PV-Integration Strategies for Low Voltage Networks

Transcription

1 PV-Integration Strategies for Low Voltage Networks Carsten Heinrich Philipp Fortenbacher Alexander Fuchs Göran Andersson ETH Zurich, Switzerland {fortenbacher, Abstract This paper proposes a method to investigate the potential of Reactive Power Control (RPC) in distribution grids with a high PV-share. The overall objective is to maximize the utilization of installed PV sources. Different RPC approaches are examined in combination with distributed storage, grid expansions and curtailment. Simulations are carried out on reference distribution grids, representing remote, rural and urban networks. Various shares of PV-penetration with different PVdistributions are simulated on a representative irradiance profile. Batteries are optimally dispatched on the basis of load and solar irradiance forecasts using a Model Predictive Control method. The hierarchical control schemes selects the optimal RPC and storage signal. The simulation results show, that curtailment and storages can represent a viable alternative to grid expansions, when the PV-penetration is moderate. The potential of Reactive Power Control is dependent on the PV-distribution and the network. Index Terms Batteries, Power distribution, Reactive power, Solar power integration I. INTRODUCTION In Germany, the total PV-generated electricity rose to 35. TWh in the year, which corresponds to 6.9% of the net electricity consumption []. Distribution system operators (DSOs) are facing challenges to guarantee power quality, since most of the solar panels are installed in low voltage grids []. These networks were initially built to provide households and small industries with power, generated in large and remote power plants. A considerable amount of small distributed generation units can invert the classical power flow direction. This new situation can lead to voltage violations and thermal overloadings of network equipment. DSOs have to make the grid more flexible to be able to react to the intermittent PV injections. Further, new policies force DSOs to reduce network losses, since the highest percentage of losses occur in this network level [3]. Measures have to be put into practice in such a way that grid stability is always ensured. Various PV-integration strategies have been proposed. Generation curtailment is the most commonly used approach. Reference [] uses a statistical method to evaluate this strategy economically in more than 3 rural distribution feeders. The authors estimate that curtailment reduces PV-integration costs by 3%. Voltage violations can be avoided by controlling Reactive Power of PV-inverters at the costs of higher line currents [5], [6], [7]. In References [8], [9], [], [] the intermittency of renewable generation is balanced with storage units. Combinations of these integration strategies have been studied as well: In [9] and [] the combination of batteries with RPC is assessed. In [] local storage units are combined with generation curtailment. In [3] the authors compares the viability of local energy storage, generation curtailment, reactive power control as well as combinations of the three to grid expansion costs. Except for [], all the above mentioned papers test the considered integration strategies on one particular distribution grid. This paper develops a guideline for PVintegration in low-voltage networks using RPC, curtailment and storage devices as well as combinations of these three strategies. It demonstrates that the effectiveness of RPC is dependent on the grid topology and the PV-distribution. Hence, each control strategy is evaluated in rural, remote and urban reference grids with different PV-distributions. In order to estimate the potential of the developed control strategies, the results are compared to usual grid expansions. The paper is structured as follows. In Section II the voltage and the thermal constraints are assessed theoretically and the used component models are presented. Section III introduces the formulations of the Multi-Period Optimal Power Flow (OPF) problem. Section IV presents the different PV-integration strategies. Section V contains the simulation results. Section VI provides a conclusion and an outlook. A. Grid Constraints II. SYSTEM DESCRIPTION Distribution grid operation is subject to the following main technical limits: voltage constraints and thermal constraints of the power cables and transformers. ) Voltage Constraints: According to the European Norm EN 56 [] customer voltages may vary % from the nominal value. This limits the power that can be delivered through a line. When a single generator is connected through a power line to an infinite bus with a constant frequency and a constant voltage, the exported power P g only depends on the power factor cos(ϕ) of the generator, the impedance Z of the line and the susceptance B. A sketch of this system can be seen in Fig.. With U = U e jϕ and U = U, the following relation can be derived: U = U Z P g ( j tan ϕ) U 3U jb. ()

2 grid jb Z I jb U U generator Fig.. Π-model for power line with a connected generator to the electricity grid. Transmitted Power [kw] l limit length l [m] Voltage limit, cosϕ = Voltage limit, cosϕ =.9 ind. Thermal limit, cosϕ = Thermal limit cosϕ =.9 ind. limit interception line RPC potential Fig.. Thermal and voltage limits for the NAYY x85mm power cable (Z = j Ω/km, B =.57 (Ωkm), I max = 3A) as a function of line lengths and different power factors. The grey area depicts the increase in transmission capacity, which can be achieved with a variable inductive power factor. It is assumed that U = 3V. The voltage on the generator side is subject to the constraint: U min (7V) U U max (53V). () The maximum power can be exported when U = 53V. ) Thermal Constraints in Power Lines: When power is transmitted through a network, losses heat up the equipment. In order to avoid faster aging or permanent damage, the power flow through transformers and cables is limited by a power rating. Manufacturers usually specify cable ratings as a maximal current: I I max. (3) The complex power is defined as: S = P + jq = P ( + j tan ϕ) = 3U I. () It follows from (), (3) and (), that P = P = 3 U I + j tan ϕ < 3U max I max + j tan ϕ =: P max. (5) The maximum transmission capacity of a power line under the thermal and the voltage constraint can be calculated using () and (5). In Fig. both the thermal and the voltage constraints are plotted for a typical cable as a function of line length and for different power factors. The thermal limit is independent of the line length and the transmittable active power decreases when the power factor cos ϕ < due to the higher currents. The voltage limit depends on the length of the cable, since the line impedances are proportional to the line length. Voltages decrease where reactive power is consumed, Volatility [W/m /min].5 Maximial Irradiance [kw/m ] Fig. 3. Day irradiance profiles plotted according to the classifiers volatility, total infalling energy and maximal solar irradiance. 8 6 [ ] kwh m so an inductive power factor of the generator counteracts the voltage rise and therefore increases the maximal deliverable power through a line. When exporting power with a power factor equal to (.9 ind.), the operational point of a power line has to lie below the red (blue) lines in order to fulfill both the thermal and the voltage constraints. A generator that is connected to the feeder with a cable of length l < l limit is limited by the thermal constraint. A power factor of will lead to the highest transmission capacity. Generators connected through cables with l > l limit can increase the transmission capacity by generating with an inductive power factor. The optimal operational point lies on the black dotted line, the intersection points of thermal and voltage limits. Hence, the shaded area shows the potential of RPC. In a distribution grid usually several consumers are connected to a line. When at least one generator is located further from the feeder than l limit, an inductive power factor can be useful. In the case when all generators are located close to the feeder (< l limit ), a capacitive power factor can be used to compensate the inductive power consumption of loads, cables and transformers in order to reduce power losses. 3) Thermal Constraints for Transformers: Power ratings for transformers are specified as active power ratings. For simplicity it is assumed, that ratings can be exceeded up to % and that this value is independent of time [5]. B. Load Profiles Loads are modeled as active and reactive power profiles. In this work, voltage and frequency independent loads are assumed. Load profiles are generated using [6]. C. Photovoltaic Model The maximal active power P max, which solar panels can feed into the grid, is assumed to be the product of the infalling solar irradiance Φ solar (t), the panel area A PV and the total PV efficiency ν PV. Total infalling energy P max = Φ solar (t)a PV ν PV (6) PV Hosting Capacity: In this work, the PV hosting capacity of a distribution grid is defined as the roof area of all houses connected to the feeder, that can potentially be used to install solar panels. PV Penetration: The term PV penetration in a distribution grid is defined as the ratio of the installed solar panel area and the PV hosting capacity.

3 Volatility - normalized Maximial Irradiance - normalized Fig.. Irradiance profiles clustered into five groups by minimizing the overall day-cluster-center-distance. Different colors symbolize the different clusters. Radiation [kw/m ] Time [days] Fig. 5. Resulting day irradiance profiles from k-means clustering. Colors according to their cluster of origin in Figure. Each irradiance profile is the closest day in the dataset to the 5 cluster centers. ) Radiation Profiles: Irradiance data on a minute basis and hourly forecast values are based on hourly data from the METEONORM database [7]. To reduce the simulation time, a reference irradiance profile is created by classifying daily radiation profiles of an entire year according to: Maximal solar irradiance of the day [ ] W m, Total infalling energy [ ] Wh m, Volatility of the irradiance, defined as the standard deviation of the minute change in irradiance [ W m min]. In Figure 3 all days of the synthetic irradiance profile of one year are plotted in these three dimensions, every dot corresponding to the profile of one day. In order to categorize the days, all values are normalized, by the maximal occurring value of the year. Then a k-means clustering algorithm is applied. This algorithm assigns days to 5 clusters, such that the overall sum of day-to-cluster-center-distances is minimized. The algorithm used for this purpose is described in [8]. The result of this clustering is shown in Fig.. Each color represents the affiliation to one of the 5 clusters. The irradiance data of the days closest to each of the 5 cluster centers are chosen. Those profiles are added together and form the reference profile, which can be seen in Fig. 5. When performing simulations on the reference profile, the used objective functions are weighted by the amount of days, that belong to the cluster. D. Storage Model Storages are modeled as generators, with the following properties: In addition to their generation capacity P max, they can absorb power from the grid P min. They charge and discharge with an efficiency η charge and η discharge, respectively. Their storage capacity is limited to E max [kwh] It is assumed that no self-discharge occurs in the storage units. The state of charge (SOC) at the sample time t is defined as: ( ) SOC(i) := t E max E + P bat (k)η bat t. (7) k= P bat (k) describes the battery power injection to and outtake from the grid, η bat is equal to: { η bat η = discharge, if P bat (k) > (8) η charge, if P bat (k), where E represents the initial stored content. The storage cost function from [9] is used. This model describes the hourly degradation costs due to battery use. Since batteries also degrade when the battery is idle, an additional constant cost term is added: J bat (SOC, P bat load, E max ) = be max (SOC a) + dp bat load + bat epload E max + Emax c inv. f Here J bat stands for the hourly cost of the battery use and c inv denotes the investment costs per kwh storage capacity. The parameters a-f are defined in Table I. III. CONTROL STRUCTURE AND MPC DESIGN The problem of continuous optimization was solved using the simulation environment MATPOWER []. In a distribution grid with n g generators and n b buses the state vector x R N(nb+ng) is defined as: x = (θ, U, P, Q) T, where θ and U R Nnb describe the voltage angles and amplitudes at the n b buses during the N timesteps. P and Q R Nng denote the power infeeds of the n g generator during the N timesteps. The problem can be formulated as: (9) J obj = min x x T Hx + c T x, () s.t. (a) h (x) =, (b) Pm(t) g Pm max, (c) Pm(t) g + Pm min, (d) Q g m(t) Pm(t) g tan(ϕ max m ), (e) Q g m(t) + Pm(t) g tan(ϕ min m ), (f) U i (t) U max, (g) U i (t) + U min, (h) Iij (t) Iij max, t (i) En max + En + ηn bat t Pn bat (k), (j) E n η bat n t k= t k= P bat n (k), m {,..., n g }, i, j {,..., n b }, t {,..., N}, n {,..., n bat }. Here n bat stands for the amount of storages in the network. The objective function J obj of the Multi-Period

4 AC OPF problem consists of the sum of the linear generation cost functions of the n g generators (c T x) and the quadratic cost functions of the storages (9), brought in the form x T Hx. h (x) contains the equality constraints like power balances at the nodes and power flow equations. The constraints (ab) incorporate the active power generation limits. (c-d) are the reactive power limits, defined through a minimal power factor. (e-g) are the voltage and nonlinear thermal constraints from Section II-A. Finally, with (h-i) the storage dynamic is enforced. These constraints introduces a time coupling, due to which a Receding Horizon technique is used. At time step t, the problem is solved for the next N time steps using the forecast values u(t), available at time t. The result is applied during the next time step. At time step t +, the problem is solved again, using the updated forecast data u(t + ). Figure 6 shows an overview of the control setup used in this work. For every scenario, first a optimal battery placing problem is solved. This is done for the 5 days of the reference year at once, using a time-granularity of h. The resulting optimal storage distribution, is tested in a two stage optimization algorithm. First the storages are dispatched using a MPC approach with a receding horizon of hours such that % of the thermal and the voltage margins remain (V max =.9 p.u.). During this step only forecast values for loads and irradiance are used. In the next step, the PV-units are optimized online with the real irradiance and load data on a minute basis. Scenario, Grid Type Battery Sizing & Placement 5 d E max Load and PV Forecast MPC AC OPF h P set bat E max Time Scale Load and PV RT data RT AC OPF min P bat Emax SOC Storage costs Curtailment costs Storage & Grid Model Fig. 6. Overview of the different steps in the control setup. A. Grid Expansion IV. SCENARIOS SOC Grid expansions (replacing or adding transmission cables and transformers) are a very conservative way to deal with high levels of PV penetration. Usually all equipments are adjusted to the most critical periods, even though these occur rarely. This makes this integration strategy very costly. B. Reactive Power Control In Germany, a new law [] has been introduced in, according to which, all generators have to be able to provide power with a power factor of: cos ϕ [.95 cap,.95 ind ], if P g 3.8kW () cos ϕ [.9 cap,.9 ind ], if P g > 3.8kW. () By default, manufacturers of PV inverters have to implement the characteristic curve seen in Fig. 7. The DSO can implement a different characteristic curve. Two Reactive Power Control cos ϕ.9 cap..95 cap..95 ind..9 ind PV-Power (p.u) kwp <3.8kW kwp >3.8kW Fig. 7. Characteristic curve and admissible range of the power factor cos ϕ which is implemented by default into power inverters in Germany 7. strategies are modeled. The first one is an optimal RPC with a power factor cos ϕ >.9. The second scenario models the RPC strategy of the characteristic curve. C. Storage While grid expansions and RPC are means to allow a higher power flow through the feeder, storages and curtailment reduce these power flows leading to active power losses. While curtailments simply discard the energy, that cannot be fed into the grid, storage devices aim to store the energy until the grid reaches a situation when the generated power can be either consumed or exported. Storage devices therefore only dissipate energy due to their efficiencies. D. Curtailment In a distribution grid the maximal solar power generation occurs at mid day. Decreasing the maximal power output of the generators during these rare hours allows to install a larger overall PV capacity, while at the same time, relatively little energy is lost. Two different curtailment scenarios are investigated: Curtailment up to % of the generators nominal power, Curtailment up to % of the generators nominal power. The first scenario represents the curtailment of the relatively high peak hours, where comparably little energy is gained. The second case represents the case where curtailment is the main PV-integration strategy. E. Voltage and Thermal Violation The question which constraint is first violated is dependent on the grid topology. The distance l between generator and feeder is crucial (see Fig. ). Here, two different PVdistributions are used. The remote placement-scenario first populates all the nodes where l > l limit with PV-units, and if none of these nodes are left, the rest is populated randomly. In the second scenario, the random placement, generators are randomly placed into the grid. F. Grid Types Six different reference grids from [] are used, representing remote, rural and urban distribution networks. The main parameters, by which grids were classified are: Amount of branches per feeder Amount of household per branch Line lengths between nodes Types of cables Transformer ratings.

5 normalized annual costs 6 6 G. Summary remote, grid 8 Remote PV-placement remote, grid rural, grid 3 rural, grid 8 Random PV-placement Grid Expansion Transformer Cost Storage Investment Cost Storage Operation Cost Curtailment Cost... : Grid Expansion : Storages 3: Storages + % curtailm. : Storages + opt. RPC 5: Storages + % curtailm. + opt. RPC 6: % curtailm. 7: % curtailm. + opt. RPC 8: % curtailm. + RPC (charac. curve) Integration Strategies Fig. 8. Cost overview of simulated integration strategies for a 3% PV share and different networks Simulations are performed on six reference grids, two remote grids, two rural grids and two urban grids. For each of the six chosen reference grids, three different PV penetrations are simulated, 3%, 5% and 7%. The PV-units are once placed far from the feeder (remote-placement), and once randomly (random-placement). For each of these setups, eight PV-integration strategies are compared: ) Simple grid expansions ) Optimal placement of storages 3) Optimal placement of storages combined with % allowed curtailment ) Optimal placement of storages combined with optimal RPC (cos ϕ >.9) 5) Optimal placement of storages combined with % allowed curtailment and optimal RPC (cos ϕ >.9) 6) % allowed curtailment 7) % allowed curtailment combined with optimal RPC (cos ϕ >.9) 8) % allowed curtailment combined with RPC of characteristic curve. V. RESULTS We use the parameters listed in Table I. Figure 8 shows the resulting costs for the remote and the rural grids, for remote and random PV-placement, each with a PV penetration of 3%. Due to the page limit results for 5% and 7% PV penetration could not be included. A. Storage Results With the assumed investment and operational costs, the optimal location for storage devices is at the PV-units. The optimal size is the minimal storage capacity, with which the grid constraints can still be fulfilled. Oversizing storages in order to reduce the storage degradation is not economical. When voltages constrain the power transmission, storages should be added to the most remote PV-nodes. Due to the penalization of SOC deviations, storages shift energy only within the same TABLE I ASSUMED PARAMETERS Description Value Unit 63 kva Transformator 5 e kva Transformator 8 e 6 kva Transformator e kva Transformator 3 e Cable tube 5 e/m Cable e/m Channel e/m Switching of cables e PV-efficiency (η PV ).8 PV-generation costs e/kwh Curtailm. reimbursement costs.3 e/kwh Storage investment cost e/kwh Storage operation cost (a).37 Storage operation cost (b).5e-3 h Storage operation cost (d) 6.5e-3 ekwh Storage operation cost (e) 6.e-3 ekw Storage operation cost (f).75e5 h Storage charging efficiency.97 Storage discharging efficiency.97 Feeder export price -.3 e/kwh Feeder import price.3 e/kwh day. Relying on storages as the only investment strategy was not economical in any grid. In grids with 3% PV penetration, storages in combination with RPC and/or curtailment can be cheaper than grid expansions, since relatively little energy has to be stored. In the cases of 5% and 7% PV penetrations, energy storage did not represent an economical alternative. B. Reactive Power Control As Fig. 8 shows, RPC is an adequate solution, in the case of Remote PV-placement. Combining storages or curtailment with RPC significantly reduces the resulting costs. When thermal ratings limit the power transmission, RPC is not beneficial. The results also show, that the application of the characteristic curve, which is used in Germany, does not represent an optimal solution. In all cases, when the power export is limited by thermal ratings, this rule is even counterproductive. Additional reactive power consumption in the grid, leads to higher current amplitudes, leading to thermal limits being reached earlier and

6 more energy being lost through curtailment as well as higher losses. Only when the power export is limited by the voltage constraint, the characteristic curve seems to be a reasonable way to increase the maximal allowed PV penetration. C. Curtailment The simulations show, that curtailment is the overall best strategy, to reduce grid expansion costs. In the 3% PV penetration scenario, curtailment is more profitable for the DSO in all reference grids. In the case of 5% PV penetration, curtailment is still more profitable in 7 of tested cases. In the 7% PV penetration scenario, curtailment is more expensive than grid expansions in all grids. D. General Implications Remote distribution grids are best suited for RPC since power lines are long and farms with large rooftops exist. Also in rural distribution grids RPC can still be beneficial. In both cases batteries in combination with RPC and % curtailment represent the most attractive alternative to plain curtailment. In the remote and rural grids first voltage violations occur, when the PV penetration exceeds 6 % and 3%, respectively. Thermal violations occur, with PV-Penetrations of around 6% in both grids. In urban grids, no nodes exist, where power infeed will rather lead to voltage violations before thermal limits are reached. Therefore, PV-units in such networks do not have to be equipped with RPC and cost for oversizing inverters could be saved. Curtailment represents a powerful tool to deal with power surpluses during the few peak hours in summer. The first thermal violations occur, when the PV penetration exceeds 5%. Storages are not suited for urban areas. When limits are reached, curtailment seems to be best suited to deal with higher PV penetrations in these networks. VI. CONCLUSION In this thesis various PV integration strategies have been investigated for rural, urban and remote distribution grids with different levels of PV penetration. A model predictive control strategy with two stages has been applied to first dispatch the storages based on weather and load forecasts and then optimize the power generation of PV-units in realtime, while complying with voltage and thermal constraints. The problem is solved for 5 days, that were chosen to best represent the solar irradiation behavior of an entire year using a k-means clustering technique. The simulations show, that curtailment represent the most economical solution. When the voltage limits constrain the grid, RPC can increase the exported energy, and therefore lower the amount of wasted energy due to curtailment. In the cases when curtailment leads to unacceptable energy losses, storages combined with a small amount of curtailment and potentially RPC can represent a cost efficient alternative. The question, if RPC is a useful tool, is very dependent on the distribution of PV-units in the grid. It was shown, that general rules, like the characteristic power factor curve, which was introduced in Germany, are counterproductive, when thermal ratings are limiting power exports. REFERENCES [] Harry Wirth and Karin Schneider. Recent facts about photovoltaics in Germany. Report from Fraunhofer Institute for Solar Energy Systems, Germany, 5. [] Die Karte der Erneuerbaren Energien [Online]. available: (accessed: 5/). [3] Wolfram Heckmann, Heike Barth, Thorsten Reimann, Lucas Hamann, et al. Detailed analysis of network losses in a million customer distribution grid with high penetration of distributed generation. In nd International Conference and Exhibition on Electricity Distribution (CIRED 3). IET, 3. [] Christophe Gaudin, Andrea Ballanti, and Emilie Lejay. Evaluation of PV curtailment option to optimize PV integration in distribution network. In Integration of Renewables into Distribution Grid (CIRED Workshop). IET,. [5] Emiliano Dall Anese, Sairaj V Dhople, and Georgios Giannakis. Optimal dispatch of photovoltaic inverters in residential distribution systems. IEEE Transactions on Sustainable Energy, 5():87 97,. [6] Xiangjing Su, Mohammad Masoum, Peter J Wolfs, et al. Optimal PV Inverter Reactive Power Control and Real Power Curtailment to Improve Performance of Unbalanced Four-Wire LV Distribution Networks. IEEE Transactions on Sustainable Energy, 5(3): ,. [7] Gustavo Valverde and Thierry Van Cutsem. Model Predictive Control of Voltages in Active Distribution Networks. IEEE Transactions on Smart Grid, ():5 6, 3. [8] Francesco Marra, Guangya Yang, Chresten Træholt, Jacob Ostergaard, and Esben Larsen. A Decentralized Storage Strategy for Residential Feeders With Photovoltaics. IEEE Transactions on Smart Grid, 5():97 98,. [9] M.N. Kabir, Yateendra Mishra, Gerard Ledwich, Zhao Yang Dong, and Kit Po Wong. Coordinated Control of Grid-Connected Photovoltaic Reactive Power and Battery Energy Storage Systems to Improve the Voltage Profile of a Residential Distribution Feeder. IEEE Transactions on Industrial Informatics, (): ,. [] Jeroen Tant, Frederik Geth, Daan Six, Peter Tant, and Johan Driesen. Multiobjective Battery Storage to Improve PV Integration in Residential Distribution Grids. IEEE Transactions on Sustainable Energy, ():8 9, 3. [] Alexander Fuchs and Turhan Demiray. Large-scale PV integration strategies in distribution grids. In PowerTech, 5 IEEE Eindhoven, 5. [] Jan von Appen, Thomas Stetz, Martin Braun, and Armin Schmiegel. Local Voltage Control Strategies for PV Storage Systems in Distribution Grids. IEEE Transactions on Smart Grid, 5(): 9,. [3] Gauthier Delille, Gilles Malarange, and Christophe Gaudin. Analysis of the options to reduce the integration costs of renewable generation in the distribution networks. Part : A step towards advanced connection studies taking into account the alternatives to grid reinforcement. In nd International Conference and Exhibition on Electricity Distribution (CIRED 3). IET, 3. [] EN Standard. 56. Voltage Characteristics of electricity supplied by public distribution networks, Cenelec,. [5] Pavlos Stylianos Georgilakis. Spotlight on modern transformer design. Springer Science & Business Media, 9. [6] Christof Bucher. Analysis and Simulation of Distribution Grids with Photovoltaics. PhD thesis, ETH Zurich,. ETH Diss No.. [7] J Remund, R Lang, and S Kunz. Software, Meteonorm v. 6., Bern, Switzerland,. [Online]. Available: [8] Jens-Rainer Ohm. Digitale Bildcodierung: Repräsentation, Kompression und Übertragung von Bildsignalen. Springer-Verlag, 3. [9] Philipp Fortenbacher, Johanna L Mathieu, and Göran Andersson. Modeling, identification, and optimal control of batteries for power system applications. In Power Systems Computation Conference,. [] Ray Daniel Zimmerman, Carlos Edmundo Murillo-Sánchez, and Robert John Thomas. Matpower: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Transactions on Power Systems, 6(): 9,. [] Verband der Elektrizitätswirtschaft. Eigenerzeugungsanlagen am niederspannungsnetz. Richtlinie für Anschluß und Parallelbetrieb von Eigenerzeugungsanlagen am Niederspannungsnetz,. [] Georg Kerber. Aufnahmefähigkeit von Niederspannungsverteilnetzen für die Einspeisung aus Photovoltaikkleinanlagen. PhD thesis, München, Technische Universität München, Diss.,.