Data-driven model of the power-grid frequency dynamics

The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, business models and market designs evolve, affecting power-grid operation and power-grid frequency. Problems raised by this ongoing transition are increasingly addressed by transdisciplinary research approaches, ranging from purely mathematical modelling to applied case studies. These approaches require a stochastic description of consumer behaviour, fluctuations by renewables, market rules, and how they influence the stability of the power-grid frequency. Here, we introduce an easy-to-use, data-driven, stochastic model for the power-grid frequency and demonstrate how it reproduces key characteristics of the observed statistics of the Continental European and British power grids. Using data analysis tools and a Fokker–Planck approach, we estimate parameters of our deterministic and stochastic model. We offer executable code and guidelines on how to use the model on any power grid for various mathematical or engineering applications

Modelling Chinese Smart Grid: A Stochastic Model Checking Case Study

Cyber-physical systems integrate information and communication technology functions to the physical elements of a system for monitoring and controlling purposes. The conversion of traditional power grid into a smart grid, a fundamental example of a cyber-physical system, raises a number of issues that require novel methods and applications. In this context, an important issue is the verification of certain quantitative properties of the system. In this technical report, we consider a specific Chinese Smart Grid implementation and try to address the verification problem for certain quantitative properties including performance and battery consumption. We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker

The stochastic nature of power-grid frequency in South Africa

In this work, we explore two mechanisms that explain non-Gaussian behaviour of power-grid frequency recordings in the South African grid. We make use of a Fokker–Planck approach to power-grid frequency that yields a direct relation between common model parameters such as inertia, damping, and noise amplitude and non-parametric estimations of the same directly from power-grid frequency recordings. We propose two explanations for the non-Gaussian leptokurtic distributions in South Africa: the first based on multiplicative noise in power-grid frequency recordings, which we observe in South Africa; the second based on the well-known scheduled and unscheduled load shedding and rolling blackouts that beset South Africa. For the first we derive an analytic expression of the effects of multiplicative noise that permits the estimation of all statistical moments—and discuss drawbacks in comparison with the data; for the second we employ a simple numerical analysis with a modular power grid of South Africa. Both options help understand the statistics of power-grid frequency in South Africa—particularly the presence of heavy tails.The stochastic nature of power-grid frequency in South AfricapublishedVersio

Performance and economic assessment of a grid-connected photovoltaic power plant with a storage system. A comparison between the north and the south of Italy

Grid-connected low voltage photovoltaic power plants cover most of the power capacity installed in Italy. They offer an important contribution to the power demand of the utilities connected but, due to the nature of the solar resource, the night-time consumption can be satisfied only withdrawing the energy by the national grid, at the price of the energy distributor. Thanks to the improvement of storage technologies, the installation of a system of battery looks like a promising solution by giving the possibility to increase auto-consumption dramatically. In this paper, a model-based approach to analyze and discuss the performance and the economic feasibility of grid-connected domestic photovoltaic power plants with a storage system is presented. Using as input to the model the historical series (2008-2017) of the main ambient variables, the proposed model, based on Stochastic Hybrid Fault Tree Automaton, allowed us to simulate and compare two alternative technical solutions characterized by different environmental conditions, in the north and in the south of Italy. The performances of these systems were compared and an economic analysis, addressing the convenience of the storage systems was carried out, considering the characteristic useful-life time, 20 years, of a photovoltaic power plant. To this end the Net Present Value and the payback time were evaluated, considering the main characteristics of the Italian market scenario