Stochastic Model for Power Grid Dynamics

Abstract

Abstract-We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy. We present numerical results comparing the responses of two power grid systems to optimization approaches with different factors of risk and select the best blackout controlling parameter.

Suppressing cascades of load in interdependent networks

“…Researchers have begun to model cascades of load and failure within individual power grids using probabilistic models (15), linearized electric power dynamics (16,17), and game theory (18).…”

Simulation Models and Implementation of a Simulator for the Performability Analysis of Electric Power Systems Considering Interdependencies

“…Also, most of existing models proposed to reproduce the behaviour of EPS does not provide explicit modeling of the main interdependent subsystems and of the interdependencies between the main subsystems, so evaluation of the impact on dependability and performability of cascading or escalating failures is not trivial. Only very recently interactions between EI disturbances and the often imperfect human operator control actions have been considered [18]. Moreover, although some approaches consider the evolution of the sequences of disruptions in time, the operator's response to disruptions is typically considered instantaneous.…”

“…In most of these approaches, the modeling of the existing SCADA systems and of CCS is not considered explicitly or is very simple. Often, only expert-based methods for the systematic control of large power systems in response to disruptions are (implicitly) modeled, since automated methods are effectively nonexistent [18]. Also, most of existing models proposed to reproduce the behaviour of EPS does not provide explicit modeling of the main interdependent subsystems and of the interdependencies between the main subsystems, so evaluation of the impact on dependability and performability of cascading or escalating failures is not trivial.…”

“…This procedure links different static and dynamic models used to asses transient stability, frequency response, voltage stability and steady state system conditions. The simulation stochastic model introduced in [16], and inspired to [7], attempts to provide a comprehensive representation of the complex behavior of both the grid dynamics under random perturbations and the operators response to disruptions. This model considers random repair times for the failed components of EI, random removing of components from service, overloadedline failure due to excessive heating, generator redispatch and load shedding as possible control system reactions to disturbances, and instantaneous operators response to disruptions.…”

“…Several models based on simulation have been proposed [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] to represent EPS in more detail compared to analytical approaches. A brief summary of some of the available cascading failure simulations and of their modeling details can be found in [17].…”