network peaking period. None of the studies have yet evaluated the benefits on an unregulated market using real measured data. Furthermore, SA distribution network expansion is also being planned without incorporating DGs on the network because of unreliability of wind and solar energy and the network operator's inability to influence the size, location and penetration level of DGs. This planning approach forces the network operator to do more to ensure high network strength. This approach can also result in network overdesign and unnecessary capital expenditure due to the potential benefits that can be deduced from DGs. This dissertation therefore aims to investigate whether incorporating future DG integration in distribution network planning can alleviate financial ramifications of grid code compliance requirements. The data used in the simulations was obtained from the distribution network operator and comprises of both real and reactive power values with a sampling time of 60 minutes for a period of a year. Simulations were conducted for both low and high load conditions to cover the extreme ends of the network and the parameters that were assessed are thermal rating, voltage regulation and network grid losses. Results showed that thermal constraints that are expected on the network when DGs are not considered are not evident when DGs are considered. Results further revealed that there are undervoltage improvements on the network when DGs are considered, and this reduces the capital expenditure that would have otherwise been incurred without DGs to result in a grid code compliant network. Furthermore, there is evidence of reduction in losses under high load conditions and increase in losses under low load conditions in the simulation results. Reduction in losses is caused by supplementary generation from wind and solar plants while increase in losses is due to excessive generation from wind plants which necessitate transportation over long distances to the nearest load centres. In addition to location, size and penetration levels as described in the literature, technology selection for a particular load type is also of utmost important to maximise the DG benefits on the network.

Dans le domaine de la distribution d’électricité, l’arrivée progressive de production décentralisée rend certains réseaux de distribution exportateurs de puissance, au point où des investissements sont nécessaires pour permettre l’évacuation de la puissance produite. La progression de l’instrumentation des réseaux permet au distributeur d’obtenir des informations de plus en plus riches sur la production décentralisée et la question d’intégrer celles-ci dans les procédés de planification français se pose. À partir de relevés de production, on vérifie que les situations de référence utilisées pour dimensionner le réseau présentent un risque d’occurrence suffisant pour nécessiter des investissements. Si des solutions offrant de la flexibilité sont utilisées, celles-ci peuvent être intégrées au processus de planification. Une étude technico-économique est nécessaire et des méthodes sont proposées pour estimer les fréquences de forte production et la dispersion possible pour un ou plusieurs producteurs. Des modèles simples de loi jointe sont proposés. Le cas pratique de l’effacement de production est testé sur des réseaux considérés réalistes. À partir des relevés réels et des modèles, l’effacement est comparé à l’option d’investir au niveau du poste source. Des abaques de décision sont tracés permettant une projection rapide du distributeur. Par ailleurs dans une optique d’utilisation de l’effacement pour gérer des contraintes intra-réseau, une méthode de calcul de load flow probabilisé est proposée ; celle-ci permet d’estimer rapidement la quantité d’effacement requise et de réaliser un comparatif économique entre plusieurs options. / In the field of electricity distribution, some grids are more and more frequently exporters due to the gradual arrival of decentralized generation. Some grid investments are required to allow the evacuation of the power generated. As more and more information about decentralized production are available for the DSO, the question of integrating them into the planning processes arises.From data of energy production, it appears that the current situations tested for sizing the grid are likely to be reached on a several years basis. If consumption or production flexibilities are used, these can be integrated into the planning process. A technical and economic study is needed and methods are proposed to estimate the frequencies of high production and possible dispersion for one or more producers. Simple models of joint distribution are proposed.The practical case of curtailing production has been tested on networks with realistic scenarios of producers arrival. From actual data and previous models, curtailment and reinforcement are compared on a technico-economic basis. A abacus is plotted as a simple decision tool for the DSO. The question of using curtailment to defer or avoid intra-grid investment has also been investigated ; a calculation method of probabilistic load flow is proposed; it gives a quick and accurate estimation of the energy to curtail in order to avoid a constraint.

Master of Science / Department of Electrical and Computer Engineering / Anil Pahwa / The unusual weather events during the polar vortex of 2014 illuminated the needs for fuel diversity for power generation in order to allow reliable operation of the electricity grid. A system wide reliability assessment for winter months should be undertaken in addition to the summer months to ensure reliable operation of the electricity grid throughout the year. Severe weather conditions that lead to equipment malfunction during the polar vortex should be thoroughly investigated and remediations to ensure satisfactory future performance of the grid must be undertaken. Environmentally unfriendly emissions from power plants must be minimized but diversity of generation fuel must be maintained. Future energy policies must be formulated with consideration that approximately 14 GW of coal generation in Pennsylvania Jersey Maryland Regional Transmission Organization’s control area available during the polar vortex will be retired by 2015 and replaced with plants that utilize fuel types other than coal.

The total energy demand in the world is expected to increase in the future years due to thehigh development rate of developing countries. Access to energy enables development, butthe current global energy mix has to be modified if a sustainable growth is desired. Renewableenergy sources (RES) benefit from both a political and economic support from manygovernments and international entities. The growing installation of RES takes place both inlarge scale, as wind farms with sizes 10 – 1000 MW, and in small scale in homes or smallenterprises with sizes 100 W – 100 kW. Small scale wind power connected to the grid is rarenowadays except in the case of remote mini-grids. By contrast, small scale solar photovoltaic(PV) power is being more and more commonly installed, especially in the form of investorownedroof-installed units. Taking increasing small scale solar and wind power into accountin network planning is a challenge faced by the distribution system operator (DSO).The aim of this thesis is to present a guideline that assists DSOs when planning lowvoltage (LV) distribution networks (DN) with a large amount of small scale distributedgeneration (DG) on a short-term perspective. A review on integration issues of DG isperformed and over-voltage constraints are identified as the most relevant issue. Simple ruleshave already been designed for individual DG units, as the one presented in the AMKhandbookpublished by Svensk Energi; but these are not valid any more when consideringmore than one DG unit. The new proposed guideline employs the AMK-handbook as astarting point and develops it further by including the interaction between DG units. Theguideline is then applicable to scenarios with more than one DG unit. The maximum capacityof a new DG unit applying for a connection to a grid is calculated based on the location andcapacity of the already installed DG units, and without any reinforcement. The proposedguideline can be applied under no load and minimum load condition.Since this thesis is a collaboration project between KTH-Royal Institute of Technologyand Vattenfall R&D, two specific Swedish LV distribution networks owned by VattenfallEldistribution AB are studied. Scenarios with different penetration levels of DG, with valuesbetween 12% and 71%, and capacity of individual DG units below 43.5 kW are analyzed.Evaluation of the results shows that the proposed guideline leads to acceptable results. Thedevelopment of future simple guidelines is suggested to be based on the following twoaspects: absolute and relative location of the DG units; and a correct identification of the weakbus. Relative location reveals the interaction with other DG units within the DN. Moreover, itis stated that the use of the penetration level as a planning measure, based on the total DGcapacity, has a limited application.

L’ouverture des marchés de l’énergie et les nouveaux usages ont induit à des changements significatifs sur les réseaux de distribution (le réseau basse tension – BT – notamment), comme : l’augmentation des interconnections de production à partir de sources d’énergies renouvelables (EnR), l’accroissement de la pointe de consommation, entre autres. Ces derniers créent des contraintes électriques. Dans l’optique d’une gestion pragmatique des réseaux électriques intelligents, des gisements de flexibilité comme le pilotage des charges/sources ou le stockage sont recherchés pour offrir des nouvelles solutions à ces contraintes. Cette thèse étudie ainsi les enjeux de la gestion du stockage et son impact dans les méthodes de planification des réseaux BT. Ainsi, dans un premier temps, les impacts du stockage et de la production photovoltaïque sur des grandeurs utilisées dans la planification des réseaux de distribution sont étudiés. Dans un second temps, une méthode de calcul des coûts des pertes est adaptée à la présence du stockage et/ou de la production PV. Dans une dernière partie, des algorithmes de fonctions avancées de conduite sont développés afin d’illustrer la valeur économique du stockage dans la planification des réseaux BT, et comparés à une planification classique plus couteuse. / The opening up of energy markets and new uses have led to significant changes in distribution grids, in particular low-voltage grids. Notably, it has led to an augmentation in the integration of renewable energy production, an increase in the peak consumption, among others. This is accompanied by the appearance of the electrical constraints with which power systems must cope. This has resulted in the development multiple flexibility capabilities such as load/source management or energy storage, providing new solutions, now to be considered in planning methods. This thesis studies the issue of energy storage in the low-voltage grid planning. The first part of this thesis studies the impact of storage and photovoltaic production on variables involved in distribution grid planning. In the second part, a method for calculating the cost of losses is adapted to the presence of energy storage and/or PV production. Finally, advanced d operation algorithms are developed to illustrate the economic value of energy storage in LV distribution grid planning, compared to a more expensive conventional planning method.

Der Ausbau dezentraler Energieanlagen wie fotovoltaischen Anlagen beeinflusst die Netzzustände signifikant. Dabei ist unsicher, wo und in welchem Maße deren Ausbau zukünftig erfolgt. Es ist nun an den Netzbetreibern gleichzeitig die aktuellen Herausforderungen zu meistern und die Netzplanung und -regelung für die Zukunft zu aktualisieren. Eine statistische Methode wird entwickelt, die Verteilnetzplanung unter Einsatz von quasi-stationär modellierten ”Smart Grid”-Lösungen wie Blindleistungsreglern und regelbaren Ortsnetztransformatoren ermöglicht. Durch Stichprobenverfahren werden Unsicherheiten wie Ort, Größe und Leistungsprofile der Energieanlagen in das Netzmodell eingebunden. Diese als probabilistischer Lastfluss bekannte Methode wird durch Gütemaße im Bereich geringer Kombination evaluiert. Beispiele probabilistischer Netzplanung werden an Netztopologien präsentiert. / Development of distributed energy units such as photovoltaic systems affects grid states significantly. It is uncertain, where and to what extent the development of these units is carried out in the future. It is now up to the distribution system operator to cope with todays grid challenges and to update grid planning and control for the future. A statistical method is developed, which incorporates quasi-stationary modeled ”smart grid” solutions such as reactive power controllers and on-load tap-changers. Uncertainties such as location, size and power profiles of energy systems are integrated into the grid model by sampling. This method is known as probabilistic load flow and is evaluated by quality measures at low combinations. Examples on probabilistic grid planning of different grid topologies are presented.

Aktuell finden umfangreiche Neuerungen und Veränderungen im Elektroenergiesystem statt. Dabei stellen die Netzintegration von Energiespeichern, EE-Anlagen und Elektrofahrzeugen sowie die Realisierung von Energiemanagementsystemen wichtige Neuerungen in der Niederspannungsebene dar. Analysen der Ladevorgänge von Elektrofahrzeugen zeigen einen nennenswerten Einfluss auf den Lastbedarf. Als ein Ergebnis wird die maximal zulässige Anzahl an Elektrofahrzeugen ermittelt, bei der kein Netzumbau notwendig wird. Neben der Untersuchung verschiedener Ladevarianten wird die zufällige Ladung als innovative Ladevariante vorgestellt und deren Nutzen simuliert. / Currently, fundamental innovations and changes are occurring in the power system. The grid integration of energy storage systems, renewable energy systems and electric vehicles as well as the implementation of energy management systems are important innovations in the low-voltage grid. Analyses of charging processes for electric vehicles show significant impacts on the load demand. As one result, the maximum number of electric vehicles is determined assuming that no grid expansion is needed. Besides studying various charging options, a random charging method is proposed as an innovative charging option and its benefits are shown by simulations.

Der Ausbau dezentraler Energieanlagen wie fotovoltaischen Anlagen beeinflusst die Netzzustände signifikant. Dabei ist unsicher, wo und in welchem Maße deren Ausbau zukünftig erfolgt. Es ist nun an den Netzbetreibern gleichzeitig die aktuellen Herausforderungen zu meistern und die Netzplanung und -regelung für die Zukunft zu aktualisieren. Eine statistische Methode wird entwickelt, die Verteilnetzplanung unter Einsatz von quasi-stationär modellierten ”Smart Grid”-Lösungen wie Blindleistungsreglern und regelbaren Ortsnetztransformatoren ermöglicht. Durch Stichprobenverfahren werden Unsicherheiten wie Ort, Größe und Leistungsprofile der Energieanlagen in das Netzmodell eingebunden. Diese als probabilistischer Lastfluss bekannte Methode wird durch Gütemaße im Bereich geringer Kombination evaluiert. Beispiele probabilistischer Netzplanung werden an Netztopologien präsentiert.:Abbildungsverzeichnis iv Tabellenverzeichnis viii Abkürzungsverzeichnis viii Formelzeichen x 1. Einleitung 1 1.1. Definition der Herausforderung 1 1.2. Netzplanung 2 1.3. Ziel der Arbeit3 1.4. Struktur der Arbeit 5 2. Normen und technische Rahmenbedingungen 6 2.1. DIN EN 50160 6 2.2. VDE-AR-N 41057 2.3. Technische Anschlussbedingungen 9 2.4. Erneuerbare-Energien-Gesetz 11 2.5. Zusammenfassung 12 3. Gliederung probabilistischer Lastflussverfahren 13 3.1. Punktschätzende und iterative Verfahren 14 3.2. Gliederung nach Stichprobenverfahren 15 3.3. Reduzierung des Grundraumes 16 3.3.1. Cluster-Analyse17 3.3.2. Ausreißerbehandlung 21 3.3.3. Wahrscheinlichkeits- und Verteilungsfunktion 21 3.4. Methode der Stichprobenziehung 22 3.4.1. Einfache Zufallsstichprobe 23 3.4.2. Systematische Stichprobe24 3.4.3. Geschichtete Zufallsstichprobe 25 3.5. Reduzierung des Stichprobenraumes 26 3.6. Invertierung von Stichproben 26 3.7. Zusammenfassung 27 4. Vergleich probabilistischer Verfahren 28 4.1. Nicht-Gaußsche Eingangsdaten 28 4.2. Bestimmung notwendiger Clusterzentren 29 4.3. Erstellung des Stichprobenraumes pro Kombination 31 4.4. Gütemaße und Effizienz von Stichprobenverfahren 33 4.4.1. Median 34 4.4.2. Median der absoluten Abweichung vom Median 37 4.4.3. Maximale normierte Perzentilsdifferenz 40 4.4.4. Zusammenfassung 43 4.5. Streuung der Stichprobenverfahren bei wiederholter Ausführung 44 4.5.1. Median 44 4.5.2. Median der absoluten Abweichung vom Median 45 4.5.3. Maximale normierte Perzentilsdifferenz 47 4.5.4. Zusammenfassung 49 4.6. Sensitivität bei unterschiedlicher Anzahl statistischer Netzknoten 52 4.6.1. Median 52 4.6.2. Median der absoluten Abweichung vom Median 54 4.6.3. Maximale normierte Perzentilsdifferenz 56 4.6.4. Zusammenfassung58 4.7. Notwendige Kombinationen für Ziel-Gütemaße 59 5. Software-basierte probabilistische Verteilnetzplanung 61 5.1. Struktur der entwickeltenSoftware 61 5.2. Last- und Erzeugungsprofile 63 5.2.1. Synthetische Haushaltslast 63 5.2.2. Elektrofahrzeug 64 5.2.3. Wärmepumpe 65 5.2.4. Photovoltaische Anlagen 66 5.2.5. Windenergieanlagen 66 5.3. Optimale Auswahl nach Regeleffizienz 67 5.4. DezentraleWirkleistungsregler 68 5.4.1. P(U)-Regler für Schnellladeinfrastruktur 68 5.4.2. P(U)-Regelung von Wärmepumpen gemäß thermischer Grenzen 69 5.5. Blindleistungsregler 72 5.5.1. Zentrale Steuerung 73 5.5.2. Dezentrale Regelung 75 5.5.3. Verteilte Regelung 79 5.6. Regelbarer Ortsnetztransformator 83 5.7. Automatisierte Netzausbauplanung 86 5.7.1. Transformatortausch 87 5.7.2. Vergrößerung des Leiterquerschnitts 89 5.7.3. Zusätzliche Stichleitung 89 5.7.4. Kostenberechnung 90 5.8. Zusammenfassung 91 6. Anwendungsfälle probabilistischer Planung 92 6.1. Verwendete Verteilnetzmodelle 94 6.2. Abschätzung der Auswirkung von PV-Anlagenausbau 95 6.2.1. Unterschiede der Planungsverfahren zur Schätzung der PVA-Nennleistung 95 6.2.2. Einfluss der Blindleistungsregelung auf mögliche Anlagenleistung 100 6.3. Abschätzung von Netzauslastungen in Wohngebieten 106 6.3.1. Annahmen und Szenarien 107 6.3.2. Auswertung der Knotenspannungen 110 6.3.3. Auswertung der Betriebsmittelauslastungen 116 6.4. Zusammenfassung 118 7. Zusammenfassung und Ausblick 119 Literaturverzeichnis 121 Anhang 135 A. Statistische Merkmale 135 A.1. Empirische Wahrscheinlichkeitsfunktion 135 A.2. Kumulative empirische Verteilungsfunktion 136 A.3. Quantile 136 A.4. Interquartilsabstand 137 B. PLF-Methoden 138 B.1. Veröffentlichte PLF-Methoden 138 B.2. Test Gaußsche Verteilung 138 C. Definitionen 140 C.1. Symbole für Flussdiagramme 140 C.2. Zählpfeilsystem 140 D. Ergänzende Ergebnisse 142 E. Danksagung 143 / Development of distributed energy units such as photovoltaic systems affects grid states significantly. It is uncertain, where and to what extent the development of these units is carried out in the future. It is now up to the distribution system operator to cope with todays grid challenges and to update grid planning and control for the future. A statistical method is developed, which incorporates quasi-stationary modeled ”smart grid” solutions such as reactive power controllers and on-load tap-changers. Uncertainties such as location, size and power profiles of energy systems are integrated into the grid model by sampling. This method is known as probabilistic load flow and is evaluated by quality measures at low combinations. Examples on probabilistic grid planning of different grid topologies are presented.:Abbildungsverzeichnis iv Tabellenverzeichnis viii Abkürzungsverzeichnis viii Formelzeichen x 1. Einleitung 1 1.1. Definition der Herausforderung 1 1.2. Netzplanung 2 1.3. Ziel der Arbeit3 1.4. Struktur der Arbeit 5 2. Normen und technische Rahmenbedingungen 6 2.1. DIN EN 50160 6 2.2. VDE-AR-N 41057 2.3. Technische Anschlussbedingungen 9 2.4. Erneuerbare-Energien-Gesetz 11 2.5. Zusammenfassung 12 3. Gliederung probabilistischer Lastflussverfahren 13 3.1. Punktschätzende und iterative Verfahren 14 3.2. Gliederung nach Stichprobenverfahren 15 3.3. Reduzierung des Grundraumes 16 3.3.1. Cluster-Analyse17 3.3.2. Ausreißerbehandlung 21 3.3.3. Wahrscheinlichkeits- und Verteilungsfunktion 21 3.4. Methode der Stichprobenziehung 22 3.4.1. Einfache Zufallsstichprobe 23 3.4.2. Systematische Stichprobe24 3.4.3. Geschichtete Zufallsstichprobe 25 3.5. Reduzierung des Stichprobenraumes 26 3.6. Invertierung von Stichproben 26 3.7. Zusammenfassung 27 4. Vergleich probabilistischer Verfahren 28 4.1. Nicht-Gaußsche Eingangsdaten 28 4.2. Bestimmung notwendiger Clusterzentren 29 4.3. Erstellung des Stichprobenraumes pro Kombination 31 4.4. Gütemaße und Effizienz von Stichprobenverfahren 33 4.4.1. Median 34 4.4.2. Median der absoluten Abweichung vom Median 37 4.4.3. Maximale normierte Perzentilsdifferenz 40 4.4.4. Zusammenfassung 43 4.5. Streuung der Stichprobenverfahren bei wiederholter Ausführung 44 4.5.1. Median 44 4.5.2. Median der absoluten Abweichung vom Median 45 4.5.3. Maximale normierte Perzentilsdifferenz 47 4.5.4. Zusammenfassung 49 4.6. Sensitivität bei unterschiedlicher Anzahl statistischer Netzknoten 52 4.6.1. Median 52 4.6.2. Median der absoluten Abweichung vom Median 54 4.6.3. Maximale normierte Perzentilsdifferenz 56 4.6.4. Zusammenfassung58 4.7. Notwendige Kombinationen für Ziel-Gütemaße 59 5. Software-basierte probabilistische Verteilnetzplanung 61 5.1. Struktur der entwickeltenSoftware 61 5.2. Last- und Erzeugungsprofile 63 5.2.1. Synthetische Haushaltslast 63 5.2.2. Elektrofahrzeug 64 5.2.3. Wärmepumpe 65 5.2.4. Photovoltaische Anlagen 66 5.2.5. Windenergieanlagen 66 5.3. Optimale Auswahl nach Regeleffizienz 67 5.4. DezentraleWirkleistungsregler 68 5.4.1. P(U)-Regler für Schnellladeinfrastruktur 68 5.4.2. P(U)-Regelung von Wärmepumpen gemäß thermischer Grenzen 69 5.5. Blindleistungsregler 72 5.5.1. Zentrale Steuerung 73 5.5.2. Dezentrale Regelung 75 5.5.3. Verteilte Regelung 79 5.6. Regelbarer Ortsnetztransformator 83 5.7. Automatisierte Netzausbauplanung 86 5.7.1. Transformatortausch 87 5.7.2. Vergrößerung des Leiterquerschnitts 89 5.7.3. Zusätzliche Stichleitung 89 5.7.4. Kostenberechnung 90 5.8. Zusammenfassung 91 6. Anwendungsfälle probabilistischer Planung 92 6.1. Verwendete Verteilnetzmodelle 94 6.2. Abschätzung der Auswirkung von PV-Anlagenausbau 95 6.2.1. Unterschiede der Planungsverfahren zur Schätzung der PVA-Nennleistung 95 6.2.2. Einfluss der Blindleistungsregelung auf mögliche Anlagenleistung 100 6.3. Abschätzung von Netzauslastungen in Wohngebieten 106 6.3.1. Annahmen und Szenarien 107 6.3.2. Auswertung der Knotenspannungen 110 6.3.3. Auswertung der Betriebsmittelauslastungen 116 6.4. Zusammenfassung 118 7. Zusammenfassung und Ausblick 119 Literaturverzeichnis 121 Anhang 135 A. Statistische Merkmale 135 A.1. Empirische Wahrscheinlichkeitsfunktion 135 A.2. Kumulative empirische Verteilungsfunktion 136 A.3. Quantile 136 A.4. Interquartilsabstand 137 B. PLF-Methoden 138 B.1. Veröffentlichte PLF-Methoden 138 B.2. Test Gaußsche Verteilung 138 C. Definitionen 140 C.1. Symbole für Flussdiagramme 140 C.2. Zählpfeilsystem 140 D. Ergänzende Ergebnisse 142 E. Danksagung 143