C Mathematical and Quantitative Methods
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Violation-mitigation-based method for PV hosting capacity quantification in low voltage grids
(2022)
Hosting capacity knowledge is of great importance for distribution utilities to assess the amount of PV capacity possible to accommodate without troubling the operation of the grid. In this paper, a novel method to quantify the hosting capacity of low voltage grids is presented. The method starts considering a state of fully exploited building rooftop solar potential. A downward process is proposed - from the starting state with expected violations on the grid operation to a state with no violations. In this process, the installed PV capacity is progressively reduced. The reductions are made sequentially and selectively aiming to mitigate specific violations: nodes overvoltage, lines overcurrent and transformer overloading. Evaluated on real data of fourteen low voltage grids from Austria, the method proposed exhibits benefits in terms of higher hosting capacities and lower computational costs compared to stochastic methods. Furthermore, it also quantifies hosting capacity expansions achievable by overcoming the effect of the violations. The usage of a potential different from solar rooftops is also presented, demonstrating that a user-defined potential allows to quantify the hosting capacity in a more general setting with the method proposed.
Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time, households hold an increasing amount of flexibility, which can be exploited by demand-side management to decrease customer cost and support grid operation. Compared to the collection of individual flexibilities, aggregation reduces optimization complexity, protects households’ privacy, and lowers the communication effort. In mathematical terms, each flexibility is modeled by a set of power profiles, and the aggregated flexibility is modeled by the Minkowski sum of individual flexibilities. As the exact Minkowski sum calculation is generally computationally prohibitive, various approximations can be found in the literature. The main contribution of this paper is a comparative evaluation of several approximation algorithms in terms of novel quality criteria, computational complexity, and communication effort using realistic data. Furthermore, we investigate the dependence of selected comparison criteria on the time horizon length and on the number of households. Our results indicate that none of the algorithms perform satisfactorily in all categories. Hence, we provide guidelines on the application-dependent algorithm choice. Moreover, we demonstrate a major drawback of some inner approximations, namely that they may lead to situations in which not using the flexibility is impossible, which may be suboptimal in certain situations.
The impact of global warming and climate change has forced countries to introduce strict policies and decarbonization goals toward sustainable development. To achieve the decarbonization of the economy, a substantial increase of renewable energy sources is required to meed energy demand and to transition away from fossil fuels. However, renewables are sensitive to environmental conditions, which may lead to imbalances between energy supply and demand. Battery energy storage systems are gaining more attention for balancing energy systems in existing grid networks at various levels such as bulk power management, transmission and distribution, and for end-users. Integrating battery energy storage systems with renewables can also solve reliability issues related to transient energy production and be used as a buffer source for electrical vehicle fast charging. Despite these advantages, batteries are still expensive and typically built for a single application – either for an energy- or power-dense application – which limits economic feasibility and flexibility. This paper presents a theoretical approach of a hybrid energy storage system that utilizes both energy- and power-dense batteries serving multiple grid applications. The proposed system will employ second use electrical vehicle batteries in order to maximise the potential of battery waste. The approach is based on a survey of battery modelling techniques and control methods. It was found that equivalent circuit models as well as unified control methods are best suited for modelling hybrid energy storages for grid applications. This approach for hybrid modelling is intended to help accelerate the renewable energy transition by providing reliable energy storage.
Increasing electric vehicle penetration leads to undesirable peaks in power if no proper coordination in charging is implemented. We tested the feasibility of electric vehicles acting as flexible demands responding to power signals to minimize the system peaks. The proposed hierarchical autonomous demand side management algorithm is formulated as an optimal power tracking problem. The distribution grid operator determines a power signal for filling the valleys in the non-electric vehicle load profile using the electric vehicle demand flexibility and sends it to all electric vehicle controllers. After receiving the control signal, each electric vehicle controller re-scales it to the expected individual electric vehicle energy demand and determines the optimal charging schedule to track the re-scaled signal. No information concerning the electric vehicles are reported back to the utility, hence the approach can be implemented using unidirectional communication with reduced infrastructural requirements. The achieved results show that the optimal power tracking approach has the potential to eliminate additional peak demands induced by electric vehicle charging and performs comparably to its central implementation. The reduced complexity and computational overhead permits also convenient deployment in practice.
In the regime of incentive-based autonomous demand response, time dependent prices are typically used to serve as signals from a system operator to consumers. However, this approach has been shown to be problematic from various perspectives. We clarify these shortcomings in a geometric way and thereby motivate the use of power signals instead of price signals. The main contribution of this paper consists of demonstrating in a standard setting that power tracking signals can control flexibilities more efficiently than real-time price signals. For comparison by simulation, German renewable energy production and German standard load profiles are used for daily production and demand profiles, respectively. As for flexibility, an energy storage system with realistic efficiencies is considered. Most critically, the new approach is able to induce consumptions on the demand side that real-time pricing is unable to induce. Moreover, the pricing approach is outperformed with regards to imbalance energy, peak consumption, storage variation, and storage losses without the need for additional communication or computation efforts. It is further shown that the advantages of the optimal power tracking approach compared to the pricing approach increase with the extent of the flexibility. The results indicate that autonomous flexibility control by optimal power tracking is able to integrate renewable energy production efficiently, has additional benefits, and the potential for enhancements. The latter include data uncertainties, systems of flexibilities, and economic implementation.
For a given set of banks, how big can losses in bad economic or financial scenarios possibly get, and what are these bad scenarios? These are the two central questions of stress tests for banks and the banking system. Current stress tests select stress scenarios in a way which might leave aside many dangerous scenarios and thus create an illusion of safety; and which might consider highly implausible scenarios and thus trigger a false alarm. We show how to select scenarios systematically for a banking system in a context of multiple credit exposures. We demonstrate the application of our method in an example on the Spanish and Italian residential real estate exposures of European banks. Compared to the EBA 2016 stress test our method produces scenarios which are equally plausible as the EBA stress scenario but yield considerably worse system wide losses.