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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.
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.